Real Exchange Rate & Central Bank Preferences: An Economic Model

Economic Modelling xxx (xxxx) xxx
Contents lists available at ScienceDirect
Economic Modelling
journal homepage: www.journals.elsevier.com/economic-modelling
The changing nature of the real exchange rate: The role of central bank
preferences☆
Rodrigo Caputo a, ∗ , Michael Pedersen b
a
b
CESS, Oxford and Universidad de Santiago, Chile
Central Bank of Chile, Chile
A R T I C L E
I N F O
JEL classification:
C32
E42
F31
F33
Keywords:
Real exchange rate
DSGE models
Central bank preferences
Structural VAR
Sign restrictions
A B S T R A C T
We investigate the sources of real exchange rate fluctuations. We do so, first, in the context of a DSGE model that
explicitly considers the central bank’s preferences. Then we estimate SVAR models, where shocks are identified
by sign restrictions derived from the DSGE model. We perform this exercise for twelve countries, nine of which
have adopted inflation targeting during the period analyzed. In sharp contrast to the previous evidence in the
literature, we find that exchange rate (country risk premium) shocks have become the main drivers of real
exchange rate dynamics, while real shocks play a less important role. Evidence from the DSGE model reveals
that, as the central bank becomes more averse to inflation movements, and cares less about nominal exchange
rate fluctuations, the impact of nominal shocks on the real exchange rate tends to increase, while the impact of
real shocks decreases. Our results suggest that the adoption of inflation targeting, along with a floating exchange
rate, contributes to a shift in the relative importance of demand and country risk premium shocks in determining
the RER.
1. Introduction
In open economies the real exchange rate (RER) is a key relative
price and its changes have implications for the external equilibrium as
well as for the internal resource allocation. Understanding the nature
of shocks that drive the RER is a challenging issue in international economics. The quest to explain RER movements has been pursued by several scholars over the years. Initially, Structural Vector Autoregression
(SVAR) methods and variance decomposition techniques were used to
determine the relative importance of real and nominal shocks for the
RER dynamics. Early studies include those of Lastrapes (1992), Clarida and Galí (1994), Enders and Lee (1997), and Rogers (1999). The
identification strategy proposed in these papers is based on the long
run restrictions suggested by Blanchard and Quah (1989).1 A system-
atic result is that in the post-Bretton Woods era nominal shocks played
a minor role in the RER dynamics in the UK, Canada, Germany, Italy
and Japan.
More recently, Farrant and Peersman (2006), Juvenal (2011) and
Craighead and Tien (2015), have employed SVAR models where shocks
are identified with the sign restriction approach suggested by Faust
(1998), Canova and De Nicolò (2002) and Uhlig (2005). This method
imposes theoretically based sign restrictions on the dynamic responses
of a vector of variables to determine the relative contribution of structural shocks to the RER dynamics. These papers conclude that demand
shocks are still the main driver of the RER dynamics at different horizons. Overall, the empirical evidence supports the notion that the RER
is a shock-absorber, rather than a source of fluctuations.
☆
The views expressed are those of the authors and do not necessarily represent the opinions of the Central Bank of Chile or its board members. We are grateful
to an anonymous referee for constructive criticism and to Christiane Baumeister, Fabio Canova, Jordi Galí, Gustavo Leyva, James Stock, and Harald Uhlig for
useful discussions and suggestions. We also thank the participants at the XVIII World Congress of the International Economic Association, the 4th Conference of the
International Association for Applied Econometrics, the 2017 Annual Congress of the European Economic Association, the 49th Money, Macro and Finance Research
Group Annual Conference, the 22nd Annual LACEA Meeting, seminars held in Danmarks Nationalbank and the Central Bank of Chile for their comments as well as
Camila Figueroa for outstanding research assistance.
∗
Corresponding author.
E-mail addresses: [email protected] (R. Caputo), [email protected] (M. Pedersen).
1 This methodology is consistent with the notion of long-run money neutrality, allowing nominal shocks to have a temporary effect on the RER, but not a
permanent one.
https://doi.org/10.1016/j.econmod.2019.11.029
Received 24 July 2018; Received in revised form 7 September 2019; Accepted 26 November 2019
Available online XXX
0264-9993/© 2019 Elsevier B.V. All rights reserved.
Please cite this article as: Caputo, R., Pedersen, M., The changing nature of the real exchange rate: The role of central bank preferences,
Economic Modelling, https://doi.org/10.1016/j.econmod.2019.11.029
R. Caputo, M. Pedersen
Economic Modelling xxx (xxxx) xxx
There are, however, several unsettled issues regarding the RER’s
behavior. In particular, with the adoption of inflation targeting (IT),
several countries have experienced a sharp decline in inflation volatility,2 while the volatility of the RER has increased substantially. The
present paper studies whether the relative contribution of real and nominal shocks to the RER has changed as countries have adopted IT. In
doing so we perform two complementary exercises. First, in a Dynamic
Stochastic General Equilibrium (DSGE) model, we analyze the determinants of the RER and the extent to which changes in the monetary policy regime could affect the way in which structural shocks are transmitted to the RER. Second, using Bayesian techniques we estimate SVAR
models, where shocks are identified by sign restrictions. We perform
rolling window estimations to determine the extent to which the contributions of real and nominal shocks may have changed with the aand
Gambettidoption of alternative monetary policy regimes.
Unlike Farrant and Peersman (2006), Juvenal (2011) and Craighead
and Tien (2015), we derive the sign restrictions from a DSGE model,
which explicitly considers the preferences of the central bank. This
model is a slightly modified version of that of Kam et al. (2009) and
it is used to study how different shocks affect the main macroeconomic
variables, particularly the RER, and the results are used to impose sign
restrictions on SVAR models, which are estimated for different subsamples during the period 1986–2014 for twelve countries. Nine of these
adopted IT during the period analyzed, while the other three have conducted a fixed exchange rate policy, though only one vis-à-vis the benchmark country.
We find that the relative contribution of shocks driving the RER has
changed over time, particularly, in IT countries. In line with the existing literature, demand shocks were the main source of RER fluctuations
in the early years, whereas nominal shocks, particularly country-risk
premium (CRP) shocks, are more important in the more recent period.
The results for the only non-inflation-targeting (NIT) countries with a
fixed exchange rate vis-à-vis the benchmark country do not show the
same changes. Evidence from the DSGE model reveals that as the central bank becomes more averse to inflation and policy rate movements,
and cares less about nominal exchange rate fluctuations, the impact
of nominal shocks on the RER tends to increase, while the impact of
real shocks decreases. The reason is that, under a fixed exchange rate
regime, the impact of nominal shocks on the RER is almost completely
muted by the policy rate reaction. In contrast, under an IT regime with a
fully floating exchange rate, the RER absorbs an important proportion
of nominal shocks as the policy rate reacts much less to these innovations. For IT countries, our results suggest that the adoption of this
regime along with a floating exchange rate, has contributed to the shift
in the relative importance of demand and CRP shocks in determining
the RER.
The rest of the paper is organized as follows. The second section
reviews the main structure of the theoretical DSGE model and discusses
the sign restrictions that can be derived from it. Section 3 presents the
empirical methodology and reports the results of the estimation. Section
4 explores the impact of alternative central bank preferences on both
the relative importance of nominal and real shocks for the RER dynamics and for the overall volatility of the main macroeconomic variables.
Section 5 concludes.
endogenous persistence in both aggregate demand and supply equations, which is crucial for bringing the model closer to the data, as
shown by Fukač and Pagan (2010). Importantly for the present analysis,
the model explicitly considers the preferences of the monetary authority
with respect to inflation, output, interest rate and exchange rate volatility.3 This type of models are generally used to assess the transmissions
of different shocks in small open economies (see, for instance, Medina
and Soto (2016) and Bhattarai and Trzeciakiewicz (2017)).
The model is useful for the present study for three reasons. Firstly,
it clearly illustrates, from a theoretical point of view, the sources of
RER volatility such that it is possible to investigate which shocks drive
the RER dynamics. Secondly, it allows for an analysis of the signs of
the responses to different shocks. Thirdly, it makes it possible to easily
assess how changes in the central bank’s preferences affect the way
different structural shocks are transmitted to the RER.
2.1. The DSGE model
In this subsection we briefly summarize the main features of the
Kam et al. (2009) DSGE model in order to introduce the shocks that
will be analyzed. The main equations in this model are derived under
the assumptions that households, firms and the central bank optimize
their relevant loss functions. Appendix A contains a detailed description
of the model.
From the first-order condition of households’ optimization problem we obtain the Euler equation for consumption. In particular, it is
obtained by log-linearizing the inter-temporal optimality condition for
a representative household that maximizes lifetime utility:
ct − hct −1 = Et (ct +1 − hct ) −
1−h
𝜎
(rt − Et 𝜋t+1 ) + 𝜀d,t .
(2.1)
Variables are expressed as deviations from steady-state values. Consumption, ct , is expressed in logarithm, whereas the nominal interest
rate, rt , and CPI inflation, 𝜋 t , are in percentage levels. The degree of
habit formation is represented by h, and 𝜎 is the coefficient of relative
risk aversion of the households. There is an exogenous demand shock,
𝜀d,t .4
Households obtain utility from consuming a basket of domestic and
foreign goods. The consumption basket is relative to an external habit
stock, such that consumption has a degree of habit persistence.
Firms producing domestic goods have a linear production technology hiring labor, which is offered by the households as the only input.
Domestic output evolves according to: YH,t = 𝜀s,t Nt , where 𝜀s,t is
an exogenous productivity shock and Nt is the level of employment.
The log-linear approximation of the optimal price decision rule can
be expressed as the following hybrid Phillips curve for domestic goods
inflation:
𝜋H,t
= 𝛽 Et (𝜋H,t+1 − 𝛿H 𝜋H,t ) + 𝛿H 𝜋H,t−1
+𝜆H (mct ) − 𝜆H (1 + 𝜙)𝜀s,t ,
(2.2)
where 𝛽 is the subjective discount factor, 𝜋 H,t is domestic inflation,
𝛿 H measures the degree of inflation indexation, and mct represent the
marginal costs associated to the production of domestic goods. The
𝜆H coefficient is the slope of this Phillips curve, which is inversely
related to the degree of domestic price stickiness. The 𝜙 coefficient
2. An open economy DSGE model
To evaluate how nominal and real shocks are transmitted to the
RER, we employ the small open economy DSGE model of Kam et al.
