144 CHAPTER | 5 Cost Models TABLE 5.3 Nerlove Original Data and Cost Model (Cobb­Douglas) Variable Constant (ln of) Y lnpl ­ lnpf [or ln(pl/pf)] lnpk ­ lnpf [or ln(pk/pf)] Parameter 0 y (lnY) 1 (lnplpf) 2 (lnpkpf) Adjusted R 2 Nerlove Model: Estimate a -4.6908 0.72069 0.59291 -0.00738 0.93 Nerlove Model: t Statistic -5.301 41.334 2.898 -0.039 a Reestimated using Nerlove (1955) data. b. What do you notice about the estimated parameters from Nerlove's log linear Cobb­Douglas specification? Do they seem reasonable? c. What do results from the Nerlove specification (log-linear Cobb­Douglas form) indicate in terms of returns to scale? 2. Table 5.3 contains results from Nerlove's original model specification. His data set contained data on total costs, output (in kilowatt hours), and prices of labor ( pl), capital ( pk), and fuel (pf ) for 145 electric utility companies in 1955. a. What do you notice about the results? b. What do they imply about returns to scale? FLEXIBLE FUNCTIONAL FORMS In addition to the previously mentioned properties, a cost function should be flexible enough so as not to restrict the substitution elasticities between inputs. The Cobb­Douglas form restricts these substitution elasticities to equal unity, and the CES function imposes that the elasticities of substitution not vary across observations. While the Leontief form provides the flexibility required, its implication that the marginal productivity of any factor is zero is troubling. As a result, many studies employ the translogarithmic functional form, which is flexible enough to allow the substitution elasticities to vary across observa- tions and conforms easily to meet many (but not all) of the qualifications of a proper cost function. TRANSLOGARITHMIC COST FUNCTION The translogarithmic (translog) function is a second-order Taylor's series approximation to any arbitrary cost function. Christensen and Greene (1976) employed this cost specification when they reexamined Nerlove's cost model.