The results of the simulation experiments of Schumpeterian Tradeoff

The data from our simulations are set out in Tables 14.1-14.6. The abbreviations used in these tables should be interpreted as follows . The first row displays for period 101 the share of industry capital held by firms that do innovative R&D. In general, a share less than 0.50 indicates that firms that did innovative R&D were less profitable than those that did not; a share slightly over 0.50 is, however, also compatible with inferior profitability. The second row shows the average rate of excess return (profit) in the industry as a whole, as a percentage rate per quarter. Rows 3 and 4 show, respectively, the percentage  margin  between  price  and  average  production  costs, (P – C)/C, in the industry as a whole, and the percentage margin for the firm with best-practice technology.

The next five rows display statistics of industry concentration in period 101 : rows 5-8 the share of industry output accounted for by the largest and second-largest innovators and imitators, and row 9 the inverse of the Herfindahl-Hirschman index of (capital) concentration -that is, the numbers equivalent of the value of the concentration index .

The next five rows outline productivity statistics: row 10 shows average industry productivity, rows 11 and 12 average productivity of innovators and imitators, row 13 best practice (all for the final period of the run) and row 14 a measure of the average gap over 101 periods between average productivity and latent productivity.

Rows 15 and 16 show total industry innovative R&D over the 101 periods and the number of innovation draws. The bottom line shows price in period 101.

The symbols 5, F, E, and H in the column headings refer, respec­ tively, to slow and fast growth of latent productivity and easy and hard imitation. The two columns under each heading show the re­ sults of two different runs with the same parameter settings.

1. Tight Oligopoly

Table 14. 1 displays data from our simulation experiment with an in­ dustry structure consisting of four firms, initially of equal size, two of which spend only on imitative R&D. The striking characteristic of all the runs shown was that the four firms tended to stay close together both in productivity and in size. Under these circum­ stances, it is not surprising that the rate of growth of best-practice productivity and the rate of growth of average productivity (or their levels at the end of the run) tended to be functions only of the rate of growth of latent productivity. These variables were insensitive to the ease or difficulty of imitation.

Table 14 .2 presents comparable data for runs that started out with sixteen firms of equal size. We shall scrutinize differences among the sixteen-firm runs shortly. Here, we make some rough comparisons of what happened in the four-firm runs as contrasted to the sixteen-firm runs. For a given rate of growth of latent productivity, there are not many noticeable differences between the rate of growth of best prac­ tice in the four-firm runs as compared with the sixteen-firm runs. However, average practice tended to be higher in the four-firm runs than in the sixteen-firm runs. In the sense of making the most wide­ spread use of the best available technologies, the more concentrated industry structure scored better than the less concentrated one. Also, the more concentrated i ndustry generally achieved this better pro­ ductivity growth performance with a smaller aggregate volume of in­ novative R&D expenditure. The concentrated industry structure was more efficient in its use of R&D.

On the other hand , average markups over variable costs were sig­nificantly higher in the four-firm runs, and the static triangle losses, therefore, were greater there. And the higher m arkups more than offset the higher average productivity in the sixteen-firm run, so that price was higher in the concentrated i ndustry case than in the sixteen- firm case, g iven the rate of growth of latent productivity.

2. A More Competitive Science-Based Industry

Perhaps the most significant aspect of the sixteen-firm runs was al­ lud ed to above when we compared growth of best practice and average productivity in the sixteen- and four-firm runs for a given rate of growth of latent productivity, without finding it necessary to take into account the settings of other parameter values, such as the ease of imitation or the degree of aggressiveness of profitable firms. Note that, in fact, these parameters seem to have only minor effects. At first thought, this might be something of a surprise. While it is plausible that growth of best-practice productivity would be insensi­ tive to these institutional variables, one might have expected that in regimes where imitation of prevailing best practice was d ifficult, average productivity in the industry would tend to lag behind best practice to a greater extent than in regimes where imitation was eas­ ier. In fact, in the cases where latent prod uctivity growth was rapid and imitation of best practice was difficult, a significant productivity gap opened up between the firms that did innovative R&D (particu­ larly the productivity leader) and the firms that only imitated . But it was also true that in these cases the imitating firms tended to shrink in s ize relative to those that successfully innovated; thus, although there was a greater gap between the leaders and the laggers, a smaller share of industry capital was accounted for toward the end of the run by the laggers.

