Papers and Proceedings of the Eighty-fifth Annual Meeting of the American Economic Association || Toward an Evolutionary Theory of Economic Capabilities

American Economic Association

Toward an Evolutionary Theory of Economic CapabilitiesAuthor(s): Richard R. Nelson and Sidney G. WinterSource: The American Economic Review, Vol. 63, No. 2, Papers and Proceedings of the Eighty-fifth Annual Meeting of the American Economic Association (May, 1973), pp. 440-449Published by: American Economic AssociationStable URL: http://www.jstor.org/stable/1817107 .

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Toward an Evolutionary Theory

0o Economic Capabl ities

By RICHARD R. NELSON AND SIDNEY G. WINTER*

This is a progress report on a project that aims at fundamental reconstruction of economic theories dealing with technological change and phenomena related, as cause or effect, to technological change. Among the related phenomena are, for example, those of firm behavior, of the product cycle in international trade, and of economic growth. It has been apparent for some time that there is a serious tension between the descriptions of the technological change process that are given in, on the one hand, the economic history literature and the micro studies of technological change and, on the other, in macro theories involving technological change (for example, neoclassical growth theory). Our ob- jective is to develop a theory of the firm, the sector, and the evolution of economic capabilities that is consistent both with detailed historical analysis and with the observed patterns in aggregate data.

There is probably wide agreement in the discipline today that the traditional, simple models of maximization and equilibrium do not correspond adequately to economic reality. At least, one can rea- sonably infer wide acceptance of this view from the existence of expanding literatures that abandon the traditional models in favor of more subtle formulations. Re-

search on the theory of the firm is increas- ingly concerned with the characterization of firm behavior in environments that are complex, uncertain, and changing in various ways. Information is imperfect or adjustment of decision variables is costly, or some combination of these conditions ob- tains. In applied econometric work, the variables that traditional theory identifies as relevant to equilibrium response appear as determinants of the pressures or targets that influence actual behavior. Or consider, more specifically, the studies of the diffusion of innovations. In this work, the typical role of the profitability variable is to determine a rate of change, not, as in traditional theory, the action chosen.

In general, the perceived inadequacy of the simple models embodying maximization and equilibrium assumptions has led to the construction of models embodying the same assumptions in more sophisti- cated forms. Theoretical progress is be- lieved to derive, in effect, from making the theoretical firms "smarter" and thus capa- ble of coping with the decision problems posed by more realistic environments. Cor- respondingly, in models that involve market interactions of many economic units, the concept of an "equilibrium" or "steady state" situation requires reformulation. Es- sentially, the concept must be defined with sufficient stringency so that even the smart new firms cannot discover, in equilibrium, any reasons for modifying their strategies. On the econometric side, the theoretical underpinnings of the popular distributed lag adjustment models are recognized to be inadequate. Attempts to invent a better story are under way, but in this area, too,

* Professors of economics at Yale University and University of Michigan, respectively. We are indebted to Herbert L. Schuette both for his assistance in the preparation of this report and, more fundamentally, for his role in the development of the simulation model that we discuss here. Financial support for this research has been provided by the Institute of Public Policy Studies at Michigan, and by the National Science Foun- dation under grant GS-35659; this support is gratefully acknowledged.

440



VOL. 63 NO. 2 INTERPRETATIONS OF ECONOMIC GROWTH 441

it is widely agreed that a "better" story is one that is linked to the optimizing behavior of a smarter economic actor.

Our own attack on these problems is from an entirely different angle. If the world is ridden with frictions, uncertain- ties, and subtle feedback loops, perhaps it is only the cruder economic mechanisms that function at all reliably. Perhaps the "real" decision problems are equally beyond the grasp of real firms and of our theoretical analyses. If so, perhaps we can make do with theoretical firms that are more simpleminded, not smarter, than the average real firm. And if it turns out that we pay some theoretical price for oversim- plifying the firms, perhaps we can recoup the loss through making the account of dynamic interactions more explicit and complete. It is, unfortunately, beyond the scope of the present report to explain in greater detail the set of general premises from which we are proceeding. Much of the relevant background is covered in our earlier papers (Nelson 1968, 1972; Winter 1964, 1971).

