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Optimal fiscal policy in the Uzawa-Lucas model with CES production.

Article Excerpt
Abstract

This paper devises an endogenous growth model with human capital in the Uzawa-Lucas framework in which the average human capital has a positive external effect on the goods sector. Unlike previous works, this paper assumes that output is produced with a CES technology and analyzes the existence, uniqueness, and stability of equilibrium. Also, a fiscal policy is devised that is capable of providing the required incentives to optimize the competitive equilibrium. In order to correct the market failure caused by the externality, the authors introduce a subsidy to human capital and analyze how it can be financed in an optimal way. Some simulation results are presented. (JEL O41, E62)

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Introduction

The Uzawa-Lucas model [Uzawa, 1965; Lucas, 1988] has been the subject of active research in the past decade [Caballe and Santos, 1993; Chamley, 1993; Mulligan and Sala-i-Martin, 1993; Bond et al., 1996; Ladron-de-Guevara et al., 1999; Gomez, 2003, 2004]. In the absence of externalities, the market equilibrium coincides with the optimal growth path and, therefore, the government intervention is not justified. Gomez [2004] points out that the mere presence of externalities does not provide an incontrovertible rationale for government intervention. It further shows that a sector-specific externality associated with human capital in the goods sector does not cause a market failure since the competitive equilibrium is optimal. However, other types of externalities may provoke a market failure. In his seminal paper, Lucas [1988] considers a case where average human capital has an external effect in the goods sector. The presence of such an externality causes the fraction of time devoted to human capital accumulation to be inferior to the optimal. The government could then intervene to induce the agents to devote more time to education, correcting the market failure, and, as a consequence, improving welfare.

Garcia-Castrillo and Sanso [2000] and Gomez [2003] derive fiscal policies that optimize the decentralized equilibrium in the Uzawa-Lucas model with externalities a la Lucas. In these papers, output is produced with a Cobb-Douglas technology. Since the Cobb-Douglas specification, with physical and human capital serving as inputs, is consistent with one of Kaldor's stylized facts of growth--that the share of income accruing to capital and labor are relatively constant over time--most researchers have not questioned its use to study growth and development. Nevertheless, some researchers have expressed doubts about the Cobb-Douglas orthodoxy. Solow [1958] pointed out that Kaldor's stylized fact is not that factor shares have been absolutely constant, as the Cobb-Douglas specification literally implies, but rather that these shares have been relatively constant over the short period of time for which there is available data. Solow noted that slight departures from a Cobb-Douglas specification, in the form of a constant-elasticity-of-substitution (CES) production technology with an elasticity of substitution that is only slightly different from unity, results in small trends in factor shares of income that are consistent with the observed relative stability of these shares over longer periods of time. The implications of the neoclassical growth model with a CES production technology were further spelled out by Pitchford [1960] and resurrected by other authors [Jones and Manuelli, 1990; Rebelo, 1991; Duffy and Papageorgiu, 2000]. Hence, this paper considers that a CES technology is more adequate than a Cobb-Douglas production function to study the economic development process.

The purpose of this paper is to develop an endogenous growth model with human capital in the Uzawa-Lucas framework with externalities a la Lucas, when output is produced with a CES technology. First, the study analyzes the existence, uniqueness, and stability of equilibrium. Then, a fiscal policy capable of providing the required incentives to attain optimal competitive equilibrium is devised. Physical capital income should be free of taxation. The optimal fiscal policy requires the use of a time-varying subsidy rate to the stock of human capital, which can be financed by means of a lump-sum tax combined with a constant tax on labor income, at least in the transitory phase. However, lump-sum taxation is not needed to balance the government budget in the steady state.

The study also performs a simulation analysis to gain some insight on the behavior of the subsidy and tax rates. As expected, as the externality increases the subsidy rate, the government's size increases steadily to correct the market failure provoked by the average human capital in the production of goods. The tax rate on labor income also increases as the externality increases to finance the higher subsidy required to correct the externality.

The remainder of this paper is organized as follows. The next sections describe the decentralized economy and the...

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