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. The paper was presented at the conferences “Irregular Growth: Beyond Balanced Growth” held on June 19–21, 2003 in Paris and “Economic Growth and Distribution: On the Nature and Causes of the Wealth of Nations” held on June 16–18, 2004 in Lucca, Italy. From the discussion with Alain Venditti at CNRS-GREQAM, Gerhard Sorger at University of Vienna and the conference participants, I have been benefited much by writing this paper. Especially Alain Venditte had given me a chance to take a look at his unpublished paper titled ” Indeterminacy and the Role of Factor Substitutability” jointly written with Kazuo Nishimura at Kyoto University and published in Macroeconomic Dynamics, Vol. 8. The author also would like to thank an anonymous referee for useful suggestions.     

Multiple steady states,indeterminacy, and cycles in a basic model of endogenous growth

The goal of this paper is to demonstrate that a basic model of endogenous growth with learning by doing may produce a rich array of outcomes. Starting point of our analysis is the Romer (1986a) approach. In contrast to Romer, however, we assume that one unit of investment shows different effects concerning the building up of physical and human capital, so that these variables cannot be merged into one single variable. With this assumption, it can be shown that multiple steady states, indeterminacy of equilibria, and persistent cycles may result in our model.     

Recursive equilibrium in endogenous growth models with incomplete markets

This paper analyzes the existence of recursive equilibria in a class of convex growth models with incomplete markets. Households have identical CRRA-preferences, production displays constant returns to scale with respect to physical and human capital, and all markets are competitive. There are aggregate productivity shocks that affect aggregate returns to physical and human capital investment (stock returns and wages), and there are idiosyncratic shocks to human capital (idiosyncratic depreciation shocks) that only affect individual human capital returns. Aggregate and idiosyncratic shocks follow a joint Markov process. Conditional on the aggregate state, idiosyncratic shocks are independently distributed over time and identically distributed across households. Finally, households have the opportunity to trade assets in zero net supply with payoffs that depend on the aggregate shock, but markets are incomplete in the sense that there are no assets with payoffs depending on idiosyncratic shocks. It is shown that there exists a recursive equilibrium for which equilibrium prices (returns) only depend on the exogenous aggregate shock variable (the wealth distribution is not a relevant state variable). Moreover, the allocation associated with this recursive equilibrium is identical to the equilibrium allocation of an economy in which households live in autarky and face both aggregate and idiosyncratic risk.I would like to thank for helpful comments Peter Howitt, Bob Lucas, Michael Magill, Tomo Nakajima, Herakles Polemarchakis, Martine Quinzii, Kevin Reffett, an anonymous referee, and seminar participants at various universities and conferences.     

On local indeterminacy and endogenous cycles in Ramsey models with heterogeneous households

It is well-known that endogenous cycles can occur in Ramsey models with heterogeneous households and borrowing constraints. In this note, we address the issue of robustness in the more general case of endogenous labor supply and we explain the occurrence of local indeterminacy under progressive taxation.

Progressive taxation and macroeconomic stability in two-sector models with social constant returns

It has been shown that, in the two-sector Benhabib–Farmer–Guo model with technologies of social increasing returns that exhibits indeterminacy, progressive income taxes de-stabilize the economy. This paper revisits the robustness of the tax implication in the two-sector Benhabib–Nishimura model with technologies of social constant returns that exhibits indeterminacy. We show that a progressive income tax stabilizes the economy against sunspot fluctuations, and thus the tax implication based on the two-sector Benhabib–Farmer–Guo model is not robust.     

Health and infrastructure in a model of endogenous growth

This paper studies the optimal allocation of government spending between infrastructure and health (which affects labor productivity as well as household utility) in an endogenous growth framework. A key feature of the model is that infrastructure affects not only the production of goods but also the supply of health services. The rate of time preference is also endogenously related to health outcomes. The first part considers the case where health enters as a flow in production and utility, whereas the second focuses on a “stock” approach. Growth- and welfare-maximizing rules for income taxation and the allocation of public spending are derived.     

A dynamic analysis of an endogenous growth model with leisure

Summary. The main goal in this paper is to analyze an economic model of endogenous growth where human capital accumulation acts as the engine propelling economic activity. The added ingredient in our model is that agents derive utility from consumption and leisure, where leisure is defined as the amount of time devoted to those activities augmented by the level of education. Under regular conditions we show that there is a unique globally stable balanced growth path. We also provide a characterization of the behavior of our economic variables along the transition. Received: May 26, 1998; revised version: September 9, 1999     

Culture and human capital in a two-sector endogenous growth model

Recent literature in the field of cultural economics highlights a possible inversion in the usual causality relation (from economic growth to culture) and points out that culture may represent an important driver of economic growth. By viewing culture in line with Throsby’s (2001) definition of cultural capital (i.e., an asset of tangible and intangible cultural expressions), in this article we analyze one possible channel through which culture may positively affect economic growth, namely the existence of a relationship of complementarity between cultural and human capital investments. Using a two-sector endogenous growth model, we find that in the long run a higher growth rate of real per-capita income can be attained the more cultural and human capital investments are complementary for each other in the process leading to agents’ skill acquisition. We also analyze the conditions under which an increase of the cultural capital share in total GDP can be conducive to a rise of real per-capita income.     

Rate of profit and interest in a growth theory with endogenous money

This paper attempts to incorporate an endogenous money approachinto post-Keynesian growth theory in order to derive the fullemployment equilibrium rate of interest as well as that of profit.This rate of interest, named the ideal rate of interest, differsfrom the rate of profit in that it is in proportion to a monetaryvariable, not a real variable. Further, the rate of profit alsodiffers from the rate of interest as a premium because it isproductive. The rate of interest could be important in explainingcircumstances in which financial capital has been accumulatedin excess.     