Our recent efforts have been concerned with the theory of economic growth in developed countries. Here we confront a well- developed theoretical structure (neoclassical growth theory) that has served as a useful framework for analyzing macro patterns of growth, but is in conflict with such micro or cross-section observations as diffusion processes for new technologies, and the existence of significant differences among firms in terms of profitability, technology used, and productivity.' The ques- tion is, can a model be developed that is more consistent with these micro phenomena, and at the same time does at least as well as the neoclassical models in explaining the aggregate data?

Our efforts toward this end have pro-

ceeded at three levels. At one level, re- ported in "Evolutionary vs. Neoclassical Theories of Economic Growth," we have described the broad outlines of an evolutionary theory. In "Technical Change in an Evolutionary Model," we set forth a simulation model that generates both micro and macro data.2 In "The Effects of Factor Price Changes in an Evolutionary Model," we make further simplifying assumptions and generate formal theorems regarding growth patterns in an evolutionary model. In this progress report we shall focus on the middle level simulation model, with occasional allusions to the levels of analysis in the other two papers.

Assumptions

Our basic assumptions regarding firm behavior are these. First, firms operate, for the most part, according to decision rules that do not (typically) arise from a deliberate maximization over some set of alternatives. Conceptually, these decision rules may be quite complex patterns of routinized behavior, keyed to market prices or other environmental signals. In the simulation model, however, we focus on the firm's decision rule for production technique, and we characterize such a rule in the simplest possible terms: The rule is identified with a pair of input coefficients, capital and labor per unit output. In the short run, a firm operates with a single technique.

Over time, the technique used by a firm may change as a result of two kinds of search processes, either of which may be triggered when rates of return fall below target levels. One process is internal to the firm and may be identified conceptually with the firm's research and development, operations analysis, and related activities. We assume that these activities turn up possible new techniques that are more

1 If it is not a conflict, perhaps it is a cold war. At the micro level, neoclassical theory predicts little that is true, and suggests much that is false.

2 Herbert L. Schuette joins us as co-author of this paper.



442 AMERICAN ECONOMIC ASSOCIATION MAY 1973

likely to be "close" to the current technique (in terms of similarity of input coefficients) than far away. In this sense we have adopted the metaphor of "local" or "incremental" search that is familiar in organization theory and also seems gen- erally consistent with studies of technical change at the firm level. The second type of search process is an imitation mecha- nism: The firm is more likely to consider a given technique the greater the percentage of current industry output produced with that technique. The possibilities turned up by these search processes are then sub- jected to a profitability test: Is the alterna- tive technique more profitable, at prevail- ing prices, than the one currently employed? If the answer is yes, the firm will switch, otherwise not.

The dynamics of firm search are comple- mented by the dynamics of "selection." To the extent that profitable firms expand and unprofitable ones contract, there will be a contribution to measured technical progress at the aggregate level that is not di- rectly traceable to individual firm search processes. Rather, it arises from the shifting of weights in economy-wide weighted averages, brought about by the differential growth of firms with superior techniques. In the simulation model, the crucial assumption linking investment to profitability appears in a stark form: Profits in ex- cess of a constant normal return on capital are reinvested. Though the assumption is empirically vulnerable in its stark form, a weaker version, compatible with empirical studies of investment behavior, would probably produce much the same effects on the aggregate measures.

The simulation model embeds the firms in a market environment. Since it is a "macro" model with Say's law implicitly assumed, there is no explicit demand curve for output. The cost of capital is taken to be exogenous and constant. There is a labor supply curve that shifts to the right

year by year, at a pace comparable to that of labor force growth in the United States, and has an elasticity of one-half.

The mathematical structure of the simulation model is that of a Markov process in a set of "industry states." A particular industry state is specified by listing the technique (input coefficients) and the capital stock (a nonnegative integer) for each firm. In each period, each firm em- ploys its entire capital stock to produce output with its current technique. Aggre- gate output and labor demand are thus implied by the industry state. The labor supply curve then generates the single endogenous price in the model, the wage rate. Firm and aggregate values for profits, labor share, etc., are thus determined. In- dustry state transitions then occur through probabilistic search and depreciation processes and through investment. A run of the simulation model corresponds to pick- ing an initial industry state and then let- ting the model generate, stochastically, the series of subsequent states. Parameters of the model have been set so that a single period corresponds to a year, wage rates are in 1929 dollars per manhour, and ratios of Q, K and L magnitudes are comparable to the historical values given in Solow's classic article of 1957.

