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E C O N O M I C S T U D I E S 101
ERIK POST
MACROECONOMIC UNCERTAINTY AND EXCHANGE RATE POLICY
ERIK POST
MACROECONOMIC UNCERTAINTY AND
EXCHANGE RATE POLICY
Department of Economics, Uppsala University
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© Department of Economics, Uppsala University
ISBN 978-91-85519-08-8
ISSN 0283-7668
Doctoral dissertation presented to the Faculty of Social Sciences 2007
Abstract
POST, Erik, 2007, Macroeconomic Uncertainty and Exchange Rate Policy;
Department of Economics, Uppsala University, Economic Studies 101, 129 pp,
ISBN 978-91-85519-08-8
This thesis consists of four self-contained essays.
Essay 1 (with Annika Alexius) uses a structural VAR model to study the role of
floating exchange rates in five "small open economies" with inflation targets. We
show that only in Sweden and Canada does the nominal exchange rate appreciate
in response to asymmetric demand shocks and depreciate in response to asymmetric
supply shocks. Most exchange rate movements are responses to non-fundamental
shocks. However, these exchange rate shocks have negligible effects on output and
inflation. Thus, our findings indicate that exchange rates are neither stabilizing nor
destabilizing but may be characterized as disconnected from the rest of the economy.
Essay 2 constructs a dynamic stochastic rational expectations model of a small
open economy to shed some light on factors determining exits from a fixed to a
flexible exchange rate regime. Exits are in the model determined by a concern for
macroeconomic stabilization. If cost-push shocks are important relative to demand
shocks exits should occur more likely in times of low consumption and output, high
interest rates, negative asset holdings, current account deficits, high inflation and
high domestic prices. If the policy maker is more sensitive to negative rather than
positive output deviations the probability of exits increases overall and is tilted
toward exits with accompanying depreciations.
Essay 3 considers foreign exchange market interventions by central banks as an
alternative monetary policy instrument. Under quadratic costs of interest rate variation and interventions the policy maker should use a combination of interest rate
adjustment and interventions to stabilize output and inflation. Interventions should
be negatively correlated with interest rate changes due to stabilization motives but
positively with other motives or a binding zero lower bound, decreasing in inflation
expectations and in the real exchange rate but increasing with expected interventions. Tests of the model on data for Australia, Japan and Sweden supports these
predictions in most dimensions.
Essay 4 (with David Kjellberg) evaluates available proxies of macroeconomic uncertainty. Using correlations, some narrative evidence and a factor analysis we find
that disagreement and volatility proxies seem to be valid measures of uncertainty
whereas probability forecast measures are not. This result is reinforced when we use
our proxies in standard macroeconomic applications where uncertainty is supposed
to matter. Derived measures of general macroeconomic uncertainty are found to be
positively correlated with the absolute value of the GDP-gap.
Acknowledgements
When I started the Ph.D. programme I could never have imagined what it would be
like. Some 0.08 pages of thesis per day later I write this. If I had known how much
time it would consume, and how consumed I have been by my research at times, I
probably would have...done it anyway!
Without my superb supervisor Nils Gottfries this thesis would never have materialized. The grinding and re-grinding of drafts, re-drafts, and additional re-drafts
have been frustrating at times, but forced me to focus on the right issues in my
writing. Needless to say there are many funny stories from our marathonian meetings. I would also like to thank my assistant supervisor Annika Alexius. Annika has
enlightened me in the necessary cost-and-benefit analysis when doing research and
has been a most valuable counterweight to Nils.
This thesis has contributed from more people than I can imagine. My discussants from the Riksbank, Malin Adolfson and Karl Walentin, have made quite an
impact on my revisions of essays contained in this thesis. Also, many participants
at conferences and seminars have made me think thrice about what I have been
doing. Mikael Carlsson needs special mentioning in this aspect. Thanks also to
Lars Lindvall who has been most helpful in solving TEX-nical, technical and nontechnical problems.
At the department, the administrative staff has made it possible to focus on research by providing the necessary infrastructure, human capital and coffee.
Christian Nilsson, Monica Ekström, Åke Qvarfort, Eva Holst, Katarina Grönvall,
Ann-Sofie Wettergren Djerf, and Berit Levin have been most helpful not only to
me but to the entire Ph.D.-student body. From a socio-environmental point of view
I cannot imagine a better department in the world to write a thesis. Needless to
say, financial support is needed to if your budget constraint is bounded from above.
Handelsbankens forskningsstiftelser has generously provided me with the means not
only to pay the rent in Uppsala, but also to pay the much higher rent while in
Berkeley. Now it is quid pro quo!
iii
While in Berkeley during the fall 2005 I was involved in an animated discussion
about the acknowledgement-part of theses. Some1 claimed that it was silly to put
down names of people in the thesis unless they had been professionally involved
in its evolution. I was one of the proud protagonists who argued that this was
an undeniably efficient way to communicate affection to persons that matter in
everyday life, and hence also for the four and something years of giving birth to a
thesis. Perhaps in the future I will be famous for the self-evident 15 words I am
about to write so I better put them down in the following axiom:
The Axiom
A Ph.D.-student seldomly gets the opportunity to express affection as credibly as in
an acknowledgement.
From the Axiom I derive the following proposition:
The Proposition
Given that a Ph.D.-student writes an acknowledgement, he or she expresses
affection.
The Proof
The first year with da boyz in F 424, Jon, Christian and Fredrik, was anything
but boring. Scotch & B-Shaking, Go-cart and Pingis made my days! Then, sharing
office with J-On just prolonged the happy-times with occasional disturbing defeats
in pool to him, but also losses in pingis to Mr Andersson, and in lost spurts to
Fidde and Jake the Snake. After an intense pinball fad, instigated by D, Laaauurs
caught on the biking craze which turned him into a shopaholic. Despite injuries and
some tactical feuds with Mikael E Formerly Known as Bengtsson innebandy has
been a regular weekly highlight. In Berkeley Jenny-Penny and Elly-Belly taught
me a thing or two about social interactions and Dam, preciiis! Check it and keep it
real Maag!
Mamma Kerstin, Pappa Claes, and my sisters Elin and Ida are the most important persons in my life. Without them I would not have been given the opportunity
to start writing this thesis and not been able to write this part to finish off with.
Thanks for always being there when I need you!
Quod Erat Demonstrandum
Erik Post
Uppsala and Stockholm, January and March 2007
1
Unreported, but available upon request from the author.
iv
Contents
Introduction
Exchange rate economics . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Macroeconomic uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 Exchange rates and asymmetric shocks in small open economies
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
Statistical model . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
Empirical results . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1
Sweden . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2
Canada . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3
Australia . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4
New Zealand . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5
United Kingdom . . . . . . . . . . . . . . . . . . . . . . . .
4.6
Empirical findings, a summary . . . . . . . . . . . . . . . . .
5
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.1
Construction of weighted data and sample periods . . . . . .
A.2
Unit root tests . . . . . . . . . . . . . . . . . . . . . . . . .
A.3
Specification tests . . . . . . . . . . . . . . . . . . . . . . . .
A.4
Identification . . . . . . . . . . . . . . . . . . . . . . . . . .
A.5
Alternative specifications . . . . . . . . . . . . . . . . . . . .
A.6
Impulse response figures . . . . . . . . . . . . . . . . . . . .
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2 Macroeconomic imbalances and exchange rate regime shifts
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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1
Demand side . . . . . . . . . . . . . . . . . . . . . . . .
2.2
Supply side . . . . . . . . . . . . . . . . . . . . . . . . .
2.3
Summary of the model . . . . . . . . . . . . . . . . . . .
3
Alternative exchange rate regimes . . . . . . . . . . . . . . . . .
3.1
A credibly fixed exchange rate . . . . . . . . . . . . . . .
3.2
A flexible exchange rate and stabilization . . . . . . . . .
3.3
A non-credible fixed exchange rate . . . . . . . . . . . .
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Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1
Impulse responses . . . . . . . . . . . . . . . . . . . . . .
5.2
Model simulation and graphical analysis . . . . . . . . .
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Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . .
6.1
Relative importance of shocks . . . . . . . . . . . . . . .
6.2
Output bias . . . . . . . . . . . . . . . . . . . . . . . . .
7
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.1
Derivation of the uncovered interest parity condition . .
A.2
Derivation of the export function . . . . . . . . . . . . .
3 Foreign exchange market interventions as monetary policy
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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
Empirical results . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1
Correlations . . . . . . . . . . . . . . . . . . . . . . . . .
4.2
Some VAR evidence . . . . . . . . . . . . . . . . . . . .
4.3
The relation between interventions and the interest rate .
4.4
The relation between interventions and fundamentals . .
5
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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4 How to evaluate proxies of macroeconomic uncertainty
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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
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A model motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
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Uncertainty proxies . . . . . . . . . . . . . . .
3.1
Stock market volatility proxies . . . . .
3.2
Disagreement proxies . . . . . . . . . .
3.3
Probability forecast proxies . . . . . .
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Do uncertainty proxies measure uncertainty? .
4.1
Narratives . . . . . . . . . . . . . . . .
4.2
Correlations . . . . . . . . . . . . . . .
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Factor analysis . . . . . . . . . . . . . . . . .
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Extensions . . . . . . . . . . . . . . . . . . . .
6.1
Co-movements with the business cycle
6.2
Precautionary savings . . . . . . . . .
6.3
Residential investment . . . . . . . . .
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Conclusions . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . .
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Introduction
This thesis consists of four self-contained essays in international macroeconomics.
Three are concerned with different aspects of exchange rates and one with macroeconomic uncertainty. This introduction contains a brief background and an overview
of my results.
Exchange rate economics
Traditional exchange rate economics has been in an abysmal state after it was recognized that we really do not understand much about the behavior of (nominal) exchange rates. Influential papers giving rise to this pessimistic view are Meese and
Rogoff (1983a, 1983b) and Baxter and Stockman (1989). Meese and Rogoff (1983a,
1983b) show that in predicting exchange rate movements, the grandiose macroeconomic models of the 70’s were unable to beat the naive forecast that the exchange
rate would remain unchanged in the next period! Baxter and Stockman (1989) find
some evidence that indicates that the choice of exchange rate regime (fixed or flexible) is of no importance for general macroeconomic performance. Moreover, those
building blocks of standard macroeconomic theory that have an immediate intuitive
appeal such as purchasing power parity (PPP) and interest rate parity have weak
empirical support. That deviations from PPP-consistent exchange rates are amazingly persistent, with year-long half-lives, and that the overall short-term feedbacks
between the exchange rate and the rest of the economy are so weak are two of the
"Six Major Puzzles in Macroeconomics" cited in Obstfeld and Rogoff (2000). The
latter of these two is referred to as the "exchange-rate disconnect puzzle", of which
the results in Meese and Rogoff (1983a, 1983b) and Baxter and Stockman (1989)
are manifestations.
So how does one proceed in these dire straits of exchange rate economics? In my
view, the literature has evolved in three directions. The first direction of the litera1
2
Introduction
ture has aimed at trying to incorporate exchange rates in dynamic stochastic general
equilibrium (DSGE) models. Instead of discarding the macroeconomic approach to
exchange rates based on the empirical failure of previous macroeconomic models,
this strand of the literature has tried to make use of full-fledged dynamic models
incorporating imperfect competition, various rigidities and other modifications. See
Sarno (2001) and Lane (2001) for surveys. The second direction of the research has
left the macroeconomic view on exchange rate determination and instead moved toward the utilization of micro order flow data to explain high-frequency movements
in the exchange rate (Evans and Lyons (2002)). This strand of the literature has
also been interested in how central bank interventions in the foreign exchange market can affect exchange rates. The third direction has discarded the traditional view
that exchange rates are driven by fundamentals and instead tried to apply purely
mathematical modeling, recognizing the (seemingly) chaotic behavior of exchange
rates (de Grauwe and Grimaldi (2006)). This strand of the literature is based on
trade profitability and chartist behavior.
In Essay 1 (with Annika Alexius) we provide some further evidence on the
exchange-rate disconnect puzzle. We use a first difference structural vector autoregressive model (VAR) to study floating exchange rates in five "small open economies"
with inflation targets. We are especially interested in whether the exchange rates
have moved in the "right" direction - so as to stabilize the economy - following various types of shocks. By including both domestic and foreign variables and using
a combination of long- and short-run restrictions, we identify asymmetric shocks
more carefully than previous studies. Specifically, we are able to separate asymmetric from world-wide shocks and use identifying restrictions that are consistent
with standard long-run neutrality assumptions. It turns out that only in Sweden
and Canada does the nominal exchange rate appreciate significantly in response to
asymmetric demand shocks and depreciate in response to asymmetric supply shocks.
These findings indicate that exchange rates sometimes moves in the right direction
to stabilize inflation. But it also turns out that most of exchange rate movements
are caused by speculation and are not responses to fundamental shocks. Thus, albeit statistically significant, the potentially stabilizing effect of the exchange rate is
small. However, the speculative shocks also have negligible effects on output and
inflation. Thus, our findings indicate that exchange rates are neither stabilizing nor
destabilizing but may be loosely characterized as disconnected from the rest of the
economy.
In Essay 2 I follow the first direction in the literature by using a dynamic stochastic equilibrium model to investigate the determinants of exits from a fixed to
3
flexible exchange rate regime. The motivation of the essay is the simple observation that between 1990 and 1998, the share of countries with fixed exchange rate
regimes decreased sharply. How can this phenomenon be explained? Two alternative explanations are given in the literature. Either the policy maker is forced
to exit because of either deteriorating international reserves (Krugman (1979)) or
speculative pressures (Obstfeld (1996)), or she chooses to do so because of the severe
consequences for the real economy in terms of staggering interest rates giving rise to
economic recessions. In my model as in Ozkan and Sutherland (1998) and Rebelo
and Vegh (2006) the policy maker chooses to exit when the costs of staying in the
fixed exchange rate regime become to large. Specifically, exits are determined by a
concern for macroeconomic stabilization in terms of output and inflation deviations
from steady state values. My results indicate that if cost-push shocks are important
relative to demand shocks, exits should be more likely to occur in times of low consumption and output, high interest rates, negative asset holdings, current account
deficits, high inflation, and high domestic prices. These findings are consistent with
exits experienced in Latin America in the 70’s and 80’s and for the countries involved in the ERM-crises in the early 90’s. Furthermore, if the policy maker is
more sensitive to negative rather than positive output deviations, the probability
of exits increases overall and is tilted toward exits with an accompanying depreciation. Such asymmetry could be the result of political monetary policy making
that opportunistically stimulates the economy. This finding is interesting per se
since countries often choose to exit fixed exchange rate regimes with accompanying
depreciations rather than with accompanying appreciations - counter to common
policy recommendations.
In Essay 3 I use the same type of high-frequency data often employed in the
second direction of the research. The purpose of the essay is to investigate if foreign
exchange interventions by central banks have been used as a complementary monetary policy instrument. In my model, the policy maker’s objective is the inflation
rate. This common assumption is in itself non-standard in the literature on foreign
exchange interventions that has made the simplifying, but unrealistic, argument
that the policy maker cares about nominal exchange rate deviations from some ad
hoc target level only (Almekinders and Eijffinger (1996)). The policy maker has
two instruments at its disposal, the interest rate and interventions. The exchange
rate is determined by a portfolio balance equation (Dominguez and Frankel (1993))
that the policy maker exploits to affect output that in turn affects the target variable, inflation. Optimization of the objective function is done taking into account
quadratic costs of interest rate variation and interventions, and a zero floor on in-
4
Introduction
terest rate setting. The zero bound is of special interest since many papers have
been concerned with the monetary policy options in a zero interest rate environment
(e.g. McCallum (2000) and Svensson (2003)). I show that the policy maker should
use a combination of interest rate adjustments and interventions to stabilize the
economy. For the interest rate, an augmented Taylor (1993) rule is obtained. For
interventions, the model predicts that interventions should be negatively correlated
with interest rate changes which are due to stabilization motives. But interventions
should be positively related to the interest rate when it moves because of other motives or a binding zero lower bound. Solving for current interventions, I find that
interventions should be decreasing in inflation expectations and in the real exchange
rate, but increasing with expected interventions. Testing the model on data for Australia, Japan and Sweden, I find support for these predictions in most dimensions.
The results indicate that interventions have been used in a way that is consistent
with medium-run monetary policy objectives and not only as a means of stabilizing
short term movements in the exchange rate itself.
Macroeconomic uncertainty
In economics, uncertainty usually refers to the second moment of the distribution of
expected outcomes. In the field of macroeconomics, there has for a long time been an
understanding that, after controlling for the expected outcome, uncertainty should
be of importance for aggregates such as investment and consumption. Bernanke
(1983) shows how uncertainty about the future increases the value-to-wait and could
depress investment. In Romer (1990) it is argued that the dramatic increase in
uncertainty caused by the stock market crash in 1929 depressed durable consumption
and exercerbated the Great Depression. When testing such hypotheses on real world
data, authors often use stock market volatility as a proxy for uncertainty. However,
one crucial question then arises: is stock market volatility a good proxy for true
uncertainty? Or, more generally, how can we evaluate proxies of uncertainty since
uncertainty is unobservable, even ex post.
In Essay 4 (with David Kjellberg) we evaluate available proxies of uncertainty
for the US based on a novel strategy. We partly rely on the idea that uncertainty
should have increased as a response to certain historical events such as the 9/11
terrorist attacks and outbreaks of military conflicts. This idea is supported by other
papers, e.g. Bloom, Bond, and Reenen (2006), where it is observed that the month
after the terrorist attacks, there was a substantial increase in the mentioning of
"uncertainty" in the FOMC meetings. Furthermore, uncertainty should decrease
5
when the outcome of a presidential election is announced, since uncertainty about
future policy making is reduced at that time. Two questions are addressed in this
essay. First, how do we evaluate proxies? Previous papers have posited some preferred proxy in order to evaluate others. If other proxies are closely related to the
preferred proxy, these are taken to be good proxies. Our approach does not take
a stand, ex ante, on which is the preferred proxy. Instead, we evaluate all available proxies independently based on how they should behave according to a stylized VAR-model. Using correlations, some narrative evidence and a factor analysis
we find that disagreement and volatility proxies are valid measures of uncertainty
whereas probability forecast proxies are not. This result is reinforced when we take
our proxies to standard macroeconomic applications where uncertainty is supposed
to be of importance. That probability forecast proxies are not appropriate measures
of uncertainty is disturbing since the probability forecast proxy has been the preferred proxy in previous studies (e.g. Zarnowitz and Lambros (1987)). Second, our
analysis also addresses the question whether it is reasonable to talk about some general macroeconomic uncertainty. A factor analysis of available proxies shows that
different proxies share a common component that explains a large part of the variations in individual proxies. This leads us to believe that there is one (unobserved)
structural shock of the economy that makes proxies co-move, i.e. general macroeconomic uncertainty. Finally, in an extension of the essay, we find that uncertainty is
positively correlated with the absolute value GDP-gap. In other words, at the turn
of the business cycle uncertainty tends to be higher than in normal states of the
economy.
6
Introduction
References
Almekinders, G. J., and S. C. W. Eijffinger (1996): “A Friction Model
of Daily Bundesbank and Federal Reserve Intervention,” Journal of Banking &
Finance, 20, 1365—1380.
Baxter, M., and A. Stockman (1989): “Business Cycles and the Exchange Rate
Regime,” Journal of Monetary Economics, 23, 377—400.
Bernanke, B. S. (1983): “Irreversibility, Uncertainty, and Cyclical Investment,”
The Quarterly Journal of Economics, 98, 85—106.
Bloom, N., S. Bond, and J. V. Reenen (2006): “Uncertainty and Investment
Dynamics,” Working Paper 12383, NBER.
de Grauwe, P., and M. Grimaldi (2006): “Exchange Rate Puzzles: A Tale of
Switching Attractors,” European Economic Review, 50, 1—33.
Dominguez, K. M., and J. A. Frankel (1993): “Does Foreign Exchange Intervention Matter? The Portfolio Effect,” The American Economic Review, 83,
1356—1369.
Evans, M. D. D., and R. K. Lyons (2002): “Order Flow and Exchange Rate
Dynamics,” Journal of Political Economy, 110, 170—180.
Krugman, P. (1979): “A Model of Balance of Payment Crises,” Journal of Money,
Credit and Banking, 11, 311—325.
Lane, P. R. (2001): “The New Open Economy Macroeconomics: A Survey,” Journal of International Economics, 54, 235—266.
McCallum, B. T. (2000): “Theoretical Analysis Regarding a Zero Lower Bound
on Nominal Interest Rates,” Jornal of Money, Credit and Banking, 32, 870—904.
Meese, R. A., and K. Rogoff (1983a): “Empirical Exchange Rate Models of the
Seventies: Do They Fit Out of Sample?,” Journal of International Economics,
14, 3—24.
(1983b): “The Out-of-Sample Failure of Empirical Exchange Rate Models: Sampling Error or Misspecification,” in Exchange Rates and International
Macroeconomics, ed. by J. A. Frenkel, Chicago. University of Chicago Press.
Obstfeld, M. (1996): “Models of Currency Crises with Self-Fulfilling Features,”
European Economic Review, 40, 1037—1047.
7
Obstfeld, M., and K. Rogoff (2000): “The Six Major Puzzles in International
Macroeconomics: Is There a Common Cause?,” NBER Macroeconomics Annual,
15, 339—390.
Ozkan, F. G., and A. Sutherland (1998): “A Currency Crisis Model with an
Optimising Policymaker,” Journal of International Economics, 44, 339—364.
Rebelo, S., and C. Vegh (2006): “When Is It Optimal to Abandon a Fixed
Exchange Rate?,” Working Paper 12793, NBER.
Romer, C. D. (1990): “The Great Crash and the Onset of the Great Depression,”
The Quarterly Journal of Economics, 105, 579—624.
Sarno, L. (2001): “Toward a New Paradigm in Open Economy Modeling: Where
Do We Stand?,” The Regional Economist, pp. 21—36.
Svensson, L. E. O. (2003): “Escaping from a Liquidity Trap and Deflation: The
Foolproof Way and Others,” Journal of Economic Perspectives, 17, 145—166.
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Zarnowitz, V., and L. A. Lambros (1987): “Consensus and Uncertainty in
Economic Prediction,” Journal of Political Economy, 95, 591—621.
Essay
1
Exchange rates and asymmetric shocks in
small open economies
1
Introduction
Some small open economies have floating exchange rates and others either peg their
exchange rate to that of a large country or participate in a monetary union. There
is an ongoing debate about the pros and cons of a floating exchange rate regime.
A crucial argument concerns the stabilizing role of a freely floating exchange rate.
If the exchange rate moves in a stabilizing manner in response to shocks that hit
the small country differently from the anchor economy, entering a monetary union
implies that the small open economy loses a stabilizing instrument. On the other
hand, substantial evidence indicates that floating exchange rates are susceptible to
non-fundamental shocks and may therefore create unnecessary variability (see, for
instance, Buiter (2000)). It is an undisputable fact that nominal exchange rates
are highly variable. Are these exchange rate movements responses to fundamental shocks and or can they be characterized as disconnected from the rest of the
economy?
Several different approaches have been employed to investigate whether exchange
rates stabilize or destabilize economies. Hochreiter, Korinek, and Siklos (2003) and
Bergvall (2005) conduct counterfactual experiments to study the effects of alternative exchange rate arrangements. Other authors use the results from Meese and
Rogoff (1983a, 1983b) and subsequent research about (the absence of) a relationship between exchange rates and fundamental variables as indirect evidence that
exchange rates do not stabilize the economy. To find out how exchange rates respond to various shocks, it is important to be able to identify these shocks from
observable data. The most common and most direct way of investigating the sta9
10
Essay 1. Exchange rates and asymmetric shocks in small open economies
bilizing role of exchange rates is to use a structural vector autoregressive model
(SVAR) to extract the responses of different variables to shocks.
Previous studies using SVARs to address the stabilizing or destabilizing role
of exchange rates include Clarida and Galí (1994), Canzoneri, Valles, and Vinals
(1996), Thomas (1997), Funke (2000), Bjorneland (2004) and Farrant and Peersman
(2005). These models use different variables in the VAR to identify shocks labeled
as supply shocks, demand shocks, monetary shocks and nominal shocks. Original
variables are transformed into relative variables1 so that any shock that does not
have a perfectly symmetric effect on the two countries is labeled as asymmetric.
Another issue concerns the variance decomposition of exchange rates. To what
extent are movements in exchange rates caused by different shocks at various horizons? Canzoneri, Valles, and Vinals (1996), Funke (2000) and Bjorneland (2004)
study the variance decompositions of output and exchange rates to establish to what
extent movements in output and exchange rate are caused by the same shocks. All
three studies conclude that output and the exchange rate predominantly respond to
different shocks. Artis and Ehrmann (2006) find that only a small portion of the
movements in exchange rates is caused by real supply and demand shocks. In these
studies, the impulse responses of exchange rates to supply and demand shocks are
insignificant in all cases. They find that as much as ninety percent of the movements
in the Swedish exchange rate are due to exchange rate shocks at all horizons, but
they also conclude that these shocks are neither transmitted to the price level nor
to the real economy. Farrant and Peersman (2005) use sign restrictions instead of
long-run zero restrictions to identify the different shocks. Their conclusion is similar
to the other studies in that most exchange rate fluctuations are due to monetary
and exchange rate shocks.
Although other studies have partly examined the questions raised in this paper,
we believe that there is still room for significant improvement. First, to our knowledge, this is the first study narrowly focusing on inflation target periods of small
open economies. We believe that by isolating those periods, we can be more certain
that major structural shifts in the policy of the government with regards to stabilization policy have not occurred. Moreover, the expected response of the exchange
rate to different shocks is more obvious. Second, our choice of trade weighted nonrelative variables seems more natural in the sense that it allows for both world-wide
symmetric shocks and domestic asymmetric shocks. It then follows that we can keep
track of the exchange rate response to both symmetric and asymmetric shocks. As
noted by Artis and Ehrmann (2006), the relative approach imposes the restriction
1
e.g. log(GDP for Sweden)-log(GDP for USA)
2. Data
11
that the cross-country effects are similar whereas the non-relative approach does
not. This restriction seems quite plausible in studying countries of similar economic
size, but considering that most of this literature is preoccupied with stabilization
properties of small open economies and that many of these studies use the USA as
the anchor economy, we find the relative approach unappealing. In constructing a
trade weighted world economy that is specific for each country and employing the
non-relative approach, we extract the various shocks more carefully than in previous
studies. Third, we employ an innovative identification scheme by using a combination of long and short-run restrictions to extract the underlying structural shocks,
whereas standard procedure in the literature is a full set of either long-run or shortrun restrictions. These restrictions can all be motivated on economical grounds and
make expected responses to various shocks straightforward.
The paper is organized as follows: The data is presented in section 2. In Section
3, we introduce the statistical model and the identification procedure that recovers
the structural shocks. Section 4 presents the empirical results. We conclude the
section of results with a full summary and discussion of the results obtained. Section
5 concludes.
2
Data
The "small open economies" in this paper are Sweden, Canada, Australia, New
Zealand and the United Kingdom. For all countries, seasonally adjusted quarterly
real GDP (y), seasonally adjusted consumer price indices (p) and nominal exchange
rates expressed as the domestic currency needed to buy one US dollar (e) have been
obtained from the Source OECD database for the respective inflation target periods.
These periods for the five countries are reported in Table 1. As the anchor world
economy, we have constructed separate world counterparts for the five countries
using TCW (Total Competitiveness Weights) supplied by the Swedish Riksbank. All
in all, the 18 countries included account for more than ninety percent of the original
trade weights for the five countries under survey in this paper.2 These weights
are then used to construct the country-specific "world" GDP (y∗), the "world"
price level (p∗) and the trade weighted nominal exchange rate (e∗) where the most
important trade counterpart will contribute with the largest weight. For example,
the relevant world counterpart for Canada will then consist of more than eighty
percent of USA, a small contribution from Japan and marginal contributions from
2
See the Appendix, section "Construction of weighted data and sample periods" for details on
data handling and weights.
12
Essay 1. Exchange rates and asymmetric shocks in small open economies
other countries. For Canada, this multilateral approach may not yield results that
differ to any large extent from a bilateral with the USA but for the other countries
where no single trade counterpart contributes with more than one third, the bilateral
approach will surely be too much of a simplification and make it less likely that we
will be able to separate world shocks from domestic shocks. Naturally, choosing a
bilateral or multilateral approach is dependent on the kind of question in which one
is interested. If the aim of the study is to narrowly investigate the policy option
of joining a monetary union with a major country, or pegging the exchange rate to
the currency of that major country, such as the US, then the bilateral approach is
appealing. If, on the other hand, the focus of the paper is a general assessment of the
role of the exchange rate in responding to and creating variability in the economy,
the natural way to proceed is by construction of a multilateral world counterpart.
Table 1: Inflation target periods
Country
Inflation target period
Sweden (SWE)
1993q1-2004q2
Canada (CAN)
1991q2-2004q1
Australia (AUS)
1993q1-2004q2
New Zealand (NZL)
1990q1-2003q4
United Kingdom (UK) 1993q1-2004q2
Since the inflation target period is quite short for all countries, we will not
consider any possible cointegration between the variables. Since we have good theoretical reasons to believe that real GDP, prices and nominal exchange rates are
unit roots, we proceed by taking first differences of our variables to produce stationary variables for estimation.3 The tests strongly indicate that the first difference
variables are all stationary.4
3
Statistical model
A characteristic feature of this paper is the way in which we identify the various
shocks. In the seminal article by Blanchard and Quah (1989), the identification
is completed by long-run restrictions only, whereas in Sims (1980) only short-run
restrictions are applied. We believe that in this context, a combination of the two
approaches yields the most convincing identification. In an n-variable system, a
3
Remember that if our variables are individual unit roots and not cointegrated, we might have
a problem with spurious regression.
