Download Interest Rate and Business Cycles in a Credit Constrained Small Open Economy

Interest Rate and Business Cycles in a Credit
Constrained Small Open Economy
Sarquis J B Sarquisy
London School of Economics and Political Science (LSE)
June 11, 2007
Abstract
The exogenous real interest rate, facing emerging economies, has been
countercyclical and has lead macroeconomic cycles in a non-neutral way,
leading to inverted hump-shaped responses and excessive volatility in general activity and of consumption relative to output. To match these regularities, standard business cycle small open economy (SOE) models, including extensions with working capital constraints, have weak propagation mechanisms. I build a model of a relatively impatient, credit constrained SOE (CCSOE) that relies on a permanently binding endogenous
credit collateral constraint on foreign liabilities. The constraint imposes
an endogenous relationship between capital as collateral and foreign net
liabilities. The model reveals considerable propagation of interest rate
shocks. A general setting of preferences and interest rate induced exogenous processes enhance the propagation e¤ects. The model implies
non-neutrality of interest rate and matches most empirical regularities, in
terms of impulse responses, business cycle moments and negative serial
correlation between output and lagged interest rate.
1
Introduction
In this paper I try to understand the business cycle implications of real interest rates which emerging economies face in international …nancial markets.
I report the empirical evidence of the non neutrality of interest rate shocks,
their propagation through the economy and their relative and absolute contribution to macroeconomic volatility. To account for these empirical regularities,
I formulate a dynamic, general equilibrium model of a credit constrained small
I thank Gianluca Benigno, Francesco Caselli, Charles Goodhart, Bernardo Guimarães,
Nobuhiro Kiyotaki, Alex Michaelides and participants at seminars of the Economics Department, LSE, and of the Financial Markets Group (FMG) at LSE for helpful comments. I am
also grateful to the hospitality of the FMG and of the Instituto Rio Branco (IRBr).
y Email address: [email protected]
1
open economy (CCSOE). The model relies on a permanently binding endogenous collateral constraint, which enhances the e¤ects of shocks, namely shocks
to (total factor) productivity and interest rates. I investigate in particular the
propagation of the latter as an independent process, as well as under alternative
speci…cations in which interest rate changes a¤ect productivity and/or collateral formation. The model is consistent with the evidence that such interest
rate shocks can determine a high proportion (over 20%) of output volatility at
business cycle frequencies.
In the last two decades emerging economies have faced real interest rates
in international …nancial markets that are higher and more volatile (at least in
absolute terms) than those observed in advanced economies. These phenomena
can be caused by international and mainly exogenous factors rather than by
endogenous and domestic variables, as argued by e.g. Calvo et al. (1996). In
these situations, international …nancial variables can contribute or even prevail
in the determination of the overall borrowing and lending conditions that a¤ect
a CCSOE - or a group of similar economies - in global …nancial markets. Extending the number of international variables used in Uribe and Yue (2006) and
focusing on monthly data for Brazil, my earlier work (Sarquis 2006) indicates
that, at least at business cycle frequencies, real interest rates (including the
country-spread) are essentially exogenous and can help to account, to a greater
extent than previously shown, for macroeconomic ‡uctuations.
I revisit in this paper the Brazilian case using a simple VAR representation,
with the purpose of elucidating and matching empirical features and regularities
that a small open economy (SOE) model of emerging economies should be able
to reproduce. Interest rates are countercyclical and leading cycles, as in Agénor
and Prasad (2000), Neumeyer and Perri (2005) and Uribe and Yue (2006).
Furthermore, such shocks are non-neutral and have strong propagation e¤ects
on the rest of the economy. In particular, they generate growth persistence and
inverted hump-shaped responses in output, consumption and investment.
Coincidently, these responses share roughly the same qualitative and quantitative features observed in responses to monetary policy shocks in advanced
economies. In this regard, a modelling strategy based on nominal rigidities has
been successful, as in Christiano et al. (2005). Extending the latter to SOEs
could be straightforward and would provide a complementary explanation to
the one o¤ered in this paper. Here, I abstract from the role of domestic monetary policy and from nominal aspects. I address exogenous real interest rate
shocks, whose propagation mechanisms and overall e¤ects in SOEs deserve a different explanation that should not rely on the dynamics resulting from nominal
rigidities.
The proposed CCSOE model contains the following main departures from
a standard RBC model. First, the economy has exchanges with the rest of the
2
world by holding net foreign liabilities - a typical feature of SOE models. Second, the stock of net liabilities is endogenously governed and constrained by the
accumulating capital stock. The latter works as collateral in the sense of Kiyotaki and Moore (1997). Third, the economy’s representative agent is relatively
impatient, so that the economy …nds itself not only in a negative net foreign
asset position, but also facing a permanently binding credit constraint. Full
consideration of the latter assures stationarity. Fourth, following Jaimovich and
Rebelo (2006), preferences are formulated in more general terms that combine
features of the widely used formulation of preferences of King, Plosser and Rebelo (1988) and Greenwood, Hercowitz and Hu¤man (1998) - henceforth KPR
and GHH preferences. I also introduce standard adjustment costs to labour and
investment, which have no major (qualitative) implications, except in helping
to control excessive variability of their respective variables.
The CCSOE model gives a non neutral role to real interest rates, whose innovations produce results that are consistent with a series of empirical evidence.
The model engenders growth persistence in response to interest rate shocks, that
is absent in standard SOE models. Its simulations match well the structure of
second moments and the negative correlations between output and lagged interest rates. They also replicate the empirical responses of output and consumption
to interest rate shocks, displaying inverted hump-shapes, occurring realistically
around 3 quarters after the shock. Analyzing such international shocks, and the
constraints a¤ecting foreign borrowing and international lending, can be key in
accounting for emerging economies stylized facts, among which volatilities of
aggregate activity and of consumption relative to output that are higher than
normally recorded in other models1 . This model can overcome the anomalies
manifested in standard SOE models as reported by Mendoza (1991): a little
correlation between output and the net export ratio to GDP and a lack of serial auto-correlation in investment. The CCSOE framework nests the standard
SOE and closed-economy RBC models in various dimensions in respect of their
ability to match business cycles.
Although widely recognized as a potentially important mechanism for transmitting international shocks, the real interest rates which SOEs face in world
markets have traditionally had a limited role in standard business cycle models
of SOEs. To …ll this gap, alterations to the standard framework, including to
shock speci…cations, have been proposed. For instance, Blankenau, Kose and
Yi (2001) reverse the standard RBC methodology, on the grounds that underlying (real interest rate) shocks are mainly unobservable, and back out from
the model a speci…cation of shocks which is consistent with the model’s observable endogenous variables. They …nd by this methodology that about one-third
of Canada’s output volatility could be explained by interest rate shocks, but
that the volatility found for these shocks is about 8 times the volatility of total factor productivity shocks. Motivated by the recent experience of emerging
1 See
for instance Agénor and Prasard (2000) and Kydland and Saragoza (1997).
3
economies, Neumeyer and Perri (2005) and Uribe and Yue (2005) incorporate,
among other features, a working capital constraint and include country-spreads
as a component of the real interest rate faced in world markets. Their models
contribute to extend our knowledge on how the standard framework can address
the stylized facts that real interest rates are counter-cyclical and lead the cycle.
The two models perform relatively well with regard respectively to the negative
correlation between output and lagged interest rate and to the responses to interest rate shocks. However, their key …ndings depend on ad hoc assumptions
on propagation 2 . Overall, as shown by Oviedo (2005), standard models rely
on an excessive volatility of interest rates and a negative correlation between
the latter and productivity. Merely incorporating a working capital constraint
would not su¢ ce to attain their results.
The limitations of all these models result intrinsically from a weakness in
modelling the propagation and transmission mechanism of shocks, in particular
to interest rates, and therefore from a search for ad hoc substitutes. The CCSOE
overcomes most of these limitations, thanks to a much stronger internal mechanism of propagation. It is capable of matching the empirical evidence on more
comprehensive and realistic bases than before. Cycles are treated as transitory
‡uctuations around a stable growth path, supporting our understanding that
emerging economies’excessive volatility and other business cycle features derive
crucially not only from domestic, but also international (…nancial) sources. In
this sense it contrasts with the view espoused by Aguiar and Gopinath (2007),
who reinterpret cycles in emerging economies as derived from shocks to trend
growth.
