The residual explanation of economic growth

1. Technological Change as a Residual “Neutrino”

This type of intellectual sleight of hand is not peculiar to economic analysis, and reasonable toleration for it is not necessarily inimical to the progress of science. The neutrino is a famous example in phys­ ics of a “labeling” of an error term that proved fru itful. Physicists ul timately found neutrinos, and the properties they turned out to have were consistent with preservation of the basic theory as amended by acknowledgement of the existence of neutrinos. A major portion of the research by economists on processes of economic growth since the late 1950s has been concerned with more accurately identifying and measuring the residual called “technical change,” and better specifying how phenomena related to technical advance fit into growth theory more generally. The issue in question is the success of this work.

Considerable effort has gone into develo ping the concept of tech­nical change within a p roduction function framework and into modi­ fying that framework to make technical change endogenous to the neoclassical system rather than exogenous. Regarding the first part of the task, the effort can be viewed as augmenting the specification of the production function so as to include more terms- for example, a term that can be interpreted as “total factor productivity” or terms that can be interpreted as the “efficiency” of labor or of capital. These terms are then treated as variables, not constants, w ithin the system. Technical advance is brought into the standard neoclassical format for economic behavior by postulating that these terms are a function of past investments (in activities called research and development) aimed specifically to advance them. The standard profit maximiza­ tion hypothesis has been employed regarding these investments.

A variety of empirical studies have proceeded guided by the above conceptual structure, and have come up with conclusions that are qualitatively consistent with it. For example, if one assumes that the profitability of an invention is proportional to the sales of an in­ dustry, one would expect that changes over time in the amount of in­ venting directed toward different industries would be correlated with changes in the sizes of industries, and that at any moment in time there would be more inventing going on relevant to “large” in­ dustries than to small ones. These are exactly Schmookler’s conclu­ sions, based on his use of patents as an indicator of inventing (Schmookler, 1966) .

A special version of the theory focuses on technical advance to “save” or increase the efficiency of various factors of production used in producing a particular product. In this version of the theo ry a ri se in the price of one factor relative to another should, other things equal, le ad to an increase in efforts aimed to augment the efficiency of that factor relative to others. Recent work by Hayami and Ruttan (1971) and others, directed toward agriculture, shows that both ti me series and cross-country data are roughly consistent with that theory.

2. The Identification Problem

In the case of the neutrino, the characteristics of the unobseIVed par­ ticle were relatively well pinned down by prevailing theory (assum­ ing that the theory itself was viable). In the case of technical change, neoclassical theory did not specify very well how “large” or impor­ tant technological change must be-only that there was “some­ thing” there. To see the problem, consider these familiar “stylized facts.” Output (gross national product) has been growing at roughly the same rate as capital and at a faster rate than labor; hence, the capital- output ratio has been constant and output per worker and the capital-labor ratio have risen in the same proportion. Factor shares have remained constant; thus, the rate of return on capital has been constant and the wage rate has risen. These “facts” very roughly characterize the Western economic experience that the growth accounting exercises seek to explain.

The facts are inconsistent with an explanation that interprets growth solely in terms of movement along a neoclassical production function. The rise in output per worker would have been less than the rise in the capital-labor ratio, whereas in fact worker productivity has grown at the same rate as capital intensity. And the returns to the factor increasing in relative supply-capital -would have fallen, not remained roughly constant. Thus, the production function must have shifted.

But within the broad framework of interpretation provided by the idea of a shifting production function, there is a wide range of quali­ tatively different explanations available. Consider the following two, both consistent with the time series data. One is that the unde rlying production function is Cobb-Douglas (unitary elasticity of substitu­ tion) and that technical change has been neutral in the sense of Hicks. The second is that the underlying production function has an elasticity of substitution less than one and that technical change has been labor-saving. The first interpretation is depicted in Figure 8. 1, the second in Figure 8.2. Points a and b in the two figures are iden­ tical and the slopes of the CUIVes (the marginal productivity of capi­ tal) at those points also are identical. Thus, both interpretations are consistent with the input, output, and factor price data.

The two interpretations are different in the following “growth accounting” sense. In the case of Figure 8. 1, output would have grown by Δ11 if capital per worker had grown as it did, but the pro­ duction function had not shifted . Δ12 represents the increase in out­ put p er worker not explained by growth of the capital-labor ratio and due, in some sense, to technical change. In Figure 8. 2, Δ21 can be attributed to growth of capital per worker and Δ22 to technical change in the sense above. In the latter interpretation the lower elasticity of substitution means that less of the productivity growth can be attrib­ uted to growing capital intensity; hence, more must be attributed to improved technology. Since both interpretations are equally consist­ ent with the time series data, there is no way to choose between them without a priori assumptions or other data.