4
For some formal unit-root tests of the first differenced variables, see the Appendix.
3. Statistical model
13
total of n(n − 1)/2 restrictions are needed for just-identification after the imposition
of an identity structural shock covariance matrix. Thus, in our five-variable system,
x = [dy ∗ dy dp ∗ dp de∗]0,
ten restrictions are needed for just-identification.5 Starting out with the VMA(∞)
form of the reduced form estimation,
(1)
xt = A(L)et ,
where A(L) is the inverted lag polynomial from the reduced form estimation and et
the reduced form residuals. Then, assume that the structural form VMA(∞) can
be written as
(2)
xt = C(L)εt ,
where C(L) is the structural counterpart to A(L) above and εt the structural shocks.
Equating the two representations of the system in (1) and (2), we finally get
(3)
C(1) = A(1)C0 ,
where C(1) is the long-run VMA impact matrix of the structural shocks, A(1) the
estimated VMA(∞) from the reduced form estimation stage and C0 the short-run
matrix defining the reduced form shocks as linear combinations of the structural
shocks.6 Maximum likelihood estimation under non-linear constraints will result in
the estimation of C0 . This short-run impact matrix is all we need for further analysis
through impulse response functions and forecast error variance decompositions, since
it traces out the effects of structural shocks to the variables. From equation (3), we
can explicitly write out the zero restrictions as
⎡
⎡
⎤
na
na 0 0 0 0
⎢
⎢
⎥
⎢na
⎢na na 0 0 0 ⎥
⎢
⎢
⎥
⎢na 0 na 0 0 ⎥ = A(1) ⎢na
⎢
⎢
⎥
⎢
⎢
⎥
⎣na
⎣na na na na na⎦
na
na na na na na
5
6
dx indicates a first difference of variable x.
See the Appendix for a complete derivation of (3).
na
na
na
na
na
na
na
na
na
na
na
na
na
na
na
⎤
na
⎥
na⎥
⎥
na⎥
⎥,
⎥
0⎦
na
(4)
14
Essay 1. Exchange rates and asymmetric shocks in small open economies
where ”na” indicates that there is no restriction on the element. The estimation
of C0 under these restrictions is performed in RATS7 . Although many of the longrun responses are restricted by long-run zero restrictions, this full impulse response
(IR) system gives an indication of whether we have been able to correctly identify
the different types of shocks. We would expect the directions of the IRs to be
those shown in Table 2. Table 2 is essentially the left-hand side of equation (4),
i.e. the (long-run) responses of the variables to structural shocks. The conjectured
directions of the variables’ responses to shocks are based on a simplified MundellFleming-Dornbusch model world with a vertical supply curve as in Taylor (2004):
Table 2: Expected responses to
Shock
Variable εs∗ εs εd∗ εd
y*
+ 0 0
0
y
+ + 0
0
p*
− 0 + 0
p
− − + +
e*
?
+ ?
−
shocks
εe∗
0
0
0
+
+
The shocks are identified as follows and are expected to have the following effects
on the variables in the VAR system:
• The shock εs∗ is the shock driving world real output in the long run; we
will label this shock a world supply shock. εs∗ is expected to have a longrun positive effect not only on world output, but also on output in the small
economy. Furthermore, we expect it to reduce prices both in the world as a
whole and in the small economy.8
• The shock εs is the shock that, apart from εs∗ , determines domestic real output
in the long run; hence an asymmetric supply shock. εs is expected to reduce
the domestic price level and if the inflation target is rigid, we would expect a
depreciation of the nominal exchange rate to restore the inflation target level.
• The shock εd∗ has no effect on output in the long run, but potentially affects
7
The estimation of C0 under restrictions is done making use of the SVAR.prg code by Giannini,
Lanzarotti and Seghelini found at RATS’ home page: www.estima.com. The constraints are written
out explicitly and in this case, 10 coefficients can be written as functions of the 9 free from equation
(4). Cast in the desired format the SVAR.prg program estimates C0 with Maximum Likelihood.
See the Appendix for a derivation of constraints. This matrix is then exported to Eviews for an
estimation output analysis.
8
One could, for example, think of the Solow-model where capital accumulation and very persistent productivity shocks alone determine real GDP in the long run.
3. Statistical model
15
world inflation as well as the domestic price level through imported inflation;
we will call εd∗ a world demand shock.
• The shock εd raises the home price level in the long run, but has no effect on
the world price level; hence we call it an asymmetric demand shock. There
are two possible interpretations of this shock: either it is a real demand shock,
such as an increased propensity to consume, which would result in higher
prices and an appreciating nominal exchange rate to restore equilibrium at a
lower (appreciated) real exchange rate. The other interpretation is that it is
some type of financial shock, e.g. in monetary policy, that results in higher
prices and a depreciating nominal exchange rate leaving the real exchange rate
unaffected in the long run. In both these cases, we would expect a temporary
effect on inflation and a permanent effect on the price level.
• The last shock, εe∗ , is identified as a shock that can potentially have longrun effects on the nominal exchange rate as well as the long-run domestic
price level. It is not allowed to affect the price within the quarter. Such
a restriction must necessarily be added to be able to separate the last two
shocks from each other. The most common way of econometrically separating
these two shocks from each other is to impose that the last shock can only
have temporary effects on the next to last shock.9 However, we find this
quite unnatural since, by construction, we then make the last shock have long
lasting effects on the real exchange rate. We find it to be intuitive that the
financial price, the exchange rate, reacts very quickly to new information on
prices but that it takes some time for changes in the exchange rate to affect
pricing behavior. Thus, making these identifying restrictions, we interpret this
shock as a speculative shock, or a risk premium on holding domestic currency.
This interpretation is close to that of Farrant and Peersman (2005). We would
expect prices to adjust in the long run so that the real exchange rate is left
unchanged.10
The summary of all IRs in Table 8 can be considered as the empirical counterpart
of Table 2.
Different variables could have been chosen in identifying the various shocks of
interest. Some of the studies mentioned in the introduction have included interest
rates to capture demand shocks. We have chosen not to, not only because of the
9
This is what is done in the "long-run identification" scheme in the Appendix.
We will see that, in fact, this long-run neutrality will not hold which is also the case in
Farrant and Peersman (2005). We conjecture that this could partly be explained by having too
few observations to infer long-run behavior, partly by the very long half-life of shocks to PPP.
10
16
Essay 1. Exchange rates and asymmetric shocks in small open economies
relatively few observations in the sample, but also because we believe that our model
is able to capture symmetric and asymmetric demand and supply shocks in the most
straightforward way possible without taking an explicit stand on optimal monetary
policy.
4
Empirical results
All countries considered in this paper have an appropriate first difference VAR specification according to the diagnostics of the series. The serial correlation tests indicate
that a VAR(2) specification is appropriate for all countries.11 Country results for the
chosen model are presented in terms of impulse response functions (IRs), displayed
in the Appendix, and variance decompositions. Impulse response functions can be
considered as characterizing the response of a certain variable to a certain structural
shock when the economy is initially in steady state 12 . The joint stationarity of the
VAR system makes the variables return to steady state in the long run, i.e. the first
difference effect dies out over time. Specifically, we are most interested in the shortand long-run responses of the exchange rate to asymmetric shocks. The objective of
the variance decomposition is to study how much of the variation in the exchange
rate that can be attributed to each of the shocks in the VAR-system.
Thus, if the exchange rate appreciates significantly in response to an asymmetric
demand shock and the asymmetric demand shocks contribute to a large portion of
the total variation in the exchange rate, we are inclined to believe that the exchange
rate has an important stabilizing role. Equivalently: if the exchange rate depreciates significantly and strongly due to a domestic supply shock, we will say that
the exchange rate provides some element of stabilization to the economy.13 Since
the expected responses of the exchange rate to various shocks under an inflation
target are quite straightforward, we will focus on these. However, the world supply
and demand shocks will not entail such clear expectations on the response of the
nominal exchange rate, since we would then have to take other monetary authorities
responses’ to such shocks into account. Furthermore, although labeled as "symmetric" shocks, we are more uncertain about the magnitude of the shocks in different
countries, thus rendering the expected response unclear.
11
See the Appendix for unit root as well as specification tests.
With five variables and five shocks, we will have a total of 25 IRs for each country.
13
Note that this entails the properties of the exchange rate as responses to unforeseen shocks.
It remains inconclusive whether the exchange rate as a whole has provided the economy with a
stabilization mechanism and here, we would have to rely on counterfactual studies.
12
4. Empirical results
4.1
17
Sweden
For Sweden, as for all countries, we can observe that long-run zero effects are all
properly restricted and that many of the impulse responses are statistically insignificant at the five-percent level. The diagonal "own-shock" effects are all significant
at all horizons. In the long run, only the asymmetric demand shock effect on the
nominal exchange rate and the world demand shock on domestic price are statistically significantly at the five-percent level.14 The magnitude of the appreciating
effect to the asymmetric demand shock is about one percent. This result is to be
interpreted in the following way: if a typical shock in asymmetric demand15 hits the
economy, the nominal exchange rate is expected to appreciate by about one percent
from its previous equilibrium value. Other short-run effects that are statistically significant are mostly of the expected sign. As predicted in Table 2, the exchange rate
depreciates to a domestic supply shock in line with restoring the inflation target.
Where does the total variation in the exchange rate come from? We would hope
that it is mostly in response to fundamental supply and demand shocks and not the
result of speculative trading, i.e. shocks in the exchange rate itself. However, Table
3 shows that most of the variation in fact originates from the speculative shock,
although its contribution decreases somewhat over time.
Table 3: Variance decompositions
Horizon εs∗
εs
1
4.8 6.0
4
9.0 9.6
12
11.9 9.3
20
11.9 9.3
of SWE TCW-exchange rate
εd∗ εd εe∗
1.3 0.7 87.2
1.6 7.1 72.7
1.9 6.9 70.1
1.9 6.9 70.1
This result is in line with Artis and Ehrmann (2006) who also note that Sweden’s
exchange market looks like a source of shocks with around ninety percent of the
variance in the exchange rates being explained by the exchange rate shock itself
at all horizons. The contribution of the other shocks to the forecast error variance
remains low at all horizons. Although the impulse responses indicate a stabilizing
role for the exchange rate when an asymmetric demand shock hits the economy,
the contribution of such shocks to the movements in the exchange rate is small.
The conclusion from these results would then be that Sweden would lose some
14
This result holds at a marginally higher significance level with bootstrapped confidence intervals over the entire horizon.
15
One could imagine a sudden positive shock in consumers’ outlook on the future, making them
consume more of their disposable income.
18
Essay 1. Exchange rates and asymmetric shocks in small open economies
stabilization due to exchange rate movements if joining a monetary union16 , but
that the effect is likely to be small.
4.2
Canada
The results for Canada are quite similar to those for Sweden. Few anomalies in the
impulse responses are found, which supports the identification scheme. The positive
short-run effects of demand shocks on output are notable. If anything, supply shocks
decrease prices which is also in line with the expectations. When it comes to the
nominal exchange rate, the appreciating effect due to asymmetric demand shocks is
similar in shape and magnitude to what we find for Sweden. However, the positive
and significant, or close to significant, effect of world demand shocks is different. In
the short run, there are significant effects of supply shocks; the world supply shock
appreciates17 and the domestic supply shock depreciates the exchange rate.18 Once
again, we find support for a stabilizing role of the exchange rate under the inflation
target period.
As for Sweden, the largest contributor to nominal exchange rate variation is the
speculative shock, although it is much smaller and decreasing over time. Artis and
Ehrmann (2006) also argue that the exchange rate shock is less important for Canada
than for Sweden. The domestic supply shock also accounts for a large share of total
variation and there are indications of a depreciation in response to domestic supply
shocks. It could be argued that the nominal exchange rate responds to stabilize
price and inflation. Thus, in the case of Canada, it seems that the exchange rate
provides some stabilization of the economy.
Table 4: Variance decompositions
Horizon εs∗
εs
1
9.6 33.8
4
11.7 27.7
12
12.0 27.5
20
12.0 27.5
of CAN TCW-exchange rate
εd∗
εd εe∗
10.5 1.2 45.0
13.8 7.7 39.0
14.1 7.8 38.6
14.1 7.8 38.6
16
In this paper, "a monetary union" should be considered as the countries in the weighing
system. For Sweden, the results do not readily apply to the EMU although the EMU contribution
in the TCW is quite large.
17
Since "the world" to ninety percent consists of USA in this case, the following scenario could
be imagined: A supply shock predominantly hits the USA and the decrease in inflation makes the
FED reduce the interest rate which, in turn, depreciates the USD against the Canadian dollar.
18
Short-run IRs for the exchange rate remain unchanged with bootstrapped confidence intervals.
4. Empirical results
4.3
19
Australia
Australia shows one striking peculiarity in the impulse response functions, namely
the positive world price-effect of a world supply shock. This result is counterintuitive
in that we believe that a supply shock, such as a sudden increase in productivity,
should reduce prices. Although the effect is statistically significant, it is very small at
one tenth of a percent. On the other hand, the asymmetric supply shock significantly
reduces the domestic price, by roughly one percent. The nominal exchange rate
seems to have some tendency to appreciate in response to the world supply shock;
otherwise the effects are small and statistically insignificant.
Although the speculative shock accounts for more than half the variation in the
exchange rate at all horizons, the world supply shock seems quite important for the
exchange rate variation in Australia. We argue that pegging the exchange rate to a
basket of currencies would not be detrimental to the Australian economy, since the
exchange rate mainly responds to symmetric world shocks. The speculative fluctuations in the exchange rate could possibly also be decreased by such an arrangement.
Table 5: Variance decompositions of AUS TCW-exchange rate
Horizon εs∗
εs εd∗
εd εe∗
1
33.1 0.0 2.2 1.0 63.7
4
30.3 5.8 11.4 1.1 51.5
12
30.2 6.2 11.3 1.3 51.1
40
30.2 6.1 11.3 1.3 51.1
4.4
New Zealand
Short-run and close to significant negative price effects of supply shocks are found
for New Zealand. The most notable result is the statistically significant effect of
the asymmetric supply shock on the nominal exchange rate. To the extent that
the inflation target is to be enforced, we find this striking. Imagine there to be a
sudden productivity increase in the New Zealand economy which reduces prices. If
the inflation target were the main priority, we would hope for the exchange rate to
depreciate so as to stimulate exports and push aggregate demand. If anything, the
opposite happens in New Zealand.19
With reference to the above reasoning about stabilization of inflation and the
appreciating movement of the exchange rate to asymmetric supply shocks, we can
see that although the exchange rate movements are not stabilizing per se, only
19
This result remains significant with bootstrapped confidence intervals in the short run.
20
Essay 1. Exchange rates and asymmetric shocks in small open economies
a small part of the exchange rate movements create (destabilizing) variability in
the exchange rate. As for the other countries, most of the variation comes from
speculative shocks in the exchange rate. It seems that, given an inflation target
and the destabilizing movements in the exchange rate following asymmetric supply
shocks, some increased stability could be the result of joining a monetary union. A
monetary union with Australia is, in fact, what is proposed in Hochreiter, Korinek,
and Siklos (2003).
Table 6: Variance decompositions of NZL TCW-exchange rate
Horizon εs∗
εs
εd∗
εd εe∗
1
0.3 9.3 3.5 0.5 86.5
4
2.7 13.8 13.8 4.3 65.4
12
3.9 13.4 14.4 4.8 63.5
40
3.9 13.4 14.4 4.8 63.5
4.5
United Kingdom
In the UK, the world supply shocks tend to appreciate the pound, at least in the
short to medium run.20 However, the major part of the nominal exchange rate
variation originates from the speculative shocks, while world supply shocks account
for some 25 percent of the variation in the long run. From the point of view of
macroeconomic stability, no clear-cut policy recommendation can be derived from
these results.
Table 7: Variance decompositions of UK TCW-exchange rate
Horizon εs∗
εs εd∗ εd εe∗
1
11.7 0.1 1.9 0.1 86.2
4
24.6 8.0 4.2 9.2 54.0
12
24.7 8.2 4.6 9.2 53.4
40
24.7 8.2 4.6 9.2 53.4
4.6
Empirical findings, a summary
First, we will summarize our findings of separate countries in two tables. In Table
8, the results for all impulse responses, short run (2 quarters) and long run (20
quarters), for all five countries are displayed. This table asks some important questions: Is our identification procedure successful? Do we come across any common
20
This result remains significant with bootstrapped confidence intervals in the short run.
4. Empirical results
21
findings for these five economies? Is there a pattern in how the variables respond
to various types of shocks? Can they be explained by individual characteristics of
the respective countries? The second table, Table 9, will summarize the variance
decompositions.
Table 8: Summary of country variables responses to shocks 2 and 20 quarters,
ordered SWE/CAN/AUS/NZL/UK
Variable
Shock Horizon
εs∗
εs
εd∗
εd
εe∗
y*
2q
20q
+/+/+/+/+
+/+/+/+/+
0/+/+/0/0
0/0/0/0/0
0/+/0/+/+
0/0/0/0/0
0/0/0/0/0
0/0/0/0/0
0/0/+/0/0
0/0/0/0/0
y
2q
20q
+/+/+/0/+
0/0/0/0/+
+/+/+/+/+
+/+/+/+/+
0/+/0/0/0
0/0/0/0/0
0/0/+/0/0
0/0/0/0/0
0/0/0/0/0
0/0/0/0/0
p*
2q
20q
0/-/0/0/0/0/+/0/0
0/0/0/0/0
0/0/0/0/0
+/+/+/+/+
+/+/+/+/+
0/0/0/0/0
0/0/0/0/0
0/0/0/0/0
0/0/0/0/0
p
2q
20q
-/-/0/-/0
0/0/0/0/0
0/-/-/0/0
0/0/-/0/0
+/0/0/+/0
+/0/0/0/0
+/+/+/+/+
+/+/+/+/+
0/0/0/0/0
0/0/0/0/0
e*
2q
20q
-/-/-/0/0/0/0/0/0
+/+/0/-/0
0/0/0/-/0
0/+/0/0/0
0/+/0/0/0
0/-/0/0/0
-/-/0/0/0
+/+/+/+/+
+/+/+/+/+
• εs∗ , what we have identified as the world supply shock, tends to raise output
both abroad and in the small open economy. The effect on domestic output
is more pronounced in the short run. With the exception of one country
(Australia), this shock tends to lower prices, at least in the short run, which
makes us believe that this shock can in fact be labeled as a supply shock.
In four countries out of five (the exception being New Zealand) the nominal
exchange rate appreciates in the short run following a world supply shock.21
• εs , the asymmetric supply shock, reduces domestic prices in the short run in
two cases out of five (Canada and Australia). The effect is negative and significant in the long run only for Australia. Although the evidence is somewhat
weak, the results provide some support for our identification of this shock.
The exchange rate depreciates in two cases out of five (Sweden and Canada)
and appreciates in one case (New Zealand).
21
Given that the world experiences a stronger effect of this shock and that the macroeconomic
policy can loosely be described as inflation targeting, we would expect this appreciation of the
small economy currency.
22
Essay 1. Exchange rates and asymmetric shocks in small open economies
• εd∗ tends to temporarily raise output in three countries out of five and increases
prices in the small economy, thus making us believe that we have correctly
identified this shock as a world demand shock. The exchange rate depreciates
in one case (Canada).
• εd has been the hardest to identify by looking at the impulse responses. Remember that its effect on all variables in the system except domestic price
and nominal exchange rate is restricted to zero in the long run. Indications
of a positive short-run effect on domestic output can be found in all cases but
one (Canada), but at poor significance levels. The shock appears to be more
of a real demand shock than a financial shock in four cases out of five (the
exception being the United Kingdom) since this shock tends to raise domestic prices and appreciate the nominal exchange rate, further appreciating the
real exchange rate to restore the equilibrium. The appreciation is statistically
significant in two cases (Canada and Sweden).
• εe∗ , the speculative shock, identified as possibly only affecting domestic prices
and the exchange rate in the long run, does not have any clear effect on
any variable except the exchange rate itself. That the effect on the nominal
exchange rate is permanent and significant would then imply that also the real
exchange rate is affected. However, it is important to remember that due to
the way we have set up the VAR, this last shock will be identified as the longrun residual determinant of the nominal exchange rate after the other shocks
have been accounted for. Keeping in mind that nominal exchange rates are
characterized by fluctuations and possibly trends over time for no apparent
reason, this might come as no surprise given that relative PPP does not hold
even with much longer time series.
The impulse responses for the five countries differ quite remarkably and some
anomalies have been found in the expected responses. For the two countries where
our identification seems to have been most successful, Sweden and Canada, the
responses of the nominal exchange rate are as expected. For the other countries,
some doubts arise of whether we have really been able to correctly identify the
various shocks and if this is indeed the case, it is not surprising that the responses
of the exchange rate are not in line with the expectations. With short samples
and employing long-run identifying assumptions, we might very well have such a
problem.
5. Conclusions
23
Table 9: Variance decompositions, summary
Horizon εs∗
εs
εd∗
εd
εe∗
1
0-33 0-34 1-11 0-1 45-87
4
3-30 6-28 2-14 1-9 39-73
12
4-30 6-28 2-14 1-9 39-70
40
4-30 6-28 2-14 1-9 39-70
Table 9 summarizes the variance decompositions presented country by country
above. The results indicate that supply shocks are more important for nominal
exchange rate behavior than demand shocks but that the speculative shock is the
most important determinant. However, the variance decompositions of inflation and
output growth indicate that the contribution of εe∗ is small. Only for Sweden’s GDP
does this contribution exceed ten percent and for inflation, the contribution is at a
mere five percent.22 This further reinforces the common belief that exchange rates
are neither a stabilizer nor a destabilizer, but can be characterized as detached from
the rest of the economy.
5
Conclusions
Are exchange rates stabilizing or destabilizing? Conditional on our structural VAR
model, we have provided some answers to specific questions concerning the role of
exchange rates and their relationship to asymmetric shocks. These results are robust
to alternative specifications23 .
We have studied the impulse responses of nominal exchange rates to asymmetric
shocks in domestic demand and supply in five small open economies. In order to
stabilize output and inflation, the nominal exchange rate should appreciate when
demand unexpectedly increases. Only in the case of Sweden and Canada is the
appreciating response statistically significant and at around one percent in magnitude. Further, for Sweden and Canada, the exchange rate tends to depreciate in
response to domestic supply shocks, at least in the short run. We have argued that
this finding is in line with an inflation target. These two findings lead us to believe
that Sweden and Canada would lose some economic stability by joining a monetary
union.
The forecast error variance decompositions of nominal exchange rates show that
exchange rates create rather than respond to shocks. While floating exchange rates
create variability, the shocks emanating from the exchange rate only have minor
22
23
These results are left unreported but are available from the authors upon request.
See the Appendix, section A.5.
24
Essay 1. Exchange rates and asymmetric shocks in small open economies
effects on the economy. Neither output nor inflation respond much to the speculative
exchange rate shock.
Most of our evidence on the behavior of exchange rates is consistent with the
exchange rate disconnect puzzle discussed by Obstfeld and Rogoff (2000). Exchange
rates are highly variable but their movements appear to be weakly related to the
rest of the economy. They are not responses to fundamental shocks and only have
minor effects on output and inflation.
References
25
References
Artis, M., and M. Ehrmann (2006): “The Exchange Rate - a Shock Absorber of
Source of Shocks? A Study of Four Open Economies,” Journal of International
Money and Finance, 25, 874—893.
Bergvall, A. (2005): “Exchange Rate Regimes and Macroeconomic Stability: The
Case of Sweden,” Oxford Economic Papers, 57, 422—446.
Bjorneland, H. (2004): “The Role of the Exchange Rate as Shock Absorber in a
Small Open Economy,” Open Economies Review, 15, 23—43.
Blanchard, O., and D. Quah (1989): “The Dynamic Effects of Aggregate Demand and Supply Disturbances,” American Economic Review, 79, 655—673.
Buiter, W. H. (2000): “Optimal Currency Areas: Why Does the Exchange Rate
Regime Matter? (With an Application to UK Membership in EMU),” Discussion
Paper 2366, CEPR.
Canzoneri, M., J. Valles, and J. Vinals (1996): “Do Exchange Rates Move
to Adress International Macroeconomic Imbalances?,” CEPR Discussion Paper
1498.
Clarida, R., and J. Galí (1994): “Sources of Real Exchange Rate Fluctuations:
How Important are Nominal Shocks?,” Carnegie-Rochester Conference Series on
Public Policy, 41(951), 1—56.
Farrant, K., and G. Peersman (2005): “In the Exchange Rate a Shock Absorber of Source of Shocks? New Empirical Evidence,” Working Paper 2005/285,
Universiteit Gent.
Funke, M. (2000): “Macroeconomic Shocks in Euroland vs the UK: Supply, Demand, or Nominal?,” Working Paper 37, EUI-RSCAS.
Hamilton, J. D. (1994): Time Series Analysis. Princeton University Press, Princeton.
Hochreiter, E., A. Korinek, and P. Siklos (2003): “The Potential Consequences of Alternative Exchange Rate Regimes: A Study of Three Candidate
Regions,” International Journal of Finance & Economics, 8, 327—349.
Meese, R. A., and K. Rogoff (1983a): “Empirical Exchange Rate Models of the
Seventies: Do They Fit Out of Sample?,” Journal of International Economics,
14, 3—24.
26
References
(1983b): “The Out-of-Sample Failure of Empirical Exchange Rate Models: Sampling Error or Misspecification,” in Exchange Rates and International
Macroeconomics, ed. by J. A. Frenkel, Chicago. University of Chicago Press.
Obstfeld, M., and K. Rogoff (2000): “The Six Major Puzzles in International
Macroeconomics: Is There a Common Cause?,” NBER Macroeconomics Annual,
15, 339—390.
Sims, C. A. (1980): “Macroeconomics and Reality,” Econometrica, 48(48), 1—48.
Taylor, M. P. (2004): “Estimating Structural Macroeconomic Shocks Through
Long-Run Recursive Restrictions on Vector Autoregressive Models: The Problem
of Identification,” International Journal of Finance and Economics, 9, 229—244.
Thomas, A. H. (1997): “Is the Exchange Rate a Shock Absorber? The Case of
Sweden,” Working Paper 97/176, IMF.
A. Appendix
A
A.1
27
Appendix
Construction of weighted data and sample periods
The same 19 OECD countries are used for all five countries in constructing the world
anchor; countries and recomputed weights are displayed in Table A.1. We have
used OECD-data from the Source OECD database for all countries but Luxemburg,
Ireland and Portugal in the original weight system. Ireland and Portugal have been
omitted because of data unavailability. Moreover, since separate data is lacking
for Luxemburg and Luxemburg is very small as compared to Belgium, we have
accepted to use the weight for Belgium-Luxemburg on Belgium data only. The
German GDP-series is rebased from 1990q1 to 1990q4 and for Sweden, constant
price data is seasonally adjusted by the moving average method and then used. All
in all, "the world" accounts for 95-99 percent of total TCW. The original weights
for the full set of OECD countries are re-weighted so that they sum to unity.
Table A.1: Transformed TCW-weights, percent
AUS CAN NZL SWE UK
Australia
0.2
17.9
0.3
0.5
Austria
0.5
0.2
0.4
1.7
1.2
Belgium-Lux.
1.2
0.5
0.9
3.6
5.6
Canada
1.8
1.9
1.2
1.4
Denmark
0.3
0.1
0.4
5.7
1.4
Finland
0.6
0.2
0.5
6.8
1.5
France
3.1
1.6
2.2
7.3
13.1
Germany
8.0
2.8
6.2
22.7 23.4
Greece
0.1
0.0
0.0
0.3
0.3
Italy
3.2
1.2
3.3
6.2
8.6
Japan
31.6
6.0
29.6
5.3
7.3
Netherlands
1.3
0.7
1.3
4.3
5.9
New Zealand
8.2
0.1
0.1
0.2
Norway
0.3
0.1
0.4
5.7
1.2
Spain
0.5
0.3
0.4
2.5
4.0
Sweden
1.7
0.6
1.9
3.6
Switzerland
1.4
0.4
1.4
2.8
3.4
United Kingdom 10.2
2.5
9.6
11.8
USA
26.1 82.6 21.7 11.8 17.2
Sum
100.0 100.0 100.0 100.0 100.0
All individual country series are transformed into natural logs and thereafter
world weighted aggregates are computed. The exchange rates are all in the domestic
currency needed to buy one US dollar and the missing bilateral exchange rates are
manually computed assuming no triangular arbitrage.
28
Essay 1. Exchange rates and asymmetric shocks in small open economies
The periods for estimation have been chosen to be those inflation target (IT) periods where the target has been announced and inflation is down within the target
band. The reason for putting this requirement on the data is that we are concerned
with exchange rate movements when the target is in operation and not during transitional periods. New-Zealand only is affected in the sense that the IT announcement
was made in March 1990, but inflation was down at the target level around the
second quarter of 1992.
A.2
Unit root tests
In Table A.2, we will report the augmented Dickey-Fuller tests (ADF-tests) for the
null hypothesis of unit roots in the first differenced data of prices, GDP levels and
nominal exchange rates. For each country, there will be five such tests since the
world weighted data differs between countries. All first difference series of the data
can clearly be rejected as unit roots.
Table A.2: ADF unit root
country
variable
SWE
CAN
AUS
dy*
4.34 (2.93) 5.20 (2.92) 3.68 (2.93)
dy
10.03 (2.93) 5.17 (2.92) 6.58 (2.93)
dp*
6.19 (2.93) 5.34 (2.92) 5.38 (2.93)
dp
8.26 (2.93) 7.94 (2.92) 5.28 (2.93)
de*
7.50 (2.93) 5.30 (2.92) 5.20 (2.93)
tests
NZL
4.48 (2.92)
7.44 (2.92)
6.55 (2.92)
4.59 (2.92)
5.39 (2.92)
Note 1: Only constant, no time trend, admitted in test equation
Note 2: SIC choose lag-length in tests, max. eight lags.
