Specification and Estimation of the Sur Equation Model with First-Order Autoregressive Errors

This paper addresses the specification and estimation of the Seemingly Unrelated Regressions (SUR) model when the error terms exhibit first-order autocorrelation (AR(1)). The standard SUR framework, while effectively handling contemporaneous correlation across equations, assumes serially uncorrelated disturbances. This assumption is often violated in economic and financial time-series data, leading to inefficient parameter estimates if not properly addressed. We develop and implement a feasible generalized least squares (FGLS) estimation procedure tailored for the SUR-AR(1) model. The methodology involves a multi-step process: initial estimation of the individual equation autoregressive parameters (ρi​), transformation of the data to correct for serial correlation, and subsequent application of the SUR technique to the transformed model to account for contemporaneous correlation. Through Monte Carlo simulations, we demonstrate that this estimator is consistent and significantly more efficient than both equation-by-equation Ordinary Least Squares (OLS) and the traditional SUR model under conditions of first-order serial correlation. The practical application of the proposed model is illustrated with an empirical example, confirming its superiority in producing reliable and efficient estimates in real-world scenarios. Keywords: Seemingly Unrelated Regressions (SUR), First-Order Autocorrelation, AR(1) Errors, Feasible Generalized Least Squares (FGLS), Serial Correlation, Contemporaneous Correlation, Monte Carlo Simulation.