برآورد بیزین یک مدل DSGE اقتصاد باز با تجربه ناقص

In this paper, we develop a dynamic stochastic general equilibrium (DSGE) model for an open economy, and estimate it on Euro area data using Bayesian estimation techniques. The model incorporates several open economy features, as well as a number of nominal and real frictions that have proven to be important for the empirical fit of closed economy models. The paper offers: i) a theoretical development of the standard DSGE model into an open economy setting, ii) Bayesian estimation of the model, including assessments of the relative importance of various shocks and frictions for explaining the dynamic development of an open economy, and iii) an evaluation of the model's empirical properties using standard validation methods.

In this paper, we develop a dynamic stochastic general equilibrium (DSGE) model for an open economy and estimate it on Euro area data. We extend the closed economy DSGE model of Christiano et al. (2005) by incorporating open economy aspects. Our model combines elements of their closed economy setting with some of the features and findings in the New Open Economy Macroeconomics literature.1 Following Christiano et al. (2005), a number of nominal and real frictions such as sticky prices, sticky wages, variable capital utilization, capital adjustment costs and habit persistence are included in the theoretical model. We also allow for incomplete exchange rate pass-through in both the import and export sectors by including nominal price rigidities (i.e., local currency price stickiness), following, for example, Smets and Wouters (2002). The relevance of these frictions will be empirically determined in the estimation procedure. Apart from introducing the exchange rate channel, we also include a working capital channel (i.e., firms borrow money from a financial intermediary to finance part of their wage bill). Examining the role of the working capital channel is of particular interest, since Christiano et al. (2005) obtain a low estimated degree of price stickiness when allowing for working capital in matching the impulse responses after a monetary policy shock. In contrast, Smets and Wouters, 2003 and Smets and Wouters, 2005 obtain a much higher degree of estimated price stickiness in a model without the working capital channel. As in Altig et al. (2003), we include a stochastic unit-root technology shock in the model which induces a common stochastic trend in aggregate quantities. This allows us to use data in the estimation that has not been pre-processed (e.g. detrended). Compared to Smets and Wouters, 2003 and Smets and Wouters, 2005, we also allow for a larger set of structural shocks, mainly due to the open economy aspects of our model. We perform relative model comparisons using Bayesian posterior densities to assess the importance of the various frictions and shocks for explaining business cycle fluctuations in the open economy. We estimate the open economy model on Euro area data using Bayesian estimation techniques.2Smets and Wouters, 2003 and Smets and Wouters, 2005 have shown that large-scale closed economy DSGE models can be successfully estimated using Bayesian methods. To simplify the analysis, we adopt the assumption that foreign inflation, output and interest rate are exogenously given. There is, however, substantial evidence in favor of this assumption. First, by estimating a VAR model with ten Euro area variables (inflation, output, interest rate, exchange rate, exports, imports, real wage, consumption, investment and employment) and three foreign variables (“rest of the world” inflation, output and interest rate), we find that the Euro area variables only account for a small fraction of the variation in the foreign variables (around 10% (20%) at the one- (five-) year horizon).3 These findings are also supported by de Walque et al. (2005) who find small spillover effects in a joint structural analysis of business cycles in the Euro area, the US and the rest of the world. Second, to check the sensitivity of our results, we have also estimated a specification of the DSGE model where we allow the Euro area variables to affect the foreign variables, both contemporaneously and with a lag. As could have been expected from the VAR analysis and the results in de Walque et al. (2005), the fit of the model is not improved by allowing for a feedback effect from the Euro area, and the parameter estimates in the DSGE, and thus the role of the various frictions and shocks, are essentially unaffected. For further details, the reader is referred to Adolfson et al. (2006). To validate the fit of the estimated open economy DSGE model, we provide a thorough evaluation of the model's empirical properties. The estimated model is able to capture the volatility and persistence in the real exchange rate very well, which has turned out to be a difficult task without detrending the data (see, e.g., Bouakez, 2005, and the references therein). In addition, previous studies have not been able to match the dynamics of the real exchange rate without assuming unreasonable degrees of price rigidity. Our model, however, is able to replicate both the properties of the real exchange rate and the dynamics of the inflation differentials between the Euro area and the rest-of-the-world, using a reasonable degree of price stickiness and without detrending the data.4 The key ingredient behind this ability of the model is that it embodies a set of time-varying markups (as suggested by Bouakez, 2005) that have rather persistent effects on the exchange rate dynamics, while generating much less fluctuations in quantities and prices. This finding is in line with the arguments of Duarte and Stockman (2005), and is attributed to the model setup which shares many of the features emphasized by Devereux and Engel (2002) as necessary to generate highly volatile exchange rates which are “disconnected” from the rest of the economy.5 Moreover, the model yields a high elasticity of substitution between domestic and imported goods. We find a preferred value in the range of 5 to 10 in the estimations. As shown by Obstfeld and Rogoff (2000), a high elasticity of substitution can explain the observed large home bias in trade. The typical estimates for the substitution elasticity between home and foreign goods are around 5 to 20 using micro data; see the references in Obstfeld and Rogoff (2000). However, using macro data, the estimates are usually considerably lower, in the range of 1.5–2, see e.g. Collard and Dellas (2002). We attribute our high estimate to the inclusion of both consumption and imports as observed variables when estimating the model. The paper is organized as follows. In Section 2, the theoretical model is derived and described with particular emphasis on its open economy aspects and Section 3 contains a short description of the data used. In Section 4, we first discuss which parameters we have chosen to calibrate, and the prior distributions for the parameters we have chosen to estimate. Then, we report our estimation results and validate the model fit. The empirical properties of the estimated DSGE model are compared with the data using autocovariance functions. In Section 5, we explore the importance of nominal and real frictions in the model. Section 6 shows the impulse responses to a monetary policy shock and discusses the role of various shocks in explaining business cycles. Finally, Section 7 provides some conclusions.

In this paper, we have modified the closed economy monetary business cycle model of Christiano et al. (2005) to an open economy model. We find there to be strong support for the nominal and real frictions that are embedded in the model; sticky prices in the domestic, import and export sectors, sticky wages, investment adjustment costs and habit persistence in consumption. We do not find any evidence that variable capital utilization is important for the empirical success of the model, nor that it has any greater impact on the estimated parameters.30 Moreover, the working capital channel is not an effective way of generating inflation persistence when subjecting the model to fit all variation in the data and not just the dynamic effects of a monetary policy shock as in Christiano et al. (2005). According to our estimated model, many shocks are of importance for the fluctuations in the 15 variables we study. There is a substantial amount of internal propagation via the high substitution elasticity between foreign and domestic consumption goods which is strongly preferable by the data. The estimated model – although fitted to explain all the variation in the data and not only the dynamics of a monetary policy shock – has a monetary transmission mechanism well in line with those reported in identified VARs (see, e.g., Angeloni et al. (2003) for Euro area evidence) for standard variables like inflation, output, consumption and investment. When the estimated model is subjected to independent empirical validation tests, we find that the empirical performance appears to be fairly good. In particular, the model can reproduce the inflation and real exchange rate dynamics, a task that has turned out to be difficult (see e.g. Bouakez (2005) for further discussion). However, it should be recognized that the model's performance in this regard is contingent upon the inclusion of some exogenous shocks. Another shortcoming of the model is that it overpredicts the persistence and volatility of exports relative to the data. By and large, our paper has shown that it is possible to extend the benchmark closed economy model into an open economy setup and obtain an empirically plausible model to analyze business cycles in the open economy.