Long-Run Policy Analysis and Long-Run Growth Sergio Rebelo The Journal of Political Economy, Vol. 99, No. 3. (Jun., 1991), pp. 500-521. Stable URL: http: //links. jstor. org/sici?sici=0022-3808%28199106%29993A3%3C500%3ALPAALG%3E2.0.CO%3B2-M The Journal of Political Economy is currently published by The University of Chicago Press Your use of the ISTOR 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 ISTOR 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/ucpress. html. Each copy of any part of a ISTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. ISTOR is an independent not-for-profit organization dedicated to creating and preserving a digital archive of scholarly journals. For more information regarding ISTOR, please contact support@jstor.org. http://www.jstor.org/ Mon Sep1800:38:072006
Long-Run Policy Analysis and Long-Run Growth Sergio rebelo Portuguese Catholic University, and Rochester Center far Economic Research The wide cross-country disparity in rates of economic growth is the most puzzling feature of the development process. This paper de scribes a class of models in which this heterogeneity in growth expe riences can be the result of cross-country differences in government policy. These differences can also create incentives for labor migra tion from slow-growing to fast-growing countries. In the models considered, growth is endogenous despite the absence of increasing returns because there is a"cote "of capital goods that can be pro- duced without the direct or indirect contribution of factors that cannot be accumulated, such as land I. Introduction One of the most surprising features of the process of economic growth is the wide cross-country dispersion in average rates of growth. In the postwar period, countries such as Japan, Brazil, and Gabon saw their level of per capita income expand at a fast pace while living.This paper studies a cls niGcant change in their standard of country differences in economic policy can generate this type of het his paper is based on the frst chapter of my Ph. D thesis defended at the University of Rochester. I am indebted to my advisors, Robert King and Paul re continuous guidance and advice. I also benefited from the comments and suggestions of Robert Barro, Marianne Baxter, Monica Hargraves, and numerous seminar pa pants. Any errors are my own. Financial port from the Amelia de Melo Foundation 91 by The University of Chicago. All rights reserved. @e22.980891A9903-000880150
LONG-RUN POLICY ANALYSIS erogeneity in growth experiences. In these models certain policy vari ables, such as che rate of income tax, affect the economy's rate of expansion through a simple mechanism: an increase in the income tax rate decreases the rate of return to the investment activities of he private sector and leads to a permanent decline in the rate of capital accumulation and in the rate of growth The class of economies that I propose in this paper shares with Romer's(1986)model the ty that growth is endogenous in the sense that it occurs in the absence of exogenous increases in produc- tivity such as those attributed to technical progress in the neoclassical growth model. But, in contrast with Romer's emphasis on increasing returns to scale and accelerating growth, the models discussed hete display constant returns to scale technologies and have steady-state growth paths, thus being compatible with the stylized facts of eco- nomic growth described in Kaldor(1961) The simplest model within the class that I consider is a one-sector economy with standard preferences and a production function that is linear in the capital stock. This simple model is usually dismissed as inappropriate to think about growth issues because labor plays apparently no role in the economy and nonreproducible factors such as land are not used in production. The analysis undertaken here more general models that surpass boch of these problems reveals that the simple linear model is a natural benchmark in terms of thinking about the growth process and a good representative of the class of endogenous growth economies that have a convex technology Throughout the paper I shall focus on the effects of taxation on e rate of growth. This focus was chosen because tax policies differ ignificantly across countries but also because the effects of taxation are suggestive of the impact of other government policies, such as those regarding the protection of property rights. The approach will be positive rather than normative: I shall cake as given that there are differences in public policy across countries and, at least for no sidestep the question of whether those different policies can viewed as optimal There is a large literature on tax policy issues in the neoclassical growth model that also concludes that high income tax rates trar late into lower rates of growth. But in the neoclassical model, this effect is too weak to explain the observed cross-country differences in growth rates. Economic policy can affect the rate of growth only luring the transition path toward the steady state since the steady- state growth rate is given by the rate of exogenous technical progress Key references in this literature include Krzyzaniak(1967), Sato(1967),Feldstein (1974), Stiglitz(1978),R. Becker( 1985), and Judd(1985)
