4. Examine whether the following statements are true or false. Give an expla- nation. (a) Serial correlation in the errors u leads to biased estimates and biased standard errors when the regression equation y 3x + u is estimated by ordinary least squares. (b) The Durbin-Watson test for serial correlation is not applicable if the errors are heteroskedastic. (c) The Durbin-Watson test for serial correlation is not applicable if there are lagged dependent variables as explanatory variables. (d) An investigator estimating a demand function in levels and first differ- ences obtained R2's of 0.90 and 0.80, respectively. He chose the equa- tion in levels because he got a higher R. This is a valid reason for choosing between the two models. (e) Least squares techniques when applied to economic time-series data usually yield biased estimates because many economic time series are autocorrelated. (f) The Durbin-Watson test can be used to describe whether the errors in a regression equation based on time-series data are serially inde- pendent. (g) The fact that the Durbin-Watson statistic is significant does not nec- essarily mean that there is serial correlation in the errors. One has to apply some other tests to come to this conclusion. (h) Consider the model y, ay- + Bx, + u, where the errors are au- toregressive. Even if the OLS method gives inconsistent estimates of the parameters, we can still use the equation for purposes of predic- tion if the evolution of x, during the prediction period is the same as in the estimation period. (i) Consider the model y = a + x + u, u = pu_ + e 0p 1 e, are IN(0, ). By regressing Ay, on Ax,, it is possible to get more efficient estimates of 3 than by regressing y, on x. (j) The Durbin-Watson test is a useless test because it is inapplicable in almost every situation that we encounter in practice.