The propagation mechanism of the CCSOE model is based on the endogenous credit constraint that governs the accumulation of net foreign liabilities and
capital stock. The model inherits some features of Kiyotaki and Moore (1997)
or Kiyotaki (1998). It di¤ers, however, from theirs in many aspects. First, as
an open economy model, the CCSOE model incorporates exogenous interest
rate shocks. Second, by the same token, the economy has a larger variety of
routes for adjusting to shocks. Third, capital rather than land becomes the collateral. Since the former asset evolves according to an aggregate accumulating
dynamics, the economy is widely subject to the adjustment processes associated
with changes in net liabilities. Fourth, combining access to foreign capital and
aggregate collateral formation enhances the propagation mechanism.
Arellano and Mendoza (2002), Chari et al (2005) and Kocherlakota (2000)
have used similar transmission mechanisms of credit constraints in SOE models. 3 These models however stop short of formulating and solving a DSGE
2 While the former explicitly acknowledges the reliance on a country-spread shock that is
independent from the world interest rate shook, but possibly induced by a negative productivity shock, the latter uses a VAR estimated equation of the country-spread to close the model
and a time-to-build formulation on investment.
3 Caballero and Krishnamurthy (2001) also develop a capital collateral on foreign borrowing
in a three-period model.
4
model in which both capital and foreign liabilities are endogenously accumulated. Mendoza (2006) more clearly takes this additional step, but is in many
ways di¤erent from that followed here. First, I am concerned with business
‡uctuations at large rather than just sudden stops. Second, while I close the
SOE model by assuming a permanently binding constraint, I rule out the nonlinearity associated with a slack credit constraint. Thus, I do not need to add
typical ad hoc assumptions to render the system stationary.4 Third, by so doing,
the CCSOE relates more directly to the RBC benchmark than standard SOE
models, overcoming anomalies of the latter and reconciling it with the former.
Fourth, my formulation for preferences do not exclude, as in his and most SOE
models, the wealth e¤ect on labour supply.
Section 2 presents the empirical evidence and regularities. Section 3 describes the model. Section 4 deals with the calibration, as well as with the
alternative speci…cations of the exogenous processes induced by interest rate.
Section 5 contrasts model simulations and the empirical evidence. Section 6
brie‡y indicates the intuition behind the propagation mechanism of the model.
Section 7 explores the robustness of the model. Section 8 concludes.
2
The Evidence on Real Interest Rate Shock
In order to revisit and to clarify the evidence on the role of real interest rate
shocks in emerging economies, as well as to give an empirical basis for the model,
I conduct a VAR exercise on Brazil for the period 1994-q2 to 2005-q4. Brazil
is one of the major developing economies, being responsible for a signi…cant
share in (the global segment of) the so-called emerging markets. The period
of analysis covers most of the Brazilian experience of closer integration with
global …nancial markets, common to similar emerging economies. 5 Moreover,
the essence of the Brazilian evidence coincides with the cross-country evidence
that has been put forward for emerging economies. 6
The VAR representation is one of a simple SOE economy, in which the following endogenous variables are included: output, hours, consumption, investment
and net trade to GDP ratio.7 They enter, with the same order, the vector y.
4 Schmitt-Grohé and Uribe (2003) address a variety of stationary assumptions in in…nitehorizon models (endogenous discount factor, debt-elastic interest rate premium and portfolio
adjustment costs). Alternatively, Blanchard (1985) and Yaari (1965) set stationarity assumptions in an overlapping generations model.
5 See Kose, Prasad, Rogo¤ and Wei (2006) for a reappraisal of …nancial globalization and
its relationship with emerging economies.
6 See e.g. Neumeyer and Perri (2005) and Uribe and Yue (2006).
7 This representation is similar to the one used by Uribe and Yue (2006), except for the
fact that I add hours. The latter and Neumeyer and Perri (2005) treat Brazil as a SOE,
whereas Kanczuk (2004) constructs a closed-economy model to study real interest rates and
the country’s business cycles.
5
Real interest rate r, is also included. It is obtained as the di¤erence between
the nominal rate of US 3-month Treasury bonds and the corresponding expected
in‡ation. 8 The variables are in logs, except for the trade ratio and interest
rate, and enter the VAR in levels. Additional details on the data are described
in the Appendix.
The VAR is set with only one (1) lag, following information criteria (Akaike,
Final Prediction Error, Hannan-Quinn and Schwartz) tests, having initially allowed a maximum of 12 lags. Apart from time trends, which are added in
the equations of output, consumption and investment, the unrestricted VAR
representation is the following:
0
[yt rt ] = C [yt
2.1
1
rt
0
1]
+ ut. .
Exogeneity and non neutrality
Using the above VAR system, Granger causality tests and variance decomposition9 analysis support …rmly the hypothesis that interest rate can be treated
as an exogenous process, independent from the representation of the macroeconomy given by the …ve endogenous variables in y. Granger causality tests
(conducted under the unrestricted VAR speci…cation) are shown in Table 1.
Table 1. Granger causality test
H0 :
p-value
y!r
0:4660
r!y
0:0023
Variance decompositions are calculated for four speci…cations: unrestricted
VAR; restricted VAR with r ordered both last and …rst; and the VAR with
exogenous r. The latter obtains by setting c21 = 0, and therefore the e¤ects
of interest rate shocks do not depend at all on the ordering. Table 2 reports
the variance decompositions for the various, but unrestricted, speci…cations, at
4, 8 and 20 quarters after the shock. Overall, they indicate a strong degree of
exogeneity for interest rate and a signi…cant e¤ect of interest rate innovations on
economic activity, whereas the reverse causality could not be found. Interests
rates could explain around 30% of the variability of output and investment, as
well as around 40% of consumption’s.
8 Expected
in‡ation is given by the estimate of an autorregressive process with 8 lags.
(2005) makes an interesting point on the possible limitations of Granger causality tests and suggest a variance decomposition analysis to further assess the hypothesis of
exogenous variables vis-à-vis SOEs.
9 Huh
6
Table 2. Variance decompositions due to interest rate in VAR models
Variable
Per cent (%) in VAR models
with exogenous
restricted with
endogenous interest rate
interest rate
0
Interest rate
Output
Hour
Consumption
Investment
T rade
0
[yt rt ]
[rt yt ]
c21 = 0
quarters
4
8
20
quarters
4
8
20
quarters
4
8
20
90
23
4
34
26
8
99
22
3
32
20
9
88
26
3
41
32
18
87
25
3
41
32
17
97
25
2
41
28
19
96
25
3
41
28
18
100
26
4
35
23
6
100
37
4
51
38
19
100
37
3
53
40
22
Note: The decomposition of the unrestricted VAR is not reported, as it is identical
to the restricted one with interest rate ordered last.
These results are consistent with those that support the hypothesis that to a large extent - exogenous shocks to emerging economies’interest rates are
key to understanding their business cycles. Uribe and Yue (2005) …nd that on
average for a group of seven emerging countries (Argentina, Brazil, Ecuador,
Mexico, Peru, Philippines and South Africa) about one third of their business
cycles is explained by disturbances in external …nancial variables. Sarquis (2006)
…nds, within a more comprehensive representation of world …nancial markets,
that over 60% of Brazil’s interest rate and therefore over 50% of its business
cycle variability is determined by innovations to external …nancial variables.
2.2
Propagation, persistence and volatility
In solid lines in Figure 1 are the estimated responses of all endogenous variables
resulting from the VAR with exogenous interest rate shocks. They are identical
to responses from other VAR speci…cations.
7
Interest Rate
Output
0.3%
2.5%
0.2%
0.1%
2.0%
0.0%
-0.1%
1.5%
-0.2%
-0.3%
1.0%
-0.4%
0.5%
-0.5%
-0.6%
0.0%
-0.7%
0
2
4
6
8
10
12
14
16
18
20
0
2
4
Hour
6
8
10
12
14
16
18
20
Consumption
0.8%
0.4%
0.2%
0.4%
0.0%
-0.2%
0.0%
-0.4%
-0.6%
-0.4%
-0.8%
-1.0%
-0.8%
0
2
4
6
8
10
12
14
16
18
0
20
2
4
6
8
10
12
14
16
18
20
Trade balance / GDP
Investment
0.5%
1.2%
1.0%
-0.5%
0.8%
-1.5%
0.6%
0.4%
-2.5%
0.2%
-3.5%
0.0%
-0.2%
-4.5%
0
2
4
6
8
10
12
14
16
18
-0.4%
20
0
2
4
6
8
10
12
14
16
18
20
Figure 1. - Model and VAR impulse responses. Solid lines are VAR responses,
accompanied by dotted lines representing 95% con…dence intervals. The vertical axis
shows deviations from steady state. Units on the horizontal axis are quarters.
