RDP 2010-07: Monetary Policy and the Exchange Rate: Evaluation of VAR Models 1. Introduction

Vector autoregressive models (VARs) are widely used for understanding the effects of monetary policy on the economy. While the results of these models are generally consistent with economic theory, they tend to suffer from various puzzles. One of these anomalies is the price puzzle, a term coined by Eichenbaum (1992), which refers to a situation in which an unexpected tightening in monetary policy leads to an increase in inflation. Other puzzles have been found regarding the behaviour of the real exchange rate in response to a monetary policy shock. Standard theory suggests that an unexpected tightening in monetary policy leads to an immediate appreciation of the currency and a future depreciation in line with uncovered interest rate parity (UIP).^[1] However, many empirical studies, particularly those based on VAR models, find that following such a shock, the real exchange rate either depreciates, or if it appreciates, it does so over an extended period. In the literature, these phenomena have been referred to as the exchange rate puzzle and the delayed overshooting puzzle, respectively.

VAR studies have typically placed recursive, contemporaneous ‘zero restrictions’ on the interaction between monetary policy and the exchange rate (for instance, see Eichenbaum and Evans 1995 and Kim and Roubini 2000 for G7 countries and Mojon and Peersman 2001 and Peersman and Smets 2003 for the euro area). Several Australian studies have also analysed the impact of monetary policy shocks using similar restrictions. Most of these studies assume that the exchange rate is the most endogenous variable (that is, the exchange rate reacts instantaneously to all shocks). Dungey and Pagan (2000, 2009) find evidence of delayed overshooting, while Brischetto and Voss (1999) and Berkelmans (2005) overcome the exchange rate puzzles by including commodity price variables;^[2] although, even the evidence from these papers is unclear because the responses are not statistically significant.

Sign restrictions are an attractive alternative to recursive VARs as they avoid the use of strong restrictions on contemporaneous relationships for identification. An increasing number of VAR studies have employed sign restrictions to identify monetary policy shocks (see, for instance, Canova and De Nicoló 2002 and Uhlig 2005), and in particular the effects of monetary policy shocks on exchange rates. Using this approach, Faust and Rogers (2003) find no robust results regarding the timing of the peak response of the exchange rate. Scholl and Uhlig (2008) impose sign restrictions on a minimal set of variables but do not restrict the response of the exchange rate when identifying the monetary policy shock. While their findings confirm the exchange rate puzzles, their ‘agnostic’ sign restriction approach is open to criticism because it identifies only one shock and ignores all others.^[3] The problem with such an approach is that the identification scheme is not unique – there are possibly other shocks which would also satisfy the minimal restrictions placed on the monetary policy shock (Fry and Pagan forthcoming). This raises the question of whether the use of a minimal set of sign restrictions is sufficient to identify a ‘true’ response of the exchange rate. This question is particularly pertinent, given that Bjørnland (2009) – using long-run restrictions on the effect of monetary policy shocks on the exchange rate – finds no evidence of exchange rate puzzles in four small open economies, including Australia.^[4]

This paper examines the consequences of using recursive and sign-restricted VAR models to identify monetary policy shocks when the data-generating process is an estimated small open economy DSGE model for Australia (in the spirit of Galí and Monacelli 2005). In particular, it tests whether estimates of these models can replicate the true impulse responses from the DSGE model.^[5] It finds that sign restriction models do reasonably well at estimating the responses of macroeconomic variables to monetary policy shocks, particularly compared to VAR models that use recursive identification structures, which are generally inconsistent with the responses of the DSGE model. Using an identification procedure that is agnostic regarding the direction of the exchange rate response, the paper examines the ability of sign-restricted VAR models to overcome puzzles related to the real exchange rate.^[6] It finds that that the sign restriction approach recovers the impulse responses reasonably well, provided that a sufficient number of shocks are uniquely identified; if we only identify the monetary policy shocks, in line with Scholl and Uhlig (2008), the exchange rate puzzle remains. In addition, we show that central tendency measures of sign-restricted VAR models can be misleading since they hardly ever coincide with the true impulses. This casts doubt on the common notion that the median impulses are ‘most probable’.

The rest of the paper is organised as follows. Section 2 outlines the small open economy DSGE model, which is used as a data-generating process in our controlled experiment. This model is estimated using data for Australia (and the United States as the ‘large’ economy) in Section 3, which also presents the theoretical impulse responses to a monetary policy shock generated from the model. Section 4 outlines the empirical VAR models and summarises the results based on estimates using simulated data. Section 5 briefly reviews some sign-restricted VAR evidence based on Australian data. Section 6 concludes.