Oxford Review of Economic Policy, Volume 23, Number 1, 2007, pp.3–14
Robert M. Solow∗ Abstract This article offers a personal view of the main achievements of (broadly) neoclassical growth theory, along with a few of the important gaps that remain. It discusses briefly the pluses and minuses of two major recent lines of research: endogenous growth theory and the drawing of causal inferences from international cross-sections, and criticizes the widespread contemporary tendency to convert the normative Ramsey model into a positive representative-agent macroeconomic model applying at all frequencies. Finally, it comments on the articles appearing in this symposium. Key words: Solow growth model, growth theory, 1956 anniversary JEL classification: B22, E13, O41
I am cheered and delighted by the attention paid to this anniversary; but I am also a little embarrassed. Why embarrassed? Because I really believe that progress in economics (and other similar disciplines) comes more from research communities than from any one individual at a time. It is research communities that separate the good stuff from the routine, and see to it that the sillier outcroppings of imagination get sanded down. At least it works that way most of the time. We owe more than we acknowledge to our colleagues and graduate students. Here is a partial example that I will come back to in a minute. If you have been interested in growth theory for a while, you probably know that Trevor Swan—who was a splendid macroeconomist—also published a paper on growth theory in 1956 (Swan, 1956). In that article you can find the essentials of the basic neoclassical model of economic growth. Why did the version in my paper become the standard, and attract most of the attention? I think it was for a collection of reasons of different kinds, none individually of very great importance. For instance, Swan worked entirely with the Cobb–Douglas function; but this was one of those cases where a more general assumption turned out to be simpler and more transparent. As a result, his way of representing the model diagrammatically was not
∗ Massachusetts Institute of Technology doi: 10.1093/icb/grm004 The Author 2007. Published by Oxford University Press. For permissions please e-mail:
[email protected]
Downloaded from http://oxrep.oxfordjournals.org/ at Universidad Nacional Autónoma de México on May 5, 2013
The last 50 years in growth theory and the next 10
4
Robert M. Solow
Downloaded from http://oxrep.oxfordjournals.org/ at Universidad Nacional Autónoma de México on May 5, 2013
so clear and user-friendly. A second and more substantial reason was that Swan saw himself as responding to Joan Robinson’s complaints and strictures about capital and growth, while I was thinking more about finding a way to avoid the implausibilities of the Harrod–Domar story (Harrod, 1939; Domar, 1946). (I will tell you a relevant anecdote in a minute.) That is to say, I happened to be coming at the problem from a more significant direction. A third reason is that Swan was an Australian writing in the Economic Record, and I was an American writing in the Quarterly Journal of Economics. The community of growth theorists took it from there. When I finished that 1956 paper, I had no idea that it would still be alive and well 50 years later, more or less part of the folklore. Nor did I understand that it would be the origin of an enormous literature and a whole cottage industry of growth-model building that is still flourishing, as the articles in this issue of the Review demonstrate. So why was it such a success? Are there methodological lessons to be learned about How To Make An Impression? My own favourite how-to-do-it injunctions are: (i) keep it simple; (ii) get it right; and (iii) make it plausible. (By getting it right, I mean finding a clear, intuitive formulation, not merely avoiding algebraic errors.) I suspect that all three of these maxims were working for that 1956 paper. It was certainly simple; it didn’t get lost in the complications and blind alleys that beset Trevor Swan’s attempt; and it was plausible in the sense that it fitted the stylized facts, offered opportunities to test and to calibrate, and didn’t require you to believe something unbelievable. Here is where the anecdote that I promised comes in. I spent the year 1963–4 in Cambridge, England, engaged in one interminable and pointless hassle with Joan Robinson about some of these issues. Interminable is bad enough, pointless is bad enough, and putting them together is pretty awful. The details are too lurid to be told to young people. At one point, however, I realized that the discussion had become metaphysical and repetitive, and I decided to try a new tack. So I buttonholed Joan in her office one day and said: ‘Imagine that Mao Tse-Tung calls you in’—she was in her Chinese period then—‘and asks a meaningful question. The People’s Republic has been investing 20 per cent of its national income for a very long time. There is now a proposal to increase that to 23 per cent. To make a correct decision, we need to know the consequences of such a change. Professor Robinson, how should we calculate what will happen if we increase our investment quota and sustain it?’ ‘So what will you tell Chairman Mao?’ I asked Joan. She baulked and bridled and dodged and changed the subject, but for once I was relentless. ‘Come on, Joan, this is Chairman Mao asking a legitimate economic question; the future of the People’s Republic and possibly of mankind may depend on the answer. What do you tell him?’ Finally, she grumbled: ‘Well, I guess a constant capital–output ratio will do.’ It made my day; I knew I could do better than that, and I knew she had been forced by practicality, even imaginary practicality, to give up the metaphysical ghost. I was smiling all the way home to tell my wife that Joan had buckled, and violated her own metaphysics. One of her major contentions had been that it was illegitimate to think of ‘capital’ as a factor of production with a marginal product. Yes, a single capital good (or its services) was a productive input. But aggregating those goods, whose services are yielded over their remaining lifetimes, introduces all sorts of complications. It is always a problem in economics to navigate between pure and abstract conceptions (how would a concept like ‘capital’ fit into a complete and formal description of an economy) and the needs of practical calculation (Mao’s hypothetical question). It can (almost) never be done perfectly. I thought that Joan Robinson had been unfairly playing on that difficulty in order to undermine the ‘neoclassical’
