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CESifo Area Conference on
Macro, Money and International
Finance
24 - 25 February 2006
CESifo Conference Centre, Munich
Monetary Policy in the Euro-Area:
An Analysis Using a Stylized
New-Keynesian Model
Harry Garretsen, Cindy Moons and
Bas van Aarle
CESifo
Poschingerstr. 5, 81679 Munich, Germany
Phone: +49 (89) 9224-1410 - Fax: +49 (89) 9224-1409
E-mail: [email protected]
Internet: http://www.cesifo.de
Monetary Policy in the Euro-Area: An Analysis Using a Stylized NewKeynesian Model*
Harry Garretsen1, Cindy Moons2 and Bas van Aarle3
Abstract
This paper analyses monetary policy in the Euro-Area using a stylized new-Keynesian model. A number of
issues are focused upon: (i) optimal monetary policy under commitment and discretion, (ii) a comparison of
optimal monetary policies and ad-hoc monetary policies, (iii) the effects of fiscal policies and foreign
variables on monetary policy in the model. Using numerical simulations, it is analyzed how these aspects
affect monetary policy of the ECB in particular and macro economic fluctuations in the Euro-Area in
general.
Keywords: EMU, Fiscal Policy, Monetary Policy
JEL Code: F31, F41, G15
February 2006
1
Utrecht School of Economics, Utrecht University, The Netherlands; Centre for German Studies (CDS),
University of Nijmegen, the Netherlands and research fellow at CESifo, Munich, Germany.
2
University of Antwerp, Department of Applied Economics, Prinsstraat 13, 2000 Antwerpen, Belgium.
3
Department of Economics, University of Maastricht, the Netherlands and research affiliate at CESifo,
Munich, Germany.
* We would like to thank seminar participants at the University of Nijmegen and the University of
Maastricht for pointing our attention to a number of unclarities in a previous version of our paper.
1
1.
Introduction.
Since its start on January 1th 1999, policymakers, financial market participants and academic researchers
alike have shown a strong interest in the effects of the Economic and Monetary Union (EMU). In particular
the design, implementation and transmission of the common monetary policy of the European Central Bank
(ECB) is often focused upon. An important question concerns the optimal monetary policy for the Euro-Area
(EA). Among other things, this question also concerns the credibility of the ECB. Some observers have
argued that the ECB practically inherited the reputation and commitment towards low inflation of the
Bundesbank. Others have assumed that as a complete new institution, the ECB would lack initially such a
possibility to commit its policies vis-à-vis the private sector and that it would need time to earn a reputation.
In other words, starting from a regime with discretionary policymaking, it may only gradually establish a
policy regime with commitment in its policies. From the academic side, e.g. adopting inflation targeting has
been proposed for the ECB to foster credibility.
Others have emphasized the need for simple policy rules in the presence of such initial institutional
uncertainties and also because of large uncertainties of the actual workings of the Euro-Area (EA) economy
(model uncertainty), the lack of consistent data initially (data uncertainty) and the possibility of structural
breaks (parameter uncertainty) due to establishment of the EA. Following that logic, we could also assume
that the ECB would follow a simple policy rule according to which its monetary policy reacts in a predefined
manner to important macroeconomic variables like output and inflation in the EA. E.g. Taylor rules relate the
short-run interest rate setting of the monetary policymaker to deviations of inflation from the inflation target,
the output gap and the exchange rate. In addition we may include an instrument smoothing objective of the
policymakers. In case of instrument smoothing policymakers perceive instrument variability as
undesirable/costly and thus prefer a gradual adjustment of the policy instruments to rapid changes in policy
variables. In the presence of instrument smoothing, the current value of the instrument variable is expressed
as a weighted average of its lagged value and an optimal value. Clearly, the inclusion of interest rate
smoothing generates history dependence of policy even in a purely forward-looking model.
In this paper we analyze the effects of such alternative monetary policy regimes in the EA using a
highly stylized New-Keynesian (NK) model. The setup of the model is rather standard and e.g. similar to
Giordani (2001), Muscatelli et al. (2004), Svensson (2000) and others. The model is stylized in two respects:
(a) while its structure is fully consistent with the NK literature it does not model contain a fully specified
underlying micro-economic structure, (b) as a counterpart of (a), we do not estimate the model parameters
for the EA but instead infer plausible values from a detailed analysis of empirical NK applications to the EA
economy. With the use of this stylized model, we illustrate a number of important results on monetary policy
in the NK literature and which are assumed to be relevant for actual monetary policymaking in the EA. A
number of issues are focused upon in particular: (i) optimal monetary policy under commitment vs.
discretion, (ii) a comparison of optimal monetary policies and ad-hoc monetary policy rules, (iii) the effects
of fiscal policies and foreign variables on monetary policy.
2
The presence of active fiscal policies will complicate the management of monetary policies in
particular if their effects are contrary to the objectives of the monetary policymakers, e.g. in case of a
positive demand shock, the monetary policy will be restrictive to contain inflationary pressure. In those
conditions, an expansionary fiscal policy shock will run counter to the monetary policy objectives, evoking a
policy conflict between the monetary and fiscal policymakers. Muscatelli et al. (2004) have analysed the
interaction of monetary and fiscal policies in a closed economy NK model and applying it to US data.
In an open economy setting, the management of monetary policy is complicated further. The
exchange rate becomes an important channel of transmission of monetary policy affecting thereby real and
nominal adjustments after macroeconomic shocks. Given the link between interest rates and exchange rate
expectations according to the UIP hypothesis, monetary policies will affects outcomes both via the interest
channel and the exchange rate channel. The transmission via the exchange rate channel will depend on the
pass-through of exchange rate fluctuations on domestic inflation and the effect of real exchange rates on net
exports. In an open economy setting, optimal monetary policies will therefore depend also on the degree of
pass-trough in the economy and the sensitiveness of net exports w.r.t. international competitiveness. Leitemo
et al. (2002) point to the fact that in the open-economy the distinction between monetary policy commitment
and discretion is even more important than in a closed economy: the introduction of another forward-looking
variable in form of exchange rate expectations implies additional time-inconsistency problems for the
monetary policymaker related to the exchange rate channel of monetary policy.
The paper has been structured as follows: Section 2 proposes a stylized NK model. Section 3
discusses the design of monetary policy in this model. Section 4 discusses the simulation results for various
shocks using a parametrization based on empirical EA studies. In Section 5 some sensitivity analysis of the
outcomes w.r.t. a few crucial model parameters is undertaken. The conclusion summarizes our main results.
2.
A Stylized NK Model of the EA.
We model the EA economy using a stylized hybrid new Keynesian/NOEM model. The basic blocs of the
model are the aggregate demand and aggregate supply curves, the Uncovered Interest Parity (UIP) condition
and the design of monetary and fiscal policies. Concerning the latter: we try to include in the model a
number of aspects that are relevant for monetary and fiscal policy design in the actual practice of the EA, in
particular the distinction between monetary policy commitment versus discretion and restrictions on fiscal
flexibility in the form of the Stability and Growth Pact (SGP).
The goods market equilibrium, or IS curve, of the EA economy1 takes the following form:
1
EA variables can be interpreted as weighted averages of individual country variables: thus, aggregate inflation, real
output and fiscal deficit can be defined as a weighted average of individual countries: ∆pt ≡ θ j ∆p j , t , yt ≡ θ j y j , t ,
∑
j
∑
j
gt ≡ ∑ θ j g j ,t in which θ j , ( ∑ θ j = 1) measures the relative size (e.g. in terms of trend output) of country j in the EA
j
j
economy.
3
yt = ψ 1 yt −1 + ψ 2 Et yt +1 − α ( it − Et ∆pt +1 − r ) + η gt + σ yt* + δ (et + pt* − pt ) + utd
(1)
y denotes EA output2, i the EA short-term nominal interest rate, (the policy instrument of the ECB), p the
general price level, g the fiscal balance (a positive value of g denotes a fiscal deficit), et is the EA exchange
rate (a positive value implying a depreciation); r is the equilibrium real interest rate3. u d is an aggregate
demand shock. All variables are given in logarithms and refer to deviations from an initial steady-state.
Foreign variables are denoted by an asterisk.
In this reduced form, EA output depends on past output, expected future output, the real interest rate
(expressed as a deviation from the equilibrium real interest rate), net government spending, net exports4 and
a demand shock. This IS curves nests several alternative formulations that can be found in the literature: the
current output gap can be positively related to past output gaps only (Fuhrer and Moore (1995), Huh and
Lansing (2000)), both past and expected future output gaps, Clarida et al., (1999)), or expected future output
gaps only (McCallum (2001), Woodford (2001)). The backward-looking component in the IS curve results
from “habit formation” in consumption decisions5. The forward-looking part is produced by rational,
intertemporally maximizing agents that apply the principles of optimal “consumption smoothing”. In case
consumers are entirely forward looking (ψ i = 0 ), (1) is also sometimes referred to as the “intertemporal IS”.
