Journal of Monetary Economics 22(1988) 3-42. North-Holland ON THE MECHANICS OF ECONOMIC DEVELOPMENT* Robert E. LUCAS, Jr. University of Chicago, Chicago, IL 60637, USA Received August 1987, final version received February 1988 This paper considers the prospects for constructing a neoclassical theory growth and interna- tional trade that is consistent with some of the main features of economic development. Three models are considered and compared to evidence: model emphasizing physical capital accumula- tion and technological change, a model emphasizing human capital accumulation through school- ing, and a model emphasizing specialized human capital accumulation through learning-by-doing. 1.Introduction By the problem of economic development I mean simply the problem of accounting for the observed pattern, across countries and across time, in levels and rates of growth of per capita income. This may seem too narrow a definition, and perhaps it is, but thinking about income patterns will neces- sarily involve us in thinking about many other aspects of societies too, so I would suggest that we withhold judgment on the scope of this definition until we have clearer idea of where it leads us. The main features of levels and rates of growth of national incomes are well enough known to all of us, but want to begin with few numbers, so as to set a quantitative tone and to keep us from getting mired in the wrong kind of details. Unless I say otherwise, all figures are from the World Bank's World Development Report of 1983. The diversity across countries in measured per capita income levels is literally too great to be believed. Compared to the 1980 average for what the World Bank calls the industrial market economies'(Ireland up through Switzerland)of U.S. $10,000, India's per capita income is $240, Haiti's is $270 , 1985.! am very grateful to the Cambridge faculty for this honor and also for the invitation's long lead time, which ga new topic with the stimulus of so distinguished an audien ersions of this lecture have been given as the David Horowitz Lectures in Israel, the kintosh Lecture at Queens University, the Carl Snyder Memorial Lecture rnia at Santa Barbara, the Chung-Hua Lecture in Taipei, the Nancy Sch artz Lecture at Northwestern University, and the Lionel nina McKenzie Lecture at the University of Rochester I have also based several seminars on various parts of this material. 0304-3932/88/$3.5001988, Elsevier Science Publishers B.V. (North-Holland)
R.E. Lucas, Jr, On the mechanics of economic deuelopment and so on for the rest of the very poorest countries. This is a difference of a factor of 40 in living standards! These latter figures are too low to sustain life in, say, England or the United States, so they cannot be taken at face value and I will avoid hanging too much on their exact magnitudes. but i do not think anyone will argue that there is not enormous diversity in living stan dards Rates of growth of real per capita GNP are also diverse, even over sustained periods. For 1960-80 we observe, for example: India, 1.4% per year; Egypt 3.4% South Korea, 7.0%; Japan, 7.1%; the United States, 2.3%; the industrial economies averaged 3.6%. To obtain from growth rates the number of years it takes for incomes to double divide these numbers into 69(the log of 2 times 100). Then Indian incomes will double every 50 years: Korean every 10. An Indian will, on average, be twice as well off as his grandfather; a Korean 32 times. These differences are at least as striking as differences in income levels, and in some respects more trustworthy, since within-country income compan ons are easier to draw than across-country comparisons i have not calculated a correlation across countries between income levels nd rates of growth, but it would not be far from zero. The poorest countries tend to have the lowest growth; the wealthiest next; the middle-income ountries highest. )The generalizations that strike the eye have to do with variability within these broad groups: the rich countries show little diversity (Japan excepted -else it would not have been classed as a rich country in 1980 at all). Within the poor countries (low and middle income)there is enormous variability. 2 Within the advanced countries, growth rates tend to be very stable over long periods of time, provided one averages over periods long enough to eliminate business-cycle effects (or corrects for short-term fluctuations in some other way). For poorer countries, however, there are many examples of sudden, large changes in growth rates, both up and down. Some of these changes are no doubt due to political or military disruption: Angola's total GDP growth fell from 4.8 in the 60s to.2 in the 70s; Irans fell from 11.3 to 2.5, comparing the same two periods. I do not think we need to look to economic theory for an account of either of these declines There are also some striking examples I The income estimates reported in Summers and Heston(1984)are more satisfactory than those in the World Development Reports. In 1975 U.S. dollars, these authors estimate 1980 U.S. real GDP per capita at $8000, and for the industrialized economies as a group, $5900. The comparable igures for India and Haiti are $460 and $500, respectively. Income differences of a factor of 16 are certainly smaller, and I think more accurate, than a factor of 40, but I think they are still fairly described as exhibiting 66)summarizes evidence, mainly from Maddison (1982)indicating apparent onvergence during this century to a common path of the income levels of the wealthiest countries. But De Long(1987)shows that this effect is entirely due to'selection bias: If one examines the countries with the highest income levels at the beginning of the century(as opposed to currently, as in Maddison's'sample')the data show apparent divergence
