15.7t Consider the production function g,: f ( K i , L i )

where Q; is output, K; is capital, and L; is labor, all for the lth firm. Suppose the function /(.) is a CES or constante lasticityo f substitutionp roductionf unction.T he elasticity of substitution that we denote by

Since these equations are linear in^yr,^yz, and o, some version(s) of least squares can be used to estimate these parameters. Data on 20 firms appear in the file cespro.dat.

(a) Find separate least squares estimates of each of the first-order conditions.
Compare the two estimates of the elasticity of substitution.
Test for contemporaneous correlation between ey &nd e2;.
Estimate the two equations using generalized least squares, allowing for the existenceo f contemporaneousc orrelation.
Repeat part (c), but impose a restriction so that only one estimate of the elasticitl of substitution is obtained. (Consult your software to see how to impose such a restriction.) Comment on the results.
Compare the standard errors obtained in parts (a), (c), and (d). Do they reflect the efficiency gains that you would expect?
lf

(d) to test whether a Cobb-Douglas production function is adequate.

In(x)=12+)+ +e, where e~N (0.07) where y~N(0.0)