In the simulations, there are one hun- dred possible techniques. These were generated as a random sample from the uni- form distribution over a square region in the space of logarithms of input coefficients; the region was chosen to bracket the historical values in Solow's time series for 1909-49. The dots in Figure 1 are the plots of the technique points thus determined; the greater density toward the origin reflects the underlying uniformity in the logarithms.

Results

In this brief report we can only attempt to evoke the general character of the simu-




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period 25

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FIGURE 1. DISTRIBUTION OF OUTPUT BY PRODUCTION TECHNIQUE, PERIODS 25 AND 40 OF RUN 0111




lation results. The circles in Figure 1 are a graphical representation of the distribution of output by technique of production, at periods 25 and 40 of the same simulation run. The area of each circle is propor- tional to the share of output produced with the technique represented by the center of the circle; the hatching identifies the earlier period. The stars identify the techniques in use in period one of the run. Note the degree of cross-sectional dispersion in both capital-labor ratios and in efficiency, the overall shift toward the origin from the earlier to the later period, and the mixture of weight-shifting and appearance of new techniques that is involved in this change.

Figure 2 displays the average input coefficients, at five period intervals, for the run underlying Figure 1 and three other runs. (For purposes of comparison, Figure 3 presents the corresponding diagram based on Solow's historical data.) The differences among the four runs are at- tributable to different settings of parameters governing the return to capital and the "localness" of the local search process, as well as to random variation. Triangles and circles mark runs with "less local" search; clearly, the result is faster progress. Tri- angles and squares mark runs in which firms pay a higher "required dividend" as the price of capital services; the typical result is drift toward lower capital-labor ratios than in the other two runs, but this appears only faintly in the diagram. Com- parison of Figures 1 and 2 reveals that the cross-sectional dispersion of capital-labor ratios in a given run is quite large relative to the variance of the ratios across runs, even when parameter changes are con- tributing to the latter variance. Thus, in spite of the random influences on period- to-period transitions, and in spite of the wide divergences among the histories of different firms, the aggregate data outcomes display quite consistent patterns.

Table 1 displays some of the aggregate

time series for the run that served as the basis for Figure 1. Both the typical trends and the characteristic irregularity of historical growth processes are visible; the year-to-year changes appear to be unrealis- tically abrupt, however. The utter absence of a production function from the underlying structure does not prevent one from calculating, a la Solow, what the rate of technical change would be if the data were generated by a neutrally shifting aggregate production function. Such a compu- tation gives rise to the index of technology displayed in the column headed A in the table; in qualitative terms this series is virtually indistinguishable from that com- puted by Solow. We can follow through on the rest of Solow's procedure, adjusting output for technical change and then re- gressing the log of adjusted output per manhour on the log of capital per manhour. When this is done, the estimated Cobb- Douglas function fits with an R2 of .998 and an estimated capital elasticity of .30, as against Solow's .997 and .34. (Run 011 1 is one of our best in terms of this comparison. However, in a 16-run experiment, half the R2 values obtained exceed .99.)

The series for "realized gross rate of return" deserves a brief comment. We have employed a depreciation rate of .04, which operates as a random failure prob- ability on each unit of the capital stock. In addition, there is in this run a "required dividend" of .06; this fraction of the capital stock is paid out in each firm and in each period as interest or dividends. This means that the "equilibrium" gross rate of return is .10, in the sense that this rate corresponds to zero expected net investment. The "target" rate of return, which deter- mines when an individual firm searches, is set at .16. The tendency of the realized gross rate of return to exceed .10 reflects the presence of "abnormal" profits generated by technical progress; these profits finance the investment that equips the in-




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FIGuxE 2. AVERAGE INPUT COEFFICIENTS AT PERIODS 1, 5, 10, ... , 50 IN FOUR RUNS

.-10001 *.01 .-0.-11




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FIGURE 3. INPUT COEFFICIENTs DERIVED FROM SoLow DATA, 1909-49




