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Growth Theory and After

By: Solow, Robert M. 2014. “Robert M. Solow – Prize Lecture: Growth Theory and After (nobelprize.org).” Nobel Prize Prize Lecture. Nobel Media AB

To be used for Educational Purposes only 

I have been told that everybody has dreams but that some people habitually forget them even before they wake up. That is what happened to me. I have never dreamt about giving this Lecture. I know I have been in this room before, but that was in real life, and I was awake. If I had given this Lecture in my dreams, there is no doubt that the topic was the theory of economic growth. I am told that the subject of the Lecture should be “on or associated with the work for which the Prize was awarded.” That is pretty unambiguous. However, I would not even wish to use the leeway offered by the phrase “associated with.” Growth theory is precisely what I want to talk about: for itself, for its achievements, for the gaps that remain to be filled, and also as a vehicle for some thoughts about the nature of theoretical research in macroeconomics and empirical research as well.

Growth theory began after my articles of 1956 and 1957, and it indeed continued. Maybe it began with The Wealth of Nations; even Adam Smith had predecessors. More to the point, in the 1950s, I followed a trail marked out by Roy Harrod, Evsey Domar, and Arthur Lewis in a slightly different context. I was trying to track down and relieve a certain discomfort that I felt with their work. I will explain what I mean in a few words.

Harrod and Domar answered a straightforward question: When is an economy capable of steady growth at a constant rate? They arrived by noticeably different routes at a classically simple answer: the national saving rate (the fraction of income saved) has to be equal to the product of the capital-output ratio and the growth rate of the (effective) labor force. Then and only then could the economy keep its stock of plant and equipment in balance with its labor supply so that steady growth could continue without the appearance of labor shortage or labor surplus and growing unemployment. They were right about that general conclusion.

Discomfort arose because they worked this out on the assumption that all three key ingredients – the saving rate, the rate of growth of the labor force, and the capital-output ratio – were given constants, facts of nature. The saving rate was a fact about preferences; the growth rate of labor supply was a demographic-sociological fact; the capital-output ratio was a technological fact.

All of them were understood to be capable of changing from time to time, but sporadically and more or less independently. In that case, however, the possibility of steady growth would be a miraculous stroke of luck. Most economies, most of the time, would have no equilibrium growth path. The history of capitalist economies should be an alternation of long periods of worsening unemployment and labor shortage.

The theory suggested something even more dramatic. Harrod’s writings, especially, were complete of incompletely worked out claims that steady growth was, in any case, a precarious equilibrium: any little departure from it would be magnified indefinitely by a process that seemed to depend mainly on vague generalizations about entrepreneurial behavior. You may remember that John Hicks’s Trade Cycle book, which was based on Harrod’s growth model, needed to invoke a whole employment ceiling to generate downturns and a zero-gross-investment floor to generate upturns. Otherwise, the model economy would have run away.

Keep in mind that Harrod’s first essay was published in 1939, and Domar’s first article was published in 1946. Growth theory, like much else in macroeconomics, was a product of the depression of the 1930s and of the war that finally ended it. So was I. Nevertheless, it seemed that the story these models told felt wrong. Having read this literature, an expedition from Mars arriving on Earth would have expected to find only the wreckage of capitalism that had shaken itself to pieces long ago. Economic history was a record of fluctuations and growth, but most business cycles seemed self-limiting. Sustained, though disturbed, growth was not a rarity.

There was another implication of the Harrod-Domar model that seemed unsound. If the condition for steady growth is that the savings rate equals the product of the growth rate of employment and a technologically determined capital-output ratio, then a recipe for doubling the growth rate in a labor surplus economy was to double the savings rate, perhaps through the public budget. Well, not simply: we all knew then – as I am not sure we all know now – that doubling the ex-ante saving rate would not double the ex-post saving rate unless something was taking care of the ex-ante investment rate simultaneously. (I hope these strange Latin phrases are still understood in Stockholm in 1987!) In underdeveloped countries, however, where the appetite for new capital is likely substantial, the recipe looked usable. I remember that writings on economic development often asserted that the key to a transition from slow to fast growth was a sustained rise in the savings rate. The recipe sounded implausible to me. I can no longer remember exactly why, but it did.

