On government-created credit markets for education and endogenous growth

Interest in public loans to fund (higher) education has been increasing in the last decades. This paper explores the general welfare properties of government-created credit markets for education in a three-period overlapping generations model with physical and human capital. It shows that the mere existence of public credit markets is second-best in nature, and cannot decentralize the optimum. Achieving the first-best “Golden Rule” balanced growth path requires a government loan system that lends the amounts required for optimal investments in education and an optimally chosen pure pay-as-you-go social security system. Student loans and pensions thus appear as two inseparable elements of the policy that maximizes social welfare.     

Optimal Taxation when Consumers Have Endogenous Benchmark Levels of Consumption

I examine optimal taxes in an overlapping generations economy in which each consumer's utility depends on consumption relative to a weighted average of consumption by others (the benchmark level of consumption) as well as on the level of the consumer's own consumption. The socially optimal balanced growth path is characterized by the Modified Golden Rule and by a condition on the intergenerational allocation of consumption in each period. A competitive economy can be induced to attain the social optimum by a lump-sum pay-as-you-go social security system and a tax on capital income.     

Effectiveness versus Efficiency: Growth-Accelerating Policies in a Model of Growth without Scale Effects

Abstract. Recent R&D growth models without strong scale effects imply that long-run growth rates depend only on parameters that are usually taken to be exogenous. However, integrating human capital accumulation into models of this type, Arnold (2002) demonstrates that subsidizing education accelerates growth. The present paper addresses welfare issues in Arnold's model. The main theoretical finding of the paper is that a system of subsidies that implements the optimal balanced growth path as a decentralized equilibrium includes zero subsidies to education, while R&D activity should be either subsidized or taxed. To shed further light on the latter result, the model is calibrated and it turns out that along the balanced growth path, the decentralized economy underinvests in R&D, i.e. R&D activities should be subsidized.     

The analytical solution of balanced growth of non-linear dynamic multi-sector economic model

In a one-sector neoclassical dynamic economic growth model, a reasonable ratio of investment to consumption exists, i.e., the “Golden Rule of Consumption”. This study is to extend one-sector neoclassical growth model to a multi-sector one. It is assumed that both the production function and the utility function are of Cobb–Douglas type, and the analytical expression of the balanced growth solution of the multi-sector model is provided, mainly including analytical expressions of the optimal distribution coefficient of fixed capital investment, the optimal distribution coefficient of labor hour, the proportion of production, the economic growth rate, the rate of change of the price index, and rental rates of different fixed capital.     

On Welfare Criteria and Optimality in an Endogenous Growth Model

In this paper, we explore the consequences for optimality of a social planner adopting two different welfare criteria. The framework of analysis is an overlapping generations model with physical and human capital. We first show that, when the social welfare function is a discounted sum of individual utilities defined over consumption per unit of natural labor, the precise cardinalization of the individual utility function becomes crucial for both the characterization of the social optimum and the policies that support it. Also, decentralizing the social optimum requires an education subsidy that is definitely positive, but its size depends in a determinant way on the aforementioned cardinalization. In contrast, when the social welfare function is a discounted sum of individual utilities defined over consumption per unit of efficient labor, the precise cardinalization of preferences becomes irrelevant. More strikingly, along the optimal growth path, the education subsidy is negative, i.e., the planner should tax rather than subsidize investments in human capital.     

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.     

A Golden Formula in Neoclassical‐Growth Models with Brownian‐Motion Shocks

In the paper, a Golden Formula, which does not depend on the specification of production and preference functions, is established to reveal that time‐average of the growth rate of optimal capital accumulation will converge to a constant, which is endogenously determined by relevant parameters, almost surely. The Golden Formula naturally implies surprisingly interesting and also intrinsic economic relations between some important macroeconomic variables; for example, it serves as a direct bridge between the modified Golden Rule and the modified Ramsey Rule. Furthermore, it indeed subsumes and hence substantially extends the classical Golden Rule in deterministic theory.     

