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

 Variable Coefficient Std. Error t-Statistic Prob. C -6.137282 8.528957 -0.719582 0.4801 Q(1) 6.329580 1.439842 4.396024 0.0003 P -1.665309 1.370766 -1.214875 0.2386 R-squared 0.616110 Mean dependent var 8.900000 Adjusted R-squared 0.577721 S. D. dependent var 21.37086 S. E. of regression 13.88743 Akaike info criterion 5.383075 Sum squared resid 3857.212 Schwarz criterion 5.531183 Log likelihood 91.54095 F-statistic 16.04912 Durbin-Watson stat 1.066618 Prob(F-statistic) 0.000070

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

 Variable Coefficient Std. Error t-Statistic Prob. C -4.953720 8.350094 -0.593253 0.5600 Q(1) 1.030343 1.442030 0.714509 0.4836 P 0.487511 1.303845 0.373903 0.7126 RESID (-1) 0.445119 0.224743 1.980572 0.0623

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

 Variable Coefficient Std. Error t-Statistic Prob. C -7.315299 7.921839 -0.923435 0.3674 Q(1) 5.905362 1.362572 4.333981 0.0004 P -1.246799 1.277783 -0.975752 0.3414 AR(1) -0.027115 0.014118 -1.920591 0.0699

 R-squared 0.677654 Mean dependent var 8.900000 Adjusted R-squared 0.626757 S. D. dependent var 21.37086 S. E. of regression 13.0562 Akaike info criterion 5.295301 Sum squared resid 3238.84 Schwarz criterion 5.492779 Log likelihood -89.5315 F-statistic 13.31429 Durbin-Watson stat 1.60964 Prob (F-statistic) 0.000065 Inverted AR Roots -0.03
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