In a paper in 1963, Marc Nerlove analyzed a cost function for 145 American electric companies Nerlov was interested in estimating a cost function C f (Q,PL,PF,PK) where the variables are listed in the table below His data set Nerlove1963 is on the textbook website C Total Cost Q Output PL Unit price of labor PK Unit price of capital PF Unit price of fuel (a) First, estimate an unrestricted Cobb Douglass specification logC 1 2 logQ 3 logPL4 logPK 5 logPF e (9 23) Report parameter estimates and standard errors (b) What is the economic meaning of the restriction H0 3 4 5 1 (c) Estimate (9 23) by constrained least squares imposing 3 4 5 1 Report your parameter estimates and standard errors (d) Estimate (9 23) by efficient minimum distance imposing 3 4 5 1 Report your parameter estimates and standard errors (e) Test H0 3 4 5 1 using aWald statistic (f ) Test H0 3 4 5 1 using a minimum distance statistic

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Question: In a paper in 1963, Marc Nerlove analyzed a cost function for 145 American electric companies. Nerlov was interested in estimating a cost function: C

In a paper in 1963, Marc Nerlove analyzed a cost function for 145 American electric companies.

Nerlov was interested in estimating a cost function: C Æ f (Q,PL,PF,PK) where the variables are listed in the table below. His data set Nerlove1963 is on the textbook website.

C Total Cost Q Output PL Unit price of labor PK Unit price of capital PF Unit price of fuel

(a) First, estimate an unrestricted Cobb-Douglass specification logC Æ ¯1 Å¯2 logQ Å¯3 logPLÅ¯4 logPK Å¯5 logPF Åe. (9.23)

Report parameter estimates and standard errors.

(b) What is the economic meaning of the restriction H0 : ¯3 Å¯4 Å¯5 Æ 1?

(c) Estimate (9.23) by constrained least squares imposing ¯3 Å¯4 Å¯5 Æ 1. Report your parameter estimates and standard errors.

(d) Estimate (9.23) by efficient minimum distance imposing ¯3 Å¯4 Å¯5 Æ 1. Report your parameter estimates and standard errors.

(e) Test H0 : ¯3 Å¯4 Å¯5 Æ 1 using aWald statistic.

(f ) Test H0 : ¯3 Å¯4 Å¯5 Æ 1 using a minimum distance statistic.

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