8
The VAR estimated responses feature (negative) growth persistence of output, consumption and investment. They conform with recessions (recoveries) in
which a variable’s drop (rise) is followed subsequently by another. The troughs
are attained after two to four quarters, and the variables appear to return to
their pre-shock levels after six to twelve quarters. Being non neutral, the responses indicate that interest rates are e¤ectively countercyclical and leading
the cycle. 10 Similarly they provoke a positive shift in trade balance (either
a larger surplus or a smaller de…cit). Responses of output, consumption and
investment can be said to show an inverted hump-shaped form, which summarizes the propagation of interest rate shocks in emerging economies in analogous
terms to those found in regard to productivity shocks and monetary shocks in
closed-economies. 11
As reported and further explored in Section 5, correlations between output
and interest rate at di¤erent lags should be negative, and they should pick in
absolute terms from two to three quartes after the schok. This fact is in line
with a certain dominancy of interest rate schocks among possible sources of
innovations over business cycles, which relies both on their non-neutrality and
the negative growth persistence they produce in estimated responses.
Moreover, considering all the above, interest rates emerge potentially as a
source to explain the excessive overall volatility of emerging economies. Over
the period of analysis Brazil reveals a standard deviation of the HP-…ltered GDP
series (in log) that is 1.78 higher than the US counterpart. At the same time
the volatility of Brazil’s real interest rate is about 2.01 greater than the US rate.
Furthermore, interest rates can be an important force behind the high volatility of consumption (relative to output’s) among emerging economies. This stylized fact is already revealed in Figure 1 by the excess shown in the maximum
deviation from steady state in consumption response vis-à-vis output response.
It is further corroborated by the unconditional second moments of the Brazilian
data in Table 5, in line with Neumeyer and Perri (2005). 12
2.3
Theoretical challenges
Elucidated by the Brazilian case, the overall evidence on interest rate and business cycle in emerging economies suggests that:
1 0 The counter-cyclical feature of real interest rate might not be exclusive of emerging
economies, despite claims by Neumeyer and Perri (2005). For instance, King and Rebelo
(1999) and Stock and Watson (1999) report similar counter-cyclical evidence in the US, perhaps due to a less stable monetary policy before the nineties.
1 1 See for instance respectively Cogley and Nason (1995) and Christiano et al. (2005).
1 2 As documented in Table 5, I calculate an excess of 29% in consumption’s deviation relative
to output’s. The latter authors calculate a similar excess of 24% for a shorter period.
9
(a) shocks to real interest rate of an emerging economy can be mainly or to a good extent - exogenous and certainly non neutral at business cycle
frequencies;
(b) output, consumption and investment respond to these shocks in inverted
hump-shaped form ;
(c) interest rate is unambiguously counter-cyclical and leads the cycle;
(d) correlation between output and lagged interest rate can be increasingly
negative during recession;
(e) consumption reacts relatively more than output to interest rate shocks;
(f) current account seems to be at least as counter-cyclical as in advanced
economies.
Most of these challenges are not found in advanced economies and cannot
be explained in an integrated way by available SOE models. To address them
all, it appears that a model must have ideally four features: …rst, non-neutral
interest rate shocks, with strong e¤ects on consumption; second, propagation
mechanisms that lead to growth persistence and inverted hump-shaped form in
responses to interest rate shocks; third, a good matching of standard second
moments of data statistics (output variability, comovement of other series with
output, and their relative volatility); and fourth, a good replication of (the
dynamic pattern of) serial correlations between output and interest rate at lags
that are empirically meaningful.
3
The Model Economy
The model economy has a single homogeneous good and is populated by a
single representative agent economy. It faces the world economy - which is
technologically at least as advanced as - and is allowed to borrow abroad or to
keep foreign liabilities at an exogenously determined gross rate Rt .The lower
bound of this gross interest rate is given by a benchmark international rate, Rt ,
Rt , and R Et Rt+1 Et Rt+1 R .
so that Rt 1 + rt .1 + rt
I assume the representative agent is relatively less (more) patient than the
world economy’s counterpart. Therefore, the CCSOE’s discount factor is lower
(higher) than the rest of the world’s, that is <
( > ).13 Such a (parametric) relative impatience in relation to the rest of the world is similar to
Paasche’s (2001). It is also analogous to the impatience gap between heterogeneous agents, assumed in a closed-economy setting in Kiyotaki and Moore (1997)
and Carlstrom and Fuerst (1997). Moreover, cross-country evidence points out
to a positive correlation between and wealth (see Becker and Mulligan 1997).
1 3 In line with the SOE assumption I do not model the rest of the world, which would
correspond strictly to the case of a patient representative agent model. Due to size e¤ects,
the latter will in the limit display equivalent features to those of a RBC closed-economy.
10
The relative impatience and the steady state properties of the model substitute one of the ad hoc assumptions that typically are used to render the SOE
model stationary (see Schmitt-Grohé and Uribe 2003). Assuming <
1
R 1 and R
R<
, a steady state equilibrium obtains in which the collateral constraint permanently binds.14 The binding of the constraint imposes
a positive shadow price on the collateral relative to the consumption good’s. If
this price was zero, there would be no constraint on the ability to borrow, as
in the case of SOE models. The de…nition of the CCSOE is consistent with a
permanently binding constraint. An impatient economy holds liabilities towards
the rest of the word. The amount of foreign liabilities depends on the capital it
accumulates in the form of disposable collateral, whose share is given by , and
is also in‡uenced by the stationary level of interest rate
The representative agent maximizes her life-time utility de…ned as in
Jaimovich and Rebelo (2006),
U = Et
1
X
s t
u(Ct ; Lt; ; Jt );
(1)
s=t
where
u(Ct ; Lt; ; Jt ) =
(Ct
aHt Jt )1
1
Jt = Ctb Jt1
1
(1a)
b
1
(1b)
Ls + Hs = 1
(1c)
and
This representation of preferences nests both King, Ploser and Rebelo (1998)
and Greenwood et al. (1988) preferences, which are widely used in respectively
closed-economy and SOE business cycle models15 . As in Jaimovich and Rebelo
(2006), it allows a realistic compromise in labour response to interest rate shocks,
thanks to a weak short-run wealth e¤ect on the labour supply. It therefore avoids
either excessive short run labour response with KPR preferences or excessive
long run labour response with GHH preferences.
The agent faces not only resource and technology contraints, but also a credit
collateral constraint on foreign borrowing.
The resource constraint is extended to account for net liability with the rest
of the world:
1 4 The proof comes from the FOC in Equation (11) . In steady state ' = 1
0<' 1
R < 1:
1 5 KPR preferences obtain for b = 1, while GHH preferences for b = 0.
11
R: Therefore,
Ct
Zt f (Kt
1; Lt )
It + Bt
Rt B t
Ht (Ht =Ht
1
1)
(2)
The function ( ) de…nes labour adjustment costs, and I assume (1) = 0 (1) =
0 and 00 (1) = h :These assumptions are su¢ cient to determine the costs incurred for changes in labour, while in steady state there are no costs in steady
state.
Zt is current total productivity. The production function is Cobb-Douglas
and therefore:
f (Kt
1; Lt )
= Kt
Lt )1
1 (1
(3)
The capital accumulation is given by:
It [1
G(It =Kt )] = Kt
(1
)Kt
1
(4)
The function G( ) represents adjustment cost to investment. Analogous to
labour adjustment costs, I simply assume G(1) = G0 (1) = 0 and G00 (1) = .
The latter parameter does not a¤ect the steady state properties of the model,
but its dynamic properties. The rate of capital depreciation is given by 2 [0; 1].