That was the spirit in which I began tinkering with the theory of economic growth, trying to improve on the Harrod-Domar model. I can not tell you why I thought first about replacing the constant capital-output (and labor-output) ratio with a richer and more realistic representation of the technology. Even as a student, I was drawn to the theory of production rather than the formally almost identical theory of consumer choice. It seemed more down to Earth. I know that it occurred to me very early, as a natural-born macroeconomist, that even if the technology itself is not so very flexible for every single good at a given time, aggregate factor intensity must be much more variable because the economy can choose to focus on capital-intensive or labor-intensive or land-intensive goods. However, I found something interesting right away.

It would sound silly to explain what I found in any detail to this audience. Nearly everyone who spends any time in this room already knows. The “neoclassical model of economic growth” started a small industry. It stimulated hundreds of theoretical and empirical articles by other economists. It quickly found its way into textbooks and the fund of common knowledge of the profession. Indeed, that is what makes me think I am a respectable person to be giving this Lecture today. Nevertheless, I must summarize the outcome in a couple of sentences to move on to the more interesting questions about what remains unknown or uncertain and what remains to be found out.

It allows for a reasonable degree of technological flexibility to accomplish two things. First, the mere existence of a feasible path of steady growth was not a singular event. A range of steady states is possible, which may even be comprehensive if the range of aggregative factor intensities is wide. There are other ways in which an economy can adapt to the Harrod-Domar condition. However, variation in capital intensity is likely the most important.

Secondly, it was an implication of diminishing returns that the equilibrium growth rate is not only not proportional to the saving (investment) rate but is independent of the saving (investment) rate. A developing economy that succeeds in permanently increasing its saving (investment) rate will have a higher output level than if it had not and must grow faster for a while. However, it will not achieve a permanently higher output growth rate. More precisely, the permanent growth rate of output per unit of labor input is independent of the saving (investment) rate and depends entirely on the rate of technological progress in the broadest sense.

There was a third result that was useful and helped to make the model appealing to economists. Earlier growth theory was mechanical or physical, not in any bad sense but in the sense that it was almost entirely a description of flows and stocks of goods. In the neoclassical model, describing equilibrium paths and working out the price and interest rate dynamics that would support an equilibrium path was natural and practical. It did not occur to me at the time that I was bringing good and bad news in doing this. The good news was that economists instinctively like to think that way, and the connection would help to get my professional colleagues interested in growth theory.

Moreover, it is a good (fruitful) instinct, whether dealing with a capitalist or a socialist economy. The bad news is that the connection is overly pretty and exciting and unleashes a temptation to sound like Dr. Pangloss, a very clever Dr. Pangloss. That tendency has won out in recent years, as I shall try to explain later, though it may be too late for me to pretend to be Candide.

When I look back now at the articles I wrote on this general subject in the 1950s and 1960s, I am struck and even a little surprised at how much effort went into broadening the technological framework of growth theory. I wanted to make sure that the model could accommodate the likelihood that new technology can only be introduced with the use of newly designed and produced capital equipment and that factor proportions might be variable only at the instant of gross investment and not after capital equipment had taken some particular form, and that enough flexibility could be achieved with discrete activities, even with only one activity so long as the length of life of capital goods could be chosen economically. Moreover, in every case, I wanted to show that the appropriate commodity-price-factor-price relations could be worked out and made intelligible in terms of the inherited instincts of economists. (In my case, I inherited them mainly from Knut Wicksell and Paul Samuelson.)

The reasons for this particular orientation seemed compelling at the time. In the first place, introducing technological flexibility opened up growth theory to a wider variety of real-world facts and a closer connection with general economic theory. Ensuring these gains were not tied too closely to an indefensibly simple version of factor substitution seemed essential. Secondly, I had already begun empirical work using an aggregate production function with meaningful and surprising results. I was very skeptical about this device, and I knew that others would have doubts about their own. It was a good idea to make sure that the method was capable, at least in principle, of dealing with the first few doses of realism.

