Substitution between energy and non-energy inputs in the Netherlands, 1950-1974

This paper seeks to estimate factor demand relations in a three factor demand model that allows for considerable freedom in the variation of the substitution parameters. Our starting point is a twice differentiable aggregate production function Y = F[,L,E.M,A1 which relates gross output Y to the services of capital (K), labor(L), energy (E), and all other materials (M). A is a technology index. Under certain conditions this function can be written Y = F1EH(K'L' E ' M ' A 2] . For purposes of estimation we choose a specific functional form for H, viz. the Generalized Cobb-Douglas (GCD) function developed by Diewert. Further restrictions of constant returns and Hicks neutrality are needed to arrive at Y = F2!['.L‘..f(K ' L ' E) ' M,A2] where f also is a GCD function. We are concerned with estimating the function k(K,L,E). Direct estimation of f is however impossible, since the value of f cannot be observed. This difficulty is solved by using the duality relationship between cost and production functions (Shephard, Arrow, Diewert). Application of Shephard's lemma leads to the following system that is linear in the unknown parameters: . (i=1,2,3), Y1 where the yi are cost shares, (pik is a function of the prices, and 13ik are the parameters to be estimated. A major problem has been to collect adequate data on factor prices. Especially the price index of capital services, which is based on Christensen and Jorgenson, can easily be challanged. We fit the model to data for the Dutch enterprise sector, 1950-1974, and find that energy and labor are substitutes, and energy and capital complements (after 1960). This justifies the inclusion of energy as a seperate input in the production function. The results can be used to assess the effect of energy price changes on energy use and total output. SUBSTITUTION BETWEEN ENERGY AND NON-ENERGY INPUTS IN THE NETHERLANDS 1950 - 1974 +)