سیاست های پولی و نرخ ارز: بررسی مدل VAR

This paper examines the ability of vector autoregressive (VAR) models to properly identify the transmission of monetary policy in a controlled experiment. Simulating data from a small open economy DSGE model estimated for Australia, we find that sign-restricted VAR models do reasonably well at estimating the responses of macroeconomic variables to monetary policy shocks. This is in contrast to models that use recursive zero-type restrictions, for which inflation can rise following an unexpected interest rate increase while the exchange rate can appreciate or depreciate depending on the ordering of the variables. Sign-restricted VAR models seem to be able to overcome puzzles related to the real exchange rate, provided that a sufficient number of different types of shocks are identified. Despite delivering the correct sign of the impulse responses, central tendency measures of sign-restricted VAR models can, however, be misleading and hardly ever coincide with the true impulses. This finding casts doubt on the common notion that the median impulses are the ‘most probable’ description of the true data-generating process

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, 1995Kim and Roubini, 2000 for G7 countries and Mojon and Peersman, 2001 and Peersman and Smets, 2003 for the euro area). 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.2 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. 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.3 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.4 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 which use a recursive identification structure, 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.5 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, it shows 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 concludes.

This paper investigates the ability of vector autoregressive (VAR) models to properly identify monetary policy shocks with data simulated from a small open economy DSGE model estimated using Australian data. Overall, 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 based on a recursive identification structure. 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. It finds that the sign restriction approach recovers the impulse responses (free of the exchange rate puzzles) reasonably well, provided that a sufficient number of shocks are uniquely identified; if only the monetary policy shocks are identified, the exchange rate puzzle remains. This suggests that identification schemes that are too parsimonious may fail to recover the ‘true’ impulse responses. The paper also finds that measures of central tendency can be misleading and that the true impulses hardly ever coincide with the median. This casts doubt on the common notion that the median impulses are ‘most probable’. There are several directions in which the analysis presented in this paper could be extended. One such avenue would allow for time-varying parameters in the data-generating process. It would be interesting to see whether regime-switching (or time-varying parameter) sign-restricted VAR models would be able to capture the break in the data-generating process at all.