The credit collateral constraint, which always binds due to the relative impatient hypothesis, is:
Bt
t [Kt 1 (1
) + It ]
(5)
where s 2 [0; 1] designates the proportion of capital that is actually accounted
as collateral formation. Current investment might play a role in collateral formation, by a proportion given by . For = 0 or = 1, the constraint would be
respectively Bt
) or Bt
t Kt 1 (1
t Kt . Correspondingly, either current
investment would have no value in collateral formation or it would have exactly
the same value as of physical capital. In the baseline calibration I set = 0,
since it assures less volatility of investment. However, an intermediary case, in
which current investment has some value should not be dismissed.
The model is subject to disturbances that can a¤ect the exogenous processes
of productivity, interest rate and collateral formation. These processes follow
an auto-regressive form:
wt = P wt
where wt =
and rt = ln Rt :
zt
rt
t
0
and "t =
12
1
+ "t ;
"zt
"rt
"t
0
. Note that zt = ln Zt
While the problem relates to a single-good economy, it departs from the
standard RBC representative agent’s problem, with adjustment costs, by three
innovations: the preferences formulation, the accumulation of foreign liabilities
and the collateral constraint. The latter governs the dynamic path of capital
in a way that is subject to a strong propagation mechanism bringing growth
persistence to the core of the responses to both productivity and interest rate
shocks. Note that disturbances can a¤ect (5) both endogenously through adjustment in capital and liability as well as exogenously, through innovations in
:
3.1
First order conditions
The problem results in maximizing the following Lagrange expression, with
, t , t qt and t 't Lagrange multipliers:
L = Et
1
X
t
8
>
>
<
>
>
:
s=t
u(Ct ; Lt; ; Jt ) + t [Jt Ctb Jt1 1b ]
It + Bt Rt Bt 1 Ct Ht (Ht =Ht
t [Zt f (Kt 1; Lt )
+ t qt [It It G(It =Kt 1 ) Kt + (1
)Kt 1 ]
+ t 't [ t Kt 1 (1
) + t It Bt ]
t
1 )]
9
>
>
=
>
>
;
Six …rst order conditions obtain from the Lagrangian maximization problem:
uL (Ct ; Lt; ; Jt ) =
fL (Kt
t
+
t
t
t
=
1; Lt )
t+1
+ (Ht =Ht
2
Ht+1
Ht
= uC (Ct ; Lt; ; Jt )
uJ (Ct ; Lt; ; Jt ) + (1
t qt
1
Et
t+1
t
Jt 1
Ct
b)
t+1
It 0
G (It =Kt
Kt
1)
Rt+1 = 1
t
Et
t+1
t
8
<
:
Zt+1 fK (Kt ; Lt+1 ) + qt+1 1
+(1
)
13
Ht
Ht 1
+
0
(Ht =Ht
1)
(6)
(Ht+1 =Ht )
b
=
G(It =Kt
0
1)
+
t+1 't+1
1 b
(7)
Jt
Ct+1
1)
+
b
(8)
t 't
't
It+1
Kt
(9)
(10)
2
t+1
G0 ( IK
)
t
9
=
;
= qt (11)
(6) and (7) govern the standard intra-temporal consumption-labour substitution, except that they contain terms related respectively to labour adjustment
costs and, more importantly, to (inter-temporal) deviations in the consumption
path. The latter enriches the standard substitution problem in ways that are
determined by (8), which sets the dynamics of the disturbances to consumption,
as in Jamovich and Rebelo (2006).
(9) controls the movements in the shadow price of investment. This price
would be constant (q = 1), had I …xed no investment adjustment cost and no
role for current investment in the credit collateral formation.
The fundamental Euler equations are (10) and (11). They di¤er sharply from
the standard Euler equations, typically found both in RBC and SOE models.
They contain both the relative multiplier of the credit collateral constraint. (10)
has been stressed in previous work, such as Chary et all (2005), Arellano and
Mendoza (2002) and Mendoza (2006). However, in their models, except to a
certain degree in the latter’s, the multiplier does not …gure explicitly in (11).
The two equations are key in generating the transmission mechanisms of shocks
that characterize the CCSOE framework. In Section 6 I try to explain the
essence of these mechanisms.
The model is fully described by Equations (2)-(5) and by the FOCs expressed
in equations (6)-(11), as well as by the speci…cation of the underlying exogenous
processes, which I address in the next Section. I solve the model by method of
logarithmic linearization, as described in Uhligh (1999).16
4
4.1
Calibration
Parameters
The calibration is guided by Brazilian data. The average real interest rate was
around 8% per annum (therefore r = 0:02 on a quarterly basis) in Brazil over
1994 to 2005. The shares of investment and net export in GDP (I=Y and X=Y )
were around 20% and 3%. Estimates of the capital ratio (K=Y ) are not precise.
I set it at 7.45 quarterly (around 1.9 annually), a value within the range typically
used in the literature.
The baseline parameters are shown in Table 3. To specify technology parameters, calculations based on income shares usually give developing countries a
higher capital share ( ) than found for developed economies. I use = 0:38, although Brazilian data would suggest a value close to 0:50. The under-estimation
of labour income results likely from the use of informal and/or self-employed
1 6 The Matlab code containing the loglinearized equations can be provided by the author.
The simulations use Uligh’s toolkit of Matlab codes for analyzing nonlinear dynamic stochastic
models.
14
labour.17 Capital and labour adjustment costs’ parameters (
typical ranges found in the literature.
and
) follow
Table 3. Baseline parameter values
Name of parameters
Symbol
Value
Rates
real interest rate
subjective rate
r
1:02
1:0251
1
Preference
discount factor
elasticity of labour supply =
utility curvature
utility parameters
1
1
a
b
0:9755
1:01
1
2:39
0:15
Technology
capital share
depreciation rate
capital adjustment cost
labour adjustment cost
0:38
0:027
2:6
2:0
Collateral formation
collateral share
current investment weight
0:2238
0
The subjective rate, that is implied by the discount factor, is higher than the
real interest rate in the CCSOE. Correspondingly, the steady state premium,
measured by ', is set on a quarterly basis at 0.0051. This is consistent with
the hypothesis of relative impatience and with estimates of Brazil’s discount
factor, which usually are close to 0.9 annually - well below the estimates for
the US. 18 Apart from the discount factor, the calibration of the preference
parameters is similar to Jaimovich and Rebelo (2006). In particular in the
baseline calibration, I use a small value for b , rendering preferences closer in
spirit to the GHH preferences. This actually permits that hours react negatively
in the short run to adverse shocks, such as interest rate shocks.
The collateral parameter is set in accordance with the observed stationary
ratio B=Y: For the latter I roughly calculate the country’s net foreign liabilities
1 7 See Golin (2002) for an overall discussion on income shares, and Caselli and Feyrer (2006)
for cross-country comparisons in capital share. Shares in Latin American economies range
from 0.4 to 0.5, while advance economies lie between 0.2 and 0.4.
1 8 Estimates by Issler and Piqueira (2000), under di¤erent utility speci…cations, and by Val
and Ferreira (2001) support this value. Erely et al. (2002) use a similar value (0.89 annually).
15
(liabilities minus assets), by adding the net foreign debt (0.28) and remaining
net foreign liabilities in equity, minus the international reserves. I arrive at a
ratio of 0.42 annually. Thus, is around 0.22. A lower would obtain had I
used a narrow concept of the country’s international investment position, such
as the stock of merely international debt contracts.
4.2
Speci…cation of the exogenous processes
The CCSOE model of Section 3 is subject to three exogenous processes, in productivity, real interest rate and collateral share. They are represented in vector
0
:The …rst two processes are conventional in SOE
form by wt = zt rt
t
models. Collateral formation is here proposed as an exogenous process that
represent innovations in the e¢ ciency by which the country can provide international creditors and investors with collateral through capital accumulation.
Let me comment on such e¢ ciency in collateral formation. It relates to a
country’s ability to borrow and creditors’s willingness to lend. It can result from
long term factors at the country level - e.g. underdevelopment of the country’s
…nancial markets and associated weakness - and also at the international level
- e.g. segmentation of international …nancial markets with regard to a country
or to a class of countries to which it belongs. Here however I am not interested in the primary roots or long term factors determining such e¢ ciency. I
am assuming, by a permanently binding credit collateral constraint, that the
country …nds itself at the extreme situation in which it is su¢ ciently ine¢ cient
to alter its …nancial situation in the world economy. Nevertheless, extent of this
ine¢ ciency may vary due to exogenous innovations.