(2009), which assumes, as does Monacelli (2005), that the pass-through
of exchange rate movements to prices is incomplete. It also introduces
3
We consider concerns about nominal exchange rate fluctuations, rather than
RER fluctuations as in Kam et al. (2009), since many countries had explicit
targets for the nominal exchange rate before adopting IT.
4
This shock is not included in the original specification of Kam et al. (2009)
but, as shown by Galí (2015), it can be derived from an exogenous preference
shifter that enters the households’ utility function. This shock can be interpreted
as a shock to the effective discount factor. We calibrate the size of this shock
so that the relative contribution of demand innovations are in line with the
empirical evidence for developed countries reported by Clarida and Galí (1994).
2
See the Great Moderation literature in Galí and Gambetti (2009) and
Canova and Gambetti (2010).
2
R. Caputo, M. Pedersen
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captures the disutility of labor. The domestic productivity shock, 𝜀s,t ,
reduces inflation and increases output. Marginal costs are increasing
in terms of trade, st , consumption, ct , and output, yt . In particular,
𝜎
(c − hct−1 ), implying that demand shocks will
mct = 𝜙yt + 𝛼 st + 1−
h t
eventually impact domestic inflation.
As is standard in the literature, firms face an independent signal that
allows a fraction of them to set prices in order to maximize their present
value of the stochastic stream of profits. Firms, that do not re-optimize
partially, index their prices to past inflation. To be more specific, the
slope of the New Keynesian Phillips curve, 𝜆H , depends on the probability that firms adjust prices optimally each period, 1 − 𝜃 H . In particular,
𝜆H = (1 − 𝛽𝜃H )(1 − 𝜃H )𝜃H−1 . If prices are more flexible, i.e. if 𝜃 H tends
to zero, the slope of (2.2) increases.
Imported inflation, 𝜋 F,t , is obtained by log-linearizing the optimality conditions of importing retailers. They purchase imported goods
at competitive world prices, but act as monopolistic competitive redistributors of these goods. This creates a gap between the price of
imported goods, in domestic currency, and the domestic retail price of
imported goods. Hence, if firms adjust prices infrequently, pass-through
of the exchange rate to prices is incomplete. The New Keynesian Phillips
curve for imported inflation is expressed as follows:
𝜋F ,t = 𝛽 Et (𝜋F ,t+1 − 𝛿F 𝜋F ,t ) + 𝛿F 𝜋F ,t−1 + 𝜆F (𝜓F ),
that the 𝜀q,t innovation may be capturing anticipated shocks (news) as
well as unanticipated ones.6 As noted by Chen and Zhang (2015), economic news may be capturing shocks to the RER that are expected by
markets participants. The relative importance of anticipated and unanticipated shocks is certainly a relevant question, but in the present context 𝜀q,t is reflecting both types of shocks.
We follow Neumeyer and Perri (2005) and Kam et al. (2009), among
many others, and assume that the relevant foreign rate, rt∗ , is denominated in U.S. dollars.7 This assumes that the relevant foreign asset market for the economies under analysis is the U.S. For most countries, this
is a reasonable assumption which is also supported by the empirical
evidence on the UIP (see Engel (2016) and Kiley (2016), among others). As a consequence, the country risk premium is measured against
a relatively stable country, the U.S., which also seems to be a sensible
metric for measuring this premium.
The real exchange rate is expressed as qt = et + p∗t − pt , where et is
the nominal exchange rate and pt and p∗t are the CPI price levels in the
domestic and the foreign economy, respectively. Using the definition of
qt and the UIP condition in (2.5), it is possible to derive a condition
that describes the evolution of qt :
Et (qt +1 − qt ) = (rt − rt∗ ) − Et (𝜋t +1 − 𝜋t∗+1 ) + 𝜀q,t ,
(2.3)
where the real exchange rate and the expected inflation differential are
defined relative to the U.S. because the interest rate differential, rt − rt∗ ,
is also relative to the U.S.
where 𝛿 F measures the degree of imported inflation persistence. The
variable
(
)𝜓 F represents the law of one price gap, defined as 𝜓F =
et + p∗F ,t − pF ,t , where et is the nominal exchange rate, p∗F ,t is the price,
2.1.2. Monetary policy
The central bank sets the nominal interest rate, rt , in order to minimize a quadratic loss function:
[
]
1
𝜇𝜋 𝜋̃2t + 𝜇y yt2 + 𝜇e Δe2t + 𝜇r (Δrt )2 ,
(2.7)
L=
2
in foreign currency, of an imported consumption basket and pF,t represents the price, in domestic currency, of an imported consumer basket.
The slope of (2.3) is 𝜆F = (1 − 𝛽𝜃F )(1 − 𝜃F )𝜃F−1 and increases if import
retailers set prices more frequently (i.e. a lower 𝜃 F ). Imperfect passthrough is a direct consequence of import retailers that do not adjust
prices instantly when the RER changes. If import retailers can set prices
at any moment, then 𝜃 F = 0. In this case, the pass-through is immediate
implying that 𝜓 F = 0. As a consequence, the pass-through is complete
and we have that:
pF ,t = et + p∗F ,t .
where 𝜇y , 𝜇 e and 𝜇 r express the central bank’s concern with respect to
output, the nominal exchange rate and policy rate stabilization, respectively. These objectives are expressed relative to a concern for annual
inflation, 𝜋̃t , which is normalized to 𝜇 𝜋 = 1. A monetary policy shock,
𝜀m,t , is appended to the optimal interest rate path that minimizes (2.7).
As noted by Kam et al. (2009), this specification of macroeconomic
objectives encompasses the expressed objectives of the so-called flexible inflation targeting central banks by allowing for positive weights of
all arguments in the loss function.
In the Kam et al. (2009) specification, foreign variables are assumed
to follow uncorrelated AR(1) processes. In our empirical exercise, output, prices, and interest rates are measured relative to the same variable in the U.S., in line with Farrant and Peersman (2006) and Juvenal
(2011). In the next subsection this approach is explained in the context
of the model specification.
(2.4)
2.1.1. Country risk premium and the exchange rate
We use the uncovered interest parity (UIP) to model the behavior of
the nominal exchange rate, et . This is a no-arbitrage condition between
investing in a domestic currency denominated asset and a foreign currency denominated asset such that:
Et (et +1 − et ) = rt − rt∗ + 𝜀q,t .
(2.6)
(2.5)
The expression in (2.5) links expected nominal devaluations and the
nominal interest rate spread, rt − rt∗ . In particular, an increase in
the foreign currency denominated interest rate, rt∗ , is associated with
an expected nominal appreciation. The stochastic term in (2.5), 𝜀q,t ,
reflects the country risk premium. As shown by Neumeyer and Perri
(2005), this premium may be affected by domestic fundamentals
(expected productivity) and, through the presence of working capital,
may exacerbate the effect of this shock on real activity. In addition, the
shock could also be interpreted as changes in capital flows or, indeed,
capital controls imposed by the domestic economy, that have an impact
on interest rate differentials.5 In Kam et al. (2009) this innovation is
interpreted as an exogenous CRP shock, reflecting foreign and domestic
elements not explicitly modeled. In this context, it is important to note
2.1.3. Equilibrium conditions: aggregate inflation and output
Households consume domestic and foreign goods, and the relevant
consumer price index is given by8 :
[
] 1
1−𝜂
1−𝜂
Pt = (1 − 𝛼)PH,t + 𝛼 PF ,t
,
(2.8)
where 𝜂 denotes the elasticity of substitution between domestic and
foreign goods and 𝛼 represents the proportion of imported goods in the
household’s consumption basket.
Log-linearizing (2.8) and first differentiating gives rise to the CPI
inflation equation:
6
See Nam and Wang (2015).
For Argentina Neumeyer and Perri (2005) notice that in the early 1990s, the
foreign rate faced by Argentina was very close to the U.S. dollar rate and during
crisis times (the hyperinflation of 1989) the country risk increased significantly.
8
Details are included in Appendix A.
7
5
As shown by Herrera and Valdés (2001), in emerging economies the effect
of capital controls on interest rate differentials, and on the RER, is considerably
smaller than what static calculations suggest.
3
R. Caputo, M. Pedersen
𝜋t = (1 − 𝛼)𝜋H,t + 𝛼𝜋F ,t .
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empirical model by including fewer observable variables.11
(2.9)
Hence, CPI inflation is a weighted average of domestic and imported
inflation, where the relative importance of imported goods inflation is
given by 𝛼 . The evolution of domestic and foreign inflation is determined by equations (2.2) and (2.3), respectively. Thus, CPI inflation
will be influenced by domestic productivity shocks affecting 𝜋 H,t and
shocks affecting 𝜋 F,t .
In the small open economy, domestic output equals total domestic
and foreign demand for goods produced at home. As a result, domestic output will depend on total consumption, ct , foreign output, yt∗ , the
RER, qt , and the terms of trade, st . In particular, the log-linear approximation of domestic output is given by9 :
yt = (1 − 𝛼)ct + 𝛼 yF∗,t + 𝛼𝜂 qt + 𝛼𝜂 st ,
2.2. Impulse-responses
Kam et al. (2009) make inferences regarding structural coefficients
and shocks using Bayesian posterior distributions of the model parameters for three IT countries: Australia, Canada and New Zealand.12 To
identify the impact that different shocks have on the RER and the rest
of the relevant variables, we use the coefficients estimated by Kam et
al. (2009) for Australia.13
Applying a given, and common, calibration enables us to derive
the response of the main variables to any given structural shock. This
calibration process is just the first step to knowing how each of the
economies we consider reacts to each shock. To be more specific, we
will obtain different posteriors for each country reflecting the individual nature of the structural coefficients across countries which are not
assumed to be equal ex-post. Hence the common calibration does not
preclude us from obtaining different responses across countries. Having said that, using Australia, or any other country, does not seem to
change the results much. For instance, the slope of the IS curve, equah
tion (2.10), is given by this expression: 1−
. If we use the calibration
𝜎
for Australia, where h = 0.925 and 𝜎 = 1.029, the calibrated slope
is 0.0729. If we use, instead, the estimated coefficients for Canada in
Kam et al. (2009), the slope is almost identical: 0.0732. If we used
the estimated values for Chile, from Gomez et al. (2019), the slope
would be 0.0607. Thus, it appears that the main features of the model
are well reflected by our initial calibration, and the specific nature of
each country will be reflected in the posterior results obtained from the
country-specific SVAR estimation.
