## Info

'Obtained from the regression Yt = ß0 + ß1Xt + ut.

'Obtained from the regression Yt = ß0 + ß1Xt + ut.

a. Use the Cochrane-Orcutt two-stage procedure and obtain the estimates of the feasible GLS or the generalized difference regression and compare your results.

b. If the p estimated from the Cochrane-Orcutt method in a differs substantially from that estimated from the d statistic, which method of estimating p would you choose and why?

12.29. Refer to Example 7.4. Omitting the variables X2 and X3, run the regression and examine the residuals for "serial'' correlation. If serial correlation is found, how would you rationalize it? What remedial measures would you suggest?

12.30. Refer to exercise 7.21. A priori autocorrelation is expected in such data. Therefore, it is suggested that you regress the log of real money supply on the logs of real national income and long-term interest rate in the first-difference form. Run this regression, and then rerun the regression in the original form. Is the assumption underlying the first-difference transformation satisfied? If not, what kinds of biases are likely to result from such a transformation? Illustrate with the data at hand.

12.31. The use of Durbin-Watson d for testing nonlinearity. Continue with exercise 12.29. Arrange the residuals obtained in that regression according to increasing values of X. Using the formula given in (12.6.5), estimate d from the rearranged residuals. If the computed d value indicates autocorrelation, this would imply that the linear model was incorrect and that the full model should include Xi2 and Xi3 terms. Can you give an intuitive justification for such a procedure? See if your answer agrees with that given by Henri Theil.*

Henri Theil, Introduction to Econometrics, Prentice Hall, Englewood Cliffs, N.J., 1978, pp. 307-308.

CHAPTER TWELVE: AUTOCORRELATION 5G1

12.32. Refer to exercise 11.22. Obtain the residuals and find out if there is autocorrelation in the residuals. How would you transform the data in case serial correlation is detected? What is the meaning of serial correlation in the present instance?

12.33. Monte Carlo experiment. Refer to Tables 12.1 and 12.2. Using st and Xt data given there, generate a sample of 10 Y values from the model

Yt = 3.0 + 0.5 Xt + ut where ut = 0.9ut—1 + st. Assume u0 = 10.

a. Estimate the equation and comment on your results.

b. Now assume u0 = 17. Repeat this exercise 10 times and comment on the results.

c. Keep the preceding setup intact except now let p = 0.3 instead of p = 0.9 and compare your results with those given in b.

12.34. Using the data given in Table 12.9, estimate the model

Yt = fa + fa Xt + ut where Y = inventories and X = sales, both measured in billions of dollars.

TABLE 12.9 INVENTORIES AND SALES IN U.S. MANUFACTURING, 1950-1991 (Millions of Dollars)

Year

Sales*

Inventories1"

Year

Sales*

Inventories1