I examine two kinds of speci…cation for the dynamics of the exogenous
processes: (a) by purely independent shocks; and (b) by interest rate induced
processes. In the former kind each process follows an independent process,
driven by their own independent shocks. In the latter kind, each process can
be driven not only by shocks of its own but also, in the case of productivity
and collateral share, by changes in real interest rate, which remains conversely
purely independent in all speci…cations. I assume that shocks to interest rate
are the sole fundamental shock that can induce other exogenous processes. The
…rst kind of speci…cations have a preliminary role in ascertaining the non neutrality of interest rate shocks and its potential of delivering some of the stylized
facts. The second kind of speci…cations try to address a more realistic setting
by which international …nancial factors a¤ect the economy.
Therefore, in vector auto-regressive form,
wt = P wt
1
+ "t ;
The exogenous processes feature the restriction that P2j = 0 for all j = 1
and 3. A diagonal matrix P implies one or a combination of purely independent
16
processes. Alternatively if one or more elements Pi2 6= 0 for i = 1 and 3, then I
study one or a combination of interest rate induced processes.
Table 4. Parameter estimates of the unrestricted VAR
Dependent variable in VAR
^
^
ht
ct
it
xt
rt
0.271
(0.154)
[1.759]
0.061
(0.230)
[0.468]
-0.163
(0.249)
[-0.654]
0.479
(0.579)
[0.826]
0.522
(0.098)
[5.308]
-0.127
(0.154)
[-0.823]
1
0.006
(0.025)
[0.227]
0.917
(0.040)
[22.773]
-0.045
(0.035)
[-1.294]
-0.155
(0.082)
[-1.891]
0.054
(0.021)
[2.608]
-0.017
(0.048)
[-0.357]
1
0.058
(0.110)
[0.525]
-0.189
(0.188)
[-1.022]
0.549
(0.145)
[3.776]
-0.180
(0.342)
[-0.234]
-0.279
(0.126)
[-2.206]
0.054
(0.223)
[0.241]
1
0.011
(0.047)
[0.235]
-0.013
(0.074)
[-0.170]
0.075
(0.065)
[1.161]
0.612
(0.152)
[4.029]
-0.136
(0.037)
[-3.664]
0.059
(0.088)
[0.674]
1
0.127
(0.074)
[1.715]
0.264
(0.129)
[2.046]
0.169
(0.097)
[1.746]
0.486
(0.228)
[2.132]
0.195
(0.101)
[1.929]
-0.043
(0.153)
[-0.282]
^
^
yt
^
yt
1
^
^
^
ht
^
ct
^
it
^
xt
^
rt
-0.170
-0.160
-0.268
-0.533
0.042
0.715
(0.053) (0.093)
(0.069) (0.163) (0.047) (0.110)
[-3.221] [-1.730]
[-3.875] [-3.274] [0.901]
[6.527]
Note: standard deviation and t-statistics are shown respectively in ( ) and [ ]
1
The values I attribute to the coe¢ cients of P derive from the estimates
from the VAR exercise, as described in Section 2. Table 4 shows parameter
estimates of the unrestricted VAR. Alternative VAR speci…cations produce almost identical estimates, not generating any statistically signi…cant di¤erence
in the coe¢ cients. In the restricted VAR, with totally exogenous interest rate,
estimates of the autoregressive coe¢ cient of output and interest rate are 0.276
(t-value= 1:789) and 0.798 (t-value= 8:523).
4.2.1
Independent processes
I analyze …rst independent processes. They are generally described by an autoregressive diagonal matrix :
17
2
z
0
PD = 4 0
0
r
0
3
0
0 5.
In the analysis of the next section, I will refer to independent processes that
conform to the following autorregressive matrix based on the VAR estimates.
2
3
0:27
0
0
0:72 0 5
PI = 4 0
0
0
0
The e¤ect of pure interest rate shocks is a central qualitative test of our
model. Among other responses, Figure 1 display responses, in (orange) lines
marked with circles, to pure interest rate shocks, from the speci…cation P I .
4.2.2
Interest rate induced processes
The interest rate induced-shocks formulation is supported by the evidence that
interest rate not only follows to a great extent an independent and exogenous
process, but also manages to a¤ect virtually all endogenous variables, in particular output, consumption and investment. The Granger causality tests, impulse
responses and the estimates of Table 4 make this same point. Conjecturing
interest rate a¤ects exogenous processes of productivity and/or collateral formation appears plausible on empirical bases and, at the same time, consistent
with the idea of an economy facing constraints to borrow, to invest and to keep
track of technological innovations. Therefore, the introduction of interest rate
induced processes should be an important step forward in bridging the model
with the reality it addresses.
Induced collateral formation
The ability to borrow can be directly a¤ected by interest rate shocks and also
by external …nancial innovations that alter the country’s collateral formation.
In the later case, adverse shocks can transmit into a tightening in the country’s
capital formation. A rise in the country’s interest rate can be the cause or at
least be associated to such tightening. This coincides in a way with a credit "rationing view", pioneered by Stiglitz and Weiss (1981), by which both price and
quantity of available capital are adjusted in response to changes in perceptions
by creditors and investors. As the interest rate process is empirically identi…ed
as exogenous, I take it as the leading external indicator of changes that impair a
country’s ability to borrow through the means of collateral formation. I set arbitrarily that a 1% rise in interest rate would cause a 2.5% fall in the e¢ ciency
to form collateral by the means of capital accumulation. Therefore a wedge
is introduced between capital and liabilities that is not endogenously given by
the model. The representation of the auto-regressive matrix P can be given as
below:
18
PC
2
0:27
=4 0
0
3
0
0:72 0 5
2:5 0
Induced productivity
Interest rate shocks might adversely a¤ect the productivity. Consistent with
the choice of the auto-regressive parameter (0:27) for the process of productivity
from the output equation, I also take from the latter the estimated value for
lagged interest rate ( 0:17). In this case of induced productivity, the representation of P becomes as below:
3
2
0:27
0:17 0
0:72 0 5
PP = 4 0
0
0
0
Induced productivity and collateral formation
The combination of both productivity and collateral formation as interest
rate induced processes is represented in the auto-regressive matrix below.
2
3
0:27
0:17 0
0:72 0 5
P CP = 4 0
0
2:5 0
5
5.1
Results
Impulse responses
The model’s simulated responses are shown in Figure 2. They come from four
speci…cations of the exogenous processes above suggested: P I ; P C ; P P and
P CP . These speci…cations represent interest rate, productivity and collateral
formation as processes merely induced by interest rate shocks. In all speci…cations the CCSOE model is able to produce growth persistence and (inverted)
hump-shaped responses, particularly of output and consumption, following interest rate shocks. This ability conforms to empirical regularities and is not
present in most SOE models based on alternative standard assumptions of stationarity.
19
Interest Rate
Output
0.3%
2.5%
0.2%
0.1%
2.0%
0.0%
-0.1%
1.5%
-0.2%
-0.3%
1.0%
-0.4%
-0.5%
0.5%
-0.6%
0.0%
-0.7%
0
2
4
6
8
10
12
14
16
18
20
0
2
4
Hour
6
8
10
12
14
16
18
20
Consumption
0.8%
0.4%
0.2%
0.4%
0.0%
-0.2%
0.0%
-0.4%
-0.6%
-0.4%
-0.8%
-1.0%
-0.8%
0
2
4
6
8
10
12
14
16
18
0
20
2
4
6
8
10
12
14
16
18
20
16
18
20
Trade balance / GDP
Investment
0.5%
1.2%
-0.5%
1.0%
-1.5%
0.8%
-2.5%
0.6%
-3.5%
0.4%
0.2%
-4.5%
0.0%
-5.5%
-0.2%
-6.5%
0
2
4
6
8
10
12
14
16
18
20
-0.4%
0
2
4
6
8
10
12
14
Figure 2. - Model and VAR impulse responses. Solid lines are VAR responses, accompanied by dotted lines representing 95% con…dence intervals. The model responses
are marked with crosses for a pure interest rate, with circles for interest rate shock and
induced collateral, with squares for interest rate shock induced productivity and with
triangles for interest rate shock and induced collateral and productivity. The vertical
axis shows deviations from steady state. Units on the horizontal axis are quarters.