Once the model is solved, it is possible to compute the responses
of the main macroeconomic variables to the four structural innovations included in the model: 𝜀s , 𝜀d , 𝜀m , and 𝜀q .14 As shown in Fig. 1
(first row), a supply shock (i.e. a positive technology shock relative to
the U.S.) increases the relative output and, at the same time, reduces
marginal costs and relative prices. Via the monetary policy, the interest rate declines importantly, although in the first quarter it increases
marginally. Given the policy reaction and the path of the relative prices,
the RER depreciates almost immediately by 4%.
A demand shock increases consumption and, as a consequence,
increases output. In this context marginal costs are higher, determining an increase in the prices of domestic goods. The increase in the
RER has a positive impact on imported inflation too. Hence, this shock
induces an increase in relative CPI inflation and output. The optimal
policy response implies that the interest rate increases. The RER appreciates nearly 4% as a consequence of the actual and expected increase
(2.10)
where 𝜂 > 0 is the elasticity of substitution between home and foreign
goods and the variable st represent the terms of trade, which evolve
according to the difference between imported and domestic inflation:
st − st −1 = 𝜋F ,t − 𝜋H,t .
(2.11)
Several of the countries in the analysis (Australia, Canada, Chile and
Norway) have an important commodity sector. In general, this sector is
not explicitly modeled, neither in the seminal contribution of Farrant
and Peersman (2006) nor in the more recent works of Kam et al. (2009)
and Gomez et al. (2019). This sector is, however, implicitly considered
in the open economy IS curve, equation (2.10). In particular, changes
in the terms of trade or world output could be related to an increase in
the demand for commodities (which is part of the domestic output) and,
hence, the estimations of 𝛼 and 𝜂 are going to reflect the extent to which
foreign variables affect the demand for commodities in these countries.
This in turn, will change domestic output and domestic marginal cost,
and will determine, eventually, changes in the domestic policy rate,
which have an impact on the RER. Hence, the commodity sector, and
its implications for the RER and output, is implicitly considered in the
model.
The model contains five relevant relationships. The first one reflects
the determination of nominal exchange rate and is given by equation
(2.5). The second describes the evolution of the real exchange rate, qt ,
which is described by equation (2.6). Monetary policy is described by
the loss function criterion, equation (2.7). The fourth relevant relationship is CPI inflation, equation (2.9), which incorporates shocks affecting domestic inflation and the variables that impact foreign inflation.
Finally, the evolution of aggregate output is determined by equation
(2.10).
Two crucial relationships, the nominal exchange rate and the real
exchange rate - equations (2.5) and (2.6) -, are measured relative to the
U.S., since this is the relevant foreign rate for most countries. Accordingly, the relevant inflation differential is also measured relative to the
U.S. To keep consistency with the equations for the nominal and real
exchange rates, we also measure CPI inflation, the policy interest rate,10
and the output gap relative to the U.S. This is an approximation of
the original model, but it does allow us to compare our results with
the existing literature and, in particular, with the paper of Farrant and
Peersman (2006). In addition, we can reduce the dimensionality of the
11
Another reason to measure the variables relative to the U.S. is that the
structural model in the domestic economy and in the U.S. are similar. This is,
perhaps, a strong assumption, so in the context of the small open economy
model, measuring the variables relative to the U.S. is an approximation. In any
case, and in order to analyze the extent to which our results may be driven by
developments in the U.S., we estimate stochastic volatility models (Chan and
Hsiao (2014)) for the raw data in each country: inflation, GDP growth and the
real interest rate. Then we estimate the models for the same series but relative
to the U.S.. It turns out that the relative series, which are the ones we use in
our empirical analysis, mimic quite well the path of the country-level series
and, hence, the behavior of the relative series does not seem to be driven by
developments in the U.S., but rather do they reflect idiosyncratic changes in
each country.
12
The Bayesian methodology closely follows related papers such as those of
Smets and Wouters (2003) and Rabanal and Rubio-Ramírez (2005).
13 The numbers are from the baseline estimation, where 𝜇 = 0. The 𝜎 coefe
d
ficient is calibrated such that demand shocks account for 50% of the RER’s
variance, which is pretty much in line with the relative importance of demand
shocks in previous empirical studies.
14
Shocks are independent and identically distributed and the size of them is
one standard deviation, as reported by Kam et al. (2009) for Australia.
9
See Appendix A for a derivation.
In terms of monetary policy identification, we can say that since the early
1980s inflation has been very stable in the U.S. According to Ilbas (2012),
inflation stabilization owes mainly to the change in monetary policy that took
place at the beginning of Volcker’s mandate in 1979. In addition, as shown
by Bauducco and Caputo (2020) inflation in the U.S. has been systematically
around 2% since the early 1990.
10
4
R. Caputo, M. Pedersen
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Fig. 1. Theoretical Accumulated IRF under Baseline Calibration (quarters after the shock).
in the policy rate (Fig. 1, second row).
A positive monetary policy shock (i.e. a decline in the policy rate)
results in increases in consumption and output. A higher demand for
domestic output increases marginal costs and prices. The consequence
of this shock is that the RER initially increases and then declines in the
second quarter (Fig. 1, third row).
In this model, a CRP shock generates an increase in the RER. This
is equivalent to a decline in the relative price of domestic goods. As
a result, the demand for and production of home goods increase, generating higher marginal costs and prices. The optimal monetary policy
response is to raise the interest rate, even though the RER is not, per se,
a policy target (Fig. 1, fourth row).
The sign restrictions imposed in the SVAR exercises are based on
the impulse-responses derived from the DSGE model. Table 1 summarizes the restrictions that will be used to identify the structural
shocks.15 Restrictions are binding for four quarters, with the exception of the interest rate, for which the restriction is binding one quarter. The response of the policy rate to a supply shock is left unrestricted
because during the first two quarters, the policy rate moves in the opposite direction in response to this shock (Fig. 1, first row).
NIT countries in a framework of vector autoregressive (VAR) models, where the shocks are identified by imposing the sign restrictions
derived from the DSGE model. This approach has gained momentum
in empirical analyses conducted since the beginning of the present millennium. Several early studies report the results by means of quantiles
of the impulse-responses acknowledging that a drawback is that the
responses shown are not necessarily from the same model and, hence,
the shocks may not be orthogonal (see Fry and Pagan (2011)). In the
present analysis we follow the approach presented by Inoue and Kilian (2013), who suggest a solution to this orthogonality problem by
reporting the results of the most likely model chosen among those that
satisfy the sign restrictions imposed. With this approach, however, the
credibility intervals are often quite wide and, to assess uncertainty, we
evaluate the histograms of all possible outcomes.
After briefly presenting the econometric model and the data utilized, we report, as a preliminary assessment, the full sample variance
decompositions for individual IT countries and compare them to previous findings in the literature. The evidence indicates that changes
have occurred over time. To gain further insight into these changes we
present results, firstly, from panel VAR (PVAR) models and, secondly,
for individual countries, IT as well as NIT, where the sample utilized
for the estimations is changed over time.16
3. Empirical estimations
This section presents exercises where we let the data “speak” in a
less structured environment. We analyze data from nine IT and three
15
Our sign restrictions are comparable to the ones in Juvenal (2011), while
those used to identify the supply shock are more restrictive than in Farrant and
Peersman (2006).
16
Since the dates of the IT adoptions are known with certainty, we opted
for a rolling approach where the time of IT increases markedly with each new
subsample estimation.
5
R. Caputo, M. Pedersen
Economic Modelling xxx (xxxx) xxx
Table 1
Sign restrictions from the DSGE model.
Supply shock
Demand shock
Monetary shock
CRP shock
𝜕(y ∕y ∗ )
𝜕𝜀s
𝜕(y ∕y ∗ )
𝜕𝜀d
𝜕(y ∕y ∗ )
𝜕𝜀m
𝜕(y ∕y ∗ )
𝜕𝜀q
𝜕(p∕p∗ )
𝜕𝜀s
𝜕(p∕p∗ )
𝜕𝜀d
𝜕(p∕p∗ )
𝜕𝜀m
𝜕(p∕p∗ )
𝜕𝜀q
≥0
≥0
≥0
≥0
3.1. Econometric model and data
≥0
≥0
≥0
𝜕(i−i∗ )
𝜕𝜀s
𝜕(i−i∗ )
𝜕𝜀d
𝜕(i−i∗ )
𝜕𝜀m
𝜕(i−i∗ )
𝜕𝜀q
≷0
≥0
≤0
≥0
𝜕q
𝜕𝜀s
𝜕q
𝜕𝜀d
𝜕q
𝜕𝜀m
𝜕q
𝜕𝜀q
≥0
≤0
≥0
≥0
Because of this, the NITs should not be regarded as a control group,
i.e. a group for which one might expect results opposite of those of the
ITs, maybe with the exception of Hong Kong. The group does, however,
represent countries that have not experienced significant changes in the
monetary policy during the period investigated. The series applied start
in 1986Q1 (Hong Kong: 1990Q4) and end in 2014Q2.
In interpreting the results, it should be noted that only Australia and
Canada have had, de jure, a freely floating exchange rate for the entire
sample, while the Philippines has had a regime of managed floating
exchange rate. In the UK and Sweden, freely floating currency started
in 1992, in Israel in 1998, in Chile in 1999, and in Norway and South
Africa in 2001. Before these years, some of the countries had a regime
that can be characterized as fixed exchange rate, while others had managed floating rates. The central banks have, however, to some extent
been buying and selling foreign currencies as shown in Fig. 2, which
illustrates average changes, in absolute values, in the foreign reserves
before and after the IT implementation. Generally, the central banks
have been less active in trading foreign currency after the IT implementation, but in Norway the reduction is quite limited and in Australia
there is practically no change.
For the empirical analysis we consider a four-dimensional reducedform VAR model with p lags:
Y = X 𝛽 + 𝜀,
≤0
(3.1)
where
Y = [Y1 , Y2 · · · YT ]′ ,
X = [X1 , X2 · · · XT ]′ ,
Xt =
[1, Yt′−1 , Yt′−2 · · · Yt′−p ]′ for t = 1, 2, … , T, 𝛽 = [c, 𝛽1 , 𝛽2 · · · 𝛽p ]′ ,
and 𝜀 = [𝜀1 , 𝜀2 · · · 𝜀T ]′ . It is assumed that 𝜀t is independent and
identically distributed with zero mean and covariance matrix Ω. The
endogenous variables are Yt = [Δ(yt ∕yt∗ ) Δqt Δ(pt ∕p∗t ) it − i∗t ]′ , where
the variable yt ∕yt∗ is the logarithm of the ratio between real gross
domestic product (GDP) in the domestic country and the real GDP
in the foreign (∗) country (the U.S.), qt is the logarithm of the real
exchange rate, pt ∕p∗t is the logarithm of the price ratio, and it − i∗t is the
difference between the real interest rates.17 The measurement of the
real exchange rate implies that an increase is a depreciation of the real
domestic currency.18 A brief summary of the methodology is presented
in Appendix B.
