ارزیابی یک مدل اقتصاد باز کوچک جدید کینزی برآورد شده

This paper estimates and tests a new Keynesian small open economy model in the tradition of Christiano et al. [2005. Nominal rigidities and the dynamic effects of a shock to monetary policy. Journal of Political Economy 113(1), 1–45] and Smets and Wouters [2003. An estimated stochastic dynamic general equilibrium model of the Euro area. Journal of the European Economic Association 1(5), 1123–1175] using Bayesian estimation techniques on Swedish data. To account for the switch to an inflation targeting regime in 1993 we allow for a discrete break in the central bank's instrument rule. A key equation in the model – the uncovered interest rate parity (UIP) condition – is well known to be rejected empirically. Therefore we explore the consequences of modifying the UIP condition to allow for a negative correlation between the risk premium and the expected change in the nominal exchange rate. The results show that the modification increases the persistence in the real exchange rate and that this model has an empirical advantage compared with the standard UIP specification.

During the last years there has been a growing interest from academia and especially central banks in using dynamic stochastic general equilibrium (DSGE) models for analyzing macroeconomic fluctuations and to use these models for quantitative policy analysis. Smets and Wouters, 2003 and Smets and Wouters, 2004 have in a series of influential papers shown that the forecasting performance of the new generation of (closed economy) DSGE models in the tradition of Christiano et al. (2005) compare very well with both standard and Bayesian vector autoregressive (VAR) models. Adolfson et al. (2007a) report similar results for an open economy DSGE model. However, even if these models appear to be able to capture the development of some key macroeconomic time series, there are still challenges to make them fulfill the observed properties in the data. Often the cross-equation restrictions implied by the DSGE model are simply too strict when taken to the data. One example is the inability of open economy models to account for the persistence and volatility in the real exchange rate, another is the failure of accounting for the international transmission of business cycles (see, e.g., Chari et al., 2002, Lubik and Schorfheide, 2005, Justiniano and Preston, 2005 and de Walque et al., 2005). A key equation in open economy DSGE models is the uncovered interest rate parity (UIP) condition, which in its simplest formulation suggests that the difference between domestic and foreign nominal interest rates equals the expected future change in the nominal exchange rate. The UIP condition is a key equation in open economy models not only for the exchange rate but also for many macroeconomic variables, since there is a lot of internal propagation of exchange rate movements working through fluctuating relative prices. There is, however, strong empirical evidence against the standard UIP condition. VAR evidence suggest that the impulse response function for the real exchange rate after a shock to monetary policy is hump-shaped with a peak effect after about 1 year (see, e.g., Eichenbaum and Evans, 1995 and Faust and Rogers, 2003), whereas the standard UIP condition imply a peak effect within the quarter followed by a relatively quick mean reversion. Moreover, a DSGE model with a standard UIP condition cannot account for the so-called ‘forward premium puzzle’ recorded in the data, i.e. that a currency whose interest rate is high tends to appreciate which implies that the risk premium must be negatively correlated with the expected exchange rate depreciation (see, e.g., Fama, 1984 and Froot and Frankel, 1989). In an attempt to account for these empirical shortcomings, we alter the structural open economy DSGE model developed in Adolfson et al. (2007b) and modify the UIP condition to allow for a negative correlation between the risk premium and the expected change in the exchange rate, following the vast empirical evidence reported in for example Engel (1996). In the log-linearized version of the model, our suggested modification of the risk premium introduces a lagged dependence between the exchange rate and the domestic interest rate (which is absent using a standard UIP condition), and this may help the model to account for the hump-shaped impulse response functions to a policy shock found in VARs. To explore the quantitative role of the UIP condition in the model we make a thorough analysis of the empirical performance of the model with the standard and modified UIP condition for a set of key aggregate quantities and prices along a number of dimensions. The model used in the analysis is a small open economy version of the closed economy DSGE model of Christiano et al. (2005) with both nominal and real frictions. As in Altig et al. (2003), we introduce a stochastic unit-root technology shock, which enables us to work with trending data. The model is estimated with Bayesian techniques on Swedish data from 1980 to 2004, following Schorfheide (2000), Otrok (2001) and Smets and Wouters (2003). Sweden went from a fixed to a floating exchange rate and adopted an inflation targeting regime in the mid 1990s. We therefore believe that there are good reasons to allow for a change in the conduct of monetary policy before and after this event when estimating the model. The Riksbank abandoned the fixed exchange rate regime in November 1992 after the turmoil in the foreign exchange markets, and adopted a 2% inflation target in January 1993. The direction of monetary policy did consequently change in the first half of the 1990s and to formally take this into account in the model we allow the central bank to behave differently before and after the regime shift.1 By comparing impulse response functions and Bayesian posterior model probabilities we show that our specification allowing for a modified UIP condition better matches the observed properties of Swedish data relative to the model using a standard UIP condition. In addition, we examine the forecasting accuracy of the two DSGE specifications using a traditional out-of-sample rolling forecast evaluation for the period 1999Q1–2004Q4. We contrast the forecasts from the alternative DSGE models to forecasts from both standard and Bayesian VAR models as well as traditional benchmark models such as the random walk, to get a better sense of the (relative) precision in the DSGE. Again we conclude that our DSGE specification with a regime shift and the modified UIP condition compares relatively well to more traditional forecasting tools. Lastly, we also use the approach in Del Negro and Schorfheide (2004) and Del Negro et al. (2007) to learn more about the misspecification in each particular DSGE model, by exploiting the DSGE as a prior for a VAR model. If a particular DSGE prior is overruled by the data when estimating the VAR this questions the theoretical restrictions included in the DSGE model and indicates misspecification. Our results indicate that our open economy DSGE model's theoretical restrictions are in fact useful for structuring reduced form VARs. However, even our relatively detailed model appears to be misspecified in the sense that a prior which is more loosely centered around the DSGE model is preferred in terms of the marginal likelihood. This is in line with the findings of Del Negro et al. (2007). The remainder of the paper is organized as follows. In Section 2, we briefly describe the theoretical open economy DSGE model. In Section 3 we discuss the data and the prior distributions used in the estimation. We also describe how to form a prior on the VAR from the DSGE model, and discuss how the (optimal) sharpness in this prior can help us characterize the degree of misspecification in our structural model. Section 4 contains the empirical results. We present the parameter estimates in the different DSGE specifications and compare the Bayesian posterior model probabilities. In addition, we report the forecasting accuracy of the two DSGE models and relate this to the forecasts from a Bayesian and a standard VAR. Subsequently we present the empirical results from the hybrid DSGE-VAR models, evaluating the degree of misspecification. Lastly, Section 6 provides some conclusions.

