On Wed, 4 Apr 2012, Daniel Bencik wrote: Precisely because you're assuming these two variables are cointegrated. I'm appending an illustrative script below. fcast, using the estimation range. They apply to the differenced series. <hansl> /* script to illustrate the point that a VECM that omits an unrestricted exogenous driver may forecast the difference between two cointegrated variables just as well as a model that includes the exogenous driver (and therefore produces a better fit for the levels of the cointegrated series) */ nulldata 200 setobs 4 1960:1 set seed 9756421 set echo off set messages off # generate cointegrated data series x = 3*uniform() series y1 = cum(normal() + x) series y2 = y1 + normal() # verify that cointegrating rank = 1 coint2 1 y1 y2 ; x # create first differences for OLS below diff y1 y2 # leave an out-of-sample period smpl ; -8 # VECM omitting x vecm 1 1 y1 y2 --silent fcast 2008:1 2009:4 --quiet matrix fcdiff1 = $fcast[,1] - $fcast[,2] series EC = $ec ols d_y1 0 EC --quiet R2_11 = $rsq ols d_y2 0 EC --quiet R2_12 = $rsq # VECM including x vecm 1 1 y1 y2 ; x --silent fcast 2008:1 2009:4 --quiet matrix fcdiff2 = $fcast[,1] - $fcast[,2] series EC = $ec ols d_y1 0 EC x --quiet R2_21 = $rsq ols d_y2 0 EC x --quiet R2_22 = $rsq # get forecast statistics for y1 - y2 smpl 2008:1 2009:4 matrix ydiff = {y1} - {y2} matrix fs1 = fcstats(ydiff, fcdiff1) matrix fs2 = fcstats(ydiff, fcdiff2) printf "\nVECM omitting x:\n" printf " R^2 for d_y1 = %.4f, for d_y2 = %.4f\n", R2_11, R2_12 printf " Out-of-sample forecast MSE = %g\n", fs1[2] printf "\nVECM including x:\n" printf " R^2 for d_y1 = %.4f, for d_y2 = %.4f\n", R2_21, R2_22 printf " Out-of-sample forecast MSE = %g\n\n", fs2[2] </hansl> Running the above script gives: VECM omitting x: R^2 for d_y1 = 0.0044, for d_y2 = 0.3387 Out-of-sample forecast MSE = 0.967382 VECM including x: R^2 for d_y1 = 0.4567, for d_y2 = 0.5582 Out-of-sample forecast MSE = 0.982461 Allin Cottrell