To focus the analysis on how different sources of RER volatility may
have changed over time, the estimations are performed with rolling
windows, each including a period of 15 years of data.19 The results are
presented as variance decompositions of the most likely model as well
as a fitted trend to evaluate changes in the contributions over time.
Furthermore, histograms of the variance decomposition contributions
of all the models, that fulfill the imposed sign restrictions, are employed
to assess uncertainty and to evaluate whether the most likely model is
representative.20
The primary source of the data is the IMF’s International Financial
Statistics (IFS) and observations from nine IT and three NIT countries
are utilized as well as U.S. data for the benchmark economy.21 The
economies classified as IT are: Australia (IT since 1993), Canada (1991),
Chile (1991), Israel (1992), Norway (2001), the Philippines (2002),
South Africa (2000), Sweden (1993), and the UK (1992), while the
NITs are Denmark (fixed exchange rate against a single currency, from
1982 the German mark and since 1999 the euro), Hong Kong (Currency
Board, 1983), and Singapore (fixed exchange rate against a revised basket of currencies, 1975). Hence, the monetary policy of the three NIT
countries has not been changed during the period analyzed. Only Hong
Kong, however, has a fixed exchange rate vis-à-vis the USD, while the
Danmarks Nationalbank states that the main objective of the monetary
policy is to ensure low inflation and the Monetary Authority of Singapore (MAS) that the primary objective is to promote price stability.22
3.2. Full sample variance decomposition
In order to make comparisons with previous literature, we estimate full-sample VARs for each IT country in our data set and compute the variance decomposition of RER fluctuations.23 As shown in
Table 2, demand and CRP shocks contribute to most of the RER volatility in the period 1986–2014. In terms of relative contribution, demand
shocks explain between 5% (Australia) and 50% (UK) of RER volatility,
whereas CRP shocks (or shocks to the RER) explain between 30% (UK)
and 90% (Philippines) of RER volatility.
The importance of demand shocks we find for Australia are in sharp
contrast to the findings of Farrant and Peersman (2006), who conclude
that around 70% of RER volatility is explained by demand shocks in
small open economies. The reason for this is that whereas Farrant and
Peersman (2006) focus on a period that includes, mostly, observations
under a non-IT regime (1974–2002), our sample contains many more
observations under the IT regime, ranging from 1986 to 2014. Once we
compare the results from 1986 to 2000, we find that demand shocks
tend to explain a substantial fraction of the RER volatility in Australia,
pretty much in line with the findings of Farrant and Peersman (2006).
The fact that, in general, CRP shocks explain a larger fraction of
RER volatility is in sharp contrast with previous empirical evidence,
as several studies have concluded that demand shocks are one of the
main drivers of the RER dynamics. For Canada we find that demand
shocks explain between 39% and 42% of RER volatility at horizons of
one quarter to four years (Table 2). In contrast, Farrant and Peersman
(2006) find that, between 1974 and 2002, demand shocks contributed
17
In terms of the model presented previously, the real rates differential is
equivalent to (rt − Et 𝜋t +1 ) − (rt∗ − Et 𝜋t∗+1 ).
18
As a robustness check, the estimations were also made with level data filtered by the Hodrick and Prescott (1997) filter. These estimations show results
similar to the ones reported.
19
To speed up the process, the windows are shifted four quarters at a time.
Hence, estimations are made for 15 overlapping periods.
20
̃ are quite close among the models with the highest values,
The values of f (Θ)
while their variance decompositions may be very different. Hence, a histogram
comparison shows whether the changes are a more general feature of the data.
21
A detailed description of the data is included in Appendix C.
22
See Danmarks Nationalbank (2009) and the MAS article “Singapore’s
Exchange Rate-Based Monetary Policy” available at http://www.mas.gov.sg/.
23
All VAR models include a constant term and, as suggested by the Schwarz
information criterion, the lag order is set to one for all countries. The results presented are, however, generally robust when including up to four lags. According
to the DSGE model, all variables should be stationary and when applying a 5%
confidence level, the Trace test of Johansen (1991) suggests that indeed all
the VARs estimated are stationary. Chile, however, is a borderline case with a
p-value of 0.0546.
6
R. Caputo, M. Pedersen
Table 2
RER variance decomposition: Full sample 1986–2014.
Horizon (Q)
7
Lower
Demand Shock
Modal
Upper
Lower
Monetary Shock
Modal
Upper
Lower
CRP Shock
Modal
Upper
Lower
Australia
1
4
16
0.034
0.066
0.065
0.781
0.724
0.709
0.000
0.000
0.000
0.048
0.083
0.082
0.942
0.916
0.886
0.000
0.000
0.001
0.229
0.214
0.237
0.765
0.744
0.742
0.000
0.002
0.003
0.689
0.637
0.617
0.978
0.961
0.960
0.000
0.002
0.003
Canada
1
4
16
0.053
0.173
0.173
0.689
0.641
0.628
0.000
0.001
0.001
0.420
0.398
0.397
0.974
0.920
0.914
0.000
0.000
0.000
0.026
0.025
0.026
0.564
0.478
0.478
0.000
0.000
0.001
0.502
0.405
0.404
0.995
0.959
0.952
0.005
0.017
0.017
Chile
1
4
16
0.006
0.044
0.044
0.655
0.630
0.630
0.000
0.001
0.003
0.246
0.263
0.263
0.975
0.931
0.930
0.000
0.000
0.000
0.087
0.084
0.084
0.975
0.934
0.930
0.000
0.001
0.001
0.661
0.608
0.608
0.995
0.977
0.976
0.000
0.003
0.003
Israel
1
4
16
0.003
0.025
0.028
0.665
0.629
0.629
0.000
0.000
0.000
0.420
0.444
0.442
0.954
0.930
0.922
0.001
0.005
0.005
0.110
0.119
0.119
0.775
0.719
0.716
0.000
0.000
0.000
0.468
0.412
0.411
0.984
0.980
0.979
0.001
0.002
0.003
Norway
1
4
16
0.009
0.047
0.048
0.817
0.803
0.787
0.000
0.000
0.000
0.442
0.455
0.454
0.972
0.936
0.929
0.000
0.004
0.004
0.105
0.095
0.097
0.644
0.626
0.637
0.000
0.000
0.001
0.444
0.403
0.402
0.979
0.964
0.961
0.001
0.004
0.004
Philippines
1
4
16
0.001
0.031
0.031
0.270
0.300
0.301
0.000
0.001
0.002
0.092
0.093
0.094
0.817
0.801
0.799
0.092
0.083
0.082
0.000
0.005
0.006
0.091
0.139
0.138
0.000
0.001
0.001
0.906
0.871
0.869
0.906
0.871
0.869
0.145
0.156
0.156
South Africa
1
4
16
0.000
0.038
0.041
0.181
0.252
0.247
0.000
0.000
0.001
0.191
0.208
0.204
0.810
0.797
0.794
0.000
0.002
0.002
0.030
0.036
0.047
0.434
0.400
0.408
0.000
0.001
0.002
0.779
0.719
0.708
0.997
0.965
0.939
0.183
0.183
0.184
United Kingdom
1
4
16
0.054
0.056
0.057
0.559
0.541
0.540
0.000
0.001
0.001
0.519
0.577
0.573
0.995
0.977
0.974
0.018
0.033
0.035
0.052
0.051
0.057
0.571
0.537
0.537
0.000
0.001
0.001
0.375
0.316
0.313
0.940
0.907
0.901
0.000
0.004
0.004
Sweden
1
4
16
0.031
0.028
0.029
0.452
0.429
0.418
0.000
0.000
0.000
0.383
0.363
0.341
0.968
0.926
0.920
0.030
0.052
0.051
0.047
0.106
0.158
0.465
0.448
0.466
0.000
0.006
0.008
0.538
0.503
0.473
0.899
0.853
0.839
0.001
0.005
0.005
Note: Modal refers to the most likely model, while Upper (Lower) indicates the maximum (minimum) among the 68% most likely models.
Economic Modelling xxx (xxxx) xxx
Supply Shock
Modal
Upper
R. Caputo, M. Pedersen
Economic Modelling xxx (xxxx) xxx
Fig. 2. Annual average of absolute changes in the
foreign reserves. Notes: Calculated with observations
from 1986 to 2014. Pre IT period includes the year
of the IT adoption. Total reserves including gold measured in current USD. (For interpretation of the references to colour in this figure legend, the reader is
referred to the Web version of this article.)
Source: Own calculations based on data from IMF
(series FI.RES.TOTL.CD).
between 70% and 80% of the RER’s volatility at similar horizons. In the
same way, Clarida and Galí (1994) find that for Canada demand shocks
account for 94%–97% of the RER volatility between 1974 and 1994.
Our estimates suggest that in this country CRP shocks explain between
40% and 50% of RER volatility at horizons of one quarter to four years,
whereas Farrant and Peersman (2006) find that this shock contributes
much less, explaining between 5% and 20% of RER volatility at similar
horizons.
In the case of the UK, we find that the relative importance of nominal shocks in the RER dynamics has increased. In particular, our results
suggest that CRP shocks explain between 31% and 37% of RER volatility at horizons of one quarter to four years, whereas Farrant and Peersman (2006) find, for similar horizons, that the weight of this shock is
between 8% and 40%.
For Chile, our results are also in sharp contrast with previous evidence documented by Soto (2003) for the 1990–1999 period. On the
one hand, we find that real shocks (supply and demand) contribute
25%–27% of RER volatility at horizons of one quarter to four years,
whereas at similar horizons Soto (2003) finds that these shocks account
for 70% and 90% of the RER variance. On the other hand, we find that
the contribution of nominal shocks to RER variance is between 61%
and 67%, whereas Soto (2003) finds, at similar horizons, that nominal
shocks contribute between 10% and 30% of RER volatility.
To explore in greater detail the differences with results from studies employing earlier samples, we estimate the models across different
periods of time.