Furthermore, thirdly, I was already trapped in the famous “Cambridge controversy.” I use the word “trapped” because that whole episode now seems to me to have been a waste of time, a playing out of ideological games in the language of analytical economics. At the time, I thought – and the literature gave some reason to think – that part of the argument was about marginalism, about smooth marginalism. So, I wanted to show that the conclusions of the theory and its empirical implementation were not bound to that exceptional formulation. It was worth doing, but it certainly did not pacify anyone.

There was one lousy by-product of this focus on the description of technology. I paid too little attention to the problems of effective demand. To put it differently, a theory of equilibrium growth badly needed – and still needs – a theory of deviations from the equilibrium growth path. I can honestly say that I realized the need at the time. A brief section at the end of my 1956 article deals in a perfunctory way with the implications of real-wage rigidity and the possibility of a liquidity trap. That was just a lick and a promise. There was also a paragraph that I am prouder of: it made the point that growth theory provides a framework within which one can seriously discuss macroeconomic policies that not only achieve and maintain full employment but also make a deliberate choice between current consumption and current investment, and therefore between current consumption and future consumption. Only a few years later, I had the memorable experience in the Kennedy-Heller Council of Economic Advisers of seeing those ideas written into the 1962 Economic Report (which is about to be republished by the MIT Press). The history of the past seven years in the United States suggests that the lesson has not yet been learned in Washington.

The problem of combining long-run and short-run macroeconomics still needs to be solved. I will come back to it later on. This is the place for me to confess to (and explain away) an inevitable youthful confusion. In the early discussions of the Harrod-Domar growth theory, there was much talk about the intrinsic instability of equilibrium growth. “Instability” could and did mean two different things, and the meanings were not always clearly distinguished. It could mean that badly-behaved equilibrium paths surround those well-behaved equilibrium paths so that a tiny sideward step could lead to eventual disaster. Alternatively, it could mean that instability applies to disequilibrium behavior so that an economy that once strays from equilibrium growth would not automatically find its way back to any equilibrium growth path.

The original Harrod-Domar model was subject to both these difficulties. I showed that the model extension took the sting out of the first sort of instability. The second sort, however, involves integrating both short- and long-run macroeconomics of growth and business-cycle theories. Harrod and many contemporary commentators went at this problem by making extraordinary (and unconvincing) assumptions about investment behavior. I may not have been as clear then as I am now about the distinction between the two notions of instability. Today, I would put the unsolved problem as follows. One of the achievements of growth theory was to relate equilibrium growth to asset pricing under tranquil conditions. The hard part of disequilibrium growth is that we need to have, and it may be impossible to have a perfect theory of asset valuation under turbulent conditions. (1987 is an excellent year in which to make that observation!)

One significant tendency in contemporary macroeconomic theory is to evade this problem in an elegant but (to me) ultimately implausible way. The idea is to imagine that a single immortal consumer or several identical immortal consumers populate the economy. The immortality itself is not a problem: each consumer could be replaced by a dynasty, each member of which treats her successors as extensions of herself. However, no short-sightedness can be allowed. This consumer does not obey any simple short-run saving function or a stylized Modigliani life-cycle rule of thumb. Instead, she, or the dynasty, is supposed to solve an infinite-time utility-maximization problem. That strikes me as far-fetched but not so awful that one would not want to know where the assumption leads.

The next step is more challenging to swallow in conjunction with the first. For this consumer, every firm is just a transparent instrumentality, an intermediary, a device for intertemporal optimization subject only to technological constraints and initial endowments. Thus, any market failure is ruled out from the beginning by assumption. There are no strategic complementarities, coordination failures, or prisoners’ dilemmas.

The result is a construction in which the whole economy is assumed to solve a Ramsey optimal-growth problem through time, disturbed only by stationary stochastic shocks to tastes and technology. To these, the economy adapts optimally. The automatic presumption that observed paths are equilibrium is inseparable from this habit of thought. So, we are asked to regard the construction I have just described as a model of the actual capitalist world. What we used to call business cycles – or at least booms and recessions- are now interpreted as optimal blips in optimal paths in response to random fluctuations in productivity and the desire for leisure.