Note 3: |t-values| with 5% critical values in parentheses
UK
4.35 (2.93)
5.64 (2.93)
6.17 (2.93)
6.09 (2.93)
4.45 (2.93)
A. Appendix
A.3
29
Specification tests
In choosing the preferred lag order model for each country, we have relied on tests
for serial correlation in the residuals. In Tables A.3-A.7, we report the p-values of
the Portmanteau multivariate residual serial correlation test at lag length 20 and
the Lagrange multiplier (LM) test at lag-length 1, LM(1) and lag length 4, LM(4).
That the residuals are in fact non-serially correlated will be the main criteria in
choosing our preferred model, since we know that the estimates could be severely
biased if serial correlation remains.
Table A.3: Asymptotic p-values of residual serial correlation for Sweden
Model
VAR(1)
VAR(2)
VAR(3)
VAR(4)
Portmanteau
0.36
0.10
0.02
0.00
LM(1)
0.51
0.29
0.59
0.98
LM(4)
0.17
0.19
0.13
0.25
Table A.4: Asymptotic p-values of residual serial correlation for Canada
Model
VAR(1)
VAR(2)
VAR(3)
VAR(4)
Portmanteau
0.48
0.19
0.09
0.01
LM(1)
0.38
0.63
0.86
0.39
LM(4)
0.64
0.74
0.61
0.67
Table A.5: Asymptotic p-values of residual serial correlation for Australia
Model
VAR(1)
VAR(2)
VAR(3)
VAR(4)
Portmanteau
0.53
0.29
0.01
0.01
LM(1)
0.46
0.99
0.80
0.45
LM(4)
0.47
0.53
0.09
0.55
30
Essay 1. Exchange rates and asymmetric shocks in small open economies
Table A.6: Asymptotic p-values of residual serial correlation for New Zealand
Model
VAR(1)
VAR(2)
VAR(3)
VAR(4)
Portmanteau
0.28
0.13
0.02
0.00
LM(1)
0.20
0.91
0.21
0.27
LM(4)
0.25
0.19
0.46
0.12
Table A.7: Asymptotic p-values of residual serial correlation for United Kingdom
Model
VAR(1)
VAR(2)
VAR(3)
VAR(4)
Portmanteau
0.07
0.10
0.05
0.02
LM(1)
0.90
0.55
0.65
0.28
LM(4)
0.43
0.71
0.21
0.15
Based on the specification test in Tables A.3-A.7, a two lag VAR model was
chosen for all countries. Although more lags would probably introduce some more
dynamics into the system, the multivariate Portmanteau serial correlation tests and
parsimony make us choose the two-lag specification as the preferred model. In fact,
lag-length criteria tests such as the likelihood ratio (LR) test generally do not suggest
more than one-lag dynamics. The Jarque-Bera residual normality tests generally
do not reject the null of univariate and multivariate normal residuals in the two
lag specification, but the one-lag specification shows some signs of non-normality
thereby making us prefer the VAR(2) model.
A.4
Identification
Suppose the reduced form VAR can be written as
D(L)xt = et ,
(5)
et ∼ i.i.d. N (0, Ω),
(6)
where
and D(L) = D0 +D1 L+D2 L2 +...+Dp Lp . L is the lag operator with Li xt = xt−i and
D0 the identity matrix I. The covariance matrix E(et e0t ) = Ω of the reduced form
residuals et is in general non-diagonal and therefore, these cannot be interpreted as
structural shocks. If the roots of the characteristic polynomial in equation (5) lie
outside the unit circle, the matrix lag polynomial D(L) is invertible and there exists
an infinite order vector moving average representation,
A. Appendix
31
xt = A(L)et ,
(7)
where A(L) = D(L)−1 . Note that the matrix polynomials above, D(L) and therefore
also A(L) can be estimated by equation by equation OLS which is consistent and
under assumption of normality of the error terms also efficient.
Suppose that the VAR representation of the structural model can be written as
B(L)xt = εt ,
(8)
E(εt ε0t ) = I,
(9)
where
so that the orthogonal shocks are all normalized to unity. If D(L) is invertible so is
B(L) and we can rewrite (8) as
xt = C(L)εt ,
(10)
where C(L) = B(L)−1 . Equation (10) has a clear economical interpretation since all
endogenous variables xt are expressed as distributed lags of the underlying structural
shocks εt .
Equating equation (7) and equation (10), we have that
C(L)εt = A(L)et .
(11)
Since A0 = I and equation (11) must hold at each point in time, we have that
C0 εt = et ,
(12)
making clear that the estimated reduced form residuals from (5) are linear combinations of the underlying structural shocks. C0 can be interpreted as the contemporaneous reaction of the variables to structural innovations. Squaring both sides
of (12) and taking expectations, we get that
C0 C00 = Ω,
(13)
using (6) and (9). Then, combining (11) and (12) yields,
C(L)εt = A(L)C0 εt ,
(14)
32
Essay 1. Exchange rates and asymmetric shocks in small open economies
which, in turn, implies that
Ci = Ai C0 ∀i.
(15)
Now, assume C0 to be known. This means that the structural shocks εt can be
identified through (12) and since we have estimated Ai in the reduced form system,
we can easily calculate all structural coefficients Ci using (15). Feeding the structural
shocks to (10), the full dynamics of the system can then be described in terms of
impulse response functions and variance decompositions.24
From (15) we have that
C(1) = A(1)C0 ,
(16)
where A(1) and C(1) represent cumulated effects of innovation. A(1) is deduced
from reduced form estimation of (7) and restrictions on C(1) can be effectively used
to identify C0 . In fact, equation (16) forms the basis for the identification procedure.
In this paper, we need to impose 25 restrictions on the C0 matrix to identify
the structural shocks. By imposing an identity covariance matrix for the orthogonal
structural shocks in (9), we are left with ten restrictions. There are many ways in
which these restrictions could be added using long-run or short-run restrictions or a
combination of both. In this paper, the main mode of attack on C0 is the usage of
a combination of restrictions on C(1) and one directly imposed on C0 .
Just to make the reader get an idea of how the restrictions are implemented, we
will give a brief description of the steps:
1. From (16) we have the VMA(∞) matrix A(1) that we know from estimation.
C(1) is the impact matrix of long-run structural shocks where we restrict the
elements as described in (4) and C0 is the matrix defining the reduced form
residuals as linear combinations of the structural shocks. All matrices are five
by five.
2. Ten restrictions are needed for just identification. In fact, we impose eleven
restrictions, one more than what is necessary but more economically plausible,
which is allowed for by the estimation algorithm. Ten of these restriction are
in the C(1) matrix and one in the C0 matrix.
3. Writing out the zero-solution equations from (16) explicitly, we start out with
ten equations (restrictions) in 19 unknowns involving the estimates of A(1).
In this system, we thus have ten restricted and nine free parameters. By
24
For a theoretical overview of the VAR, representations and identification issues see Hamilton
(1994).
A. Appendix
33
extensive repeated substitution, we end up with a system of linear constraints
where the 25 parameters of C0 (with 24 non-zero) can all be written as linear
combinations of the estimated parameters in A(1) and the 14 free parameters.
The validity of the restrictions imposed is checked by using the identity in
(16).
4. The restrictions are then provided to the SVAR.prg procedure that estimates
C0 by maximum likelihood.
A.5
Alternative specifications
Short-run identification scheme
Using the standard short-run identification scheme (Sims (1980)) is not as theoretically convincing, since the shocks are directly associated by the variables in the
system and identified through the sequence of admissible contemporaneous effects.
In the impulse responses, we find some irregularities in which we have a difficult time
believing, violating the long-run neutrality assumption inferred above and letting
the small economy affect the world at all horizons. Nevertheless, it turns out that the
results concerning the qualitative responses of the exchange rate remain the same,
but the results tend to be more accentuated and more often statistically significant
in our preferred model. The variance decompositions show the same pattern of most
variation at all horizons due to the last shock25 , but this contribution decreases over
time. A more pronounced role of the third and fourth shock is now given relative
to the first and second, but since this identification scheme is non-structural, it is
difficult to compare the two in terms of demand and supply shocks as previously.
Long-run identification scheme
Using the standard recursive long-run identification scheme originally proposed by
Blanchard and Quah (1989), we get the same qualitative results as in our preferred
model. The imposition of a long-run zero response of the domestic price level to
the fifth shock makes the real exchange rate appreciate by definition, which is an
undesirable property. The variance decompositions virtually remain unchanged.
25
The shock is now defined as the one not having any contemporaneous effect on any of the
other variables, only on the exchange rate itself.
34
Essay 1. Exchange rates and asymmetric shocks in small open economies
A.6
Impulse response figures
The full impulse response output is presented below in Figures A.1-A.5. The accumulated effect of a one standard deviation structural shock are traced out country
by country. The dotted lines are 95 percent confidence intervals based on the asymptotic standard errors. The most interesting figures, the response of the exchange
rate to asymmetric demand and supply shocks are shaded in grey.
.010
.010
.010
.010
.008
.008
.008
.008
.004
.004
.004
.004
.004
.002
.002
.002
.002
.002
-.002
-.002
-.002
-.002
-.002
-.004
-.004
-.004
-.004
-.004
2
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
20
.012
.012
.012
.012
.012
.008
.008
.008
.008
.008
.004
.004
.004
.004
.004
.000
.000
.000
.000
.000
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
4
6
8
10
12
14
16
18
4
6
8
10
12
14
16
18
20
.0020
.0020
.0020
.0020
.0016
.0016
.0016
.0016
.0008
.0008
.0008
.0008
.0008
.0004
.0004
.0004
.0004
.0004
-.0004
-.0004
-.0004
-.0004
-.0004
-.0008
-.0008
-.0008
-.0008
-.0008
2
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
2
20
10
12
1 4 16
18
20
2
4
6
8
10
12
1 4 16
18
20
2
4
6
8
10
12
1 4 16
18
20
2
4
6
8
10
12
1 4 16
18
20
2
4
6
8
10
12
1 4 16
18
20
.0000
.0000
.0000
.0000
.0000
8
.0012
.0012
.0012
.0012
6
.0024
.0024
.0020
.0016
.0012
4
-.004
2
20
.0024
.0024
.0024
2
20
2
-.008
-.008
-.008
-.008
2
-.004
-.004
-.004
-.004
-.008
p*
.000
.000
.000
.000
.000
y
.006
.006
.006
.006
.006
y*
epsilon_e*
epsilon_d
epsilon_d*
epsilon_s
epsilon_s*
.010
.008
4
6
8
10
12
14
16
18
20
.008
.008
.008
.008
.008
.004
.004
.004
.004
.004
p
.000
.000
.000
.000
.000
-.004
-.004
-.004
-.004
-.004
2
e*
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
2
20
-.008
-.008
-.008
-.008
-.008
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
20
.03
.03
.03
.03
.03
.02
.02
.02
.02
.02
.01
.01
.01
.01
.01
.00
.00
.00
.00
.00
4
6
8
10
12
14
16
18
20
2
4
6
8
10
12
14
16
18
20
-.01
-.02
-.02
-.02
-.02
2
-.01
-.01
-.01
-.01
-.02
2
4
6
8
10
12
14
16
18
20
2
4
6
8
10
12
14
16
18
20
Figure A.1: Sweden: Accumulated responses to one standard deviation structural
shocks
A. Appendix
35
y*
.004
.004
.004
.004
.004
.000
.000
.000
.000
.000
2
4
6
8
10
12
14
16
18
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
-.004
2
20
4
6
8
10
12
14
16
18
20
.016
.016
.016
.016
.016
.012
.012
.012
.012
.012
.008
.008
.008
.008
.008
.004
.004
.004
.004
.004
-.004
-.004
-.004
-.004
-.004
-.008
-.008
-.008
-.008
-.008
2
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
20
.004
.004
.004
.004
.004
.003
.003
.003
.003
.003
.001
.001
.001
.001
.001
.000
.000
.000
.000
.000
-.002
-.002
-.002
-.002
-.002
-.003
-.003
-.003
-.003
-.003
2
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
2
20
8
10
12
14
16
18
20
2
4
6
8
10
12
14
16
18
20
2
4
6
8
10
12
14
16
18
20
2
4
6
8
10
12
14
16
18
20
2
4
6
8
10
12
14
16
18
20
-.001
-.001
-.001
-.001
-.001
6
.002
.002
.002
.002
.002
4
.005
.005
.005
.005
.005
2
20
2
.000
.000
.000
.000
.000
p*
2
20
-.004
-.004
-.004
-.004
y
.008
.008
.008
.008
epsilon_e*
epsilon_d
epsilon_d*
epsilon_s
epsilon_s*
.008
4
6
8
10
12
14
16
18
20
.006
.006
.006
.006
.006
.004
.004
.004
.004
.004
.002
.002
.002
.002
.002
.000
.000
.000
.000
.000
p
4
6
8
10
12
14
16
18
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
-.002
-.004
2
20
4
6
8
10
12
14
16
18
20
.04
.04
.04
.04
.04
e*
2
20
-.004
-.004
-.004
2
-.002
-.002
-.002
-.002
-.004
.03
.03
.03
.03
.03
.02
.02
.02
.02
.02
.01
.01
.01
.01
.01
.00
.00
.00
.00
.00
-.01
-.01
-.01
-.01
-.01
4
6
8
10
12
14
16
18
20
2
4
6
8
10
12
14
16
18
20
-.02
-.03
-.03
-.03
-.03
2
-.02
-.02
-.02
-.02
-.03
2
4
6
8
10
12
14
16
18
20
2
4
6
8
10
12
14
16
18
20
Figure A.2: Canada: Accumulated responses to one standard deviation structural
shocks
36
Essay 1. Exchange rates and asymmetric shocks in small open economies
y*
.008
.008
.008
.008
.006
.006
.006
.006
.004
.004
.004
.004
.004
.002
.002
.002
.002
.002
-.002
-.002
-.002
-.002
-.002
-.004
-.004
-.004
-.004
-.004
2
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
20
.008
.008
.008
.008
.008
.006
.006
.006
.006
.006
.002
.002
.002
.002
.002
.000
.000
.000
.000
.000
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
4
6
8
10
12
14
16
18
20
.003
.003
.003
.003
.003
.002
.002
.002
.002
.002
.001
.001
.001
.001
.001
.000
.000
.000
.000
.000
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
4
6
8
10
12
14
16
18
4
6
8
10
12
14
16
18
20
.008
.008
.008
.008
.004
.004
.004
.004
16
18
20
2
4
6
8
10
12
14
16
18
20
2
4
6
8
10
12
14
16
18
20
2
4
6
8
10
12
14
16
18
20
2
4
6
8
10
12
14
16
18
20
.000
.000
.000
.000
14
.012
.012
.008
.004
.000
12
-.001
2
20
.012
.012
.012
2
20
10
-.002
-.002
-.002
-.002
2
-.001
-.001
-.001
-.001
-.002
8
-.002
2
20
6
-.004
-.004
-.004
-.004
2
-.002
-.002
-.002
-.002
-.004
4
.004
.004
.004
.004
.004
2
.010
.010
.010
.010
.010
p*
.000
.000
.000
.000
.000
y
epsilon_e*
epsilon_d
epsilon_d*
epsilon_s
epsilon_s*
.008
.006
p
-.004
-.004
-.004
-.004
-.004
-.008
-.008
-.008
-.008
-.008
e*
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
2
20
-.012
-.016
-.016
-.016
-.016
2
-.012
-.012
-.012
-.012
-.016
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
20
.06
.06
.06
.06
.06
.04
.04
.04
.04
.04
.02
.02
.02
.02
.02
.00
.00
.00
.00
.00
4
6
8
10
12
14
16
18
20
2
4
6
8
10
12
14
16
18
20
-.02
-.04
-.04
-.04
-.04
2
-.02
-.02
-.02
-.02
-.04
2
4
6
8
10
12
14
16
18
20
2
4
6
8
10
12
14
16
18
20
Figure A.3: Australia: Accumulated responses to one standard deviation structural shocks
A. Appendix
37
y*
.008
.008
.008
.008
.006
.006
.006
.006
.004
.004
.004
.004
.004
.002
.002
.002
.002
.002
-.002
-.002
-.002
-.002
-.002
-.004
-.004
-.004
-.004
-.004
2
4
6
8
10
12
14
16
18
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
4
6
8
10
12
14
16
18
20
.012
.012
.012
.012
.008
.008
.008
.008
.004
.004
.004
.004
.004
.000
.000
.000
.000
.000
4
6
8
10
12
14
16
18
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
4
6
8
10
12
14
16
18
20
.004
.004
.004
.004
.004
.003
.003
.003
.003
.003
.001
.001
.001
.001
.001
.000
.000
.000
.000
.000
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
4
6
8
10
12
14
16
18
20
.008
.008
.008
.008
.008
.006
.006
.006
.006
.006
.002
.002
.002
.002
.002
.000
.000
.000
.000
.000
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
4
6
8
10
12
14
16
18
4
6
8
10
12
14
16
18
20
.04
.04
.04
.04
.03
.03
.03
.03
.01
.01
.01
.01
.01
.00
.00
.00
.00
.00
4
6
8
10
12
14
16
18
20
4
6
8
10
12
14
16
18
20
2
4
6
8
10
12
14
16
18
20
6
8
10
12
14
16
18
20
2
4
6
8
10
12
14
16
18
20
2
4
6
8
10
12
14
16
18
20
2
4
6
8
10
12
14
16
18
20
-.01
-.03
-.03
-.03
2
4
-.02
-.02
-.02
-.02
-.03
2
-.01
-.01
-.01
-.01
-.02
-.03
2
.02
.02
.02
.02
20
.05
.05
.04
.03
.02
18
-.002
2
20
.05
.05
.05
2
20
16
-.004
-.004
-.004
-.004
2
-.002
-.002
-.002
-.002
-.004
14
.004
.004
.004
.004
.004
12
-.001
2
20
10
-.002
-.002
-.002
-.002
2
-.001
-.001
-.001
-.001
-.002
8
.002
.002
.002
.002
.002
6
-.004
2
20
4
-.008
-.008
-.008
2
20
-.004
-.004
-.004
-.008
2
2
.016
.016
.016
.016
2
20
.012
-.004
e*
4
.008
-.008
p
2
20
.016
p*
.000
.000
.000
.000
.000
y
epsilon_e*
epsilon_d
epsilon_d*
epsilon_s
epsilon_s*
.008
.006
2
4
6
8
10
12
14
16
18
20
Figure A.4: New Zealand: Accumulated responses to one standard deviation structural shocks
38
Essay 1. Exchange rates and asymmetric shocks in small open economies
y*
.008
.008
.008
.008
.008
.004
.004
.004
.004
.004
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
4
6
8
10
12
14
16
18
.000
2
20
4
6
8
10
12
14
16
18
20
.006
.006
.006
.006
.006
.004
.004
.004
.004
.004
.002
.002
.002
.002
.002
.000
.000
.000
.000
.000
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
4
6
8
10
12
14
16
18
4
6
8
10
12
14
16
18
20
.003
.003
.003
.003
.002
.002
.002
.002
10
12
14
16
18
20
2
4
6
8
10
12
14
16
18
20
2
4
6
8
10
12
14
16
18
20
2
4
6
8
10
12
14
16
18
20
2
4
6
8
10
12
14
16
18
20
.001
.001
.001
.001
8
.004
.004
.003
.002
.001
6
-.002
2
20
.004
.004
.004
2
20
4
-.004
-.004
-.004
-.004
2
-.002
-.002
-.002
-.002
-.004
2
.008
.008
.008
.008
.008
2
20
-.004
-.004
-.004
-.004
2
.000
.000
.000
.000
-.004
y
.012
.012
.012
.012
epsilon_e*
epsilon_d
epsilon_d*
epsilon_s
epsilon_s*
.012
p*
.000
.000
.000
.000
.000
-.001
-.001
-.001
-.001
-.001
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
2
20
-.002
-.003
-.003
-.003
-.003
2
-.002
-.002
-.002
-.002
-.003
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
20
.004
.004
.004
.004
.004
.002
.002
.002
.002
.002
p
.000
.000
.000
.000
.000
-.002
-.002
-.002
-.002
-.002
2
4
6
8
10
12
14
16
18
4
6
8
10
12
14
16
18
2
20
4
6
8
10
12
14
16
18
-.004
2
20
4
6
8
10
12
14
16
18
20
.06
.06
.06
.06
.06
e*
2
20
-.004
-.004
-.004
-.004
.04
.04
.04
.04
.04
.02
.02
.02
.02
.02
.00
.00
.00
.00
.00
-.02
-.02
-.02
-.02
-.02
4
6
8
10
12
14
16
18
20
2
4
6
8
10
12
14
16
18
20
-.04
-.06
-.06
-.06
-.06
2
-.04
-.04
-.04
-.04
-.06
2
4
6
8
10
12
14
16
18
20
2
4
6
8
10
12
14
16
18
20
Figure A.5: United Kingdom: Accumulated responses to one standard deviation
structural shocks
Essay
2
Macroeconomic imbalances and exchange
rate regime shifts
1
Introduction
According to the de facto classification in IMF (2003), the share of countries with
pegged exchange rates decreased from about 80 to about 60 percent between 1990
and 1998. What explains exits from a fixed to a flexible exchange rate regime?1 The
literature explains this in two ways:
(i) Economic fundamentals or speculators drive the authorities towards a point
of no return where the only option is to let the currency float.
(ii) Parity is at an unacceptable level for the decision makers which triggers an
optimizing decision to exit from the fixed exchange rate regime.
The first explanation involves what is called "first generation" and "second generation" models of currency crises. In the "first generation" model by Krugman (1979),
it is the macroeconomic fundamentals themselves that create the breakdown of the
fixed exchange rate regime. The breakdown is inevitable since an exogenous government deficit is financed by borrowing from the central bank. Since the nominal
exchange rate is fixed and purchasing power parity holds, the depreciation pressure
on domestic currency is offset by the central bank buying domestic currency with
international reserves. With limited reserves, there will be a time when speculators realize that the fixed exchange rate regime cannot be sustained and then the
currency inevitably depreciates. This model of currency crises appeared to be appropriate for the Latin-American countries experiencing sharp currency depreciations
1
The "fixed" arrangement comes in many flavors: peg to a single currency (such as the USD),
peg to a basket of currencies (which was the case in the ERM) or a currency union such as the
EMU.
39
40
Essay 2. Macroeconomic imbalances and exchange rate regime shifts
following a fixed exchange rate regime in the 1970’s and 1980’s.
For the countries involved in the ERM-crisis in the early 1990’s, there seemed to
be less of a problem of poor fundamentals and more of a problem of inconsistencies
in policy making that lead to more or less "self-fulfilling" currency crises. Obstfeld
(1986) stresses the importance of expectations in the collapse of a fixed exchange
rate regime and investigates the possibility of multiple equilibria. This model has
been called "second generation" as it stresses the importance of the expectations
channel for depreciations and fixed exchange rate regime collapses.
However, there is a considerable similarity in that both the Krugman and the
Obstfeld models treat the occurrence of the exchange rate regime collapse as more or
less inevitable and something that the policy maker only passively observes without
taking a stand on what is preferable and what actions would be necessary to defend
the fixed exchange rate regime. But as argued by Obstfeld and Rogoff (1995), a
country is always able to resist a speculative attack if it is truly committed. It
can do so by buying back the entire monetary base and driving up interest rates.
Therefore, the policy maker always has the option of not exiting the fixed exchange
rate regime; it is only a matter of the willingness of the policy maker to bear the
costs of staying.2
The second explanation of fixed regime exits instead emphasizes the optimizing
decision of the policy maker. Edwards (1996), Bensaid and Jeanne (1997), Ozkan
and Sutherland (1998), Bénassy-Quéré and Coeuré (2002) and Rebelo and Vegh
(2006) present stylized models within this category.3 These studies all have in common that they view the choice of exchange rate regime as an optimizing decision
involving economic and political elements. Bensaid and Jeanne (1997) and Ozkan
and Sutherland (1998) consider an optimizing policy maker who may voluntarily
choose to exit from a fixed exchange rate regime. In these models, it is concerns
about macroeconomic stability that may make the policy maker exit from the fixed
exchange rate regime. Obstfeld (1996) and others argue that this type of model appears to offer a more accurate portrayal of the ERM-crisis and aspects of other crises
such as that in Mexico 1994-95. Although it is an oversimplification that countries
which exit from a fixed exchange rate regime do so only for stabilization purposes,
stabilization motives will most certainly be important. For example, high unemployment could be costly for the incumbent government and trigger the decision to
exit from the fixed exchange rate regime to get a temporarily higher output level
2
As expressed at a seminar: "If someone comes up to you and asks for your money, there is
always the option not to give up the money although doing so might involve a very high cost..."
3
These studies are in turn partly based on Barro and Gordon (1983).
1. Introduction
41
under a flexible exchange rate regime.4 In Rebelo and Vegh (2006), it is shown that
the mechanical rule of the Krugman-type of model, i.e. to leave the fixed exchange
rate regime when international reserves are depleted, is at odds with many historical
episodes. Instead, it is argued that a country will choose to leave a fixed exchange
rate regime because of large expected increases in government spending.
In the empirical literature, there seems to be some disagreement with regards
to why countries choose to exit from a fixed exchange rate regime. Eichengreen,
Rose, and Wyplosz (1995) and Duttagupta and Otker-Robe (2003) find little evidence of systematic correlations between macroeconomic fundamentals and exits.
Detragiache, Mody, and Okada (2005) find that episodes of exits are characterized
by similar circumstances: an overvalued real exchange rate, falling reserves, and
high world interest rates. However, the empirical studies usually do not offer any
rigorous justification of the choice of variables that enter the regressions. This paper
is intended to give some guidance as to what variables should predict exchange rate
regime exits and therefore also be the focus of future empirical work.
Following the optimizing approach in the second strand of the literature described
above, the purpose of this paper is to use a dynamic stochastic equilibrium model for
a small open economy to examine what variables should endogenously predict exits
from a fixed to a flexible exchange rate regime if the policy maker is concerned with
stabilization of output and inflation. Simulation of the model is done in DYNARE
(see Collard and Juillard (2005)) and simulated data is further studied by graphical
analysis to investigate the links between the endogenous probability of exit and
observable fundamentals.
The results indicate that consumption, the current account, interest rates and
domestic prices are related to the probability of exits from a fixed exchange rate
regime. The relative importance of factors is dependent on the relative importance
of cost-push and preference shocks. If cost-push shocks are relatively important,
low consumption, a negative current account, high interest rates, and high domestic
prices all increase the probability of an exit with an accompanying depreciation of
the domestic currency.
The paper is organized as follows. Section 2 presents the model and section 3
considers alternative exchange rate regimes. In section 4, parameters are calibrated,
section 5 presents the numerical results and section 6 presents some sensitivity analyses. Section 7 concludes.
4
In Bergvall (2002, 2005), the author shows by counterfactual simulations that a flexible exchange rate regime is more apt at stabilizing fluctuations in output and prices. This result also
comes out endogenously in my model.
42
2
Essay 2. Macroeconomic imbalances and exchange rate regime shifts
Model
The model presented below is a dynamic stochastic rational expectations model of
a small open economy intended to capture the dynamics of exchange rate regime
exits from a fixed to a flexible exchange rate regime. The model is stripped down
to the bare minimum. The representative agent in the economy only cares about
consumption; production is constant returns to scale and entirely demand driven;
there is no capital and the government minimizes a discounted loss of deviations
from steady state output and inflation. The government cannot levy taxes nor
make transfers. No stabilization policy is available when staying in a fixed exchange
rate regime, since monetary policy is restrained by the defense of the currency peg.
In the alternative flexible exchange rate regime, monetary policy is carried out by
changes in the interest rate. The world is in continuous steady state with constant
prices and interest rates. There are two exogenous shocks that create deviations
from the steady state; one is a cost-push shock, the other is a preference shock. The
latter can be interpreted as a pure domestic demand shock. The model, however
stylized, puts the optimizing decision of the policy maker within a more realistic
setting than previous studies of the issue. The dynamic stochastic setting gives us
the ability to evaluate the relative importance of different factors for the probability
of exit that emerges endogenously from the model.
The policy maker makes a discrete choice between staying in a fixed exchange rate
regime, at some economic cost in terms of excessive misalignments of fundamentals,
and leaving the fixed exchange rate regime. Either the policy maker chooses to stay
in the fixed exchange rate regime, retaining the option of leaving the arrangement
in the future, or exits to a flexible exchange rate regime today with monetary policy
carried out by an independent and perfectly credible monetary authority.5 Once the
economy has left the fixed exchange rate regime, it cannot revert to the fixed regime.
Opting out involves some loss of benefits from leaving the fixed exchange rate regime.
This loss of benefits may involve the inability to participate in a fixed exchange rate
system which in itself could be an objective due to national pride or commitment
to international cooperation. Moreover, it may include negative effects on trade
because of an increase in the short-term volatilities of the exchange rate. The
policy maker will choose to exit if the perceived benefit in terms of macroeconomic
stability outweighs the benefits in the fixed exchange rate environment. The benefit
of increased stabilization will be a function of the variables and shocks hitting the
5
This assumption is important in that the policy maker in the fixed exchange rate arrangement
might use monetary policy for political reasons, whereas monetary policy in the floating regime is
solely for the purpose of macroeconomic stability.
2. Model
43
economy in each period. Purchasing power parity does not hold continuously, not
even for tradable goods. Sticky prices will imply that following a negative demand
shock, domestic prices will decrease, which depreciates the real exchange rate, but
not enough to offset the demand shock. With the nominal exchange rate fixed, the
gross domestic product will decrease in the short run.
