Question

To test the hypothesis that a rise in the relative price of energy leads to a decline in the productivity of capital, measured by the ratio of output to capital, the output capital ratio is regressed on labour capital ratio, the relative price of energy, and time trend (Annual data from 1950 to 1980). The result is as follows: ln(Y/K) = 1.55 + 0.72ln(L/K) – 0.11ln(Pe/P) + 0.003t + e R 2 = 0.977 (16.13) (22.59) (-6.46) (15.99) where Y = output, K = capital input, L = labor input, Pe = price index for fuel and related products, P = price deflator for output, t = time, and e = the residual. The numbers in parentheses are the t statistics. (Note that Y/K measures the productivity of capital.)

a. Do the results support the hypothesis that a rise in the relative price of energy leads to a decline in the productivity of capital?

b. Between 1972 and 1977 the relative price of energy, (Pe/P), increased by 50 percent. From the estimated equation, what is the loss in the productivity of capital (in percentage)?

c. Controlled for the changes in (L/K) and (Pe/P), what has been the annual rate of growth in the productivity of capital?

d. Interpret the coefficient of ln(L/K).

Answer 1