R E. Lucas Jr, On the mechanics of economic development of sharp increases in growth rates. The four East Asian"miracles'of South Korea, Taiwan, Hong Kong and Singapore are the most familiar: for the 1960-80 period, per capita income in these economies grew at rates of 7.0, 6.5 6.8 and 7.5, respectively, compared to much lower rates in the 1950,'s and earlier. 3.4 Between the 60s and the 70s, Indonesia's gDP growth increased from 3.9 to 7. 5; Syria's from 4.6 to 10.0 I do not see how one can look at figures like these without seeing them as representing possibilities. Is there some action a government of India could take that would lead the Indian economy to grow like Indonesia's or Egypts? ly? If not, what is it abo ture of India that makes it o? The consequences for human welfare involved in questions like these are simply staggering: Once one starts to think about them, it is hard to think about anything else This is what we need a theory of economic development for: to provide some kind of fr ork for organizing facts like the dging which represent opportunities and which necessities. But the term theory'is used in so many different ways, even within economics, that if i do not clarify what I mean by it early on, the gap between what I think I am saying and what you think you are hearing will grow too wide for us to have a serious discussion I prefer to use the term theory'in a very narrow sense, to refer to an explicit dynamic system, something that can be put on a computer and run This is what I mean by the'mechanics'of economic development-the construction of a mechanical, artificial world, populated by the interacting robots that economics typically studies, that is capable of exhibiting behavior the gross features of which resemble those of the actual world that I have just described My lectures will be occupied with one such construction, and it will take some work: It is easy to set out models of economic growth based on reasonable- looking axioms that predict the cessation of growth in a few decades, or that predict the rapid convergence of the living standards of different economies to a common level, or that otherwise produce logically possible outcomes that bear no resemblance to the outcomes produced by actual economic systems On the other hand, there is no doubt that there must be mechanics other than the ones i will describe that would fit the facts about as well as mine. this is why I have titled the lectures 'On the Mechanics. 'rather than simply'The of Economic Development. At some point, then, the study of development will need to involve working out the implications of competing theories for data other than those they were constructed to fit, and testing these implications against observation. But this is getting far ahead of th 3The World Bank no longer transmits data for Taiwan. The figure 6.5 in the text is from Harberger(1984, table 1, p. 9) 4According to Heston and Summers( 1984), Taiwans per-capita GDP growth rate in the 1950s was 3. 6. South Korea's was 1.7 from 1953 to 1960
6 R.E. Lucas, Jr, On the mechanics of economic development story I have to tell, which will involve leaving many important questions open even at the purely theoretical level and will touch upon questions of empiric My plan is as follows. I will begin with an application of a now-standard neoclassical model to the study of twentieth century U.S. growth, closely following the work of Robert Solow, Edward Denison and many others. I will then ask, somewhat unfairly, whether this model as it stands is an adequate model of economic development, concluding that it is not. Next, I will consider two adaptations of this standard model to include the effects of human capital accumulation. The first retains the one-sector character of the original model and focuses on the interaction of physical and human capital accumulation. The second examines a two-good system that admits specialized human capital of diferent kinds and offers interesting possibilities for the interaction of trade and development. Finally, I will turn to a discussion of what has been arrived at and of what is yet to be done In general, I will be focusing on various aspects of what economists, using the term very broadly, call the'technology,'. I will be abstracting altogether from the economics of demography, taking population growth as a given throughout. This is a serious omission, for which i can only offer the excuse that a serious discussion of demographic issues would be at least as dificult as the issues i will be discussing and i have neither the time nor the knowledge to do both I hope the interactions between these topics are not such that they cannot usefully be considered separately, at least in a preliminary way. I will also be abstracting from all monetary matters, treating all exchange as though it involved goods-for-goods. In general, I believe that the importance of financial matters is very badly over-stressed in popular and even much professional discussion and so am not inclined to be apologetic for going to the