DSGE Models in Macroeconomics: Estimation, Evaluation, and New Developments: Volume 28

This volume of Advances in Econometrics is devoted to dynamic stochastic general equilibrium (DSGE) models, which have gained popularity in both academic and policy circles as a theoretically and methodologically coherent way of analyzing a variety of issues in empirical macroeconomics. The volume is divided into two parts. The first part covers important topics in DSGE modeling and estimation practice, including the modeling and role of expectations, the study of alternative pricing models, the problem of non-invertibility in structural VARs, the possible weak identification in new open economy macro models, and the modeling of trend inflation. The second part is devoted to innovations in econometric methodology. The papers in this section advance new techniques for addressing key theoretical and inferential problems and include discussion and applications of Laplace-type, frequency domain, empirical likelihood, and method of moments estimators.

This paper surveys the treatment of expectations in estimated Dynamic Stochastic General Equilibrium (DSGE) macroeconomic models.

A recent notable development in the empirical macroeconomics literature has been the rapid growth of papers that build structural models, which include a number of frictions and shocks, and which are confronted with the data using sophisticated full-information econometric approaches, often using Bayesian methods.

A widespread assumption in these estimated models, as in most of the macroeconomic literature in general, is that economic agents' expectations are formed according to the Rational Expectations Hypothesis (REH). Various alternative ways to model the formation of expectations have, however, emerged: some are simple refinements that maintain the REH, but change the information structure along different dimensions, while others imply more significant departures from rational expectations.

I review here the modeling of the expectation formation process and discuss related econometric issues in current structural macroeconomic models. The discussion includes benchmark models assuming rational expectations, extensions based on allowing for sunspots, news, sticky information, as well as models that abandon the REH to use learning, heuristics, or subjective expectations.

We analyze fluctuations in inflation and the nominal exchange rate under optimal monetary policy with local currency pricing by developing two-country DSGE local currency pricing and producer currency pricing models. We estimate our models using Bayesian techniques with Japanese and US data, and calculate impulse response functions. Our estimation results show that local currency pricing is strongly supported against producer currency pricing. From the estimated parameters, we show that completely stabilizing consumer price index inflation is optimal from the viewpoint of minimizing welfare costs and that completely stabilizing consumer price index inflation is consistent with completely stabilizing the nominal exchange rate.

A state space representation of a linearized DSGE model implies a VAR in terms of observable variables. The model is said be non-invertible if there exists no linear rotation of the VAR innovations which can recover the economic shocks. Non-invertibility arises when the observed variables fail to perfectly reveal the state variables of the model. The imperfect observation of the state drives a wedge between the VAR innovations and the deep shocks, potentially invalidating conclusions drawn from structural impulse response analysis in the VAR. The principal contribution of this chapter is to show that non-invertibility should not be thought of as an “either/or” proposition – even when a model has a non-invertibility, the wedge between VAR innovations and economic shocks may be small, and structural VARs may nonetheless perform reliably. As an increasingly popular example, so-called “news shocks” generate foresight about changes in future fundamentals – such as productivity, taxes, or government spending – and lead to an unassailable missing state variable problem and hence non-invertible VAR representations. Simulation evidence from a medium scale DSGE model augmented with news shocks about future productivity reveals that structural VAR methods often perform well in practice, in spite of a known non-invertibility. Impulse responses obtained from VARs closely correspond to the theoretical responses from the model, and the estimated VAR responses are successful in discriminating between alternative, nested specifications of the underlying DSGE model. Since the non-invertibility problem is, at its core, one of missing information, conditioning on more information, for example through factor augmented VARs, is shown to either ameliorate or eliminate invertibility problems altogether.

Open-Economy models are central to the discussion of the trade-offs monetary policy faces in an increasingly more globalized world (e.g., Marínez-García & Wynne, 2010), but bringing them to the data is not without its challenges. Controlling for misspecification bias, we trace the problem of uncertainty surrounding structural parameter estimation in the context of a fully specified New Open Economy Macro (NOEM) model partly to sample size. We suggest that standard macroeconomic time series with a coverage of less than forty years may not be informative enough for some parameters of interest to be recovered with precision. We also illustrate how uncertainty also arises from weak structural identification, irrespective of the sample size. This remains a concern for empirical research and we recommend estimation with simulated observations before using actual data as a way of detecting structural parameters that are prone to weak identification. We also recommend careful evaluation and documentation of the implementation strategy (specially in the selection of observables) as it can have significant effects on the strength of identification of key model parameters.

