Balanced Growth Equilibrium Research Articles

HUMAN CAPITAL ACCUMULATION, HOME PRODUCTION AND EQUILIBRIUM DYNAMICS*

In this paper, we construct a three-sector endogenous growth model in which long-run growth is propelled by human capital accumulation. We show that although the addition of a home sector to the standard two-sector endogenous growth model preserves the well-behaved balanced growth equilibrium properties, it generates new transitional dynamics around the balanced growth path. It is shown that, when there is a positive shock to physical capital, our model is more likely to exhibit paradoxical growth than are standard multisector endogenous growth models that exclude home production. Our analysis adds new results to those from the related literature on leisure.

Optimal balanced growth in a general multi-sector endogenous growth model with constant returns

I will study a multi-sector endogenous growth model with general constant returns to scale technologies and demonstrate the existence, uniqueness and the saddle-path stability of the balanced growth equilibrium. I will first demonstrate the existence of a balanced growth equilibrium, by showing that the balanced growth rate associated with the balanced growth equilibrium is solely determined by solving a Frobenius root problem of the price equations derived from the Euler equations and the property of the nonsubstitution theorem. Then I will show the saddle-path stability of the balanced growth equilibrium without any capital intensity conditions, which is a generalized property proved in the two-sector endogenous growth models by de Guevara et al. (J Econ Dyn Control 21, 115–143, 1997), Bond et al. (J Econ Theory 68, 149–173 1996) and Mino (Int Eco Rev 37, 227–251 1996). The theorem clearly implies that the balanced growth equilibrium has a transition path in the neighborhood of the balanced growth equilibrium.

Equilibrium Dynamics in an Endogenous Growth Model of Money and Banking

We construct an analytically tractable endogenous growth model of money and banking where money provides “liquidity services” to facilitate transactions and banks convert non‐reserve deposits into productive capital. We examine both the long‐ and short‐run effects of changes in the money growth rate or the reserve requirement ratio. In response to a change in the required reserve ratio, the inflation rate and the growth rates of capital, real balances, and consumption need not adjust monotonically along the transition path. While the balanced growth equilibrium may be either a saddle or a source locally, the global dynamical system exhibits flip bifurcation.

Technological spillovers and patterns of growth with sector-specific R&D

This paper studies a two-sector model of endogenous technical change in which expansion of each production sector is associated with sector-specific R&D investment. It is shown that the pattern of growth is sensitive to the specification of intersectoral technological spillover as well as to the preference structure. If technological spillovers and preferences of consumers are represented by CES functional forms, the balanced-growth equilibrium may not exhibit a well-behaved saddle-point property: it is possible that the balanced-growth path is locally indeterminate or unstable. In addition, a slight modification of technological spillover effects easily yields multiple balanced-growth paths. In contrast, Cobb–Douglas specifications present a unique and determinate balanced-growth path.

A neoclassical Kaldor model of real wage declines

A model linking macroeconomic equilibrium and income distribution in balanced growth equilibria is developed as a variant to the Kaldor model of factor shares. It departs from the original Kaldor model in assuming equal saving rates and a neoclassical production function. Macroeconomic equilibrium (national savings equal to investment) combines with competitive microeconomic behavior to determine the real wage and real interest rate. An increase in the ratio of national debt to labor reduces the real wage, explaining recent declines.

Recursive preferences and balanced growth

We study a class of utility functions that are defined recursively by an aggregator W x , y where u t = W c t , u t + 1 . In single-agent economies it is known that a sufficient condition for the existence of a balanced growth path is that utility should be homogenous of degree γ . In the context of a multi-agent economy we show that this restriction implies that either a balanced growth equilibrium fails to exist or all agents have the same constant discount factor. We suggest a generalization of recursive preferences wherein the intertemporal utility function is time dependent. Within this class we establish that there may exist a balanced growth equilibrium even if agents are different.

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.

