RDP 9612: External Influences on Output: An Industry Analysis Appendix B: Estimation Methodology for the Error-Correction Equations

The error-correction equations are estimated using the Seemingly Unrelated Regression (SURE) technique, a systems form of estimation which makes use of the cross-correlation of error terms in the equations to obtain more precise coefficient estimates. With the data set at hand, there is a strong expectation that ‘shocks’ to sectoral output are highly correlated. For example, a tightening of monetary policy would enter Equation (1) in the text as a shock but this would most likely be felt in all sectors. Similarly, a technological shock would most likely be experienced by a number of manufacturing sub-sectors, rather than be isolated to just one sub-sector. While equations estimated by OLS are consistent and unbiased, efficiency is improved by SURE estimation and making use of the contemporary correlation of the residuals of the equations. The downside is that precious degrees of freedom are lost in calculating the covariance matrix of residuals of the OLS equations. Our judgment is that using SURE substantially increases the efficiency of the estimates: as shown in Tables B.1 and B.2, correlations between the residuals of the OLS equations at the one and two-digit levels, respectively, are often high and significant. Accordingly, the standard errors of the SURE estimates tend to be substantially smaller than those of the OLS estimates, presented in Table B.3. Whatever the case, the interpretation does not change qualitatively between the two methods.