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This article reviews the literature on the econometric relationship between DSGE and VAR models from the point of view of estimation and model validation. The mapping between DSGE and VAR models is broken down into three stages: (1) from DSGE to state-space model; (2) from state-space model to VAR( ∞ ); (3) from VAR( ∞ ) to finite-order VAR. The focus is on discussing what can go wrong at each step of this mapping and on critically highlighting the hidden assumptions. I also point out some open research questions and interesting new research directions in the literature on the econometrics of DSGE models. These include, in no particular order: understanding the effects of log-linearization on estimation and identification; dealing with multiplicity of equilibria; estimating nonlinear DSGE models; incorporating into DSGE models information from atheoretical models and from survey data; adopting flexible modeling approaches that combine the theoretical rigor of DSGE models and the econometric model’s ability to fit the data.

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.

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.

Recently, it has been suggested that macroeconomic forecasts from estimated dynamic stochastic general equilibrium (DSGE) models tend to be more accurate out-of-sample than random walk forecasts or Bayesian vector autoregression (VAR) forecasts. Del Negro and Schorfheide (2013) in particular suggest that the DSGE model forecast should become the benchmark for forecasting horse-races. We compare the real-time forecasting accuracy of the Smets and Wouters (2007) DSGE model with that of several reduced-form time series models. We first demonstrate that none of the forecasting models is efficient. Our second finding is that there is no single best forecasting method. For example, typically simple AR models are most accurate at short horizons and DSGE models are most accurate at long horizons when forecasting output growth, while for inflation forecasts the results are reversed. Moreover, the relative accuracy of all models tends to evolve over time. Third, we show that there is no support to the common practice of using large-scale Bayesian VAR models as the forecast benchmark when evaluating DSGE models. Indeed, low-dimensional unrestricted AR and VAR forecasts may forecast more accurately.

After briefly reviewing the past history of Bayesian econometrics and Alan Greenspan's (2004) recent description of his use of Bayesian methods in managing policy-making risk, some of the issues and needs that he mentions are discussed and linked to past and present Bayesian econometric research. Then a review of some recent Bayesian econometric research and needs is presented. Finally, some thoughts are presented that relate to the future of Bayesian econometrics.

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.

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.

This paper aims to develops an estimable hybrid model that combines the micro‐founded DSGE model with the flexibility of the atheoretical VAR model.

The model is estimated via the maximum likelihood technique based on quarterly data on real gross national product (GNP), consumption, investment and hours worked, for the South African economy, over the period of 1970:1 to 2000:4. Based on a recursive estimation using the Kalman filter algorithm, the out‐of‐sample forecasts from the hybrid model are then compared with the forecasts generated from the Classical and Bayesian variants of the VAR for the period 2001:1‐2005:4.

The results indicate that, in general, the estimated hybrid‐DSGE model outperforms the classical VAR, but not the Bayesian VARs in terms of out‐of‐sample forecasting performances.

The model lacks nominal shocks and needs to be extended into a small open economy framework.

The paper was able to show that, even though the DSGE model is outperformed by the BVAR, a microfounded theoretical DSGE model has a future in forecasting the South African economy.

To the best of the authors' knowledge, this is the first attempt to use an estimable DSGE model to forecast the South African economy.

Pesaran and Smith (2011) concluded that Dynamic Stochastic General Equilibrium (DSGE) models were sometimes a straitjacket which hampered the ability to match certain features of the data. In this chapter, the authors look at how one might assess the fit of these models using a variety of measures, rather than what seems to be an increasingly common device – the Marginal Data Density. The authors apply these in the context of models by Christiano, Motto, and Rostagno (2014) and Ireland (2004), finding they fail to make a match by a large margin. Both of these models feature more shocks than observed variables, resulting in the empirical shocks having a singular density, and so making them correlated. When correlated one can neither interpret impulse responses nor perform variance decompositions. Against this, there is a strong argument for having a straitjacket, as it enforces some desirable behavior on models and makes researchers think about how to account for any non-stationarity in the data. The authors illustrate this with examples drawn from the SVAR literature and also more eclectic models such as Holston, Laubach, and Williams (2017) for extracting an estimate of the real natural rate.