The last 50 years in growth theory and the next 10
5
Downloaded from http://oxrep.oxfordjournals.org/ at Universidad Nacional Autónoma de México on May 5, 2013
attempt to construct a usable model of investment and growth. Faced with the need to be pragmatic, she had no recourse but the kind of statement that she had criticized in others. That is what I mean by making it plausible: a simple, clear model should tell you how to get from empirical beliefs to practical conclusions. There will always be additions and modifications to fit the occasion, but the model should provide a road map. I still think that is how growth theory should be done, though the beliefs and conclusions may, of course, change through trial and error and the passage of time, and reasonable conclusions can’t be more detailed than the model will bear. With those general principles as background, I suppose I should say something about the two most important innovations to come along in the past 50 years within the framework of neoclassical growth theory. The two I have in mind are, as I hope you would guess, first, ‘endogenous growth theory’ as pioneered by Paul Romer (1986) and Robert Lucas (1988), and then taken up by an army of economists, and, second, the drawing of inferences about the determinants of economic growth from international cross-sections, an activity whose first protagonist may have been Robert Barro (1991), also with innumerable followers among individuals and institutions. This second line of thought only became thinkable after the publication of the Penn World Tables by Robert Summers and Alan Heston. No arguments without numbers, and they provided the numbers. The story of endogenous growth theory may (repeat: may) turn out to be a good example of the way a research community takes a new thought and moulds it into something useful. One of the earliest products of endogenous growth theory was the so-called AK model, which I thought from the first to be a distraction. It claimed to endogenize the steady-state growth rate by what amounted to pure surface assumption. It was simple, all right, but neither right nor plausible. The community eventually made an implicit judgment and sees less of it these days. Then a further thought dawned on me. If you want to endogenize ‘the’ growth rate of x, you are going to need a linear differential equation of the form dx/dt = G(.)x, where the growth-rate G is a function of things you think you know how to determine (but not a function of x or its growth rate). Exponential curves come from that differential equation. So buried in every ‘endogenous growth’ model there is going to be an absolutely indispensable linear equation of that form. And sure enough, if you root around in every such model you find somewhere the assumption that dx/dt = G(.)x, where x is something related to the level of output. It may be the production function for human capital, or the production function for technological knowledge, or something else, but it will be there. And the plausibility of the model depends crucially on the plausibility and robustness of that assumption. I want to emphasize how special this is: it amounts to the firm assumption that the growth rate of output (or some determinant of output) is independent of the level of output itself. If you want to endogenize the steady-state growth rate in a model driven by human-capital investment or technological progress, you need precisely this linearity. But then, I think, you owe the community a serious argument that this assumption is either self-evident or robustly confirmed by observation. My impression is that this demonstration has not been forthcoming. The literature seems to take it for granted and move on to elaboration. Is that just all in the game? I think there has been one unfortunate semi-practical consequence. Some of the literature gives the impression that it is after all pretty easy to increase the long-run growth rate. Just reduce a tax on capital here or eliminate an inefficient regulation there, and the reward is fabulous, a higher growth rate forever, which is surely more valuable than any lingering bleeding-heart reservations about the policy itself. But in real life it is very hard to move the permanent growth rate; and when it happens, as
6
Robert M. Solow
Downloaded from http://oxrep.oxfordjournals.org/ at Universidad Nacional Autónoma de México on May 5, 2013
perhaps in the USA in the later 1990s, the source can be a bit mysterious even after the fact. Endogenizing the steady-state growth rate is a serious ambition and deserves serious effort. An alternative idea may be to focus less on the notion of exponential growth. One can easily imagine classes of models and exogenous influences that do not even allow for episodes of steady-state exponential growth. That would have to be a more computer-oriented project, but the building-up of simulation experience under varied assumptions may lead to general understanding. In the meantime, I suspect that the most valuable contribution of endogenous growth theory has not been the theory itself, but rather the stimulus it has provided to thinking about the actual ‘production’ of human capital and useful technological knowledge. An important example of progress in this direction is the body of work on ‘Schumpeterian’ models, much of it focused on the idea of ‘creative destruction’. There have been several contributions, dominated by the impressive collection of results by Philippe Aghion and Peter Howitt, together and separately (see, for example, Aghion and Howitt, 1992). I cannot do justice here to their translation of Schumpeter’s imprecise notion into explicit models that can be and have been pursued to a very detailed level. But it illustrates how progress can be made. Their 1998 book is a monumental compilation (Aghion and Howitt, 1998). I have no idea whether it will be possible to reduce these motives and processes to the simple formulas that can go into a growth model. It is not so important; any understanding that is gained can probably be patched into growth theory, formally or informally. Precisely for that reason, one wonders why there has been so little contact with those scholars who study the organization and functioning of industrial laboratories and