other extreme. Yet insofar as the development of financial institutions is a limiting factor in development more generally conceived I will be falsifying the picture, and I have no clear idea as to how badly. But one cannot theorize about everything at once. I had better get on with what i do have to say 2. Neoclassical growth theory: Review The example, or model, of a successful theory that I will try to build on is the theory of economic growth that Robert Solow and Edward Denison developed and applied to twentieth century U.S. experience. This theory will serve as a basis for further discussion in three ways: as an example of the form that I believe useful aggregative theories must take, as an opportunity to BEcker and Barro(1985)is the first attempt known to me to analyze fertility and capital accumulation decisions simultaneously within a general equilibrium framework. Tamura (1986) contains further results this line
R. E. Lucas, Jr, On the mechanics of economic develop explain exactly what theories of this form can tell us that other kinds of theories cannot, and as a possible theory of economic development. In this third capacity, the theory will be seen to fail badly, but also suggestively Following up on these suggestions will occupy the remainder of the lectures Both Solow and Denison were attempting to account for the main features of U.S. economic growth, not to provide a theory of economic development, and their work was directed at a very different set of observations from the cross-country comparisons I cited in my introduction. The most useful summary is provided in Denisons 1961 monograph, The Sources of Economic Growth in the United States. Unless otherwise mentioned, this is the source for the figures I will cite next. During the 1909-57 period covered in Denison's study, U.S. real output grew at an annual rate of 2.9%, employed manhours at 1. 3%, and capital stock at 2.4%. The remarkable feature of these figures, as compared to those cited earlier, is their stability over time. Even if one takes as a starting point the trough of the Great Depression(1933)output growth to 1957 averages on 5%6. If business-cycle effects are removed in any reasonable way(say, by using peak-to-peak growth rates)U.S output growth is within half a percentage point of 3% annually for any sizeable subperiod for which we have data Solow(1956)was able to account for this stability, and also for some of the itudes of the ith a mple but refineable model.6 There are many variations of this model in print. I will set out a particularly simple one that is chosen also to serve some later purposes. I will do so without much comment on its assumed structure: There is no point in arguing over a models assumptions until one is clear on what questions will be used to answer We consider a closed economy with competitive markets, with identical rational agents and a constant returns technology. at date t there are N() persons or, equivalently, manhours devoted to production. The exogenous given rate of growth of N(t)is A. Real, per-capita consumption is a stream c(),t20, of units of a single good Preferences over(per-capita)consumption streams are given by N(edt 6Solow's 1956 paper stimulated a vast literature in the 1960s, exploring many variations on the original one-sector structure. See Burmeister and Dobell (1970) for an excellent introduction and survey. By putting a relatively simple version to empirical use, as I shall shortly do i do not ntend a negative comment on this body of research. On the contrary, it is exactly this kind of theoretical experimentation with alternative assumptions that is needed to give one the confidence that working with a particular, simple parameterization may, for the specific purpose at hand, be adequate
R.E. Lucas, Jr, On the mechanics of economi where the discount rate p and the coefficient of (relative)risk aversion o are both positive Production per capita of the one good is divided into consumption c(t)and capital accumulation. If we let K(r) denote the total stock of capital, and K () its rate of change, then total output is N((c(1)+k(). [Here k(t)is net investment and total output N(()c()+K(r)is identified with net national product. Production is assumed to depend on the levels of capital and labor inputs and on the level A(t)of the technology, according to N()c(n)+k(1)=A(t)k(t)3N(1}- where 00 The resource allocation problem faced by this simple economy is simply to choose a time path c(r)for per-capita consumption. Given a path c(t)and an initial capital stock K(O), the technology(2)then implies a time path K(r)for capital. The paths A(n )and N(t) are given exogenously. One way to think about this allocation problem is to think of choosing c(t)at each date, given the values of K(1), A(() and N(t) that have been attained by that date Evidently, it will not be optimal to choose c(t)to maximize current-period utility, N(o(/(1-o)lc(r)-1]-, for the choice that achieves this is to set net investment K(t) equal to zero(or, if feasible, negative): One needs to set some value or price on increments to capital. A central construct in the stud of optimal allocations, allocations that maximize utility(1)subject to the technology (2), is the current-value hamiltonian h defined by N H(K AcDI-olc-0-1]+0[AK] which is just the sum of current-period utility and [from(2)] the rate of increase of capital, the latter valued at the price(0). An optimal allocation must maximize the expression H at each date t, provided the price a(t)is correctly chosen The first-order condition for maximizing H with respect to c is 日, which is to say that goods must be so allocated at each date as to be equally valuable, on the margin, used either as consumption or as investment. It is 7The inverse o-i of the coefficient of risk aversion is sometimes called the intertemporal elasticity of substitution. Since all the models considered in this paper are deterministic, this latter terminology may be more suitable
