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### Abstract

It is well recognized that the statistical reliability of the conventional method of estimating the effects of technological change on producer welfare is often quite poor. I present a method that enhances the statistical reliability of such estimates. I emphasize that when measuring the welfare effects of technological change, valuable information can be gleaned from data on input prices and quantities. This type of data is often available, but the conventional measure typically does not take full advantage of its availability.
Letting T0 be some initial level of technology and T1 be a subsequent level, the conventional measure of producer welfare change due to a technology change is the change in the “triangle” area under the price and behind the supply curve. The change in welfare is measured as the difference in the producer surpluses under the two (price, technology) scenarios. Attempts to this measure to gauge the producer welfare effects of changes in technology date back to Griliches’s (1957, 1958) studies of the economics of hybrid corn technology. Since then, scores of articles have reported estimates of the costs and returns of research and resultant technology change. The conventional method of estimation of the producer welfare effects of a technology change is burdened by a well-recognized difficulty: the method usually requires extrapolation of the econometric estimation of the supply function to regions outside the range the data (Scobie 1976; Lindner and Jarett 1978; Rose 1980; Voon and Edwards 1991). There is a large and involved literature discussing how supply should be assumed to shift, whether in a parallel, pivotal, or some other fashion. Strong critiques about the dependence of producer welfare measures on assumptions about supply shifts have appeared in the literature. The assumed functional form of the supply curve is of ultimate importance in the conventional measure of producer welfare change. It easily may be the case that an assumed functional form fits the data well locally, i.e., in its range, and therefore passes all goodness-of-fit statistical tests, but that the estimate is poor globally. If the global fit is poor, then the estimate using the conventional measure of welfare change is likely to be poor.
In the following, I derive and discuss a new measure of the change in producer welfare due to technology change. The measure does not generally require estimation of the supply curve far beyond the range of the data, and therefore when using this new measure, increased statistical confidence can be placed on the estimation of the change in producer welfare. The key to the new method is to use data from input markets in the measurement of producer welfare change. Since a supply curve reflects marginal costs of production, it is natural to take advantage of available data by estimating input costs in input markets, instead of ignoring input market data and attempting to measure input costs in the output market. By making use of input market data, the new measure can help solve this problem. The new measure finds cost changes not by integrating behind supply curves, but rather by examining “rectangles” associated with input demand curves and output supply curves. The bases of such rectangles require estimation of “K-shifts” in input demand and output supply. In the conventional method, only the K-shift in output supply need be estimated. But, if data from input markets is available, and reasonable estimates of the input demand shifts are obtainable, the new measure can ameliorate the statistical unreliability endemic in the conventional measure’s literature.
To demonstrate potential benefits of the new measure of producer welfare change I present results from a Monte Carlo simulation. At the beginning of each Monte Carlo run, one hundred “firms” were created by drawing values of the production coefficient vectors b1, … , b100. This defined one hundred production functions, firm input demand functions, and firm supply functions. In each run, market prices and quantities were determined in two equilibria, each under a different level of technology. Each run created a simulated “data set” with forty observations. Taking on the role of a researcher having access to the run’s data set, but not knowing the true model that generated it, I assumed the linear functional forms for supplies and demands, and estimated the coefficients. Then I measured the true change in profits and the estimated change in profits caused by the technological change, first by using the model’s true supply and demand functions, and then using its estimated supply and demand functions. Both the conventional measure and the new measure were used, and then the differences between the true change in profits and the estimated change in profits were calculated for both measures, in order to compare the statistical reliability of each. In every Monte Carlo run, as expected, when the true supply and demand functions were used, the change of profits was calculated exactly using the conventional measure or the new measure. But when the estimated functions were used, the mistaken assumptions about global functional form caused much smaller errors in estimation when the new measure was used than when the traditional measure was used. The (true) baseline profits for the first Monte Carlo run can be calculated directly or as a change in producer surplus as measured behind the baseline true supply curves, or by using the new measure with the true curves. As expected, the statistical reliability of the new measure was shown to be much greater than the statistical reliability of the conventional measure.