nergy prices and capital formation: United States, 1948-1978. To test the hypothesis that a rise in the price of energy relative to output leads to a decline in the productivity of existing capital and labor resources, John A. Tatom estimated the following production function for the United States for the quarterly period 1948-I to 1978-II*:
ln ( y/k) = 1.5492 + 0.7135 ln (h/k) - 0.1081 ln (Pe/P) (16.33) (21.69) (-6.42)+ 0.0045t R2 = 0.98 (15.86)
where y = real output in the private business sector
k = a measure of the ?ow of capital services
h = person hours in the private business sector
Pe = producer price index for fuel and related products
P = private business sector price de?ator
t = time.
The numbers in parentheses are t statistics.
a. Do the results support the author's hypothesis?
b. Between 1972 and 1977 the relative price of energy, (Pe/P), increased by 60 percent. From the estimated regression, what is the loss in productivity?
c. After allowing for the changes in (h/k) and (Pe/P), what has been the trend rate of growth of productivity over the sample period?
d. How would you interpret the coef?cient value of 0.7135?
e. Does the fact that each estimated partial slope coef?cient is individu- ally statistically signi?cant (why?) mean we can reject the hypothesis that R2 = 0? Why or why not?