Testing DSGE Models by Indirect Inference: a Survey of Recent Findings

Abstract

We review recent findings in the application of indirect inference to DSGE models. We show that researchers should tailor the power of their test to the model under investigation in order to achieve a balance between high power and finding a robust model; this will involve choosing only a limited number of variables on whose behaviour they should focus. Also recent work reveals that it makes little difference which these variables are or how their behaviour is measured whether via a VAR, IRFs or moments. We also review identification issues, how to test part of a model and whether alternative evaluation methods such as forecasting or likelihood ratio tests are potentially helpful.

Can a small New Keynesian model of the world economy with risk‐pooling match the facts?

“…We establish through this that the true model parameters, including consumer risk‐aversion, cannot in general lie more than 5% from the estimated ones, since the latter passed our test. We also know from other work on similar macro models (Le, Meenagh, Minford, Wickens, & Xu, 2016; Meenagh et al, 2018) that model mis‐specification is rejected 100% of the time; so we can be entirely confident that entirely different specifications (including of consumption utility) cannot be correct. To put these results another way, we can give assurance—and be robust in our belief—that the true model, including in its consumption aspects, lies fairly close to the model and parameters we have estimated.…”

“…The state‐space representation of log‐linearized DSGE model in general has a restricted VARMA representation for the endogenous variables or a finite order VAR model. However, if the observed data are non‐stationary, following Meenagh et al (2018) and Le, Meenagh, and Minford (2016), an unrestricted version of VECM can be used as an auxiliary model when errors are stationary. The VECM model is an approximation of the reduced form of DSGE model and can be represented as a cointegrated VAR with exogenous variables (VARX) model.…”

“…In this paper, we have a twofold empirical aim: to discover whether a three‐country New Keynesian model of the world economy can match world data behaviour and as part of that endeavour whether a risk‐pooling variant of that model can also do so. We do this using a testing and estimation approach, indirect inference, that has been found in recent work (see Le, Meenagh, Minford, Wickens, & Xu, 2016 and Meenagh, Minford, Wickens, & Xu, 2018 for comprehensive surveys of this work) to heavily dominate other non‐Bayesian methods in the small samples we typically have to deal with in open‐economy macroeconomics. When, as here, there are fundamental questions of what modelling assumptions are appropriate, and the assumptions are the very things we wish to test, Bayesian methods, which rely on generally agreed priors, cannot be used.…”

Are We Better Off Working in the Public Sector?

“…Hence, we really need to know how powerful our tests are in small samples. The evidence on this we have so far about II (see Le et al, 2016, andMeenagh et al, 2019, for recent surveys) is that it is considerably more powerful than the LR test. Furthermore, by increasing the number of "data features" to be matched its power can be increased steadily until the data features exhaust the differential implications from the model: for example, in a large macro model such as Smets and Wouters (2007) the VAR reduced form extends to some 200 coefficients and as the VAR used to describe the data is increased in size so does the power of the II Wald test.…”

“…We also know (from both Le et al, 2016 andMeenagh et al, 2019) that under this test misspecified models are rejected with high, close to 100%, probability; therefore, if the model we have tested were to be true, then other models would be rejected. Arguably, we cannot rule out the possibility that our model is somewhat false and hence that another model, also somewhat false, could also pass our test, but we leave the search for such a model for future research.…”