روشهایی به منظور برآورد مدل تعادل عمومی تصادفی پویا

This paper employs the one-sector real business cycle model as a testing ground for four different procedures to estimate dynamic stochastic general equilibrium (DSGE) models. The procedures are: (1) maximum likelihood, with and without measurement errors and incorporating priors, (2) generalized method of moments, (3) simulated method of moments, and (4) indirect inference. Monte carlo analysis is used to study the small-sample properties of these estimators and to examine the implications of misspecification, stochastic singularity, and weak identification.

This paper employs the one-sector real business cycle (RBC) model as a testing ground for four different methods to estimate dynamic stochastic general equilibrium (DSGE) models. The estimation methods are maximum likelihood (ML), generalized method of moments (GMM), simulated method of moments (SMM), and the indirect inference procedure proposed by Smith (1993). All these methods are standard and their asymptotic properties are well known. The goals of this paper are to describe in a pedagogical manner their application to the estimation of DSGE models, to study their small-sample properties, to compare their computational costs, and to examine the implications of weak identification and misspecification. Monte Carlo experiments are carried out under the null hypothesis and under three possible alternatives using samples of the size typically found in empirical work. Under the null, the data generating process (DGP) and the estimated model are the same. Although all methods deliver consistent parameter estimates, weak identification, stochastic singularity, and small-sample distortion are (or should be) important considerations in their practical application. Weak identification may arise intrinsically from the model solution1 and/or from an unfortunate choice of variables or moments to estimate the model. For example, we will see that the log likelihood function of output is flatter with respect to the discount factor than that of consumption or hours worked, and that the objective function used in indirect inference may be less locally convex than that of GMM because they focus on different moments of the data. Stochastic singularity imposes restrictions on the variables and moments that may be used for model estimation, and on the VAR representation of artificial data generated by a DSGE model. DSGE models are singular because they use a small number of structural shocks to generate predictions about a large number of observable variables. Hence, these models predict that linear combinations of observable variables should hold without noise.2 This prediction is not satisfied by the data and is only the result of a particular misspecification, namely that the model assumes a smaller number of shocks than are present in the real world. This paper shows that singularity affects more severely ML than moment-based methods: ML estimation is limited by the number of linearly independent variables while moment-based estimation is limited by the number of linearly independent moments. The latter is a weaker restriction because it is possible to find independent moments that incorporate information about more variables than those that are linearly independent. The use of measurement errors to sidestep stochastic singularity in the ML framework is studied here as well. The small-sample distortion in statistical inference is primarily due to fact that the asymptotic distributions of test statistics may be different from their small-sample analogues. For example, we will see that the empirical size of the t test that the parameter takes its true value may be quite different from the nominal size because asymptotic standard errors are not always a good measure of the small-sample variability of the estimates. Under the alternative, the data are not generated by the model of interest but instead by an alternative model. Three alternative models are considered. First, the DGP is the linearized RBC model, but with multiple structural shocks. Second, the DGP is a linearized RBC model with habit formation in consumption. Third, the DGP is the nonlinear version of the one-shock RBC model. In all cases, the estimated model is the economically interesting but (now) misspecified RBC model with time separable preferences and only one technology shock. The goal of these experiments is to study the robustness of each method to misspecification. The main results of this analysis are that GMM and SMM are generally more robust to misspecification than ML, but that adding measurement errors and using informative priors are helpful in limiting the effects of misspecification in the ML framework. The paper is organized as follows: Section 2 outlines the DSGE model that will be used as backdrop for the analysis, Section 3 describes the estimation methods and their application to DSGE models, Section 4 presents the Monte Carlo design and report the results, and Section 5 concludes.

The paper studies the application of standard econometric techniques for the estimation of DSGE models. Monte Carlo analysis shows that all procedures deliver reasonably good estimates under the null but that important practical considerations are weak identification, stochastic singularity, small-sample distortions in statistical inference, robustness to misspecification, and computational convenience. Although ML is more severely affected by singularity and generally less robust to misspecification than moment-based methods, adding measurement errors and incorporating priors may be helpful in empirical applications. Overall results indicate that moment-based methods (specially in their GMM and SMM formulations) compare very favorably to the more widely used method of ML and are an attractive addition to our toolbox to estimate DSGE models. A general issue uncovered here is that the choice of variables or moments used to estimate the model is important for at least two reasons. First, identification depends on the shape of the objective function which, in turn, depends on the data series or moments used to estimate the model. Second, a misspecification may affect more severely some variables than others. Thus, a selection based on a good understanding of the strengths and weaknesses of the economic model and on the diagnostics mentioned above may be beneficial in actual empirical analysis.