I find none of this convincing. The markets for goods and labor look to me like imperfect pieces of social machinery with important institutional peculiarities. They do not behave like transparent and frictionless mechanisms for converting households’ consumption and leisure desires into production and employment decisions. I can not imagine shocks to taste and technology large enough on a quarterly or annual time scale to be responsible for the ups and downs of the business cycle. However, now I have to report something disconcerting. I refer you to an able, civilized, and severe example of this approach and suggest that you will find it hard to refute. You can find non-trivial objections to essential steps in the argument, but that would be true of any powerful macroeconomic model.

There is a dilemma here. When I say that Prescott’s story is hard to refute, it does not follow that his case can be proved. Quite the contrary: there are other models, inconsistent with his, that are just as hard to refute, maybe harder. The conclusion must be that historical time series do not provide a critical experiment. This is where a chemist would move into the laboratory to design and conduct just such an experiment. That option is not available to economists. My tentative resolution of the dilemma is that we have no choice but to take seriously our own direct observations of the way economic institutions work. There will, of course, be arguments about the modus operandi of different institutions, but there is no reason why they should not be intelligible, orderly, fact-bound arguments. This sort of methodological opportunism can be uncomfortable and unsettling, but at least it should be able to protect us from foolishness.

Since what I have just said goes against the spirit of the times, I would like to be very explicit. No one could be against time-series econometrics. When we need estimates of parameters for prediction or policy analysis, there is no reasonable alternative to the specification and estimation of a model. To leave it at that, however, to believe, as many American economists do, that empirical economics begins and ends with time series analysis is to ignore much valuable information that can not be put into a convenient form. I include the sort of information that is encapsulated in the qualitative inferences made by expert observers, as well as direct knowledge of the functioning of economic institutions. Skepticism is always in order, of course. Insiders are sometimes the slaves of silly ideas. However, we are not so well off for evidence that we can afford to ignore everything but time series of prices and quantities.

After this methodological digression, I should remind you of the direction of my main argument. Growth theory was invented to provide a systematic way to talk about and compare economic equilibrium paths. In that task it succeeded reasonably well. In doing so, however, it could have come to grips adequately with an equally important and interesting problem: the right way to deal with deviations from equilibrium growth. One possible solution strikes me as wrong-headed: denying the existence of an analytical problem by claiming that “economic fluctuations” are not deviations from equilibrium growth at all but examples of equilibrium growth. My impression is that belief in this story is more or less confined to North America. Maybe the experiences of European economies do not lend themselves to this interpretation at all. What alternatives are there?

It will not do simply to superimpose your favorite model of the business cycle on an equilibrium growth path. That might do for minimal deviations, more like minor, slightly autocorrelated “errors.” However, suppose one looks at substantial, more-than-quarterly departures from equilibrium growth, as suggested, for instance, by the history of the large European economies since 1979. In that case, it is impossible to believe that the equilibrium growth path itself is unaffected by the short- to medium-run experience. In particular, the amount and directions of capital formation are bound to be affected by the business cycle, whether through gross investment in new equipment or the accelerated scrapping of old equipment. I am also inclined to believe that the labor market segmentation by occupation, industry, and region, with varying amounts of unemployment from one segment to another, will also react back on the equilibrium path. So, a simultaneous analysis of trends and fluctuations does involve an integration of long-run and short-run, or equilibrium and disequilibrium.

The most straightforward strategy is a familiar one from other contexts. In a wholly aggregated growth model, the relevant prices are the real wage and actual interest rate. Suppose they are both rigid or merely adjust very slowly to excess supplies in the markets for labor and goods. (The more usual assumption is that only the wage is sticky, but in Wicksell’s native habitat, we should allow for a divergence between the “natural” and “market” rates of interest.) Then, the economy may be away from any full equilibrium path for a long time. During that time, its evolution will be governed by short-run dynamics, much like everyday business-cycle theory.