JOURNAL OF POLITICAL ECONOMY These transitional effects of economic policy cannot have a large im pact on the rate of growth, given that the rough constancy of the eal interest rate during the last century suggests that transitional dynamics play a modest role in the growth process(King and Rebelo 1989) This paper is organized as follows. Section II studies a two-sector extension of a linear growth model that incorporates nonreproduc ible factors in the production process. This model is used to study he effects of taxation and the influence of the rate of savings on the rate Section III expands this model to distinguish the role of physical apical and human capital along the lines suggested by Lucas (1988 This extended model shows that the feasibility of sustained growth does not require capital to be produced with a linear technology, as might be suggested by Section II and by the models discussed by Uzawa(1965) and Lucas (1988). All that is required to assure the feasibility of perpetual growth is the existence of a"core"of capital goods that is produced with constant returns technologies and with out the direct or indirect use of nonreproducible factors Treating separately the accumulation of physical and human capi tal introduces transitional dynamics that are absent in Section IL. Br the implications obtained for the effects of taxes and of the savings rate along the steady-state path are basically those of Section II, in he case of both exogenous and endogenous leisure choice The remainder of Section III is devoted to generalizing the model of Section II along two different directions. First, capital goods pro- duced with nonreproducible factors are introduced in the economy Second, the consequences of introducing multiple consumptio oods are examined. the main policy implications derived in Section Ii prove to be robust to these generalizations Section iv relates the models discussed here to the neoclassical model and to some of the recent growth literature. Section V provides some conclusions and outlines directions for future research II. A Basic Endogenous Growth Model The point of departure in this paper will be an economy in which there are two types of factors of production: reproducible, which can be accumulated over time(e.g, physical and human capital), and nonreproducible, which are available in the same quantity in ever (e. g, land). The quantity of all rep factors will be summarized by che capital good Ze, which can be viewed as a compos ite of various types of physical and human capital. Similarly, the fixed amount available of nonreproducible factors will be summarized by he composite good T
LONG-RUN POLICY ANALY The economy has two sectors of production. The capital sector uses a fraction(1- e)of the available capital stock to produce investment roods(L,)with a technology that is linear in the capital stock: I Az (1-d). Capital depreciates at rate 8 and investment is irrevers ible (1, 20): Z,=L-8Z2 The consumption sector combines the remaining capital stock with nonreproducible factors to produce con sumption goods(C). Since for steady-state growth to be feasible it must be possible for both consumption and capital to grow at constant (but possibly different) rates, the production function of the con- sumption industry is assumed to be Cobb-Douglas: C:=B(,,)T This technology permits capital to grow at any rate between A-8 production is consumed), and consumption to grow at a rate propor- tional to that of capital: ge =aga The economy has a constant population composed of a large num- ber of identical agents who seek to maximize utility, defined as These preferences imply that the optimal growth rate of consumption (get) is solely a function of the real interest rate (e): gu=(r-p)/o Since in all the economies considered here the real interest rate is constant in the steady state, this ensures that when it is feasible for consumption to grow at a constant rate it is also optimal to do so The competitive equilibrium under perfect foresight for all the cconomies studied in this paper can be computed as a solution to planning problem by exploring the fact that, in the absence of distor tions, the competitive equilibrium is a Pareto optimum. Instead of taking this approach, we shall study directly the competitive equilib rium focusing on the conditions that are relevant to determine the growth rate, since this will be more informative about the economic mechanisms at work in the model To describe the competitive equilibrium, it is necessary to have a market structure in mind. In chis case, it is easiest to think of the economy as having spot markets for all goods and factors and one period credit markets. Firms make their production decisions seeking to maximize profits, while households rent the two factors of produc- tion(Z and T) to firms and choose their consumption so as to max imize lifetime utility(1) To maximize profits, firms have to be indifferent about employing heir marginal unit of capital to produce either consumption goods or capital goods; that is, P,A=aB(p2Z)-, where P is the relative price of capital in terms of consumption. Since in the steady state the The dot notation is used for the time derivative, so Z,=dzldt