As mentioned earlier, the IT countries included in our analysis experienced important policy changes during in the mid 1990s and early
2000s. In particular, they moved, with different speed, towards a fully
fledged IT regime.24 As a first step to detect possible structural changes,
we estimate two PVAR(1) models, one for the IT economies and another
for the NITs.25 The rolling variance decompositions are presented in
Figs. 3 and 4, while Fig. 5 shows changes in the distribution of the
weights in the variance decompositions of the RERs for the first and
last subsamples.
There are several differences between the changes in the variance
decompositions of IT and NIT countries, where most notable are the
following: (1) The impact of supply shocks on inflation volatility has
increased markedly in NIT countries,26 while the impact of monetary
shocks has decreased. In IT countries, the impact of monetary and CRP
shocks has increased, while that of demand shocks has decreased. This,
as we will explain later, can probably be attributed to the shift to inflation targeting. (2) Across the whole period, monetary shocks explain the
main part of the interest rate volatility in NITs, while there appears to
have been a change in ITs, such that CRP shocks explained an important
part in the early periods, while monetary shocks explain the main part
in the later subsamples. For economies that have adopted IT policies,
these results are expected: If there is some form of exchange rate control, then the policy rate should move in the face of CRP shocks to avoid
exchange rate fluctuations. As economies move towards an IT regime,
monetary policy shocks become more important for interest rate fluctuations. For the same reason, one could expect, a priori, the CRP to
explain a larger part of interest rate volatility in the NIT countries. (3)
Generally, demand shocks explain a smaller part of the RER’s volatility,
while CRP shocks explain a larger part. This is more pronounced in the
ITs. When looking at the distributions of the contributions to the RER
variance decompositions (Fig. 5) it is notable how it, particularly in the
ITs, moves to the left in the case of a demand shock and to the right for
a CRP shock.27
To sum up the results with respect to RER volatility, in both NITs
and ITs it seems that demand shocks (real shocks) explain a smaller
part, while CRP shocks explain a larger part. This is particularly true
for the economies that have adopted IT, which supports the view that
when the central bank becomes more averse to inflation, the relative
contribution of the CRP shocks to the volatility of the RER increases,
while the importance of demand shocks is reduced. The similar results
for the NITs may be because two of them, Denmark and Singapore,
24
The UK, for example, abandoned the exchange-rate-based nominal stabilization programs, in place since 1987, and left the Exchange Rate Mechanism of
the European Monetary System and established an inflation target of 1%–4% in
1992 (see Levant and Ma (2016)). Another example is Chile that in the second
half of 1999 implemented a number of changes in the macroeconomic policy
framework, including the adoption of a fully-fledged IT regime. In September
1999 it adopted a free-floating exchange rate regime (see Valdés (2007)).
25
The Abrigo and Love (2016) GMM estimates are utilized as input in the
Inoue and Kilian (2013) routine.
26
With only three NIT countries in our sample, however, one should be careful
not to interpret these results as general for NIT countries.
27
Even though there are apparent differences between the two groups of countries, there are also important similarities and one might suspect that the results
could be driven by U.S.-specific factors. If this is the case, the variability of the
variables included in the analysis would be explained by one factor and, given
the results, the loadings would be higher for the IT countries. Estimations of
simple factors models, for the relative as well as individual country variables,
suggest that this is not the case.
3.3. PVAR estimations
8
R. Caputo, M. Pedersen
Economic Modelling xxx (xxxx) xxx
Fig. 3. Rolling Variance Decompositions for IT Countries. Horizon: Four Quarters. Notes: Dotted lines show the contribution to the
variance decomposition of the most likely model for the 15-year period ending the year indicated on the first axis. The solid line is a
fitted trend. CRP: Country Risk Premium.
the CRP shock shifts to the right.28 Hence, also in this case the evidence
suggests that CRP shocks have become more important as an underlying source of RER fluctuations. Comparing the results of Canada and
the UK from the first subsample with those of Clarida and Galí (1994)
and Farrant and Peersman (2006), our evidence suggests that demand
shocks explain less and CRP shocks a greater part of the RER volatility.
Both countries implemented IT in the early 1990s, and we will show
that changes in the monetary policy regime could explain this pattern.
Turning to the developing IT countries (Figs. 8 and 9), the results
for Chile and Israel are similar to those of the developed economies.
In particular, we find for both countries that the relative importance
of demand shocks has declined over time, whereas the importance of
CRP shocks has increased. As mentioned earlier, Chile implemented IT
in 1991 and adopted a regime of freely floating exchange rate in 1999.
In the case of Israel, IT was adopted in 1992 although there was an
exchange rate band in place until mid 2005. The changes in the distributions are also statistically significant for both countries. The evidence
for the Philippines and South Africa is less clear, even though for South
Africa the histogram of the demand shocks does shift slightly to the left,
and for the Philippines there appears to be a movement to the right of
the histogram of the CRP shock. Both of these movements are statistically significant. On the other hand, for South Africa the CRP histogram
also seemed to have moved to the left, while it is not evident that the
explicitly have stated that an objective of the central bank is related
to price stability. Hence, only Hong Kong has a fixed exchange rate
policy with the USD as nominal anchor. The next subsection presents
individual country results.
3.4. The changing nature of RER fluctuations: evidence from individual
countries
In this subsection we assess the impact across time in individual
countries. We perform the same rolling window estimations as in the
previous subsection and report the results for three groups of countries:
Developed ITs, developing ITs, and NITs, with an emphasis on the contributions of demand and CRP shocks to the overall RER volatility.
For most developed IT countries (Australia, Canada, Sweden and the
UK) the message is clear: The contribution of demand shocks to the RER
has declined steadily since 2000 (Fig. 6). In contrast, the contribution
of CRP has increased substantially and, as a consequence, it has become
the main driver of the RER in the latter part of the sample (Fig. 7). The
histograms show a similar pattern: the distribution of demand shock
contributions shifted to the left in the latter sample, whereas the distribution of CRP shocks shifted to the right. For Norway the outcomes
of the most likely models are less clear, but when looking at the histograms of all the admissible models, it appears that the most likely
models are not representative. Also for this country, the distribution of
the contributions of the demand shock shifts to the left, whereas that of
28
According to the Kolmogorov (1933) and Smirnov (1939) test - see e.g.
Conover (1999) for a description - the distributions have in all cases moved
statistically significantly to the left for the demand shocks and to the right for
the CRP shocks.
9
R. Caputo, M. Pedersen
Economic Modelling xxx (xxxx) xxx
Fig. 4. Rolling Variance Decompositions for NIT Countries. Horizon: Four Quarters. Notes: Dotted lines show the contribution to the
variance decomposition of the most likely model for the 15-year period ending the year indicated on the first axis. The solid line is a
fitted trend. CRP: Country Risk Premium.
demand histogram has moved across time. These results may have to do
with the fact that they adopted IT later, in 2002 and 2000, respectively.
Finally, to evaluate the impact of the three countries that have had
a fixed exchange rate policy during the entire period analyzed, Figs. 10
and 11 show the results of the three NITs. For Denmark and Singapore,
the tests suggest that the importance of demand and CRP shocks has
moved in the same directions as in the IT countries. This may be, as
mentioned earlier, because the exchange rate policy in the these countries is implemented with the objective of maintaining prices stable. On
the other hand, for Hong Kong, the only country in the sample with
a fixed exchange rate vis-à-vis the U.S., there is no statistical evidence
of movements in these two distributions. This may be due to a smallsample problem, but the same test indicates that the distribution of the
contributions of supply shocks has moved to the left (are less important), while that of monetary shocks has moved to the right.
Overall, our results show that the relative importance of real and
nominal shocks has changed importantly in IT countries during the last
couple of decades. In particular, during the first 15 years of the sample,
demand shocks accounted for a significant fraction of RER variance,
whereas CRP shocks were, in general, less important. As the estimation window moves forward to include only periods of IT policies, the
results are reversed: demand shocks account for a smaller fraction of
the RER volatility, whereas CRP shocks are the main driver. Similar
results, although seemingly less pronounced compared to the IT countries, were obtained for Denmark and Singapore, while in the currency
board economy, Hong Kong, there appeared to be no change.
As argued in the previous subsection, it does not seem likely that
the results are due to specific factors in the benchmark economy. In
this context, it should also be mentioned that our results are, to some
extent, coherent with Engel and West (2010), who find that for the
U.S. few of the movements in the dollar, during the recent financial
crisis of 2008–2009, were directly attributable to the real interest rate
component, suggesting that most of the movements were due to the
residual risk premium component. The present analysis indicates, however, that the importance of CRP shocks increased before the recent
financial crisis of 2008–2009 and was particularly evident in countries
that followed an IT monetary regime. In addition, given the fact that
the importance of the CRP shock has increased in recent years, and that
the variance decomposition suggests that the importance of this shock
is quite persistent, it could be argued that this is a real shock rather
than a nominal shock. In this context, and in line with Nam and Wang
(2015), one could claim that this is a misspecified news shock or real
shock driving the U.S real exchange rate behavior, which in turn has
an impact on the RER of the countries under analysis. However, since
changes in the RER behavior appear to be more pronounced in IT countries, it seems less likely that common news shock affecting the U.S.
exchange rate is driving our results.
4. Central bank preferences, RER volatility and variance
decomposition
We find that the relative importance of demand and CRP shocks
changed gradually as countries moved towards full-fledged IT regimes.
In this context a relevant question is whether shifts in central bank
objectives, namely an increase in policymakers’ preferences for inflation
stability, can explain the relative contribution of structural shocks to
10
R. Caputo, M. Pedersen
Economic Modelling xxx (xxxx) xxx
Fig. 5. Histograms of Variance Decompositions. Horizon: Four Quarters. Notes: Histograms of contributions to the RER variance decomposition made with the
models that fulfill the imposed sign restriction. The two periods shown are the first and the last in the rolling sample. The vertical lines show the contributions of
most likely models.
Fig. 6. Developed IT countries. Variance Decompositions. Horizon: Four
Quarters. Notes: In the first row, dotted
lines show the contribution to the variance decomposition of the most likely
model for the 15-year period ending
the year indicated on the horizontal
axis. The solid line is a fitted trend.
Histograms of contributions to the RER
variance decomposition, in the second
and third row, are obtained from models that fulfill the imposed sign restrictions. The two periods shown are the
first and the last in the rolling sample.
The vertical lines show the contributions of the most likely models.
the overall RER volatility. In this section we show that central bank
preferences play a crucial role in the way that shocks are transmitted to
the RER. We interpret shifts in central bank preferences as changes in
the monetary policy regime.
