UNIQUENESS AND INDETERMINACY OF THE EQUILIBRIUM GROWTH PATH IN THE UZAWA‐LUCAS MODEL WITH SECTOR SPECIFIC EXTERNALITIES*

We introduce sector specific external effects of human capital on production in an otherwise Uzawa‐Lucas model of endogenous growth; and show that the problem of indeterminacy of the competitive equilibrium growth path does not exist even if the production function satisfies the increasing returns to scale at the social level.     

Liquidity constraint, increasing returns and endogenous fluctuations

In this paper we show that local indeterminacy, endogenous fluctuations, and periodic and quasi-periodic orbits may emerge in a one-sector infinite-horizon competitive economy where (1) at the end of each period agents must hold a share of their wealth in the form of money and (2) technology exhibits increasing returns to scale. In contrast to other contributions on this subject, we find that such phenomena occur when consumption is intertemporally substitutable and labour is supplied inelastically. The scope for indeterminacy depends basically on the fact that, in view of the financial constraint, total returns on investment represent a weighted average of capital marginal productivity and deflation, and the latter is positively related to the rate of growth of capital.     

Stabilization policy and indeterminacy in a small open economy

This paper studies the (de)stabilizing effects of income tax rules in a two-sector small open economy with production externalities. The paper shows that in the model with positive sector-specific externalities in the investment sector and negative sector-specific externalities in the consumption sector (or positive aggregate investment externalities), a regressive income tax rule can stabilize such an economy against indeterminacy, whereas a progressive income tax rule can increase the tendency for indeterminacy to occur. This paper also studies two variants that consider an imperfect world bond market and an endogenous labor supply, respectively, and shows that the qualitative results stated above remain valid. Moreover, increasing the level of sector-specific investment externalities can decrease (increase) the minimal level of tax progressivity required for indeterminacy if the investment externalities are below (above) a certain critical value and if the negative externalities in the consumption sector are taken as given.     

Income Taxation Rules and Stability of a Small Open Economy

This paper examines the stability of a small open economy under alternative income taxation rules. Using a one-sector real business cycle model with external increasing returns, we show that if the income tax schedule is linear, the small open economy will not generate equilibrium indeterminacy, but it exhibits a diverging behavior under certain conditions. In this case, an appropriate choice of nonlinear tax on the factor income may recover the saddle-point stability. We also reveal that if the taxation on the interest income on financial assets is regressive, then the small open economy may exhibit equilibrium indeterminacy. In this situation, a progressive tax rule on the interest income can contribute to eliminating sunspot-driven fluctuations.     

Government expenditure,external and domestic public debt,and economic growth

This paper analyzes the relationship between government expenditure, tax on returns to assets, public debt, and growth in an endogenous growth model. Public debt is composed of two components, domestic debt and external debt. We show conditions for existence, uniqueness, and multiplicity of the steady states. More precisely, existence of steady state requires a sufficiently high productivity and a sufficiently low tax on returns to assets. We also provide the effects of an increase in the tax rate on returns to assets on the steady state. In particular, the relation between public spending and the tax rate has a bell shape. Domestic debt unambiguously increases with tax whereas external debt displays an inverted U‐shaped curve. A high tax rate leads to a reallocation of public debt in favor of domestic debt (to the detriment of external debt). The effect of taxation on consumption (and production) also displays a nonlinear pattern when the output elasticity of capital is lower than unity (the effect is monotonously increasing if this elasticity is unity). We also derive the conditions under which a tax increase can boost or reduce the balanced growth rate.     