Expectations concerning the exchange rate of the euro adjusts in such a manner that uncovered
interest rate parity holds throughout:
Et et +1 − et = it − it* + utr
(2)
where u tr represents random exchange rate shocks (risk premium shocks, expectation shocks or other shocks
in international financial markets) that cause temporary deviations from UIP.6
Inflation dynamics are given by hybrid Phillips-curves which contain elements of both forward and
backward-looking price setting. In addition, demand-pull and cost-push factors affect inflation,
∆pt = ω1∆pt −1 + ω2 Et ∆pt +1 + γ ( yt − y t ) + τ∆( pt* + et ) + uts
2
(3)
Output and output gap in fact can be used interchangeably as long as equilibrium output remains constant. Ehrmann
and Smets (2003) analyze the case where monetary authorities are uncertain whether supply shocks are the result of
cost-push shocks or shocks to equilibrium output. They analyze the implications of such a “signal-extraction problem”
facing (optimal) monetary policy. In this paper we will ignore aspects relating to parameter uncertainty, model
uncertainty and measurement errors. See e.g. Ehrmann and Smets (2003) and Giordani and Soderlind (2004) on such
issues and their implications in New-Keynesian models of monetary policymaking.
3
In practice, it may be quite complicated to determine the equilibrium real rate of interest, r , as the study on real
equilibrium interest rates in the EA by Giammarioli and Valla (2003) shows. Similar to estimating equilibrium output y
and equilibrium inflation ∆p it would be crucial, however, for the monetary authority to get its estimations on this
variable right.
4
Net exports are a function of foreign output and price competitiveness: net exports = σ yt* + δ (et + pt* − pt ) .
5
Leith and Malley (2002), Batini et al. (2003) and McCallum and Nelson (1999) provide micro-foundations for the
presence of habit formation in consumption. Empirical evidence is provided that the backward looking component in
consumption is substantial.
6
For empirical studies on deviations of UIP see e.g. Jeanne and Rose (2002). McCallum and Nelson (1999) analyze the
effects of deviations from UIP on the exchange rate and the current account in a framework that is related to ours.
4
Inflation equals the first difference of the general price level and is assumed to be a function of past inflation,
expected future inflation, the output gap, yt − y t , -reflecting demand pull inflation- and inflation of import
prices, ∆ ( pt* + et ) , which induces cost-push inflation.7 uts , are domestic cost push shocks (or “mark-up”
shocks) which will be interpreted as supply-shocks in the remainder of the analysis since (3) can also be
considered as describing the short-run aggregate supply (AS) curve. In addition, the supply side of the
economy can be hit by shocks to potential output viz. productivity shocks.
If ω = 1 , we obtain the backward-looking Phillips curve, if ω = 0 , on the other hand, we obtain the
forward-looking New-Keynesian Phillips curve8. In the first case, only past economic conditions matter for
determining current inflation. In the presence of forward-looking expectations, current price setting depends
on expectations about future economic conditions solely. The hybrid Phillips curve assumes that both
backward and forward-looking price setting are present, it results if ω lies in between 0 and 1.9 The hybrid
Phillips curve allows for both a forward-looking component and a backward-looking component, reflecting
e.g. learning effects, staggered contracts or other institutional arrangements that affect pricing behavior.
The output gap proxies the effects of demand-pull factors on the general price level. Foreign
inflation spillovers affect domestic prices via the price of imported raw-, intermediate and final goods used in
the domestic production process. The strength of the foreign inflation and depreciation spillovers, depends
not only on the intensity with which foreign goods are absorbed but also on the amount of pass-through in
import pricing. Recent empirical research suggests that pass-through is generally non-negligible.10 Inflation
will be affected by changes in the exchange rate through the direct effect via import prices, implying costpush inflation. Exchange rate changes can also affect inflation indirectly through aggregate demand, since
they will affect the relative price between domestic and foreign goods, thereby influencing net exports and
domestic output, which in turn will affect prices through demand-pull inflation.
Demand shocks (ud), cost-push shocks (us), potential output ( y ), fiscal shocks (ug), exchange rate
shocks (ur) and foreign output (uy*), price (up*) and interest rate (ui*) shocks are all assumed to follow
7
See e.g. Gagnon and Ihrig (2002), Leitemo et al. (2002), Coenen and Wieland (2002) that use similar open economy
Phillips curves.
8
See e.g. Clarida et al. (1999) for a similar analytical framework and a detailed discussion on the generalised IS (1) and
Phillips curves (2). They illustrate how ψ and ω jointly determine the endogenous inflation and output persistence.
Leith and Malley (2002) derive (2) from the overlapping contracts model a la Calvo.
9
In empirical applications, more lags of output (in case of the IS curve) and output and inflation (Phillips curve) are
often included to improve the empirical fit. Adding these lags will also induce a more persistent and therefore more
realistic adjustment to shocks. In empirical studies and monetary policy analysis sometimes concepts of equilibrium
and/or core inflation are added to (2), to distinguish short-run fluctuations of inflation from longer term, equilibrium
inflation. In our analysis this issue is not dealt with and inflation (as all other variables) is defined in terms of deviations
from (possibly non-zero inflation) steady-state. See Vega and Wynne (2001) and references therein on core inflation in
the EA.
10
See e.g. Gagnon and Ihrig (2002) and Anderton (2003). Apart from “pass-through” by importers of foreign price
changes, including exchange rate changes, it is sometimes also argued that importers will consider domestic inflation
when setting import prices as they seek to react to the pricing of domestic competitors. Such a “pricing to market” could
be added to our analysis as well by adding domestic inflation to the RHS of (2).
5
stationary AR(1) processes ut = ρ ut −1 + vt , with 0 ≤ ρ < 1 and vt is white noise, v ∝ N (0, σ v2 ) , all shocks are
assumed to be contemporaneously uncorrelated, E ⎡⎣ vi v j ⎤⎦ = 0, ∀i, j .
In the model, macroeconomic shocks lead to fluctuations in output and prices. This will affect the
interest rate and through (5) the exchange rate. External exchange rate adjustment in the form of changes of
the euro exchange rate, et, therefore, remains a potentially important shock absorber in the EA, in particular
in case the shocks are of foreign origin. In fact, whereas a monetary union precludes internal exchange rate
adjustments by definition, external exchange rate adjustments may partly take over as a shock absorber. In
the context of the EA, one should in other words not only focus on the interest rate channel of its monetary
policy but also the exchange rate channel is important in assessing the transmissions of monetary policy of
the ECB.
Macroeconomic stabilization policies are another shock-absorber. The macroeconomic policy regime
consists of the monetary and fiscal policy strategies that are implemented in the EA. The monetary and fiscal
policy strategies are interacting and their joint implementation affects macroeconomic adjustments. The three
direct transmission channels of the interest rate (the interest rate channel of monetary policy) in the model
are: (i) a change in nominal interest rates, changes the real interest rate in the short-run, thereby output, (ii) a
change of the interest rate affects the rate of exchange rate depreciation through the uncovered interest rate
parity condition and (iii) by influencing macro-economic conditions, an interest change may also induce
policy responses of the fiscal authorities. The three direct transmission channels of the euro exchange rate
(the exchange rate channel of monetary policy) in the model are: (i) a nominal depreciation (viz. higher
foreign prices) stimulates net exports in the short-run because of the induced real depreciation, (ii) a nominal
depreciation (viz. higher foreign prices) generates a positive spillover on domestic inflation and (iii) a
nominal depreciation may elicit a policy response of the monetary authorities. The transmission of fiscal
policy takes the form of (i) a direct impact on aggregate demand, (ii) thereby an indirect effect on prices,
interest rates and exchange rate, (iii) fiscal policy may elicit, by impacting on macro-economic conditions,
policy responses of the monetary authorities.
Concerning fiscal policy we assume that net government spending is determined by a fiscal policy
rule. Taylor (2000), developed a framework for simple fiscal policies that relate net government spending to
the structural fiscal balance, g , and the cyclical fiscal stance, as measured by the automatic stabilizers
− χ yt , the elasticity of the deficit to cyclical output fluctuations times output. In addition, we allow for the
possibility of deficit smoothing and the occurrence of stochastic deficit shocks, ug:
gt = λg gt −1 + (1 − λg ) ( g − χ g yt ) + utg
(4)
If χ > 0 , fiscal policy contains a countercyclical component that provides automatic stabilization of the
business cycle fluctuations. The parameter λg (where 0 ≤ λg ≤ 1 ) captures the degree of fiscal policy
inertia/activism: a high value of λg would mean a very inert –but highly persistent- fiscal policy that could
6
be explained by difficulties to implement changes in tax policies (e.g. pension reforms) and government
spending (e.g. healthcare reforms).
The fiscal policy rule (4) enables to represent in the model -albeit in a highly stylized way- the
various budgetary rules and strategies one may observe in practice. Here, we would like also to relate the
fiscal policy rules with the provisions in the Stability and Growth Pact. The budgetary target g can be
thought e.g. as being the “close-to balance or in surplus medium term objective”, reflecting a preference for
long-run sustainability and neutrality. The build-in flexibility in the Stability Pact relies on allowing as much
as possible the workings of the automatic stabilizers in the short-run. Finally, the amount of inertia in fiscal
policy, summarized by λg , reflects the ability of fiscal policymakers to adjust fiscal policy in the short-run. If
λg = 0 fiscal flexibility is the highest and the fiscal balance only driven by the automatic stabilizers. If λg
increases, fiscal flexibility declines, implying more persistence in fiscal adjustments. In the limiting case
where λg = 1, fiscal deficits do not adjust at all over time. Ignoring fiscal shocks, this would imply the
absence of fiscal stabilization. This element of deficit smoothing seems therefore quite related to the recent
discussion on the question if the SGP is not too rigid in some circumstances and should not be amended in
any form to become more flexible and e.g. to let automatic stabilizers work freely in a recession.
