Springer Texts in Business and Economics

Using EViews, Qt+i is simply Q(1) and one can set the sample range from 1954-1976

a. The OLS regression over the period 1954-1976 yields RSt = -6.14 + 6.33 Qt+1 - 1.67 Pt

(8.53) (1.44) (1.37)

with R2 = 0.62 and D. W. = 1.07. The t-statistic for у = 0 yields

t = -1.67/1.37 = -1.21 which is insignificant with a p-value of 0.24.

Therefore, the inflation rate is insignificant in explaining real stock returns.

LS // Dependent Variable is RS Sample: 1954 1976 Included observations: 23

b. The D. W. = 1.07. for n = 23 and two slope coefficients, the 5% critical

values of the D. W. are dL = 1.17 and dU = 1.54. Since 1.07 < dL, this

indicates the presence of positive serial correlation.

c. The Breusch and Godfrey test for first-order serial correlation runs the regression of OLS residuals et on the regressors in the model and et_i. This yields

et = -4.95 + 1.03 Qt+1 + 0.49 Pt + 0.45 et_

(8.35) (1.44) (1.30) (0.22)

with R2 = 0.171 and n = 23. The LM statistic is nR2 which yields 3.94. This distributed as x1 under the null hypothesis and has a p-value of 0.047. This is significant at the 5% level and indicates the presence of first-order serial correlation.

Breusch-Godfrey Serial Correlation LM Test:

F-statistic 3.922666 Probability 0.062305

Obs* R-squared 3.935900 Probability 0.047266

Test Equation:

LS // Dependent Variable is RESID

d. The Cochrane-Orcutt yields the following regression RS* = - 14.19 + 7.47 Q* , - 0.92 P*

(9.34) (1.20) + 1 (1.63)

where RS* = RSt — pRSt_1, Qt*+1 = Qt+1 — pQt and Pt* = Pt — pPt_1 with

Pco = 0.387.

e. The AR(1) options on EViews yields the following results:

RSt = —7.32 + 5.91 Qt+1 — 1.25 Pt

(7.92) (1.36) (1.28)

with R2 = 0.68. The estimate of p is p = —0.027 with a standard error of 0.014 and a t-statistic for p = 0 of —1.92. This has a p-value of 0.07. Note that even after correcting for serial correlation, Pt remains insignificant while Qt+1 remains significant. The estimates as well as their standard errors are affected by the correction for serial correlation. Compare with part (a).

PRAIS-WINSTEN PROCEDURE

LS // Dependent Variable is RS Sample: 1954 1976 Included observations:23 Convergence achieved after 4 iterations