Economics Letters 123 (2014) 160–163

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Real exchange rate dynamics in sticky wage models✩ Mario J. Crucini a,b,∗ , Mototsugu Shintani a , Takayuki Tsuruga c a

Department of Economics, Vanderbilt University, Nashville, TN 37235-1819, USA

b

NBER, USA Graduate School of Economics, Kyoto University, Japan

c

highlights • • • • •

Real exchange rates often exhibit hump-shaped responses to macroeconomic shocks. Sticky wages and prices are contrasted in a New Open Economy Macroeconomics framework. Shocks to an interest rate rule, TFP and government spending are considered. Only fiscal policy generates a hump-shaped response in the sticky wage framework. Consideration of sticky wages is therefore important in the open economy setting.

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Article history: Received 20 December 2013 Received in revised form 28 January 2014 Accepted 2 February 2014 Available online 14 February 2014

abstract We investigate the role of sticky wages in accounting for real exchange rate dynamics. Unlike the sticky price economy, government spending shocks play a more important role than technology shocks in explaining the hump-shaped impulse responses of real exchange rates. © 2014 Elsevier B.V. All rights reserved.

JEL classification: E31 F31 Keywords: PPP puzzle Real exchange rate persistence Sticky prices

1. Introduction To explain the dynamics of real exchange rates, it is common to use open economy macroeconomic models that feature sticky goods prices and flexible wages. For example, Chari et al. (2002) show that a standard sticky price model can go a long way to help bring the predicted volatility and persistence of the aggregate real exchange rate into agreement with what is observed in the data

✩ Crucini and Shintani gratefully acknowledge the financial support of NSF (SES1030164). Tsuruga gratefully acknowledges the financial support of Grant-in-aid for Scientific Research. ∗ Correspondence to: Department of Economics, Box 351819-B, Vanderbilt University, Nashville, TN 37235-1819, USA. Tel.: +1 615 322 7357; fax: +1 615 343 8495. E-mail addresses: [email protected] (M.J. Crucini), [email protected] (M. Shintani), [email protected] (T. Tsuruga).

http://dx.doi.org/10.1016/j.econlet.2014.02.003 0165-1765/© 2014 Elsevier B.V. All rights reserved.

when the frequency of price changes is about once a year. Many authors have emphasized the role of monetary shocks when attempting to explain the high persistence and volatility of real exchange rates.1 A notable exception is Steinsson (2008), who claims that it is not monetary shocks, but real shocks, such as technology and government spending shocks, that are key, particularly for their ability to generate a hump-shaped impulse response of the real exchange rate. In this note, we turn the standard international finance model on its head, assuming that wages are sticky and prices are flexible. In closed-economy models, it is widely known that inflation persistence can be explained either by sticky prices or by sticky wages.2 Chari et al. (2002) thus point out that the sticky wages are

1 Examples include Bergin and Feenstra (2001), Benigno (2004), Bouakez (2005), and Johri and Lahiri (2008). 2 See Christiano et al. (2005) and Galí (2008) among others.

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a promising avenue to increase the persistence of real exchange rates by monetary shocks. We examine the shape of impulse responses of real exchange rates in a sticky wage model and show that the relative role of the two types of real shocks emphasized by Steinsson (2008), technology and government spending shocks, is starkly different than in a model with sticky prices. In particular, the two shocks play equivalent roles in the sticky price model while government spending shocks are the main driver of real exchange rate persistence and the only one that generates a hump-shaped real exchange rate impulse response when prices are flexible and wages are sticky.3 2. The model The model we consider here is a simple two-country monetary model with nominal rigidities based on local currency pricing. The model shares a variety of features that characterize the New Open Economy Macroeconomics paradigm. Here we extend the symmetric two-country model of Steinsson (2008) who assumes Calvo (1983)-type nominal price rigidities. In particular, we consider the interaction of wage stickiness and government spending shocks in Steinsson’s model with the goal of clarifying the roles of price and wage stickiness in real exchange rate determination. The model has a rich stochastic structure with three types of exogenous shocks driving the real exchange rate: shocks to nominal interest rates, technological innovations and government spending shocks. In what follows, we describe the key linearized equations of the model and leave the details to the technical appendix. Aggregate consumption of the representative agent in each country follows the standard consumption Euler equation: ct = Et ct +1 − σ (it − Et πt +1 ) , ∗

ct =

Et ct∗+1

− σ it − ∗

Et πt∗+1



(1)

,

(2)

where ct , it , and πt denote consumption, the nominal interest rate, and inflation in the home country, respectively (in terms of logdeviations from the steady state). Et is the expectation operator. Note that inflation is measured by the change in the logarithm of the CPI. The parameter σ is the degree of constant relative risk aversion. Foreign variables are indicated with an asterisk. The optimal risk-sharing condition is ct − ct∗ = σ qt ,