In this paper we have tried to improve on a small open economy dynamic model in the new Keynesian tradition to make it comply better with the empirical evidence on the transmission mechanism of monetary policy and the forward discount puzzle. The former is especially important for a policy making institution such as a central bank. Even if a DSGE model is able to capture the main development of the key macroeconomic time series and can forecast these well, one may also want to use the structural model for carrying out policy experiments such as evaluating alternative interest rate paths. It is then of crucial importance that the mechanisms in the model conform to the central bank's view of the workings in the economy. We have therefore addressed the common problem that open economy sticky price models where agents are allowed to freely trade in foreign and domestic bonds are typically not able to reproduce the observed persistence and volatility of the real exchange rate. This is troublesome when analyzing the effects of changes in monetary policy because the UIP condition is an integral part of determining how interest rate adjustments affect nominal and real exchange rates. The way the exchange rate responds to various shocks through the UIP condition is also important for many macroeconomic variables because of the nominal frictions in the model. Sticky prices increase the exchange rate's effect on relative prices which in turn have an impact on aggregate quantities and prices. To be able to generate intrinsic persistence of the exchange rate in the model, we introduced a negative correlation between the risk premium on foreign investments and the expected change in the exchange rate, following the empirical evidence in for example Engel (1996). Our tools to evaluate the modification empirically were Bayesian posterior model probabilities, impulse response functions, out-of-sample forecasts, and an analysis of the different DSGE restrictions’ empirical coherence by examining the suitability of the DSGEs as a prior for a VAR model. We find that the modified UIP condition is strongly preferable to a standard specification according to the Bayesian posterior odds, and that it has a significant effect on the impulse response functions of a monetary policy shock. The transmission mechanism of monetary policy in the modified model is more in line with the results obtained from the identified VAR literature, in the sense that the effects on the real exchange rate becomes hump-shaped with a peak effect after a year. The modified DSGE model also produces more accurate forecasts on the real exchange rate and the interest rate compared with a standard UIP specification. We therefore think it is worthwhile exploring alternative structural models of the interest rate parity condition. This remains an important challenge to academics as well as model builders at central banks.