Structural Break Inference Using Information Criteria in Models Estimated by Two‐Stage Least Squares

Alastair R Hall,Denise R Osborn,Nikolaos Sakkas

doi:10.1111/jtsa.12107

Abstract

This paper makes two contributions in relation to the use of information criteria for inference on structural breaks when the coefficients of a linear model with endogenous regressors may experience multiple changes. First, we show that suitably defined information criteria yield consistent estimators of the number of breaks, when employed in the second stage of a two‐stage least squares (2SLS) procedure with breaks in the reduced form taken into account in the first stage. Second, a Monte Carlo analysis investigates the finite sample performance of a range of criteria based on Bayesian information criterion (BIC), Hannan–Quinn information criterion (HQIC) and Akaike information criterion (AIC) for equations estimated by 2SLS. Versions of the consistent criteria BIC and HQIC perform well overall when the penalty term weights estimation of each break point more heavily than estimation of each coefficient, while AIC is inconsistent and badly over‐estimates the number of true breaks.

Highlights

Information criteria (IC) are routinely employed in many contexts to select a model from a range of time-invariant linear specifications, such as selecting predictors (Pesaran and Timmermann, 1995) or specifying dynamics (Shibata, 1976; Ng and Perron, 2001)
In line with our ordinary least square (OLS) analysis in Hall et al (2013b), we find that Bayesian information criterion (BIC) and Hannan– Quinn information criterion (HQIC) perform well when combined with the higher relative weight for break estimation, and this applies in cases with both i.i.d. and positively autocorrelated disturbances
When no breaks occur in the data generating processes (DGPs) for either the structural form (SF) or reduced form (RF) equations (h D 0, m D 0), case 1 of Tables II, IV, VI and VIII show a good performance of BIC when the disturbances are i.i.d

Summary

Introduction

Information criteria (IC) are routinely employed in many contexts to select a model from a range of time-invariant linear specifications, such as selecting predictors (Pesaran and Timmermann, 1995) or specifying dynamics (Shibata, 1976; Ng and Perron, 2001) These methods are attractive to practitioners because they typically perform well, while the penalty functions on which they are based provide an intuitively attractive interpretation as a tradeoff between goodness-of-fit and the dimension of the model, both defined appropriately. Not widely used for estimation of the number of structural breaks in linear economic models, where, following the seminal studies of Andrews (1993) and Bai and Perron (1998), the predominant approach is based on the sequential application of hypothesis tests One disadvantage of such a procedure is that the resulting estimator of the number of breaks is not consistent when the tests are performed at a fixed significance level. Appropriately defined IC yield consistent estimators for the number of breaks. Yao (1988) develops a version of the criterion of Schwarz (1978) [referred to as Bayesian information criterion (BIC)] for structural break inference.

Objectives

Methods

Results

Conclusion