IN recent years, economists have shown a lively and growing interest in the factors determining how rapidly a new technique is substituted for older methods. This rate of substitution, or rate of diffusion, merits such attention because it determines how rapidly productivity rises in response to the new technique. The full social benefits from the innovation will not be realized if the diffusion process goes on too slowly.' This paper for the first time studies the intrafirm rate of diffusion the rate at which a particular firm, once it has begun to use a new technique, proceeds to substitute it for older methods.2 Once they become familiar with an innovation, some firms abandon the older technology and replace it very quickly with the new. Others are much slower to make the transition. Given that a firm has begun to use a new type of equipment, what determines how rapidly it goes on to substitute it for an older type? To help answer this question, we single out one of the most significant innovations that occurred in the interwar period the diesel locomotive. We construct and test an econometric model to help explain differences among railroads in the rate at which, once they had begun to dieselize, they substituted diesel motive power for steam. Although this model is rough and over-simplified, it seems to stand up quite well; and with appropriate modification, it is likely to prove useful for other innovations as well.3 * The work on which this report is based is part of a larger project on industrial research and technical change supported by a grant from the National Science Foundation, by research funds of the Graduate School of Industrial Administration at Carnegie Institute of Technology, by a contract with the Office of Special Studies of the National Science Foundation, by a Ford Foundation Faculty Research Fellowship, and by the Cowles Foundation for Research in Economics at Yale University. It will be reprinted as a Cowles Foundation Paper. I am particularly indebted to K. Healy, whose comments on an earlier draft eliminated several errors. In addition, the paper has benefited from discussions with various colleagues, particularly A. Meltzer, J. Muth, R. Nelson, and N. Seeber. My thanks also go to G. Haines and D. Remington for their assistance and to the many people in the railroad and related industries who provided information. 1 It seems obvious that productivity in an industry can be regarded as a weighted average of the productivity with the old technique and the productivity with the new, the weights reflecting the extent to which the new technique has replaced the old. (Whether one has in mind labor, capital, or total productivity is irrelevant, although it affects the sort of weights one would use.) Thus, if the productivity with the new technique exceeds that with the old, productivity in the industry will rise as the new technique is substituted for the old. The rate at which it rises depends clearly on the rate of diffusion. And if the diffusion process goes on more slowly than it should, productivity will not rise sufficiently rapidly and output will fall below its potential. (Of course, if the diffusion process goes on too rapidly, inefficiencies result as well.) For further discussion, see Salter [16]. 2Note that the intrafirm rate of diffusion measures how quickly a firm substitutes the new technique for the old once it has begun to use the technique. It does not tell us anything about the speed at which it began to use it. (See Section II.) Note too that some innovations can be introduced only on such a large scale that the intrafirm rate of diffusion is of little relevance. The firm either adopts the innovation or it does not. In addition, we presume here that there is an old technique that the innovation replaces. Assuming that the new technique will completely displace the old, a reasonable, but arbitrary, measure of the intrafirm rate of diffusion is the time interval separating the date when the innovation accounts for 10 per cent of the firm's output from the date when it accounts for 90 per cent of the firm's output. This sort of measure (which is inversely related to the intrafirm rate of diffusion) is used in Section II. If the new technique will eventually displace the old in B per cent of the cases, .1B and .9B can be used instead of 10 and 90. Studies of the diffusion process are relatively rare for industries other than agriculture. For some studies bearing on the spread of innovations among industrial firms, see Enos [6], Healy [9], Mansfield [12, 13, 15], and Sutherland [18]. For some investigations of agricultural innovations, see Beal and Bohlin [1] and Griliches [8]. For the diffusion of an antibiotic, see Coleman, Katz, and Menzel [4]. Some attention was devoted to the diesel locomotive by Healy [9]. Moreover, Yance [20] did some unpublished work on this innovation. But most of their work pertained to the spread of the diesel locomotive among firms, not to the intrafirm rates of diffusion. Thus, the amount of overlap with the present study is relatively small. 3 Given that one knows the per cent of the firms in the industry that have begun to use the innovation at each point in time and the average per cent of output produced with the innovation (or some similar measure of the intrafirm rate of diffusion) by these firms at each point in time, one can simply multiply them to get the corresponding measure of the rate of diffusion in the industry (if the firms are roughly of the same size). The rate at which firms begin to use an innovation is studied in [12], and the factors determining whether one firm will be quicker than another to begin using it is studied in [13]. Thus, the combined results of these previous papers and the present one
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