20
It is worth noting that, apart from the adjustment provoked by the constraint, no other mechanism in the CCSOE model is able to assure the essence
of its features. Furthermore, they do not depend necessarily on induced process,
but are an essential characteristics of independent interest rate shocks. Growth
persistence would obtain from standard models only if some ad hoc elements
are introduced, such as time to build, but even in these cases persistence tends
to be very short-lived.19
The independent speci…cation P I is a …rst step in matching, qualitatively,
the essence of the empirical responses: inverted hump-shaped responses and
trough that are su¢ ciently distant from the shock so to induce propagation and
therefore replicate recession as a dynamic process. The induced processes given
by the speci…cations P C , P P and P CP improve quantitatively the ability of
the model’s simulated responses to match empirical responses. The induced
collateral formation helps in aggravating the negative growth and the trough.
Interest rate shocks that impair the country’s collateral and productivity can
be bring about dramatic implications to the economy.
In judging di¤erent speci…cations, a note of caution on the consumption
responses should be made. Contrary to the spirit of the model, data on consumption does not exclude durables. Therefore we should not really want to
account for all the excess deviation in responses of this variable. At the same
time, as most RBC and SOE models, the CCSOE model does not generate
generate growth persistence in investment response to match the empirical evidence, despite assuring a level persistence in investment response that is absent
in standard SOE models. Matching non neutrality and second moments
5.2
Matching non-neutrality and second moments
From now on I report the model’s implications with regard to non-neutrality of
interest rate and the second moments. For the sake of transparency, I proceed
so by preserving the same di¤erent speci…cations of the exogenous processes
that I have used to generate the model’s responses. I also add a hypothetical
speci…cation to check the extent of non neutrality.
The benchmark is given by Brazilian statistics (second column in Tables 5 to
7), with two caveats. First, as an alternative reference to total consumption’s
standard deviation, I calculate an estimate of the standard deviation of non
durable consumption, which is lower than the former.20 . Second, I also provide
along with moments of total …xed capital investment, moments of investments
1 9 See for instance the simulated responses in Uribe and Yue (2006), who use time to build
in a standard SOE model.
2 0 This is a back-of-the-enveloppe calculation, based on domestic production series for
durables and non durables.
21
in machine and equipment. The latter is more volatile than the former, in part
because durables is not comprehended. Such alternative statistics for consumption and investment help in avoiding an automatic and sometimes misguided
comparison with the simulated moments of a single-good model of RBC, which
conventionally refers to non-durable consumption and to …xed capital investment, including durables consumption.
5.2.1
Non-neutrality
The assessment of non-neutrality, as a general property of the model, should not
be con…ned to the speci…cations that are empirically motivated. To illustrate
this property, Table 5 presents simulated moments for hypothetically speci…ed
shocks to productivity and/or to interest rate. They are independent shocks
and are analyzed both separately and simultaneously. The idea behind this
hypothetical speci…cation is to be somehow agnostic on the exogenous processes
and simply explore the potential for non neutrality of interest rates. Therefore,
in contrast to the estimates of the VAR, they are merely conceived with identical
persistence and perturbation: z = r = 0:78 and z = r = 1%:
According to the results gathered in Table 5, interest rate shocks are responsible from 3% to 26% of the output volatility, under the hypothetical speci…cation. Their relative strength is even more determinant in consumption and
investment volatility. For instance, they can determine from 17% to 55% of
consumption variability. In contrast to standard SOE models21 , non-neutrality
of interest rate is assured, and it emerges as a central feature of the CCSOE
model.
Moreover, the CCSOE does not reveal anomalies typical of standard SOE
models, with regard to moments related to investment and trade balance. It
overcomes such anomalies22 and, thanks to the non neutrality of interest rate
shocks, moments become more in line with real data. Signi…cant examples of
this abilities are the standard deviation of trade balance, the serial correlation
of investment, and the correlations of output with investment, on the one hand,
and with trade balance, on the other.
I should note that while interest rate shocks are non neutral, collateral formation shocks are not. I do not report the second moments for these shocks.
With the same hypothetical persistence ( = 0:78) and perturbation ( = 1%
), they would generate on their own a negligible variation in output (of 0.03%).
Combined with shocks to productivity and to interest rate, they would account
for less than 2% of the output variability. Curiously, collateral formation shocks
2 1 See
Mendoza (1991) and Schmitt-Grohé and Uribe (2003).
see Mendoza (1991) and Schmitt-Grohé and Uribe (2003). Anomalies typically found
in SOE models are: the absence of serial correlation in investment and of signi…cantly negative
correlation between output and trade ratio.
2 2 Also
22
are therefore, in the context of the CCSOE model, as insigni…cant and neutral
as interest rate shocks in the context of standard SOE models.
Table 5. Second moments and non-neutrality of interest rate within
hypothetical speci…cations P I
Real data
Simulated model with shocks to:
Productivity Interest Rate Both
z
z
Standard deviation (%)
Output
2.1
Consumption
2.7
non durables
1.8
Investment
5.5
mach. & equip.
11.0
Hour
3.1
Trade balance
2.3
Correlation with output
Consumption
0.77
Investment
0.74
mach. & equip.
0.59
Hour
0.71
Trade balance
-0.02
Serial correlation
Output
Consumption
Investment
mach. & equip.
Hour
Trade balance
0.75
0.69
0.67
0.70
0.84
0.21
= 0 .7 8
r
;
= 1% ,
r
=0
= 0%
z
z
= 0,
= 0% ,
r
= 0 .7 8
r
= 1%
z
z
= 0 .7 8
= 1% ,
r
;
r
= 0 .7 8
= 1%
1.82
0.91
0.50
0.60
1.88
1.09
7.35
9.89
12.33
1.36
0.38
0.44
2.01
1.43
2.05
0.87
0.98
0.97
0.29
0.84
0.62
0.96
-0.76
0.82
-0.27
0.95
-0.21
0.67
0.85
0.69
0.93
0.92
0.66
0.69
0.87
0.67
0.80
0.74
0.93
0.64
0.81
0.64
Note: The real data statistics are population moments calculated by the author
based on original quarterly series for Brazil over 1990q1 to 2005q4. National accounts
are seasonally adjusted. All variables are in logarithms, except trade balance ratio to
GDP, and detrended with Hodrick and Prescott (1980) …lter ( = 1600). Hours only
available from 1992q1. stands for standard deviation of shock.
5.2.2
Independent processes
I now address independent processes of productivity and/or interest rates using
empirically motivated auto-regressive coe¢ cients. Table 6 is equivalent to Table
5, apart from the fact that interest rate shocks are more persistent and volatile
23
than productivity shocks. As a result, when both shocks are considered simultaneously, interest rate shocks account for a larger share (between 8% to 40%)
of output variability, and the volatility of consumption relative to output’s has
risen. Moreover, some measures of correlation with output also become more
realistic.
Table 6. Second moments and non-neutrality of interest rate within
empirically motivated speci…cations P I
Real data
Simulated model with shocks to:
Productivity
Interest Rate
Both
z
z
Standard deviation (%)
Output
2.1
Consumption
2.7
non durables
1.8
Investment
5.5
mach. & equip.
11.0
Hour
3.1
Trade balance
2.3
Correlation with output
Consumption
0.77
Investment
0.74
mach. & equip.
0.59
Hour
0.71
Trade balance
-0.02
Serial correlation
Output
Consumption
Investment
mach. & equip.
Hour
Trade balance
0.75
0.69
0.67
0.70
0.84
0.21
= 0 .2 7
r
;
= 1 .2 % ,
r
=0
= 0%
z
z
= 0,
= 0% ,
r
= 0 .7 2
r
= 1 .6 %
z
z
= 0 .2 7
;
= 1 .2 % ,
r
r
1.58
0.60
0.69
0.84
1.73
1.03
6.31
14.88
16.16
0.89
0.38
0.58
3.08
1.06
3.10
0.86
0.99
0.96
0.23
0.77
0.44
0.93
-0.36
0.83
-0.21
0.89
-0.11
0.26
0.59
0.34
0.92
0.91
0.62
0.36
0.80
0.58
0.54
0.45
0.93
0.59
0.66
0.59
= 0 .7 2
= 1 .6 %
Note: The real data statistics are population moments calculated by the author
based on original quarterly series for Brazil over 1990q1 to 2005q4. National accounts
are seasonally adjusted. All variables are in logarithms, except trade balance ratio to
GDP, and detrended with Hodrick and Prescott (1980) …lter ( = 1600). Hours only
available from 1992q1. stands for standard deviation of shock.
