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 Especially Alain Venditte had given me a chance to take a look at his unpublished paper titled ” Indeterminacy and the Role of Factor Substitutability” jointly written with Kazuo Nishimura at Kyoto University and published in Macroeconomic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.     

Constant-returns endogenous growth with pollution control

Pollution control with positive externality from the government is incorporated in an endogenous growth model with AK production function. The result indicate that if consumption and abatement expenditure grows at a constant rate, pollution stock will have smaller growth rate. The growth rate of consumption in a command economy will in general be greater than in a competitive economy. A greater intertemporal elasticity of substitution will result in a lower growth rate only if the household's preference parameter against pollution is sufficiently small. The development strategy of pursuing higher growth rate accompanied by more pollution in the early stage of economic development is economically justifiable. The utility in a wealthier economy is always higher in all stages of development than in a poorer economy, as is the pollution stock, although it may converge in the steady state.An earlier version of this paper was presented at the International Congress on Modelling and Simulation, December 6–10, 1993, Perth, Australia. Constructive comments and suggestions from two anonymous reviewers of this journal are greatly appreciated, and so is the financial support from the Bureau of Industrial Development in Taiwan.     

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.

On the dynamics of an endogenous growth model with learning by doing

Summary. The paper studies the local dynamics of an endogenous growth model with externalities of investment. It is demonstrated that, in case of sustained per capita growth, the competitve economy is characterized by a situation with a unique balanced growth path which is saddle point stable or by a situation with two balanced growth paths. If there are two balanced growth paths, the one with the higher growth rate is a saddle point whereas the path with the lower growth rate is either completely stable, with convergence to a rest point or limit cycle, or completely unstable. In the social optimum the existence of a balanced growth path implies that it is unique and that this path is a saddle point. Received: May 15, 2000; revised version: December 14, 2001     

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.     

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.     

Testing endogenous growth in South Korea and Taiwan

We evaluate the endogenous growth hypothesis using sectoral productivity data and the product variety of exports for South Korea and Taiwan. We find that changes in relative export variety (entered as either a lag or a lead) have a positive and significant effect on total factor productivity (TFP) in nine of the 16 sectors. Seven out of these sectors are what we classify as secondary industries, in that they rely on and produce differentiated manufactures, and therefore seem to fit the idea of endogenous growth. Among the primary industries, which rely more heavily on natural resources, we find mixed evidence.     

Government financing in an endogenous growth model with financial market restrictions

Summary. In this paper, we develop an endogenous growth model with market regulations on explicitly modeled financial intermediaries to examine the effects of alternative government financing schemes on growth, inflation, and welfare. In the presence of binding regulation, there is always a unique equilibrium. We perform four alternative policy experiments; a change in the seigniorage tax rate, a change in the seigniorage tax base, a change in the income tax and a change in the fiscal-monetary policy mix. We find that in the presence of binding legal reserve requirements, a marginal increase in government spending need not result in a reduction in the rate of economic growth if it is financed with an increase in the seigniorage tax rate. Raising the seigniorage tax base by means of an increase in the reserve requirement retards growth and it has an ambiguous effect on inflation. An increase in income tax financed government spending also suppresses growth and raises inflation although not to the extent that the required seigniorage tax rate alternative would. Switching from seigniorage to income taxation as a source of government finance is growth reducing but deflationary. From a welfare perspective, the least distortionary way of financing an increase in the government spending requirements is by means of a marginal increase in the seigniorage tax rate. Under the specification of logarithmic preferences, the optimal tax structure is indeterminate. Received: March 20, 2000; revised version: June 26, 2001     

Optimal monetary policy in a New Keynesian model with endogenous growth

We study optimal monetary policy in a New Keynesian (NK) model with endogenous growth and knowledge spillovers external to each firm. We find that, in contrast with the standard NK model, the Ramsey dynamics implies deviation from full inflation targeting in response to technology and government spending shocks, while the optimal operational rule is backward looking and responds to inflation and output deviations from their long-run levels.     

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.     

Business cycles in a two-sector model of endogenous growth

Summary. This paper analyzes the impact of cyclical volatility on long-term economic growth: does growth increase or decrease with increased cyclical volatility? We construct a stochastic two-sector model of endogenous growth to analyze this question in detail. We will show that economic growth is higher in the presence of business cycles, since people devote more time to learning activities in an uncertain economic environment. Human capital is a hedge against future income uncertainty. Hence, the rate of economic growth will be higher in a stochastic environment. Based on a calibration of the model, we find that economic growth increases by 0.46%-point as a result of observed business cycle variability. When account is taken of the interaction between the model's general equilibrium and the cycle, welfare gains (measured in units of a permanent percentage increase in consumption) from eliminating business cycle volatility are approximately 1.87%. Received: January 25, 2000; revised version: November 3, 2000     

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     

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.     

Private versus social returns to human capital: Education and economic growth in India

This paper investigates whether differences between private and social returns to education of government sector employees can contribute to an explanation of the “micro–macro paradox” in the literature on education and growth. We hypothesize that in India educated people find privately rewarding jobs in a sector in which social returns are low, namely the government sector. This could help explain high returns to education at the micro level and small or negative coefficients on education growth in growth regressions at the macro level. The empirical results, which are consistent with this hypothesis, are based on an analysis of state-level data from India spanning 40 years.     

A note on the effect of patents in endogenous growth models

This note examines the effect of patent protection in an endogenous growth model with a generic innovation process. It indicates that increasing patent breadth stimulates innovation when R&D is less intermediates-intensive than production, whereas it has a non-monotonic effect on innovation when the former is more intermediates-intensive than the latter.