Money and growth in a cash-in-advance economy with costly credit

This paper develops a stochastic growth model with a cash-in-advance constraint, costly credit, and intermediary services. We study how the behavior of financial intermediaries affects the relationship between economic growth and the monetary system. We show that the payment that intermediaries charge for providing financial services influences the money–growth relationship. When the intermediation cost increases proportionally with credit purchases, we do not observe any influence of growth on the monetary system. When the intermediation cost is not proportional to credit purchases, growth is responsible for a transformation of the monetary system, i.e. money is relatively driven out of the economy as the economy grows.     

Can market power sustain endogenous growth in overlapping-generations economies?

Summary. Sustained endogenous growth is known to be impossible in OLG one-sector models without non-convexities and externalities, unless income is redistributed to the young generation. No redistribution proper is however necessary, as shown in two simple examples, if positive profits accruing to young monopolistic entrepreneurs can be sustained in equilibrium, and/or if young unionised workers can guarantee a non-vanishing share of aggregate income. In this context, market power appears, in two different forms, as a significant source of sustained endogenous growth. Received: October 3, 2000; revised version: March 9, 2001     

Scale effects in endogenous growth theory: an error of aggregation not specification

Modern Schumpeterian growth theory focuses on the product line as the main locus of innovation and exploits endogenous product proliferation to sterilize the scale effect. The empirical core of this theory consists of two claims: (i) growth depends on average employment (i.e., employment per product line); (ii) average employment is scale invariant. We show that data on employment, R&D personnel, and the number of establishments in the US for the period 1964–2001 provide strong support for these claims. While employment and the total number of R&D workers increase with no apparent matching change in the long-run trend of productivity growth, employment and R&D employment per establishment exhibit no long-run trend. We also document that the number of establishments, employment and population exhibit a positive trend, while the ratio employment/establishment does not. Finally, we provide results of time series tests consistent with the predictions of these models.     

Consumption taxation, social status and indeterminacy in models of endogenous growth with elastic labor supply

In this paper, we examine the effects of consumption taxation on long-run growth in an infinitely lived representative-agent model of endogenous growth with endogenous labor supply in which the desire for social status induces private agents to care about others’ wealth or consumption levels. This analysis shows that the increase in consumption taxation raises (reduces) the long-run growth rate when the equilibrium path is locally indeterminate (determinate), provided the desire for social status is not too strong in the relative wealth model. By contrast, in the consumption externalities model, the same result holds, if the Frisch labor supply and labor demand curves have the ‘normal’ slopes at their intersection point, while the result is reversed if these two curves have the ‘wrong’ slopes.     

Stability, global dynamics and Markov equilibrium in models of endogenous economic growth

This paper studies the local and global dynamics of two-sector models of endogenous growth with economy-wide external effects and taxes on capital and labor. The local analysis classifies the parameter space depending on the number of stationary solutions and local stability of equilibria. The global analysis shows that if taxes are within certain bounds and the size of the external effects on the average level of human capital is smaller than the share of physical capital, the equilibrium path is monotone and therefore a continuous Markov equilibrium can be constructed.     

On the effects of human capital and R&D policies in an endogenous growth model

We introduce an external effect of existing technologies in human capital accumulation in an endogenous growth model and describe its steady-state and transition. We numerically solve the model to compare the quantitative effects of R&D policy with the quantitative effects of human capital policy in wealth and welfare. Although R&D subsidies have now an overall positive effect on growth, wealth and welfare, the calibration exercise shows that for plausible values for the parameters, human capital policy is simultaneously the most income and welfare-improving and the less expensive to the government.     

Fluctuations in convex models of endogenous growth, II: Business cycle properties

Using ideas from the endogenous growth literature, we present a model of the endogenous determination of productivity growth based on individual worker decisions about human capital investment. We calibrate a version of the model to match long run growth facts from the US and study the business cycle properties of this model. This approach offers improvements along several dimensions over standard exogenous growth methodologies. Most importantly, our stochastic endogenous growth model generates much greater serial correlation in output growth and labor supply volatility relative to its real business cycle counterpart. We conclude that using the extra discipline of reproducing the trend productivity growth features of the data endogenously constitutes an important missing component from the real business cycle approach.     

Optimal fiscal policy in an endogenous growth model with public capital: a note

This note presents an investigation of the optimal tax rule in endogenous growth models with public capital. It is presumed that the government levies only an income tax in addition to financing public investment. Furthermore, a household’s saving is deducted from the income tax. We find the optimal tax rule whereby the social optimum is attainable. The manner by which a government imposes a tax on income and administers tax deductions is important for attaining a socially optimal situation.      

Inequality,unemployment, and endogenous growth in a political economy with a minimum wage

This paper presents development of an endogenous growth model with heterogeneous households and political determination of the minimum wage. We investigate the interaction of inequality, unemployment, and economic growth. First, the arguments in this paper show that a positive correlation exists between inequality and unemployment, Second, the interaction between inequality and economic growth is shown to be a positive relation if high inequality pertains in a society. It is a negative relation if low inequality pertains.      

On perfect equilibria in stochastic models of growth with intergenerational altruism

Summary. The well-known model of altruistic growth/strategic bequest is studied. A stochastic transition function is considered and fairly general sufficient conditions for the existence of Markov-stationary subgame-perfect equilibrium are given. Also some special cases in which the equilibrium policy is continuous and nondecreasing are discussed.Received: 20 September 2003, Revised: 11 December 2004, JEL Classification Numbers: C73, D91, O40.Research was partially supported by KBN grant 5 PO3A 01420.