Agents will realize that leaving the fixed exchange rate regime is always an option
for the policy maker and will require a compensation for holding domestic currency
depending on the perceived probability of an exit from the peg. This premium will
drive a wedge between interest rates in the small open economy and the world, even
in the fixed exchange rate regime.6 By treating the exit probability as an endogenous
variable, we can study how competitiveness, international indebtedness and the
current account and domestic interest rates affect the probability of a country exiting
from the fixed exchange rate regime. The model is symmetric in that it treats the
probabilities of de- and appreciations analogously. The calibration of parameters in
the model is partly based on micro studies and partly done to make the model fit
some stylized facts.
2.1
Demand side
The utility, Ut , for the representative consumer is given by a utility function with
constant relative risk aversion and consumption, Ct , as the only argument,
1
C 1−θ .
(1)
1−θ t
Consumption is a geometric average of home goods consumption,Ch,t , and foreign
goods consumption, Cf,t ,
γ
Cf,t 1−γ .
(2)
Ct = Ch,t
Ut =
Assuming that the small economy representative agent can only invest in domestically denominated assets, Bth , the intertemporal budget constraint becomes
¡ h
¢
Bth
= Bt−1
+ Ph,t Yt − Pc,t Ct .
h
1 + it
(3)
The representative agent enters period t with the home currency denominated assets,
h
, gross of interest rate. The agents work in and own all domestic firms so that
Bt−1
the representative agent gets income Ph,t Yt , where Ph,t is the price of domestically
produced goods and Yt is gross domestic production. Part of the nominal income is
6
Agents are risk neutral in investment so the premium only compensates investors for expected
depreciation of the currency.
44
Essay 2. Macroeconomic imbalances and exchange rate regime shifts
consumed, Pc,t Ct , where Pc,t is the consumer price index. What is not consumed is
then carried over to the next period with interest.
Optimization on the part of the consumer with respect to Ct and Bth with a time
varying discount factor, β t ,
max Et
Ct ,Bth
∞
X
t=τ
β ττ
∙
∙ h
¸¸
Bτ
h
Uτ − λτ
− Bτ −1 − Ph,τ Yτ + Pc,τ Cτ ,
1 + idτ
(4)
yields the following conditions:
Ct−θ = λt Pc,t
(5)
λt
= β t Et (λt+1 ) .
1 + iht
(6)
and
Combining (5) and (6) yields the Euler equation,
Ct−θ
= β t (1 + iht )Et
Pc,t
µ
−θ
Ct+1
Pc,t+1
¶
(7)
,
which determines the intertemporal allocation of consumption. The discount factor,
β t , evolves according to
(8)
β t = β̄ + et ,
where et is a persistent preference shock. A sudden decrease in the discount factor
makes consumers value future consumption lower, and makes consumption increase
today.
Assuming the equivalent utility function and budget constraint for the representative world consumer, but allowing foreign consumers to invest in both small
open economy denominated assets and foreign assets, we can derive the uncovered
interest-rate parity condition,
(1 + iht ) = (1 + ift )Et
µ
St+1
St
¶
(9)
,
where St is defined as the domestic currency needed to buy one unit of foreign
currency.7 A default risk premium, φt , is appended to the uncovered interest parity
condition so that we get
(1 + iht ) = (1 + ift )φt Et
7
µ
St+1
St
¶
.
For a derivation of the standard UIP condition, see the Appendix.
(10)
2. Model
45
The default risk premium takes the functional form
¡
¢
φt = exp −ψBth .
(11)
The risk premium captures the default risk as perceived by investors with the domestic interest rate being higher than the world interest rate, if the economy is a
net borrower, i.e. Bth < 0.8
The Cobb-Douglas utility function also implies constant expenditure shares on
home and foreign goods,9
Ph,t Ch,t = γPc,t Ct ,
(12)
St Pf,t Cf,t = (1 − γ)Pc,t Ct .
(13)
and
By substitution of (12) and (13) back into (2), we get the relevant consumer price
index (CPI),
1 γ
Pc,t =
P (St Pf,t )1−γ ,
(14)
γ w h,t
where γ w = γ γ (1 − γ)1−γ . The export function is derived by making analogous
assumptions about the world economy:10
EXt = χQ−η
t ,
(15)
Ph,t
.
St Pf,t
(16)
where
Qt =
EXt is exports and Qt is a measure of the competitiveness of domestically produced
goods in the international market. An increase of Qt indicates that the relative
price of domestic goods increases, i.e. domestic goods become uncompetitive on the
international market.
In the following, we set foreign prices and interest rates constant and only focus
on domestic variables with Pf,t = Pf = 1 and ift = if .
8
See Benigno (2001) for a version of this risk adjusted formulation. Allowing for the premium
is needed for a well defined steady state of the model, but the premium can be made arbitrarily
small.
9
Constant expenditure shares become obvious if optimizing the object function in (4) with
respect to Ch,t and Cf,t .
10
For derivation of the export function, see the Appendix.
46
Essay 2. Macroeconomic imbalances and exchange rate regime shifts
2.2
Supply side
Output is entirely demand driven but also subject to the effects of a cost-push
shock. Market clearing in the goods market implies that production is equal to the
consumption of domestic goods plus exports,
Yt = Ch,t + EXt .
(17)
Inflation is assumed to follow a purely forward-looking Phillips curve (e.g. Clarida, Gali, and Gertler (1999)), to which a transitory cost-push shock, u, is appended:
π t = λ (Yt − Yn ) + β̄Et (π t+1 ) + ut .
(18)
λ captures the effect of excess demand pressure on inflation and β̄ is the discount
factor. The logic of equation (18) is that as output increases, firms will raise prices
and overall inflation will increase.
2.3
Summary of the model
Combining key equations and assuming that preference shocks are autoregressive of
order one, we get
¸
Pc,t −θ
Ct+1 ,
Pc,t+1
h
(1 + it ) (Bt−1 + Ph,t Yt − Pc,t Ct ) ,
µ
¶
St+1
,
(1 + if )φt Et
St
γPc,t Ct
+ χQ−η
t ,
Ph,t
λ(Yt − Yn ) + β̄Et π t+1 + u,
Ct−θ = β t (1 + iht )Et
Bt =
1+
iht
=
Yt =
πt =
∙
(19)
(20)
(21)
(22)
(23)
β t = β̄ + et ,
(24)
et = ρe et−1 + vt ,
(25)
and
ut ∼ i.i.d.N (0, σ 2u ), vt ∼ i.i.d.N (0, σ 2v ).
P
(26)
γ
c,t
Qt = Sh,t
, Pc,t = γ1 Ph,t
St1−γ and inflation is given by π t = PPc,t−1
− 1. Equation (19)
t
w
is the Euler equation, (20) the equation governing the evolution of assets and (21)
the uncovered interest-rate parity condition. Equation (22) is the aggregate demand
relation, (23) is the Phillips curve and (24) the time variant discount factor. (25) is
3. Alternative exchange rate regimes
47
the persistent preference shock that governs the discount factor and (26) describes
the pure shocks. This system cannot be solved without further assumptions since
there are ten equations and eleven variables, (C, ih , Pc , B, Ph , S, Y, Q, π, β, e).
3
Alternative exchange rate regimes
So far a model has been presented without taking a stand on how monetary policy
is conducted. In this section, I first present two possible solutions to the model; one
with a perfectly credible fixed exchange rate where monetary policy has the sole
purpose of upholding the value of the domestic currency and one with a flexible
exchange rate where monetary policy is used for stabilization purposes. Then, in
section 3.3, I study a fixed exchange rate regime that is non-credible.
3.1
A credibly fixed exchange rate
Assuming that the fixed exchange rate regime is perfectly credible, we have
St = St+1 = 1,
(27)
1 + iht = (1 + if )φt .
(28)
and equation (21) becomes
The steady state solution can then be solved as11
1
, B = 0, Ph = 1, S = 1, Y = 1, Q = 1, π = 0, β = β̄ and e = 0.
γw
(29)
Under the credibly fixed exchange rate regime, the interest rate is fully tied down
by maintenance of the fixed exchange rate regime and cannot help stabilizing fluctuations. For example, if the economy is hit by a sudden preference shock, vt , the
domestic interest rate cannot be increased to offset output deviations and inflation. Instead, it must stay equal to the world interest rate (abstracting from the
risk-premium) and there will be an economic downturn.
At each point in time, we can compute an expected discounted loss in the credibly
C = γ w , ih = if , Pc =
11
Guess e = 0, B = 0, Ph = 1 and proceed. Obtain ih = if from the UIP, Y = Yn from the PC
and C = γ w from the asset equation. The steady state solution also yields that 1 + if = β1 from
the Euler and that χ = 1 − γ.
48
Essay 2. Macroeconomic imbalances and exchange rate regime shifts
fixed regime, Lft ix , in terms of economic destabilization
Lcred
= π2t + λL (Yt − Yn )2 + β L Et Lcred
t
t+1 .
(30)
λL denotes the relative weight put on the stabilization of output and β L is the
discount factor of the policy maker. The loss is quadratic in inflation and output
deviations from natural output. The modelling of the loss belongs to a class of loss
functions commonly used in the monetary policy literature; see Walsh (2003) p. 366.
3.2
A flexible exchange rate and stabilization
Now, allow for a flexible exchange rate, so that S is endogenous. First, take the
exceptional case of perfect stabilization of both inflation (and prices) and output:
Pc,t = Pc,t−1 ,
(31)
π t = 0,
(32)
Yt = Yn = 1.
(33)
Bt = (1 + iht ) (Bt−1 + Ph,t Yn − Pc,t Ct ) ,
(34)
and
Equation (20) becomes
and equation (22) becomes
Yt =
γPc,t Ct
+ χQ−η
t = Yn .
Ph,t
(35)
The Phillips curve is replaced by equation (31). Yt is replaced by Yn in the asset
equation to yield equation (34) and equation (35) denotes perfect stabilization of
output. The steady state solution is identical to the fixed exchange rate regime
augmented with the nominal exchange rate being unity and prices and output unity
by assumption. Because of the assumption of perfect stabilization, the loss will be
equal to zero at all times and, by definition, there will be a positive exit probability
in each period.
Obviously, the assumption of perfect stabilization of output and inflation is an
oversimplification. For the sake of realism I assume that, under the flexible exchange
3. Alternative exchange rate regimes
49
rate regime, monetary policy is determined by a standard Taylor (1993) rule,
iht = if + 0.5(Y − Yn ) + 1.5πt,
(36)
so that in steady state, the interest rate will be constant and equal to the foreign
interest rate but increase when inflation and output are above steady state. The
steady state of the model will be left unchanged as compared to the case of a
credible fixed regime.12 Relaxing the assumption of perfect stabilization makes
the economy go through periods of high and low inflation and output. Although
there is superior stabilization relative to the fixed exchange rate environment, some
fluctuations of output and inflation occur and the policy maker observes a loss
equivalent to equation (30):
lex
.
Lft lex = π2t + λL (Yt − Yn )2 + β L Et Lft+1
(37)
Appending the Taylor rule equation to the generic model in equations (19)(26), we are able to solve the model numerically without further assumptions.
We then obtain closed form solutions for the endogenous variables as functions
of deviations around steady state in the state variables Pc,t−1 , Bt−1 ,et−1 and in
the contemporaneous shocks, ut and vt . The solutions are Taylor approximations
of the
³ first order where the´vector of deviations from steady state is denoted by
h = hB he hP hu hv .
We get the solution, calibrated with parameter values presented below, for the
exchange rate:
(38)
St = f (a + h) = F (a) + DFa h
∂F
∂F
∂F
∂F
∂F
= F (a) +
(a)hB +
(a)he +
(a)hP +
(a)hu +
(a)hv
∂Bt−1
∂et−1
∂Pc,t−1
∂ut
∂vt
= 1 − 0.13hB + 1.19he + γ w hP + 0.05hu − 1.32hv ,
for consumption:
Ct = g(a + h) = G(a) + DGa h
(39)
∂G
∂G
∂G
∂G
∂G
= G(a) +
(a)hB +
(a)he +
(a)hP +
(a)hu +
(a)hv
∂Bt−1
∂et−1
∂Pc,t−1
∂ut
∂vt
= γ w + 0.06hB − 1.07he + 0hP − 0.22hu + 1.19hv ,
12
Guess e = 0, B = 0, Ph = 1, S = 1 and proceed.
50
Essay 2. Macroeconomic imbalances and exchange rate regime shifts
for inflation:
π t = h(a + h) = H(a) + DHa h
(40)
∂H
∂H
∂H
∂H
∂H
(a)hB +
(a)he +
(a)hP +
(a)hu +
(a)hv
= H(a) +
∂Bt−1
∂et−1
∂Pc,t−1
∂ut
∂vt
= 0 − 0.005hB − 0.14he + 0hP + 0.98hu + 0.16hv ,
for consumer prices:
(41)
Pc,t = k(a + h) = K(a) + DKa h
∂K
∂K
∂K
∂K
∂K
(a)hB +
(a)he +
(a)hP +
(a)hu +
(a)hv
= K(a) +
∂Bt−1
∂et−1
∂Pc,t−1
∂ut
∂vt
1
=
− 0.008hB − 0.25he + 1hP + 1.71hu + 0.28hv ,
γw
and for output:
yt = j(a + h) = J(a) + DJa h
(42)
∂J
∂J
∂J
∂J
∂J
= J(a) +
(a)hB +
(a)he +
(a)hP +
(a)hu +
(a)hv
∂Bt−1
∂et−1
∂Pc,t−1
∂ut
∂vt
= 1 − 0.01hB − 0.41he + 0hP − 0.99hu + 0.45hv .
The exchange rate moves with the CPI-price level in the previous period to leave
the real exchange rate unaffected.13 With lower asset holdings, the exchange rate
depreciates to make domestic goods cheaper and restore asset equilibrium. The
preference shock makes the exchange rate appreciate to stabilize output and prices.
Under the current parameterization, the cost push shock makes the exchange rate
depreciate to stabilize output at the cost of some inflation.
Note that consumption, inflation and output all are unaffected by the past price
level and that inflation increases close to one-to-one to cost-push shocks whereas
output decreases by the same magnitude. The preference shock temporarily makes
all three variables increase whereas the cost-push shock increases inflation at the
expense of lower output and consumption. The dynamics of consumer prices follows
c,t
− 1.
that of inflation since π t = PPc,t−1
Note that we also can derive an expression for losses in the flexible regime, see
equation (37), as a function of inflation and output in the flexible regime. This will
be used in the solution of the full model below.
13
This becomes obvious if using the definition of the consumer price index combined with the
definition of the terms of trade, keeping the latter constant.
3. Alternative exchange rate regimes
3.3
51
A non-credible fixed exchange rate
Having considered the limiting cases of a credibly fixed exchange rate regime and
a fully flexible exchange rate regime, I now introduce an active policy maker that
makes optimizing decisions to stay in or exit from the fixed exchange rate regime in
each period. Figure 1 describes the timing of the model. At the beginning of each
period, the policy maker and the agents observe the preference and the cost-push
shocks. The policy maker alone observes a stochastic positive value of staying in the
fixed exchange rate regime as compared to being in a flexible regime and decides
whether to exit from or stay in the fixed exchange rate regime. Ex post, on the
basis of the policy maker’s decision, the agents know whether the realized stochastic
value of staying in the fixed exchange rate regime was below or above the loss of
staying in the fixed exchange rate. Prices are set and production occurs. Thereafter
the credit market opens, consumers observe the interest rate and make their saving
decisions. Provided that the economy remains in the fixed exchange rate regime, the
interest rate on loans in domestic currency from period t to period t + 1 will depend
on the probability of an exit at the beginning of period t + 1. This probability
depends on the expected loss in period t + 1. Moreover, the perceived probability of
exits affects inflation in the forward looking Phillips curve and consumption today
via the forward looking Taylor rule. Agents compute a probability that the policy
maker will exit from the regime in period t + 1 based on the assumed probability
distribution of the benefit of staying in the fixed exchange rate regime.
t-1
t
Shocks at t
observed
by all.
Policy shock
observed by
policy maker
alone.
Bt-1
Policy
maker
decides
on
regime
for
period
t.
Price
setting
occurs.
t+1
Shocks at
t+1observed
by all.
Output is
realized;
utility max
gives
consumption
, net assets
and the
interest rate
given
probability of
exit in t+1.
Policy shock
observed by
policy maker
alone.
Bt
Figure 1: Timing of the model
Policy
maker
decides
on
regime
for
period
t+1.
52
Essay 2. Macroeconomic imbalances and exchange rate regime shifts
The relative discounted loss, Lrt , of staying in the fixed exchange rate regime is
defined as
− Lft lex ,
(43)
Lrt = Lnon−cred
t
where Lcred
in equation (30) is modified to allow for the possibility of leaving the
t
fixed exchange rate regime in the next period so that
h
i
lex
non−cred
,
= π 2t + λL (Yt − Yn )2 + β L Et (1 − zt+1 ) Lt+1
+ zt+1 Lft+1
Lnon−cred
t
(44)
where zt+1 denotes the probability that the policy maker exits in t + 1 and Lf lex
is defined in equation (37). The additional loss of staying in a fixed exchange rate
environment, with the option to exit in the future, Lrt , is compared to the benefit of
staying. As previously described, countries with fixed nominal exchange rates experience some relative benefit of staying in the regime. In my model, such a relative
benefit is needed to make the model non-deterministic. If there were no benefits
from the fixed exchange rate regime, immediate exit would always be optimal. A
similar result is reported in Rebelo and Vegh (2006). Under the assumption by
the agents of the economy that the benefit is uniformly distributed over 0 − ε̄, the
perceived probability of the policy maker leaving the fixed environment is
zt = P (εt ≤ Lt ) =
Lrt
.
ε̄
(45)
Now, I merge the non-credible fixed exchange rate regime with the closed form
solutions for relevant variables under the alternative, flexible exchange rate regime.
These solutions are represented by equations (38)-(41). In the following, I will call
the flexible solution the "shadow" solution, since it can be seen as the shadow alternative at all points in time. Replicating the closed forms from above for those
entering in t + 1, equations (38)-(41), and denoting the shadow solution with subscript "s", we obtain
Ss,t = f (a + h),
(46)
Cs,t = g(a + h),
(47)
πs,t = h(a + h),
(48)
Pcs,t = k(a + h).
(49)
These solutions are appended to the general model in equations (19)-(26) when
variables are forward-looking. This is the case for the Euler equation, (19), where
future consumption and consumer prices enter, the uncovered interest rate parity
3. Alternative exchange rate regimes
53
equation, (21), where the future nominal exchange rate enters and the Phillips curve,
(23), where future inflation enters. Appending the shadow solutions to the generic
model, weighted by the expected probability of an exit in the next period, Et (zt+1 ),
yields
∙
¸
Pc,t −θ
Ct+1
Ct−θ = β t (1 + iht )Et (1 − zt+1 )
Pc,t+1
∙
¸
P
c,t
h
−θ
,
C
+β t (1 + it )Et zt+1
Pcs,t+1 s,t+1
Bt = (1 + iht ) (Bt−1 + Ph,t Yt − Pc,t Ct ) ,
∙
¸
Ss,t+1
,
1 + iht = Et (1 − zt+1 ) (1 + if )φt + zt+1 (1 + if )φt
1
γPc,t Ct
+ χQ−η
Yt =
t ,
Ph,t
πt = λ(Yt − Yn ) + β̄Et [(1 − zt+1 ) π t+1 + zt+1 π s,t+1 ] + u
et = ρe et−1 − vt ,
ut ∼
(51)
(52)
(53)
(54)
(55)
β t = β̄ + et ,
i.i.d.N (0, σ 2u ), vt
(50)
(56)
∼
i.i.d.N (0, σ 2v ).
(57)
The system constitutes 18 equations in 18 unknowns:
(C, Cs , ih , Pc , Pcs , B, Ph , Ss , Y, Q, π, π s , β, e, z, Lnon−cred , Lf lex , Lr ), where Lf lex and
Lnon−cred are given by equations (37) and (44) and the other equations are given
in (43)-(57) and in the definitions for Pc , Q and π. The steady state is solved for in
DYNARE and displayed in Table 1.
Table 1: Steady state values for key variables
Variable Steady state value
C
γw
ih
if
1
Pc
γw
B
0
Ph
1
Ss
1
Y
Yn
Q
1
π
0
β̄
β
e
0
54
Essay 2. Macroeconomic imbalances and exchange rate regime shifts
The steady state is identical to the solution in the credible and flexible cases
presented in (29). However, compared to the credible fixed exchange rate regime,
under the non-credible fixed exchange rate regime, the probability of an exit with accompanying de- or appreciation will make the fluctuations even more severe, ceteris
paribus, due to the rate of return compensation that must be offered to investors
when buying domestic currency. When a negative demand shock hits, the shadow
exchange rate depreciates and there is a positive probability that the policy maker
will exit from the fixed exchange rate regime. This will make investors require a
compensation of higher interest rates when investing in domestic bonds since they
expect a depreciation of a certain magnitude and probability in the next period.
This, in turn, makes the economic downturn more protracted.
4
Calibration
For a numerical evaluation of the model, we need to calibrate the parameters of the
model. I employ micro estimates for a representative small open economy to the
extent that it is possible and if not available, I calibrate the parameter in question
to fit some stylized fact. The time period is taken to be a quarter. The parameter
values presented in Table 2 are used to solve for the shadow variables’ closed form
solutions, presented above, as well as for the model of a fixed exchange rate regime.
Table 2: First set of calibration
Parameter Calibrated value
if
0.006
0.9940
β̄(if )
γ
0.75
γ w (γ)
0.5699
χ(γ)
0.25
η
1.5
θ
2.0
ρe
0.9
λ
0.025
ψ
0.02
σ 2u
0.0001
σ 2v
0.0001
if = 0.006 corresponds to a 2.4 percent annual interest rate and makes β̄ =
¢
¡
1/ 1 + if = 0.9940.
γ is the parameter governing the preferences over home and foreign goods. Under
Cobb-Douglas preferences over home and foreign goods, we know that the consumer
4. Calibration
55
will consume γ of its income on home goods and 1 − γ on foreign goods. I set
γ = 0.75 so that the share of domestic goods in the consumer price index is 75
percent. γ w is a function in γ defined in equation (14) and χ = 1 − γ, the level effect
of changes in the real exchange rate to exports, can be solved for in steady state as
shown in footnote 13.
η is the elasticity of exports with respect to changes in the relative price of
foreign goods (η > 0). η = 1.5 suggests that for a one percent depreciation in the
real exchange rate, exports are expected to increase by 1.5 percent.14
θ is the coefficient of relative risk aversion in the utility function with constant
relative risk aversion. In Mehra and Prescott (1985), various studies are cited and
estimates are reported between unity and two for macroeconomic applications. I set
θ = 2 to get quite risk averse consumers who would like to smooth consumption to
a large extent.
λ in the Phillips curve is the contemporaneous effect of the output gap on inflation which should be positive. Holmberg (2006) estimates both closed and open
economy versions of the Phillips curve and the estimates range from negative to
0.064, depending on model, estimation technique and proxy for demand pressure.
In this paper, I set λ = 0.025, which is in the upper part of the distribution of
estimates.
ψ is the premium that must be offered to investors when the net asset position
differs from zero. I assume that if the whole gross domestic income is borrowed, the
domestic interest rate should be about two percentage points higher, i.e. ψ = 0.02.15
ρe is the coefficient of persistence in the preference shocks I set to ρe = 0.9.
σ2u = 0.0001 reflects a standard deviation of the cost-push shock of 0.01, i.e. a
sudden one percent increase in home prices.
σ2v = 0.0001 reflects a standard deviation of the preference shock of 0.01, i.e.
a one percent deviation in the valuation of future consumption relative to current
consumption.
14
In Johansson (1998), the short-run relative price elasticity is estimated to 0.3 and the long-run
price elasticity to 1.3 for Sweden.
15
Benigno (2001) uses 0.01 and 0.001 as values for ψ.
56
Essay 2. Macroeconomic imbalances and exchange rate regime shifts
For the model of a non-credible fixed exchange rate regime, we need to impose
another set of calibrated parameters. These values are presented in Table 3.
Table 3: Second set of calibration
Parameter Calibrated value
λL
0.7
βL
0.9
ε̄
0.35
λL is the relative value that the policy maker attaches to output deviations. I set
λL = 0.7 so that the policy maker cares relatively more about inflation than about
output deviations.
β L reflects the decision making horizon of the policy maker. Setting β L = 0.9
makes the policy maker value losses in 16 periods (the usual time in office) to less
than 20 percent of today’s loss.
ε̄ is the highest value the stochastic benefit of staying in the fixed environment
can take. To get an unconditional probability of exit of ≈ 0.025, reflecting one
expected exit in every ten years, I set ε̄ = 0.35.
5
Numerical results
Using the calibrated parameter values, we can study the dynamics of the model.
First, I present the effect on variables from shocks by plotting their impulse response
functions. Second, I simulate the model over a number of periods and study the
relations between the probability of exit and other variables.
5.1
Impulse responses
The impulse response functions are presented in Figures 2-3. A cost-push shock
makes inflation increase temporarily with a persistent effect on home prices. Output
and consumption decrease with a jump and increase back to baseline. With an
increased probability of exits with depreciation, reflected in the shadow exchange
rate in the next period, the nominal interest rate increases to maintain interest
parity. This result closely resembles the argument in Ozkan and Sutherland (1998)
that expectations of a sudden depreciation can build up because of the government’s
interest in stabilizing the shock. With such expectations of exits with a depreciation
of the currency, risk-neutral investors will require a compensation in the form of
higher interest rates. The interest rate also increases because of the negative asset
5. Numerical results
57
position that builds up when output decreases. These high interest rates will then,
in turn, accentuate the business cycle downturn.
-4
10
x 10
z
ss
y
0.01
0.01
0
5
0.005
0
-5
-0.01
10
20
30
40
0
infl
0.01
2
0
1
-0.01
10
20
30
40
0
0.02
0
0
-2
10
20
20
-4
ih
x 10
30
40
-4
30
40
-0.02
10
20
30
40
30
40
30
40
ihs
0.01
0
10
-3
ph
-0.02
10
x 10
20
30
40
-0.01
10
c
20
b
0
-0.005
10
20
30
40
-0.01
10
20
Figure 2: Responses of key variables to cost-push shock
-3
4
x 10
z
ss
y
0.01
0.04
2
0
0.02
0
-0.01
0
-2
10
-3
2
x 10
20
30
40
infl
2
0
-2
5
10
20
-3
ih
x 10
30
40
10
20
-3
ph
x 10
30
40
10
20
0
-0.02
10
40
40
30
40
30
40
0
10
20
30
40
-0.02
10
0
0
-0.05
10
20
20
b
0.02
-0.02
30
0.02
c
30
20
ihs
1
0
-5
-0.02
30
40
-0.1
10
20
Figure 3: Responses of key variables to preference shock
58
Essay 2. Macroeconomic imbalances and exchange rate regime shifts
A persistent preference shock increases consumption and output today. The
increase in output also makes inflation increase through the Phillips curve. The
increase in consumption is partly financed by borrowing abroad. On the one hand,
borrowing abroad makes interest rates increase while on the other hand, the expectations of an appreciation make interest rates decrease. For the current parameterization, the net contemporaneous effect is positive.
5.2
Model simulation and graphical analysis
Can we find a relation between the underlying variables, either in levels or first
differences, and the probability of exit? To answer this question, I simulate the model
over 2100 periods and drop the first 100 observations to reduce the role of initial
conditions. Then, I separate those episodes for which Ss,t > 1, representing periods
when the policy maker is tempted to let the currency float with accompanying
depreciation. The symmetry of the model makes the arguments the same for exits
with appreciations. The simulation can be interpreted as follows. Imagine that we
start out with a large number of representative small open economies such as the
one described in this paper. Then, in each period, some countries exit to flexible
regimes and these are thereafter dropped from the analysis. Modeling when this
happens for single economies is not the purpose of this paper, nor modeling these
economies after the float has taken place. Instead, recognizing the general tendency
of economies to float, we want to see under what circumstances the representative
small open economy will do so with a high probability.
In interpreting the results from the model, I focus on observables to see whether
these variables can help us understand when an economy with a fixed exchange rate
regime will be inclined to exit to a flexible exchange rate regime. All scatterplots
display observables on the horizontal axis and the probability of exit on the vertical
axis. All observables are displayed as deviations from their steady state value converted to easily interpretable numbers, except for Ss that is only used to separate
depreciation (Ss > 1) and appreciation episodes (Ss < 1). Figure 4 displays the full
results for the simulations, without separating episodes of exits with depreciation
from exits with appreciation. The symmetry of the model is revealed in the results
by observing the non-linear relation between exits overall and output.