The role of trend inflation shocks for the U.S. macroeconomic dynamics is investigated by estimating two DSGE models of the business cycle. Policymakers are assumed to be concerned with a time-varying inflation target, which is modeled as a persistent and stochastic process. The identification of trend inflation shocks (as opposed to a number of alternative innovations) is achieved by exploiting the measure of trend inflation recently proposed by Aruoba and Schorfheide (2011). Our main findings point to a substantial contribution of trend inflation shocks for the volatility of inflation and the policy rate. Such contribution is found to be time dependent and highest during the mid-1970s to mid-1980s.

Empirical work in macroeconomics almost universally relies on the hypothesis of rational expectations (RE).

This chapter departs from the literature by considering a variety of alternative expectations formation models. We study the econometric properties of a popular New Keynesian monetary DSGE model under different expectational assumptions: the benchmark case of RE, RE extended to allow for “news” about future shocks, near-RE and learning, and observed subjective expectations from surveys.

The results show that the econometric evaluation of the model is extremely sensitive to how expectations are modeled. The posterior distributions for the structural parameters significantly shift when the assumption of RE is modified. Estimates of the structural disturbances under different expectation processes are often dissimilar.

The modeling of expectations has important effects on the ability of the model to fit macroeconomic time series. The model achieves its worse fit under RE. The introduction of news improves fit. The best-fitting specifications, however, are those that assume learning. Expectations also have large effects on forecasting. Survey expectations, news, and learning all work to improve the model's one-step-ahead forecasting accuracy. RE, however, dominate over longer horizons, such as one-year ahead or beyond.

The Laplace-type estimator (LTE) is a simulation-based alternative to the classical extremum estimator that has gained popularity in applied research. We show that even though the estimator has desirable asymptotic properties, in small samples the point estimate provided by LTE may not necessarily converge to the extremum of the sample objective function. Furthermore, we suggest a simple test to verify if the estimator converges. We illustrate these results by estimating a prototype dynamic stochastic general equilibrium model widely used in macroeconomics research.

The chapter considers parameter identification, estimation, and model diagnostics in medium scale DSGE models from a frequency domain perspective using the framework developed in Qu and Tkachenko (2012). The analysis uses Smets and Wouters (2007) as an illustrative example, motivated by the fact that it has become a workhorse model in the DSGE literature. For identification, in addition to checking parameter identifiability, we derive the non-identification curve to depict parameter values that yield observational equivalence, revealing which and how many parameters need to be fixed to achieve local identification. For estimation and inference, we contrast estimates obtained using the full spectrum with those using only the business cycle frequencies to find notably different parameter values and impulse response functions. A further comparison between the nonparametrically estimated and model implied spectra suggests that the business cycle based method delivers better estimates of the features that the model is intended to capture. Overall, the results suggest that the frequency domain based approach, in part due to its ability to handle subsets of frequencies, constitutes a flexible framework for studying medium scale DSGE models.

In this chapter we approach the estimation of dynamic stochastic general equilibrium models through a moments-based estimator, the empirical likelihood. We attempt to show that this inference process can be a valid alternative to maximum likelihood, which has been one of the preferred choices of the related literature to estimate these models. The empirical likelihood estimator is characterized by a simple setup and only requires knowledge about the moments of the data generating process of the model. In this context, we exploit the fact that these economies can be formulated as a set of moment conditions to infer on their parameters through this technique. For illustrational purposes, we consider a standard real business cycle model with a constant relative risk averse utility function and indivisible labor, driven by a normal technology shock.

This chapter analyzes the empirical relationship between the pricesetting/consumption behavior and the sources of persistence in inflation and output. First, a small-scale New-Keynesian model (NKM) is examined using the method of moment and maximum likelihood estimators with US data from 1960 to 2007. Then a formal test is used to compare the fit of two competing specifications in the New-Keynesian Phillips Curve (NKPC) and the IS equation, that is, backward- and forward-looking behavior. Accordingly, the inclusion of a lagged term in the NKPC and the IS equation improves the fit of the model while offsetting the influence of inherited and extrinsic persistence; it is shown that intrinsic persistence plays a major role in approximating inflation and output dynamics for the Great Inflation period. However, the null hypothesis cannot be rejected at the 5% level for the Great Moderation period, that is, the NKM with purely forward-looking behavior and its hybrid variant are equivalent. Monte Carlo experiments investigate the validity of chosen moment conditions and the finite sample properties of the chosen estimation methods. Finally, the empirical performance of the formal test is discussed along the lines of the Akaike's and the Bayesian information criterion.