Mastering Seemingly Unrelated Regressions (SUR) in Stata: Efficiency Gains and System Estimation скачать в хорошем качестве

Mastering Seemingly Unrelated Regressions (SUR) in Stata: Efficiency Gains and System Estimation

Seemingly Unrelated Regressions (SUR), proposed by Arnold Zellner (1962), represents a system of linear equations that are statistically linked through their error structures. While individual equations may appear independent with distinct dependent and independent variables, the SUR framework assumes that the error terms are contemporaneously correlated across equations for a given observation. The primary advantage of SUR over equation-by-equation Ordinary Least Squares (OLS) is the substantial gain in estimation efficiency. By employing Feasible Generalized Least Squares (FGLS), SUR exploits the information contained in these cross-equation correlations to produce parameter estimates with smaller standard errors than those obtained via OLS. These efficiency gains are most pronounced when the correlation among residuals is high and the sets of explanatory variables differ distinctively across the equations. Conversely, if all equations share identical regressors, SUR estimates are numerically identical to OLS results. In Stata, the sureg command is the standard tool for fitting these models. The basic syntax involves specifying each equation within parentheses, such as sureg (depvar1 varlist1) (depvar2 varlist2). Stata also offers options like dfk to adjust for small-sample sizes, correcting variance estimates. A key post-estimation feature is the ability to perform joint hypothesis testing across equations using the test command, which is invaluable for validating structural economic theories. Furthermore, researchers should use the corr option to perform the Breusch-Pagan test of independence, ensuring that the cross-equation correlation is statistically significant enough to justify the use of the SUR estimator over simple OLS.