# Estimating Break Points in Linear Models: A GMM Approach

Odaro Augustine-Ohwo

Research output: ThesisDoctoral Thesis

The University of ManchesterOdaro Augustine-OhwoDoctor of Philosophy in EconomicsBreak Point Estimation In Linear Models: A GMM Approach2015\end{center}In estimating econometric time series models, it is assumed that the parameters remain constant over the period examined.This assumption may not always be valid when using data which span an extended period, as the underlying relationships between the variables in these models are exposed to various exogenous shifts.It is therefore imperative to examine the stability of models as failure to identify any changes could result in wrong predictions or inappropriate policy recommendations.This research proposes a method of estimating the location of break points in linear econometric models with endogenous regressors, estimated using Generalised Method of Moments (GMM).The proposed estimation method is based on Wald, Lagrange Multiplier and Difference type test statistics of parameter variation.In this study, the equation which sets out the relationship between the endogenous regressor and the instruments is referred to as the Jacobian Equation (JE).The thesis is presented along two main categories: Stable JE and Unstable JE.Under the Stable JE, models with a single and multiple breaks in the Structural Equation (SE) are examined.The break fraction estimators obtained are shown to be consistent for the true break fraction in the model.Additionally, using the fixed break approach, their $T$-convergence rates are established. Monte Carlo simulations which support the asymptotic properties are presented.Two main types of Unstable JE models are considered: a model with a single break only in the JE and another with a break in both the JE and SE.The asymptotic properties of the estimators obtained from these models are intractable under the fixed break approach, hence the thesis provides essential steps towards establishing the properties using the shrinking breaks approach.Nonetheless, a series of Monte Carlo simulations conducted provide strong support for the consistency of the break fraction estimators under the Unstable JE.A combined procedure for testing and estimating significant break points is detailed in the thesis.This method yields a consistent estimator of the true number of breaks in the model, as well as their locations.Lastly, an empirical application of the proposed methodology is presented using the New Keynesian Phillips Curve (NKPC) model for U.S. data.A previous study has found this NKPC model is unstable, having two endogenous regressors with Unstable JE.Using the combined testing and estimation approach, similar break points were estimated at 1975:2 and 1981:1.Therefore, using the GMM estimation approach proposed in this study, the presence of a Stable or Unstable JE does not affect estimations of breaks in the SE.A researcher can focus directly on estimating potential break points in the SE without having to pre-estimate the breaks in the JE, as is currently performed using Two Stage Least Squares.