5 Consider the linear model logyt Beta0 xtBeta logyt1 ut

5. Consider the linear model log(yt) = Beta0 + xtBeta + log(yt1) + ut where E[ut|xt,yt1] = 0. Show that you obtain the same value of Beta whether you use lagged y (i.e., log(yt1)) or growth in y (i.e., log(yt)log(yt1)) as the dependent variable.

Solution

E[u_t|x_t,y_t1] = 0 where t=0,1,2....

that means the error in any given period does not correlated with explanatory variables in any time periods and this also implies that x is contemporaneously exogenous.

From the above we can see that x is not constant and or a linear combination of others.

Therefore we can say that we will obtain same value of B.