Monetary policy objectives and targets are not necessarily constant
over time. Furthermore, there is extensive evidence that central bank
preferences have changed as monetary authorities have moved towards
full-fledged IT regimes. For instance, Clarida et al. (1998) conclude that,
11
R. Caputo, M. Pedersen
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Fig. 7. Developed IT countries. Variance Decompositions. Horizon: Four
Quarters. Note: In the first row, dotted
lines show the contribution to the variance decomposition of the most likely
model for the 15-year period ending
the year indicated on the horizontal
axis. The solid line is a fitted trend.
Histograms of contributions to the RER
variance decomposition, in the second
and third row, are obtained from models that fulfill the imposed sign restrictions. The two periods shown are the
first and the last in the rolling sample.
The vertical lines show the contributions of the most likely models.
Fig. 8. Developing IT countries. Variance Decompositions. Horizon: Four
Quarters. Notes: In the first row, dotted
lines show the contribution to the variance decomposition of the most likely
model for the 15-year period ending
the year indicated on the horizontal
axis. The solid line is a fitted trend.
Histograms of contributions to the RER
variance decomposition, in the second
and third row, are obtained from models that fulfill the imposed sign restrictions. The two periods shown are the
first and the last in the rolling sample.
The vertical lines show the contributions of the most likely models.
from 1979 to 1990, the Bank of England reacted mainly to the German
interest rate (DTD) and to a lesser extent to inflation and output. During this period, the reaction to inflation was quite mild and, because the
UK was part of the Exchange Rate Mechanism of the European Monetary System, there were greater concerns about exchange rate fluctuations. After the introduction of the IT regime in the UK, in October
1992, there has been a substantial increase in central bank preferences
for inflation stability, as shown by Arestis et al. (2016). For Sweden,
Adolfson et al. (2008) find that, after the adoption of IT in 1993, the
policy response to inflation increased, whereas the response to the RER
and output declined. Similar evidence is found for Chile by Caputo et al.
(2007). Findings for the U.S. are similar to those for IT countries. In particular, Clarida et al. (2000), Fernández-Villaverde and Rubio-Ramírez
(2008), Dennis (2006) and Ilbas (2012) show that the Fed, in the post
12
R. Caputo, M. Pedersen
Economic Modelling xxx (xxxx) xxx
Fig. 9. Developing IT countries. Variance Decompositions. Horizon: Four
Quarters. Notes: In the first row, dotted
lines show the contribution to the variance decomposition of the most likely
model for the 15-year period ending
the year indicated on the horizontal
axis. The solid line is a fitted trend.
Histograms of contributions to the RER
variance decomposition, in the second
and third row, are obtained from models that fulfill the imposed sign restrictions. The two periods shown are the
first and the last in the rolling sample.
The vertical lines show the contributions of the most likely models.
Fig. 10. NIT countries. Variance
Decompositions. Horizon: Four Quarters. Notes: In the first row, dotted lines
show the contribution to the variance
decomposition of the most likely model
for the 15-year period ending the year
indicated on the horizontal axis. The
solid line is a fitted trend. Histograms
of contributions to the RER variance
decomposition, in the second and third
row, made with the models that fulfill
the imposed sign restriction. The two
periods shown are the first and the last
in the rolling sample. The vertical line
shows the contributions of most likely
models.
Volcker era, has assigned more importance to inflation and interest rate
volatility.29
Our conjecture is that, during the inflation targeting period, the relevance of the exchange rate in the central bank loss function has declined
importantly. There is evidence that, indeed, in inflation targeting countries this is the case. Based on panel data techniques, Aizenman et al.
(2011) investigate IT in emerging markets, focusing on the role of the
real exchange rate in the Taylor rule. The main findings of this contribution is that IT emerging markets appear to follow a strategy that puts
substantially more weight on inflation and much less on real exchange
rate fluctuations once countries adopt an IT regime. To be more specific,
once countries move from a NIT regime to an IT one, the response to
inflation increases by a factor of two, whereas the response to exchange
29
Uribe and Yue (2006) and Caputo and Herrera (2017) assess the importance, in different contexts, of the foreign rates (or the Fed funds rate) for
emerging economies.
13
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Fig. 11. NIT countries. Variance
Decompositions. Horizon: Four Quarters. Notes: In the first row, dotted lines
show the contribution to the variance
decomposition of the most likely model
for the 15-year period ending the year
indicated on the horizontal axis. The
solid line is a fitted trend. Histograms
of contributions to the RER variance
decomposition, in the second and third
row, are obtained from models that fulfill the imposed sign restrictions. The
two periods shown are the first and the
last in the rolling sample. The vertical lines show the contributions of the
most likely models.
Table 3
Policy preferences and sources of RER volatility.
Configuration
A
B
C
D
E
F
G
Variance Decomposition Δ q
Preferences
𝜇r
𝜇𝜋
𝜇y
𝜇e
𝜀q
𝜀d
𝜀d ∕𝜀q
0.000
0.517
0.517
6.067
10.660
23.727
40.442
1.000
1.000
1.000
1.205
1.182
1.342
1.352
0.000
0.404
0.404
0.404
0.404
0.404
0.404
1.000
0.700
0.500
0.000
0.000
0.000
0.000
1.6%
7.6%
8.4%
15.0%
17.0%
18.6%
20.0%
40.8%
42.0%
43.4%
40.0%
38.0%
35.9%
35.0%
24.8
5.5
5.2
2.7
2.2
1.9
1.8
once countries implemented IT. In this context, Gomez et al. (2019) find
support for the type of policies that these central banks implemented
de jure.
Given the evidence from these studies it appears that the preferences
of several of the central banks in our sample did actually change with
the adoption of IT. In particular, the exchange rate was given less, or
zero, weight in the loss function once the new regime was implemented.
To understand how changes in central bank preferences affect the
relative contribution of shocks to the RER variance, we simulate the
DSGE model presented in Section 2 under alternative policy preferences.30 In particular, we assess the consequences of increasing, gradually, the central bank’s preference for inflation stabilization and reducing the importance it gives to exchange rate fluctuations.
In the first scenario, configuration A in Table 3, the central bank
cares only about stabilizing inflation and the nominal exchange rate:
𝜇 𝜋 = 𝜇 e = 1 and 𝜇y = 𝜇r = 0. In this case, demand shocks contribute
41% of RER volatility whereas CRP shocks contribute only 2%. Hence,
in this configuration, the relative contribution of demand to CRP shocks
is 24.8. If the central bank moves towards a more flexible exchange rate
regime (configurations B and C), the contribution of demand shocks
declines importantly. In particular, if preferences for exchange rate sta-
rate declines by 50%. As a result, the ratio between the inflation and
exchange rate response increases by a factor of four.
In terms of the welfare loss weights, Kam et al. (2009) provide
robust evidence for three developed countries, which is coherent with
the evidence discussed previously, on the importance of inflation objectives vis-à-vis exchange rate stabilization or other concerns. In particular, Kam et al. (2009) estimate underlying structural macroeconomic
policy objectives for Australia, Canada and New Zealand from 1990 to
2005, concluding that none of the central banks shows a concern for
stabilizing the real exchange rate. All three central banks share a concern for minimizing the volatility of the change in the nominal interest
rate.
For developing countries under IT, Gomez et al. (2019) find similar
results: Inflation stabilization in these countries has a higher priority
than other objectives such as interest smoothing, GDP and exchange
rate stabilization. In particular, they find significant evidence against
a systematic objective to stabilize the exchange rate when the central
banks set the interest rate. This is true when Gomez et al. (2019) consider the period of explicit IT in Chile, Colombia, Brazil and Peru. This is
perhaps not surprising since many developing countries used the nominal exchange rate as a nominal anchor during the inflation stabilization
periods. Examples from Latin America are Mexico, Peru, Chile, Brazil,
and Argentina that used fixed or managed exchange rate regimes in the
1980s and 1990s. In general, exchange rate targeting was abandoned
30
We modify only the central bank preferences in equation (2.4). The other
coefficients in the model are maintained.
14
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Table 4
Policy preferences and macroeconomic volatility.
Configuration
A
B
C
D
E
F
G
Preferences
Macro Volatility (%)
𝜇r
𝜇𝜋
𝜇y
𝜇e
𝜎𝜋2̃
𝜎Δ2 q
𝜎Δ2 y
𝜎Δ2 r
0.000
0.517
0.517
6.067
10.660
23.727
40.442
1.000
1.000
1.000
1.205
1.182
1.342
1.352
0.000
0.404
0.404
0.404
0.404
0.404
0.404
1.000
0.700
0.500
0.000
0.000
0.000
0.000
8.12
7.64
6.93
1.31
1.63
2.04
2.46
2.47
3.37
4.00
27.21
25.38
24.22
23.23
1.32
1.27
1.25
1.15
1.18
1.20
1.21
1.14
0.35
0.33
0.14
0.09
0.05
0.03
Fig. 12. Volatility of inflation, output growth, interest rate, and RER depreciation: 1986–2010 (in %).
bility decline to 𝜇 e = 0.7 and 𝜇 e = 0.5 and the importance given to
output and the interest rate increases to 𝜇y = 0.404 and 𝜇r = 0.517,
respectively, then the relative contribution of demand to CRP shocks
declines to 5.5 and 5.2.
Clearly, as the central bank moves towards a more flexible exchange
rate regime (from configuration A to C), the importance of CRP shocks
increases. The contribution of a CRP shock is, however, still below what
we find empirically for the latter period and, to investigate possible
explanations, we consider four additional policy configurations where
the central bank is embracing a fully flexible exchange rate regime,
𝜇e = 0, while 𝜇 𝜋 and 𝜇 r are calibrated to match specific values for
the contribution of CRP and demand shocks (configurations D to G). In
order to increase the contribution of CRP to 15% and reduce the contribution of demand shocks to 40%, the central bank should become more
hawkish, increasing preferences for inflation stabilization to 𝜇 𝜋 = 1.205
and for interest rate stabilization to 𝜇r = 6.057. If the contribution of
CRP shocks is increased further, up to 20%, and the contribution of
demand shocks is reduced, down to 35%, the central bank should further increase preferences for inflation and interest rate stabilization to
𝜇 𝜋 = 1.352 and 𝜇 r = 40.442. In this last configuration the relative contribution of demand to CRP shocks is 1.8.
From these exercises we draw two important conclusions. First, the
relative importance of demand and CRP shocks depends, crucially, on
the preferences of the central bank. Second, as the central bank moves
towards a flexible exchange rate regime, in which the main objectives are inflation and interest rate stability, the importance of demand
shocks, relative to CRP innovations, declines importantly. Our results
suggest that the gradual adoption of full-fledged IT regimes, in which
the importance of exchange rate fluctuations is reduced, can explain
the changing nature of RER fluctuations we observe. To lend additional
support to our exercises, we need to check if the gradual convergence
towards IT in the model is able to match additional features of the data.