3. Monetary Policy: Optimal Policies vs. Ad hoc Rules
As noted in the introduction, it is of significant importance, whether the ECB would be able or not to
implement its policies under discretion or commitment. In our dynamic NK model, the difference between
the commitment and discretionary case results from the forward-looking part of the model (the expectations
of the private sector about output, inflation and exchange rates) and is essentially an extension to a dynamic
setting of the time-inconsistency problem in the well-known static setting a la Barro-Gordon. It is important
to realize here that the transmission of monetary policy also takes place through the private expectations
about current and future monetary policy behavior, the s.c. expectations channel of monetary policy.
Commitment enables the policymaker to smooth the stabilization costs over time: if a macroeconomic shock
hits the economy, the policymaker can announce a path of current and future policy actions and credibly
implement this strategy. The private sector sets its expectations accordingly. Under discretion, such
announcements of future policy contingent on past commitments are not credible. As a result, under
commitment adjustments of interest rates, inflation and output will typically display more inertial adjustment
and less volatility than under discretion, given this ability to smooth out the adjustment costs over time.
Under discretion, policies and inflation are excessively volatile in the short run compared to the commitment
case and also welfare losses will be higher with discretionary policymaking due to the existence of a
stabilization bias in the short-run11. The differences between commitment and discretion will vanish when
11
Discretionary policies will also induce an inflationary bias in case the policymaker chooses an output objective that
7
output and inflation expectations become increasingly backward-looking12, since in that case the private
sector expectations are less and less affected by policy commitments, or stated differently, optimal policies
will suffer less and less from time-inconsistency problems when expectations become less and less forwardlooking. In a purely backward-looking model, the time-inconsistency problems of optimal monetary policy
disappear by definition.
Optimal monetary policy under commitment and discretion has received ample interest in the NK
literature but most results relate to a closed economy setting and ignores the effects of fiscal policy. Clarida
et al. (1999) demonstrate that in the closed-economy NK model if expectations are entirely forward-looking
the optimal monetary policy is history dependent under commitment and contemporaneous under discretion
following a cost-push shock. The history dependency under commitment gives rise to an improved trade-off
between output and inflation variability as it enables the monetary authorities to smooth out over time the
adjustments resulting from the cost-push shock. Jensen (2002) shows that in a closed-economy setting
without fiscal policy, with purely forward-looking output and inflation expectations and a monetary authority
that has no interest rate smoothing objective, the distinction between commitment and discretion is
essentially only relevant in the presence of cost-push shocks. There, stabilization of output and inflation is
subject to a trade-off between the variability of output and inflation. Demand and potential output do not
pose such dilemmas as monetary policy can then always be set –both under commitment and discretion- to
perfectly offset demand shocks and to perfectly accommodate potential output shocks.
We note that in case monetary policymakers also are concerned about interest rate smoothing, these
closed-economy results need to be modified since then the immediate full stabilization of demand and
potential output shocks will be costly because of the interest rate variability and hence not be optimal and
outcomes under monetary policy with commitment and discretion will differ. Moreover if output and
inflation expectations also contain backward looking elements, the above results need to be modified further
as the backward-looking components imply persistence of output and price adjustments making immediate
full stabilization no longer possible. Finally, the introduction of an active fiscal policy and an open economy
will further complicate the design of monetary policy. It is on these extensions of the basic optimal monetary
policy problem in a NK model that our analysis will focus.
Concerning the design of monetary policy by the ECB, we will distinguish between two different
settings: (i) a setting where the ECB implements an optimal policy, where we need to distinguish between
discretion and commitment strategies. (ii) a setting where the ECB implements an ad-hoc policy rule.
Following the terminology of Svensson (2000), the first case falls into the category of targeting rules and the
second case into the category of instrument rules.
(i )
Targeting rules
exceeds the potential output, reflecting e.g the case of a dependent Central Bank that is steered by political objectives.
In the remainder of this study we will, however, not deal with such cases.
12
Note that in our analysis, we will assume that exchange rate expectations are always set in an entirely forward-
8
Targeting rules seek to determine optimal policy responses to economic conditions, given a set of objectives.
In the context of the above model, we look at the policy strategies that minimize the following intertemporal
quadratic loss function of the ECB:
∞
(
LEt = Et ∑ Γτ [ β ( ∆pt +τ ) + ξ yt +τ − y t +τ
2
τ =0
)
2
+ ν ( ∆it +τ ) + κ ( ∆et +τ ) ]
2
2
(5)
subject to the adjustment dynamics of the economy and under assumptions whether or not the ECB acts
under commitment or discretion. Strict inflation targeting implies β > 0, ξ = ν = κ = 0 , strict output gap
targeting β = 0, ξ > 0, ν = κ = 0 , strict interest targeting β = ξ = 0, ν > 0, κ = 0 and strict exchange rate
targeting β = ξ = ν = 0, κ > 0 . Note that in a setting of perfect capital mobility as expressed by the UIP
condition (3), interest rate stability and stability of (the rate of change of) the exchange rate are intrinsically
linked. Flexible inflation targeting implies that inflation targeting is an important objective of the CB but that
it is also concerned about output and interest rate / exchange rate stability, β > 0, ξ > 0, ν > 0, κ > 0 which
seems to be the most realistic case.
(ii) Instrument rules
From an institutional point of view, the advantage of simple rules is their transparency and their ease to in
communicating and monitoring to/by the outside world. It is therefore interesting to confront the monetary
policy regimes outlined in (i) with the alternative of simple Taylor rule of the following form:
(
)
it = λi it −1 + (1 − λi ) i + φi (∆pt − ∆p ) + χ i ( yt − y t ) + µi ∆et + uti
(6)
with i ≡ r + ∆p (cf. footnote 3). The feedback on the output gap and inflation are standard in arguments of
the Taylor rule. A feedback on the exchange rate has been investigated in some open-economy Taylor rules,
and we have followed Taylor (2001) in this specification13. Monacelli (1999) shows that, under incomplete
exchange rate pass-through, an exchange rate augmented Taylor rule performs better than the standard
Taylor rule (be it based on CPI inflation or domestic inflation) in terms of inflation stabilization (but not in
terms of output stabilization). The preference for instrument smoothing is measured by the value of λi ,
where 0 ≤ λi ≤ 1 if λi goes to zero the original Taylor rule, which ignores instrument-smoothing objectives,
is obtained.
It is useful to note that the Taylor rule above can be seen as an example out of a broader class of
simple policy rules. Along this lines, Söderlind (1999) defines simple policy rules as optimal policies that
looking manner.
In Taylor (2001) the real rather than the nominal exchange rate features in the policy rule. Like Clarida (2001) we
adopt nominal exchange rate targeting here as it seems to be a more realistic and operational target in the monetary
policy rule. Given price-stickiness in the model, it should be stressed that this difference may in fact have only minor
implications and the more so if the exchange rate feedback is small, of course.
13
9
result from the general optimal policy problem defined under (i) but augmented with restrictions on the
coefficients and/or number of state variables to which the policymaker reacts. This definition of the simple
rules case as a restricted optimal policy problem is shown by the equivalent structure of both solutions in
terms of optimal policy. Depending on the amount of restrictions, the policy rule can be made more or less
complicated and in the absence of restrictions the optimal policy under commitment results. In this
interpretation the parameters {λi ,φi , χ i , µi } that the CB operates would be resulting from the solving an
optimal monetary policy problem like under (i) but one with a set of additional restrictions.
4.
The Effects of Macroeconomic Shocks: A Simulation Analysis.
This section uses simulations to illustrate a number of insights that can be obtained from the model
introduced in Section 3. We simulate the effects of demand shocks, cost-push shocks, potential output
shocks, fiscal shocks, exchange rate shocks and foreign shocks in the model of the EA. All shocks are 1
percent in size, occur in period 1, are unanticipated and have zero-persistence.
As outlined above, we compare the adjustments under 3 scenarios: (i) optimal monetary policy in
case of policy discretion, (ii) optimal monetary policy in case of commitment, (iii) ad-hoc monetary policy
rule. The simulations of the shocks provide (a) impulse response functions that give the dynamics
adjustments resulting from the shocks, including the transmission of macroeconomic policies (b) variances
and welfare losses resulting from the shocks, allowing us to investigate into more detail aspects of efficiency.
In these simulations we in particular want to obtain insights into: (i) optimal monetary policies of the
ECB both under discretion and commitment and in comparison to a simple monetary policy rule, (ii) the
consequences of alternative fiscal policy rules in EMU, (iii) the effects of foreign shocks, the dynamics of
the euro exchange rate and EA trade balance, (v) the role of alternative degrees of backward and forward
looking in output and inflation.
Underlying all the simulations in this section is a set of baseline model parameters that is broadly
consistent with empirical estimates for the EA (see Table 1) or plausible/convenient as a reference point14.
This paper in other words does not attempt itself to estimate the model for the EA. The baseline parameters
concern : (i) the hybrid IS and Phillips curves: ψ 1 ,ψ 2 , ω1 , ω2 , (ii) other structural parameters: α ,η ,σ , δ , γ ,τ ,
(iv) parameters that characterize monetary and fiscal policy rules λi ,φi , χ i , µi , λg , χ g , (iii) assumptions on
variances and autocorrelations of shocks, ρ v ,σ v2i . Note in particular that the empirical studies suggest that
i
the EA economy is characterized by a (i) substantial degree of backward lookingness in output and inflation,
(ii) a substantial degree of deficit and interest rate smoothing in the policy rules. In the remainder of the
14
While the absence of any own empirical estimations may seem a bit unsatisfying this type of analysis based on
calibrated parameters and/or parameters that appears plausible from empirical studies, is quite common in NK papers.
