Instrumental Variable Estimation of Autoregressive Models

Abstract

In this paper, we propose a new instrumental variables estimator for autoregressive (AR) models, including univariate and vector autoregressive models with an intercept and/or time trend. The new estimator has two distinct features. First, to remove deterministic terms, such as the intercept and/or time trend, we apply an upper triangular GLS transformation, which is often used in panel data analysis. Second, we propose using lagged variables and deterministic terms in the model as instruments. Although the deterministic terms are irrelevant instruments, we demonstrate that (sometimes substantially) irrelevant instruments enhance the strength of instruments in terms of a concentration parameter. We then show that the proposed estimator has the same asymptotic distribution as the OLS estimator. A Monte Carlo simulation is carried out to investigate the finite sample performance of the estimator, revealing that the proposed estimator performs better than does the OLS estimator in finite samples. The improvement is substantial when persistency is strong and a time trend is included. In addition, as a by-product of using instrumental variables, we are able to conduct a Sargan test as a specification test. The performance of Sargan test is also investigated by simulation and is shown to perform well.