15
R. Caputo, M. Pedersen
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Fig. 13. Accumulated IRF under Exchange Rate Targeting (red) and IT (blue) (quarters after the shock). (For interpretation of the references to colour in this figure
legend, the reader is referred to the Web version of this article.)
As shown in Table 4, the volatility of inflation, interest rate and output declines as the central bank moves from managed exchange rate
regimes (configurations A to C) to fully flexible exchange rate regimes
(configurations D to G). As expected, the volatility of the RER increases
substantially between regimes. These results are in line with the empirical evidence for countries that have moved towards full-fledged IT
regimes over time, as shown in Fig. 12, where stochastic volatility models (Chan and Hsiao (2014)), are employed for estimations.31
shock, so the exchange rate, output and inflation are fully stabilized.
For demand shocks, the results are completely different under
exchange rate targeting. In particular, if the central bank cares about
the nominal exchange rate, the policy rate does not increase significantly, so inflation and output absorb an important part of this shock.
Even if the nominal rate does not react significantly, the RER will appreciate as a consequence of increasing inflation (Fig. 13, second row).
Similarly, in the case of a supply shock the inflation rate declines significantly, inducing a RER appreciation.
Under configuration A, the impact of nominal shocks on the RER
is almost fully offset by an aggressive policy response. For nominal
shocks the policy trade-off between stabilizing RER, output and inflation is almost absent as long as the policy rate can react. Real shocks, on
the other hand, are absorbed by output, inflation and the RER (mainly
through changes in prices). As a consequence, under configuration A,
the contribution of nominal shocks to the RER is almost completely
muted given the fact that the policy rate can be adjusted. At the same
time real shocks are the main drivers of RER dynamics.
In the case of an inflation targeting regime, with fully floating
exchange rate and concerns about inflation and interest rate stabilization (configuration G), the relative importance of nominal shocks
increases substantially. In particular, in the face of a CRP shock, the policy rate does not move significantly and the RER absorbs an important
proportion of the CRP shock. In the case of demand shocks, the policy
rate increases so as to stabilize inflation generating also a decline in
the nominal exchange rate. Consequently, the RER absorbs part of the
4.1. Responses to demand and CRP shocks under alternative preferences
To understand the mechanism behind the declining importance of
demand shocks and the increasing relevance of CRP innovations, we
compare the dynamic response of the main macro variables under
exchange rate targeting (configuration A) and inflation targeting (configuration G). As shown in Fig. 13, under exchange rate targeting, the
impact of CRP shocks on the RER is almost fully offset by an aggressive
increase in the policy rate. The impact of this shock on output growth
is also offset to a great extent.32 In the case of a monetary shock, the
aggressive increase in the policy rate fully offsets the impact of this
31 The decline in inflation and output growth volatility has been documented
for the U.S., by Galí and Gambetti (2009) and Canova and Gambetti (2010),
and has been referred to as the Great Moderation episode.
32
There is still a small RER appreciation, which given the nature of the model
has an expansive impact on output. The increase in the policy rate, however,
determines minor contractions in output and inflation.
16
R. Caputo, M. Pedersen
Economic Modelling xxx (xxxx) xxx
shock through the nominal appreciation and increase in prices.
Under a flexible exchange rate regime (configuration G), the RER
is much more volatile for any given shock. When compared to configuration A, however, the increase in volatility due to nominal shocks
is substantially larger. The reason is that the policy rate cannot move
freely, so both the nominal and the real exchange rates absorb an important proportion of monetary policy and CRP shocks. Hence, the relative
contribution of CRP and demand shocks crucially depends on the preferences of the central bank.
shocks tended to explain a relatively small proportion of RER volatility in most IT countries. In that period, nominal shocks were relatively
more important in explaining RER fluctuations. When we perform a
sub-sample analysis, however, we can practically reconcile the empirical findings in the literature with our results for the early subsamples. We conclude that the relative importance of demand shocks has
declined importantly over time. In contrast, the relative importance of
nominal shocks and, in particular of CRP shocks, has increased in recent
years.
We show that our empirical results could be explained by gradual
shifts in monetary policy regimes towards full-fledged IT regimes. In
particular, if exchange rate targets are abandoned, and inflation and
policy rate stability become the main concerns of the central bank, the
policy rate will not offset the impact that nominal shocks have on the
RER. Accordingly, nominal shocks, and in particular CRP shocks, will
have a greater impact on the RER. Overall, we conclude that central
bank preferences play a crucial role in the way that shocks are transmitted to the RER.
In a world with reduced inflation rates, the variation in the nominal exchange rate dominates in the RER volatility. In this context, one
might argue that a low U.S. inflation rate has contributed to the decline
in the rates in other countries. In this sense, the U.S. may be the driving
force behind the results presented in this study. However, existing evidence suggests that falling inflation rates, inflation volatilities and the
sacrifice ratios in IT countries are due to the adoption of IT. One of the
first scholars to notice this was Rogoff (2003) and subsequent research
tends to confirm his claim (see Gonçalves and Salles (2008), Svensson
(2010) and, more recently, Huang et al. (2019)). In this setting, the
results obtained in the present paper are in line with previous evidence
on the reasons for lower inflation rates in IT countries. In this environment, the role of financial integration is certainly an issue that deserves
more analysis. This is, however, beyond the scope of the present paper
and is left to future research.
5. Conclusions
Understanding the sources of real exchange rate (RER) variability
is one of the challenging issues in international economics. Based on
earlier empirical evidence, there is general consensus that real shocks
(i.e. demand and supply shocks) play the most important role in determining RER fluctuations. On the contrary, nominal shocks (monetary
policy and country risk premium (CRP) shocks) contribute very little
to the RER dynamics. In this context, the objective of this paper is
twofold. First, we examine a dynamic stochastic general equilibrium
(DSGE) model in order to understand how different shocks affect the
RER dynamics in a small open economy. Second, we estimate structural
vector autoregressive (SVAR) models for several inflation targeting (IT)
and non inflation targeting (NIT) countries using the sign restriction
approach suggested by Inoue and Kilian (2013). These restrictions are
derived from the open economy DSGE model of Kam et al. (2009). Estimations of the SVAR models are performed for different sub-samples in
order to detect changes in the relative importance of the contributions
of real and nominal shocks to the RER dynamics. The sample employed
is large enough to take into account possible changes of the monetary
policy objectives. We perform the empirical exercise for the set of IT
and NIT countries from 1986 to 2014.
Our main findings are as follows. In sharp contrast with previous
empirical evidence, we find that for the period 1986–2014, demand
Appendix A. The DSGE model
Households
Our model is based on Kam et al. (2009). Households have a period utility function of the form:
1+𝜙
U (Ct , Ht , Nt ) =
N
(Ct − Ht )1−𝜎
− t ,
1−𝜎
1+𝜙
(5.1)
where Ct represents the consumption basket, Ht = hCt −1 is an external habit stock with h between 0 and 1 and Nt is labor hours. Househols
maximize the utility function U(.) subject to the sequential budget constraint:
Bt ≥ PH,t CH,t + PF ,t CF ,t +
Bt +1
− Wt Nt ,
Rt
(5.2)
where Bt is an Arrow security that pays out contingent on the state of the economy, Rt is the gross return on a nominal riskless one-period bond,
and Wt Nt is the total wage income. The expenditure in home goods is given by PH,t CH,t , whereas the expenditure in foreign consumption goods is
given by PF,t CF,t .
The consumption index, Ct , is linked to domestic, CH,t , and foreign goods, CF,t , such that:
[
1
𝜂−1
𝜂
1
𝜂−1
𝜂
] 𝜂−1
Ct = (1 − 𝛼) CH,t + 𝛼 CF ,t
𝜂
𝜂
𝜂
,
(5.3)
where the elasticity of substitution between home and foreign goods is given by 𝜂 > 0. It can be shown that the optimal allocation of expenditures
across each good type gives rise to the demand functions:
(
)−𝜂
P
Ct ,
(5.4)
CH,t = (1 − 𝛼) H,t
Pt
(
CF ,t = 𝛼
)
PF ,t −𝜂
Ct .
Pt
(5.5)
Substitution of these demand functions into (5.3) yield the consumer price index as:
[
] 1
1−𝜂
1−𝜂 1−𝜂
Pt = (1 − 𝛼)PH,t + 𝛼 PF ,t
.
(5.6)
17
R. Caputo, M. Pedersen
Economic Modelling xxx (xxxx) xxx
The intertemporal optimality condition for the households yields the familiar stochastic Euler equation:
(
)−𝜎 (
)
Ct +1 − Ht +1
Pt
𝛽 Rt Et
= 1.
Ct − Ht
P t +1
(5.7)
Log-linearizing this expression gives rise to the standard stochastic linear Euler expression, which is equation (2.1) in the main text.
International risk sharing and the uncovered interest rate parity conditions
Prices in the rest of the world are given by:
1
[
(
)1−𝜂
(
)1−𝜂 ] 1−𝜂
+ 𝛼 ∗ P∗F ,t
,
P∗t = (1 − 𝛼 ∗ ) P∗H,t
(5.8)
where ∗ denotes foreign variables. Because the domestic economy is a small one, for the rest of the world 𝛼 ∗ is equal to zero. As a consequence,
international prices are given by:
P∗t = P∗H,t .
(5.9)
For the rest of the world, the first-order condition for optimal consumption, i.e. the Euler equation, is analogous to the one derived for the
domestic economy. In short, given complete international markets, we obtain the perfect risk sharing condition:
(
)−𝜎 (
)(
(
)−𝜎 (
)
)
Ct∗+1 − Ht +1
P∗t
C
− Ht+1
ERt
Pt
𝛽 t +1
= Qt,t+1 = 𝛽
,
(5.10)
∗
∗
Ct − Ht
P t +1
ERt +1
Ct − Ht
P t +1
where Qt ,t +1 =
1
Rt
is the discount factor, which is inversely related to the gross return on a nominal riskless one-period bond. The expression in (5.10)
holds for all dates and states, where ERt represents the nominal exchange rate. From (5.10) it is possible to derive the non-arbitrage conditions for
the exchange rates, or the uncovered interest rate parity condition in levels:
Rt − R∗t
ERt
= 0.