See e.g. Jensen (2002) that follows this line of thought and analysis and refers to “compromise values” when choosing
parameter values that would seem plausible for the U.S. case in his analysis.
10
paper we will assume that the monetary and fiscal rules based on the estimates of Table 1 are a relatively
accurate representation of policies in the EA and refer to them as the “actual policies”.
Naturally, outcomes may be more or less specific to this set of baseline assumptions. In case of small
changes in the parameters, the differences compared to the baseline are typically of a quantitative nature
rather than a qualitative nature. If changes get larger, the results can also change qualitatively. In Section 5
we will undertake some sensitivity analysis to try to shed some light on that aspect of the analysis. To some
extent our results are likely to be model-specific as well. However, we noted that in several cases larger,
estimated EA models yield similar adjustments as in our model in case comparable shocks are studies. E.g.
the Dieppe and Henry (2004) Area-Wide Model gives comparable adjustment dynamics as our model in case
of a demand shocks, fiscal shocks and productivity shocks. Smets and Wouters (2002) model gives
qualitatively similar outcomes in case of exchange rate shocks, a foreign output shocks and productivity
shocks.
i)
A positive demand shock
Figure 1 displays the adjustments that are produced by a positive one percent demand shock in the EA at t =
1 (vd(1) = 1%). Outcomes under discretion, commitment, and the Taylor rule are denoted by _dis, _com and
_rul, respectively.
[Insert Figure 1 here]
The demand shock increases output in the short-run which will tend to increase inflation. The ECB reacts by
raising the interest rate. This causes an initial appreciation after which the exchange rate depreciates
according to the UIP condition. The increase of the real interest rate and the real appreciation contribute to a
stabilization of output and inflation. The automatic stabilizers of the fiscal policy rule generate a fiscal
surplus which also contributes to the stabilization of output and inflation. The real appreciation causes a
current account deficit. It is seen that the monetary policy regime has a significant impact on the outcomes
produced by the demand shock. Compared to discretion, commitment results in a more smooth adjustment of
the interest rate and inflation, reflecting the stabilization bias present under discretion as noted in the
introduction. The actual monetary policy rule case with strong interest rate smoothing is marked by a
somewhat higher persistence in the adjustments compared to optimal policies under commitment and
discretion. Because of the high interest rate and deficit smoothing, macroeconomic policies react too slowly
and the policies are moreover too persistent, implying that at some point in time they actually may contribute
to fluctuations in output and inflation.
Table 2 provides the variances of output, inflation, changes in interest rates and exchange rates and
the welfare losses that result in the different regimes and for the type of shocks studied in this section. It is
directly seen that commitment reduces in particular inflation variability compared to discretion, contributing
to the lower losses under commitment. The Taylor rule case leads to the highest variance of inflation and
11
interest rate changes. The difference in losses between discretion and the Taylor rule based on actual
estimates for the EA are relatively small an observation that is also seen in the other examples below.
ii)
A positive cost-push shock
Next, we analyse the effects of a non-persistent one percent cost-push shock in Figure 2 (vs(1) = 1%):
[Insert Figure 2 here]
A cost-push shock results in a stagflation: there is a substantial decline in output and a burst in inflation.
Given the prevalence of inflation stabilization in its motives, the ECB raises the interest rate. The inflation
and initial appreciation erode competitiveness and the current account deteriorates. The prolonged recession
and the presence of deficit smoothing imply a substantial fiscal deficit. This implies a policy conflict with the
ECB: whereas the ECB follows a restrictive policy, the fiscal policy is expansionary. That in particular costpush shocks are prone to policy conflicts as monetary and fiscal policies tend to act as policy substitutes
rather than complements, has also been note in several empirical studies, see e.g. Muscatelli et al. (2004) for
an insightful application to the U.S. case.
The difference in adjustment dynamics between commitment and discretion are considerable and
even more substantial than in the previous case. Commitment produces a much smoother stabilization of
inflation and less strong monetary policy intervention. The Taylor rule induces relatively similar adjustments
patterns as policy discretion, although the persistence seems to be somewhat higher. The resulting losses in
Table 2 show that commitment leads to the lowest losses and discretion to the highest.
iii)
A positive productivity shock
The effects of a one percent productivity shock ( v y (1) = 1%) are provided in Figure 3.
[Insert Figure 3 here]
The negative output gap that initially results and that positive thereafter is the result of the initial shock to
potential output and the resulting increase in actual output. Inflation tends to drop initially in the case of
discretion and the simple rule case, thereby evoking an expansionary monetary policy. The (real) exchange
rate depreciation and decrease of the (real) interest rate that are produced stimulate output and inflation. The
depreciation also contributes to a current account surplus as it boosts competitiveness. The small fiscal
surplus is resulting from the increase in output.
Under commitment, inflation is positive and stabilizes again faster as in the other cases. As noted
earlier, commitment avoids the emergence of a suboptimal stabilization bias that is present in the discretion
case. The resulting lower volatility of inflation, interest rates and exchange rates is a general feature of the
12
commitment regime also found in the other examples (cf. Table 2). In most cases the initial output
fluctuations are larger under commitment but thereafter also output tends to stabilize faster under
commitment. Compared to optimal policies, the monetary policy rule regime is marked by higher persistence
in the fluctuations in inflation in particular but also in other variables. Most of the observations concerning
losses and variances for different monetary policy regimes in the previous examples are also seen here.
Interestingly, this example (like the first example concerning demand shocks) illustrates that the
conclusion of Jensen (2002) that the distinction between commitment and discretion only matters in case of
cost-push shocks needs to be modified in this more general setting of the NK model. The presence of
backward-looking output and inflation dynamics, an interest rate smoothing objective, the presence of fiscal
policy and the link between interest rates and exchange rates in an open economy context, imply that
commitment and discretion result in different outcomes also in case of demand and productivity shocks.
iv)
A positive fiscal shock
g
The workings of a fiscal shock (v (1) = 1%) are relatively similar to a demand shock as shown in Figure 4.
[Insert Figure 4 here]
One important difference comes from the fiscal rule itself: the initial shock leads to a dynamic adjustment
process in the fiscal deficit itself due to the deficit smoothing mechanism. This is clearly seen in the
adjustment of the deficit in Figure 4. The adjustments of other variables are quite similar to the adjustments
in Figure 1. The expansionary fiscal policy is counteracted by a restrictive monetary policy in order to
combat inflation. In contrast to Figure 1 where the automatic stabilizers result in a counter-cyclical fiscal
policy that is supportive of monetary policy, here we observe the opposite. The pro-cyclical fiscal policy is
not in line with the restrictive monetary policy that aims at combating inflation. The induced appreciation of
the exchange rate reduces the competitiveness so that net exports are crowded out and the current account
remains in deficit. Concerning variability of output, inflation and interest rate and welfare losses we reach
the same conclusions as in case of the demand shocks.
v)
A positive exchange rate shock
As discussed earlier, exchange rate adjustment is an important variable in the dynamic adjustments in this
model. Figure 5 displays the effects from a shock to the exchange rate (vr(1) = 1%) itself.
[Insert Figure 5 here]
The initial appreciation shock induces modest but highly cyclical fluctuations in output and inflation.
Monetary and fiscal policy are expansionary for most of the time. Monetary policy commitment delivers
13
significant gains in stabilizing inflation and output compared to discretionary monetary policy and rule-based
monetary policy.
vi)
A positive foreign output shock
Since the EA is an open economy, it is interesting to analyze the effects of foreign shocks and how these
affect monetary policy of the ECB e.g. Figure 6 shows the adjustments produced by a foreign output shock
(vy*(1) = 1%).
[Insert Figure 6 here]
The direction of the effects are very similar to those produced by a demand shock but the size of the effects
is considerably smaller given that net exports are only a fraction of total demand. In addition, the foreign
output shock leads to a current account surplus rather than a deficit. Also the conclusions concerning welfare
losses and variability of inflation, output, interest rates and exchange rates in the different regimes are the
same as in the case of the demand shock in (i).
5.
A Robustness /Sensitiveness Check of the Results.
The results obtained above were based on the specific set of baseline parameters that was used. Though their
values were made plausible by considering empirical estimations in the literature, it may well be that some
values may be inaccurate. It is therefore interesting and useful to check if the outcomes change if we change
the baseline parameters. We experimented with the following variations relative to the baseline set of
parameters:
(i)
the degree of forward-lookingness of the IS and Phillips curves: ψ 1 ,ψ 2 , ω1 , ω2 .
Clearly, the amount of forward-lookingness in the IS and Phillips curves plays a crucial role in the
transmission of shocks and therefore in policymaking. In addition it is one of the key parameters that
determine the differences between the commitment and discretion regimes: the higher the degree of forwardlooking, the more commitment matters, and the more adjustment under commitment differs from discretion,
think e.g. of the stabilization bias problem associated with discretion. We focus here on the role of forwardlookingness w.r.t. inflation. Figure 7 shows the effects of a cost-push shock in the baseline model for three
alternative values of ω1 : (i) ω1 = 0 implying a forward-looking Phillips curve, (ii) ω1 = 0.5 implying a hybrid
Phillips curve and (iii) ω1 = 1 implying a backward-looking Phillips curve. We show these cases for the three
monetary policy regimes since the effects of changing the amount of forward-lookingness depends among
others also on the monetary policy regime.