(3)

where qt is the real exchange rate. The home and foreign nominal interest rate processes are determined by a Taylor rule featuring interest rate smoothing: it = ρi it −1 + (1 − ρi ) αc ct + (1 − ρi ) απ πt + umt , ∗

it =

ρi i∗t −1

+ (1 − ρi ) αc ct + (1 − ρi ) απ πt + umt , ∗

∗

∗

(4) (5)

where ρi is the parameter controlling the extent of interest rate smoothing and umt is the monetary shock. The parameters ρi , αc and απ are chosen by the central bank. The home and foreign New Keynesian Phillips Curves (NKPC) are

  πt = β Et πt +1 + κ φH mc t + φF mc ∗t + κφF qt ,   πt∗ = β Et πt∗+1 + κ φH mc ∗t + φF mc t − κφF qt ,

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where β ∈ (0, 1) is the discount factor and κ > 0 is a function of the degree of price stickiness and the discount factor. If prices are completely fixed (or flexible), κ = 0 (or κ = ∞). Here, φH (φF ) is the steady state consumption expenditure share of domestic (imported) goods (i.e., φH + φF = 1). Firms’ real marginal cost is denoted by mc t . We assume that each country’s production technology is linear in labor and therefore real marginal cost simplifies to: mc t = wt − at and mc ∗t = wt∗ − a∗t , where wt is the real wage rate and at is the level of technology. We introduce nominal wage stickiness as in Erceg et al. (2000). Based on their assumptions, the home (πtw ) and foreign wage inflation (πtw∗ ) evolve as

πtw = β Et πtw+1 + χ (mrst − wt ) ,  ∗  ∗ πtw∗ = β Et πtw∗ +1 + χ mrst − wt ,

(8) (9)

where mrst denotes the economy’s average marginal rate of substitution between labor and consumption. The coefficient χ > 0 is a composite parameter which depends upon the degree of wage stickiness, the discount factor, the labor demand elasticity, and the elasticity of marginal disutility for labor. Analogous to the role of κ in the NKPC, χ = 0 (or χ = ∞) when wages are assumed to be completely fixed (or perfectly flexible). The expressions in parentheses are the deviations of real wages from the marginal rate of substitution between consumption and labor resulting from wage rigidities. The marginal rates of substitution can be expressed as mrst = σ −1 ct + ψ[φH (ct + gt − θ pH ,t ) + φF (ct∗ + gt∗ − θ p∗H ,t ) − at ],

(10)

mrs∗t = σ −1 ct∗ + ψ[φH (ct∗ + gt∗ − θ p∗F ,t ) + φF (ct + gt − θ pF ,t ) − a∗t ],

(11)

where gt denotes government spending in the home country and pH ,t (or pF ,t ) is the relative price of domestic (or imported) goods to the domestic CPI. The parameter ψ is the elasticity of marginal disutility of labor and θ is the elasticity of substitution between domestic and imported goods. In (10), the first term (σ −1 ct ) on the right-hand side represents the marginal utility of consumption and the second term arises from the economy’s average marginal disutility of labor. The home labor supply is proportional to total demand for domestic goods which is the weighted average of home and foreign demands. The domestic (foreign) CPI inflation can be written as the weighted average of inflation rates of domestic and imported goods: πt = φH πH ,t + φF πF ,t (πt∗ = φH πF∗,t + φF πH∗,t ) where πH ,t (πF ,t ) is the inflation rate of domestic (imported) goods. Real wage changes and relative price changes follow wt − wt −1 = πtw − πt , and pj,t − pj,t −1 = πj,t − πt for j = H , F , and, along with their foreign analogs, constitute six identities in total. We assume that all exogenous variables (i.e., umt , u∗mt , at , a∗t , gt , and gt∗ ) follow AR(1) processes.

(6)

3. Comparing the sticky price and sticky wage models

(7)

The aim of our exercise is to compare and contrast the implications of sticky prices and sticky wages for real exchange rate dynamics. Toward this end, we focus on only one of the two nominal rigidities in the model at a time and refer to these cases as the sticky price (SP) economy and the sticky wage (SW) economy. To emulate the SP economy, we set κ = 0.086 and χ = ∞. We set this value of κ such that nominal prices are reoptimized every four quarters on average, when combined with the parameterization of β = 0.99. For the SW economy, we set κ = ∞ and χ = 0.0028. We set the value χ to emulate an average duration of wage contracts of four quarters, consistent with estimates in the range of 3.8–4.7 quarters

3 Our focus differs from some previous studies that introduce sticky wages and/or government spending shocks into open economy models with nominal price rigidities. For instance, Søndergaard (2004) investigates real exchange rate dynamics in the sticky price model armed with sticky wages and variable capital utilization. In his model, real shocks are represented by only technology shocks. Campolmi (2014) studies the optimal monetary policy under sticky prices and wages in a small open economy model. Lubik and Schorfheide (2006) analyze the effect of government spending shocks on real exchange rates when the nominal rigidities are present only in prices.

