An important objective of structural macroeconomic models is to characterize deep structural relationships that are invariant to changes in the distribution of the data. The parameters of such models admit a structural interpretation and are assumed to be stable over time. Models that do not possess that property are subject to the well-known Lucas (1976) critique. Lucas (1976) pointed out that econometric models will break down when the underlying economic environment changes, for example because of policy shifts, unless these models adequately account for agents’ reaction to these changes. In econometric terms, the parameters of models that are immune to the Lucas critique should remain invariant to exogenous changes in the data generating process.
The contribution of this paper is twofold. First, we show that stability restrictions (i.e., immunity to the Lucas critique) constitute an important and powerful source of identification in Euler equation models. The key insight is that changes in the distribution of the data induced by, for example, policy regime shifts, provide additional exogenous variation that can be usefully exploited for inference. The usual estimation approach relies only on the identifying assumption that certain moment restrictions hold on average over the full sample, and this ignores subsample variation in the data. We show that this approach can only be justified when there are no changes in the data generating process. We think this assumption is too strong in many context, especially in macroeconomics, where there is considerable evidence of parameter instability, see, for example, Stock and Watson (1996), Clarida, Gal?, and Gertler (2000) and Sims and Zha (2006). So, we expect a priori that the information contained in stability restrictions will be nontrivial, and our applications confirm this empirically.
It is common practice to use stability restrictions exclusively for post-estimation misspecification testing by means of the various parameter stability or structural change tests, that have been proposed in the literature, see Andrews (1993), Andrews and Ploberger (1994), Elliott and Mueller (2006), or Perron (2005) and the references therein. When the null hypothesis of parameter stability is rejected, the Lucas critique applies and the validity of the model is put into question. Thus, to the best of our knowledge, stability restrictions are being used exclusively to detect weaknesses of a model. We show that this approach does not make efficient use of the information in the data, and we propose instead to use stability restrictions constructively in order to sharpen inference on the parameters of the model.
The second contribution of this paper is to propose econometric tools that can be used to extract the information in the stability restrictions for structural inference. The methods we propose require only mild assumptions about the nature of instability in the distribution of the data. It should be stressed that these assumptions are weaker than those needed to justify the standard parameter stability tests mentioned above, and therefore the scope of the proposed methods is very wide. Specifically, they do not require any assumptions about identification of the structural parameters, nor any prior knowledge about the incidence, number and timing of breaks in reduced-form parameters. Our analysis is carried out in the framework of the Generalized Method of Moments (GMM), which is suitable for estimating Euler equation models. Our proposed methods can be used to obtain confidence sets for the structural parameters that have the interpretation that they contain all the values of the parameters (i.e., all possible ‘structures’) for which the model’s identifying restrictions hold in every subsample and the model is immune to the Lucas critique.
We examine the empirical relevance of the proposed methods by applying them to two equations that form the core of the new Keynesian macroeconomic policy model: the new Keynesian Phillips curve, and the Euler equation for output, which is sometimes also referred to as the new Keynesian IS curve. These models are well-known to suffer from problems of weak instruments, see Kleibergen and Mavroeidis (2009) and Fuhrer and Rudebusch (2004) for the inflation and output models, respectively. The parameter that is typically most difficult to estimate accurately is the coefficient that governs the degree of forward-looking behavior, or rational versus adaptive expectations. Identification-robust 90% confidence intervals for this parameter that use only full-sample information contain the entire parameter space. However, using methods that exploit the stability restrictions, we find that the confidence sets on the parameters become smaller, and these results are robust to alternative datasets and sample periods. Moreover, the results indicate that the most commonly used versions of the models are immune to the Lucas critique.
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Identifying Euler equation models via stability restrictions
