By Soderlind P.
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It is clear that the choice of the weighting matrix has no effect in this case O D 0 at the point estimates ˇ. O since m. y t T tD1 T 1X z t x t0 T t D1 D ˙O zx1 ˙O zy ; x t0 ˇOI V / or ! 1 T 1X zt yt T t D1 T where ˙O zx D ˙ tD1 z t x t0 =T and similarly for the other second moment matrices.
15), then there is a correlation between the residual and (some of) the regressors. 11). The vector of predetermined variables, z t , could very well include lags of y t without affecting the econometric endogeneity problem. 1 (Supply and Demand. ) Consider the simplest simultaneous equations model for supply and demand on a market. Supply is q t D p t C ust ; where A t is an observable demand shock (perhaps income). 1, then the reduced form shows that p t is correlated with ust , so we cannot hope that LS will be consistent.
For instance, we could sample the regressors and residuals independently of each other and construct an artificial sample of the dependent variable yQ t D xQ t0 ˇO C uQ t . This clearly makes sense if the residuals and regressors are independent of each other and errors are iid. In that case, the advantage of this approach is that we do not keep the regressors fixed. , and R. J. Tibshirani, 1993, An Introduction to the Bootstrap, Chapman and Hall, New York. Greene, W. , 2000, Econometric Analysis, Prentice-Hall, Upper Saddle River, New Jersey, 4th edn.