Question

A "Cobb-Douglas" production function relates production () to factors of production, capital (K), labor (), and raw materials (), and an error term u using the equation = K123, where ,1,2, and 3 are production parameters. Suppose that you have data on production and the factors of production from a random sample of firms with the same Cobb-Douglas production function. (a) (5p) How would you use regression analysis to estimate the production parameters? (b) (4p) Suppose that you would like to test that there are constant returns to scale in this industry. How would you do that? (c) (3p) Is there a way to impose the constant returns to scale in estimating the production parameters?

Answer 1

Use regression analysis, specifically OLS, to estimate the Cobb-Douglas production parameters by linearizing the equation. Then test for constant returns to scale by verifying if the sum of labor and capital coefficients equals one. Finally, to enforce constant returns to scale in estimation, constrain the model before running the regression.

Step-by-step explanation:

To estimate the production parameters of a Cobb-Douglas production function using regression analysis, you would take the natural logarithm of both sides of the production function to linearize the equation. This results in a linear equation of the form ln(Y) = ln(A) + α1*ln(L) + α2*ln(K) + α3*ln(M) + u, which allows the parameters to be estimated using ordinary least squares (OLS) regression.

In order to estimate the production parameters of the Cobb-Douglas production function, regression analysis can be used. Regression analysis involves fitting a statistical model to the data and estimating the parameters of the model. In this case, we would use the production data and factors of production data from the sample of firms to estimate the parameters α, 1, 2, and 3 in the production function equation Q = KαL1L2L3.

For constant returns to scale, we test if the sum of the estimated parameters of labor and capital equals one (α1 + α2 = 1). We perform a hypothesis test, usually an F-test, to determine if there is evidence against the hypothesis of constant returns to scale.

To impose the constant returns to scale while estimating the production parameters, you can constrain the model by setting α1 + α2 = 1 directly and then running the regression to estimate the parameters of the constrained model accordingly.