other research groups. Now, what about international cross-section regressions, or what is sometimes called ‘empirical growth theory’? There are two distinct varieties. The first, which is primarily aimed at using cross-section observations to learn something about the aggregative technology, is a serious matter. I think one has to be precise about what the countries in the sample are assumed to have in common and what is allowed to differ among them. The literature has not always been careful about this. The paper in this issue by Erich Gundlach is an excellent example of the genre. I think I will save my handful of comments for later. The second variety proceeds by regressing the country-specific growth rates during some medium-long period on a potentially long list of country characteristics. Many of the right-hand-side variables are socio-political, some are intended as indicators of regulatory inefficiency, some are ‘cultural’. Here I think a little modesty is in order. At a minimum, those regressions provide interesting descriptive statistics. It can only be useful to have a good idea of which national characteristics are associated with faster growth during a fairly long period across a large sample of countries. It is when the regressions are interpreted causally that I begin to look for an exit. Reverse causation is only the most elementary of the difficulties. Maybe democracy and social peace lead to growth; I certainly hope so. But growth may also lead to democracy and social peace; and since both sides of that relation are likely to change slowly, the usual econometric dodge of lagging a variable cannot convincingly settle the issue. There is also reason to wonder about the robustness of the regression coefficients against variations in sample period, functional form, choice of regressors, and so on. But there are other, deeper, problems. The proper left-hand-side variable is growth of total factor productivity (TFP) rather than of output itself, because that is what the right-hand-side variables are likely to be able to affect. The array of non-economic influences on TFP is certainly large and interrelated. Anyone who wants to interpret a cross-country regression causally has to believe that a particular coefficient really tells you what will happen to the
The last 50 years in growth theory and the next 10
7
Downloaded from http://oxrep.oxfordjournals.org/ at Universidad Nacional Autónoma de México on May 5, 2013
growth rate of a country that experiences an increase of the variable in question by , and also tells you what will happen if, a few years later, the same variable decreases by the same . Maybe so; but it is surely troubling that we have not observed such manoeuvres. I will continue to think of these things as shorthand descriptions rather than as recipes for economic change. You should, of course, ask yourself whether one of those regressions plausibly represents a surface along which countries can actually ‘decide’ to move (back and forth, remember). That is the acid test. There is very little space left for stray thoughts about the future of growth theory, which is probably a good thing; no one can know what the next advance (or fad) is likely to be. I will just mention a couple of issues that seem to me to have been under-researched until now. The first is open-economy growth theory—the incorporation of trade, capital movements, and technology transfer into a multi-country model of growth. Grossman and Helpman (1991) was the pioneering text; but it attracted attention more for its quality-ladder models than for its analysis of trading economies. There have been a few further contributions, but nothing definitive. Laundry-list regressions have sometimes found an association between an economy’s openness to trade and its growth rate. Classical gains-from-trade theory would suggest an association between openness and the level of output. If there is a connection between trade and growth, one ought to be able to model it convincingly. I am not aware that there is any generally accepted story about this. Perhaps there is and I have missed it. Otherwise one wonders why more growth theorists aren’t trying. Foreign direct investment plays a very important role in practice. Why not in theory? That brings me naturally to a second analytical gap that could perhaps be filled in the next few years. We have watched the major European economies almost reach US productivity levels, and then fall back slightly; we remember the years of extremely fast growth in Japan, once the source of much hand-wringing in the all-too-scrutable West; we now see China, or at least part of China, growing faster than we can imagine. Inevitably we see all these as instances of ‘catch-up’ to a technological leader, the USA. In the background is always the need to evolve a skilled labour force. This seems to be another modelling opportunity. How does, or how should, an economy deploy its resources when it has the opportunity, via foreign investment, to attract both capital and already-known technology from abroad? Among the resources I have in mind are intellectual resources. Imitation of known technology is not always effortless. How should research capacity be divided between imitation–adaptation on one side, and the search for brand-new technology on the other? I am not sure that theory has much to say about a question like this, at least partly because the ‘ripeness’ of a particular technological area has to matter, and this is something that theories of endogenous technological change seem to ignore. It may even have a significant exogenous element. As a last comment, I would like to drag my feet about a methodological fashion—but one with real substantive implications—that seems to have taken root in growth theory, and appears likely to persist. Fifty years ago, the research community would have made a sharp distinction between descriptive models of economic growth and normative models of optimal growth. In that view, the Ramsey model was important precisely because it would define a growth trajectory quite different from the paths actually followed by observed economies. Indeed, the first calibrations of the Ramsey model suggested optimal saving-investment rates far higher than anything to be found in modern capitalist economies. The excess was large enough to constitute a serious puzzle (to which Olivier de La Grandville’s article in this issue proposes a resolution).
