Optimal Lending Contracts and Firm Dynamics

We develop a general model of lending in the presence of endogenous borrowing constraints. Borrowing constraints arise because borrowers face limited liability and debt repayment cannot be perfectly enforced. In the model, the dynamics of debt are closely linked with the dynamics of borrowing constraints. In fact, borrowing constraints must satisfy a dynamic consistency requirement: the value of outstanding debt restricts current access to short-term capital, but is itself determined by future access to credit. This dynamic consistency is not guaranteed in models of exogenous borrowing constraints, where the ability to raise short-term capital is limited by some prespecified function of debt. We characterize the optimal default-free contract—which minimizes borrowing constraints at all histories—and derive implications for firm growth, survival, leverage and debt maturity. The model is qualitatively consistent with stylized facts on the growth and survival of firms. Comparative statics with respect to technology and default constraints are derived.     

Aggregate savings when individual income varies

This paper examines aggregate savings in a general equilibrium model where infinitely lived households face volatile (and possibly uncertain) income paths, hold a risk-free asset, and face a borrowing constraint. I first show that the equilibrium capital stock in an economy without uncertainty, but where individual income varies, can be larger than in an economy where each household's income is constant. When individual income is stochastic and uninsurable, the equilibrium capital stock is always larger than when income is constant. This additional capital accumulation has sometimes been interpreted as precautionary savings, but I argue that much of the additional savings are generated by permanent-income motives in combination with strict borrowing constraints.     

Equilibrium existence in infinite horizon economies

In sequential economies with finite or infinite-lived real assets in positive net supply, we introduce constraints on the amount of borrowing in terms of the market value of physical endowments. We show that, when utility functions are either unbounded and separable in states of nature or separable in commodities, these borrowing constraints not only preclude Ponzi schemes but also induce endogenous Radner bounds on short-sales. Therefore, we obtain existence of equilibrium. Moreover, equilibrium also exists when both assets are numéraire and utility functions are quasilinear in the commodity used as numéraire.     

Government size and economic growth in an endogenous growth model with rent‐seeking

We explore the relationship between government size and economic growth in an endogenous growth model with human capital and an unproductive capital which facilitates rent‐seeking. With exogenous as well as endogenous time discounting, we find a non‐monotonic relationship between the size of government and economic growth. We find that with very high (low) discounting, there is a unique low (high) growth equilibrium, regardless of the size of government. For the intermediate range of discounting, there are multiple equilibria and the growth outcome depends on the size of government. With endogenous time discounting, the growth outcome is path dependent and depends on the level of inherited human capital. However, there is only one stable growth regime and the economy endogenously switches to it. When the institutional constraints on rent‐seeking are not extremely high, the stable regime is the one in which there is a high‐growth equilibrium for a smaller size of the government and for larger size, both the high‐growth and the low‐growth equilibrium coexist. When the institutional constraints on rent‐seeking are extremely high, there exists only a unique high‐growth equilibrium irrespective of the size of government. Furthermore, economies with bigger size of the government and/or with poor quality institutions will take longer to endogenously switch to this stable growth regime.     

Endogenous trading constraints with incomplete asset markets

This paper endogenizes the borrowing constraints on capital in a production economy with incomplete markets. We find that these limits get looser with income, a property that is consistent with US data on credit limits. The framework with endogenous limits is then used to study the effects of a revenue neutral tax reform that eliminates capital income taxes. Our results illustrate that it is very important to take into account the effects of tax policies on the limits. Throughout the transition, these effects can be big enough to change the overall conclusion about the desirability of a tax reform.     

Educational choice, endogenous inequality and economic development

This paper investigates the mechanics through which wealth may, in the long run, trickle down from the rich to the poor. In the presence of indivisibilities in investment of human capital and impossibility of borrowing money, investment in education is financed through an intergenerational transfer. In an OLG model where aggregate production requires capital and both skilled and unskilled labor, it is shown that the long run equilibrium outcome depends on the values of few key parameters. A complete characterization of the steady state is provided. Under some configurations of the parameter values a unique invariant equilibrium exists where inequality vanishes asymptotically. Under others, multiple equilibria exist and the equilibrium outcome crucially depends on the initial conditions of the system. These equilibria are characterized by a negative relationship between inequality and economic development.     