Hyperbolic discounting and the time-consistent solution of three canonical environmental problems

In this paper I propose a time-consistent method of discounting hyperbolically and apply it to three canonical environmental problems: (i) optimal renewable resource use, (ii) the tragedy of the commons, and (iii) economic growth and pollution. I show that, irrespective of potentially high initial discount rates, time-consistent hyperbolic discounting leads always to a steady state of maximum yield, or, if the environment enters the utility function, a steady state where the Green Golden Rule applies. While (asymptotic) extinction is a real threat under exponential discounting it is impossible under time-consistent hyperbolic discounting. This result is also confirmed for open-access resources. In a model of economic growth and pollution, hyperbolic discounting establishes the Golden Rule of capital accumulation and the modified Green Golden Rule.     

Population and economic growth with human and physical capital investments

We present a two-sector endogenous growth model with human and physical capital accumulation to analyze the long-run relationship between population growth and real per capita income growth. Formal education and investment in physical capital are assumed to be two separate components of human capital production. Along the balanced growth path equilibrium, population change may have a positive, negative, or else neutral effect on economic growth depending on whether physical and human capital are complementary/substitutes for each other in the formation of new human capital and on their degree of complementarity.

Family Policies: What Does the Standard Endogenous Fertility Model Tell Us?

Very few studies have explored the optimality properties of the “standard model” of fertility where parents must determine their optimal trade‐off between quality and quantity. The present paper works to fill that gap and find three main results. First, when there exist positive externalities in the accumulation of human capital, it is optimal to subsidize education and to tax births. Second, when the Social Welfare Function does not consist of the average utility, the social returns on educational investments can be weaker than the private returns when the optimal population growth rate is negative. In this case, the optimal economic policy consists in subsidizing births and taxing education. Finally, when the health expenditure is introduced as another source of positive externalities, it can be optimal to tax the parental health expenditure to decentralize the first‐best path even if this expenditure is always too low at the laissez‐faire equilibrium.     

Risky human capital and deferred capital income taxation

We study the structure of optimal wedges and capital taxes in a dynamic Mirrlees economy with endogenous distribution of skills. Human capital is a private, stochastic state variable that drives the skill process of each individual. Building on the findings of the labor literature, we construct a tractable life-cycle model of human capital evolution with risky investment and stochastic depreciation. In this setting, we demonstrate the optimality of (a) a human capital premium, i.e., an excess return on human capital relative to physical capital, (b) a large intertemporal wedge early in the life-cycle, and (c) a non-zero intratemporal wedge even at the top of the skill distribution at all dates except the last date in the life-cycle. The main implication for the structure of optimal linear capital taxes is the necessity of deferred taxation of physical capital. The average marginal tax rate on physical capital held in every period is zero in present value. However, expected capital tax payments do not equal zero in every period. Necessarily, agents face negative expected capital tax payments early in the life-cycle and positive expected capital tax payments late in the life-cycle.     

Endogenous Growth and Publicly Funded Knowledge Accumulation

We investigate a centrally planned, infinite horizon, single good economy in which new knowledge is generated in a separate R&D sector with government subsidy. The rate of growth of new ideas is assumed to be linear in the amount of labor devoted to R&D. Perpetual growth in per capita output and consumption is sustained by the spillover effects of knowledge creation. Using an isoelastic social welfare function and a general production function, the unique balanced growth path is characterized and the conditions for balanced growth to take place derived. In analyzing standard balanced growth, we demonstrate that so long as physical capital and knowledge grow at some arbitrarily constant rates along an optimal time path, the two rates must necessarily be equal. Using a Cobb–Douglas production function, the dynamic evolution of the economy is explicitly described in closed form for each state and control variables. In particular, it is shown that the economy either (i) attains the balanced growth path from the initial time, or (ii) converges monotonically to the balanced growth path. An asymptotic balanced growth path along which labor input in manufacturing tends to zero in the long run is ruled out by the tranversality condition on knowledge.     