8.1 One interpretation of productivity growth

One could view this identification problem as posing difficulties for statistical estimation but as not raising any major theoretical issues; most economists look at the problem this way. For example, it has been proposed that if one had access to cross-section data showing firms operating at the same moment in time using different input coefficients, as well as time series data, one might be able to disentangle the two sources of growth. Contemporaneous observa­ tions would be presumed to re flect the same underlying store of tech­ nical knowledge. However, if these firms are within the same economy, these differences in choice of inputs must reflect either the fact that they face different factor prices at the same time, or the fact that they are making different technological choices given the same factor prices; either assumption presents difficulties for the neoclas­ sical formulation that have not really been confronted.

8.2 Another interpretation of productivity growth

3. Some Maj or Conceptual Issues

There are deeper theoretical and conceptual issues behind the scenes. The neoclassical formulation rests on the assumption that at any given time there is a wide range of technological possibilities from which firms may choose, including alternatives that no firm has ever chosen before . The initial period production functions in Fig­ures 8.1 and 8.2 are drawn so as to extend a considerable distance to the right of point a, to depict production possibilities employing capital-labor ratios significantly greater than any firm had up to that time experienced. What is the meaning of that? What does one mean when one says that a production possibility exists even though no one is using it or has ever used it? As stated earlier, we do not think it realistic to assume that a sharply defined body of technical knowl­ edge exists that governs production possibilities at input combina­ tions remote from actual experience. Exploration of technologies that have not been used before involves in an essential way the character­ istics of “innovation” that we described earlier. If this position is ac­ cepted, it is not merely that movements along preexisting production functions explain little of experienced growth. It is that the idea of movements along the production function into previously unex­ perienced regions- the conceptual core of the neoclassical explana­ tion of growth- must be rejected as a theoretical concept.

The problems with rectifying the production function at remote input combinations are not satisfactorily resolved by grafting onto the theory a neoclassical model of induced innovation. The graft as­ sumes that “inventing” or “doing R&D” is an activity whose out­ come can be predicted in advance in fine detail. In effect, there is no difference in the amended theory between moving along the produc­ tion function by increasing one kind of capital (plant and equipment) through physical investment, and “pushing outward” the produc­ tion function by increasing another form of capital (knowledge?) through investing in R&D. Both kinds of investments are explained by the same behavioral model. The distinction between innovation and routine operation is totally repressed.

It is repressed at the level of description of the activities involved. There is no room in the neoclassical formulation for nontrivial uncer� tainty, or for differences of opinion regarding what will work best, Or for recognition of the fact that the set of innovation alternatives is shrouded in fundamental ambiguity.

It is repressed in the characterization of the “output” of the activities involved. The models discussed above, which view ” shifts” in production functions as resulting from investment undertaken by firms as part of the profit- maximizing portfolio of investments, rest on the presumption that the ou tcome of research and development is a “private good .” Ye t certainly there is often an important degree of “publicness” about new knowledge, whether that knowledge is in the form of “blueprints” or in the form of experience. This is so even if the innovating firm tries to restrict access to that knowledge. At the least, knowledge that another firm has done something successfully changes the thinking of other firms regarding what is feasible . And, in some cases, enough knowledge is published or is evident to the sophisticated observer to provide very good clues as to how to pro­ ceed.

It could be that the neoclassical induced innovation models impli­citly postulate a system of patents. But th is certainly is not built spe­ cifically into the theoretical formulation. If it were, the theory would need to take account of the ‘fact that firms at any time differ in terms of the technologies they can use, or would have to postulate a perfect system of patent licensing. However, in either case, as long as firms differ in terms of what they come up with as a result of their research and development activities, firms will differ in terms of their profita­ bility.

4. Inconsistency with Micro Data

The amended neoclassical formulation represses the uncertainty as­ sociated with attempts to innovate, the publicness of knowledge as­ sociated with the outcomes of these attempts, and the diversity of finn behavior and fortune that is inherent in a world in which inno­ vation is important. Thus, it is unable to come to grips with what is known about technological advance at the level of the individual firm or individual invention, where virtually all studies have shown these aspects to be central. This has caused a curious disjunction in the economic literature on technological advance, with analysis of eco­ nomic growth at the level of the economy or the sector proceeding with one set of intellectual ideas, and analysis of technological ad� vance at a more micro level proceeding with another.