Educational Policy in a Credit Constrained Economy with Skill Heterogeneity*

An overlapping‐generations model where agents choose whether to become educated when young is presented. Education enhances productivity, but needs to be financed by borrowing. Because of the possibility of default, lenders may ration credit. We characterize the steady‐state equilibrium with and without credit constraints and show that credit constraints are associated with lower education and a lower real interest rate. We then study the role of public policy in remedying the inefficiency which occurs with credit market imperfections and examine whether public education can improve on the constrained equilibrium.     

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.     

Physical and human capital,fertility, and childcare services

We shed light on a nexus between fertility transitions and economic growth patterns. We construct a two-sector overlapping generations (OLG) model with endogenous fertility, physical capital, and human capital, where one sector produces goods, and another produces childcare services. If the elasticity of fertility for expenditure on childcare services is zero, the economy experiences endogenous growth, and fertility does not depend on physical and human capital, but it increases with parental child-rearing time. On the other hand, if elasticity is positive, the economy converges to a steady state, and the number of children becomes the homogenous function of degree of elasticity (less than one). In other words, fertility is the decreasing-return-to-scale function of physical and human capital. We show that a subsidy policy for education is more desirable than a subsidy for childcare services.     

The Uzawa–Lucas model without scale effects: theory and empirical evidence

Numerous cross-sectional tests have been performed to evaluate the predictions of recent growth theories such as the Uzawa–Lucas growth model. In a series of papers and in his book, Jones [Q. J. Econ. 110 (1995a) 495; J. Political Econ. 103 (1995b) 759; The upcoming slowdown in US economic growth, Stanford University, Stanford] has shifted the attention toward the time series predictions of endogenous growth models. By contrasting endogenous growth models with facts, one is frequently confronted with the prediction that levels of economic variables, such as human capital, imply lasting effects on the per capita growth rate of an economy. As stylized facts show, measures of education or human capital in most advanced countries have dramatically increased, mostly more than the gross domestic production (GDP). Yet, the growth rates have roughly remained constant or even declined. In this paper we modify the growth effects of education and human capital in our variant of the Uzawa–Lucas growth models and test the model using time series data for the US and Germany from 1962.1 to 1996.4. We consider two versions. In the first, we treat the time spent for education as exogenously given and we neglect the external effect of human capital. In the second version, the time spent for education is an endogenous variable and the external effect of human capital is taken into account. Our results demonstrate that the model is compatible with the time series for aggregate data in those countries. The parameters fall into reasonable ranges.     

The effects of households’ and firms’ borrowing constraints on economic growth

This paper considers an endogenous growth model with asymmetric information between lenders and borrowers, that leads to credit-rationing a proportion of borrowers. However, in contrast to the existing literature, in this model, both firms and consumers face borrowing constraints. Nonetheless, the borrowing constraints facing a firm and those encountered by a consumer have opposing effects on growth. Relaxing borrowing constraints on firms is growth-promoting, as more funds become available for productive investment. In contrast, relaxing borrowing constraints facing consumers has a detrimental effect, as funds are diverted from productive investment to consumption. Such an adverse effect may offset the externality effect present in the production function that would otherwise ensure perpetual growth. Furthermore, it is shown that the interaction between households’ and firms’ borrowing constraints may give rise to endogenous cycles.     