59
10
10
9
9
9
8
8
8
7
7
7
6
6
6
5
5
4
4
3
3
3
2
2
2
1
0.90
1
0.95
1.00
1.05
1.10
-15
-10
-5
0
5
10
1
-.15
15
10
9
9
8
8
8
7
7
7
6
6
6
5
Z*100
10
9
5
4
4
3
3
3
2
2
2
1
1
-4
0
4
8
12
0
20
40
60
80
-6
9
8
8
8
7
7
7
6
6
6
Z*100
10
9
Z*100
10
9
5
4
4
3
3
3
2
2
2
1
1
1
-2
0
2
(I-0. 006)*4*100
4
6
. 15
-2
2
4
6
-.0012 -.0008 -.0004 . 00 00 . 00 04 . 00 08 .0012
DI
Figure 4: Both shocks: all periods
0
5
4
-4
.10
(DB/Y )*100
10
-6
-4
(B/Y )*100
5
.05
1
-80 -60 -40 - 20
(C01-0 .5699) *100
.00
5
4
-8
-.05
INFL*4
10
-12
-.10
(Y -1) *100
Z*100
Z*100
5
4
SS
Z*100
Z*100
10
Z*100
Z*100
5. Numerical results
-10
-5
0
(PH-1) *100
5
10
Essay 2. Macroeconomic imbalances and exchange rate regime shifts
9
9
8
8
8
7
7
7
6
6
6
5
Z*100
9
Z*100
5
4
4
3
3
3
2
2
2
1
1
0.98
1.00
1.02
1.04
1.06
1.08
1.10
1
-15
-10
-5
0
5
-.15
9
8
8
7
7
7
6
6
6
Z*100
9
8
5
5
4
4
3
3
3
2
2
2
1
1
-6
-4
-2
0
2
4
-80
(C01-0 .5699 )*100
-40
-20
0
20
40
60
-4
9
8
8
7
7
7
6
6
6
Z*1 00
9
8
5
4
4
3
3
3
2
2
2
1
1
-2
0
2
(I-0 .006)*4*10 0
-2
4
6
0
2
4
6
4
8
5
4
-4
. 10
(DB/Y )*100
9
-6
.05
1
-60
(B/Y )*100
5
.00
5
4
-8
-.05
INFL*4
9
-12 - 10
-.10
(Y -1)*100
Z*100
Z*100
SS
Z*1 00
5
4
Z*1 00
Z*100
60
1
-.0012 -.0008 -.0004 .0000
. 00 04
.0008
-12
DI
Figure 5: Both shocks: periods for which Ss,t > 1
-8
-4
0
(PH-1) *100
5. Numerical results
61
As can be seen in Figure 5, the probability of exit with an accompanying depreciation is decreasing in consumption and output. If consumption and output
are low, the policy maker may use the option to exit from the fixed exchange rate
regime with a depreciation of the currency, an increase of exports, an increase of
output and consumption. Moreover, it appears as if a positive current account as a
percentage of GDP and lower interest rates increase the exit probability. No clear
pattern for the domestic prices and exits with depreciation exists.
The empirical distributions of appreciations and depreciation probabilities, using the simulated data displayed in Figure 4, are displayed in Figures 6-7. The
results indicate that exits with appreciations or depreciations should, on average,
be equally likely to occur. The mean probability of exits, regardless of the following
appreciation or depreciation, is about 2.7 percent.
240
200
160
120
80
40
0
0.025
0.050
0.075
Figure 6: Both shocks: histogram of exit probabilities with accompanying depreciation, Ss,t > 1
400
300
200
100
0
0.025
0.050
0.075
Figure 7: Both shocks: histogram of exit probabilities with accompanying appreciation, Ss,t < 1
62
6
Essay 2. Macroeconomic imbalances and exchange rate regime shifts
Sensitivity analysis
First, I will present the results when the relative importance of shocks is altered.
Then, I will study what happens to the results if the policy maker in the fixed
exchange rate regime consistently aims at a higher output than natural.
6.1
Relative importance of shocks
2.4
2.4
2.0
2.0
2.0
1.6
1.6
1.6
1.2
Z*100
2.4
Z*100
1.2
0.8
0.8
0.4
0.4
0.4
0.0
0.0
0.99 1.00
1.01
1.02
1.03
1.04
1.05
0.0
-6
-5
-4
-3
-2
-1
0
1
2
3
-.16 -.12 -.08 -.04 .00
(Y -1)*100
2.4
2.0
2.0
1.6
1.6
1.6
Z*100
2.4
2.0
1.2
1.2
0.8
0.8
0.4
0.4
0.4
0.0
-2.5 -2.0 -1.5 -1.0 -0.5
0.0
0.0
0.5
1.0
-8
-6
-4
-2
0
2
4
0.0
-1.2
6
2.4
2.0
2.0
1.6
1.6
1.6
Z*100
2.4
2.0
1.2
0.8
0.8
0.4
0.4
0.4
0.0
0.0
-.2
.0
.2
(I -0.006)*4*100
.4
.6
-.0002 -.0001
-0.4
0.0
0.4
0.8
4
6
1.2
0.8
-.4
.12
(DB/Y )*100
2.4
-.6
-0.8
(B/Y )*100
1.2
.08
1.2
0.8
(C01- 0.5699) *100
.04
INFL*4
2.4
Z*100
Z*100
SS
Z*100
1.2
0.8
Z*100
Z*100
Shutting down the preference shock and only subjecting the model to cost-push
shocks, the results in Figure 8 are obtained. These results are clearly more clearcut than the full model and some of them are reversed. Exits with accompanying
depreciation are more likely in times of low output, low consumption, a deficit in the
current account, high and increasing interest rates and high domestic prices. The
mean probability of exits, regardless of the following appreciation or depreciation,
is about 0.6 percent. This small figure is explained by the trade-off in stabilization
policy under a flexible regime.
0.0
.0000
. 00 01
DI
.0002
.0003
-4
-2
0
2
(P H-1)*100
Figure 8: Only cost-push shocks: periods for which Ss,t > 1
6. Sensitivity analysis
63
7
7
6
6
6
5
5
5
4
Z*100
7
Z*100
4
3
3
2
2
2
1
1
0.99 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07
1
-12
-8
-4
0
4
-.04
7
6
6
5
5
5
4
Z*100
7
6
4
3
3
2
2
2
1
1
-6
-4
-2
0
2
4
-40
-20
0
20
40
60
80
-3
7
6
6
5
5
5
Z*1 00
7
6
4
3
3
2
2
2
1
1
-3
-2
-1
0
1
(I-0 .006)*4*10 0
-1
2
3
4
0
1
2
3
4
5
6
4
3
-4
. 01
(DB/Y )*100
7
-5
-2
(B/Y )*100
4
.00
1
-60
(C01-0 .5699 )*100
-.01
4
3
-8
-.02
INFL*4
7
-10
-.03
(Y -1)*100
Z*100
Z*100
SS
Z*1 00
4
3
Z*1 00
Z*100
Shutting down the cost-push shock and subjecting the model to preference shocks
only, the results in Figure 9 are obtained. Exits with an accompanying depreciation
are more likely to occur when output and consumption are low. Moreover, as in the
baseline model, exits are more likely in times of positive current accounts and low
interest rates. No clear effect of domestic prices is detected. The mean probability of
exits, regardless of the following appreciation or depreciation, is about 1.8 percent.
This relatively high figure is due to the fact that if only demand shocks are present,
the flexible regime will be attractive since no trade off in balancing effects on output
and inflation exists.
1
-.0012 -.0008 -.0004 .0000
DI
. 00 04
.0008
-6
-4
-2
0
(PH-1) *100
Figure 9: Only preference shocks: periods for which Ss,t > 1
2
4
64
Essay 2. Macroeconomic imbalances and exchange rate regime shifts
The different predictions about the relation between the domestic interest rate,
the asset position or the current account and the probability of exit are due to the
different dynamics of the model when subjected to different shocks, as illustrated by
the impulse response figures. Following a cost-push shock, inflation increases temporarily followed by a few periods of deflation. At the same time, output decreases
with a jump and slowly reverts to baseline. In such circumstances, the economy
would unambiguously need lower interest rates after the initial response when inflation is positive which, in turn, implies a depreciation of the domestic currency. This
happens at the same time as the net asset position decreases, i.e. the current account
is negative, since output is not sufficient to cover current consumption. Therefore,
we have a negative relation between the current account and the exit probability.
Following a preference shock, consumption and output increase resulting in higher
inflation via the Phillips curve. In such a situation, the economy needs higher interest rates to stabilize the economy, implying a appreciation of the domestic currency.
However, part of the increased consumption is financed by a negative current account. Therefore, we have a negative relation between the current account and an
appreciation of the currency, or equivalently, a positive relation between the current
account and the exit probability.
6.2
Output bias
So far, we have assumed the policy objective to be the same across exchange rate
regimes. Now, instead suppose that the policy maker in the non-credible fixed regime
has some incentives to push output above the steady state, whereas the monetary
authority in the flexible regime has no such objectives. Such a difference in policy
objectives might arise if the monetary authority in the fixed exchange rate regime is
political, and the probability of getting elected for the next term of office is increasing
in economic activity, whereas policy in the flexible exchange rate regime is governed
by an independent central bank. The loss function in equation (44) is appended by
an output bias term, k, and becomes
h
i
f lex
2
2
non−cred
(1
−
z
=
π
+
λ
(Y
−
Y
−
k)
+
β
E
)
L
+
z
L
Lnon−cred
L
t
n
t
t+1
t+1
L
t+1 . (58)
t
t
t+1
The other equations of the model are left unchanged. With a positive output bias,
setting k > 0 in equation (58), there will be an incentive for the policy maker to
stimulate the economy even in steady state so as to attain the desirable output
(Yn + k). The steady state values of the model will be left unchanged with the
6. Sensitivity analysis
65
20
20
16
16
16
12
12
12
8
4
8
4
0
0.95
1.00
1.05
1.10
-10
-5
0
5
10
15
-.15
20
16
16
16
12
12
12
8
4
Z*100
20
8
4
0
-4
0
4
8
12
-20
0
20
40
60
-6
16
16
16
12
12
12
Z*100
20
Z*100
20
8
4
0
-6
-4
-2
0
2
4
(I-0.0 06)*4*1 00
6
8
10
.15
-4
-2
2
4
6
0
(DB/Y )*100
20
4
.10
8
(B/Y )*100
8
.05
0
-100 -80 -60 -40
(C0 1-0. 5699) *100
.00
4
0
-8
-.05
INFL*4
20
-12
-.10
(Y -1) *100
Z*100
Z*100
0
-15
SS
8
4
0
0.90
Z*100
Z*10 0
20
Z*10 0
Z*10 0
exception of there being a steady state loss different from zero and an associated
positive probability of exit. Setting k = 0.05, the mean probability of an exit
increases to 4.7 percent, which is a reflection of the increased mean probability of
exits with depreciations at 7.2 percent.
8
4
0
-.006 -.004 -.002 .000
.002
.004
.006
0
-10
-5
DI
Figure 10: Both shocks with output bias: all periods
0
(PH- 1)*1 00
5
10
Essay 2. Macroeconomic imbalances and exchange rate regime shifts
20
20
16
16
16
12
12
12
8
4
8
4
0
1.00
1.02
1.04
1.06
1.08
1.10
-12
-8
-4
0
4
8
-.15
20
16
16
16
12
12
12
8
4
Z*100
20
8
4
0
-6
-4
-2
0
2
4
6
-20
0
20
40
60
-6
16
12
12
12
Z*100
20
16
Z*100
20
16
8
4
0
-6
-4
-2
0
2
4
(I-0.0 06)*4*1 00
-4
-2
6
8
10
0
-.006 -.004 -.002
0
2
4
6
(DB/Y )*100
20
4
.10
8
(B/Y )*100
8
.05
0
-100 -80 -60 -40
(C0 1-0. 5699) *100
.00
4
0
-8
-.05
INFL*4
20
-10
-.10
(Y -1) *100
Z*100
Z*100
0
-16
SS
8
4
0
0.98
Z*100
Z*10 0
20
Z*10 0
Z*10 0
66
8
4
0
.000
DI
.002
.004
.006
-10
-5
0
5
(PH- 1)*1 00
Figure 11: Both shocks with output bias: periods for which Ss,t > 1
10
6. Sensitivity analysis
67
The scatterplots in Figure 11 indicate that exits with depreciations will be more
likely to occur when output and consumption are low, and when domestic prices are
high. Now, based on the simulated data displayed in Figure 10, the exits are heavily
tilted toward depreciations as displayed in Figures 12-13. This happens because
the policy maker is tempted to boost output above the natural output rate, which
can be done temporarily by a depreciation of the domestic currency. This occurs
although the effect of the one time depreciation would not be sustainable, since
natural output remains unchanged.
100
80
60
40
20
0
0.025
0.050
0.075
0.100
0.125
0.150
0.175
Figure 12: Both shocks with output bias: histogram of exit probabilities with
accompanying depreciation, (Ss,t > 1)
140
120
100
80
60
40
20
0
0.02
0.03
0.04
0.05
0.06
0.07
Figure 13: Both shocks with output bias: histogram of exit probabilities with
accompanying appreciation, (Ss,t < 1)
68
Essay 2. Macroeconomic imbalances and exchange rate regime shifts
The output bias can help us understand the strong bias in the data toward realignments with depreciations rather than appreciations. The conventional wisdom
is that, given that they are to exit from a fixed exchange rate regime, countries
would be better off doing so when the going is good. If countries take this advice
seriously, more exits should be observed with appreciation than with depreciation
of the exchange rate. However, Detragiache, Mody, and Okada (2005) identify only
three out of forty exits during 1980-2001 that were followed by a nominal appreciation. The authors infer that exits often occur when times are bad. With a positive
output bias, my model produces the same results; realignments are tilted toward
cases of realignments with depreciations. My model offers an explanation to this
observation. Since the policy maker intends to push the economy above the natural
rate of output, she is more inclined to act on negative rather than positive shocks to
output. In fact, even with no shocks at all, the policy maker will have an incentive
to exit with a depreciating exchange rate, resulting in the bias of exits towards exits
with accompanying depreciation.
7
Conclusions
This paper makes use of a dynamic stochastic rational expectations model of a
representative small open economy to study under what circumstances there is likely
to be an exit from a fixed to a flexible exchange rate regime. In the shadow flexible
alternative, monetary policy is guided by a simple Taylor rule that is superior from
the point of view of stabilization of economic shocks. The purpose of the paper is
to investigate how observables relate to the probability of an exit when the policy
maker is concerned with macroeconomic stabilization.
The main results are summarized as follows. Regardless of the relative size of
cost-push and demand shocks, low consumption and low output should trigger exits
with depreciations to help stimulate the economy. It is also shown that high domestic
prices, making domestic goods uncompetitive at the international market, also make
exits with depreciation more likely. If the domestic debt is large and interest rates are
high, exits with depreciations are more likely to occur. These results are stronger the
larger are the cost-push shocks. Inflation and the current account have ambiguous
effects on exits with depreciations, depending on the relative size of the two types
of shocks.
Saxena (2004) describes episodes of currency crises with resulting depreciations.
For Latin American countries during the 1970’s and 1980’s, she points out that
the episodes of currency crises and the following depreciation were preceded by
7. Conclusions
69
high current account deficits and an increase in interest rates.16 For the European
countries during the 1990’s, current account deficits also preceded the crises but the
reason for exits out of concerns for international competitiveness is pointed out.17
My model is capable of replicating these findings if cost-push shocks are assumed to
be large relative to preference (demand) shocks.
The introduction of an output bias, caused by an opportunistic policy maker,
makes exits with depreciation more likely than exits with appreciation, since a depreciation temporarily boosts output above the natural level. My model gives some
intuition to why countries exit with depreciations in bad times rather than in good
times.
My model can be extended in several directions. The most obvious extension
would be to endogenize the world economy. This would introduce more dynamics
since world interest rates and prices would be of importance for how the small open
economy evolves over time. Another possible extension would be to endogenously
model the benefits of the fixed exchange rate regime.
16
17
93.
Bolivia 1982-85, Brazil 1983; 1986; 1989-90, Chile 1971-74, Peru 1976;1987 and Uruguay 1982
Germany 1992-93, France 1992-93, United Kingdom 1992-93, Spain 1992-93 and Sweden 1992-
70
References
References
Barro, R., and M. Gordon (1983): “Rules, Discretion and Reputation in a
Model of Monetary Policy,” Journal of Monetary Economics, 12, 101—121.
Bénassy-Quéré, A., and B. Coeuré (2002): “The Survival of Intermediate
Exchange Rate Regimes,” Working Paper 2002-07, CEPII.
Benigno, P. (2001): “Price Stability with Imperfect Financial Integration,” Working Paper mimeo, New York University.
Bensaid, B., and O. Jeanne (1997): “The Instability of Fixed Exchange Rate
Systems When Raising the Nominal Interest Rate is Costly,” European Economic
Review, 41, 1461—1478.
Bergvall, A. (2002): “Essays on Exchange Rates and Macroeconomic Stability,”
Ph.D. thesis, Department of Economics, Uppsala University.
(2005): “Exchange Rate Regimes and Macroeconomic Stability: The Case
of Sweden,” Oxford Economic Papers, 57, 422—446.
Clarida, R., J. Gali, and M. Gertler (1999): “The Science of Monetary Policy:
A New Keynesian Perspective,” Journal of Economic Literature, 37, 1661—1707.
Collard, F., and M. Juillard (2005): “DYNARE,” For documentations of
DYNARE, practical guide and manual see http://www.cepremap.cnrs.fr/dynare/.
Detragiache, E., A. Mody, and E. Okada (2005): “Exits from Heaviliy Managed Exchange Rate Regimes,” Working Paper 05/39, IMF.
Duttagupta, R., and I. Otker-Robe (2003): “Exits from Pegged Regimes: An
Empirical Analysis,” Working Paper 03/147, IMF.
Edwards, S. (1996): “The Determinants of the Choice Between Fixed and Flexible
Exchange Rates,” Working Paper 5756, NBER.
Eichengreen, B., A. K. Rose, and C. Wyplosz (1995): “Exchange Market
Mayhem: The Antecedents and Aftermath of Speculative Attacks,” Economic
Policy, 21, 249—296.
Holmberg, K. (2006): “Derivation and Estimation of a New Keynesian Phillips
Curve in a Small Open Economy,” Working Paper 197, The Swedish Riksbank.
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IMF (2003): Exchange Arrangements and Foreign Exchange Markets. IMF, Washington, D.C.
Johansson, K. (1998): “Exports in the Econometric Model KOSMOS,” Working paper 62, National Institute of Economic Research Sweden (Konjunkturinstitutet).
Krugman, P. (1979): “A Model of Balance of Payment Crises,” Journal of Money,
Credit and Banking, 11, 311—325.
Mehra, R., and E. C. Prescott (1985): “The Equity Premium-A Puzzle,”
Journal of Monetary Economics, 15, 145—161.
Obstfeld, M. (1986): “Rational and Self-Fulfilling Balance F Payment Crises,”
The American Economic Review, 76, 72—81.
(1996): “Models of Currency Crises with Self-Fulfilling Features,” European
Economic Review, 40, 1037—1047.
Obstfeld, M., and K. Rogoff (1995): “The Mirage of Fixed Exchange Rates,”
The Journal of Economic Perspectives, 9, 73—96.
Ozkan, F. G., and A. Sutherland (1998): “A Currency Crisis Model with an
Optimising Policymaker,” Journal of International Economics, 44, 339—364.
Rebelo, S., and C. Vegh (2006): “When Is It Optimal to Abandon a Fixed
Exchange Rate?,” Working Paper 12793, NBER.
Saxena, S. C. (2004): “The Changing Nature of Currency Crises,” Journal of
Economic Surveys, 18, 321—350.
Taylor, J. B. (1993): “Discretion versus Policy Rules in Practice,” CarnegieRochester Conference Series on Public Policy, 39, 195—214.
Walsh, C. E. (2003): Monetary Theory and Policy. The MIT Press, Cambridge.
72
A
A.1
Essay 3. Macroeconomic imbalances and exchange rate regime shifts
Appendix
Derivation of the uncovered interest parity condition
The representative world consumer’s intertemporal budget constraint is
Bth
St Btf
f
h
³
´ = Bt−1
+
+ St Bt−1
+ Pf,t YW,t − PcW,t CW,t ,
1 + iht
1 + ift φt
(59)
where consumption, CW,t , is a geometric average of world produced good consumption, Cf,t , and consumption goods from the small economy, Ch,t , so that
γ
CW,t = Cf,tw Ch,t 1−γ w .
(60)
PcW,t is derived accordingly. The interpretation of the budget constraint in equation
(59) is that the world representative agent enters period t with the small economy
f
h
, gross of interest rate and world denominated assets Bt−1
,
denominated assets Bt−1
gross of interest rate, and denominated in the small economy currency at time t. The
agent receives work income (Pf,t YW,t ) and spends some on consumption (PcW,t CW,t )
in the same period. This value equals the discounted value of what is brought over
to t + 1. Households work in and own all firms in the economy so that all income
accrues to households.
Optimization on the part of the consumer with respect to CW,t , Bth and Btf ,
⎤⎤
h
f
S
B
B
τ
f
τ
τ
´ − Bτh−1 − Sτ Bτ −1 − Pf,τ YW,τ + PcW,τ CW,τ ⎦⎦ ,
max Et
β ⎣Uτ − λτ ⎣
+³
1 + idτ
Ct ,Bth ,Btf
1 + ift
t=τ
(61)
yields the following conditions:
∞
X
τ
⎡
⎡
−θ
= λt PcW,t ,
CW,t
(62)
λt
= βEt (λt+1 ) ,
1 + iht
(63)
and
λS
³ t t ´ = βEt (λt+1 St+1 ) .
1 + ift
Equating marginal utilities intertemporally yields the Euler equation,
(64)
A. Appendix
73
−θ
CW,t
= β(1 + iht )Et
PcW,t
Ã
−θ
CW,t+1
PcW,t+1
!
(65)
.
Combining equations (63) and (64), we get the uncovered interest-rate parity condition,
(1 + iht ) = (1 + ift )
Et (λt+1 St+1 )
.
St Et (λt+1 )
(66)
Using the expression for the marginal utility of consumption in (62), we can rewrite
equation (66) as
µ
¶
Et
(1 + iht ) = (1 + ift )
−θ
CW,t+1
S
PcW,t+1 t+1
St Et
µ
−θ
CW,t+1
PcW,t+1
which cannot generally be further simplified since Et
µ
¶ ,
−θ
CW,t+1
S
PcW,t+1 t+1
(67)
¶
6= Et
µ
−θ
CW,t+1
PcW,t+1
¶
Et (St+1 ),
unless the covariance of real consumption and the bilateral exchange rate is zero.
However, it can be argued that the small open economy exchange rate will carry
such a small weight in the uncovered interest-rate parity condition that the covariance terms will tend to zero. This yields the uncovered interest-rate parity condition
that will bind for investors and equation (67) can be approximated by the most familiar version of the condition,
(1 + iht ) = (1 + ift )Et
µ
St+1
St
¶
.
(68)
Equation (68) is the uncovered interest-rate parity condition used in solving the
model.
74
A.2
Essay 3. Macroeconomic imbalances and exchange rate regime shifts
Derivation of the export function
World utility is given by
1
C 1−θ ,
(69)
1 − θ W,t
where CW,t is defined as in section A.1. Abstracting from investments and exports
to the small economy, the world budget constraint is given by18
UW,t =
Pf,t YW,t = Pf,t Cf,t +
Ph,t Ch,t
.
St
(70)
Maximizing (69) subject to (70) and solving for Ch,t gives
Ch,t =
SP
Pf,t YW,t
³
´ = (1 − γ w ) YW,t t f,t ,
1
Ph,t
Ph,t
St
(71)
1−γ w
which then constitutes the world import of goods produced in the small open economy, IMW,t . In equilibrium, world imports must equal small open economy exports,
IMW,t = (1 − γ w ) YW,t
St Pf,t
= EXt .
Ph,t
(72)
Taking Sweden as an example of a small open economy with about 0.5 percent of
world GDP and Sweden’s steady state output normalized to unity, we have that the
world economy is about 200 times the economy of Sweden. Assuming a constant
world output at this level and using that from the steady state solution, we also know
that (1 − γ w ) YW,t should equal 1 − γ. This implies that γ w = 0.99625, indicating
that small open economy imports account for 0.375 percent of world consumption
in steady state. Thus,
St Pf,t
Ph,t
= (1 − γ) Q−η
t .
EXt = (1 − γ)
(73)
with η = 1. I allow for η 6= 1 to better match the empirical evidence.
Equation (73) is the export function used in solving the model.
18
Asset holdings are abstracted from for clarity in derivations. The exchange rate is written in
the small economy currency units needed to buy world currency to comply with the notation in
the main text.
Essay
3
Foreign exchange market interventions as
monetary policy
1
Introduction
No interventions in the foreign exchange market are carried out in a pure flexible
exchange rate regime. The exchange rate is allowed to dance as it wishes and the
monetary authorities stabilize the economy solely by the interest rate which, in
turn, will affect exchange rate movements. Thus, the exchange rate is not seen as
the instrument but is rather residually determined.
In reality, however, many countries characterized by flexible exchange rates intervene in the foreign exchange market.1 These interventions are most commonly
carried out in conjunction with domestic bond sales, so that potential effects on the
money supply are offset. In this sense, interventions cannot be interpreted as regular monetary policy since they do not change domestic money supply. Moreover,
interventions have historically been carried out more or less in secret. Until recently,
data on historical interventions by central banks has not been made official. The
secrecy involving interventions is somewhat of a puzzle given that signaling — affecting expectations about future monetary policy — is considered as one of the main
explanations of interventions (Mussa (1981)). The other explanation of intervention offered in the literature relies on the portfolio balance model. By altering the
relative supplies of domestic and foreign bonds, the central bank might be able to
affect the exchange rate. Dominguez and Frankel (1993) present some evidence that
this might actually work. Many questions remain, however, regarding the possibility of moving the exchange rate by interventions. For recent surveys of the theory
1
E.g. Japan, Australia, Norway, Turkey, USA, Switzerland, Sweden and West Germany.
75
76
Essay 3. Foreign exchange market interventions as monetary policy
of interventions, see Sarno and Taylor (2001), Sarno and Taylor (2002) and Neely
(2005).
No matter how plausible it is that the central bank can move the exchange
rate, the simple observation remains that central banks intervene heavily at times.
Why do central banks intervene? They must clearly believe that interventions work
since they keep making them! But what are the motives driving interventions?
Many studies have postulated an intervention reaction function in terms of nominal
exchange rate deviations from some target level (Almekinders and Eijffinger (1996)
and Ito and Yabu (2004) inter alia). The argument is that the central bank will
intervene to smooth deviations from some target level of the nominal exchange rate.
From such studies, evidence has emerged that central banks seem to "lean against the
wind", i.e. central banks attempt to smooth excessive fluctuations by interventions
of the appropriate sign. Only a few studies have considered other determinants than
nominal exchange rate deviations, most notably Kim et al. (2002, 2003, 2006) where
prevention of exchange rate misalignment and monetary policy considerations are
considered as possible, but peripheral, determinants of interventions in Australia
and Japan.
Is it possible that interventions have been carried out partly to reinforce or
counteract regular monetary policy, especially in periods where interest rate policy
was restrained? A quote from a former Swedish Riksbank Governor and the present
Swedish Minister of Finance seems to indicate that this is an option for central
banks. Borg and Heikensten (2002) state on page 31 that:
In addition to adjusting the interest rate, the Riksbank can resort to
interventions in the foreign exchange market and a number of other measures for the purpose of maintaining price stability. The most obvious
case for a central bank with an inflation target considering interventions
is when the interest rate instrument no longer functions effectively. One
such situation is when the steering interest rate is zero and the real interest rates are nevertheless unjustifiably high as a result of the economy
being in a deflation process, with a general and persistent fall in prices.
Interventions with the aim of achieving more expansionary monetary
conditions through a weakening of the exchange rate would be a possible
measure here. The fact that there is a possibility, which is not negligible, of getting into a situation where the interest rate is zero and thereby
constitutes a restraint for monetary policy, is a strong reason for having
interventions in the monetary policy arsenal.
1. Introduction
77
In Sweden, the Riksbank has intervened in the foreign exchange market a number of times after the float of the krona in November 1992. The possibility of moving
the exchange rate through these interventions has been questioned by e.g. Aguilar
and Nydahl (2000) and Humpage and Ragnartz (2006). Nevertheless, after a series of interventions in June 2001, the governor at the time, Bäckström (June 14
2001), indicated that the Riksbank views interventions as a supplementary policy
instrument:
Currency market interventions are one of the instruments at the disposal of a central bank. For a central bank that targets inflation, the
primary instrument is, however, the interest rate. But at a time when
the exchange rate is a serious upside risk in the inflation forecast and
deviates markedly from a reasonable value, a situation may arise where
currency market interventions are motivated as an additional element in
the work of continuously ensuring price stability.
In Japan, the official reason of the Bank of Japan for intervening in the foreign
exchange market is stated as:
The Foreign Exchange and Foreign Trade Law stipulates that the Minister of Finance shall endeavor to stabilize the external value of the yen
by taking necessary measures including foreign exchange transactions.2
In the introduction to this policy document, written in July 2000, the policy
with regards to interventions is explained:
Since the introduction of a floating exchange rate system in February
1973, the Japanese economy has experienced large fluctuations in foreign
exchange rates, with the yen on a long rising trend. In order to mitigate
the negative influence of such fluctuations on the Japanese economy,
foreign exchange market interventions (...) have been conducted from
time to time.
As made clear by the first quote, it is not the Bank of Japan that decides on
interventions, but the Ministry of Finance with the Bank of Japan solely acting as
the agent of operations. This might lead to principal agent problems in that the
Bank of Japan executes the order by the Ministry of Finance, but not necessarily
2
Source: Outline of the Bank of Japan’s Foreign Exchange Intervention Operations at the Bank
of Japan home page, http://www.boj.or.jp/en/type/exp/faqkainy.htm
78
Essay 3. Foreign exchange market interventions as monetary policy
deems interventions to be appropriate. The possible misalignment of objectives is
not addressed in this paper, but interest rate policy and interventions are assumed
to be decisions of the same policy maker. The interested reader can read more about
this issue in Bernal (2006).
In Australia, the Reserve Bank of Australia has not described interventions as an
explicit concern for monetary policy. Deputy Governor Macfarlane (1993) explains:
We would not wish to use intervention to correct a monetary policy
imbalance, or to resist changing fundamentals. (...) What then is the
role of foreign exchange intervention? The answer is that it is a modest
one — it is to make some contribution towards reducing the extent and
duration of overshooting and to bring a little more short-term stability
when markets threaten to overreact to news.