Over the years economists, other social scientists, and historians have done an enormous amount of research on the more micro as­ pects of technological change. We shall discuss this literature in some detail in Chapter 11. Suffice it to say here that studies by historians like Landes (1970), Habakkuk (1962), David (1974), and Rosenberg (1972), and by students of industrial organization and technical change like Schmookler (1966), Jewkes, Sawers, and Stillerman (1961 ), Peck (1962), Griliches (1957), Mansfield (1968), and Freeman (1974 ) have revealed extremely interesting facts about the tech­ nological change process. While some of these are in harmony with neoclassical themes, others are quite discordant. We have, for ex­ ample, much evidence of the role of insight in the maj or invention process, and of significant differences in ability of i nventors to “see things” that are not obvious to all who are looking. Yet once one has made a breakthrough, others may see how to do similar, perhaps even better, things. The same patterns apparently obtain in innova­ tion. Relatedly, there are considerable differences among firms at any time in terms of the technology used, productivity, and profitability. Although these studies show clearly that purpose and calculation play an important role, the observed differences among persons and firms are hard to reconcile with simple notions of maximization unless some explicit account is taken of differences in knowledge, maximizing capabilities, and luck. The role of competition seems better characterized in the Schumpeterian terms of competitive ad­ vantage gained through innovation or through e arly adoption of a new product or process than in the equilibrium language of neoclas­ sical theory.

It is not possible to reconcile what is known about the p henomena at a micro level with the intellectual structure used to model technical advance at the macro or sectoral level by arguing that the macro model deals with the average or the modal firm. The differences among firms and the disequilibrium in the system appear to be an essential feature of growth driven by technical change. Neoclassical modeling cannot avail itself of this insight .

There have been a few noteworthy if neglected attempts to square the neoclassical theory of industry production and growth with the observed facts of very considerable diversity of techniques and prof­ itability of firms within an industry at any time. Houthakker (1956) developed a model in which firms at a given time are endowed with different techniques, with each firm being profitable under some sets of product and factor prices but not under others. These techniq ues are fixed and given, as are the capacities of the various firms. Firms either produce at capacity or produce nothing, depending on the vector of prices. Within such a model it is possible that the aggregate industry data from different periods and different prices will have a form  that resembles  that of orthodox neoclassical theory.  But the model would predict that in a given time there would exist consider­ able diversity across firms in productivity levels and profitability.

The Houthakker model does not explain why the techniques in ex istence (with positive capacity) at any time are what they are, and in his m odel the distribution of capacity over techniques is treated as a constant. There are several different models that “explain” cross­ industry diversity of techniques at any time as a result of the dates at which various plants were put in place. See notably Solow, Tobin, von Weizsacker, and Yaari (1966), Salter (1966), and Johansen (1972). But in these vintage models new investment is always in “best prac­ tice” technology, and firms are never uncertain about the character­ istics of new technologies. And the evoluti on of “best practice” is unexplained. Thus, the neoclassical vintage models, at least their present versions, abstract away much of what scholars of the micro­ economics of technical advance have learned about the topic.

Theoretical schizophrenia thus forces economists to keep their understandings in different boxes. A central purpose of a theoretical structure – to enable one to see links between apparently disparate phenomena and thus to enable knowledge to be superadditive -is thwarted by this neoclassical partitioning of technical advance. Re­ latedly, the structl1re of contempo rary formal theory drives a wedge between the analysis of those economists who take the theory seriously, and those,- such as economic historians, who pay more attention to the phenomena involved.

The tension has been recognized in the profession. For example, Nordhaus and Tobin have remarked : “The [neoclassical] theory con­ ceals, either in aggregation or in the abstract generality of multi­ sectoral models, all of the drama of events-the rise and fall of prod­ ucts, technologies, and industries, and the accompanying transfor­ mation of the spacial and occupational distributions of the popula­ tion. Many economists agree with the broad outlines of Schum­ peter’ s vision of capitalist development, which is a far cry from growth models made nowadays in either Cambridge, Massachusetts or Cambridge, England. But visions of that kind have yet to be trans­ formed into a theory that can be applied to everyday analytic and empirical work” (Nordhaus and Tobin, 1972, p. 2).

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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