Estimating a non-minimum cost function for hospitals: reply.

• Author: Eakin, B. Kelly
• Position: Response to Scott E. Atkinson and Robert Halvorsen, Southern Economic Journal, p. 1114, April 1992

1. Introduction

   There were typographical errors in equations (18), (19), (27), and (28) in the theoretical section of our original manuscript [5]. The corrected equations are (18) [Mathematical Expression Omitted] (19) [Mathematical Expression Omitted] (27) [Mathematical Expression Omitted] (28) [Mathematical Expression Omitted] where T [Mathematical Expression Omitted] There were no programming errors and all estimates we reported in our original paper [5] are unchanged.

   In what follows, we clarify three issues--that

   1. If the shadow price of the ith input exceeds its market price [Mathematical Expression Omitted

      then there is relative underemploymentof the ith input [X.sub.i];

   2. If any [Mathematical Expression Omitted then there is empirical allocative inefficiency; and

   3. if [Mathematical Expression Omitted] = [[Theta].sub.i] = 0 then there is conditional efficient

      employment of input [X.sub.i] Our first two points should rectify possible confusion over the roles of absolute versus relative input prices in the non-minimum cost function. Our third point refines the concept of conditional efficient employment of an input.

2. Relative Underemployment of an Input

   Empirical inefficiency first appeared in the Cobb-Douglas profit function of Lau and Yotopolus [6].Toda [10] modeled non-minimization of quadratic average cost. Eight years later Atkinson and Halvorsen [1] adopted Toda's approach in using a translog shadow cost function to investigate possible Averch-Johnson [2] overcapitalization in regulated electric power generation. The model use in [5] resembles the Atkinson and Halvorsen model with two differences. First, we choose an additive ([W.sub.i] + [[Theta].sub.i]) rather than a multiplicative [[Theta].sub.i] [W.sub.i]) parameterization of shadow input prices and second, we model a multiproduct firm and consequently choose a hybrid-translog multiproduct shadow-cost function that permits some outputs to be zero.

   We emphasize that when using an estimated cost function to discuss economic efficiency over- or underemployment of an input is both conditional on the levels of the other inputs and is relative to the numeraire input. In our earlier paper [5] the estimated shadow price of capital ([kappa]) was below the observed price, [[Theta] [caret].sub.k] < 0, and the estimated shadow price of physicians' services (d) was above the observed price [[Theta] [caret].sub.d] > 0, while equality between the shadow and the observed prices of...