As suggested above, a striking contrast between the four-firm runs and the sixteen-firm runs was a tendency for industry structure to change significantly in the latter but not in the former. The initial distribution of firm sizes tended to be moderately stable where latent productivity growth was slow (regardless of the ease of imitation) or where latent productivity growth was rapid but imitation easy, so long as profitable firms showed restraint regarding their output expansion as they grew large. In runs with these settings, the firms that did not engage in innovative R&D tended to be more profitable than those that did. In other words, innovat ive R&D was not profitable to undertake. But given the output restraint showed by the slightly more profitable imitators, competition was o rderly enough so that innovators were not driven out of business.

Where latent p roductivity growth was rapid and imitation h ard, the firms that did innovative R&D fared much better and the firms that only imitated did much worse, even though profitable firms showed output growth restraint. In these runs it was apparent that the imitators were gradually being driven out of business, even though the innovators were showing considerable restraint in push­ ing their advantage.

Table 14 .3 displays statistics for runs in which profitable firms continued to expand aggressively even when they grew large in rela­ tion to the market. The comparison between Tables 14 .2 and 14.3 is q ui te interesting. If one n ormalizes for the rate of latent productivity growth and for the . imitation regime, in each and every case where profitable firms did not show output restraint the fate of the inno­ vators was less fortunate relative to the i mitators than it was when large profitable firms did show output restraint. In every one of the runs of the aggressive competition case, by the end innovators ac­ counted for significantly less than half of the industry capital stock. The  comparison  is  particularly  striking  for the  case  of  rapid growth of latent p roductivity and hard imitation . Under restrained competition, the innovators clearly dominate and have 70 percent or more of industry capital by the end of the run. When firms have ag­ gressive investment policies, the imitators prevail, and by much the same decisive margin. Although it would be easy to understand why the intensity of the struggle might affect the margin of “victory,” it is something of a surprise to find that it also affects, quite systemat­ically, the identity of the victor.

The explanation for this phenomenon, and for the asymmetry of results in the investment restraint case, resides in the following. In this model an imitating firm can never achieve a higher productivity level than the best of the innovators. An imitator that matches an i n­ novator’ s productivity will have higher profits, because it does not incur the innovative R&D costs. But if it stops its output growth at reasonable size, pressures on the innovating firm to contract are re-laxed, the R&D budget is not eroded, and there is a chance of recov­ ery for the innovating firm . (On the other hand a large innovator will stochastically extend its advantage over a small imitator.) But if the large imitating firm continues to grow,  it forces the innovating firm to continue to contract. As the innovator’s R&D budget contracts, the chances of an innovative success that will spark recovery diminish, and the expected lead time before the big imitator imitates dimin­ ishes as well.

We think there is a phenomenon here, albeit in stylized model form, that is well worth pondering. In our model world, an imitative strategy may, if supported by luck early in the industry’s evolution, be a runaway winner. And certainly imitators will have good luck at least some of the time. Is it really socially desirable that they should press their advantage? Earlier we argued that the answer might de­ pend on what a lower level of innovative R&D costs society.

In these simulation runs there was little tendency for best practice or average practice in the last period to be lower in the aggressive in­ vestment case than in the restrained investment case, for a given rate of growth of latent productivity. To some extent this is because total industry output and capital tended to be greater (although in the former case the innovators’ share of total capital tended to be less) and total innovative R&D spending over the simulation run was therefore not radically different in the two cases. The result points in part to the real social advantage of a structure dominated by large imitators: once an innovation exists, it is rapidly applied to a large fraction of industry capacity. (Note the high average productivity of imitators in the FH cases of Table 14. 3.)

But the central reason is that relatively sharply diminishing re­ turns on innovative R&D are inherent in the science-based tech­ nological regime. A smaller R&D expenditure means that the path of latent productivity is tracked less well and that on average the dif­ ference between industry best practice and latent productivity is greater. But even an occasional innovative R&D hit suffices to keep the average distance from being very great. However, the social costs that occur if imitators come to dominate an industry might be signif­ icantly greater in a regime where the opportunities for today’s tech­ nical change are more influenced by the industry’s own prior R&D efforts and less influenced by developments outside the industry than has been the case in the runs considered thus far.