ERt +1
(5.11)
Log-linearizing (5.11) we obtain the UIP condition:
Et (et +1 ) − et = rt − rt∗ ,
(5.12)
where et = ln(ERt ∕ERss ), the percentage deviation of the nominal exchange rate from its steady-state (ss) value, and the domestic and foreign rates
of net return are rt = Rt − 1 and rt∗ = R∗t − 1. The expression in (5.12) gives rise to the stochastic UIP condition, equation (2.5) in the main text.
Domestic firms optimal pricing
Domestic goods firms operate a linear production technology. These firms face an independent signal that allows them to set prices optimally
each period with probability 1 − 𝜃 H . In each period t, the remaining fraction 𝜃 H ∈ (0, 1) of firms partially index their prices to take into account
past aggregate inflation. Given the Calvo price setting, it is possible to define the aggregate price level of domestic goods:
1
1−𝜖
(
⎧
(
) )1−𝜖 ⎫
(
)1−𝜖
PH,t −1 𝛿H
⎪
⎪
new
PH,t = ⎨(1 − 𝜃H ) PH,t
+ 𝜃H PH,t−1
⎬ ,
PH,t −2
⎪
⎪
⎩
⎭
(5.13)
is the optimal price set by firms that are able to optimally set prices, 𝛿 H ∈ (0, 1) measures the degree of inflation indexation, and 𝜖
where Pnew
H ,t
represents the elasticity of substitution between home differentiated goods. Consider a firm i that has set its price optimally in time t as PH,t (i). The
firm faces the following demand for its product:
[
(
) ]−𝜖
P(i)H,t PH,t +s−1 𝛿H
Y (i)H,t +s =
(CH,t+s + CH∗ ,t+s ),
(5.14)
PH,t +s
PH,t −1
The first-order necessary condition characterizing domestic firms’ optimal pricing function in a symmetric equilibrium is:
(
)
(
)
∞ s
∑
𝜃H Y (i)H,t+s
PH,t +s−1 𝛿H
̃
Et
PH,t
− 𝜁 P(i)H,t+s MCH,t+s = 0,
Rt +s−1
PH,t −1
s=0
(5.15)
PH,t is the price set (optimally) today by firms, which has a probability 𝜃 H of remaining fixed in the next period. The variable MCH,t +s is the
where ̃
marginal cost of producing one unit of domestic goods. Let the home goods inflation rate be 𝜋 H,t = ln(Ph,t ∕PH,t −1 ). Then log-linearizing (5.15) it is
possible to get a New Keynesian Phillips curve for home goods, which is given by:
𝜋H,t
= 𝛽 Et (𝜋H,t+1 − 𝛿H 𝜋H,t ) + 𝛿H 𝜋H,t−1 + 𝜆H (mct + (1 + 𝜙)𝜖s,t ),
(5.16)
𝜎
The above Phillips curve corresponds to equation (2.2) in the main text, where 𝜆H = (1 − 𝛽𝜃H )(1 − 𝜃H )𝜃H−1 and mct = 𝜙yt + 𝛼 st + 1−
(c − hct−1 ).
h t
Import firms optimal pricing
Import retailers are assumed to purchase imported goods at competitive world prices. These firms, however, act as monopolistically competitive
redistributors of these goods creating a gap between the price of imported goods in domestic currency, et + p∗t , and the domestic retail price of
imported goods, pF,t . This gap is reflected in the variable 𝜓 F,t as follows:
𝜓F ,t = et + p∗t − pF ,t .
(5.17)
18
R. Caputo, M. Pedersen
Economic Modelling xxx (xxxx) xxx
Import firms face an independent signal that allows them to set prices optimally each period with probability 1 − 𝜃 F . In each period t, the remaining
fraction 𝜃 F ∈ (0, 1) of firms partially index their prices to take into account past aggregate inflation. Given the Calvo price setting, it is possible to
define the aggregate price level of foreign goods:
1
1−𝜖
(
⎧
(
) )1−𝜖 ⎫
(
)1−𝜖
PF ,t −1 𝛿F
⎪
⎪
P
+
𝜃
PF ,t = ⎨(1 − 𝜃F ) Pnew
⎬ ,
F
F ,t −1
F ,t
PF ,t −2
⎪
⎪
⎩
⎭
(5.18)
where Pnew
is the optimal price set by firms who are able to optimally set prices, 𝛿 F ∈ (0, 1) measures the degree of inflation indexation, and 𝜖
F ,t
represents the elasticity of substitution between home differentiated goods. Consider a firm j that has set its price optimally at time t as PF,t (i). Then
the firm faces the following demand for its product:
[
(
) ]−𝜖
PF ,t (j) PF ,t +s−1 𝛿F
CF ,t +s .
(5.19)
Y (j)F ,t +s =
PF ,t +s
PF ,t −1
The first-order necessary condition characterizing domestic firms’ optimal pricing function in a symmetric equilibrium is:
[
]
(
)
∞ s
∑
𝜃F Y (j)F ,t+s
PF ,t +s−1 𝛿F
∗
̃
Et
PF ,t
− 𝜁 ERt+s Pt+s = 0,
Rt +s−1
PF ,t −1
s=0
(5.20)
PF ,t is the price set (optimally) today by firms that have a probability 𝜃 F of remaining fixed in the next period. The variable ERt +s P∗t +s is the
where ̃
cost, in domestic currency, of importing one unit of the foreign good. If equation (5.20) is log-linearized around the non-stochastic steady-state we
get:
𝜋F ,t = 𝛽 Et (𝜋F ,t+1 − 𝛿F 𝜋F ,t ) + 𝛿F 𝜋F ,t−1 + 𝜆F (𝜓F ).
(5.21)
The above expression is the New Keynesian Phillips curve for imported goods, which corresponds to equation (2.3) in the main text.
Aggregate output
In log-linear terms, aggregated output is the sum of domestic goods consumed by nationals and domestic goods consumed by foreigners:
yt = cH,t + c∗H,t .
(5.22)
From equations (5.4) and (5.5) we obtain the log-linear expressions for home, CH,t , and foreign, CF,t , consumption of domestic goods as cH,t =
[ (
)
]
(1 − 𝛼)[𝛼𝜂 st + ct ] and c∗H,t = 𝛼 𝜂 st + 𝜓F ,t + yt∗ , respectively. Using the previous expressions and the definition of 𝜓 F,t , we can express yt as:
yt = (1 − 𝛼)ct + 𝛼 yF∗,t + 𝛼𝜂 qt + 𝛼𝜂 st ,
(5.23)
which is equation (2.10) in the main text.
Appendix B. Econometric details
The VAR models are estimated with a Bayesian method where the prior and posterior distributions belong to the normal-inverse Wishart
distributions.33 Hence, the prior distribution for the parameters of (3.1) is
vec(𝛽) ∣ Ω ∼ N (vec(𝛽 0 ), Ω ⊗ K0−1 ), Ω ∼ IWn (v0 S0 , v0 ),
where K0 is a positive definite matrix, S0 a covariance matrix, and v0 > 0. The posterior is
vec(𝛽) ∣ Ω ∼ N (vec(𝛽 T ), Ω ⊗ KT−1 ), Ω ∼ IWn (vT ST , vT ),
where 𝛽 T = NT−1 (N0 𝛽 0 + X ′ X 𝛽̂ols ), NT = N0 + X′ X, vT = T + v0 , ST =
(5.24)
v0
vT
S0 +
T
vT
̂+
Ω
1
vT
̂ ols are the
(𝛽̂ols − 𝛽 0 )′ N0 N0−1 X ′ X (𝛽̂ols − 𝛽 0 ), and 𝛽̂ols and Ω
ordinary least squares (OLS) estimates of (3.1).
To obtain the random draws needed for the estimation, the covariance matrix is decomposed as Ω = AUU′ A′ , where A is the lower triangular
Cholesky decomposition of Ω and U is an orthogonal matrix such that UU′ = I. As mentioned earlier, we follow the approach of Inoue and Kilian
(2013) for a fully identified model such that U is obtained as in Uhlig (2005), i.e. the prior distribution is a uniform distribution, which is defined
̃ denotes the structural impulse-responses, Inoue and Kilian (2013) show that the posterior density of
on the space of orthonormal matrices U. If Θ
̃ is
Θ
(
)
|
| −1 | 𝜕Ω |
̃
𝜕 vec(Θ)
|
|
̃
|
|
f (Θ) ∝ |
(5.25)
|
| 𝜕 A | f (𝛽 |𝛺)f (𝛺),
| 𝜕[vec(𝛽)′ vech(A)′ veck(U )′ ] |
|
|
|
|
where vech(A) is the vector that contains the elements of A that are on and below the diagonal, while veck(U) includes the elements of U that are
above the diagonal.
The following process is applied to obtain the results: (1) Take 20,000 random draws from (5.24). (2) For each (𝛽, Ω) take 5,000 random draws
̃ and
̃ for each (𝛽, Ω, U). (4) Keep the Θ
̃ s that satisfy the sign restrictions and delete the rest. (5) Calculate f (Θ)
of the rotation U. (3) Compute Θ
̃ f (Θ)}
̃ in descending order by the value of f (Θ)
̃ . The so-called most likely model is the one with maximum value of the posterior
sort the pairs {Θ,
density (5.25).
33
See for example Gelman et al. (2014).
19
R. Caputo, M. Pedersen
Economic Modelling xxx (xxxx) xxx
Appendix C. Data description
The IFS codes of the series applied are as follows: NGDP_R for the real gross domestic product (index, 2010 = 100), PCPI for the all items in the
consumer price index (index, 2010 = 100), FILR for the lending interest rates (percent per annum), and ENDA for the exchange rates measured as
units of national currency per US dollar, period average. Where the series were not available, the following were utilized: Chilean consumer prices
are extended backwards from 2008Q4 with the annual changes of all CPI items, capital city (IFS: PCPI_A1). From 2003 onwards the Danish interest
rate is the weighted average of all lending rates supplied by the Danmarks Nationalbank. The Norwegian interest rate is the rate of bank loans,
which was extracted from Bloomberg. For the United Kingdom the price index utilized is the retail price index (IFS: CPRPTT01). From 1994Q2
the series of the Swedish interest rate is extended with quarterly changes of the lending rate extracted from the Riksbank. Real GDP data and
price indices are seasonally adjusted. When data from the original source were not adjusted, this was done with the X-13 ARIMA routine. The real
exchange rate is calculated with the nominal rate and the price indices, while the real interest rate is calculated ex-post, i.e. assuming simply that
the expected annual inflation is the current rate.
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