This strong statement is somewhat softened in the conclusion where the Deputy
Governor elaborates on the issue:
[Being in a floating exchange rate system] does not mean that we
can be indifferent to where the exchange rate ends up and sometimes
monetary policy or foreign exchange intervention must be brought into
play. We have been less inclined than most other countries to direct
monetary policy at the exchange rate, but have used intervention quite
often.
The quotes above illustrate that at least some policy makers view interventions
as potentially effective and a concern for monetary policy. Few papers have incorporated such monetary policy considerations when studying interventions. Kaminsky
and Lewis (1996) and Kim (2003) study the signaling hypothesis. Kim et al. (2002,
2006) include interest rate changes as a possible determinant of interventions in their
estimated reaction functions and argue that interventions in Australia and Japan
have partly been used to support monetary policy. A few other papers have proposed interventions as a viable temporary monetary policy instrument, especially
when short-term interest rates approach zero. McCallum (2000) appends a portfolio balance effect to the uncovered interest rate parity condition and argues that
interventions can affect the exchange rate and help the economy out of a liquidity
trap. Svensson (2001) argues that interventions are a crucial ingredient in a policy
mix that is a "foolproof way" of getting out of a liquidity trap. Nishimura and Saito
(2003) argue that intervention policy is a promising candidate to get out of the zero
interest rate environment, but difficult to pursue for political reasons.
2. Model
79
Given the puzzle concerning motives of interventions, it is relevant to revisit the
determinants of interventions. The above quotes indicate that some central bankers
clearly think that interventions are effective in moving the exchange rate. However,
the question of whether the central banks are really able to alter the exchange rate
level, or its volatility, is left to other researchers. The model in this paper should
therefore be seen as a simple description of how central bankers may think when
they intervene in the foreign exchange market given that they believe interventions
to be effective. Specifically, under what macroeconomic circumstances should central
bankers be expected to intervene?
To my knowledge, no unifying model with an optimizing central bank has been
proposed to theoretically derive what should be the determinants for interventions if
the central bank cares about what it is said to care about: deviations in output and
inflation from target levels. This paper attempts to do exactly that and finds that
intervention should, on average, be negatively correlated with interest rates, but
positively correlated with persistent shocks to the interest rate, which are unrelated
to macroeconomic stabilization. Interventions should be larger in magnitude in times
of an overvalued exchange rate and low inflation. Moreover, the model predicts a
positive relation between current interventions and interventions in the future.
These predictions are taken to data for daily interventions by the Bank of Japan,
the Reserve Bank of Australia 1991-2004 and the Swedish Riksbank 1993-2004. The
results indicate that these central banks have used interventions in a way that is
broadly consistent with monetary policy, since most predictions derived from the
model are supported by the data.
The paper is organized as follows. Section 2 sets up the theoretical model and
derives some empirical predictions. Section 3 presents the data used in estimations.
Section 4 presents the results from testing the predictions derived from the model
and section 5 concludes.
2
Model
Consider a monetary authority that wishes to stabilize inflation, π t , around a constant target level, π̄. The central bank has two instruments at its disposal, the
nominal interest rate, it , and sales of domestic bonds that alter the outstanding
stocks of bonds held by investors, zt . Sterilized interventions, ∆zt , can be used to
change the relative supplies of foreign and domestic bonds. Sterilization of interventions makes the money supply stay unaffected. Effectively, the central bank changes
the private sector’s relative holdings of foreign and domestic bonds. Through the
80
Essay 3. Foreign exchange market interventions as monetary policy
portfolio balance channel, the central bank is able to influence the level of the real
exchange rate, qt , since a premium must be given on domestic currency assets if
investors are to hold a larger share.
The model economy is described by a Phillips curve, an aggregate demand function, a portfolio balance equation and a loss function that the authorities wish to
minimize. The policy maker can stabilize the economy by interest rate policy and
through sales (or purchases) of domestic bonds, i.e. interventions. The nominal
interest rate is bounded by the zero lower bound.
Inflation is determined by demand pressure and inflation expectations according
to a forward-looking Phillips curve as in Clarida, Gali, and Gertler (1999),
π t = β 1 yt + ωπ et+1 ,
(1)
where yt is the deviation from potential output and π et+1 is expected inflation in the
next period.3 β 1 is the demand pressure effect on inflation and ω the discount factor.
All parameters in the model have positive values. Output depends on the expected
real interest rate, rt = it − π et+1 , and the real exchange rate according to
¡
¢
yt = −α1 it − π et+1 + α2 qt ,
(2)
that is the "IS" curve. Variables are normalized so that output is equal to zero when
the nominal interest rate equals expected inflation and the (log) real exchange rate
is zero. The real exchange rate level is determined by a simple portfolio balance
equation along the lines of Dominguez and Frankel (1993) and McCallum (2000),
³
´
qt = ut − γ 1 it − ift + γ 2 (zt − z̄) ,
(3)
where ift is the foreign interest rate and z̄ the level of outstanding domestic bonds
at which no risk premium is required by risk averse investors.4 qt is defined as the
relative price of domestic to foreign goods so that an increase in qt is a depreciation.
Consider a risk averse foreign investor who initially has an optimal risk/return portfolio with some share of domestic bonds. Domestic and foreign bonds are imperfect
substitutes and a larger share of any type must be compensated by a higher ex3
Inflation is home inflation only, but the model could easily be extended to allow for imported
inflation. With imported inflation present, the implications of the model would only be strengthened in that a depreciation of the nominal exchange rate would not only boost exports, and via
the Phillips curve induce inflation, but also make imported goods more expensive and increase
inflation even more.
4
Equation (3) is the inverted form of demand for the portfolio share allocated to domestic
bonds, zt .
2. Model
81
pected return. If more bonds are supplied to the market, the representative investor
will be willing to hold these only if the foreign currency is expected to appreciate
relative to the domestic currency. In other words, for foreign investors to be willing to hold domestic bonds, the domestic currency must depreciate and therefore q
must increase. In steady state, with zt − z̄ and a zero interest rate differential, the
real exchange rate level is pinned down by exogenous movements in the catch-all
variable ut . ut is a stationary albeit persistent shock variable with an unconditional
zero mean that captures expectations of the future evolution of the real exchange
rate. These expectations may depend on the relative price of foreign goods, foreign
bond supplies, central bank credibility, productivity movements etc.
Substituting equations (2) into (1), we find that inflation can be written as
π t = (ω + β 1 α1 ) πet+1 − β 1 α1 it + β 1 α2 qt .
(4)
The loss of the central bank is
Lt =
1
1
1
(πt − π̄)2 + δ1 (it − ı̄ − dt )2 + δ 2 ∆zt2 .
2
2
2
(5)
This loss function is one of the possible variations of the generic loss function proposed in Svensson (2000) and the same as in Woodford (2003), excluding the usual
output gap term.5 The variable dt captures other motives than macroeconomic stabilization that affect interest rate setting, e.g. the central bank’s concerns about
asset price bubbles, political pressures, the foreign economy etc. δ 1 > 0 can be
motivated by the unwillingness of the central bank to use the interest rate very aggressively, which could induce excessive fluctuations in the financial market. This is
not interest rate smoothing or policy inertia, since the authorities do not care about
the change in interest rates from the previous period, but the deviation from the
long-run normal interest rate level.
Although deliberate interest rate smoothing has been advocated as a reason for
the observed high serial correlation of interest rates (see e.g. Clarida, Gali, and
Gertler (2000)), many papers have recently contended this assumption. The seminal paper is Rudebusch (2002) which argues that what appears to be policy inertia
is more likely to be the result of persistent shocks faced by the central bank rather
than deliberate interest rate smoothing. Rudebusch (2002) points at the credit
crunch as the reason for excessively low interest rates in the United States in 19921993 and worldwide financial crises as the reason for sustained high interest rates
5
Note, however, that although the output gap is excluded in the loss function, it is nevertheless
implicitly included by the tight connection between inflation and the output gap through the
Phillips curve.
82
Essay 3. Foreign exchange market interventions as monetary policy
in 1988-1989 and 1994-1995. The inclusion of financial variables in the Taylor rule
is discussed at length by Borio and Lowe (2004). For both Japan and Australia,
some evidence is found of financial variables having affected interest rate setting.
Söderlind, Söderström, and Vredin (2005) show that although traditional determinants of interest rate setting are easily predicted, interest rate changes are highly
unpredictable. Welz and Österholm (2005) provide Monte-Carlo evidence of a bias
in the estimation of the coefficient of policy inertia that is most likely due to the
omission of relevant variables in the central bank reaction function. Once more, this
casts doubt on the presence of interest rate smoothing and suggests that interest
rate policy systematically responds to other types of shocks than those considered
in the standard Taylor rule. This paper assumes that the policy maker sets policy
partly based on standard indicators of macroeconomic stability, captured by inflation and the output gap, and partly based on other objectives, dt . Equation (10),
derived below, describes interest rate setting as a standard Taylor rule augmented
by dt and subject to a non-negativity constraint.
The motivation of δ 2 > 0 is that excessive interventions could make the central
bank end up with such massive holdings of foreign bonds that in the long run, it
could be detrimental to the central bank’s own risk composition of foreign versus
domestic assets.6
The problem facing the central bank is to minimize the present value loss, L,
with respect to the outstanding stock of bonds zt and the interest rate it under the
additional constraint that the interest rate cannot fall below zero,
min Et
zt ,it
̰
X
ρτ Lt+τ
τ =0
!
s.t. i ≥ 0,
(6)
where ρ is the policy maker discount factor, 0 ≤ ρ ≤ 1. The Lagrangian becomes
Λ = Et
̰
X
τ =0
τ
ρ Lτ
!
− λt it ,
(7)
where λt is a shadow value that will be zero if it > 0 and positive otherwise.
6
Think of China and Japan buying US assets, but eventually considering a reoptimization
of their foreign asset portfolio. Under reasonable parameterizations and future expectations, the
assumptions of convex adjustment costs also ensure an inner solution of it and ∆zt .
2. Model
83
The first-order conditions are
∂Λ
= − (π t − π̄) β 1 (α1 + α2 γ 1 ) + δ 1 (it − ı̄ − dt ) − λt = 0,
∂it
¡
¢
∂Λ
e
= (π t − π̄) β 1 α2 γ 2 + δ 2 ∆zt − ρ∆zt+1
= 0.
∂zt
(8)
(9)
Substitute the Phillips curve, equation (1), into (8) and solve for it to obtain an
augmented Taylor rule,
it = ı̄ +
¢
β 21 (α1 + α2 γ 1 )
β (α1 + α2 γ 1 ) ¡ e
λt
yt + 1
ωπ t+1 − π̄ + dt + .
δ1
δ1
δ1
(10)
If dt = 0 so that the central bank has no other concerns than stabilization and
λt = 0 so that the zero lower bound is not binding, equation (10) reduces to the
standard Taylor rule where the interest rate is increasing in the output gap and
inflation expectations. Denote this interest rate by i∗t . If, on the other hand, other
concerns are present and the zero lower bound applies, we have that
it = i∗t + dt +
λt
δ1
(11)
or
it − i∗t = xt ,
(12)
λt
,
δ1
(13)
where
xt = dt +
and the actual interest rate deviates from what would be recommended by stabilization concerns alone. If other motives such as asset price stabilization exist, then
interest rates will be higher or lower than what is suggested by the standard Taylor
rule. Moreover, if the macroeconomic situation really warrants a negative interest
rate, as indicated by a negative i∗t , this will also show up as a discrepancy between
the actual interest rate and that implied by the standard Taylor rule, i∗t .
Should we expect interventions to be positively or negatively related to the interest rate? To find out, rearrange the first-order conditions, divide one by the other
and solve for ∆zt to get
∆zt = −
¶
µ
α2 γ 2 δ 1
λt
e
+ ρ∆zt+1
it − ı̄ − dt −
.
δ2 (α1 + α2 γ 1 )
δ1
(14)
84
Essay 3. Foreign exchange market interventions as monetary policy
Note that it − ı̄ − dt −
∆zt = −
λt
δ1
= it − ı̄ − xt so that (14) becomes
α2 γ 2 δ 1
α2 γ 2 δ 1
e
(it − ı̄) +
xt + ρ∆zt+1
.
δ 2 (α1 + α2 γ 1 )
δ 2 (α1 + α2 γ 1 )
(15)
From equation (15), we see that interventions will decrease with the observed interest rate deviation from the long-run level ı̄ to support interest rate policy if xt is
zero, i.e. if the interest rate is optimally set from a stabilization point of view. If,
however, xt is non-zero, we expect there to be no relation between interest rates and
interventions. Therefore, if stabilization motives dominate, we expect a significant
negative correlation between the interest rate and interventions, but in cases where
other motives are important, we might have no significant correlation. The last
e
, reflects that if interventions are expected tomorrow, then interventerm, ρ∆zt+1
tions will begin today since the policy maker cares about the future and balances
the cost of interventions today against the cost of interventions tomorrow.
Proposition 1 Interventions are expected to be negatively correlated to the interest rate to support monetary policy but positively correlated to the misalignment of
the interest rate from the standard Taylor interest rate to offset excessively contractionary policy. Therefore, if inflation stabilization concerns dominate other motives
in interest rate setting, then we expect interventions to be overall negatively correlated with the interest rate. Interventions are expected to be positively related to
future interventions.
In order to see how interventions are related to fundamentals, substitute the
first-order condition for the interest rate, equation (8), into equation (4) and solve
for inflation to get
πt =
µ
¶¸
∙
1
λt
, (16)
(ω + β 1 α1 ) π et+1 + β 1 α2 qt − β 1 α1 ı̄ + (χ − 1) π̄ − β 1 α1 dt +
χ
δ1
2
where χ = δ1 +β 1 α1δ(α1 1 +α2 γ 1 ) . Substitution of this expression of inflation into the firstorder condition for the domestic outstanding bonds, equation (9), yields an alternative expression of the determinants of interventions,
∆zt =
¤
β 1 α2 γ 2 £
e
π̄ + β 1 α1 ı̄ − (ω + β 1 α1 ) π et+1 − β 1 α2 qt + β 1 α1 xt + ρ∆zt+1
.
δ2 χ
The result in equation (17) is summarized in the following proposition.
(17)
3. Data
85
Proposition 2 We expect interventions to decrease in expected inflation and the
real exchange rate to boost aggregate demand. Interventions should be positively correlated with misalignment of the interest rate from the standard Taylor interest rate
to offset excessively contractionary policy. Interventions are expected to be positively
related to future interventions.
The remainder of the paper is intended to empirically test the two propositions
derived from equations (15) and (17) for interventions carried out by the Bank of
Japan, the Reserve Bank of Australia and the Swedish Riksbank.
3
Data
For Japan, daily data on spot rates and interventions is identical to the data used in
Ito and Yabu (2004).7 This data covers the period 4/01/1991 to 3/31/2003. Daily
spot rate and intervention data for Australia covers the same period and is provided
by the Reserve Bank of Australia. Swedish data is provided by the Riksbank and
covers 01/14/1993 to 3/31/2004. Although intervention data is available from 1991,
only data from January 1993 is used since up until that time, Sweden was in a
fixed exchange rate regime. Descriptive statistics of interventions are supplied in
Table 1 and time series intervention graphs are displayed in Figures 1-3. Monthly
and quarterly data on prices, total industrial production and daily target rates is
collected from the SOURCE OECD database, Ecowin and central bank sources.
The daily overnight uncollaterilized call rate for Japan, the target interest rate for
Australia and the repo rate for Sweden are used as the monetary policy target
interest rates.
Table 1: Descriptive statistics, interventions by country
Australia Japan Sweden
Mean
2.5
172.5
-3.5
Median
0
0
0
Maximum
376
16664
251
Minimum
-1256
-26201
-460
Std. Dev.
66.4
1141.0
27.2
No of interventions
907
343
180
Observations
3393
3393
2889
Note 1: AUD millions, JPY 100 millions, and USD millions
Note 2: Interventions are net purchases of foreign currency
7
Data
is
publicly
available
on
http://www.mof.go.jp/english/e1c021.htm
the
Ministry
of
Finance
home
page,
86
Essay 3. Foreign exchange market interventions as monetary policy
400
0
-400
-800
-1200
-1600
91 92 93 94 95 96 97 98 99 00 01 02 03
Figure 1: The Reserve Bank of Australia interventions (sales of AUD), AUD millions
20000
10000
0
-10000
-20000
-30000
91 92 93 94 95 96 97 98 99 00 01 02 03
Figure 2: The Bank of Japan/Ministry of Finance interventions (sales of JPY),
100 million JPY
300
200
100
0
-100
-200
-300
-400
-500
92 93 94 95 96 97 98 99 00 01 02 03
Figure 3: The Swedish Riksbank interventions (sales of SEK), USD millions
4. Empirical results
4
87
Empirical results
Looking at the data, it is readily observed that interventions are clustered with
long periods of no interventions followed by periods of consecutive interventions.
Therefore, in the empirical literature of foreign exchange market interventions, the
empirical models employed have often been some type of discrete choice model, or
friction model (see Rosett (1959)), where constant thresholds of misalignments of
determinants must be breached before actual interventions take place. The model
derived in this paper does no handle this property of the data since interventions are
continuous in the determinants and therefore, the model predicts that interventions
will very seldom be zero. The inclusion of a fixed cost of interventions could possibly
solve this issue, but would also be analytically much more complicated and hard to
motivate from an economic point of view. Ito and Yabu (2004) suggest that such a
fixed cost could be attributed to the political cost of obtaining the mandate to carry
out the intervention. For Japan, this might be a possible explanation since some
(policy) coordination of the BOJ and the MOF must be ensured before interventions
are carried out. For other countries, where intervention decisions and operations rest
at the same administrative body, this explanation seems far-fetched. An alternative
explanation is that actual policy makers, or their priorities, vary over time so that
in some periods, interventions are not considered at all, simply because the current
policy makers do not even put the intervention issue on the agenda. Implicitly, this
is also what has been done in Ito and Yabu (2004) and Kim and Sheen (2006) where
separate reaction functions are estimated over different time periods defined by the
person in charge of the intervention policy. In this paper, different policy makers
are not controlled for, but instead an average response by a two stage least squares
model is estimated. The results when dropping periods with zero interventions are
also reported. As an alternative, ordered probit models that explain the probability
of interventions as functions of the same determinants are also estimated.
4.1
Correlations
Equation (15) implies that if interest rate movements are primarily driven by the stabilization motive, we expect the correlation between interventions and interest rates
to be negative. Table 2 shows negative but low correlations for all three countries
indicating that purchases of foreign currency tend to occur at times when interest
rates are low. Using the non-parametric Spearman rank correlation coefficient and
computing corresponding significance levels, it is found that for Japan and Sweden,
all correlations of the level interest rate and interventions are significant at the one-
88
Essay 3. Foreign exchange market interventions as monetary policy
percent level whereas for Australia most are barely significant.8 This observation is
consistent with the view that interventions are used as a complement to the interest
rate to boost aggregate demand.
Table 2: Cross correlations of interventions and interest rates
Interest rate Australia Japan Sweden
t-5
-0,01
-0,09
-0.02
t-4
-0,01
-0,09
-0.02
t-3
-0,01
-0,08
-0.02
t-2
-0,01
-0,09
-0.02
t-1
0
-0,08
-0.02
t
0
-0,09
-0.02
t+1
0
-0,08
-0.02
t+2
0
-0,09
-0.02
t+3
0
-0,09
-0.02
t+4
0
-0,08
-0.02
t+5
0
-0,09
-0.02
Obs.
3393
3344
2815
4.2
Some VAR evidence
Another way of describing the data is to estimate a simple trivariate VAR with the
target interest rate, interventions and the nominal exchange rate. The full samples
are used for this exercise. The VAR is kept very general by including 20 lags.
For Japan, only the time period 04/01/1991-01/02/1998 is used since after 1998,
the target rate has been stuck at the zero lower bound with hardly any variation.
For Sweden, the TCW-weighted exchange rate is used; for Australia and Japan the
bilateral USD exchange rate. For Sweden, joint stationarity of the VAR necessitated
first differencing of the interest rate. All results are robust to ordering in the VAR
and the inclusion of contemporaneous controls such as the output gap, inflation and
the US federal funds rate. The results are reported in Figures 4-6 and those that
are robust across countries can be summarized as follows.
A (depreciating) shock in the exchange rate makes the authorities inclined to
intervene by buying domestic currency so as to "lean against the wind". This result
corroborates the previous findings in the literature. (See element 2,3 in the impulse
response figures.)
There appears to be some cyclicality in the way interventions occur in that
interventions are serially correlated with a two-week lag. This could probably be
8
At the magnitude of —0.03 for Australia, -0.13 for Japan and -0.26 for Sweden.
4. Empirical results
89
attributed to intervention decisions regularly taken at a certain day of the week.
(See element 2,2 in the impulse response figures.)
There does not appear to be any robust connection neither between interest
rate shocks and interventions nor between unforeseen interventions and interest rate
changes. (See elements 1,2 and 2,1 in the impulse response figures.)
Response to Cholesky One S.D. Innovations ± 2 S.E.
Res ponse of SPOTRATE to AUSCASHTARGET
Response of AUSC ASHTARGET to INT
Response of AUSCASHTARGET to SPOTRATE
.08
.08
.08
.07
.07
.07
.06
.06
.06
.05
.05
.05
.04
.04
.04
.03
.03
.03
.02
.02
.02
.01
.01
.01
.00
.00
-.01
.00
-.01
2
4
6
8
10
12
14
16
18
20
-.01
2
4
Response of INTto AUSCASHTARGET
6
8
10
12
14
16
18
20
2
Respons e of I NT to INT
60
60
50
50
50
40
40
40
30
30
30
20
20
20
10
10
10
0
0
4
6
8
10
12
14
16
18
20
Res ponse of SPOTRATE to AUSCASHTARGET
4
6
8
10
12
14
16
18
20
2
Respons e of SPOTRATE to INT
.012
.010
.010
.010
.008
.008
.008
.006
.006
.006
.004
.004
.004
.002
.002
.002
.000
.000
.000
-.002
-.002
-.002
6
8
10
12
14
16
18
20
12
14
16
18
20
2
4
6
8
10
12
14
16
4
6
8
10
12
14
16
18
20
Response of SPOTRATE to SPOTRATE
.012
4
10
-10
2
.012
2
8
0
-10
2
6
Response of INT to SPOTRATE
60
-10
4
18
20
2
4
6
8
10
12
14
Figure 4: Australia: Impulse responses to interest rate and intervention shock
16
18
20
90
Essay 3. Foreign exchange market interventions as monetary policy
R esponse to Cho lesky On e S.D. Innovati ons ± 2 S.E.
Response of JPNUNCOLL to JPNUNCOLL
Response of JPNUNCOLL to INT
Response of JPNUNCOLL to SPOTRATE
.05
.05
.05
.04
.04
.04
.03
.03
.03
.02
.02
.02
.01
.01
.01
.00
.00
.00
-.01
-.01
-.01
-.02
-.02
2
4
6
8
10
12
14
16
18
20
-.02
2
4
Response of INT to JPNUNCOLL
6
8
10
12
14
16
18
20
2
Response of INT to INT
500
500
400
400
400
300
300
300
200
200
200
100
100
100
0
0
0
-100
-100
-100
4
6
8
10
12
14
16
18
20
2
Response of SPOTRATE to JPNUNCOLL
4
6
8
10
12
14
16
18
20
2
Response of SPOTRATE to INT
1.0
1.0
0.8
0.8
0.8
0.6
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.2
0.0
0.0
0.0
-0.2
-0.2
-0.2
-0.4
2
4
6
8
10
12
14
16
18
20
8
10
12
14
16
18
20
4
6
8
10
12
14
16
18
20
Response of SPOTRATE to SPOTRATE
1.0
-0.4
6
Response of INT to SPOTRATE
500
2
4
-0.4
2
4
6
8
10
12
14
16
18
20
2
4
6
8
10
12
14
Figure 5: Japan: Impulse responses to interest rate and intervention shock
16
18
20
4. Empirical results
91
Response to Cholesky One S.D. Innovations ± 2 S.E.
Response of D(SWE REPO) to D(SWEREPO)
Response of D(SWEREPO) to INT
Response of D(SWEREPO) to SPOTRATE
.05
.05
.05
.04
.04
.04
.03
.03
.03
.02
.02
.02
.01
.01
.01
.00
.00
.00
-.01
-.01
-.01
2
4
6
8
10
12
14
16
18
20
2
4
Response of INT to D(SWEREPO)
6
8
10
12
14
16
18
20
2
Response of INT to INT
20
20
16
16
16
12
12
12
8
8
8
4
4
4
0
0
0
-4
-4
-4
4
6
8
10
12
14
16
18
20
2
Response of SPOTRATE to D(SWEREPO)
4
6
8
10
12
14
16
18
20
2
Response of SPOTRATE to INT
.6
.6
.5
.5
.5
.4
.4
.4
.3
.3
.3
.2
.2
.2
.1
.1
.1
.0
.0
.0
-.1
-.1
-.1
-.2
2
4
6
8
10
12
14
16
18
20
8
10
12
14
16
18
20
4
6
8
10
12
14
16
18
20
Response of SPOTRATE to SPOTRATE
.6
-.2
6
Response of INT to SPOTRATE
20
2
4
-.2
2
4
6
8
10
12
14
16
18
20
2
4
6
8
10
12
14
Figure 6: Sweden: Impulse responses to interest rate and intervention shock
16
18
20
92
4.3
Essay 3. Foreign exchange market interventions as monetary policy
The relation between interventions and the interest rate
An empirical counterpart to equation (15) is estimated in order to investigate the
empirical relevance of Proposition 1. To get at the possible link between interest
rate policy and interventions, we need to compute a difference between the actual
and the "optimal" target rate from a stabilization point of view, xt .
To obtain a value of the optimal interest rate policy from a stabilization point
of view, it is assumed that optimal policy can be described by the simplest possible
estimated Taylor rule. Although a simple description of optimal stabilization policy,
the Taylor rule has been found to conform with the actual interest rate setting by
the central bank and is found to be close to optimal for a wide range of macro
models. The Taylor rule in Taylor (1993) is formulated as
it = i∗t + xt
= c + αyt + β (πt − π̄ t ) + xt ,
(18)
where it = c if the output gap equals zero, yt = 0, inflation is at the target, π t − π̄ t =
0, and no other factors influence interest rate setting, xt = 0.9 For the USA during
1987-1992, Taylor suggests a target inflation rate of two percent and c = 5 consistent
with a constant real neutral rate of three percent and estimated α = 1.5 and β = 0.5.
Instead of taking these numbers for granted, equation (18) is estimated for each
country.
Equation (18) is the empirical counterpart of (10) and is used to obtain estimates
∗
of it and xt . The estimated residuals obtained from estimation of equation (18) are
interpreted as the variable xt . These residuals are used to evaluate whether the
central bank has had too tight a monetary policy, from a pure stabilization point of
view, and are used as possible determinants of interventions.
From equations (15) and (17), we know that the mean value of interventions
should be higher at times when the zero lower bound on interest rates is binding.
The fitted values (i∗t ) of the Taylor rule will define such periods. From mid 1998 and
onward, the zero lower bound binds for Japan according to i∗t , which corresponds to
the period when Japan has been said to have been caught in the "liquidity trap".
There are no such episodes for Australia and Sweden. Therefore, for Japan we have
that xt = dt + λδ1t but for Australia and Sweden, the zero lower bound never binds
so that xt = dt .
9
The industrial production trend is measured by the HP-filter for Japan and Australia, with
a smoothing parameter of 126400 recommended for monthly data. For Sweden, estimates of the
output gap are directly provided by the Riksbank.
4. Empirical results
93
Estimation of (18) for Australia 1990-2004, Japan 1986-2001 and Sweden 19932004 yields the results in Table 3 and Figures 7-9.10
Table 3:
Coefficient Australia
c
8.03
(1.39)
y
0.31
(0.45)
π − π̄
1.06
(0.71)
Adj R2
0.11
Obs
157
Taylor rule estimates
Japan
Sweden I
4.24
5.21
(0.33)
(0.36)
0.07
-0.46
(0.07)
(0.13)
1.88
0.64
(0.19)
(0.18)
0.66
0.46
170
135
Sweden II
5.48
(0.34)
0.92
(0.16)
0.37
135
Note: NW standard errors below estimates in parentheses
12
10
8
6
4
2
91 92 93 94 95 96 97 98 99 00 01 02 03
AUSCASHTARGET
AUSISTAR
Figure 7: Australia: actual and Taylor rule interest rate
10
The motivation for extending the sample backwards to 1986 for Japan is to avoid estimation
in an economic downturn and instead capture a full cycle. Exclusion of the post 2001 period is
warranted by the zero interest rate environment in Japan. The results are robust to exclusion of
data up to 1998, however.
For Sweden, we restrict the sample to 1993m1-2004m03 because of the early 1990’s crises. Since
the sign on the output gap for Sweden is perversely negative, this variable is excluded. If included,
however, the final results remain unchanged.