The most interesting case to consider is where real wage and interest rates are stuck at levels that lead to an excess supply of labor and goods (saving greater than investment ex-ante). This is the sort of configuration we call “Keynesian.” The big difference is that net investment may be positive or negative; industrial capacity may rise or fall. The economy may eventually return to an equilibrium path, perhaps because “prices are flexible in the long run,” as we keep telling ourselves. If and when it does, it will not continue the equilibrium path it was on before it slipped off. The new equilibrium path will depend on the amount of capital accumulation that has occurred during the period of disequilibrium and probably also on the amount of unemployment, especially long-term unemployment, that has been experienced. Even the level of technology may be different if technological change is endogenous rather than arbitrary.

This is the amendment that I mentioned in 1956 but did not pursue very far. An excellent exploratory sketch by Edmond Malinvaud uses this fix-price approach to growth theory. As you would expect, the investment function plays an important role. This is what I meant when I referred earlier to the complex asset valuation problem away from an equilibrium path. We are reduced to some more or less plausible formulation guided by more or less robust econometric results and by whatever we think we know about investment decision-making in actual firms. Malinvaud emphasizes “profitability” as a determinant of investment, but he also emphasizes that the precise meaning of profitability is unclear whenever the future is unclear.

The main result of Malinvaud’s analysis is clarifying the condition under which a “Keynesian” steady state is possible and when it is locally stable, i.e., when it will be approached by an economy disturbed from a nearby equilibrium path. The unstable case is just as interesting because it suggests the possibility of small causes having significant results. All these stability arguments must be tentative because the interest rate and real wage are assumed to be fixed while quantities move. That is not an adequate reason to dismiss the results in a purist spirit, but the research program is obviously incomplete.

A sketch by Malinvaud is as good as a book by someone else. My own inclination – it is just an inclination – is to try a slightly different slant. Thinking about the ambiguousness of the concept of profitability and its relation to investment reminds one that many firms react to changed circumstances precisely by changing their prices. The obvious alternative to a model with sticky prices is a model with imperfectly competitive price-setting firms. Then, of course, one can no longer speak simply of an excess supply of goods. However, we can find something just as interesting: the possibility of many coexisting equilibrium paths, some of which are unambiguously better than others. (Usually, the better ones have higher output and employment than the worse ones, so something like a recession makes an appearance anyway.) The interaction of growth and business cycle can take a slightly different form: alternating good and bad equilibria is not just a simple averaging.)

This model is now familiar in a static context, where it can make good working sense of the notion of “effective demand.” Firms will naturally condition their actions on beliefs about economic aggregates. Frank Hahn and I are working on extending it to a model of overlapping generations so that it would be easy to convert any stationary equilibrium state into a growing steady state. Preliminary indications are that the thing can be done. Therefore, there is hope that either the fixed-price or imperfect-competition approaches can allow us to talk sensibly about macroeconomic policy in a growth context.

In my 1956 paper, there was already a brief indication of how neutral technological progress could be incorporated into an equilibrium growth model. It was a necessary addition because otherwise, the only steady states of the model would have constant income per person, which could hardly be a valid picture of industrial capitalism. Technological progress, very broadly defined to include improvements in the human factor, was necessary to allow long-run growth in real wages and the standard of living. Since an aggregate production function was already part of the model, it was natural to think of estimating it from long-run time series for a real economy. That, plus a few standard parameters – like saving rate and population growth – would make the model operational.

Estimating an aggregate production function was a familiar idea. However, I did have a new wrinkle in mind: to use observed factor prices as indicators of current marginal productivities so that each observation would give me an approximate point on the production function and an approximate indication of its slopes. This idea was suggested to me by equilibrium growth theory. I did not then have any notion I was doing something intensely controversial.

The first few paragraphs of my 1957 article are thoroughly ambivalent, not about the method but about using aggregate data on inputs and output. After expressing my doubts, I went ahead in a pragmatic spirit. One can only do macroeconomics with aggregative relationships; at least for now, there is no substitute for macroeconomics. The only way I can account for the intensity of controversy over this point is to ascribe it to the belief that there is something intrinsically ideological about the notion that profits on “capital” represent the return to a factor of production as imputed by the market. John Bates Clark may have thought, a century ago, that distribution according to marginal products was “just,” but no modern economist, no modern “bourgeois” economist, would accept that reasoning.