Growth and welfare analysis of tax progressivity in a heterogeneous-agent model

In this paper, we use a general equilibrium model of endogenous growth in which there is heterogeneity in skill, income, and tax rates to evaluate the effect of progressivity of taxes on growth and welfare. In this framework, changes in the progressivity of tax rates can have positive growth effects even in situations where changes in flat rate taxes have no effect. Experiments on a calibrated model indicate that the quantitative effects of moving to a flat rate system are economically significant. The assumption made about the “engine” of growth—an external effect arising from production activities of skilled workers or intentional employment of skilled workers for research and other productivity enhancing activities—has an important effect on the impact of a change in progressivity. Welfare is unambiguously higher in a flat rate system when comparisons are made across balanced growth equilibria; however, when the costs of transition to the higher growth equilibrium are taken into account, only the currently skilled slightly prefer the flat rate system.

A Kaldor Matching Model of Real Wage Declines

A model linking macroeconomic phenomena and income distribution in balanced growth equilibria is developed as a variant to the Kaldor model of factor shares. It departs from the original Kaldor model in assuming equal savings rates and production determined by a matching process between workers and jobs. Macroeconomic equilibrium (national savings equal to investment) determines the ratio of jobs to employment and the ratio of unemployed to vacancies. Competitive microeconomic behavior then determines the wage and interest rates. Changes in the ratio of national debt to employment have real effects on factor prices. Implications for effects of taxes and unemployment benefits are derived. The model explains recent declines in real wages relative to productivity. Unemployment Benefits, Efficient Taxation, Matching, Factor Prices

Government Policy in a Stochastic Growth Model with Elastic Labor Supply

Endogenous labor supply is introduced into a stochastic growth model. Money is superneutral, and the real part of the equilibrium can be characterized by two nonlinear trade‐off loci between the time devoted to leisure and the mean growth rate that ensure the following: (i) equality among the risk‐adjusted rates of return and (ii) equilibrium in the output market. The balanced growth equilibrium is characterized analytically and policy implications derived. Extensive numerical simulations are also conducted. These assess the effects of risk on growth and the impact of fiscal policy on both the mean growth rate and its volatility. Implications for optimal monetary policy are also addressed.

Fiscal policy, elastic labor supply, and endogenous growth

Endogenizing labor supply leads to fundamental changes in the equilibrium structure of the AK growth model. The balanced growth equilibrium can be described in terms of two tradeoff loci relating the equilibrium growth rate to the fraction of time devoted to leisure. The implications of endogenous labor supply for fiscal policy are analyzed. Three issues are addressed. First, the effects of various distortionary tax changes and government expenditure changes on the equilibrium growth-leisure (employment) tradeoff are analyzed. Second, optimal fiscal policy is characterized. Finally, the formal analysis is supplemented by numerical results, focusing particularly on the quantitative welfare implications.

International risk sharing, learning by doing, and growth

This paper explores the influence of international risk sharing on aggregate growth for a country that trades with the rest of the world. Learning by doing supports long-run growth as it generates sector-specific increases in productivity proportional to labor's allocation across sectors. The paper shows that trade permits specialization in production which raises the growth rate of aggregate output. Uncertainty in productivity, however, discourages growth since greater diversification in production reduces aggregate risk. Consequently, international risk sharing raises growth during transition to the balanced growth equilibrium, although it leaves long-run growth unchanged. The model also helps to explain related empirical observations.

Keeping one step ahead of the Joneses: Status, the distribution of wealth, and long run growth

Assuming that the utility of each agent depends on its relative wealth position in the society, this paper constructs an endogenous growth model. It is shown that even if the subjective discount rates differ across agents, there exists a unique balanced growth equilibrium in which each agent owns a positive share of the world wealth. It is also shown that if the agents are identical then an increase in savings incentives always raises the long run growth rate but if they are heterogeneous then an increase in savings incentives may lower the long run growth rate.