8
Robert M. Solow
Downloaded from http://oxrep.oxfordjournals.org/ at Universidad Nacional Autónoma de México on May 5, 2013
More recently, it has become almost universally the custom to use the Ramsey construction as if it described macroeconomic fact, rather than a hypothetical social-consensus target. The omniscient social planner has morphed into an immortal representative household; and other economic institutions are assumed to have just those characteristics that will induce them straightforwardly to carry out the owner–worker–consumer household’s desires. For example, the identical perfectly competitive firms have to share the household’s version of perfect foresight or rational expectations. Some minor imperfections may be allowed, but not such as to get in the way of the basic formulation. Groups of agents are not allowed to have different beliefs about the way the economy works, or conflicting objectives. All this is too well known to require elaboration. The neatness-freak in me can see why this conversion of normative into positive might have some initial intellectual appeal. But the pages of a Review of Economic Policy are an appropriate place to say that the model lacks plausibility as a basis for practical proposals about growth policy. The only sort of empirical argument in its favour that has been offered by protagonists is surprisingly weak. The idea is to ‘calibrate’ the model by choosing parameter values that have respectability in the literature of economics generally. (Understandably, some tweaking is permitted.) When the model is simulated with those parameter values, it can match some very general properties of observed time series, usually the absolute or relative magnitudes of significant variances and co-variances. This is a very lax sort of criterion, and cannot hope to earn much in the way of credibility. There must be scores of quite different models that could pass the same test, but would have different implications for policy. No one could claim that this sort of model has won its popularity by empirical success. Instead, the main argument for this modelling strategy has been a more aesthetic one: its virtue is said to be that it is compatible with general equilibrium theory, and thus it is superior to ad hoc descriptive models that are not related to ‘deep’ structural parameters. The preferred nickname for this class of models is ‘DSGE’ (dynamic stochastic general equilibrium). I think that this argument is fundamentally misconceived. We know from the Sonnenschein–Mantel–Debreu theorems that the sole empirical implication of a classical general-equilibrium genealogy is that excess-demand functions are continuous and homogeneous of degree zero in prices, and satisfy Walras’s Law. Those conditions can be imposed directly on a large class of macroeconomic models. I have made this point in another context, the example being the monetary macro-models of James Tobin (see Solow, 2004). It applies just as forcefully here. The cover story about ‘microfoundations’ can in no way justify recourse to the narrow representative-agent construct. Many other versions of the neoclassical growth model can meet the required conditions; it is only necessary to impose them directly on the relevant building blocks. The nature of the sleight-of-hand involved here can be made plain by an analogy. I tell you that I eat nothing but cabbage. You ask me why, and I reply portentously: I am a vegetarian! But vegetarianism is reason for a meatless diet; it cannot justify my extreme and unappetizing choice. Even in growth theory (let alone in short-run macroeconomics), reasonable ‘microfoundations’ do not demand implausibility; indeed, they should exclude implausibility. Maybe it would be helpful (to myself, at least) if I said in a couple of sentences what I think the function of growth theory is. It would go something like this. The long-run behaviour of a (fully employed) modern economy is the outcome of the interplay of some identifiable forces. The main ones seem to be the volume of investment in tangible and human capital, the strength of diminishing returns, the extent of economies of scale, the pace and direction of technological and organizational innovation. Even this sample list leaves out some
The last 50 years in growth theory and the next 10
9
Downloaded from http://oxrep.oxfordjournals.org/ at Universidad Nacional Autónoma de México on May 5, 2013
significant and interesting factors: natural-resource availability, environmental constraints, and the complex question of the relation between short-run fluctuations and medium-run and longer-run growth. The function of an aggregative growth model is to provide a handy way of describing how these factors interact, partly to help clear thinking, and partly to guide empirical research. The articles in this issue of the Oxford Review all fit within this framework. Two preliminary comments may be in order. First, my picture of the convergence issue is that the key question turns on which of the main forces are held in common by various national economies, and how they differ on the others. Presumably that is how one would define ‘convergence clubs’. It might take a more subtle specification of factors than I suggested here; so much the better. Second, I interpret the recent surge of interest in the aggregative elasticity of substitution as a very useful attempt to probe more deeply into the sources and consequences of diminishing returns. At the aggregative level, this has to be more than a merely technological fact. Substitution on the demand side must play an equal role, and also any institutional factors that affect the geographical, occupational, and industrial mobility of labour and capital. Sorting all this out, theoretically and empirically, is an exciting and important task. We now know, for example, that the elasticity of substitution has, in a well-defined sense, implications for the level of output: if two economies are in other respects identical, and start from the same initial conditions, the one with a larger elasticity of substitution will have a higher growth trajectory, and the benefit is comparable in size to what would be achieved from a somewhat faster rate of technological progress, It is interesting that most (not all) recent attempts to estimate the economy-wide elasticity of substitution have come