[Insert Figure 7 here]
14
With decreasingly forward-looking expectations, the persistence of output, inflation and interest rates
fluctuations caused by the cost-push shocks increases substantially. This is the case in all three regimes.
Clearly, stabilizing an economy that is more backward-looking, is more costly and time-consuming for the
policymakers. The efficiency of commitment with an increasing degree of forward-looking inflation
expectations is also visible: inflation and interest rates are much less volatile under commitment than under
discretion when the economy is more forward-looking and the volatility of output is not much higher.
(ii)
other structural parameters: α ,η ,σ , ζ , δ , γ ,τ .
As seen from Table 1 there is considerable variation in the estimates of the other parameters of the IS and
Phillips curves. Figure 8 shows the effects of a fiscal shocks in the baseline model with commitment but
where we vary γ , τ and α .
[Insert Figure 8 here]
γ measures the output elasticity of inflation in the Phillips curve and by linking demand and supply in the
model it is one of the key parameters. With higher values of γ the flexibility of output and prices in the
model increases in panel (a): output and inflation stabilize faster. This also reduces −cet.par.− the amount of
monetary policy activity to obtain the same amount of stabilization. A stronger pass-through parameter τ ,
implies a stronger effect from exchange rate fluctuations on domestic prices, see panel (b). The fiscal shock
leads to an appreciation and interest rate increases as we know from before (see Figure 4), but these effects
themselves depend also on τ as we see here. The appreciation reduces inflation which restores
competitiveness. The effects of varying α in panel (c) are not as strong as the effects of γ or τ . This would
suggest that the interest rate channel of monetary policy –which is captured by α - is actually not very strong
in this case.
(iii)
parameters that characterize monetary and fiscal policy rules λi ,φi , χ i , µi , λg , χ g and
monetary policy preference parameters Γ, β , ξ ,ν , κ .
First, we experimented with alternative fiscal policy rules to assess their effects. In Figure 9 the variance of
inflation, output and interest rate changes is plotted as a function of the deficit smoothing parameter λg in
case of a demand shock (panel (a)) and a cost-push shock (panel (b)).
[Insert Figure 9 here]
Both in case of demand and cost-push shocks, a more inert and persistent fiscal policy increases the variance
of inflation and output. In case of demand shocks, less fiscal flexibility raises the variance of interest rate,
whereas the variance of interest rate is lowered in case of cost-push shocks. This suggests that from the
15
perspective of the monetary policymaker, fiscal flexibility is preferred in case of demand shocks, but in case
of cost-push shocks constraints on fiscal flexibility are needed. This outcome is robust across the three
monetary policy regimes.
Next, we varied the preferences of the ECB under commitment and discretion. Table 3 gives the
effects of changing the preferences w.r.t. output stabilization, ξ , and interest rate smoothing, ν , for the case
of demand shocks. The effects are straightforward: (except for a few corner cases with either ξ or ν equal to
zero or one) (a) the variance of inflation increases if the preferences for interest rate smoothing increase and
it decreases with a higher preference for output stability. (b) The variance of the output gap increases if
interest rate smoothing increases and it decreases with preferences for higher output stability. (c) Interest rate
variability decreases with higher preferences for interest rate stability and it increases with higher
preferences for output stability. Moreover, these effects conclusions hold both in case of commitment and
discretion.
(iv) assumptions on variances and autocorrelations of shocks, σ v2i , ρ i .
The effects of increasing or decreasing the variance of shocks are straightforward: this will lead to
proportional changes in the variances of inflation, output etc. In addition, in the baseline equal variances of
all shocks were assumed and it was seen that e.g. in terms of variability of output, cost-push shocks imply
the highest variability of output and foreign output shocks the lowest. Increasing e.g. the variability of
foreign output shocks will, ceteris paribus, increases the relative importance of foreign output shocks -and
decreases the relative importance of the other type of shocks- in explaining the variability of output. Finally,
the baseline set of parameters assumes that all shocks are uncorrelated with each other and are uncorrelated
over time. The last assumption was not only done because of absence of empirical estimations but also for
expositional reasons: increasing the degree of persistence of shocks has strong effects on all adjustments.
The increased persistence of shocks will add to the internal persistence of the model produced in particular
by the backward-lookingness in inflation and output and the policy regime (commitment vs discretion or rule
based). In case of persistent shocks it will be impossible to distinguish how much of the persistence of
variables is due to the persistence of shocks and how much of the persistence is intrinsic to the model. On the
other hand, in case of non-persistent shocks we know that the entire persistence of variables is due to the
intrinsic dynamics of the model.
Conclusions
The design of monetary policy by the ECB is likely to have important impacts in the EA. Conversely,
monetary policy in the EA is affected by many factors. In this paper, we focused on the role of the monetary
policy regime using a very stylized NK model of the EA: given the structural parameters of the EA economy,
the effects were shown to be strongly conditional upon the monetary policy regime: whether monetary policy
16
was implemented under commitment, discretion or a rule-based framework was seen to have important
consequences.
In addition, we highlighted the role of fiscal policy and external factors in the EA. Fiscal policies
matter for the monetary policymaker: in particular the degree of deficit smoothing and their cyclical
component have a strong influence. Moreover, in an open economy like the EA, exchange rate adjustment
and foreign shocks are of fundamental importance and may substantially change adjustment dynamics
compared to a closed economy setting. This has clearly implications for the monetary policy: not only the
interest rate channel will determine outcomes, but also the exchange rate channel of monetary policy.
To illustrate this, we analyzed the effects of a series of macroeconomic shocks to assess their impact
on monetary policy in the EA model. As to be expected, commitment strategies yield the best outcomes in
many respects. In particular, inflation stabilization is fostered under commitment. Optimal policies under
discretion suffer from a short-run stabilization bias compared to commitment. Results based on empirical
estimates of the Taylor rule are also inferior necessary to commitment. Compared to discretion, its
performance was in most cases not much worse or even slightly outperforming the optimal discretionary
policy.
The difference between the monetary policy regimes was also seen to be a function of many
mechanisms. The existing NK literature on optimal monetary policy under commitment and discretion
focuses on cost-push shocks in a purely forward-looking setting of a closed economy and in the absence of
interest rate smoothing objectives and an active fiscal policy. It finds that in that setting, the difference
between commitment and discretion is only important in case of cost-push shocks since potential output and
demand shocks are always fully stabilized in both cases. Our analysis showed that the introduction of
backward-looking expectations, an interest rate smoothing objective, active fiscal policy and an open
economy setting, implies that this finding needs modifications and that the distinction between commitment
and discretion becomes also important in case of demand and potential output shocks.
Extensions of the analysis could go into several directions: in particular one could envisage: (i) a
further working out of the simple rules regimes allowing for various other simple rules e.g. (ii) The model
can be extended to include to include the possibility that the monetary authorities are facing parameter
uncertainty and data uncertainty since these have been shown in the literature to have important
consequences for monetary policy. (iii) enriching the effects of monetary and fiscal policy, one could think
of including the LM curve to analyze monetary targeting and fiscal effects on the supply side of the
economy.
Appendix
The model (1)-(4) can be written in state-space form:
⎡ X t +1 ⎤
⎡Xt ⎤
⎢
⎥ = A ⎢ ⎥ + Bit + Cvt +1
⎣ xt +1 ⎦
⎣ xt ⎦
17
(A.1)
X t = ⎡⎣ yt −1 ∆pt −1 et −1 pt −1 pt*−1 utd y t uts utr yt* pt* it* it −1 g t pt ⎤⎦
where
is a 15*1 vector of predetermined
variables in the model, xt = [ yt ∆pt et ] a 3*1 vector of forward-looking variables, it = [it ] a 1*1 vector of
instruments and vt = ⎡ vtd vty vts vtr vty* vtp* vti* vtg ⎤ a 8*1 vector of macroeconomic shocks.
