The Origins of Endogenous Growth

The Origins of Endogenous Growth Paul M. Romer The Journal of Economic Perspectives, Vol. 8, No. 1. (Winter, 1994), pp. 3-22. Stable URL: http://links.jstor.org/sici?sici=0895-3309%28199424%298%3A1%3C3%3ATOOEG%3E2.0.CO%3B2-H The Journal of Economic Perspectives is currently published by American Economic Association. Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/journals/aea.html. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academic journals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers, and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community take advantage of advances in technology. For more information regarding JSTOR, please contact support@jstor.org. http://www.jstor.org Thu Oct 25 06:23:12 2007 Journal of Economic Perspectives- Volume 8, Number 1- Winter 1994-Pages 3-22 The Origins of Endogenous Growth Paul M. Romer The phrase "endogenous growth" embraces a diverse body of theoretical and empirical work that emerged in the 1980s. This work distinguishes itself from neoclassical growth by emphasizing that economic growth is an endogenous outcome of an economic system, not the result of forces that impinge from outside. For this reason, the theoretical work does not invoke exogenous technological change to explain why income per capita has in- creased by an order of magnitude since the industrial revolution. The empirical work does not settle for measuring a growth accounting residual that grows at different rates in different countries. It tries instead to uncover the private and public sector choices that cause the rate of growth of the residual to vary across countries. As in neoclassical growth theory, the focus in endogenous growth is on the behavior of the economy as a whole. As a result, this work is complemen- tary to, but different from, the study of research and development or produc- tivity at the level of the industry or firm. This paper recounts two versions that are told of the origins of work on endogenous growth. The first concerns what has been called the convergence controversy. The second concerns the struggle to construct a viable alternative to perfect competition in aggregate-level theory. These accounts are not sur- veys. They are descriptions of the scholarly equivalent to creation myths, simple stories that economists tell themselves and each other to give meaning and structure to their current research efforts. Understanding the differences be- tween these two stories matters because they teach different lessons about the relative importance of theoretical work and empirical work in economic analy- sis and they suggest different directions for future work on growth. Paul M . R o m r is Professor of Economics, University of Calijiornia, Berkeley, Calijiornia. Version # 1: The Convergence Controversy The question that has attracted the most attention in recent work on growth is whether per capita income in different countries is converging. A crucial stimulus to work on this question was the creation of new data sets with information on income per capita for marly countries and long periods of time (Maddison, 1982; Heston and Summers, 199 1). In his analysis of the Maddison data, William Baumol (1986) found that poorer countries like Japan and Italy substarltially closed the per capita income gap with richer countries like the United States and Canada in the years from 1870 to 1979. Two objections to his analysis soon became apparent. First, in the Maddison data set, convergence takes place only in the years since World War 11. Between 1870 and 1950, income per capita tended to diverge (Abrarnovitz, 1986). Second, the Maddison data set included only those economies that had successfully industrialized by the end of the sample period. This induces a sample selection bias that apparently accounts for most of the evidence in favor of convergence (De Long, 1988). As a result, attention then shifted to the broad sample of countries in the Heston-Summers data set. As Figure 1 shows, convergence clearly fails in this broad sample of countries. Income per capita in 1960 is plotted on the horizontal axis. The average annual rate of growth of income per capita from 1960 to 1985 is plotted on the vertical axis.' On average, poor countries in this sample grow no faster than the rich countries. Figure 1 poses one of the central questions in development. Why is it that the poor countries as a group are not catching up with the rich countries in the same way that, for example, the low income states in the United States have been catching up with the high income states? Both Robert Lucas (1988) and I (Romer, 1986) cited the failure of cross-country convergence to motivate models of growth that drop the two central assumptions of the neoclassical model: that technological change is exogenous and that the same techrlological opportunities are available in all countries of the world. To see why Figure 1 poses a problem for the corlventiorlal analysis, consider a very simple version of the neoclassical model. Let output take the simple Cobb-Douglas form Y = In this expression, Y denotes net A ( ~ ) K ' - ~ L ~ . rlatiorlal product, K denotes the stock of capital, L denotes the stock of labor, and A denotes the level of technology. The notation indicating that A is a function of time signals the standard assumption in neoclassical or exogenous growth models: the technology improves for reasons that are outside the model. Assume that a constant fraction of net output, s, is saved by consumers each year. Because the model assumes a closed economy, s is also the ratio of net investment to net national product. Because we are working with net 'The data here are taken from version I\' of the Penn \\.orld Table. 'l'he income measure is RGDPZ See Summers and Heston (1988) for details. 