JOURNAL OF POLITICAL ECONOMY fraction of capital devoted to consumption, dr is constant, the relative price of capital declines at the rate g, =(a- 1)g2. Given that p, is not constant, the real interest rate for loans denominated in capital goods (ra)is different from that of consumption-denominated loans (ra). Since the (net) marginal productivity of capital in the sector that roduces capital goods is constant and equal to A-8,, equilibrium the capital market requires that rx =A-82.A standard arbitrage argument implies that the interest rate for consumption-denom- inated loans is related to ra by ra =ru+ ge. The steady-state value of ra is chen given by r =A-8+(a-1)g Faced wich this interest rate, households choose to expand con sumption at rate ge=(r-pa. Substituting r, by its expression and ge=ag, yield the steady-state value of income measured in terms of consumption goods, which is given by Y,=C,+Pl-8, Z, grows at rate There are three properties of the competitive equilibrium that are worth noting. First, this economy has no transitional dynamics;it expands always at rate gy. Second, the parameter B and the amount of land services available in each period()are absent from the growth rate expression. They determine che level of the consumption path but not the growth rate, suggesting that countries with different endowments of natural resources will have different income levels but not different growch rates. Third, although CI and I, grow at different rates, their relative price adjusts in such a manner that the shares of investment and consumption in output(p, L,/Y and C/ are conscant The influence of preferences and technology on the rate of expan sion of this economy is rather intuitive. The rate of growth is higher the greater the net marginal product of capital (A-8)and the elasticity of intertemporal substitution(1/o)and the lower the pure rate of time preference(). 3 Equation(2)provides no reason to believe that unceasing growth is more likely than perpetual regression; whether the economy grows )In order for lifetime utility (U in [11)to be finite, it is necessary that p >a( JXA-8, )to ensure that the growth rate of momentary utiliy, (1 a)ge is lower than the discount rate, p. If (1-ag. 2 p, there is a set of feasible paths among which houscholds are indifferent because they all yield infinite utility. The requirement p I -(A -8, )is also necessary and sufficient for the transversality condition assoc ated with the households' maximization problem to hold. In all the other models assumed to hold per, this type of condicion, although not stated explicitly, is implicitly studied in this
LONG-RUN POLICY ANALYSIS or regresses depends on whether A-8,-p is positive or negative However, in the derivation of (2), the irreversible nature of invest- ments in Z was ignored. This irreversibility implies that the lowest feasible growth rate of output is-a8,, which corresponds to the path in which investment is zero. When the value of g, implied by(2)is lower than -a8u, the economy reverts to a corner solution in which investment is zero and the growth rate is -a8 A. Long-Run Effects of Taxation To illustrate the effects of taxation on this model, two proportional taxes will be introduced: one on consumption at rate t, and the other n investment at rate T,. The analysis will be undertaken in a closed economy context, but it is valid in a world of open economies con nected by international capital markets if all countries follow the worldwide tax system. Government revenue, measured in terms of the consumption good is given by T,=T C:+7p.. To isolate the effects of taxation fr those of government expenditures, I assume throughout the paper that this revenue is used to finance the provision of goods that do not affect the marginal utility of private consumption or the production possibilities of the private sector The only equation used to derive (2)affected by the presence of taxation is the one that determine hich is not by (1+7)(1+r2)=A+(1-8)+r(1-8) The left-hand side of this expression represents the opportunity cost of investing one unit of capital. The right-hand side is the result of using that unit of capital to produce during one period and selling the nondepreciated capital. The term T,(I-8)reflects the invest ment tax refund associated with that sale The growth rate of income is in this case [A/(1+-)-8,-p -as where the possibility of a corner solution in which the nonnegativity estriction on investment is binding, and hence g2 --82, is made explicit. Expression(3) shows that the influence of an inctease in T, on the growth rate is the same as that of a decrease in A: a higher f According to this system, investors pay taxes in their own country on capital riginated abroad but receive credit for paid abroad on the same ee Jones and Manuelli(1990) and King and Rebelo(1990) for discussions cffects of taxation in open economies
JOURNAL OF POLITICAL E investment tax rate leads to a lower growth rate in economies with strictly positive investment levels. In contrast, permanent changes in T. have effects that are similar to changes in B: they do not affect the rate of growth but solely the level of the consumption path.A onsumption tax does not distort the only decision made by agents in this economy, the decision of consuming now versus later, it is equivalent to a lump-sum tax. Since a proportional tax on Income amounts to taxing consumption and investment at the same rate, an increase in the income tax rate induces a decrease in the rate of growth of this economy In Solows(1956)original version of the neoclassical growth model, the savings rate(s)was fixed at an exogenous level. In that context Solow concluded that the savings rate determines only the stead state levels of the diffetent variables but not their growth rates. In is model, although the speed of convergence toward the steady state depends on s, the steady-state growth rate is exogenous and all s does is determine the capital/labor ratio The simple model just described can be used to illustrate that this result is an artifact of the exogenous nature of steady-state growth in the neoclassical model. Suppose that the savings rate, defined as the fraction of net output devoted to net investment, is exogenously fxed t the level s 20 rather than being chosen