Econometrics

1. The file busco.prn contains data on 243 U.S. bus companies obtained from the Federal Transit Administration, National Transit Database. The variables are: tcost (the total operating expense of the company, in thousands of dollars; RVM (the total output of the firm, in thousands of revenue vehicle miles); PL (the price of driver labor in dollars per hour); PA (the price of administrative labor in dollars per hour); PM (the price of maintenance service in dollars per hour); and PF (the price of diesel fuel in dollars per gallon). Use SAS to generate new variables for the logarithms of total cost, RVM, and all four of the price variables. On the basis of the economic model of a Cobb-Douglass cost function

TC =KP(^B1sub^L)P(^B2sub^A)P(^B3sub^M)P(^B4sub^F)RVM^B5

(a) please estimate the following econometric model and write your results in equation form (please round your parameter estimates to the nearest hundredth when reporting the results):
log (tcosti) = B0 + B1logPLi +B2logPAi +B3logPMi + B4logPFi + B5logRVMi + i

(b) Economic theory suggests that if bus firms are cost-minimizers, then if all prices rise by the same percentage, then total costs should rise by the same percentage. This implies that B1 + B2 + B3 + B4 = 1. Use a 0.05 level of significance, test this null hypothesis, and state your conclusion.

(c) What are your estimates for the elasticity of costs with respect to each price? Are the estimates statistically significant? Interpret the economic significance of the coefficients that are statistically significant.

(d) The specification in (a) might not be correct if the elasticity of total costs with respect to output is not constant. Generate the quadratic term for logRVM, estimate the equation and write your results in equation form (aga in, round parameter estimates to the nearest thousandth):
log (tcosti) = a0 + a1logPLi +a2logPAi +a3logPMi + a4logPFi + a5logRVMi + a6(logRVMi)^2 + I
Test the null hypothesis that a1 + a2 + a3 + a4 = 1. Does the addition of the quadratic term to the cost function change the result? Explain.

(e) Use the results from the model estimated in part (d) and interpret the economic significance of RVM. In other words, by how much does a change in total output affect total operating expense?

(f) The R2 values in parts (a) and (d) seem suspiciously high. Should we be concerned about multicollinearity? Explain why or why not.

(g) Which model is better, the one from part (a) or the one from part (d)? Explain.