24
5.2.3
Induced processes
Induced processes of productivity and/or collateral formation further strengthens the role of interest rate shocks in the CCSOE. Table 7 displays the second
moments for the three speci…cations suggested in the previous Section. Interest
rate induced productivity and collateral can act as an additional mechanism of
further transmitting shocks and rising the economy’s overall volatility. They
help in amplifying the e¤ects of interest rate shocks.
Table 7. Second moments within induced speci…cation
Real data
Simulated model with induced:
collateral
productivity
both
PC
P CP
z
Standard deviation (%)
Output
2.1
Consumption
2.7
non durables
1.8
Investment
5.5
mach. & equip. 11.0
Hour
3.1
Trade balance
2.3
Correlation with output
Consumption
0.77
Investment
0.74
mach. & equip. 0.59
Hour
0.71
Trade balance
-0.02
Serial correlation
Output
Consumption
Investment
mach. & equip.
Hour
Trade balance
Note:
0.75
0.69
0.67
0.70
0.84
0.21
PP
= 1 .2 % ,
r
= 1 .6 %
z
= 1 .2 % ,
r
= 1 .6 %
z
= 1 .2 % ,
1.77
1.07
1.98
1.27
2.05
1.31
19.46
17.67
20.96
1.11
3.80
1.35
3.15
1.41
3.83
0.78
0.35
0.82
0.57
0.83
0.49
0.89
-0.07
0.90
-0.28
0.90
-0.24
0.39
0.81
0.58
0.47
0.84
0.64
0.50
0.84
0.61
0.68
0.58
0.74
0.61
0.76
0.59
stands for standard deviation of shocks. In all speci…cations
r
= 1 .6 %
=0
To ascertain which speci…cation is the most appropriate or realistic is not
at all simple. Table 8 gathers a summary of comparative statistics resulting
from the independent and induced processes. The empirical VAR exercise (see
25
Table 2) suggest that interest rate shocks can determine from 23% to 37% of
the output variability. Table 8 shows all proposed speci…cations are consistent
with these evidence.
However, as long as some importance is given for the ability of the model of
producing a higher relative standard deviation of consumption and, above all,
a greater ampli…cation of shocks, the introduction of some degree of (interest
rate) induced productivity could help the model’s strength. The weaker impact
of induced collateral derives from the intrinsic neutrality of this process, in sharp
contrast to productivity, as an independent source of determinant innovations,
as discussed above.
Table 8. Economy-wide e¤ects of interest rate shocks under di¤erent speci…cations of exogenous processes under identical productivity and interest rate
shocks
Speci…cation of exo-
St: dev:(C)
St: dev:(Y )
St:dev:(Y )
St:dev:(Y I )
genous processes
St:dev:(Y ) explained by
interest rate shock (%)
minimum
maximum
8
40
11
45
20
59
23
63
Independent, P I
1
0.60
Induced collateral, P C
1.02
0.60
Induced productivity, P P
1.14
0.64
Induced collateral
1.18
0.64
& productivity, P CP
Note: St:dev:(Y I ) refers to the standard deviation in the independent,
P I speci…cation of the exogenous process.
5.3
Serial correlation with interest rates
The four empirically motivated speci…cations (P I , P C , P P and P CP ) of the
exogenous processes generate simulated serial correlations between output and
interest rates that match qualitatively and quantitatively the empirical correlations of unconditional data. Figure 2 below depicts these cross-correlations.
As expected in an environment of non neutral and determinant interest rate at
the business cycle frequencies, they follow overall a pattern over time that is
convergent with the pattern of the output estimated and simulated responses
in respectively Figures 1 and 2.
26
0.5
0.3
0.1
-0.1
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
-0.3
-0.5
-0.7
Figure 3. Serial correlations between GDP an interest rates, corr(rt+j ; yt ). The
correlations are in (orange) lines marked with crosses for a pure interest rate, in (green)
lines marked with circles for interest rate shock and induced collateral, in (brown) lines
marked with squares for interest rate shock induced productivity, and in (blue) lines
marked with triangles for interest rate shock and induced collateral and productivity.
The vertical axis represent correlations and the horizontal axis j quarters.
6
Understanding the Model
The CCSOE model comprehends two aspects that are absent in most SOE
standard models. First, as a means to complement domestic savings, net foreign
liabilities are permanently constrained. Second, such a constraint is dynamically
subject to an accumulation process, given capital’s role as a collateral.
The FOCs translate these two aspects into the Euler conditions. On the one
side, the stock of net liabilities is endogenized so to bring about an additional
term in the consumption Euler equation, as shown in Kocherlakota (2000),
Arellano and Mendoza (2002) and Chari et al (2005). On the other side, capital
is endogenised so to produce an additional term in the Euler equation governing
capital accumulation.
These two Euler equations - (10) and (11) - are non-standard. Deprived
from adjustment costs and with = 1, they would result in the following by
substituting out the multiplier:
1= E
1
1
t+1
t
[Zt+1 fK (Kt ; Lt+1 ) + 1
t
27
t Rt+1 ]
(12)
The latter conveys the essence of the model. It is an extended Euler equation
though which, having (10) and (11) in mind, standard neoclassical business cycle models of both closed-economy and SOE can be seen as special extreme
cases. The former obtains when the multiplier approaches zero ('s ! 0),
[Zt+1 fK (Kt ; Lt+1 ) + 1
] and
since (10) and (11) conform to 1 = E t+1
t
1 = E t+1
Rt+1 : Implicit in this, loosely speaking, is the following equivalence:
t
Rt+1 = Zt+1 fK (Kt ; Lt+1 ) + 1
. Such equivalence is behind the neutrality of
interest rate in standard models.
Within the mechanics of the CCSOE framework, the equivalence between
gross interest rate and gross marginal product of capital would only be consistent
with (12) if the economy had the ability to use 100% of its capital as a collateral
( ! 1). Approaching this limit, the dynamics of the CCSOE model becomes
closer to the one of standard SOE models. At the limit, it would be deprived
of its characterizing features . On the other hand, approaching ! 0 leads to
a dynamics convergent with RBC models.
In SOE models the marginal product of capital coincides with an exogenous interest rate, whereas in the RBC models it is totally endogenous. In the
CCSOE framework the inter-temporal consumption substitution and capital adjustment problems are born inter-twined. In contrast to the SOE models and
closed-economy RBC models, the CCSOE model relies on a wedge between the
marginal product of capital and interest rate.
(12) governs an interplay between consumption growth and the adjustment of
capital’s marginal product, by an enhanced process of consumption-investment
substitution. These interactions do not appear in either standard SOE models or
RBC models. Shocks to productivity, interest rate and collateral directly a¤ect
the extended Euler condition set above. A temporary shock to productivity
propagates further due to the discipline brought about by the credit constraint.
1
Note in (12) that consumption growth is proportional to (1
: This term
t)
gives the amplitude of the growth rate and therefore the pattern of adjustment
following shocks: ! 1 would imply a prompt adjustment, while ! 0 would
lead to a minimum rate of adjustment.
The CCSOE makes adjustment a progressive process. Following a favorable (adverse) shock, such as positive changes in productivity (interest rate),
the economy accumulates (liquidates) capital, via the use of foreign (domestic)
savings. This process is further enhanced by the fact that capital accumulation
leads to collateral formation and the expansion of liabilities in foreign markets.
Note crucially in (12) that interest rate is negatively correlated to consumption growth, in sharp contrast to most standard SOE models. Shocks to interest
rate propagate by leading to negative growth before displaying positive growth.
28
The decline in consumption and output produce realistic recessions and recoveries, in the hump-shape form of their responses to these shocks. Following an
interest rate shock the economy has to reduce its liabilities and, by doing so, is
forced to further liquidate its assets.