Anyway, the main result of that 1957 exercise was startling. Gross output per hour of work in the U. S. economy doubled between 1909 and 1949, and some seven-eighths of that increase could be attributed to “technical change in the broadest sense,” and only the remaining eight could be attributed to conventional increase in capital intensity. Actually, Solomon Fabricant at the National Bureau of Economic Research had come up with a similar breakdown for a slightly earlier period, using methods with less in the way of an analytical foundation. I think I had expected to find a more prominent role for straightforward capital formation than I found; I will come back to that point soon.

The broad conclusion has held up surprisingly well in the thirty years since then, during which “growth accounting” has been refined quite a lot, especially by Edward Denison. The primary refinement has been to unpack “technical progress in the broadest sense” into several constituents, of which various human-capital variables and “technological change in the narrow sense” are the most important. To give you an idea of the current state of play, I shall quote Denison’s most recent estimates for the United States.

Taking the period from 1929 to 1982 and smoothing away the business cycle, he finds that the actual non-residential business output increased at an average rate of 3.1 percent a year. The problem now is to parcel this out among several primary determinants of growth. Denison estimates that a quarter of it can be attributed to increased labor input of constant educational level. Another 16 percent (i.e., about 1/2 percent a year) is credited to the increased educational qualifications of the average worker. The growth of “capital” accounts for 12 percent of the output growth; this is coincidentally almost exactly what I found for 1909-1949 using my original method, of which Denison’s is in some ways a practical refinement. Then Denison imputes 11 percent of total growth to “improved allocation of resources” (by which he means labor movement from low-productivity agriculture to higher productivity industry). Another 11 percent goes to “economies of scale” (but this must be a very insecure imputation). Finally, 34 % of recorded growth is credited to “the growth of knowledge” or technological progress in the narrow sense. If you add these percentages, you will see that Denison has accounted for 109 percent of measured growth. Miscellaneous factors must have reduced output growth by nine percent of 3.1 percent, or just under 0.3 percent yearly. (These negative factors could include investment in environmental improvement, which uses resources but does not appear in measured output, though it may be very valuable.)

This detailed accounting is an improvement on my first attempt but leads to roughly the same conclusion. Remember that I distinguished only three factors: straight labor, straight capital, and residual “technical change.” Denison decomposes the residual into five components, but the flavor is similar.

The similarity is more substantial if one looks at Denison’s results on a “per person employed” basis. Actual output per person employed grew by 1.7 percent per year between 1929 and 1982. Labor input per person employed accounted for – 23 percent of this. That sounds strange, but it means that hours worked per year per person employed fell during the period, so the average employed person provided less straight labor time. I will not go over the full imputation. I want to point out that education per worker accounts for 30 percent of the increase in output per worker, and the advance of knowledge accounts for 64 percent in Denison’s figures. Thus, technology remains the dominant growth engine, with human capital investment in second place. One does not have to believe in the accuracy of these numbers; the message they transmit is pretty clear anyway.

That is meant as a profound remark. If I reverted to methodological propaganda again, I want to remind my colleagues and their readers that every piece of empirical economics rests on a substructure of background assumptions that are probably not entirely true. For instance, these total-factor-productivity calculations require that market prices can serve as a rough and ready approximation of marginal products. That aggregation does not hopelessly distort these relationships. Under those circumstances, robustness should be the supreme econometric virtue, and over-interpretation is the endemic econometric vice. So, I would be happy if you accepted that the results I have been quoting point to a qualitative truth and give some guide to orders of magnitude. To ask for much more than that is to ask for trouble. I would also like to quote the profound warning the leading student of baseball statistics issued – it hangs in my office – “No amount of (apparent) statistical evidence will make a statement invulnerable to common sense.”