5 Paul M . Romer Figure 1 Testing for Convergence I a4----Singapore I 01-----chad 0.0 0.2 0.4 0.6 0.8 1 .O 1.2 Income per capita relative to United States in 1960 (rather than gross) national product and investment, sY is the rate of growth of the capital stock. Let y = Y / L denote output per worker and let k = K/L denote capital per worker. Let n denote the rate of growth of the labor force. Finally, let a "^ " over a variable denote its exponential rate of growth. Then the behavior of the economy can be summarized by the following equation: The first line in this equation follows by dividing total output by the stock of labor and then calculating rates of growth. This expression specifies the procedure from growth accounting for calculating the technology residual. Calculate the growth in output per worker, then subtract the rate of growth of the capital-labor ratio times the share of capital irlconle in total income from the rate of growth of output per worker. The second line follows by substituting in an expression for the rate of growth of the stock of capital per worker, as a function of the savings rate s, the growth rate of the labor force n , the level of the technology A( t ) , and the level of output per worker, 4'. Outside of the steady state, the second line of the equation shows how variation in the investment rate and in the level of output per worker should translate into variation in the rate of growth. The key parameter is the exponent p on labor in the Cobb-Douglas expression for output. Under the neoclassical assumption that the economy is characterized by perfect competi- tion, p is equal to the share of total income that is paid as conlperlsation to 6 journal of Economic Perspectives labor, a number that can be calculated directly from the national income accounts. In the sample as a whole, a reasonable benchmark for @ is 0.6. (In industrialized economies, it tends to be somewhat larger.) This means that in the second line of the equation, the exponent (-@)/(I - @) on the level of output per worker y should be on the order of about - 1.5. We can now perform the followirlg calculation. Pick a country like the Philippines that had output per worker in 1960 that was equal to about 10 percent of output per worker in the United States. Because 0. is equal to about 30, the equation suggests that the United States would have required a savings rate that is about 30 times larger than the savings rate in the Philip- pines for these two countries to have grown at the same rate. If we use 2/3 instead of .6 as the estimate of @, the required savings rate in the United States would be 100 times larger than the savings rate in the Philippines. The evidence shows that these predicted saving rates for the United States are orders of magnitude too large. A key assumption in this calculation is that the level of the technology A(t) is the same in the Philippines and the United States. (The possibility that A(t) might differ is considered below.) If they have the same technology, the only way to explain why workers in the Philippines were only 10 percent as productive as workers in the United States is to assume that they work with about 0.1'/('-~) or between 0.3 percent and 0.1 percent as much capital per worker. Because the marginal product of capital depends on the capital stock raised to the power -@, the marginal product of an additional unit of capital is O.l-P/"-P' times larger in the Philippines than it is in the United States, so a correspondingly higher rate of investment is needed in the United States to get the same effect on output. Figure 2 plots the level of per capita income against the ratio of gross investment to gross domestic product for the Heston-Summers sample of countries. The correlation in this figure at least has the correct sign to explain why poor countries on average are not growing faster than the rich countries-that is, a higher level of income is associated with a higher invest- ment rate. But if @ is between 0.6 and 0.7, the variation in investment between rich and poor countries is at least an order of magnitude too small to explain why the rich and poor countries seem to grow at about the same rate. In concrete terms, the share of investment in the United States is not 30 or 100 times the share in the Philippines. At most, it is twice as large. Of course, the data in Figures 1 and 2 are not exactly what the theory calls for, but the differences are not likely to help resolve the problem here. For example, the display equation depends on the net investment rate instead of the gross investment rate. Because we do not have reliable data on depreciation for this sample of countries, it is not possible to construct a net investment ratio. A reasonable conjecture, however, is that depreciation accounts for a larger share of GDP in rich countries than it does in poor countries, so the difference between the net investment rate in rich and poor countries will be even smaller 7 The Origins of Endogenous Growth Figure 2 Per Capita Income and Investment United States 0.0 0.2 0.4 0.6 0.8 1.O 1.2 Income per capita relative to United States in 1960 than the difference between the gross investment rates illustrated in the figure. The display equation also calls for output per worker rather than output per capita, but for a back-of-the-envelope calculation, variation in income per capita should be close enough to variation in output per worker to show that a simple version of the neoclassical model will have trouble fitting the facts. The way to reconcile the data with the theory is to reduce /?so that labor is relatively less important in production and diminishing returns to capital accumulation set in more slowly. The theoretical challenge in constructing a formal model with a smaller value for /3 lies in justifying why labor is paid more than its marginal product and capital is paid less. To explain these divergences between private and social returns, I proposed a model in which A was determined locally by knowledge spillovers (Romer, 1987a). I followed Arrow's (1962) treatment of knowledge spillovers from capital investment and assumed that each unit of capital investment not only increases the stock of physical capital but also increases the level of the technology for all firms in the economy through knowledge spillovers. I also assumed that an increase in the total supply of labor causes negative spillover effects because it reduces the incentives for firms to discover and implement labor-saving innovations that also have positive spillover effects on production throughout the economy. This leads to a functional relationship between the technology in a