7
7.1
Robustness
Shock persistence
In the baseline simulations, the choice of the autoregressive coe¢ cients for both
productivity and interest rate shocks is dictated by the unrestricted VAR coef…cients ( z = 0:27 and r = 0:72). The restricted VAR with exogenous interest
rate would suggest a marginally higher r , close to 0.80, and the RBC literature
usually attributes a higher value for z . Raising the autoregressive coe¢ cients
requires lower standard deviations for the shocks in order to match the overall
volatility of the macroeconomic series and their serial correlation with interest
rate. While higher z might weaken somehow the role of pure interest rate
shocks and reduce the relative volatility of consumption in explaining business
cycle ‡uctuations, higher r would have the opposite e¤ects. The moments
shown in Tables 5 and 6 illustrate these e¤ects.
7.2
Collateral formation parameters
In the CCSOE collateral formation parameters are key to determine the steady
state levels of consumption and investment. At the same time they can alter
the dynamics of these variables. Higher values for either or strengthen the
economy’s capacity of taking the bene…t of collateral formation and therefore
expose it to more ampli…ed volatility in investment and consumption relative to
output. Relative excess in consumption’s volatility is a feature of the CCSOE
model that is observed in emerging economies. Conditional on sharing the
features of a CCSOE, emerging economies with stronger collateral formation either by domestic merits or by international endorsement - might reveal larger
volatility in consumption.
7.3
Functional form of utility
The speci…cation of utility I use is a general one, mixing features of both GHH
and KPR preferences, although closer to the latter, as b = 0:15. A higher (lower)
value for b would diminish (augment) the overall volatility of the economy and
also the relative volatility of consumption. Underlying both e¤ects is the reduced
(expanded) growth persistence of shocks. For, distancing from GHH preferences
and approaching KPR preferences enhances the short term responsiveness of
labour. Figure 4 shows responses to interest rate shocks under the speci…cation
with induced productivity & collateral formation (P CP ). There I contrast the
29
baseline response (line marked with triangles) with the alternative response
under b = 0:20 (dotted line). .
Output
0.3%
0.2%
0.1%
0.0%
-0.1%
-0.2%
-0.3%
-0.4%
-0.5%
-0.6%
-0.7%
0
2
4
6
8
10
12
14
16
18
20
Figure 4. E¤ects of higher b within the induced productivity & collateral
formation speci…cation
8
Conclusion
In this paper I try to elucidate some features and stylized facts that characterize the role of (exogenous) real interest rate in determining business cycles in
emerging economies. To that end, I report evidence on Brazil and relate it to
cross-country evidence in the literature. Real interest rates are countercyclical
and lead cycles in a non-neutral way. They might be key to explain excessive
volatility of the general activity, as well as the higher relative volatility of consumption in emerging economies. Moreover, responses to interest rate shocks
are (inverted) hump-shaped, and the correlations between output and interest
rate at di¤erent lags follow a pattern that is consistent with these responses and
with the non-neutrality of interest rates.
Standard business cycle SOE models, including extensions with working capital constraints, cannot match these regularities, because they reveal weak propagation mechanisms. The model I propose of a credit constrained SOE (CCSOE)
relies fundamentally on a permanently binding endogenous credit collateral constraint on foreign liabilities. It reveals considerable propagation of shocks, in
particular of innovations to interest rates. The model bene…ts as well from
a general setting of preferences and interest rate induced exogenous processes
of productivity and collateral formation. The CCSOE appears to match in a
comprehensive way most empirical regularities.
30
As discussed in Section 6, it is precisely the mechanics brought about by
the inter-temporal consumption substitution, implicit in the inter-play of the
Euler equations governing capital and consumption adjustment, that assures
the envisaged properties. Actually, the model manages to match responses of
output and consumption. It does a good job in replicating second moments in
a more realistic way than usually achieved by SOE models. The non-neutrality
of interest rate appears to be key in explaining the mentioned absolute and
relative excessive volatilities. Moreover, the model delivers a good description
of the correlation between output and lagged interest rate.
While successful at these levels, the model also avoids anomalies of standard
SOE models with respect to moments related to investment and trade ratio.
Despite introducing realistic investment serial correlation, the CCSOE deserves,
as most business cycle models, to be enriched by an appropriate mechanism that
could provide investment also with realistic hump shapes.
The model captures by an impatience hypothesis and by the implication of a
permanently binding collateral constraint two aspects of the economy’s …nancial
integration with world economy. On the one hand, it stresses the inability
of some emerging economies, namely in Latin America, to generate domestic
savings and therefore their dependence on foreign credit. On the other hand,
it underlines frictions in international …nancial markets, which by the means of
collateral provide foreign creditors and investors with some control or discipline
over the country’s international exposure, measured by the stock of international
liabilities.23
The paper shows consistently that …nancial foreign constraints help in making the economy prone to su¤er from disturbances in international …nancial
variables. It shares some of the concerns manifested in Aghion, Bachetta and
Banerje (2004), Aoki, Benigno and Kiyotaki (2006), Caballero and Krishnamurthy (2001) and Gertler, Gilchrist and Natalucci (2003). It contributes in
exploring further, in a simple and quantitatively tractable model, the macroeconomic implications of …nancial frictions, in the spirit of Bernanke and Gertler
1989, Carlstrom and Fuerst 1997, and Kiyotaki and Moore 1997, but merely at
the level of SOEs.
This is not a paper on sudden stops. From the CCSOE framework, however,
they would manifest, in contrast to Mendoza (2006), not through non linear
changes in the country’s international …nancial condition (from being credit unconstrained to credit constrained) that are driven by a series of shocks, but
rather directly through e¤ects of interest rate shocks in an already constrained
SOE. The intensity of the output drop and current account reversal would depend on whether and to which extent these shocks can, beyond their purely
independent e¤ects, be re‡ected in swings in the net foreign liability position
2 3 Such
a view is somehow consistent with home bias puzzle in international debt and equi-
ties.
31
and/or shifts in total factor productivity. Such a topic might merit further
investigation.
Future research might seek to understand the speci…c role of country-spread
within the CCSOE framework. I do not di¤erentiate shocks to country-spread
from innovations to an international interest rate. Furthermore, guided by empirical reassurance, I do not consider the feedback e¤ects from the domestic
economy to the interest rate. Nevertheless, as argued e.g. Arellano (2005), we
should not neglect that a country’s interest rate, through the country spread,
might react somehow to changes in domestic variables. Beyond seeking to understand the strength of exogenous …nancial factors, another contribuiton of
this paper relates to the view that some of the referred feedback e¤ects could be
originated rather from the processes led by those same exogenous factors than
from the domestic (endogenous) core of the economy.
An underlying question to be further investigated relates to the generality of
the CCSOE model. Given its powerful mechanism to engender growth persistence and therefore realistic responses, could we consider applying it beyond the
scope of emerging economies? Before answering that question, we might need
to focus some research e¤orts on the conditions by which impatient (patient)
SOEs in general face quantity frictions in expanding its net foreign liabilities
(assets).
32
A
Appendix
All Brazilian quarterly series are available at IPEAData (www.ipeadata.gov.br),
the on-line macroeconomic database of the Instituto de Pesquisa Pura e Aplicada
- IPEA. The national account series are originally from the Instituto Brasileiro
de Geogra…a e Estatística (IBGE) - www.ibge.gov.br. Further details of the
data are the following:
Output. Real GDP from the IBGE National Accounts. The series was
expressed in natural logarithmic of available seasonally adjusted series.
Hours. Industrial hours from the Confederacao Nacional das Industrias (CNI).
The series was expressed in natural logarithmic of available seasonally adjusted
index.
Consumption. Total consumption from the IBGE National Accounts. The
series was expressed in natural logarithmic of the available seasonally adjusted
index.
Durables. Production of consumption durable good from the IBGE National
Accounts. The series was expressed in natural logarithmic of the available seasonally adjusted index.
Investment. Total …xed capital investment from the IBGE National Accounts. The series was expressed in natural logarithmic of the available seasonally adjusted index.
Machine and equipmet. Total investment in machine and equipment from
the IBGE National Accounts. The series was expressed in natural logarithmic
of the available seasonally adjusted index.
Ratio of export to import. The series was calculated by the author as a
ratio of net export to GDP. O¢ cial foreing trade statistics are produced by the
Ministry for Development, Industry and Foreign Trade - Minsitério do Desenvolvimento, da Indústria e do Comércio Exterior (MDIC).
Country spread. EMBI Plus index for Brazil from JPMorgan. The series is
available from Datastream.
US in‡ation and 3-month nominal interest rate are available from the FRED
database of the Federal Reserve Bank of St Louis.
33
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