up with values far smaller than one. That suggests a sharper role for diminishing returns than we are used to imagining. This finding, if it holds up, could liberate growth theory from the grip of the Cobb–Douglas function, whose special properties get embedded in many model-building exercises for no better reason than its soothing convenience. It is worth noting, on the other side, that large, but not extreme, values of the elasticity of substitution allow sustained growth without technological progress. These matters are at the very heart of neoclassical growth theory and what it has to say about the constraints on growth (other than those connected with natural resources). There is, therefore, every reason to welcome continued empirical research on these topics, like that contained in the paper by Rainer Klump, Peter McAdam, and Alpo Willman in this issue. I would like to conclude with a few, necessarily brief and sketchy, comments on the research papers that follow. They are very diverse in content and method. I found every one of them interesting and provocative. It says something about the neoclassical growth model that it can provide the framework for such a varied collection of investigations. It is convenient to start with the paper by Erich Gundlach. I am entirely in sympathy with his basic insistence: if you want to use the neoclassical growth model to understand the differences between countries, you have to be clear from the beginning about what parameters they have in common, and in what ways they are allowed to differ. For simplicity, suppose there are just two countries. One very common, probably too common, assumption is that they have the same depreciation rate, the same population growth rate, and the same rate of technological progress. But they have different saving-investment rates and different current levels of labour-augmenting technology. In effect, we assume they are in or near their steady states when we observe them, and we want to know how much of the observed difference in output per head results from the difference between s1 and s2 , and how much from the difference between A1 and A2 .
10
Robert M. Solow
Downloaded from http://oxrep.oxfordjournals.org/ at Universidad Nacional Autónoma de México on May 5, 2013
Gundlach observes that empirical capital–output ratios vary very little across countries, and points out that this is exactly what you would expect, according to the model, if differences in productivity reflect primarily differences in technological level. I would put this in a slightly different way, without the possibly misleading Cobb–Douglas assumption. One can solve the model to give the steady-state productivity (y) and capital intensity (k) as a function of the parameters that are allowed to differ, A and s. If only A varied from country to country, y and k for each country would lie on a ray from the origin. They don’t quite do that, according to Gundlach’s scatter diagram—though nearly. What kind of and how much variation in s would account for the deviation from a ray, and does that correspond in any way to the observed cross-country differences in s? My guess is that Gundlach’s evaluation is about right, but I would like to see how the fuller treatment works out. In any case, accounting for the cross-country relation between y and k —which covers both very rich and very poor countries—is an important matter. Suppose that the data in Gundlach’s diagram do not quite fit with theory, when account is taken of differences in both A and s? There would be at least two implications worth considering. One is that the model is simply inadequate. Another is that the assumption that all the observations describe steady states is seriously misleading. Remember that all cross-country growth regressions of this kind find a negative and statistically significant coefficient on the country’s initial level of income. That by itself contradicts the steady-state assumption; the question is how much this matters. One minor detail: Gundlach remarks, correctly, that we lack a good index of technological level (A) for each country. One device that he tries is to use a conventional measure of institutional quality, on the hypothesis that this is likely to be correlated with technological level. My inclination would be to try for something more direct, if possible, such as industrial electricity consumption per unit of output, or the number of computers. The very valuable paper by Kieran McQuinn and Karl Whelan carries this general line of thought in a different direction, with some exciting results. Nearly everyone takes it for granted that the rate of growth of TFP is the same everywhere. The only thing that justifies this remarkable presumption is the fairly mechanical thought that knowledge of new technology diffuses rapidly around the world. Maybe so, but productivity performance depends on many other influences besides the content of the latest engineering textbook. (The paper by David Audretsch, to which I will come in a moment, is precisely about one set of forces that drives a wedge between mere ‘knowledge’ and TFP.) Even if TFP is likely to increase more or less uniformly across regions on the time-scale of centuries, common observation suggests (and more than suggests, according to McQuinn and Whelan) that rates of TFP growth can differ substantially even among advanced national economies on the time-scale of decades. This seems correct and theoretically and empirically important to me. McQuinn and Whelan then go on to make a neat analytical point: the model says that the law of motion of the capital–output ratio is independent of the TFP growth rate, unlike the dynamics of output per unit of labour. One important consequence of this insight is that inferences from cross-country observations can be made without assuming a common TFP growth rate if the analysis is carried on in terms of the capital–output ratio. I don’t suppose I had noticed this in 1956, although I certainly messed around with the capital–output ratio, because the idea of cross-country inferences was not in my head. I was thinking only about single closed-economy time series. (I have never had any sympathy for the uniform-TFPgrowth-rate assumption.) The reader of this paper will see that doing the analysis their way leads to some substantial revisions of conventional estimates.