Endogenous growth and the balanced growth equilibrium

This paper shows that the Romer (1990)Journal of Political Economy, 98, 71–102 model of endogenous growth, its version for the social planning problem, has a unique steady state and is saddle path stable. The steady state can be monotonically reached by an appropriate choice of the initial values of the control variables if the initial values of the state variables lie in the vicinity of the steady state. For the original version, as well as for generalizations of it, we demonstrate that Hopf bifurcation can be excluded. We also demonstrate that the market variant of the Romer model as, for example, presented in Benhabib, Perli and Xie (1994)Ricerche Economiche, 48, 279–298, does admit Hopf bifurcation and stable periodic solutions. The technique employed here may be useful in studying other variants of endogenous growth models.

Long-Run Effects of Monetary Expansion in a Two-Sector Model of Endogenous Growth

This paper explores the long-run effects of monetary expansion by introducing a cash-in-advance constraint into one of the basic models of endogenous growth. In our model, the real side of the economy consists of two production sectors, one of which produces a final good that can be used either for consumption or for investment and the other produces new human capital. Both sectors use physical and human capital under constant returns to scale technologies. We first characterize the balanced-growth equilibrium and then examine how a rise in money growth affects the relevant variables, such as the long-term growth rate and the relative prices.

A simple endogenous growth model with endogenous fertility: indeterminacy and uniqueness.

This paper studies the equilibrium dynamics and indeterminacy of equilibria in an endogenous growth model with endogenous fertility choice. We characterize the conditions that give rise to an unique equilibrium as well as multiple equilibria. Whenever there exists a unique equilibrium, it will be globally determinate; when multiple equilibria arise, indeterminacy occurs. In particular, we find that two equilibria occur – one is associated with high fertility and low growth, while the other is associated with low fertility and high growth. A parameterized example is given to assess the empirical feasibility of our results. The validity of the neo-Malthusian relation between fertility and growth is then re-examined. Finally, we study the relation between growth and welfare and compare different balanced growth equilibria in terms of their lifetime-attained utility.

On the Existence of Balanced Growth Equilibrium

The authors characterize the class of dynamic models that allow for the most commonly used types of sustained economic growth (balanced and asymptotically balanced). They show that, under a constant returns to scale technology, (asymptotically) constant discount rate and (asymptotically) constant elasticity of marginal felicity are not only necessary but also sufficient conditions for the existence of a(n) (asymptotically) balanced growth equilibrium path. The authors provide examples of recursive utility models that accept a(n) (asymptotically) balanced growth equilibrium and discuss their implications on cross-country differences in growth rates as well as on savings behavior and wealth distribution. Copyright 1997 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

A General Two-Sector Model of Endogenous Growth with Human and Physical Capital: Balanced Growth and Transitional Dynamics

We examine a two-sector endogenous growth model with general constant-return-to-scale production technologies governing the evolution of human and physical capital. We prove the existence, uniqueness, and saddle-path stability of the balanced growth equilibrium. A dual approach drawing on techniques from international trade theory is used to provide complete characterization of the transitional dynamics of consumption, goods and education outputs, human and physical capital inputs, and the relative price of human capital investment. We investigate the long-run effects of changes in time preference and factor taxation, and show the emergence of instability or indeterminacy when factor taxes are too distortionary.Journal of Economic LiteratureClassification Number: D90.

Flexibility, investment, and growth

This paper proposes a model of growth with diversifiable microeconomic uncertainty and uses it to study the efficiency costs and distributional effects of obstacles to labor mobility. Labor mobility costs reduce private and social returns to irreversible investment decisions, decrease the speed of capital accumulation, and lower a representative agent's welfare. They can however shift income distribution towards ‘workers’, or individuals who own no accumulated factors of production and have no incentives to save any portion of their income flows in balanced-growth equilibrium. This may help explain why labor's political representatives often favor provisions which decrease socially desirable labor mobility.

Dynamic inefficiency, endogenous growth, and Ponzi games

We show that in competitive endogenous growth models without externalities, balanced growth equilibria are dynamically efficient. With learning-by-doing externalities, dynamic inefficiency may exist, but due to the mix of capital rather than its scale. These results are obtained independent of whether or not lifetimes are finite or generations overlap. In OLG models with externalities we show that Ponzi games may be feasible even though equilibria are characterized by undersaving.