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Empirical Economics

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01-05-2014

Why does monetary policy respond to the real exchange rate in small open economies? A Bayesian perspective

Authors: Carlos J. Garcia, Wildo D. Gonzalez

Published in: Empirical Economics | Issue 3/2014

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Abstract

To estimate how monetary policy works in small open economies, we build a dynamic stochastic general equilibrium model that incorporates the basic features of these economies. We conclude that the monetary policy in a group of small open economies (including Australia, Chile, Colombia, Peru, and New Zealand) is rather similar to that observed in closed economies. Our results also indicate, however, that there are strong differences due to the shocks from the international financial markets (mainly risk premium shocks). These differences explain most of the variability of the real exchange rate, which has important reallocation effects in the short run. Our results are consistent with an old idea from the Mundell–Fleming model: namely, a real depreciation to confront a risk premium shock is expansive or procyclical, in contradiction to the predictions of the balance sheet effect, the J curve effect, and the introduction of working capital into RBC models. In line with this last result, we have strong evidence that only in one of the five countries analyzed in this study does not intervene the real exchange rate, the case of New Zealand.

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García et al. (2011a) use a more theoretical version of this model to examine whether explicitly including the exchange rate in the central bank’s policy reaction function can improve macroeconomic performance. See also García and Gonzalez (2013).

Several authors build DSGE models to analyze macroeconomic policies in open economies. Those using Bayesian estimation techniques include Adolfson et al. (2007), Castillo et al. (2006), Caputo et al. (2006), Cook (2004), Devereux et al. (2006), Elekdag et al. (2006), García et al. (2011a, b), García and Gonzalez (2013), Hamann et al. (2006), Medina and Soto (2007), and Tovar (2006).

The real exchange rate is obtained from Eq. (2) using the following transformation of the external debt in domestic real terms: $S_t B_t^{{\mathrm{o}}^*} /P_t =b_t^{{\mathrm{o}}*} $ and

$$\begin{aligned}&S_t \left\{ {\Phi \left( {\frac{b_{t+1}^{{\mathrm{o}}^*} }{{\mathrm{GDP}}_t },\frac{b_{t+1}^{{\mathrm{o}}^*} }{Q_t K_{t+1} },u_t^{RK} } \right) R_t^*} \right\} ^{-1}B_{t+1}^{{\mathrm{o}}^*} (i)\\&\quad =\left( {Q_t^*/Q_{t+1}^*} \right) \left\{ {\Phi \left( {\frac{b_{t+1}^{{\mathrm{o}}^*} }{{\mathrm{GDP}}_t },\frac{b_{t+1}^{{\mathrm{o}}^*} }{Q_t K_{t+1} },u_t^{RK} } \right) R_t^*} \right\} ^{-1}\left( {P_{t+1}^*/P_t^*} \right) b_{t+1}^{{\mathrm{o}}^*} (i). \end{aligned}$$

The first-order condition for utility maximization is obtained with respect to $b_{t+1}^{{\mathrm{o}}^*} \left( i \right) $.

See Schmitt-Grohé and Uribe (2003).

Céspedes et al. (2004), following Bernanke et al. (1999), assume that the risk premium is given by:

$$\begin{aligned} 1+\eta _{t+1} =F\left( {\frac{{\mathop {Q_{t}}\limits ^{\smile }}K_{t+1} }{\mathop {Q_{t}}\limits ^{\smile }K_{t+1}-S_t B_{t+1}^*}} \right) =G\left( {\frac{{S_t B_{t+1}^*}}{\mathop {Q_{t}}\limits ^{\smile }K_{t+1} }}\right) \qquad \quad F\left( 1 \right) =1,\,\,F^{\prime }>0,\,\, Q=\frac{\mathop {Q_{t}}\limits ^{\smile }}{P} \end{aligned}$$

We assume that the risk premium can be represented by a similar function to characterize the balance sheet effect:

$$\begin{aligned} 1+\eta _{t+1} =\Phi \left( {\frac{b_{t+1}^{{\mathrm{o}}^*} }{{\mathrm{GDP}}_t },\frac{b_{t+1}^{{\mathrm{o}}^*} }{Q_t K_{t+1} },u_t^{RK} } \right) ,\quad \quad b_{t+1}^{{\mathrm{o}}^*} =\frac{S_{t+1} B_{t+1}^{{\mathrm{o}}^*} }{P_{t+1} }. \end{aligned}$$

$b_{t+1}^{{\mathrm{o}}^*} =\frac{S_{t+1} B_t^{{\mathrm{o}}^*} }{P_{t+1} }=\frac{S_{t+1} B_t^{{\mathrm{o}}^*} }{P_{t+1} }\frac{P_{t+1}^*}{P_{t+1}^*}={\mathrm{real}}\;{\mathrm{exchange}}\;{\mathrm{rate}}\times \frac{B_{t+1}^{{\mathrm{o}}^*} }{P_{t+1}^*}\quad $

This approach similar to Laxton and Pesenti (2003).

We are aware that the GDP with natural resource will be in our model this expression: ${\mathrm{GDP}}_t =P_t^D Y_t^D -S_t P_t^*I_t +(S_t P_t^{cu} Q\_c)$, but we consider that the relevant concept for monetary policy is the definition of Eq. (36).

All this information (code and steady state) is available on request.

The details of the estimation of all parameters can be requested to the authors by email.

The real wage elasticity in the labor supply was calibrated; we chose a value for this parameter of 0.75 (Chetty et al. 2011).

To interpret the Bayes factor in comparing two models, we follow to Kass and Raftery (1995). So, if M1 is the model with the largest marginal likelihood, then there is positive evidence against model M0 if $2^{*}\ln (Bayes\,factor\,between\,M1\,and\,M0)$ is large than six, strong evidence if this expression is larger than six, and definitive if it is larger than ten (page 789). This value is arbitrary in the same sense as a significance level of $\upalpha $ = 0.05 is arbitrary in classical statistics, but, just like this value of $\upalpha $, these categories seem to give an appropriate rule.

Studies that report a GDP contraction is in the first period all include working capital in the model. Thus, more expensive working capital should have a negative effect on output.

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Title: Why does monetary policy respond to the real exchange rate in small open economies? A Bayesian perspective
Authors: Carlos J. Garcia
Wildo D. Gonzalez
Publication date: 01-05-2014
Publisher: Springer Berlin Heidelberg
Published in: Empirical Economics / Issue 3/2014
Print ISSN: 0377-7332
Electronic ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-013-0697-2

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