⎣
⎦
The objective function of the policymaker (6) can be rewritten as;
∞
min LEt = Et ∑ Γτ Yt +τ 'WYt +τ s.t. (A.1)
it
(A.2)
τ =0
⎡ yt − y t ⎤
⎡β 0 0 0 ⎤
⎢
⎥
⎢
⎥
π
⎥ = D ⎡ X t ⎤ + C i is a 4*1 vector of target variables and W = ⎢ 0 ξ 0 0 ⎥ ,
where Yt = ⎢ t
i t
⎢ ⎥
⎢i − i ⎥
⎢0 0 ν 0⎥
⎣ xt ⎦
⎢ t t −1 ⎥
⎢
⎥
⎢⎣ et − et −1 ⎥⎦
⎣⎢ 0 0 0 κ ⎥⎦
⎡ 0
⎢ 0
⎢ 0
⎢ 0
⎢ 0
⎢ 0
⎢ 0
⎢ 0
⎢ 0
⎢ 0
⎢
A=
⎢ 0
⎢ 0
⎢ 0
⎢ 0
⎢ 0
⎢ ψ
⎢−
⎢ ψ
⎢ 0
⎢
⎢⎣ 0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
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
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
0
(1 − λ g ) χ g
0
0
d
0
0
0
0
0
0
0
0
0
0
ρ
y
0
ρ
s
r
0
0
0
0
0
0
0
ρ
0
0
0
0
0
0
0
0
ρ
y*
ρ
p
*
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
λg
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
1
0
1
0
αγ
α
σ
ατ − δω 2
δ
(1 + ζ )ω 2 + αγ
α
ατ − δω 2
ψ 2ω2
γ
ψ 2 ω2
ψ 2ω2
ψ 2ω2
τ
ψ2
ψ 2 ω2
γ
ψ2
1
ψ 2ω2
τ
ω2
ω2
ω2
0
0
αω1
ψ 2ω2
ω1
−
ρ
−
ατ
ψ 2ω2
τ
ω2
ω2
0
0
0 −
0
0
ατ
ψ 2ω2
τ
ω2
0
−
1
ψ2
0
0
−
ω2
0
−
0
−
1
ω2
0
18
0
0
1
0
−
ω2
0
ρ
i*
0
η
ψ2
0
0
0
0
0
−1
0
0
0
−
−
−
1
⎡ 0 ⎤
⎢ 0 ⎥
⎢
⎥
⎢ 0 ⎥
⎢
⎥
⎢ 0 ⎥
⎢ 0 ⎥
⎢
⎥
⎢ 0 ⎥
⎢ 0 ⎥
⎢
⎥
⎢ 0 ⎥
⎢ 0 ⎥
⎢
⎥
B=⎢ 0 ⎥
⎢
⎥
⎢ 0 ⎥
⎢ 0 ⎥
⎢
⎥
⎢ 0 ⎥
⎢ 1 ⎥
⎢
⎥
⎢ 0 ⎥
⎢ α ⎥
⎢
⎥
⎢ψ 1ψ 2 ⎥
⎢
⎥
⎢ 0 ⎥
⎢⎣⎢ 1 ⎥⎦⎥
⎡0 ⎤
⎡0
⎢0 ⎥
⎢0
⎢
⎥
Ci =
, D=⎢
⎢1 ⎥
⎢0
⎢ ⎥
⎢
⎣⎢0 ⎦⎥
⎣⎢ 0
⎡0
⎢0
⎢
⎢0
⎢
⎢0
⎢0
⎢
⎢0
⎢1
⎢
⎢0
⎢0
C=⎢
⎢0
⎢
⎢0
⎢0
⎢
⎢0
⎢0
⎢
⎢0
⎢0
⎢
⎢0
⎢
⎢⎣⎢ 0
0 0
0 0
0 0
0 −1
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
0
0
0
1
0
0
0
0
1
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
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
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⎥
⎥
0⎥
1⎥
⎥
0⎥
0 ⎥⎥
0⎥
⎥
0 ⎥⎥⎦
0 0
0 −1
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 −1
0 0
0
0
0
0
0
1
0
0
1
0
0
0
0⎤
0 ⎥⎥
.
0⎥
⎥
1 ⎦⎥
The model (A.1)-(A.2) is a standard linear stochastic regulator problem with rational expectations and
forward-looking variables Optimal policies can be determined (a) under a regime of policy commitment, (b)
under policy discretion (see e.g. Oudiz and Sachs (1985), Backus and Driffill (1986), and Söderlind (1999),
Jensen (2002) for the detailed working out of the optima; policies under commitment and discretion cases).
In the discretion case, the policymaker reoptimizes each period by taking the process by which
private agents form their expectations as given, where the expectations are consistent with actual policies.
The optimal reaction function and forward-looking variables will be linear functions of the predetermined
variables. The dynamics of the economy are then described by:
X t +1 = M 11 X t + vt +1
xt = HX t
(A.3)
it = FX t
Yt = (C1 + C2 H + Ci F ) X t
19
⎡M
where M ≡ ( I − F )−1 ( A + BF ) and M = ⎢ 11
⎣ M 12
M 21 ⎤
⎡C1 ⎤
, C = ⎢ ⎥ are partitioned according to Xt and xt.
⎥
M 22 ⎦
⎣C2 ⎦
Standard solution algorithms (see Söderlind (1999)) are used to determine H and F and derive the adjustment
dynamics and variance-covariance matrices under discretion.
In the commitment case, the policymaker optimises at the beginning of the planning period. The
policymaker acts as a Stackelberg leader w.r.t. the private sector, taking into the equations of motion of the
forward looking variables (i.e. the expectations of the private agents) as additional constraints It adopts this
optimal policy and sticks to it during the entire planning period. The optimal reaction function and the
forward-looking variables depend not only on the predetermined variables but also depend on the shadow
prices of the forward-looking variables. The latter measure the costs from reneging upon the committed
policy. The optimal reaction function commitment solution is determined by a decomposition of the stable
eigenvalues from the first-order conditions of the optimization problem (A.2) subject to the transition
equation (A.1), see e.g. Söderlind (1999) for the different optimization procedures.
In the simple policy rule regime, the rule is inserted as it = QX t into the dynamic system (A.3)
instead of the optimal policy, see again Söderlind (1999) on the simple rule regime.
20
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mimeo.
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Economics and Dynamics, vol.27, p.1611-1638.
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22
1.29
1.5
0.87
0.76
0.94
0.75
85:I-02:IV
80:I-97:IV
79:1-97:12
0.5
0.32
0.76
0.28
2.61
1.00
3.20
0.0
0.52
0.75
0.61
0.4
0.42
1.0
0.96
0.003
r
1.0
σ v2
0.4
0.54
0.63
0.13
0.46
0.24
0.33
ω1
0.48
s
1.0
0.002
0.001
0.42
σ v2
0.6
0.46
0.37
0.75
0.54
0.60
0.38
1.00
0.99
ω2
0.52
y
1.0
0.38
0.13
σ v2
0.1
0.06
0.12
0.07
0.06
0.02
0.17
0.04
0.02
γ
0.18
y*
1.0
σ v2
0.15
0.2
τ
1.0
p*
σ v2
23
Table 1
Estimations of the IS and Phillips curves, Taylor rules and macroeconomic shocks characteristics for the euro-area. a Germany.
1.20
1.93
1.73
1.29
0.88
0.87
1974-2000
1979-1998
1.40
0.90
1.00
2.02
83:I-00:IV
0.80
0.83
0.90
1.00
d
σ v2
?
70:III-99:IV
λg
0.25
cal./est.
GMM
0.87
µi
0.25
χg
0.005
0.77
χi
0.5
0.02
δ
75:I-00:IV
φi
0.3
0.06
σ
VAR
λi
0.6
0.51
0.45
0.93
0.48
η
0.63
period
0.4
0.49
1974-2000
70:I-99:IV
90:1-02:IV
0.50
0.22
0.45
86:1-00:IV
71:2-97:IV
83:I-00:IV
0.08
0.06
0.03
0.11
0.06
0.30
0.44
1977-1997
0.70
0.56
0.08
0.97
α
0.06
75:I-00:IV
ψ2
0.56
ψ1
0.44
period
calibration
Djoudad and Gauthier
GMM
(2003)
Sahuc (2002)
FIML
Ballabriga and Mongay GMM
(2002)a
Gerdesmeier and Roffia
(2003)
Peersman and Smets
2SLS
(1999)
Peersman and Smets
2SLS
(1999)a
memo: our parametrisation
Ehrmann and Smets
(2002), Smets (2003)
Coenen and Wieland
(2002)
Casares (2004)
Domenech et al. (2001)
Authors
method
Ehrmann and Smets
calibration
(2002), Smets (2003)
Coenen and Wieland
VAR
(2002)
Casares (2004)
calibration
Smets (2003)
GMM
Gali et al. (2003)
GMM
Domenech et al. (2001)
GMM
Leith and Malley (2002)
GMM
Djoudad and Gauthier
GMM
(2003)
Sahuc (2002)
FIML
Jondeau and Bihan
GMM
(2005)
Faruqee (2004)
VAR
memo: our parametrisation
Authors
method
1.0
i*
σ v2
vd
vs
vy
vg
vr
vy*
var(π)
var( y − y )
var(∆i)
L
var(π)
var( y − y )
var(∆i)
L
var(π)
var( y − y )
var(∆i)
L
var(π)
var( y − y )
var(∆i)
L
var(π)
var( y − y )
var(∆i)
L
var(π)
var( y − y )
var(∆i)
L
Discretion
0.56052
0.52439
Commitment
0.40124
0.5247
Rules
0.68548
0.027576
0.37473
38.7753
2.2655
5.194
0.87441
24.2006
3.9398
4.4996
0.29158
40.994
3.1108
1.5612
3.7284
579.1957
0.69531
8.4316
329.3528
0.56016
5.5866
522.8561
0.8313
0.17243
0.16038
0.026585
0.24426
43.5491
0.6489
0.47727
0.63027
31.6109
0.46742
0.51582
0.18622
46.2364
0.77972
0.075355
3.1489
69.2403
0.023087
0.056781
2.5494
33.5866
0.021023
0.011569
3.272
66.9626
0.052449
0.10706
0.58686
13.1091
0.035032
0.032774
0.64
9.4203
0.025077
0.032794
0.92955
14.7021
0.042842
0.0017235
0.023421
2.4235
0.05465
1.5125
0.018224
2.5621
Table 2
Variance analysis and losses from various shocks.