Endogenous technological progress in a multi-sector growth model

This paper presents an endogenous growth model driven by human capital, where human capital can be allocated across three sectors: the production of the final consumption good, the educational sector and the production of technological capital (in the form of knowledge or ideas). In our model, which also includes public expenditure and population growth, labor augmenting technical progress is endogenous and this enriches the transitional dynamics of the economy. With respect to ideas-based growth models, we assume knowledge is produced according to a neoclassical technology, combining ideas and human capital. Such an assumption is motivated by empirical works showing the existence of significant decreasing returns in the creation of ideas at the aggregate level (as Kortum, 1993; and Pessoa, 2005) and of the weak relationship between some inputs of the knowledge production process (as the number of researchers) and the total factor productivity growth rate (as Jones, 2002). Under some general conditions, this economy exhibits the existence of a steady state equilibrium and an unstable multidimensional manifold. Numerical examples are provided to show the existence of stable arms.     

Collateral secured loans in a monetary economy

This paper presents a microfounded model of money where durable assets serve as a guarantee to repay consumption loans. We study a steady state equilibrium where money and credit coexist. In such an equilibrium, a larger investment in durable capital relaxes the borrowing constraint faced by consumers. We show that the occurrence of over-investment and the behavior of capital accumulation depend on the rate of inflation, the relative risk aversion of agents and the marginal productivity of the capital goods.     

Optimal Fiscal Policy with Endogenous Time Preference

This paper studies the role of Ramsey taxation under the assumption that the individual rate of time preference is determined by the publicly provided social level of education. We show how intertemporal complementarities of aggregate human capital can generate multiple equilibria and we examine the role of endogenous fiscal policies in equilibrium selection. Our analysis implies a lower optimal government size due to the effect of human capital on time preference.     

Collateral constraints and rental markets

We study a benchmark model with collateral constraints and heterogeneous discounting. Contrarily to a rich literature on borrowing limits, we allow for rental markets. By incorporating this missing market, we show that impatient agents choose to rent rather than to own the collateral in the neighborhood of the deterministic steady state. Consequently, impatient agents are not indebted and borrowing constraints play no role in local dynamics.     

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     

Ramsey Equilibrium in a Two-Sector Model with Heterogeneous Households

We prove an existence theorem for a stationary perfect foresight equilibrium under borrowing constraints in a two-sector model with infinitely lived heterogeneous agents. The most patient agent holds all the capital in this solution. We also show that if the capital goods sector is capital intensive and capital income is increasing in the aggregate capital stock, then the aggregate capital stock eventually is monotonic and converges to the steady state stock. If the consumption goods sector is more capital intensive and capital income is increasing in aggregate capital we prove convergence to the steady state under more restrictive conditions. Periodic equilibria are shown to exist under weaker hypotheses. Journal of Economic Literature Classification Numbers: D52, D90, E13.     

组合、套利和资本市场的均衡特征——对资本市场均衡“异化”现象的一种解释

无套利均衡是新古典主义理论在特定条件下所界定的市场均衡特征。考察卖空限制和借款约束行为对资本市场上的组合和套利行为的影响,并结合市场从非均衡向均衡的调整过程,定性考察不同行为假设之下资本市场均衡特征的变化,可以发现,资本市场均衡和套利机会之间的共存或排斥状态,直接受制于有关市场参与者的初始行为假设。在不同的行为假设之下,市场参与者的组合和套利行为具有不同的特征和不同的影响。     

A Case Against Zero Capital-Income Taxation

This paper develops a dynamic general equilibrium model to investigate the optimal level of capital income taxation in light of stochastic endogenous economic growth. Although endogenous human capital is incorporated into our model, we restrict our investigation to the issue of optimal physical capital income tax; and the labor supply is also endogenously determined. This paper proves that the optimal capital income tax should be zero provided exogenous government expenditure on production; however, capital income should be taxed if we consider endogenous government consumption.     

Competitive equilibria with limited enforcement

We show how to decentralize constrained efficient allocations that arise from enforcement constraints between sovereign nations. In a pure exchange economy these allocations can be decentralized with private agents acting competitively and taking as given government default decisions on foreign debt. In an economy with capital these allocations can be decentralized if the government can tax capital income as well as default on foreign debt. The tax on capital income is needed to make private agents internalize a subtle externality. The decisions of the government can arise as an equilibrium of a dynamic game between governments.