On indeterminacy and growth under progressive taxation and productive government spending

We examine the theoretical interrelations between equilibrium (in)determinacy and economic growth in a one‐sector representative‐agent model of endogenous growth with progressive taxation of income and productive flow of public spending. We analytically show that, if the demand‐side effect of government purchases is weaker, the economy exhibits an indeterminate balanced‐growth equilibrium and belief‐driven growth fluctuations when the tax schedule is sufficiently progressive or regressive. If the supply‐side effect of public expenditures is weaker, indeterminacy and sunspots arise under progressive income taxation. In sharp contrast to traditional Keynesian‐type stabilization policies, our analysis finds that raising the tax progressivity may destabilize an endogenously growing economy with fluctuations driven by agents’ self‐fulfilling expectations.     

Growth and equilibrium indeterminacy: the role of capital mobility

Summary. The paper presents a human capital driven endogenous growth model which, in general, permits a multiplicity of equilibrium balanced growth paths. It is shown that allowing for perfect capital mobility across countries increases the range of parameter values for which the model permits equilibrium indeterminacy. As opposed to the closed capital markets case, simple restrictions on preferences are no longer sufficient to eliminate the indeterminacy. Intuitively, under perfect capital mobility agents are able to smooth consumption completely. This induces an economy with open capital markets to behave like a closed economy with linear preferences thereby increasing the possibility of equilibrium indeterminacy. Received: 18 November 1998; revised version: 10 August 1999     

Intersectoral Externalities and Indeterminacy

We consider a two-sector economy with positive intersectoral external effects and nonincreasing social returns. We show that if the discount factor ρ is close to 1 then local indeterminacy may be obtained with mild market imperfections. Moreover, with additional conditions, when ρ is made smaller the steady state becomes totally unstable and quasi-periodic cycles, along which equilibrium paths are indeterminate, may appear through a Hopf bifurcation. This will be proved even if the investment good is capital intensive at the private level while this condition guarantees local determinacy in the sector specific case. Journal of Economic Literature Classification Numbers: C62, E32, O41.     

Superneutrality, indeterminacy and endogenous growth

In this paper, we explore the possibility of having money as a source of indeterminacy in endogenous growth models. We adopt the simple Ak model of endogenous growth to be the main analytical vehicle whose balanced growth paths do not display local indeterminacy. Money is introduced via either a general cash-in-advance (CIA) constraint or a pecuniary transactions costs (PTC) technology. It is shown that local indeterminacy of the dynamics is due to the presence of an intertemporal substitution effect on capital accumulation that works against and dominates the conventional inflation effect of Tobin [1965, Money and economical growth. Econometrica 33(4), Part 2, 671]. If money is growth-rate superneutral, then the intertemporal substitution effect is absent so that local indeterminacy cannot occur. Finally, the strength of the intertemporal substitution effect depends positively on the intertemporal elasticity of substitution in consumption.     

Ramsey fiscal policy and endogenous growth

This paper examines the effects of fiscal policies on capital accumulation and economic performance in a simple endogenous growth model with elastic labor supply by focusing on the implementability of a competitive equilibrium with productive public spending and distortionary taxation. Given a feasible exogenous fiscal policy, productive public spending can, at first, lead to positive short-run and long-run growth in the unique competitive equilibrium. However, although strictly positive growth is possible in the short run, a Ramsey policy with productive public spending does not implement positive capital accumulation in the long run. Also, the local indeterminacy of Ramsey allocations, in conjunction with the global multiplicity, arises as an implementable competitive equilibrium with Ramsey policies: namely, a continuum of transitional dynamics and multiple balanced growth paths. I am grateful to Kazuo Nishimura, Theodore Palivos, Sang Hee Won, John Conlon, Apostolis Philippopoulos, Arved Ashby, In Ho Lee, Katsuaki Terasawa, and an anonymous referee of this journal for valuable comments and suggestions. I also thank seminar participants at Ioannina University, Kyoto University, University of Mississippi, and Seoul National University. This paper is supported by 2006 Sabbatical Project, Kyung Hee University.     