to maximize(1).This implies that Z, -sY /p Following the same steps as before, we can compute the steady-state growth rate as This expression implies that higher savings rates lead to higher growth rates, which accords with the positive correlation of these wo variables in the data(see Romer 1987). The concept of savings employed here is, however, broader than usual since Z composite of physical and human capital and hence s is the fraction of total resources devoted to both of these accumulation activities. I der to study the effects of ch in che defined in stricter sense that encompasses only physical capital accumulation,it is necessary to distinguish between these two types of accumulation This is one of the objectives of the next section 'This is also the mechanism at work in Bo economy the production technology is lineat, so an i acts as
LONG-RUN POLICY ANALYSIS C. A Linear Endogenous Growth Model The basic model can be simplified further by assuming that &= I and B-A. This generates a one-sector economy with a linear production unction Y,=AZ,. This linear model in which everything is repro- ducible captures the essential features of the class of endogenous growth models with a convex technology. It points to the same growth rate determinants and to the same policy implications as the model just described. It also captures the main qualitative features of the economies studied in the next section in which physical and human capital are treated separately IIL. Extensions of the Basic Model This section seeks to investigate whether the properties described in Section II hold more generally by extending that model in several directions: First, the composite capital good Z is disaggregated into physical and ht pital, and the resulting the cases of exogenous and endogenous labor supply. Second, capital goods produced with nonreproducible factors are incorporated in the model. Finally, multiple consumption goods are introduced. To simplify the exposition, each of these aspects is considered separately A. Disaggregating Z, into Physical and Human Capita A natural direction along which the basic model can be expanded to disaggregate the composite capital Z, into one type of physical and one human capital. To study such a model without burdening the discussion with too much notation it is convenient to assume thad consumption and investment goods are produced in the same sector Introducing a separate consumption sector as in Section II would not give rise to any substantive changes in the properties discussed below As before, the economy is populated by a constant number of iden tical agents with preferences described by(1). Production takes place according to a Cobb-Douglas production function th. fraction of the stock of physical capital with N H, efficiency units of labor, which are the result of N, hours of work undertaken by an individual with H, units of human capital: 7 n This simple lincar cconomy resembl m已c discussed in Knight (1935, 1944 in the sense that all factors of this one have also been employed by McFadden(I967), Benveniste(1976), (1981) See Martins(1987)for an analysis of growth models with different definitions of ciency units of labor
5 OURNAL OF POLITICAL ECONOMY A1(d2K)-(N2H2)=C1+1 (4) Physical capital depreciates at rate 8, and investment is irreversible (≥0) K2=1-8K Human capital, which is embodied in each worker, depreciates at rate 8 and can be produced by combining physical capital-k(1-2) units-with efficiency units of labor. 8 Each worker has one unit of time in each period and consumes an exogenously specified number L of leisure hours. The remaining 1-L-N, hours are devoted to accumulation of human capital generating(I-L- N)H, efficiency units of labor. H2=A2{E1-(1-L-N1)HP-8H2(6) The technology described by equations(4)-(6)is similar to the one adopted by Lucas(1988, scc. 4), with two main differences: chere are no externalities, and physical capital is used in the production of human capital In specifying this technology, I made three assumptions that make it possible to solve in closed form for the steady-state growth rate he two production functions were chosen to be Cobb-Douglas, and K and H were assumed to depreciate at the same rate 8. The appendix to the working paper version of this research( Rebelo 1990)demon strates that the properties emphasized below continue to hold when the production functions are neoclassical with positive cross-partial derivatives and the two depreciation rates are different. Equations(4)-(6)imply that in the steady state, Cp Ke I, and H, all grow at the same rate. there is a continuum of values for chis com- mon growth rate that can be sustained with this technology. This makes clear that in order for endogenous steady-state growth to be feasible, the technology to produce capital does not need to be linear but only constant returns to scale, that is, linearly homogeneous. The The embodiment assumption plays a key role in the analysis. It implies that nd the number of efficiency units that would result from their collaboration would be 4NH. In the economy described in this section. this would introduce increasing returns to scale, and hence a competitive equilibrium ould not exist: production and accumulation of skills would take pl an eco The range of sustainable rates of growth is harder to c because it is determined both by the equations that describe gy and by those that characterize efficient production plans(see eqg. [7]-[121) analogous to that of the basic model conomy can sustain th rate between the steady-state interest rate r, described in(13), and -8