TABLE 1-SELECTED TimFE SERIES, RUN 0111

Yr. w r SK QIL K/L A Yr. w r SK QIL K/L A

1 .45 .102 .295 .64 1.87 1.000 26 .65 .141 .309 .94 2.06 1.427 2 .47 .104 .286 .66 1.83 1.032 27 .68 .130 .300 .97 2.08 1.460 3 .47 .109 .300 .67 1.85 1.047 28 .64 .154 .350 .98 2.23 1.449 4 .44 .132 .361 .69 1.90 1.069 29 .68 .134 .309 .98 2.28 1.445 5 .49 .109 .288 .69 1.83 1.086 30 .74 .099 .224 .96 2.18 1.427 6 .50 .118 .299 .71 1.80 1.116 31 .68 .128 .298 .97 2.24 1.431 7 .50 .124 .309 .72 1.80 1.130 32 .63 .161 .376 1.02 2.36 1.479 8 .47 .151 .376 .76 1.89 1.175 33 .62 .184 .433 1.09 2.55 1.535 9 .53 .124 .309 .76 1.90 1.181 34 .71 .150 .354 1.10 2.59 1.543

10 .61 .089 .209 .77 1.81 1.205 35 .79 .120 .280 1.10 2.57 1.557 11 .56 .118 .280 .78 1.84 1.215 36 .80 .125 .288 1.12 2.59 1.576 12 .57 .116 .273 .78 1.83 1.218 37 .81 .122 .282 1.13 2.61 1.590 13 .59 .101 .235 .78 1.81 1.218 38 .82 .134 .302 1.17 2.64 1.641 14 .60 .104 .236 .78 1.79 1.234 39 .84 .115 .263 1.14 2.61 1.604 15 .56 .130 .295 .79 1.80 1.245 40 .79 .149 .336 1.19 2.69 1.658 16 .58 .121 .276 .79 1.80 1.246 41 .83 .139 .315 1.21 2.73 1.675 17 .57 .129 .290 .81 1.82 1.263 42 .91 .097 .220 1.17 2.65 1.632 18 .56 .141 .318 .82 1.85 1.281 43 .87 .119 .267 1.19 2.67 1.659 19 .54 .162 .366 .85 1.91 1.309 44 .94 .097 .212 1.19 2.60 1.676 20 .67 .091 .206 .84 1.88 1.302 45 .87 .126 .280 1.21 2.69 1.693 21 .59 .139 .313 .86 1.94 1.325 46 .93 .107 .232 1.21 2.64 1.699 22 .62 .126 .289 .87 2.00 1.334 47 .85 .157 .335 1.28 2.73 1.789 23 .63 .121 .277 .87 2.00 1.334 48 .97 .121 .253 1.30 2.70 1.813 24 .69 .100 .222 .88 1.96 1.335 49 .99 .107 .226 1.28 2.70 1.795 25 .63 .144 .315 .91 2.01 1.396 50 .97 .134 .271 1.33 2.69 1.856

W: wage rate, 1929 dollars QIL: output per manhour r: realized gross rate of return on capital KIL: capital (1929 dollars) per manhour SK: capital share (= 1-labor share) A: Solow technology index

creasing labor force and, further, permits the capital-labor ratio to rise.

The ability of the simulation model to generate plausible aggregate time series data is quite encouraging-especially in view of the fact that the model represents an early state in the development of an evolutionary theory. We think that further effort should yield, fairly easily, models that are at least a match for those generated from neoclassical theory when judged in terms of the ability to fit and, hence, "explain" the aggregate data. How- ever, we do not intend to base our case for the superiority of an evolutionary theory on the outcomes of tests narrowly focused on aggregate data. Rather, as we empha- sized at the outset, the appeal of the evolutionary theory lies in the promise of greater consistency between the accounts

given of phenomena at the macro and micro level, including in the latter category the phenomena of individual firm behavior. We now turn, therefore, to a brief discus- sion of some features of the simulation output that reveal the sort of consistency with micro phenomena, at least in qualitative terms, that the evolutionary approach offers.

The model generates, for example, size distributions of firms that are qualitatively realistic. The simulated data can be inter- preted in much the same terms that Yuji Ijiri and Herbert Simon have recently pro- posed for the analysis of real data of this type. A plot of firm size against firm rank on double log paper reveals a downward concavity. This deviation from the Pareto law (which would yield a straight line) has been attributed by Ijiri-Simon to a mecha-




nism that involves, roughly speaking, Gibrat's Law modified by serial correlation in individual firm growth experience. The investment assumption of our model provides the Gibrat's Law element, while the dynamics of technical change provide the serial correlation. There are significant differences among the firms in the industry in their profit rate and total factor productivity in any given time period (see Figure 1). Innovating firms tend for awhile to have higher profits and to grow more rapidly than firms that do not innovate. However lagging firms, while disadvan- taged, are able to look to leading firms in their search processes. Thus technological leads, and lags, tend to dissolve with time.