94
Essay 3. Foreign exchange market interventions as monetary policy
10
8
6
4
2
0
-2
91 92 93 94 95 96 97 98 99 00 01 02 03
JPNUNCOLL
JPNISTAR
Figure 8: Japan: actual and Taylor rule interest rate
11
10
9
8
7
6
5
4
3
2
93
94
95
96
97
98
SWEREPO
99
00
01
02
03
SWEISTAR
Figure 9: Sweden: actual and Taylor rule interest rate
4. Empirical results
95
Having a measure of xt for all three countries, equation (15) is estimated by
regressing monthly aggregated interventions on the estimated monthly Taylor rule
residuals, xt , and the deviation of the actual interest rate from its mean throughout
the sample period, it − ı̄.11 We have controlled for the endogeneity of the interest
rate and x using instruments. The instruments are xt−1 , the foreign interest rate
and a money supply indicator.12
Table 4 displays the estimation results using two stage least squares for different
specifications, with and without the xt term. Furthermore, recognizing the many
observations of no interventions at all, the third column for all countries reports the
results when excluding all zero-intervention periods. The results in this column can
be said to reflect the determinants of interventions given that the authorities are to
decide on an optimal non-zero intervention amount. The signs of the estimates are
as expected in all cases. Australia, Japan and Sweden have intervened more when
interest rates have been higher than suggested by the simple Taylor rule. Japan
and Sweden have intervened more heavily when the interest rate has been below
its mean over the period for all specifications, except the very short subsample for
Sweden. For Australia, the result is of the same sign but insignificant. We proxy
e
= ∆zt+1 . This
the expected future interventions by the actual interventions, ∆zt+1
assumes that when the authorities decide on intervention today, they know the size
of the interventions tomorrow. Or, equivalently, the authorities set up a plan of
interventions that span at least this month and the next. The estimated parameter
for future interventions is positive and statistically significant across all countries
and specifications.
As can be seen in Figures 1-3, many periods are characterized by no interventions
at all. As an alternative, an ordered probit model is estimated where the dependent
indicator variable is defined as ∆ztI = 1 if ∆zt > 0, ∆ztI = 0 if ∆zt = 0 and
∆ztI = −1 if ∆zt < 0. This ordered probit model estimation is more appropriate if
some fixed cost of intervention is assumed so that interventions only occur if a loss
threshold is reached.
The results in Table 5 indicate that Australia has been more inclined to intervene
by selling domestic currency when interest rate policy has been too contractionary
according to the Taylor rule. The results for Japan and Sweden are of the same
sign, but insignificant. Furthermore, both Sweden and Japan have intervened more
frequently when interest rates have been lower than the mean throughout the period.
11
For Australia, the mean of the target interest rate (ı̄) is 8.0, for Japan 4.2, and for Sweden
5.5 percent.
12
Since interventions are sterilized, they should not be correlated with money supply and therefore constitute a suitable instrument for the target interest rate.
Table 4: 2SLS estimation of equation (13)
Japan
Sweden
zt 6= 0
Incl. x
Excl. x
zt 6= 0 Incl. x Excl. x
zt 6= 0
3.6
2095.3*** 2044.7*** 5781.4*** -49.4*
-50.1* -482.0**
(76.9)
(745.7)
(769.7)
(1946.4)
(29.2)
(26.2)
(219.0)
-96.2
-1120.0** -1210.1** -2783.6** -115.4* -45.0*
-153.4
(62.7)
(558.2)
(538.5)
(1098.9)
(61.1)
(26.7)
(94.0)
264.5*** 1063.2**
na
6925.4**
92.8*
na
187.7*
(85.7)
(541.4)
na
(2714.2)
(53.1)
na
(108.3)
0.36***
0.36**
0.38***
0.29*
0.48** 0.33*** 0.47***
(0.10)
(0.15)
(0.14)
(0.17)
(0.19)
(0.12)
(0.16)
0.30
0.19
0.19
0.33
0.26
0.19
0.26
104
154
155
63
133
133
27
Note1: NW standard errors below estimates in parentheses
Note2: Instruments are lagged x, tcw-interest rate for SWE and FFR rate and real M1 for AUS and JPN
Australia
Incl. x Excl. x
c
68.9
25.9
(50.8)
(48.7)
i i
-67.9
-19.6
(45.4)
(34.0)
x
130.5**
na
(51.2)
na
zt+1 0.42*** 0.50***
(0.09)
(0.11)
Adj R2
0.27
0.24
Obs
155
155
96
Essay 3. Foreign exchange market interventions as monetary policy
Note: Threshold terms left unreported but available upon request
Table 5: Ordered probit estimation of equation (13)
Australia
Japan
Sweden
Incl. x Excl. x Incl. x Excl. x Incl. x Excl. x
i i
-0.00
0.06
-0.11*
-0.09* -0.26*** -0.14**
(0.08)
(0.07)
(0.06)
(0.06)
(0.10)
(0.06)
x
0.16**
na
0.10
na
0.18
na
(0.08)
na
(0.08)
na
(0.12)
na
zt+1
1.11*** 1.18*** 1.71*** 1.75*** 0.82*** 0.87***
(0.14)
(0.14)
(0.22)
(0.21)
(0.26)
(0.25)
Pseudo R2
0.26
0.25
0.35
0.34
0.16
0.15
Obs
155
155
155
155
134
134
4. Empirical results
97
98
4.4
Essay 3. Foreign exchange market interventions as monetary policy
The relation between interventions and fundamentals
In order to investigate the empirical relevance of Proposition 2, an empirical counterpart to equation (17) is estimated. Equation (17) suggests that intervention
should be decreasing with expected inflation and the real exchange rate. The real
exchange rate is measured as the bilateral CPI based real exchange rate between
Australia/Japan and the USA and the TCW-weighted exchange rate and CPI for
Sweden. The expected inflation rate in the next period is modeled by assuming that
the central bank has a naive forecast of future inflation, so that π et+1 = π t .
Regressing monthly aggregated intervention amounts on inflation, the real exchange rate and xt yield the results in Table 6 for the same set of specification
alterations as in the estimation of equation (15). The Reserve Bank of Australia
has intervened more heavily at times when the real exchange rate has been low, i.e.
when it has been overvalued and when interest rate policy has been too restrictive,
as captured by the positive coefficient on x. Japan and Sweden have intervened
more heavily when inflation has been low. Given that interventions take place, all
significant signs except the positive sign on the real exchange rate for Japan are as
expected.
Ordered probit models are also estimated. The results in Table 7 support the
findings that the interventions by Reserve Bank of Australia have been carried out
at times of an overvalued exchange rate. The interventions by the Bank of Japan
and the Riksbank have occurred in times of low inflation. Japan also appears to
have intervened when the exchange rate has been overvalued. Except the significant
positive sign on inflation for Australia in the specification including x, all results are
of the predicted sign.
Note1: NW standard errors below estimates in parentheses
Note2: Instruments are lagged x, and q
Table 6: 2SLS estimation of equation (15)
Australia
Japan
Incl. x
Excl. x
zt 6= 0
Incl. x
Excl. x
zt 6= 0
c
293.2*
243.2*
292.9
-9063.8
-9913.7
-78491.5*
(153.9)
(129.1)
(211.9)
(20362.3)
(20339.9)
(40209.0)
93.3
59.6
182.3
-1169.8*** -1377.5*** -4939.2***
(91.4)
(79.1)
(199.1)
(359.2)
(510.7)
(1389.1)
q
-736.3** -649.0** -1009.3
2465.4
2659.8
18672.7**
(372.4)
(302.5)
(612.8)
(4465.2)
(4455.8)
(8927.1)
x
110.4***
na
205.7***
405.3
na
5636.7*
(41.0)
na
(469.3)
(412.7)
na
(3083.1)
zt+1
0.41*** 0.48***
0.36**
0.38**
0.39***
0.26
(0.07)
(0.10)
(0.08)
(0.15)
(0.15)
(0.17)
Adj R2
0.30
0.26
0.33
0.19
0.20
0.32
Obs
155
155
104
154
154
63
Sweden
Incl. x Excl. x
zt 6= 0
-4276.6 -3420.5
4104.2
(2835.8) (2080.5) (11290.5)
-65.8*
-75.2*
-107.1
(37.1)
(45.2)
(75.4)
1101.9
886.7
-1071.5
(730.8) (539.9) (2913.3)
10.5
na
12.9
(17.7)
na
(51.7)
0.52***
0.29**
0.53***
(0.19)
(0.12)
(0.16)
0.29
0.21
0.26
133
134
27
4. Empirical results
99
Note: Threshold terms left unreported but available upon request
Table 7: Ordered probit estimation of equation (15)
Australia
Japan
Sweden
Incl. x Excl. x Incl. x
Excl. x
Incl. x
Excl. x
0.30*
0.20
-0.30** -0.32*** -0.24*** -0.24***
(0.17)
(0.16)
(0.12)
(0.12)
(0.09)
(0.09)
q
-2.10*** -1.71** -3.05*** -3.00***
0.24
1.65
(0.77)
(0.75)
(0.95)
(0.94)
(2.75)
(1.90)
x
0.21***
na
0.04
na
-0.07
na
(0.08)
na
(0.08)
na
(0.10)
na
zt+1
1.03*** 1.14*** 1.59*** 1.59*** 0.81*** 0.82***
(0.15)
(0.14)
(0.22)
(0.22)
(0.26)
(0.26)
Pseudo R2
0.29
0.26
0.38
0.38
0.16
0.16
Obs
155
155
155
155
134
134
100
Essay 3. Foreign exchange market interventions as monetary policy
5. Conclusions
5
101
Conclusions
This paper sets up a simple model for interventions and interest rate setting, assuming that the policy maker cares about deviations in inflation from a target level.
Under a quadratic cost of interest rate variation and interventions, the policy maker
should use a combination of interest rate adjustments and interventions to stabilize
the economy. According to the model, interventions (purchases of foreign currency)
should be negatively correlated with interest rate deviations from the natural level
but positively correlated with interest rate deviations pertaining to non-stabilizing
motives or a binding zero lower bound. The model also predicts that interventions
will be decreasing with inflation expectations and (depreciation of) the real exchange
rate and increasing with expected future interventions.
Testing the model on intervention data for the Bank of Japan, the Reserve Bank
of Australia and the Swedish Riksbank, it is shown that interventions are in general
negatively correlated with the interest rate. All countries also show a "leaning
against the wind" behavior in intervention policy.
Closely following the theoretical model, two sets of regressions are presented using both a two stage least squares model and an alternative ordered probit approach.
All countries appear to have intervened more when interest rate policy has been too
contractionary according to the Taylor rule. Japan and Sweden have intervened
more when interest rates and inflation have been low. Australia has intervened
more when the exchange rate has been overvalued.
Overall, the predictions of the model are supported in most dimensions, indicating that interventions have been used in a way consistent with monetary policy
considerations.
102
References
References
Aguilar, J., and S. Nydahl (2000): “Central Bank Intervention and Exchange
Rates: The Case of Sweden,” Journal of International Financial Markets, Institutions and Money, 10, 303—322.
Almekinders, G. J., and S. C. W. Eijffinger (1996): “A Friction Model
of Daily Bundesbank and Federal Reserve Intervention,” Journal of Banking &
Finance, 20, 1365—1380.
Bäckström, U. (June 14 2001): “Currency Interventions Cannot Be Ruled Out,”
Riksbank Press Release.
Bernal, O. (2006): “Do Interactions Between Political Authorities and Central
Banks Influence Fx Interventions? Evidence from Japan,” Working Paper 06-03,
DULBEA, Brussels.
Borg, A., and L. Heikensten (2002): “The Riksbank’s Foreign Exchange Interventions Preparations, Decision and Communication,” Discussion Paper 2002:1,
Sveriges Riksbank.
Borio, C., and P. Lowe (2004): “Securing Sustainable Price Stability: Should
Credit Come Back from the Wilderness?,” Working Paper 157, Bank for International Settlements.
Clarida, R., J. Gali, and M. Gertler (1999): “The Science of Monetary Policy:
A New Keynesian Perspective,” Journal of Economic Literature, 37, 1661—1707.
(2000): “Monetary Policy Rules and Macroeconomic Stability,” Quarterly
Journal of Economics, 115, 147—180.
Dominguez, K. M., and J. A. Frankel (1993): “Does Foreign Exchange Intervention Matter? The Portfolio Effect,” The American Economic Review, 83,
1356—1369.
Humpage, O. F., and J. Ragnartz (2006): “Swedish Interventions and the Krona
Float, 1993-2002,” Working Paper 192, Sveriges Riksbank.
Ito, T., and T. Yabu (2004): “What Promotes Japan to Intervene in the Forex
Market? A New Approach to a Reaction Function,” Discussion Paper Working
Paper 10456, NBER.
References
103
Kaminsky, G. L., and K. K. Lewis (1996): “Does Foreign Exchange Intervention
Signal Future Monetary Policy?,” Journal of Monetary Economics, 37, 285—312.
Kim, S. (2003): “Monetary Policy, Foreign Exchange Interventions, and the Exchange Rate in a Unifying Framework,” Journal of International Economics, 60,
355—386.
Kim, S.-K., and J. Sheen (2002): “The Determinants of Foreign Exchange Intervention by Central Banks: Evidence from Australia,” Journal of International
Money and Finance, 21, 619—649.
(2006): “Interventions in the Yen-Dollar Spot Market: A Story of Price,
Volatility and Volume,” Journal of Banking & Finance, 30, 3191—3214.
Macfarlane, I. J. (1993): “The Exchange Rate, Monetary Policy and Intervention,” Bulletin December 1993, Reserve Bank of Australia.
McCallum, B. T. (2000): “Theoretical Analysis Regarding a Zero Lower Bound
on Nominal Interest Rates,” Jornal of Money, Credit and Banking, 32, 870—904.
Mussa, M. L. (1981): “The Role of Official Intervention,” Discussion Paper Group
of Thirty Occasional Papers, no. 6, New York: Group of Thirty.
Neely, C. J. (2005): “An Analysis of Recent Studies of the Effect of Freign Exchange Intervention,” Federal Reserve Bank of St. Louis Review, 87, 685—717.
Nishimura, K. G., and M. Saito (2003): “On Alternatives to Aggresive Demand
Policies to Revitalize the Japanese Economy,” Asian Economic Papers, 2, 87—126.
Rosett, R. N. (1959): “A Statistical Model of Friction in Economics,” Econometrica, 26, 263—267.
Rudebusch, G. D. (2002): “Term Structure Evidence on Interest Rate Smoothing
and Monetary Policy Intertia,” Journal of Monetary Economics, 49, 1161—1187.
Sarno, L., and M. P. Taylor (2001): “Official Intervention in the Foreign Exchange Market: Is It Effective, and, If so, How Does It Work?,” Journal of Economic Literature, 39, 839—868.
(2002): The Economics of Exchange Rates. Cambridge University Press,
Cambridge.
Söderlind, P., U. Söderström, and A. Vredin (2005): “Dynamic Taylor Rules
and the Predictability of Interest Rates,” Macroeconomic Dynamics, 9, 412—428.
104
References
Svensson, L. E. O. (2000): “Open-Economy Inflation Targeting,” Journal of International Economics, 50, 155—183.
(2001): “The Zero Bound in an Open Economy: A Foolproof Way of
Escaping from a Liquidity Trap,” Monetary and Economic Studies, pp. 277—322.
Taylor, J. B. (1993): “Discretion versus Policy Rules in Practice,” CarnegieRochester Conference Series on Public Policy, 39, 195—214.
Welz, P., and P. Österholm (2005): “Interest Rate Smoothing versus Serially
Correlated Errors in Taylor Rules: Testing the Tests,” Working Paper 2005:14,
Department of Economics, Uppsala University.
Woodford, M. (2003): “Optimal Interest-Rate Smoothing,” Review of Economic
Studies, 70, 861—886.
Essay
4
How to evaluate proxies of
macroeconomic uncertainty
1
Introduction
Uncertainty constitutes a crucial element in modern macroeconomic theories and
policy analysis. Since uncertainty cannot be directly observed, we must use proxies
in economic applications. It is therefore surprising that very few studies have taken
a critical look at available proxies of macroeconomic uncertainty to discern which
are more appropriate as measures of uncertainty. In the few studies that exist, some
preferred proxy is usually assumed to be the correct measure of uncertainty, and
the applicability of other proxies is evaluated against this preferred proxy. Such a
procedure requires that we know which is the correct measure of uncertainty, at
least ex post, which is something we really cannot know with any certainty.
In this paper, we offer an alternative narrative methodology that does not take
a stand, ex ante, on a preferred proxy. Instead, we subject all available proxies to
a test where we study if they react as expected to exogenous shocks to uncertainty.
Moreover, we will argue that although different proxies of uncertainty capture different types of macroeconomic uncertainty, they should be positively correlated under
reasonable assumptions. We empirically investigate whether this is the case. Moreover, given that uncertainty could vary substantially across different variables, we
ask the question whether different types of uncertainty share a common factor.
The most commonly used proxy of uncertainty in applied work is some proxy of
stock market volatility (e.g. Romer (1990) and Hassler (1996)). This proxy is usually
employed without due motivation or reference to why stock market volatility would
be appropriate. In this paper, we also consider uncertainty proxies derived from
surveys, targeted both at professional forecasters and the general public. These
105
106
Essay 4. How to evaluate proxies of macroeconomic uncertainty
proxies are disagreement proxies, as they reflect the disparity of individual point
forecasts. The ability of such disagreement proxies to capture aggregate uncertainty
has been discussed in some papers (Zarnowitz and Lambros (1987) and Giordani
and Söderlind (2003) inter alia). Disagreement proxies have been extensively used
in the previous literature; see e.g. Bomberger (1996) and Sepulveda (2003) who
also provide further references. Finally, we also consider probability forecast proxies
derived from professional forecasters who assign probabilities to interval outcomes
of key variables. From a theoretical point of view, such a type of proxy is appealing
since it relies on an approximation of the entire probability distribution of forecasts
to construct the uncertainty proxy.
We also try to evaluate the effect of uncertainty on aggregate consumption and
residential investment, which could also provide some further evidence on the applicability of available proxies, and study the co-movement of uncertainty proxies
with the business cycle.
The results can be summarized as follows. The (implied) volatility proxy behaves
as expected since it is shown that it increases to exogenous events such as terrorist
attacks and outbreaks of war, and decreases at presidential election outcome dates.
The disagreement proxies also increase in response to conflict and financial crises
events. Surprisingly, the probability forecast proxies do not react in any systematic way to these events. This finding is of special importance since the probability
forecast proxies have been posited as "true" uncertainty and used to evaluate other
proxies (e.g. in Zarnowitz and Lambros (1987)). Such a supposition is dubious in
the light of our results. The correlation table of all available proxies indicates that
disagreement proxies are positively correlated, regardless of the targeted variable.
Furthermore, the correlations give some indication of volatility and probability forecast proxies are co-moving. Using factor analysis, we only find one common factor
across different proxies of uncertainty. This could be interpreted as there only being
one fundamental factor of uncertainty that shows up in most proxies. When we add
proxies of uncertainty to standard macroeconomic applications where uncertainty
is supposed to be of importance, we find all but the probability forecast proxies to
be of importance. This could be taken as further evidence of the inability of the
probability forecast proxies to pick up uncertainty. Finally, we look at the evolution
of proxies and the business cycle over time. We find that uncertainty seems to be
higher the further we are from the normal level of real activity in the economy.
The paper is organized as follows. In section 2, we introduce the concept of
uncertainty within a simple model. The model is used to derive some properties
of uncertainty used in the subsequent analysis. Section 3 describes the different
2. A model motivation
107
types of proxies considered. Section 4 attempts to identify suitable uncertainty
proxies based on some narrative evidence. Section 5 uses factor analysis to extract
common factors across different proxies and section 6 uses proxies of uncertainty in
standard macroeconomic applications and examines how uncertainty co-moves with
the business cycle. Section 7 concludes.
2
A model motivation
The aim of this section is to give some structure to the way we think about macroeconomic uncertainty. We will discuss under what circumstances different types
of uncertainty are related and under what circumstances it is appropriate to talk
about general macroeconomic uncertainty. A simple VAR model will be presented
to illustrate how uncertainty in different variables will co-move under reasonable
assumptions. For each variable, uncertainty is defined as its expected variance.
Consider a model economy that can be described by a trivariate VAR in GDP
growth (y), inflation (π) and interest rates (i). The first equation is an aggregate
demand relation; the second can be said to represent supply and the third describes
monetary policy. This model can be compactly written in matrix form as
AXt+1 = C + B(L)Xt + εt+1 ,
(1)
i0
i0
h
h
with Xt = yt π t it , εt = ε1,t ε2,t ε3,t . εt are interpreted as the structural, unobserved, shocks to the economy.
Further, make the standard assumption that
⎡ 2
⎤
σ 1,t+1
0
0
³
´
0
⎢
⎥
Covt (εt+1 ) = Et εt+1 εt+1 = ⎣ 0
0 ⎦,
σ 22,t+1
0
0
σ 23,t+1
(2)
indicating that the structural shocks
i0 other and have condih are orthogonal to each
tional expected variances σ 2t+1 = σ 21,t+1 σ 22,t+1 σ 23,t+1 . Note that we allow for
structural variances to be time-variant. Rewrite equation (1) in its reduced form by
pre-multiplying by A−1 . We then get
A−1 AXt+1 = A−1 C + A−1 B(L)Xt + A−1 εt+1
Xt+1 = D + G (L) Xt + et+1
where et+1 are the reduced form residuals obtained by estimation.
(3)
108
Essay 4. How to evaluate proxies of macroeconomic uncertainty
These observed residuals are linear combinations of the structural shocks εt+1 . Redefine A−1 = F and write the residuals explicitly as
(4)
et+1 = F εt+1 .
The coefficients in F capture the structural contemporaneous relations between the
variables in the VAR and the structural shocks. In general, all elements of F will
be non-zero so that the variance covariance matrix of the reduced form residuals
Ωt+1 6= 0 for all elements. The general expression for Ωt+1 becomes
³
´
³
´
0
0
Ωt+1 = Et et+1 et+1 = Et F εt+1 εt+1 F 0 .
(5)
2 2
2 2
2 2
V art (yt+1 ) = f11
σ 1,t+1 + f12
σ 2,t+1 + f13
σ 3,t+1 ,
(6)
The variances of the variables, the diagonal elements in Ωt+1 , can be expanded as
V art (π t+1 ) =
2 2
f21
σ 1,t+1
V art (it+1 ) =
2 2
f31
σ 1,t+1
+
2 2
f22
σ 2,t+1
+
2 2
f32
σ 2,t+1
+
2 2
f23
σ 3,t+1 ,
(7)
+
2 2
f33
σ 3,t+1 ,
(8)
where we see that the variance of each variable is a linear combination of all structural shock variances, σ2t+1 . This implies that a shock to any element in σ 2t+1 will
spread through the economy and affect uncertainty in all variables. This occurs
because of the contemporaneous relations through the F -matrix.
Proposition 1 All proxies of uncertainty are expected to move in the same direction
to large exogenous shocks to uncertainty.
Proposition 1 forms the basis for the narrative approach in section 4.1 when
evaluating available proxies of uncertainty.
In order to make statements about the possible correlations between V art (yt+1 ),
V art (π t+1 ), and V art (it+1 ), we need to consider the correlations of σ 2t+1 . According
to expressions (6)-(8), with positive correlations between σ 2t+1 , the variable variances V art (yt+1 ), V art (π t+1 ), and V art (it+1 ) will also be positively correlated. In
fact, even if σ 2t+1 are uncorrelated, we will still have positive correlations among
V art (yt+1 ), V art (π t+1 ), and V art (it+1 ) provided that the off-diagonal elements in F
differ from zero. Imagine that uncertainty about the demand shock, σ21,t+1 , suddenly
increases and σ 22,t+1 and σ 23,t+1 are unchanged. Since all expected variable variances
contain σ 21,t+1 , the correlations should be positive.1 2
1
However, the correlations might be very small, but nevertheless positive. The size of the
relation depends on the coefficients in F and the relative size of structural shock variances.
2
Alternatively, if we assume the Choleski decomposition with f12 = f13 = f23 = 0, as is
3. Uncertainty proxies
109
This result is summarized in a second proposition.
Proposition 2 If structural shock variances, σ 2t+1 , are non-negatively correlated
and at least one structural shock has contemporaneous effects on all variables in the
economy, uncertainty about all variables will be positively correlated.
In section 4.2, we study the correlation table of all available proxies to see whether
the result in Proposition 2 holds. This proposition indicates that the variance of
any relevant macroeconomic variable should in theory be a relevant proxy of macroeconomic uncertainty.
With several structural shocks variances, σ 2t+1 , the model suggests that we could
have as many underlying factors of uncertainty as the number of variables. To
investigate how many factors that drive uncertainty, we will perform a factor analysis
on the expected macroeconomic variable variances in section 5.
3
Uncertainty proxies
Both expected levels and expected distributions are unobservable in the sense that
they are only available in the minds of the agents of the economy. While we can
usually observe the outcome of a variable to evaluate level expectations, the expected distributions (i.e. uncertainty) have the disadvantage that there is no ex post
observation of the actual distribution. We exclude more complex methods of estimating the whole expected distribution, and focus on easily interpreted proxies of
uncertainty that can be expressed by a single number, i.e. their expected variances.3
The data are in monthly or quarterly frequency for the US from 1980 to 2005. For
several proxies, we cannot find data as far back as 1980, which means that we must
settle for what can be obtained. The proxies connected to the financial markets,
i.e. the volatility proxies, are available for higher frequencies but for comparison
purposes, we also use the monthly and quarterly versions of these proxies.
The acronyms are constructed according to the following logic. The first letter of the acronym denotes the type of proxy method: "D" for disagreement, "P"
for probability forecast, and "V" for volatility. For the disagreement proxies we
have two additional subgroups, proxies belonging to the quantitative Survey of Professional Forecasters and proxies belonging to the qualitative Michigan Consumer
Survey. Thus, after "D", the next letter denotes the subgroup: "S" for the Survey
of Professional Forecasters and "M" for the Michigan Consumer Survey. The last
commonly done in the monetary policy literature, then all variables will share the σ 22,t+1 component
and there will still be positive correlation.
3
The interested reader can consult Aguilar and Hördahl (1999) for a description on how to
derive the full distribution of expectations through option pricing.
110
Essay 4. How to evaluate proxies of macroeconomic uncertainty
letter for all acronyms denotes the variable connected to each specific proxy. Table 1 illustrates the logic of the acronym constructions. See Tables 2 and 3 for a
description of data and data handling.
Table 1: Construction of acronyms for uncertainty proxies
First letter
D (Disagreement)
Second letter
S (Survey of Prof. Forecasters)
M (Michigan Consumer Survey)
V (Volatility)
O (Implied, based on Option prices)
H (Historical)
P (Probability forecast) Y (Real GDP % change)
I (Inflation)
Third letter
7 variables, see Table 3
8 variables, see Table 2
See Table 2
See Table 2
See Table 3
See Table 3
Table 2: Acronyms and descriptions of uncertainty proxies
Acronym
Description
Sample
DMB
Business conditions during coming 12 months
1980m1-2005m6
DMF
Financial situation in 12 months
1980m1-2005m6
DMH
Buying conditions for houses
1980m1-2005m6
DMR
Expected change in interest rates the coming 12 months
1980m1-2005m6
DML
Buying conditions for large goods
1980m1-2005m6
DMD
Expected change in real family income the next years
1980m1-2005m6
DMU
Expected change in unemployment the coming 12 months 1980m1-2005m6
DMV
Buying conditions for vehicles
1980m1-2005m6
VH
Historical volatility, rolling 1-year standard deviation
1980m1-2005m12
VO
Implied volatility, monthly averages on daily OEX index 1986m1-2005m12
Note: Proxies derived from the Michigan Consumer Survey and Volatilities, monthly data
3.1
Stock market volatility proxies
A commonly used proxy for uncertainty is stock market volatility, which describes
the variability of stock market returns. The typical volatility proxy for a stock
market is the standard deviation, or variance, of stock index returns. Stock market
volatility is an example of a market based proxy of uncertainty.
We use two different stock market volatilities, historical (VH) and implied volatilities (VO). The historical volatility is a moving standard deviation for a certain time
span. In this paper, we have included the monthly and quarterly frequencies for historical volatility of the S&P 500 index during the last 12 months, based on daily
index returns. We have also included the implied stock market volatility, derived
from prices of stock index options, in the form of an implied volatility index known
3. Uncertainty proxies
111
Table 3: Acronyms and descriptions of uncertainty proxies, cont’d
Acronym
Description
DSP
Expected %-change in corporate profits 4 quarters ahead
DSI
Expected CPI-inflation 4 quarters ahead
DSH
Expected %-change in new housing starts 4 quarters ahead
DSC
Expected %-change in real consumption 4 quarters ahead
DSY
Expected %-change in real GDP 4 quarters ahead
DSR
Expected T-Bill interest rate 4 quarters ahead
DSU
Expected unemployment rate 4 quarters ahead
PY
Probability distribution for changes in real GDP next year, sa
PI
Probability distribution for inflation next year, sa
Sample
1980q1-2005q4
1981q3-2005q4
1980q1-2005q4
1981q3-2005q4
1981q3-2005q4
1981q3-2005q4
1980q1-2005q4
1992q1-2005q4
1992q1-2005q4
Note: Proxies derived from the Survey of Professional Forecasters, quarterly data
as the VIX.4 Implied volatility can therefore be considered to be a more forward
looking proxy than historical volatility.
3.2
Disagreement proxies
Another type of proxy for uncertainty is the disagreement proxy as derived from survey responses. This proxy typically observes the cross-sectional standard deviation
across individual point forecasts. It is important to recognize that this is a simple proxy of uncertainty as it only reflects the average disparity of the individuals’
expected means of the distribution.
The disagreement proxies are of two different types. The first type consists of
disagreement estimates based on quantitative point forecasts. These proxies all come
from the Survey of Professional Forecasters and include inflation (DSI), corporate
profits (DSP), housing starts (DSH), real GDP (DSY), real consumption (DSC),
T-bill (DSR), and the unemployment rate (DSU).