known that the price 8(()must satisfy 6(1)=p6(t)-xH(K(1),6(2),c(),) p-BA()N()2k(1)21]( at each date t if the solution c(r) to(3)is to yield an optimal path(c(t)ao (3 )is used to express c(t)as a function A((), and this fur is substituted in place of c(t)in(2)and (4), these two equations are a pair of first-order differential eq K(r)and its 'pricea(t). Solving th system, there will be a one-parameter family of paths(K(o), e(t), satisfying the given initial condition on K(O). The unique member of this family that satisfies the transversality condition ime-°(t)K(r)=0 is the optimal path. I am hoping that this application of Pontryagin's Maxi mum Principle, essentially taken from David Cass(1961), is familiar to most of you. I will be applying these same ideas repeatedly in what follows For this particular model, with convex preferences and technology and with no external effects of any kind, it is also known and not at all surprising that the optimal program characterized by(2),(3),(4)and(5)is also the unique competitive equilibrium program, provided either that all trading is consum- mated in advance, Arrow-Debreu style, or(and this is the interpretation I favor)that consumers and firms have rational expectations about future prices n this deterministic context, rational expectations just means perfect fore- sight. For my purposes, it is this equilibrium interpretation that is most interesting: I intend to use the model as a positive theory of U.S. economic growth In order to do this, we will need to work out the predictions of the model in more detail, which involves solving the differential equation system so we can see what the equilibrium time paths look like and compare them to observa tions like Denison,s. Rather than carry this analysis through to completion, I will work out the properties of a particular solution to the system and then just indicate briefly how the rest of the answer can be found in Cass's paper Let us construct from(2), (3)and(4)the systems balanced growth path: the particular solution(K(1), 8(r),c(r)such that the rates of growth of each of these variables is constant. (I have never been sure exactly what it is that is balancedalong such a path, but we need a term for solutions with this constant growth rate property and this is as good as any. Let k denote the rate of growth of per-capita consumption, c(r)/c(o), on a balanced growth
R.E. Lucas, Jr, On the mechanics of economic development path. Then from(3), we have 8()/0(t)=-oK. Then from(4), we must have BA(t)N(t)bK()=p+aκ (6) That is, along the balanced path, the marginal product of capital must equal the constant value p+oK. With this Cobb-Douglas technology, the marginal product of capital is proportional to the average product, so that dividing(2) through by K(r)and applying(6)we obtain K()K(o) A(t)K()2-N() B B By definition of a balanced path, K(()/K(r)is constant so(7) implies that N(c(t)/K(r)is constant or, differentiating, that K(1 N(1) c(r) K(t)N(t)c(t)=k+λ (8) Thus per-capita consumption and per-capita capital grow at the common rate K. To solve for this common rate differentiate either(6)or(7)to obtain Then(7)may be solved to obtain the constant, balanced consumption-ci ratio N(rc(o)/K(ror, which is equivalent and slightly easier to interpret constant, balanced net savings rate s defined by B(K+入) (10) N(t)c(t)+R(t)p+oκ Hence along a balanced path, the rate of growth of per-capita magnitudes is simply proportional to the given rate of technical change, l, where the constant of proportionality is the inverse of labor's share, 1-B. The rate of time preference p and the degree of risk aversion o have no bearing on this long-run growth rate. Low time preference p and low risk aversion o induce a high savings rate s, and high savings is, in turn, associated with relatively high output levels on a balanced path. a thrifty society will, in the long run, b wealthier than an impatient one, but it will not grow faster In order that the balanced path characterized by(9)and(10) satisfy the transversality condition(5), it is necessary that p+ox >x+X[From(10),one sees that this is the same as requiring the savings rate to be less than capital's