The mention of common sense brings to mind another aspect of this story that is still unsettled in the literature. Initially, I was surprised at the relatively minor part of the model ascribed to capital formation. Even when Denison and others confirmed this, the result seemed contrary to common sense. The fact that the steady-state growth rate is independent of the investment quota was easy to understand; it only required thinking through the theory. It took more work to feel comfortable with the conclusion that even in the shorter run, increased investment would do very little for transitory growth. The transition to a higher equilibrium growth path offers very little leverage for a policy-promoting investment.

The formal model omitted one mechanism whose absence would bias the predictions against investment. That is what I call “an embodiment,” much technological progress, maybe most of it, could find its way into actual production only with the use of new and different capital equipment. Therefore, the effectiveness of innovation in increasing output would be paced by the gross investment rate. A policy to increase investment would thus lead not only to higher capital intensity, which might not matter much but also to a faster transfer of new technology into actual production, which would. Steady-state growth would not be affected, but intermediate-run transitions would, and those should be observable.

That idea corresponded to common sense, and it still does. By 1958, I produced a model that allowed for the embodiment effect. A certain amount of simplicity was lost because the capital stock could no longer be regarded as a homogenous lump. One had to keep track of its age structure, but that was precisely the point. The model was workable, even if it needed to be more neat. If common sense was proper, the embodiment model should have fit the facts significantly better than the earlier one. However, it did not. Denison, whose judgment I respect, concluded that the embodiment idea had no explanatory value. I do not know if that finding should be described as a paradox, but it was at least a puzzle.

While preparing this Lecture, I came across a recent working paper by Professor Edward N. Wolff (of New York University) offering a longer-run perspective. Wolff compiled data for seven large countries (Canada et al., the United Kingdom, and the United States) covering the whole century from 1880 to 1979. He also paid particular attention to the postwar period 1950-79. These countries were selected for data availability only, so they can not be considered representative samples. Wolff’s result is, therefore, only suggestive, but it is an exciting suggestion.

For each of the countries, he calculates the average growth rate of Total Factor Productivity (i.e., what I have called the rate of technical progress in the broad sense) and various measures of the speed of investment. (For instance, he looks at the capital stock’s growth rate, the capital-labor ratio’s growth rate, and the average investment quota itself.) Then, looking across countries, he finds a robust positive correlation between the rate of technical progress and the speed of investment. His interpretation is that this strongly confirms the embodiment hypothesis. If all these countries had access to roughly the same pool of technological innovations, then the ones that invested fastest were best able to take advantage of the available knowledge. That is undoubtedly one reasonable interpretation, and it is one I like. Keep in mind that, by using total factor productivity, Wolff has already “given” to investment its traditional function of increasing productivity by increasing capital intensity, so the remaining correlation is between investment and the shift of the aggregate production function.

To be faithful to my own methodological precepts, however, I remind you that other interpretations are also possible. For example, it could be the case that some countries are better able to exploit the shared pool of technological progress than others for reasons that have nothing to do with the rate of capital formation, but in precisely those technologically progressive countries, investment is most profitable, so naturally the rate of investment is higher. Alternatively, rapid technical progress and high investment could be the result of some third factor, like the presence of conditions that encourage entrepreneurial activity. High investment and fast technical progress will then go together.

I can not argue strongly one way or the other. However, at least the way remains open for a reasonable person to believe that the stimulation of investment will favor faster intermediate-run growth through its effect on the transfer of technology from laboratory to factory.

Before I finish, combining most of the building blocks I have discussed in a small but relatively complete econometric model is possible. If that were not possible, I would find the ideas less interesting. It has been done. One example is the “annual growth model of the U.S. economy” by Bert Hickman and Robert Coen.

This is a model whose production side is ultimately aggregated and is, in fact, just precisely the sort of thing I have been talking about. (The demand side is disaggregated, which is not important now.) The full equilibrium paths of the Hickman-Coen model are precisely those made familiar by growth theory, more general because the determination of saving and the evolution of the labor force are looked after in more detail.