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Fig. 1. Impulse response functions of the real exchange rate.

in Barattieri et al. (2014). The other parameters in the models are standard: ψ = 3, σ = 1/5, ρi = 0.85, αc = 0.5, απ = 2.0, φH = 0.94, and θ = θw = 10, where θw is the elasticity of substitution across differentiated labor. Finally, the first-order autocorrelation of all exogenous shocks is set at 0.9. Fig. 1 compares the impulse response functions of the real exchange rate to a negative shock to monetary policy, a positive shock to technology and a negative shock to government spending in the home country. The signs of the shocks are set to ensure that the real exchange rate in the home country depreciates on impact. For comparison purposes, the initial responses in the figure are normalized to unity. Note that the impulse responses to monetary shocks in both the SP and SW economies exhibit monotonic decay back to the steady state, with no hump-shape profile. When the interest rate unexpectedly declines, the demand for the home consumption increases. Higher demand for goods combined with either sticky prices or sticky wages results in slow adjustment of the price level to a higher level. The monetary shock also generates a depreciation of the nominal exchange rate due to the uncovered interest parity condition. Note that the sticky wage economy exhibits somewhat slower convergence of the real exchange rate, but the differences are not very large across the two cases. Turning to the two types of real shocks emphasized by Steinsson (2008), the contrasts are striking. In the SP economy, the real exchange rate responds in the same dynamic fashion to technology and government spending shocks (up to a normalization of the impact effect, recall the initial response is normalized to one). Importantly, unlike monetary shocks, these real shocks may generate hump-shaped impulse responses, which are arguably consistent with the data. The real exchange rate is also more persistent in these cases. By contrast, in the SW economy, productivity shocks and government spending shocks have different effects. Only government spending shocks can successfully generate hump-shaped responses of the real exchange rate. The response to the technology shock is monotonically decaying and the real exchange rate is less persistent than the case of a monetary shock. As emphasized in Steinsson (2008), the key to understanding the hump-shaped response of the real exchange rate is the response of the real interest rate which governs consumption dynamics. In the model, a shock in the home country has a weaker effect on foreign consumption than on home consumption because of home bias in tastes. Given (3) and the relatively weak response of foreign consumption, the real exchange rate necessarily moves closely with home consumption through time. In addition, (1) implies that the consumption growth ct +1 − ct is positively correlated with the real interest rate.

Fig. 2 shows the impulse response function of the (a) real interest rate, (b) nominal interest rate and (c) inflation rate to a technology shock in SP and SW economies. As shown in panel (a) of the figure, the response of the real interest rate in the SP economy is positive for a few periods before turning persistently negative in transition back to the steady state. This dynamic pattern of the real interest rate results in the hump-shaped response of home consumption and the real exchange rate. As shown in panel (b), relatively high inertia of the nominal interest rate is playing a crucial role in this mechanism. Why does the SW economy fail to generate hump-shaped responses to technology shocks? In the SW economy, prices are completely flexible. Thus, at the impact period, inflation substantially declines in response to a technology shock. As shown in panel (b) of Fig. 2, this leads to a large decline in the nominal interest rate due to (4). Furthermore, as shown in panel (c), inflation after the impact period is expected to be higher in the SW economy than the SP economy since prices are more quickly adjusted to the steady state level. The combination of responses of the nominal interest rate and inflation yields an immediate reduction in the real interest rate in the SW economy, in contrast to a temporary increase in the real interest rate in the SP economy. Therefore, even if there is relatively high inertia of the nominal interest rate, negative responses of the real interest rate lead to monotonically decaying responses of the real exchange rate. Recall that a shock to government spending can generate the hump-shaped response of the real exchange rate even in the SW economy. The reason for the hump-shaped dynamics is that a shock to government spending affects wages that are sticky. In particular, an unexpected decline in the government spending decreases wages via lower demand for labor, but wages adjust only slowly. As a result, even in the SW economy, prices adjust slowly in response to a government spending shock, and inflation exhibits a pattern similar to the case of a technology shock in the SP economy shown in panel (c) of Fig. 2. 4. Conclusion We investigated the role of sticky wages in accounting for real exchange rate dynamics. We showed that when wages are sticky, the ability of nominal rigidities to account for the humpshaped real exchange rate responses is retained, but productivity shocks no longer do so. Thus, government spending shocks are more important than previously thought if, as seems reasonable, nominal wages are not perfectly flexible. Moreover, in cases in

M.J. Crucini et al. / Economics Letters 123 (2014) 160–163

(a) Real interest rate.

(b) Nominal interest rate.

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(c) Inflation.

Fig. 2. Impulse response functions of real and nominal interest rates and inflation to a technology shock.

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