Indeterminate Balanced Growth under Habit Persistence and Fiscal Policies

This paper studies a dynamic general equilibrium model with habit persistence in preferences and fiscal policies of taxation and expenditures. Preference takes a subtractive form of habits (the marginal rate of substitution between the agent's own consumption and habit stocks is constant), and technology is linear in aggregate capital (the economy grows without a limit in the long run). We find a continuum of competitive equilibrium paths in conjunction with a unique balanced growth path in the growing economy, in which habits represent both envy/jealousy and altruism/admiration. In addition, in the social optimum under second-best fiscal policies, we show the existence of indeterminacy in transitional allocations along with a unique balanced growth path. Thus, we find that the introduction of habits influences the patterns of the transitional paths but has no impact on the balanced growth path in either competitive or social optimum allocations. The second-best fiscal policy, therefore, restores the socially optimal balanced growth rate but fails to select the unique transitional path among multiple competitive equilibrium paths in the imperfectly competitive economy.     

Optimal income taxation in models with endogenous fertility

This paper studies the efficient taxation of factor income in infinite-lived models with elastic fertility choices. Two models are considered, one with physical capital only, and one with physical and human capital. In the model with physical capital only, capital income should be subsidized, while labor income taxed. In the model with two types of capital, instead, Ramsey optimality prescribes that the tax on physical capital is zero (negative), if effective labor is constant (decreasing) returns to scale in human capital and market goods, while the tax on human capital is negative and the tax on effective labor positive. Our findings depart from those obtained in immortal models with an endogenous labor supply and constant population growth, because physical and human capital affect the demand for fertility.     

A model with endogenously determined cycles, discounting and growth

Summary. This article reexamines the role of consumption in growth and emphasises the external effects of aggregate consumption, viewed as consumption standards, as an additional impediment in the growth process. These external effects raise the productivity of the individuals and are positively related to their valuation of the future. Conditions are established under which this results in a marginal value of wealth that is an increasing function of consumption. This brings new types of multiple steady states, local indeterminacies and cyclical motions. Imposing extra homogeneity restrictions, balanced growth solutions with endogenous impatience emerge. The possibility of multiple convergent paths is univocally related to endogenous discount effects. A comparison with a benchmark planning economy indicates an excessive value for the rate of time preference and emphasises its insufficient adaptation to future utility in a stationary setting. Discrepancies along the transition path that rest on endogenous impatience versus fixed discount appear in a non-stationary environment when the competitive balanced growth solution is indeterminate. Received: May 5, 1996; revised version: May 19, 1997     

Balanced‐Budget Rules,Elasticity of Substitution,and Macroeconomic (In)Stability

This paper examines the relation between factor substitution and (local) stability of equilibria in a one‐sector real business cycle model under balanced‐budget rules. We show that under non‐unitary elasticity of factor substitution, the Schmitt‐Grohé‐Uribe indeterminacy result can be altered. Using the two‐step normalization procedure, we highlight two opposing effects of factor substitution, namely, the efficiency effect and the distribution effect, on aggregate stability. With endogenous distortionary taxes and gross substitutability between capital and labor, the existing literature overlooks the distribution effect and finds that balanced‐budget rules are likely to deliver indeterminacy. However, if capital stock is relatively more abundant, a higher elasticity of substitution generates a source of stability due to the distribution effect. Our calibration shows that the distribution effect is always the dominating force.     

Complementarity of Labor Market Institutions, Equilibrium Unemployment and the Propagation of Business Cycles

This paper evaluates complementarities of labor market institutions and the business cycle in the context of a stochastic dynamic general equilibrium model economy. Matching between workers and vacancies with endogenous time spent in search, Nash-bargained wages, payroll taxation, and differential support for unemployed labor in search and leisure are central aspects of the model. For plausible regions of the policy and institutional parameter space, the model exhibits more persistence than standard real business cycle models and can exhibit indeterminacy of rational expectations paths without increasing returns in production. Furthermore, labor market institutions act in a complementary fashion in generating these effects.     