That part is relatively straightforward. In some recent exercises, however, Hickman and Coen have started a serious study of deviations from equilibrium growth in precisely the spirit that Malinvaud and me recommended. They allow for absolute wage rigidity and model their producing sector as a price-setting monopolistic competitor. Now, investment does not have to be equal to full-employment saving, except in complete equilibrium. Periods of boom and stagnation can appear, to almost no one’s surprise. There can be “Keynesian” and “classical” unemployment. Indeed, there can be both simultaneously: the real wage might be too high to allow full employment with existing capital stock, while at the same time, aggregate demand is inadequate to take off the market what firms wish to produce. Changes in the real wage could have demand-side and supply-side effects.

All this sounds very good. It sounds like the macroeconomics that pragmatic Americans and Swedes have practiced. I can not vouch for the Hickman numbers, but they are at least sensible. By the way, they show that high-real-wage induced unemployment was negligible in the U.S. between 1959 and 1978 and was then again dwarfed by low-demand induced unemployment in 1981 and 1982. I am still determining their story for the years after 1982, but the fact that I would like to know speaks well for the model.

In this brief review of the goals and achievements of growth theory, I have referred as much to the work of others as to my own. That is more than mere modesty: the choice reflects my belief that any successful line of economic analysis will almost certainly be a group product. We attach names to ideas for good and bad reasons, but valuable ideas are usually worked out and critically refined by a research community. I have some faith that the ideas of “neoclassical” growth theory are viable just because they have attracted a research community, even a relatively diverse community: Lucas and Prescott build on the basic model, and so do Malinvaud and “sunspot” theorists like Karl Shell and others.

When I read Robert Frost’s lines from “The Black Cottage”:

Most of the changes we think we see in life

is due to truths being in and out of favor

It occurred to me at once that they sound altogether too much like economics. Some of that feeling is inevitable and not necessarily to be regretted. The permanent substructure of applicable economics can not be too large because social institutions and norms evolve, and the characteristics of economic behavior will surely evolve with them. I also believe that part of the changeability of economic ideas on a shorter time scale is our own doing. It comes from trying too hard, pushing too far, asking more refined questions of limited data, over-fitting our models, and over-interpreting the results. This, too, is probably inevitable and not primarily to be regretted. You never know if you have gone as far as you can until you try to go further.

Naturally, growth theory can serve in both ways: as a background on which to hang multi-sector models that probably try to do more that can be done and as a framework for simple, robust, loosely quantitative propositions about cause and effect in macroeconomics. The fundamental intellectual need for both roles is for a common understanding of medium-run departures from equilibrium growth. That is the stuff of everyday macroeconomics. It has happened in English-speaking countries since Keynes and in Sweden since Lindahl and the Stockholm School. It is going on in both places today.

References

Denison, E., Trends in American Economic Growth, 1929-1982, Brookings Institution, 1985
Hickman, B., “Real Wages, Aggregate Demand, and Unemployment,” European Economic Review December 1987.
Hickman, B. and R. Coen, An Annual Growth Model of the U.S. Economy, North-Holland, 1976
Malinvaud, E., “Notes on Growth Theory with Imperfectly Flexible Prices,” in Modern Macroeconomic Theory, (ed. J-P Pitoussi) Basil Blackwell, 1983
Prescott, E., “Theory Ahead of Business Cycle Measurement,” Working Paper, Federal Reserve Bank of Minneapolis, February 1986
Solow, R., “A Contribution to the Theory of Economic Growth,” Quarterly Journal of Economics, February 1956
– “Technical Change and the Aggregate Production Function,” Review of Economics and Statistics, August 1957
– “Investment and Technical Progress” in Mathematical Methods in the Social Sciences, 1959 (ed. K. Arrow, S. Karlin, P. Suppes) Stanford University Press, 1960
– J. Tobin, C. von Weizsaecker, and M. Yaari, “Neoclassical Growth with Fixed Factor Proportions,” Review of Economic Studies, April 1966
Wolff, E., “Capital Formation and Long-Term Productivity Growth,” Working Paper, C. V. Starr Center for Applied Economics, New York University, September 1987

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