R.E. Lucas, Jr, On the mechanics of economic share. Under this condition, an economy that begins on the balanced path will find it optimal to stay there. What of economies that begin of the balanced path-surely the normal case? Cass showed- and this is exactly hy the balanced path is interesting to us-that for any initial capital K(O)>0, the optimal capital-consumption path(K(t), c(r) will converge to the balanced path asymptotically. That is, the balanced path will be a good approximation to any actual path 'mostof the time Now given the taste and technology parameters(p, o, x, B and u)(9)and (10) can be solved for the asymptotic growth rate x of capital, consumption and real output, and the savings rate s that they imply. Moreover, it would be straightforward to calculate numerically the approach to the balanced path from any initial capital level K(O). This is the exercise that an idealized planner would go through Our interest in the model is positive, not normative, so we want to go in the opposite direction and try to infer the underlying preferences and technology from what we can observe. I will outline this, taking the balanced path as the model's prediction for the behavior of the U.s. economy during the entire (1909-57)period covered by Denisons study. From this point of view, Denisons estimates provide a value of 0.013 for A, and two values, 0.029 and 0.024 for K +A, depending on whether we use output or capital growth rates (which the model predicts to be equal). In the tradition of statistical inference, let us average to get x+x=0.027. The theory predicts that 1-B should equal labor's share in national income, about 0.75 in the U.S., averaging over the entire 1909-57 period. The savings rate (net investment over NNP)is fairly constant at 0. 10. Then(9)implies an estimate of 0. 0105 for p. Eq.(10) implies that the preference parameters p and o satisfy p+(0.014)o=0.0675 The parameters p and o are not separately identified along a smooth consumption path, so this is as far as we can go with the sample averages I have provided These are the parameter values that give the theoretical model its best fit to the U. S. data. How good a fit is it? Either output growth is underpredicted or capital growth overpredicted, as remarked earlier(and in the theory of growth a half a percentage point is a large discrepancy ). There are interesting secular changes in manhours per household that the model assumes away, and labor's share is secularly rising(in all growing economies), not constant as assumed There is, in short, much room for improvement, even in accounting for the secular changes the model was designed to fit, and indeed, a fuller review of with the parameter values described in this paragraph, the half-life of the approximate linear system associated with this model is about eleven years
R.E. Lucas, Jr, On the mechanics of economic development the literature would reveal interesting progress on these and many other fronts.A model as explicit as this one, by the very nakedness of its simplify ing assumptions, invites criticism and suggests refinements to itself. This is exactly why we prefer explicitness, or why I think we ought to Even granted its limitations, the simple neoclassical model has made basic contributions to our thinking about economic growth. Qualitatively, it empha sizes a distinction between'growth effects'-changes in parameters that alter growth rates along balanced paths- 'level effects'-changes that raise or lower balanced growth paths without affecting their slope - that is fundamen- tal in thinking about policy changes. Solow's 1956 conclusion that changes in savings rates are level effects(which transposes in the present context to the conclusion that changes in the discount rate, p, are level effects) was startling at the time, and remains widely and very unfortunately neglected today. The influential idea that changes in the tax structure that make savings more attractive can have large, sustained effects on an economys growth rate sounds so reasonable and it may even be true, but it is a clear implication of the theory we have that it is not Even sophisticated discussions of economic growth can often be confusing as to what are thought to be level effects and what growth effects. Thus Krueger(1983)and Harberger(1984), in their recent, very useful surveys of the growth experiences of poor countries, both identify inefficient barriers to trade as a limitation on growth, and their removal as a key explanation of several rapid growth episodes. The facts Krueger and Harberger summarize are not in dispute, but under the neoclassical model just reviewed one would not expect the removal of inefficient trade barriers to induce sustained increases in growth rates. Removal of trade barriers is, on this theory, a level effect, analogous to the one-time shifting upward in production possibilities, and not a growth effect. Of course, level effects can be drawn out through time through adjustment costs of various kinds, but not so as to produce increases in growth rates that are both large and sustained. Thus the removal of an inefficiency that reduced output by five percent(an enormous effect) spread out over ten years in simply a one- half of one percent annual growth rate stimulus Inefficiencies are important and their removal certainly desirable, but the familiar ones are level effects, not growth effects.( This is exactly why it is not paradoxical that centrally planned economies, with allocative inefficiencies of legendary proportions, grow about as fast as market economies. ) The empirical connections between trade policies and economic growth that 9In particular, there is much evidence that capital stock growth, as measured by Denison understates true capital growth due to the failure to correct price deflators for quality improve ments. See, for example, Griliches and Jorgenson( 1967)or Gordon (1971). These errors may well account for all of the 0.005 discrepancy noted in the text(or more varable, and which has the potential (at least) to account for long- run changes in manhours y is Boxall(1986)develops a modification of the Solow-Cass model in which labor suppl