24
output gap (demand shock)
inflation (demand shock)
1
0.15
0.8
0.1
0.6
0.05
0.4
0
0
0.2
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
-0.05
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
-0.1
-0.2
-0.4
-0.15
ygap_dis
ygap_com
ygap_rul
dp_dis
interest rate (demand shock)
dp_com
dp_rul
real interest rate (demand shock)
0.3
0.3
0.25
0.25
0.2
0.2
0.15
0.15
0.1
0.1
0.05
0
0.05
-0.05
0
0
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
-0.1
10 11 12 13 14 15 16 17 18 19 20
-0.05
0
-0.15
i_dis
i_com
i_rul
r_dis
fiscal deficit (demand shock)
r_com
r_rul
current account (demand shock)
0.04
0.05
0
0.02
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
-0.05
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
-0.1
-0.02
-0.15
-0.04
-0.2
-0.06
-0.25
-0.08
-0.3
-0.1
-0.35
g_dis
g_com
g_rul
cua_dis
exchange rate (demand shock)
cua_rul
real exchange rate (demand shock)
0.1
0.2
0.1
0
0
-0.1
-0.1
cua_com
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
10 11 12 13 14 15 16 17 18 19 20
-0.2
-0.2
-0.3
-0.3
-0.4
-0.4
-0.5
-0.5
-0.6
-0.6
-0.7
-0.7
-0.8
-0.8
e_dis
e_com
e_rul
rer_dis
Figure 1
A Demand Shock
25
rer_com
rer_rul
output gap (cost-push shock)
inflation (cost-push shock)
0.400
1.400
0.200
1.200
1.000
0.000
-0.200
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
0.800
0.600
-0.400
0.400
-0.600
0.200
-0.800
0.000
-1.000
-0.200
-1.200
-0.400
-1.400
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-0.600
ygap_dis
ygap_com
ygap_rul
dp_dis
interest rate (cost-push shock)
dp_com
dp_rul
real interest rate (cost-push shock)
0.500
0.600
0.400
0.400
0.200
0.300
0.000
0.200
-0.200
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
0.100
-0.400
0.000
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-0.100
-0.600
-0.800
-0.200
-1.000
-0.300
-1.200
i_dis
i_com
i_rul
r_dis
fiscal deficit (cost-push shock)
r_com
r_rul
current account (cost-push shock)
0.300
0.100
0.250
0.050
0.200
0.000
0.150
1
0.100
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-0.050
0.050
-0.100
0.000
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-0.050
-0.150
g_dis
g_com
g_rul
ca_dis
exchange rate (cost-push shock)
ca_rul
real exchange rate (cost-push shock)
0.800
0.200
0.600
0.000
0.400
-0.200
0.200
-0.400
0.000
-0.200
ca_com
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-0.600
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-0.800
-0.400
-1.000
-0.600
-1.200
-0.800
-1.400
-1.000
-1.600
-1.200
-1.800
e_dis
e_com
e_rul
rer_dis
Figure 2
A Cost-Push Shock
26
rer_com
rer_rul
output gap (pot.output shock)
inflation (pot.output shock)
0.400
0.100
0.080
0.200
0.060
0.000
0.040
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
0.020
-0.200
0.000
-0.400
-0.020
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-0.040
-0.600
-0.060
-0.800
-0.080
-1.000
-0.100
ygap_dis
ygap_com
ygap_rul
dp_dis
interest rate (pot.output shock)
dp_com
dp_rul
real interest rate (pot.output shock)
0.150
0.050
0.100
0.000
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
0.050
-0.050
0.000
-0.100
-0.050
-0.150
-0.100
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-0.150
-0.200
-0.200
-0.250
-0.250
-0.300
-0.300
i_dis
i_com
i_rul
r_dis
net government spending (pot.output shock)
r_com
r_rul
current account (pot.output shock)
0.010
0.090
0.080
0.000
1
2
3
4
5
6
7
8
9
0.070
10 11 12 13 14 15 16 17 18 19 20 21
-0.010
0.060
0.050
-0.020
0.040
-0.030
0.030
0.020
-0.040
0.010
-0.050
0.000
-0.060
-0.010
g_dis
g_com
1
2
3
4
5
7
8
9
ca_dis
exchange rate (pot.output shock)
10 11 12 13 14 15 16 17 18 19 20 21
ca_com
ca_rul
real exchange rate (pot.output shock)
0.800
0.800
0.700
0.700
0.600
0.600
0.500
0.500
0.400
0.400
0.300
0.300
0.200
0.200
0.100
0.100
0.000
-0.100
6
g_rul
0.000
1
2
3
4
5
6
7
8
9
e_dis
10 11 12 13 14 15 16 17 18 19 20 21
e_com
-0.100
1
2
3
e_rul
4
5
6
7
8
9
rer_dis
Figure 3
A Potential Output Shock
27
10 11 12 13 14 15 16 17 18 19 20 21
rer_com
rer_rul
output gap (fiscal shock)
inflation (fiscal shock)
0.700
0.250
0.600
0.200
0.500
0.150
0.400
0.100
0.300
0.050
0.200
0.000
0.100
-0.050
0.000
-0.100
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-0.100
-0.150
-0.200
-0.300
-0.200
ygap_dis
ygap_com
ygap_rul
dp_dis
interest rate (fiscal shock)
dp_com
dp_rul
real interest rate (fiscal shock)
0.250
0.300
0.200
0.200
0.150
0.100
0.100
0.000
1
0.050
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-0.100
0.000
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-0.200
-0.050
-0.100
-0.300
i_dis
i_com
i_rul
r_dis
fiscal deficit (fiscal shock)
r_com
r_rul
current account (fiscal shock)
0.050
1.200
0.000
1.000
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-0.050
0.800
-0.100
0.600
-0.150
0.400
-0.200
-0.250
0.200
-0.300
0.000
1
2
3
4
5
6
7
8
9
g_dis
10 11 12 13 14 15 16 17 18 19 20 21
g_com
-0.350
g_rul
ca_dis
exchange rate (fiscal shock)
ca_rul
real exchange rate (for.int shock)
0.600
0.600
0.400
0.400
0.200
0.200
0.000
-0.200
ca_com
1
2
3
4
5
6
7
8
9
0.000
10 11 12 13 14 15 16 17 18 19 20 21
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-0.200
-0.400
-0.400
-0.600
-0.600
-0.800
-0.800
-1.000
-1.200
-1.000
e_dis
e_com
e_rul
rer_dis
Figure 4
A Fiscal Shock
28
rer_com
rer_rul
output gap (exr shock)
inflation (exr shock)
0.250
0.100
0.200
0.050
0.150
0.000
1
2
3
4
5
6
7
8
9
0.100
10 11 12 13 14 15 16 17 18 19 20 21
0.050
-0.050
0.000
1
-0.100
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-0.050
-0.150
-0.100
ygap_dis
ygap_com
ygap_rul
dp_dis
interest rate (exr shock)
dp_com
dp_rul
real interest rate (exr shock)
0.050
0.100
0.050
0.000
0.000
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-0.050
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-0.050
-0.100
-0.150
-0.100
-0.200
-0.250
-0.150
-0.300
-0.200
-0.350
i_dis
i_com
i_rul
r_dis
fiscal deficit (exr shock)
r_com
r_rul
current account (exr shock)
0.030
0.100
0.025
0.050
0.020
0.000
0.015
-0.050
0.010
-0.100
0.005
-0.150
1
0.000
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-0.200
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-0.005
-0.250
g_dis
g_com
ca_dis
g_rul
exchange rate (exr shock)
ca_com
ca_rul
real exchange rate (exr shock)
0.400
0.400
0.200
0.200
0.000
0.000
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
1
-0.200
-0.200
-0.400
-0.400
-0.600
-0.600
-0.800
-0.800
-1.000
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-1.000
e_dis
e_com
e_rul
rer_dis
Figure 5
An Exchange Rate Shock
29
rer_com
rer_rul
output gap (for.output shock)
inflation (for.output shock)
0.250
0.040
0.200
0.030
0.150
0.020
0.100
0.010
0.050
0.000
0.000
-0.010
1
1
2
3
4
5
6
7
8
9
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
10 11 12 13 14 15 16 17 18 19 20 21
-0.050
-0.020
-0.100
-0.030
ygap_dis
ygap_com
ygap_rul
dp_dis
interest rate (for.output shock)
dp_com
dp_rul
real interest rate (for.output shock)
0.070
0.080
0.060
0.060
0.050
0.040
0.040
0.030
0.020
0.020
0.010
0.000
1
0.000
-0.010
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-0.020
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-0.020
-0.040
i_dis
i_com
i_rul
r_dis
net government spending (for.output shock)
r_com
r_rul
current account (for.output shock)
0.200
0.010
0.005
0.150
0.000
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
0.100
-0.005
-0.010
0.050
-0.015
0.000
-0.020
1
-0.025
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-0.050
g_dis
g_com
g_rul
ca_dis
exchange rate (for.output shock)
ca_com
ca_rul
real exchange rate (for.output shock)
0.050
0.050
0.000
0.000
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
1
-0.050
-0.050
-0.100
-0.100
-0.150
-0.150
-0.200
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-0.200
e_dis
e_com
e_rul
rer_dis
Figure 6
A Foreign Output Shock
30
rer_com
rer_rul
output gap (cost-push shock, discretion)
0.5
inflation (costpush shock, discretion)
0.7
0.9
0.6
0.0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
0.5
0.7
0.4
0.5
-0.5
interest rate (cost-push shock, discretion)
1.1
0.3
0.3
0.2
-1.0
0.1
-0.1
-1.5
-2.0
omega1=0
omega1=0.5
0.1
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
0.0
-0.3
-0.1
-0.5
-0.2
omega1=1
omega1=0
omega1=0.5
0
1
2
3
4
5
omega1=1
6
7
8
omega1=0
9
10 11 12 13 14 15 16 17 18 19 20
omega1=0.5
omega1=1
(a) discretion
output gap (cost-push shock, commitment)
0.500
inflation (cost-push shock, commitment)
0.7
0.9
0.6
0.000
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
0.5
0.7
0.4
0.5
-0.500
interest rate (cost-push shock, commitment)
1.1
0.3
0.3
0.2
-1.000
0.1
-0.1
-1.500
-2.000
omega1=0
omega1=0.5
0.1
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
0.0
-0.3
-0.1
-0.5
-0.2
omega1=1
omega1=0
omega1=0.5
1
2
3
4
5
6
omega1=1
7
8
9
omega1=0
10 11 12 13 14 15 16 17 18 19 20 21
omega1=0.5
omega1=1
(b) commitment
output gap (cost-push shock, Taylor rule)
0.5
inflation (cost-push shock, Taylor rule)
0.7
0.9
0.6
0.0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
0.5
0.7
0.4
0.5
-0.5
interest rate (cost-push shock, Taylor rule)
1.1
0.3
0.3
0.2
-1.0
0.1
-0.1
-1.5
-2.0
omega1=0
omega1=0.5
omega1=1
0.1
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
0.0
-0.3
-0.1
-0.5
-0.2
omega1=0
omega1=0.5
1
2
3
4
5
6
omega1=1
(c) Taylor rule
Figure 7
Effects of backward-looking inflation expectations (cost-push shocks).
