Testing for Structural Instability in Moment Restriction Models: An Info-Metric Approach

Abstract

In this paper, we develop an info-metric framework for testing hypotheses about structural instability in nonlinear, dynamic models estimated from the information in population moment conditions. Our methods are designed to distinguish between three states of the world: (i) the model is structurally stable in the sense that the population moment condition holds at the same parameter value throughout the sample; (ii) the model parameters change at some point in the sample but otherwise the model is correctly specified; and (iii) the model exhibits more general forms of instability than a single shift in the parameters. An advantage of the info-metric approach is that the null hypotheses concerned are formulated in terms of distances between various choices of probability measures constrained to satisfy (i) and (ii), and the empirical measure of the sample. Under the alternative hypotheses considered, the model is assumed to exhibit structural instability at a single point in the sample, referred to as the break point; our analysis allows for the break point to be either fixed a priori or treated as occuring at some unknown point within a certain fraction of the sample. We propose various test statistics that can be thought of as sample analogs of the distances described above, and derive their limiting distributions under the appropriate null hypothesis. The limiting distributions of our statistics are nonstandard but coincide with various distributions that arise in the literature on structural instability testing within the Generalized Method of Moments framework. A small simulation study illustrates the finite sample performance of our test statistics.

Econometricians Have Their Moments: GMM at 32

“…For example, Hall et al . () find that how is chosen has a substantial effect on the behaviour of sup‐type structural stability tests based on IM/GEL estimators, and renders inferences based on these tests markedly less reliable than their GMM counterparts.…”

“…60 However, the need to select the bandwidth during the optimisation can severely complicate the computations, and also impact on the reliability of subsequent inferences. For example, Hall et al (2015) find that how b T is chosen has a substantial effect on the behaviour of sup-type structural stability tests based on IM/ GEL estimators, and renders inferences based on these tests markedly less reliable than their GMM counterparts.…”

Structural change tests for GEL criteria

“…The Pearson-type tests are easily computed and have a nice intuitive interpretation. Recently, Hall et al (2011) propose Andrews-based tests but derived from an information-metric perspective.…”

A multifactor transformed diffusion model with applications to VIX and VIX futures

“…See, for example, Racine (2002, 2008),Hall et al (2015) for more examples of the informationtheoretical approach for testing model speci…cations.…”