country and the other variables that can be written as A(K, L). Then output for firm j can be written as Y, = A(K , L)K~-*LT,where variables with subscripts are ones that firm j can control, and variables without subscripts represent economy- wide totals. Because the effect that a change in a firm's choice of K or L has o n A is an external effect that any individual firm can ignore, the exponent a measures the private effect of an increase in employment on output. A 8 Journal of Economic Pprspectivps 1 percent increase in the labor used by a firm leads to an a percent increase in its output. As a result, a will be equal to the fraction of output that is paid as compensation to labor. Suppose, purely for simplicity, that the expression linking the stock of A to K and L takes the form A(K, L) = KYL-Y for some y greater than zero. Then the reduced form expression for aggregate output as a function of K and L would be Y = K'-OLO where P is equal to a - y . This exponent /3 represents the aggregate effect of an increase in employment. It captures both the private effect a and the external effect -y. In the calculation leading up to the equation displayed above, it is this aggregate or social effect that matters. According to this model, /3 can now be smaller than labor's share in national income. Using a simple cross-country regression based on an equation like the display equation, I found that the effect of the investment rate on growth was positive and the effect of initial income on growth was negative. Many other investigators have found this kind of negative coefficient on initial income in a growth regression. This result has received special attention, particularly in light of the failure of overall convergence exhibited in Figure 1. It suggests that convergence or regression to the mean would have taken place if all other variables had been held constant. After imposing the constraint implied by the equation, I estimated the value of p to be in the vicinity of 0.25 (Romer, 1987a, Table 4). With this value, it would only take a doubling of the investment rate-rather than a 30- or 100-fold increase-to offset the negative effect that a ten-fold increase in the level of output per worker would have on the rate of growth. These figures are roughly consistent with the numbers for the United States and the Philippines. For the sample as a whole, the small negative effect on growth implied by higher levels of output per worker are offset by higher investment rates in richer countries. Robert Barro and Xavier Sala i Martin (1992) subsequently showed that the conclusions about the size of what I am calling /3 (they use different - notation) were the same whether one looked across countries or between states in the United States. They find that a value for P on the order of 0.2 is required to reconcile the convergence dynamics of the states with the equation presented above. Convergence takes place, but at a very slow rate. They also observe that this slow rate of convergence would be even harder to explain if one intro- duced capital mobility into the model. As a possible explanation of the slow rate of convergence, Barro and Sala i Martin (1992) propose an alternative to the r~eoclassical model that is somewhat less radical than the spillover model that I proposed. As in the endogenous growth models, they suggest that the level of the technology A(t) can be different in different states or countries and try to model its dynamics. They take the initial distribution of differences in A(t) as given by history and suggest that knowledge about A diffuses slowly from high A to low A regions. This would mean that across the states, there is underlying variation in A(t) that 9 Paul M . Romrr causes variation in both k and y. As a result, differences in output per worker do not necessarily signal large differences in the marginal product of capital. In fact, free mobility of capital can be allowed in this model and the rate of return on capital can be equalized between the different regions. Because the flow of knowledge from the technology leader makes the technology grow faster in the follower country, inconle per capita will grow faster in the follower as diffusion closes what has been called a technology gap.' The speed of convergence will be determined primarily by the rate of diffusion of knowledge, so the conver- gence dynamics tell us nothing about the exponents on capital and labor. The assumption that the level of technology can be different in different regions is particularly attractive in the context of an analysis of the state data, because it removes the prediction of the closed-economy, identical-technology r~eoclassical model that the marginal productivity of capital can be many times larger in poorer regions than in rich regions." According to the data reported by Barro and Sala i Martin (1992), in 1880, income per capita in states such as North Carolina, South Carolina, Virginia, and Georgia was about one-third of income per capita in industrial states such as New York, Massachusetts, and Rhode Island. If P is equal to 0.6, -P/(l - P) is equal to - 1.5 and (1/3)-'.' is equal to about 5. This means that the marginal product of capital should have been about five times higher in the South than it was in New England. It is difficult to imagine barriers to flows of capital between the states that could have kept these differences from rapidly being arbitraged away. In particular, it would be difficult to understand why any capital investment at all took place in New England after 1880. But if there were important differences in the technology in use in the two regions, the South may not have offered higher returns to capital investment. In a third approach to the analysis of cross country data, Greg Mankiw, David Romer, and David Weil(1992) took the most conservative path, showing that it is possible to justify a low value for /3 even in a pure version of the closed economy, neoclassical model which assumes that the level of technology is the same in each country in the world. The only change they make is to extend the usual two-factor r~eoclassical model by allowing for human capital H as well as physical capital K. They use the fraction of the working age population th