3. Cumulative  Technological  Advance

In the simulation runs reported here, there is no outside augmenta­ tion of the set of possible innovations. Rather, the outcome of any in­ novation draw is very much influenced by the prevailing technique of the fi rm making that draw. In particular, technological advance is assumed to be cumulative in the sense defined above.

Tables 14.4 and 14.5 display relevant industry statistics for runs with a structure of different parameter settings that is similar to that in Tables 14.2 and 14.3. Many of the same relationships that held in the earlier cases hold in these as well: the character of innovation and imitation affects industry concentration in the same way; the fast in­ novation, hard imitation condition tends to lead to concentration; where innovation is slow and imitation easy, s uch tendencies were far less marked. Regarding the competitive contest between inno­ vators and imitators, innovators do well when the conditions permit fast technical advance and where imitation is difficult, provided large firms show restraint in further expanding output. The imitators do well and the innovators do poorly in the opposite parameter set­ tings. Where firms continued to be aggressive in their output deci­ sions even as they grew large, profits of both innovators and imi­ tators were less than in cases where more restrained behavior obtained. But it was especially the innovators whose fortunes were hurt. The asymmetry in the model continues to have force under these different assumptions regarding the nature of innovation. Imi­ tators cannot have a higher product ivity level than that of the best of the innovators. If they restrain their output growth, innovators can recover. But if a profitable imitator grows aggressively, the recupera­ tive powers of the innovators are diminished. These results are simi­ lar to those reported above.

What is different about these simulation runs is that aggressive competitive behavior has a clear negative effect on both best-practice productivity and average productivity. Comparing runs with the same setting of other parameters, each of the pair of best-practice sta­ tistics almost invariably is larger in the runs where the fi rms restrained their output growth than in the runs where they did not. As in the earlier runs, aggressive competitive behayior tends to gen­ erate a structure in which there is at least one large imitator that is capable of quickly mimicking any new innovation and that operates with lower costs than the innovators. As the profitless innovating firms shrink, so does total industry innovative R&D. In every one of the comparisons, innovative R&D for the industry was less in the ag­ gressive competition case than in the restrained competition case and the number of innovation draws was smaller. And in contrast to the science-based cases, where such a cutback in industry innovative R&D and innovation draws had little effect on the time path of in­ dustry best practice (save to make it more j agged and somewhat lower), in these runs reduced industry innovation shows up in a slower growth of best practice.

As one would expect, there is less of an effect on average prod uc-tivity than on best practice. Where there is one huge imitator com­ prising a large share of industry capital, average productivity is largely determined by its productivity, and its productivity stays close to best practice. In most of th e cases, however, average produc­tivity was lower in the aggressive competition case than in the com­ parable case of more restrained competition.

The effect of aggressive competition on the price of the industry product is less certain. To some extent, lower markups over costs in the strong competition case offset higher costs in that case. Nonethe­ less, and in striking contradiction to textbook wisdom, by and large end-period industry price tended to be higher in the aggressive com­petition case than  in  the restrained competition case,  for similar parameter settings. Furthermore, examination of price trends in the two contrasting settings suggests that, if the simulation run were longer, price under aggressive competition would grow progres­ sively higher than would price under more gentlemanly competition. Our 101-period simulation runs end with some innovators contin­ uing to exist with nontrivial capital stocks, but in retreat. As the re­ treat continues, industry innovative R&D expenditures should dry up. And ultimately the industry should settle into something quite close to a competitive equilibrium with zero profits and static tech­ nology.

Table 14 .6 presents data for simulations that we ran for 201 periods. In the science- based technology regime the innovators have indeed shrunk further in the aggressive investment behavior case, but best-practice productivity is not badly affected. On the other hand, in the cumulative technology regime, period 201 best practice is much lower in the aggressive competition case than in the case where competition is more restrained. The hidden hand has throt­ tled the goose that lays the golden eggs.

Source: Nelson Richard R., Winter Sidney G. (1985), An Evolutionary Theory of Economic Change, Belknap Press: An Imprint of Harvard University Press.

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