In a study of the production function of the United Kingdom bricks, pottery, glass, and cement industry for the period 1961 to 1981, R. Leighton Thomas obtained the following results:
1. log Q = - 5.04 + 0.887 log K + 0.893 log H
se = (1.40) (0.087) (0.137) R2 = 0.878
2. log Q = - 8.57 + 0.0272J + 0.460 log K + 1.285 log H
se = (2.99) (0.0204) (0.333) (0.324) R2 = 0.889
where
Q = the index of production at constant factor cost
K = the gross capital stock at 1975 replacement cost
H = hours worked
t = the time trend, a proxy for technology
The figures in parentheses are the estimated standard errors.
a. Interpret both regressions.
b. In regression (1) verify that each partial slope coefficient is statistically significant at the 5% level.
c. In regression (2) verify that the coefficients of t and log K are individually insignificant at the 5% level.
d. What might account for the insignificance of log K variable in Model 2?
e. If you were told that the correlation coefficient between t and log K is 0.980, what conclusion would you draw?
f. Even if t and log K are individually insignificant in Model 2, would you accept or reject the hypothesis that in Model 2 all partial slopes are simultaneously equal to zero? Which test would you use?
g. In Model 1, what are the returns to scale?