The last 50 years in growth theory and the next 10
11
Downloaded from http://oxrep.oxfordjournals.org/ at Universidad Nacional Autónoma de México on May 5, 2013
I think this is a real advance. Two further questions occur to me. One is minor. They find that their empirical estimate of the speed of adjustment to steady state is always close to but a little larger than the value suggested by the model, using standard stylized facts. What might account for this directional difference? The second question is much broader. Once growth theory abandons the implausible limitation to uniform TFP growth rates, it is natural to wonder about the actual pattern of national growth rates, and about the likely determinants of this pattern. David Audretsch observes that it is useful—and correct—to say that an important function of what we call entrepreneurship is precisely to bridge the gap between specific pieces of technological knowledge and innovations in actual production, often through the creation of new firms. He remarks in passing that the efficiency of this nexus is a major source of regional differences in the growth of TFP. This is easy to believe, especially for anyone who has eavesdropped on discussions of growth policy. If this idea can be embodied in empirical growth accounting, it would add a lot to the explanatory power of growth theory. There is also a connection to another long-standing worry of mine. We estimate time series of TFP in the conventional way, more or less completely detached from the narrative of identifiable technological changes that a historian would produce for the same stretch of time. There are reasons for this disjunction. TFP is estimated for aggregates, for a whole industry at a minimum, whereas the historical narrative is usually about single firms or even single individuals. Both temporal aggregation and cross-sectional aggregation will mask individual events. Besides, a lot of productive innovation has nothing to do with research or with research workers; it is created in the act of production through ‘learning by doing’ or some similar process. And then there are what I have already vaguely called ‘other influences’. Nevertheless, it would be interesting to see if any connection can be made, perhaps in a specific industry, between the time series of TFP and an informed narrative of significant innovations and their diffusion. (One can see in principle how TFP should be related to new-product innovations, but it is not clear what would happen in practice.) This train of thought leads naturally to the very attractive paper by Klump et al. The connection is that one of their goals is a flexible estimate of the character of factoraugmenting technical progress from US and euro-area time series. Their preferred finding is a combination of exponential labour-augmenting and sub-exponential capital-augmenting technical progress. In the long run, then, Harrod-neutrality dominates. (They do not tell us how long a run that is.) So steady-state growth is possible eventually, but perhaps not now. (When, exactly?) Among the other nice aspects of this paper is the effort to put together a consistent data set, and the use of a three-equation model for estimating the elasticity of substitution. The three equations are the production function itself and the two first-order conditions on labour and capital. (The original 1961 paper by Arrow, Chenery, Minhas, and me used only the condition for labour; we were doing cross-sections and did not have data on capital stocks.) Their main finding for both economies is an elasticity of substitution significantly less than one, in fact about 0.6. I have one major reservation about this. The empirical basis consists of annual time series for the USA from 1953 to 1998 and quarterly for the euro area from 1970 to 2003. The tacit assumption is that the business cycle can be ignored, which means in effect that the capital stock is assumed to be fully utilized all the time. Think what this does. Recessions tend to be fairly short, but they must leave traces in annual data. In a recession, the capital–labour ratio will appear to rise, because recorded employment will catch the diminished use of labour, but the recorded capital stock does not catch idle capacity. Also, in recessions the income
12
Robert M. Solow
Downloaded from http://oxrep.oxfordjournals.org/ at Universidad Nacional Autónoma de México on May 5, 2013
share of capital tends to be depressed, for the usual reasons. This is the standard recipe for an elasticity of substitution less than one: the increasingly abundant factor loses relative share. So I wonder if the Klump et al. finding contains some downward bias. I worried about this under-utilization problem in 1957; the best I could do then was to assume that the unemployment rate of capital was the same as that of labour in the same year. It should be possible to do better now. I don’t know how serious this bias could be, but I want to assure Rainer Klump and his co-authors that I don’t mention it just because Olivier de La Grandville and I have found interesting implications of a large elasticity of substitution. I am more worried about the tendency of modern (American) macroeconomists to forget about the pathology of business cycles. The paper by Davide Fiaschi and Andrea Mario Lavezzi is hard to discuss in just a few minutes, because its relation to the others is indirect. It also deals with international cross-sections, but in a very different way; in other respects it stands by itself, but still broadly within the neoclassical growth framework. All I can do is to make one or two casual remarks. The descriptive basis of the analysis is a plot of dlog GDP/dt against log GDP for a large group of countries and times. Then, in a key step, the observations are translated into the transition matrix of a Markov chain, where the states are defined by the same two dimensions. This is an interesting approach. Notice that the name of the country has disappeared from view. The Markov hypothesis says that the probability of moving from one class to each other class depends only on the starting state; no longer is history relevant. Is it easy to believe that? In the language I have been using, a particular country at a particular time is characterized by values of A and s, technology level and rate of investment. Do