31
7
8
9
omega1=0
10 11 12 13 14 15 16 17 18 19 20 21
omega1=0.5
omega1=0
output gap (fiscal shock, commitment)
inflation (fiscal shock, commitment)
interest rate (fiscal shock, commitment)
0.6
0.2
0.4
0.5
0.1
0.3
0.4
0.1
0.3
0.0
0.2
-0.1
0.1
-0.1
0.3
0.2
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
0.2
0.1
0.0
0.1
-0.2
0
1
2
3
4
5
6
7
8
9
0.0
10 11 12 13 14 15 16 17 18 19
-0.1
-0.2
-0.1
-0.2
-0.3
-0.1
gamma=0
gamma=0.1
gamma=0.2
gamma=0.3
gamma=0
gamma=0.1
gamma=0.2
0
1
2
3
gamma=0.3
4
5
6
gamma=0
7
8
9
gamma=0.1
10 11 12 13 14 15 16 17 18 19 20
gamma=0.2
gamma=0.3
(a) varying γ
output gap (fiscal shock, commitment)
inflation (fiscal shock, commitment)
interest rate (fiscal shock, commitment)
0.6
0.2
0.3
0.5
0.1
0.2
0.4
0.1
0.2
0.3
0.0
1
0.2
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
0.1
-0.1
0.1
0.1
-0.1
0.0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
-0.1
-0.2
-0.2
-0.2
0.0
1
tau=0
tau=0.1
tau=0.2
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-0.1
tau=0.3
tau=0
tau=0.1
tau=0.2
tau=0.3
tau=0
tau=0.1
tau=0.2
tau=0.3
(b) varying τ
output gap (fiscal shock, commitment)
inflation (fiscal shock, commitment)
0.5
0.2
0.4
0.1
0.3
0.1
0.2
0.0
interest rate (fiscal shock, commitment)
0.16
0.14
0.12
0.10
0.08
1
0.1
-0.1
0.0
-0.1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
0.06
0.04
1
2
3
4
5
6
7
8
9
0.02
10 11 12 13 14 15 16 17 18 19 20 21
-0.1
-0.2
-0.2
-0.2
alpha=0
alpha=0.2
alpha=0.4
alpha=0.6
0.00
-0.02
alpha=0
alpha=0.2
alpha=0.4
1
2
3
4
alpha=0.6
(c) varying α
Figure 8
Sensitiviteness w.r.t. γ , τ and α , fiscal shocks, commitment.
32
5
6
7
alpha=0
8
9
10 11 12 13 14 15 16 17 18 19 20 21
alpha=0.2
alpha=0.4
alpha=0.6
Variance of inflation as a function of lambda_g
Variance of output gap as a function of lambda_g
0.8
0.6
0.7
0.5
0.6
0.4
0.5
0.3
0.4
0.2
0.3
0.1
Variance of interest rate changes as a function of lambda_g
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.2
0
0
0.1
0.2
0.3
0.4
var(inf)_dis
0.5
0.6
var(inf)_com
0.7
0.8
0.9
1
0
0
0.1
0.2
var(inf)_rul
0.3
0.4
var(ygap)_dis
0.5
0.6
var(ygap)_com
0.7
0.8
0.9
0
1
0.1
0.2
var(ygap)_rul
0.3
0.4
var(di)_dis
0.5
0.6
var(di)_com
0.7
0.8
0.9
1
var(di)_rul
(a) demand shocks
Variance of inflation as a function of lambda_g
Variance of output gap as a function of lambda_g
5
4.5
Variance of interest rate changes as a function of lambda_g
5.5
14
5
12
4.5
4
10
4
8
3.5
3.5
6
3
3
4
2.5
2.5
2
2
2
1.5
0
0.1
0.2
0.3
0.4
var(inf)_dis
0.5
0.6
var(inf)_com
0.7
var(inf)_rul
0.8
0.9
1
0
0
0.1
0.2
0.3
0.4
var(ygap)_dis
0.5
0.6
var(ygap)_com
0.7
0.8
var(ygap)_rul
(b) cost-push shocks
Figure 9
Effects of deficit smoothing
33
0.9
1
0
0.1
0.2
0.3
0.4
var(di)_dis
0.5
0.6
var(di)_com
0.7
var(di)_rul
0.8
0.9
1
DISCRETION
var(π)
ξ
ν
0
0
0.64283
0.2
0.62207
0.4
0.62998
0.6
0.63915
0.8
0.6481
1
0.65663
0.2
0.4
0.6
0.8
1
0.42157
0.31902
0.25802
0.21727
0.18794
0.56038
0.51199
0.46675
0.42745
0.39354
0.59224
0.56187
0.5274
0.49507
0.46575
0.61137
0.59134
0.56344
0.53581
0.50995
0.62527
0.61214
0.58877
0.56454
0.54132
0.63631
0.62815
0.6081
0.58646
0.56532
0
0.64283
0.62233
0.61968
0.61879
0.6185
0.6185
0.2
0.4
0.6
0.8
1
0.405
0.3123
0.27846
0.26984
0.27422
0.53825
0.47358
0.43789
0.4154
0.40125
0.55674
0.5014
0.46989
0.44825
0.43283
0.56508
0.51575
0.48737
0.46701
0.45166
0.56987
0.52506
0.49916
0.48005
0.46514
0.57299
0.53182
0.50797
0.48998
0.47561
0
0.42999
0.44718
0.4243
0.4024
0.38293
0.36567
0.2
0.4
0.6
0.8
1
0.61898
0.89802
1.1644
1.3931
1.5879
0.40821
0.38963
0.43286
0.49338
0.56059
0.36768
0.31846
0.33225
0.36345
0.40227
0.34145
0.28118
0.28314
0.30161
0.32743
0.32144
0.25662
0.25261
0.2641
0.2825
0.30508
0.23864
0.2313
0.23852
0.25218
0
0
0.64283
0.2
0.61148
0.4
0.61861
0.6
0.62496
0.8
0.63032
1
0.6349
0.2
0.4
0.6
0.8
1
0.30608
0.21806
0.17504
0.14846
0.12993
0.41331
0.34944
0.31197
0.28082
0.25537
0.44329
0.38091
0.34781
0.32068
0.29701
0.46074
0.39869
0.36725
0.34298
0.32099
0.4728
0.4107
0.37988
0.35775
0.33738
0.48188
0.41956
0.38887
0.36843
0.34972
var( y − y )
ξ
var(∆i)
ξ
COMMITMENT
var(π)
ξ
ν
var( y − y )
ξ
0
0.64283
0.62452
0.6255
0.62655
0.62735
0.62795
0.2
0.4
0.6
0.8
1
0.40462
0.31823
0.27101
0.24189
0.22302
0.52785
0.4927
0.46773
0.44359
0.42293
0.55206
0.52219
0.5043
0.48609
0.46853
0.56451
0.53726
0.52269
0.50848
0.49343
0.57238
0.5468
0.53412
0.52296
0.51018
0.57787
0.55353
0.54204
0.53333
0.52276
0
0.42999
0.36001
0.3441
0.33339
0.32507
0.31819
0.2
0.4
0.6
0.8
1
1.3843
1.9116
2.2293
2.4439
2.6003
0.80188
1.1601
1.3979
1.5518
1.6643
0.73147
1.0542
1.2876
1.4426
1.551
0.6928
0.99725
1.2283
1.3884
1.4989
0.66623
0.95893
1.188
1.3535
1.4681
0.64606
0.9303
1.1575
1.328
1.4478
var(∆i)
ξ
Table 3
Effects of varying ξ and ν
34