Indeterminacy and multiple steady states with sector-specific externalities

This paper studies a two-sector model with aggregate and sector-specific external effects in production and inelastic labor supply. We first characterize the existence, uniqueness and multiplicity of the steady states as well as their welfare properties. We particularly focus on the CES production functions and show that the steady state is generically either unique or there are exactly two. A simple geometrical methodology enables us to characterize the local dynamics of the steady state. We show that in order to get indeterminacy, the presence of both aggregate and sector-specific external effects is needed, along with low capital–labor elasticities of substitution and high, but bounded from above, elasticities in intertemporal consumption. We perform a sensitivity analysis and show that indeterminacy emerges for parameter values in line with those used in calibrations of standard RBC models, that is for unitary elasticities of input substitution and of intertemporal substitution in consumption.     

Factor Accumulation and Trade: Dynamic Comparative Advantage with Endogenous Physical and Human Capital*

This article develops a two‐country endogenous growth model with accumulation of both physical and human capital. We establish the existence of two‐country balanced growth equilibria with physical and human capital in which a static and dynamic version of the Heckscher–Ohlin (HO) hypothesis hold true. We also show the existence of unbalanced growth equilibria in which the static and dynamic HO hypotheses can be violated. The multiplicity of paths with international trade emerge as a result of the intertemporal no‐arbitrage condition when factor prices are equalized across countries.     

Trade and Indeterminacy in a Dynamic General Equilibrium Model

This paper introduces sector-specific externalities in the Heckscher-Ohlin two-country dynamic general equilibrium model to show that indeterminacy of the equilibrium path in the world market can occur. Under certain conditions in terms of factor intensities, there are multiple equilibrium paths from the same initial distribution of capital in the world market, and the distribution of capital in the limit differs among equilibrium paths. One equilibrium path converges to a long-run equilibrium in which the international ranking of factor endowment ratios differs from the initial ranking; another equilibrium path maintains the initial ranking and converges to another long-run equilibrium. Since the path realized is indeterminate, so is the long-run trade pattern. Therefore, the Long-Run Heckscher-Ohlin prediction is vulnerable to the introduction of externality. Journal of Economic Literature Classification Numbers: E13, E32, F11, F43.     

Managerial delegation and partial privatization in general equilibrium with sector-specific unemployment

This paper explores the effects of managerial delegation in a general-equilibrium, oligopolistic competition model with sector-specific unemployment. It specifically examines the effects of managerial delegation on outputs, factor returns and the urban unemployment ratio. It is found that if the managerial firm is less profit-oriented, managerial delegation can lead to an increase in the urban output, a decrease in the rural output, an increase in the capital rental and a decrease in the rural wage. In particular, it worsens the urban unemployment ratio.     

Equilibrium dynamics in discrete-time endogenous growth models with social constant returns

The existing literature establishes possibilities of local determinacy and dynamic indeterminacy in continuous-time two-sector models of endogenous growth with social constant returns. The necessary and sufficient condition for local determinacy is that the factor intensity rankings of the two sectors are consistent in the private/physical and social/value sense. The necessary and sufficient condition for dynamic indeterminacy is that the final (consumable) good sector is human (pure) capital intensive in the private sense but physical (consumable) capital intensive in the social sense. This paper re-examines the dynamic properties in a discrete-time endogenous growth framework and finds that conventional propositions obtained in continuous time need not be valid. It is shown that the established necessary and sufficient conditions on factor intensity rankings for local determinacy and dynamic indeterminacy are neither sufficient nor necessary, as the magnitudes of time preference and capital depreciation rates both play essential roles. We have benefitted from discussion with Robert Becker, Eric Bond, Michael Kaganovich, Karl Shell and participants of the Midwest Macroeconomic Conference in Chicago and the Midwest Economic Theory and International Trade Meetings at Indiana University. The fourth author acknowledges financial support from the Institute of Economics and Business Administration of Kobe University and the Institute of Economic Research of Kyoto University to enable this international collaboration.