two countries in the same state, but with different values of A and s necessarily share the same transition probabilities? I suppose this could be tested; in fact, when the authors sort observations by rate of investment, they are testing it. The only other observation I have time for relates to a very interesting analytic step in the paper. Fiaschi and Lavezzi try to interpret their data in light of a standard neoclassical model with a novel twist. They introduce a level-of-technology parameter and then suppose there are technological spillovers from each country to other countries. The strength of the spillover between any pair depends on the ‘distance’ between them; and distance means economic, not geographical, distance, measured by the disparity between their levels of income per head. What is more, a country receives positive spillovers from more advanced countries, and negative spillovers from less advanced countries. I find that a little hard to believe; it seems to treat having a low technological level like a sort of contagious disease. But the focus on international technological spillovers strikes me as important and relevant. Casual observation says that the catch-up process is a vital part of the evolution of national economies. Its relation to trade and to foreign direct investment needs to be incorporated into a theory of open-economy growth. Here I come to the highly interesting paper by my friend and collaborator Olivier de La Grandville. I leave aside the kind things he said about me; he was not under oath (and neither am I). He goes on to raise a question that has bothered me, and many others, for a very long time. Richard Goodwin was one of my teachers; I probably read his 1961 paper on optimal growth in manuscript. Goodwin found, and de La Grandville verifies on a broader and more detailed scale, that straightforward application of the Ramsey principle to a reasonably calibrated growth model leads to absurdly high estimates of the socially optimal ratio of saving-investment to income (and may sometimes lead to mathematical pathologies). What should we think?
The last 50 years in growth theory and the next 10
13
Downloaded from http://oxrep.oxfordjournals.org/ at Universidad Nacional Autónoma de México on May 5, 2013
I spoke of a reasonably calibrated model. But we really don’t know how to calibrate an essential part of the model: the function that gives the per capita social utility of per capita consumption. De La Grandville shows that to get the optimal saving rate down to a reasonable size would require so much concavity in the social utility function as to cast doubt on the verisimilitude of the whole procedure. Then he takes an altogether different tack that requires much more discussion than I can give it here. He gives up on fiddling with the utility function, and simply maximizes the time-discounted sum of consumption per head. That seems to be moving in the wrong direction: a linear utility function calls for a bang-bang solution to the problem. (I wonder if the fact that the Fisher equation appears as the formal Euler equation for this problem is a reflection of this.) But he also confines the applicability of the model to situations in which the marginal product of capital is already very near the social rate of discount. That gets the optimal saving rate back in the common sense range, as he shows. It also forces us to rethink the original question in a different way: suppose that a comfortable situation of the de La Grandville type were suddenly to be disturbed by the destruction of a substantial part of the capital stock, by a natural disaster, for instance. Are we not right back in the Goodwin–Ramsey problem? Now comes a further radical suggestion: if the Ramsey formulation is really intuitively satisfying only near the steady state, why should we use it in the recovery-from-catastrophe context? So he proposes a different sort of rule of thumb, and restores common sense once again. Does that way of thinking truly resolve the Ramsey paradox? That is a question that should be discussed at leisure. But it is a useful question not only for its own sake, but because it reminds us that every abstract model needs this kind of plausibility–reasonableness smell test before one starts just applying it. We need the reminder because that sort of consideration is too often omitted. The compact paper by Philippe Aghion and Peter Howitt teaches a useful lesson about interpreting growth theory, even if it is more directly relevant for growth accounting. The general admonition is that the choice of what is exogenous and what is endogenous is an intrinsic part of any theory. The particular application to growth theory is not necessarily new, but is certainly still worth stating. One striking conclusion from the original neoclassical model was that the long-run growth rate is independent of the saving-investment quota. But that was under the assumption that technological change entered exogenously. Aghion and Howitt exhibit a model which is like the original one in every respect but one: technological change is endogenized in a particular way. In their modified model, the saving-investment rate does influence the steady-state growth rate. No mechanism in the original model is contradicted; but the size of the capital stock has an effect on the rate of technological innovation, and that relationship opens a channel from the saving-investment rate to the growth rate. This is a worthwhile and interesting reminder. It also gives me a chance to ride a few paces on an old hobby-horse that made a brief appearance earlier in these notes. The Cobb–Douglas production function is a wonderful vehicle for generating instructive examples. But it has special Santa Claus properties, and one must not be misled about the generality of those examples. The Aghion–Howitt machinery resembles something I proposed in my own first paper on ‘embodiment’. To get clean results I had to assume that technological change was purely capital-augmenting, just the opposite of the conventional assumption of Harrodneutrality. (See the paper by Klump et al. in this issue for empirical indications.) In the case of the Cobb–Douglas function (and only then) the distinction between labour-augmenting, capital-augmenting, and output-augmenting (Hicks-neutral) technological change evaporates.