The second type of disagreement proxies is based on qualitative survey data. The
data are presented as proportions of respondents who believe that a variable will go
up, down, or stay the same.5 To derive proxies of uncertainty we follow Lyhagen
(2001). By letting the proportions be parameters in a multinomial distribution,
we can calculate a variance to serve as a proxy of uncertainty. Let Pu denote
the proportion of respondents who answer "Up", and Pd denote those who answer
"Down". The sum of variances of these proportions becomes (1−Pu )Pu +(1−Pd )Pd .
This variance proxy implies that if one of these proportions is equal to unity, there
is no uncertainty, and if both proportions equal 0.5, uncertainty is at its maximum.
4
5
Supplied by the Chicago Board Options Exchange (CBOE).
Or equivalently: "better", "same" or "worse".
112
Essay 4. How to evaluate proxies of macroeconomic uncertainty
The qualitative proxies of disagreement used in this paper are all derived from
the Michigan Consumer Survey and include business conditions (DMB), financial
situation (DMF), buying conditions for houses (DMH), borrowing rate (DMR), buying conditions for large goods (DML), real family income (DMD), unemployment
rate (DMU), and buying conditions for vehicles (DMV).
3.3
Probability forecast proxies
The theoretically most appealing type of uncertainty proxy in this paper is what
Sepulveda (2003) refers to as the probability forecast proxy. It is appealing because
not only does it take into account disagreement but also the average individual
forecast distribution. The Survey of Professional Forecasters includes a section in
its questionnaire where the respondents are asked to state their expected probability
over intervals of GDP growth and inflation for the next year. This yields a histogram
representation of each forecaster’s expected distribution at a certain point in time,
making it possible to derive an average distribution of expectations.
In deriving the probability forecast proxies, we follow Sepulveda (2003) as we
first calculate each forecaster’s mean and standard deviation of the expectations at
t. Then, we simply take the average of the mean and the standard deviation, across
all forecasters, to obtain both the average mean and the average standard deviation.
Our derivation is somewhat different from what is used in Sepulveda (2003), as
we acknowledge the seasonality in the series and use a seasonal dummy approach to
adjust for this pattern. The reason for seasonality is the declining forecast horizon as
the forecaster approaches the forecast period. In other words, the forecaster obtains
more and more information as he or she approaches the forecast period starting date
and this is taken into account in deriving the proxy.
We include the derived expected variance of both real GDP growth and inflation
(PY and PI).
4
Do uncertainty proxies measure uncertainty?
As stated in Proposition 1, we expect appropriate proxies to behave as expected
to exogenous shocks to uncertainty. Furthermore, referring to Proposition 2, we
have reasons to believe that uncertainty in all macroeconomic variables should be
positively correlated.
4. Do uncertainty proxies measure uncertainty?
4.1
113
Narratives
Our identification procedure for uncertainty proxies relies on the idea that an appropriate uncertainty proxy should react to an unforeseen event that is considered to
either increase or decrease uncertainty exogenously. The advantage of this approach
to what has previously been done is that we need not assume that e.g. probability
forecast proxies are the true uncertainty measures and proceed to evaluate other
proxies based on their affinity with this type of proxy. Instead, we assume that
uncertainty proxies should increase with some unforeseen and exogenous events at
certain dates, if they cannot be said to measure uncertainty well. This narrative
approach relies on identifying dates, corresponding to months or quarters, and evaluating if the event leads to a higher or lower level of the proxy.6
For comparison purposes, we restrict our attention to the time period 1987-2005
for which all but the probability forecast proxies are available. The choice of dates
is subjective by nature, but we have carefully applied the following criteria. First,
the event should be such that when it occurs, it more or less instantaneously creates
a change of uncertainty in a particular direction. Second, it should be exogenous to
the variable subjected to the test. We only want to include events that would unambiguously change uncertainty and conform with our two criteria. We construct
three sets of dummy variables. One is a dummy variable for military conflicts,
CONF LICT , that includes two terrorist attacks and one military conflict. These
episodes are also included in Chen and Siems (2004), where the authors study how
returns of stocks have evolved during periods of military conflicts. One is a financial dummy, F INCRISIS, that includes two financial crises, and one is a dummy
for regular US presidential elections, ELECT ION, that includes five events. The
episodes and dates are displayed in Table 4.
To most people, the horrifying terrorist attacks on September 11 2001 should
constitute an event that must instantaneously have raised uncertainty. Bartram,
Brown, and Hund (2005) find evidence of an increase in the systematic component
of risk and Bloom (2006) documents a dramatic increase in the number of times the
wording "uncertainty" was used in the FOMC meetings right after the 9/11 attacks.
These findings support the idea that uncertainty increased sharply with the 9/11
terrorist attacks.
6
In this paper, we use an identification strategy by choosing dates that should represent shocks
to uncertainty. An alternative, but much more difficult, strategy would be to measure the arrival
rate and signal quality of incoming information. The more information we acquire and the better
the information is, the less uncertain we are. Imagine a person reporting a probability forecast
distribution of the weather tomorrow and then moving into a room without windows and no contact
with the outside world. After a few days, a new probability forecast distribution is reported.
Supposedly, the mean is unchanged but the variance of the distribution has increased!
114
Essay 4. How to evaluate proxies of macroeconomic uncertainty
Table 4: Periods of shocks to uncertainty
CONF LICT
F INCRISIS
Oct 19 1987
Black Monday
ELECT ION
Nov 8 1988
Aug 2 1990
Iraq invasion
Nov 3 1992
Feb 26 1993 WTC bombing
Nov 5 1996
March 10 2000 Dot Com crash
Jan 6 2001
Sep 11 2001
Terror attacks
Nov 2 2004
The financial crisis episodes in October 1987 and March 2000 are endogenous
to the volatility proxies and therefore only included as controls in these regressions.
No such problem should exist for the other proxies and we expect that all proxies
should increase with these events as people were likely to become uncertain about
the future performance of the economy, given such large disruptions of the stock
market.7
The presidential election outcomes are different from the other episodes. Although the presidential elections occur on regular dates, the outcome is unknown
beforehand. When the outcome of the election becomes known, this implies a reduction of uncertainty, thus satisfying our first criterion of selection.8 Furthermore, the
outcomes of presidential elections can be said to comply with our second criterion,
exogeneity, since uncertainty does not affect the date of resolved uncertainty.
To test whether proxies of uncertainty have reacted as expected to these types of
events, we run the following regression for each of the considered uncertainty proxies
(U Pt ),
U Pt = c +β LAG UPt−1 + β C CONF LICT +β F F INCRISIS +β E ELECT ION +εt ,
(9)
where one lag of the proxy is included to purge the series of a predictable autoregressive component in the evolution of proxies.9 We expect β C and β F to be positive
7
As expressed by Fed Governor Phillips (1997): "Such episodes [stock market crashes] are
generally accompanied by dramatic increases in uncertainty".
8
Naturally, election polls might indicate how uncertain the outcome is. This issue is ignored
in this analysis and the negative shocks to uncertainty at the resolve of uncertainty are treated
equally across elections.
9
For quarterly measures, the dummies are lagged one period to ensure that the effect of the
event at the time of the survey is picked up.
4. Do uncertainty proxies measure uncertainty?
115
and β E to be negative. The estimated parameters for the dummy variables will
simply tell us if the unpredictable component in the proxy is significantly different
from non-dummy periods.
Table 5 indicates that we seem to have been quite successful in identifying dates
that are supposed to increase uncertainty, CON F LICT and F INCRISIS. The
presidential election dummy, on the other hand, does not come in significant in any of
the regressions. However, if looking at daily data of VO (implied volatility) in Figure
1, it is clear that for all elections except in the year 2000, the volatility decreased the
day after the election. For the 2000 election, the volatility increased the day after
the election, since the election outcome was not known at that time! However, the
day after the decisive meeting in Congress on January 6 2001, volatility decreased.
Further, VO exhibits a highly significant and positive sign on CONF LICT . These
findings support the use of VO as a suitable proxy of uncertainty.
Table 5: Dummy regression results
UP
CONF LICT
DMB
-**
DMF
+
DMD
+
DMU
+
DML
+*
DMV
+*
DMH
+*
DMR
+
F INCRISIS
+***
+
+
+**
+***
+
-
ELECT ION
+
+
+
+
Old R2 New R2 Obs
0.76
0.77
222
0.18
0.17
222
0.01
0.01
222
0.59
0.54
222
0.75
0.75
222
0.64
0.66
222
0.73
0.73
222
0.80
0.80
222
VO
VH
+***
+
(+***)
(+***)
+
0.76
0.89
0.82
0.91
222
222
DSY
DSC
DSP
DSU
DSH
DSI
DSR
+
+***
+
+***
+***
+**
+
+**
+**
+
+
-
+
+
+
-
0.06
0.13
0.34
0.29
0.22
0.19
0.17
0.13
0.28
0.30
0.39
0.31
0.22
0.19
74
74
74
74
74
74
74
PY
PI
+
+
+
+
-
0.08
-0.02
0.07
-0.06
55
55
Note: *, ** and *** denote 10, 5 and 1 percent significance levels.
116
Essay 4. How to evaluate proxies of macroeconomic uncertainty
Figure 1: Daily implied volatility (VO) around US presidential elections 1992-2004
Note: The solid line indicates the election date (11/3/1992, 11/5/1996, 11/7/2000 and 11/2/2004.
The dashed line indicates the certification of the electoral vote in Congress 1/6/2001)
4. Do uncertainty proxies measure uncertainty?
117
For the Michigan consumer survey proxies, DMV, buying condition for vehicles,
seems to be the best indicator by reference to its positive and significant estimates to
both CONF LICT and F INCRISIS and some increase in the adjusted R-squared.
For the survey of professional forecasters, DSC, real consumption, seems to be the
most appropriate proxy of uncertainty with highly significant coefficient estimates
on both the CONF LICT and the F INCRISIS coefficient and a large increase in
the adjusted R-squared.
Most notably, the probability forecast proxies, PY and PI, do not pick up any
effects of the dummy dates. This is surprising, given that these proxies are often
believed to be more refined proxies of uncertainty. A possible reason could be that
the sample period is somewhat shorter than for the other proxies. Nevertheless, this
finding casts some doubt on the usefulness of these proxies of uncertainty.
Thus, the narrative evidence indicates that most survey based proxies and the
volatility proxies have reacted as expected to exogenous shocks to uncertainty. The
probability forecast proxies, on the other hand, show strikingly weak responses to
these shocks. This result casts some doubt on the appropriateness of using these
proxies as the preferred proxies of uncertainty.
4.2
Correlations
The Pearson’s correlation coefficients between all considered proxies are illustrated
in Figure 2.
Figure 2: Correlations of all uncertainty proxies
118
Essay 4. How to evaluate proxies of macroeconomic uncertainty
Indeed, a large share of the correlations is positive. Out of 190 correlations, 84
are significantly positive at the one percent level, as indicated by *. Only eleven
correlations are significantly negative. Generally, the disagreement proxies from
the Michigan Consumer Survey and the Survey of Professional Forecasters survey
data show rather high and significant correlations, both within and between groups.
There are two exceptions. DMD, real family income, is predominantly negatively
correlated with the other proxies with eight out of 19 correlations being significantly
negative. DMB, business conditions, is positively correlated with DMD and negatively correlated with a few other proxies. The results here thus indicate that DMD
and DMB do not capture the same phenomenon as the other proxies.
The correlation coefficients between the disagreement proxies and the other proxies are mostly insignificant. Only six out of 64 correlations are significant at the one
percent level. This result is very different from the positive relation between probability forecast proxies and disagreement proxies found in Zarnowitz and Lambros
(1987). The reason for this finding could be that the sample periods are nonoverlapping and that we address the problem of different forecast horizons. The
non-disagreement proxies, the volatility and probability forecast proxies, exhibit a
significant and positive correlation with each other.
Thus, within the groups of proxies, indicated by shaded areas, the correlation table supports Proposition 1. As expected, we see positive correlations across variablespecific uncertainty proxies. However, the two groups seem to give different answers
to how uncertainty varies over time.
5
Factor analysis
In section 2, we concluded that any proxy of uncertainty could be driven by many
underlying factors. In this section, we are interested in investigating how many underlying common factors that are suggested by the data reduction technique known
as factor analysis.10 For a complete description of factor analysis, see Sharma (1996)
and Johnson (1998). Factor analysis is performed on each of the subgroups constituted by the Michigan Consumer Survey and the Survey of Professional Forecasters.
Common factors are searched for across variables, using the same proxy type, to
avoid problems of mixing different types of proxies. For the probability forecast of
proxies and volatilities, there are only two proxies of each and no factor analysis is
conducted.
The purpose of factor analysis is to search for underlying latent factors that ex10
Entia non sunt multiplicanda praeter necessitatem!
5. Factor analysis
119
plain co-movements in different variables. The number of common factors can in
general be as many as the number of variables less one. Common factors are searched
for in each of the separate subgroups that capture disagreement, the Michigan Consumer Survey and the Survey of Professional Forecasters. This analysis provides us
with some useful results. First, it can help us in identifying which proxies are more
closely connected to any common factors, and which proxies are more idiosyncratic.
Second, it turns out that we detect and compute only one common factor for each
subgroup, and we interpret this factor as general macroeconomic uncertainty. Third,
this common factor will be used for applications in section 6. Below, these steps are
described in more detail.
The Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy is used to determine the appropriateness of performing factor analysis on the data. No formal
statistical test is available, but an overall KMO-value of 0.60 is the recommended
minimum value.11 We also restrict individual KMO-proxies to be above 0.50 for
inclusion in the common factor extraction. If any proxy is below 0.50, this proxy is
excluded. We rerun the KMO-test until all separate proxies are above 0.50 so that
all idiosyncratic proxies are excluded.12 For Michigan Consumer Survey proxies, we
must first disqualify DMU, unemployment, and then DMB, business conditions, because of individual KMO-values lower than 0.50. Referring to Table 5, the narrative
evidence also indicates that DMU and DMB are weak proxies of uncertainty. For the
Survey of Professional Forecasters proxies, we find strong results for the KMO test
with no values below 0.80. Overall, the average KMO-value is 0.74 for the Michigan
Consumer Survey group and 0.86 for the Survey of Professional Forecasters group
after exclusion of DMU and DMB, which indicates that the remaining proxies are
well suited for factor analysis. All variables with their respective KMO-values and
average KMO-values for the two subgroups are displayed in Table 6.
Next, we estimate factor models, one for each subgroup, by principal axis factoring (PAF) to determine how many factors are suggested by this formal procedure.13
The eigenvalues of the sample covariance or correlation matrix measure the strength
of the factors in explaining the total variance in all variables. According to the often
employed larger-than-one-eigenvalue criterion as well as a screenplot analysis, there
is exactly one common factor each for the Michigan Consumer Survey and the Sur11
A KMO-value of below 0.50 is deemed "unacceptable", 0.50-0.59 "miserable", 0.60-0.69
"mediocre", 0.70-0.79 "middling", 0.80-0.89 "meritorious and 0.90-1.00 "marvelous". (Sharma
(1996) p. 116)
12
Referring to the model in Section 2, these excluded proxies can be seen as representing those
variables in the economy that do not enter endogenously in the VAR.
13
Alternative methods such as Iterated Principal Factors and Maximum Likelihood give very
similar results.
120
Essay 4. How to evaluate proxies of macroeconomic uncertainty
Table 6: Kaiser-Meyer-Olkin values for sampling
Uncertainty proxy
DMF
DMH
DMR
DML
DMD
DMV
Michigan Consumer Survey average
DSP
DSI
DSH
DSC
DSY
DSR
DSU
Survey of Professional Forecasters’ average
adequacy
KMO
0.78
0.66
0.74
0.71
0.90
0.75
0.74
0.86
0.86
0.81
0.96
0.89
0.92
0.80
0.86
vey of Professional Forecasters subgroups. The eigenvalues above zero are displayed
in Table 7. The fact that we can only detect one common factor for each subgroup
indicates that there is one prime driver of uncertainty common to all proxies. This
common factor is interpreted as general macroeconomic uncertainty.
Table 7: Eigenvalues for the number of common factors
Factors Michigan Consumer Survey Survey of Professional Forecasters
1
2.36
4.04
2
0.42
0.30
3
0.04
0.07
With one factor for each subgroup, we take a look at the factor loadings of each
proxy. It turns out that for the Michigan Consumer Survey subgroup, DMD, real
family income, is negatively related to the common factor but positively related to
all others. DMD was also considered to be a weak proxy of uncertainty judging from
the narrative evidence in Table 5. That DMD has the lowest communality indicates
that the negative loading for this factor is significant but small. Furthermore, DMD
seems quite closely related to DMB from the correlation table and is somewhat
guilty of association to DMB. Thus, although formally not disqualified, DMD must
be considered a weak proxy for uncertainty. DML, buying conditions for large
goods, has the highest communality with the common factor and DMD the lowest.
DML also seemed to be an adequate proxy by looking at Table 5. For the Survey
of Professional Forecasters proxies, all factor loadings are positive. DSY has the
5. Factor analysis
121
highest communality and DSP the lowest. The narratives in Table 5 also indicate
that DSY, real GDP, is a better proxy than DSP, corporate profits.
Finally, to get an estimate of the underlying factor, we need to score the data
to produce an estimate of the latent common factor. The scoring coefficients are
essentially the weights put on each variable so we can produce an estimate of general
macroeconomic uncertainty at time t. The factor loadings, variance contributions
and the scoring coefficients, using the regression method, are reported in Table 8.14
Table 8: Loadings, variance decompositions and scoring coefficients
Factor loading Communality Uniqueness Scoring coeff.
Michigan Consumer Survey
DMF
0.65
0.42
0.58
0.15
DMH
0.47
0.23
0.77
0.11
DMR
0.57
0.32
0.68
0.11
DML
0.85
0.73
0.27
0.47
DMD
-0.36
0.13
0.87
-0.06
DMV
0.73
0.53
0.47
0.27
DSP
DSI
DSH
DSC
DSY
DSR
DSU
Survey of Professional Forecasters
0.46
0.21
0.82
0.67
0.84
0.71
0.72
0.52
0.87
0.76
0.79
0.62
0.74
0.55
0.79
0.33
0.29
0.48
0.24
0.38
0.45
0.05
0.17
0.25
0.11
0.31
0.14
0.11
The factors we identify as general macroeconomic uncertainty are weighted combinations of the included proxies. As such, the Survey of Professional Forecasters
factor (SFactor) contains all the Survey of Professional Forecasters proxies, but
DSY, real GDP, contributes the lion’s share followed by DSH, buying conditions for
houses, and DSI, CPI-inflation. The Michigan Consumer Survey factor (MFactor)
contains all proxies but DMU and DMB and assigns the largest weight to DML,
buying conditions for large goods, followed by DMV and DMF.
In this section, we have reduced our survey based disagreement proxies of uncertainty from 15 (eight from the Michigan Consumer Survey and seven from the
Survey of Professional Forecasters) to two, MFactor and SFactor. In the process,
we have excluded those few proxies that are considered to be mostly idiosyncratic
(DMU and DMB) and have assigned larger weights to those that are closely connected to the others. Thus, we believe that these two factors could be reasonable
representations of general macroeconomic uncertainty as captured by disagreement.
14
The alternative Bartlett scoring method yields nearly identical results.
122
6
Essay 4. How to evaluate proxies of macroeconomic uncertainty
Extensions
The correlation table, the narrative evidence, and the factor analysis helped us
evaluate uncertainty proxies. In this section, we will look more closely at how uncertainty proxies co-move with the business cycle and thereafter study if uncertainty
is of importance for aggregate consumption and residential investment. We will use
our factors for the Michigan consumer survey group (MFactor) and the survey of
professional forecasters (SFactor) along with volatility proxies (VO and VH) and
probability forecast proxies (PY and PI).
6.1
Co-movements with the business cycle
The relation between business cycles and uncertainty is largely left unexplored in
the previous literature. Some papers relating macroeconomic uncertainty to the
business cycle are Ball (1992) and Shields, Olekalns, Henry, and Brooks (2005). Ball
(1992) analyzes the relation between inflation and inflation uncertainty and argues
that higher inflation should raise inflation uncertainty. Shields, Olekalns, Henry,
and Brooks (2005) find that uncertainty about inflation and output increases with
shocks to output and inflation. This section provides some empirical evidence on
the co-movement of uncertainty with the business cycle in general by comparing the
time series evolution of uncertainty proxies with the real GDP-gap.
The co-movement of proxies of uncertainty and the business cycle is shown in
Figure 3.15
15
The business cycle measure is obtained by standard Hodrick—Prescott (HP) filtering of the
log real output with a smoothing weight set to 1600. The Michigan Consumer Survey measures
and volatility measures have been converted from monthly to quarterly by averaging.
6. Extensions
123
Figure 3: The Business Cycle and Uncertainty Proxies 1980-2005
Note: Displayed are the GDP HP-filtered business cycle (RHS) and selected uncertainty proxies
(LHS). MFactor, SFactor, VO and VH have been normalized to 100 at their respective first observation. NBER peak to recession periods are displayed as shaded areas and cover the following
peak-through periods: January 1980-July 1980, July 1981-November 1982, July 1990-March 1991,
and March 2001-November 2001. Source: www.nber.org/cycles.html
124
Essay 4. How to evaluate proxies of macroeconomic uncertainty
Looking at the co-movements of the business cycle and the proxies, it appears
as if uncertainty seems to be higher the further we are from the "normal" state of
the economy. Looking at the official NBER business cycle dates, it appears as if
uncertainty has been higher at the turn of the business cycle moving away from a
recession.16 For the probability forecast measures PY and PI, these findings are not
as clear. To further explore the relation between the business cycle and uncertainty,
Table 9 shows the correlations between the absolute value of the GDP-gap and
uncertainty proxies.17 All uncertainty proxies are positively correlated with the
business cycle, in particular the survey based proxies, SFactor and MFactor, show
strong correlations.
Table 9: Correlations of uncertainty proxies with the business cycle
UP
Corr(UP, |GDP gap|)
MFactor
0.44
SFactor
0.49
VO
0.26
VH
0.15
PY
0.33
PI
0.20
6.2
Precautionary savings
Next, we estimate Euler equations following Campbell and Mankiw (1991), which
allows for precautionary savings effects on consumption, ∆ct , through an uncertainty
proxy, U Pt ,
(10)
∆ct = α + β 1 rt−1 + β 2 ∆ydt−1 + γ c UPt−1 + εt .
The log change in disposable income, (∆ydt ), is added to control for hand-to-mouth
behavior of consumers. When we estimate equation (10), the uncertainty proxy,
the real interest rate (r), and disposable income must be instrumented due to time
aggregation issues. Our instruments are lagged values of ∆c, ∆yd, r and UP .18
The precautionary savings effect would show up as a significantly positive γ c ,
meaning that high uncertainty would lead to consumption being postponed into the
future. It might seem counter-intuitive to expect a positive effect on ∆ct from UPt−1 ,
16
Peak-Through: January 1980-July 1980, July 1981-November 1982, July 1990-March 1991,
March 2001-November 2001. Source: www.nber.org/cycles.html
17
The GDP-gap is measured as the absolute real percentage deviation of GDP from its HP-trend
(w=1600).
18
See Hall (1988) for further motivation. The lag structure follows Hall (1988) and Campbell
and Mankiw (1991).
6. Extensions
125
but as the contemporaneous consumption level decreases with higher uncertainty,
the change in consumption to the next period increases ceteris paribus.
Table 10: Estimates of the consumption Euler equation
r
∆yd
UP
R2
Obs
MFactor 0.028
0.236
-0.166 -0.07
97
(0.83)
(1.02)
(-1.13)
SFactor -0.018
0.298
0.308** -0.02
91
(-0.57)
(1.59)
(2.58)
VO
-0.016
0.268
0.010 -0.03
73
(-0.67)
(1.26)
(1.03)
VH
-0.007 0.439*** 0.021 -0.28
97
(-0.25)
(2.84)
(-0.59)
PY
-0.009
0.043
-0.016 -0.12
53
(-0.28)
(0.18)
(-0.69)
PI
-0.012
-0.096
-0.037* -0.16
53
(-0.55) (-0.43)
(-1.69)
Note: *, ** and *** denote 10, 5 and 1 percent significance levels.
The results from our two-stage least squares regressions, shown in Table 10,
indicate mixed results for our set of uncertainty proxies. The Survey of Professional
Forecasters factor (SFactor) is significant at the five-percent level. The Michigan
Consumer Survey disagreement factor (MFactor) is negative, but insignificant. The
VO and VH volatility proxies show no significant effects. For the probability forecast
measures PY and PI, the estimates are negative, with the one for PI significant at
the ten-percent level.
6.3
Residential investment
Finally, following Downing and Wallace (2005), we study how uncertainty influences
the decision to invest in residential housing. Uncertainty is expected to decrease investment, due to the increased value-to-wait when uncertainty is high. See Bernanke
(1983) on uncertainty and the irreversibility of investment.
For all qualified proxies, we estimate an extension of the model in Downing and
Wallace (2005) adding U Pt ,
Startst = β 0 + β 1 HRt + β 2 T Rt + β 4 HRvolt + β 5 T Rvolt
+γ r UPt + controls + εt ,
(11)
where Startst is the number of housing starts for quarter t. HRt is housing returns;
T Rt is the T-bill rate; HRvolt is the historical volatility of housing returns and
126
Essay 4. How to evaluate proxies of macroeconomic uncertainty
T Rvolt is the volatility on the T-bill rate. The controls are the spread between
the thirty-year and the ten-year bond yields and a set of seasonal dummies. The
estimation technique is adapted to the dependent variable being an integer count
variable. In particular, we use the Poisson based estimation technique as described
in Greene (2003).
Downing and Wallace (2005) use HRvolt as their only proxy of uncertainty but
we find that the reported negative sign for this proxy is unstable over subperiods.
The results when adding uncertainty proxies are shown in Table 11. The sign on
the uncertainty proxy is negative and significant for all but the probability forecast
proxies PY and PI. This constitutes further support for survey proxies of uncertainty
(except PY and PI), given that uncertainty should decrease the number of housing
starts.
Table 11: Estimates of
HR
TR
MFactor 0,016*** -0,029***
(5,6)
(-6,33)
SFactor 0,025*** -0,033***
(6,7)
(-6,87)
VO
0,024*** -0,049***
(5,32)
(-11,63)
VH
0,027*** -0,036***
(7,69)
(-8,99)
PY
0,016*** -0,031***
(3,29)
(-4,52)
PI
0,016*** -0,030***
(3,2)
(-3,99)
the residential investment decision
HRvol
T Rvol
UP
R2 Obs
0,019
0,055** -0,137*** 0,87 102
(1,64)
(2,16)
(-6,06)
-0,0001
-0,03
-0,059** 0,81 98
(-0,01)
(-1,14)
(-2,45)
-0,019 -0,103*** -0,005*** 0,82 80
(-1,03)
(-4,38)
(-3,01)
-0,016
-0,04
-0,012*
0,8 104
(-0,99)
(-1,55)
(-1,68)
0,032** -0,074***
0,031
0,81 56
(2,00)
(-2,89)
-0,22
0,031* -0,078***
0,192
0,81 56
(1,84)
(-3,30)
(0,93)
Note: *, ** and *** denote 10, 5 and 1 percent significance levels.
7
Conclusions
The main purpose of this paper is to evaluate available proxies of uncertainty. Using a simple VAR-model of the economy, we derive two propositions. The first
states that different proxies of uncertainty should react with the expected sign to
large exogenous shocks to uncertainty. The second states that, under reasonable
assumptions, uncertainty proxies should be positively correlated. We follow these
implications when evaluating proxies of uncertainty. The first implication is studied
by identifying dates that should increase or decrease uncertainty. The second is
studied by correlation analysis. Further, using factor analysis, we investigate how
7. Conclusions
127
many factors of uncertainty that are common across proxies. Finally, in some extensions, we include proxies of uncertainty in standard macroeconomic applications
where uncertainty is supposed to be of importance.
We show that volatility proxies behave as expected to exogenous shocks to uncertainty and are also of importance for residential investment. Therefore, this paper
finds some support for the use of stock market volatility as a measure of uncertainty.
This is especially true for the implied volatility proxy derived from option prices. A
notable finding in this paper is the weak support for the probability forecast proxies as suitable proxies for uncertainty. The narrative evidence finds little support
for those proxies picking up uncertainty. Moreover, in applications where uncertainty could be of importance, these proxies do not add any explanatory power.
The disagreement proxies pick up exogenous shocks to uncertainty and are also of
importance for economic decisions. The strongest support is given to the use of
quantitative disagreement proxies. Zarnowitz and Lambros (1987) and Giordani
and Söderlind (2003) also claim that disagreement proxies are viable proxies for
true uncertainty. However, the crucial assumption made by Zarnowitz and Lambros
(1987) to draw this conclusion is that true uncertainty is equal to the diffuseness
of probability forecasts. Our paper indicates that such a supposition is incorrect.
Giordani and Söderlind (2003) instead use an asset pricing model to evaluate disagreement proxies but have the same problem since they rely on time series proxies
of uncertainty as their solutions key.
From the correlation between proxies of uncertainty, we find that there are two
independent groups. One group consists of the survey disagreement proxies, the
other consists of the probability forecast and stock market volatility proxies. Most
proxies are positively correlated within groups. This result is reinforced by factor
analysis through which we find that all proxies from the Survey of Professional
Forecasters and most proxies from the Michigan Consumer Survey are tied together
by exactly one common factor for each survey. By factor analysis, we are also able
to compute common factors, supposedly uncertainty, that drive proxies within each
survey. These factors are taken to be general macroeconomic uncertainty.
We also find proxies of uncertainty to be positively correlated with the absolute
value of the business cycle. The further away from a "normal" state of the economy
we are, the higher is the uncertainty. The co-movement of uncertainty and the state
of the economy could be important for the conduct of policy and has previously
remained undetected in the literature.
128
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