We have run the simulation model a number of times, with different settings for key parameter values. Of particular interest for the illustration considered here is the fact that different runs involved different assumptions about the ease with which a lagging firm could imitate a leading firm. Each run yielded a measure of the "degree of concentration," in particular, the arbitrary but traditional four-firm concentration ratio. We regressed this ratio against the imitation parameter (among other variables) in the various runs we made. Interestingly, the degree of concentration (measured toward the end of the simulation run) was negatively related to the ease of imitation. In this re- spect, and in others, our simple and ab- stract model generates quantitative results that are highly reminiscent of Schumpe- ter's account of the competitive process.

If one looked in detail at any of the simulation runs, one would be strongly tempted to tell stories, like the economic historians tell, of the rise and fall of particular firms, of the competitive advantage grabbed initially by firm X as the result of the significant innovation that nearly drove all the other firms out of the market, of the nick-of-time imitation by firms Y

and Z that kept them in the business, and of their eventual discovery of new innovations which put them in the competitive lead. One is tempted to climb inside those firms to try to understand the changes in their relative competitive positions. Was the early advantage of firm X due to the presence of the well-known great inventor there? Did the recovery of firm Y hinge on a change in presidents and the establish- ment of a new research and development capability? Of course, events like these do not happen explicitly; it is the random number generators of the computer pro- gram that do the work of the fortuitous circumstances that affect the histories of individual firms. But we can claim that the model's characterization of individual firm behavior is at least consistent with the existence of those fortuitous circumstances. We would argue, further, that ad- mitting a degree of indeterminancy at the level of individual actors is an important step in the development of theory that can successfully address a variety of types of data at all levels of aggregation.

We believe that an evolutionary theory, constructed along the lines sketched here, can meet this challenge of integrating the different types of data and levels of analysis. In future work we intend to broaden and deepen the developing theory in many ways. We hope that this brief report is sufficient to indicate that the endeavor shows some promise.

REFERENCES Y. Ijiri and H. A. Simon, "The Relative

Strength of Middle-Sized Firms and the Curvature in Firm-Size Distributions," paper presented to the Econometric Society, De- cember 1971.

R. R. Nelson, "A 'Diffusion' Model of Interna- tional Productivity Differences in Manufac- turing Industry," Amer. Econ. Rev., Dec. 1968, 58, 1219-48.

, "Issues and Suggestions for the Study




of Industrial Organization in a Regime of Rapid Technical Change," in V. R. Fuchs, ed., Policy Issues and Research Opportuni- ties in Industrial Organization, New York 1972.

and S. G. Winter, "Evolutionary vs. Neoclassical Theories of Economic Growth," Univ. of Mich. Inst. of Public Policy Studies Disc. Paper 46, Jan. 1973.

and , "The Effects of Factor Price Changes in an Evolutionary Model," Univ. of Mich. Inst. of Public Policy Studies Disc. Paper 47, Jan. 1973.

5 5,and H. L. Schuette, "Techni- cal Change in an Evolutionary Model,"

Univ. of Mich. Inst. of Public Policy Studies Dis. Paper 45, Jan. 1973.

J. A. Schumpeter, The Theory of Economic De- velopment, Cambridge 1934.

, Capitalism, Socialism and Democracy, 3rd ed., New York 1950.

R. M. Solow, "Technical Change and the Ag- gregate Production Function," Rev. Econ. Statist., Aug. 1957, 39, 312-20.

S. G. Winter, "Economic 'Natural Selection' and the Theory of the Firm," Yale Econ. Essays, Spring 1964, 4, 225-72.

"Satisficing, Selection and the Innovat- ing Remnant," Quart. J. Econ., May 1971, 85, 237-61.



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Papers and Proceedings of the Eighty-fifth Annual Meeting of the American Economic Association || Toward an Evolutionary Theory of Economic Capabilities