14
Robert M. Solow
References Aghion, P., and Howitt, P. (1992), ‘A Model of Growth through Creative Destruction’, Econometrica, 60(March), 323–51. — — (1998), Endogenous Growth Theory, Cambridge, MA, MIT Press. — — (2007), ‘Capital, Innovation, and Growth Accounting’, Oxford Review of Economic Policy, 23(1), 79–93. Audretsch, D. B. (2007), ‘Entrepreneurship Capital and Economic Growth’, Oxford Review of Economic Policy, 23(1), 63–78. Barro, R. J. (1991), ‘Economic Growth in a Cross Section of Countries’, Quarterly Journal of Economics, 106(May), 407–43. Domar, E. (1946), ‘Capital Expansion, Rate of Growth, and Employment’, Econometrica, 14(April), 137–47. Fiaschi, D., and Lavezzi, A. M. (2007), ‘Appropriate Technology in a Solovian Nonlinear Growth Model’, Oxford Review of Economic Policy, 23(1), 115–133. Grossman, G., and Helpman, E. (1991), Innovation and Growth in the Global Economy. Cambridge, MA, MIT Press. Gundlach, E. (2007), ‘The Solow Model in the Empirics of Growth and Trade’, Oxford Review of Economic Policy, 23(1), 25–44. Harrod, R. (1939), ‘An Essay in Dynamic Theory’, Economic Journal, March, 13–33. Klump, R., McAdam, P., and Willman, A. (2007), ‘The Long-term SucCESs of the Neoclassical Growth Model, Oxford Review of Economic Policy, 23(1), 94–114. La Grandville, O. de (2007), ‘The 1956 Contribution to Economic Growth Theory by Robert Solow: A Major Landmark and Some of its Undiscovered Riches’, Oxford Review of Economic Policy, 23(1), 15–24. Lucas, R. E., Jr (1988), ‘On the Mechanics of Economic Development’, Journal of Monetary Economics, 22(July), 3–42. McQuinn, K., and Whelan, K. (2007), ‘Solow (1956) as a Model of Cross-country Growth Dynamics’, Oxford Review of Economic Policy, 23(1), 45–62. Romer, P. (1986), ‘Increasing Returns and Economic Growth’, Journal of Political Economy, 94(October), 1002–37. Solow, R. (2004), ‘The Tobin Approach to Monetary Economics’, Journal of Money, Credit and Banking, 36(4), 657–63. Swan, T. (1956), ‘Economic Growth and Capital Accumulation’, Economic Record, 32(November), 334–61.
Downloaded from http://oxrep.oxfordjournals.org/ at Universidad Nacional Autónoma de México on May 5, 2013
I wonder how much of the Aghion–Howitt story will hold up outside the Cobb–Douglas case, without some other restrictive assumption. However that turns out, the basic reminder is valid. Exogeneity assumptions matter beyond themselves. I wrote that 1960 paper trying to find a path by which the savinginvestment quota could after all affect the asymptotic growth rate. The particular mechanism I explored—embodiment itself—did not have that effect. We all believe that the determinants of long-run growth are somehow endogenous, but the ‘somehow’ is not obvious, nor is it easy to test hypotheses. Aghion and Howitt have found one hypothesis that does implicate the saving-investment quota, but the range of its field of application should be investigated. They go about it in the right way, and they may be on the right track. The more the merrier.
