Refer to the example of the Cobb-Douglas production function discussed in class, where the GDP (Y), Total Employment (X2 ), and Stock of Fixed Capital (X3 ), are measured for the output, labor input and capital input, respectively. The following model is fitted and the R output is below. The data are yearly data from 1955 to 1974.
lnY = B1 +B2lnX2 + B3lnX3 + u
a. Interpret the coefficient estimate of B3 specific to this problem.
b. Find the rate of change of Y with respect to the change of X2 , at Y=218506.3 and X2=11152.6, and X3 = 340072.45.
c. Find the estimate of the return to scale parameter. (3 pts.)
d. Is there strong evidence that the GDP is inelastic relative to the stocks of fixed capital? Justify your answer at a=0.05.
e. Test if there is a positive (first order) autocorrelation in the error term using a=0.05 . Make sure to state the null and alternative hypotheses, to provide the values of the test statistic and the critical value(s), and to draw a conclusion. (6 pts.)
Regression output for Problem 3.
> fit<-lm(log(y) ~ log(x2) + log(x3))
> summary(fit)
Call:
lm(formula = log(y) ~ log(x2) + log(x3))
Residuals:
Min 1Q Median 3Q Max
-0.057142 -0.016250 -0.005793 0.023512 0.038739
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.65233 0.60619 -2.726 0.0144 *
log(x2) 0.33972 0.18569 1.830 0.0849 .
log(x3) 0.84600 0.09335 9.063 6.42e-08 ***
Signif. codes: 0 0.001Â 0.01 0.05Â 0.1Â 1
Residual standard error: 0.02829 on 17 degrees of freedom
Multiple R-squared: 0.9951, Adjusted R-squared: 0.9945
F-statistic: 1719 on 2 and 17 DF, p-value: < 2.2e-16
Durbin-Watson Statistic = 0.425618