AN ENDOGENOUS GROWTH MODEL WITH PUBLIC CAPITAL AND SUSTAINABLE GOVERNMENT DEBT*

This paper presents and analyses an endogenous growth model with public capital and public debt. It is assumed that the ratio of the primary surplus to gross domestic income is a positive linear function of the debt income ratio which assures that public debt is sustainable. The paper then derives necessary conditions for the existence of a sustainable balanced growth path for the analytical model. Further, simulations are undertaken in order to gain insight into stability properties of the model and in order to analyse growth effects of deficit financed increases in public investment. The latter is done for the model on the sustainable balanced growth path as well as for the model along the transition path.     

Replacing the U.S. income tax with a progressive consumption tax: A sequenced general equilibrium approach

This paper examines the welfare consequences of changing the current U.S. income tax system to a progressive consumption tax. We compute a sequence of single period equilibria in which savings decisions depend on the expected future return to capital. In the presence of existing income taxes, the U.S. economy is assumed to lie on a balanced growth path. With the change to a consumption tax, individuals save more and initially consume less. As the capital stock grows, consumption eventually overtakes that of the original path, and the economy approaches the new balanced growth path with higher consumption and a greater capital stock. Both the transition and the balanced growth paths enter our welfare evaluations. We find the discounted present value of the stream of net gains is approximately $650 billion in 1973 dollars, just over 1 percent of the discounted present value of national income. Larger gains occur if further reform of capital income taxation accompanies the change. We examine the sensitivity of the results, both to the design of the consumption tax and to the values of elasticity and other parameters. The paper also contains estimates of the time required to adjust from one growth path to the other.     

Capital Accumulation in an Economy with Dynasties and Uncertain Lifetimes

This paper studies how the lack of an annuities market affects savings behavior and intergenerational transfers in a dynastic overlapping generations economy. I find that the answer to this question depends crucially on altruism. On the one hand, if the altruistic bequest motive is operative, then the lack of annuity markets enhances capital accumulation. On the other hand, if the altruistic bequest motive is not operative, the absence of annuity markets can either increase or decrease aggregate savings. I characterize under which conditions capital accumulation is enhanced. I also prove that an overlapping generations economy with altruism and uninsurable lifetime risk faces capital overaccumulation relative to the modified Golden Rule. The efficient allocation corresponding to the modified Golden Rule can be decentralized as a competitive equilibrium by a pay-as-you-go social security system, and this can only be done if individuals are altruistic.     

The impact of artificial intelligence on economic growth and welfare

Focusing on the self-accumulation ability and the nonrival characteristic of artificial intelligence (AI), this paper develops a three-sector endogenous growth model and investigates the impact of the development of AI along the transitional dynamics path and the balanced growth path. The development of AI can increase economic growth along the transitional dynamics path, and can increase household short-run utility if an increase in the accumulation of AI is due to the rising productivity in the goods or AI sector, but can be detrimental to household short-run utility if an increase in the accumulation of AI is because firms use more AI to replace human labor. In addition, the development of AI is not necessarily beneficial to household welfare in the long run. The main results are unaffected when considering the case where AI can improve the accumulation of human capital, the traditional research and development model, and different kinds of physical capital.     

Government spending and growth in second-best economies

This paper extends public spending-based growth theory along three directions: we assume a logistic trajectory for the ratio of government expenditure to aggregate income, self-limiting population change, and exogenous technological progress. By focusing on the choices of a benevolent social planner we find that, if the inverse of the intertemporal elasticity of substitution in consumption is sufficiently high, the ratio of consumption to private physical capital converges towards zero when time goes to infinity. Depending on the form of the underlying aggregate production function and on whether, for given production function, technological progress equals zero or a positive constant, our model may or may not yield an asymptotically balanced growth path (ABGP) equilibrium. When there is no exogenous technological progress, an equilibrium where population size, the ratio of government spending to aggregate income and the ratio of consumption to private physical capital are all constant does exist and the equilibrium is a saddle point. In case of positive technological progress numerical simulations show that the model still exhibits an ABGP equilibrium.     

Optimal Monetary Policy, Taxes, and Public Debt in an Intertemporal Equilibrium

This article is devoted to a study of the optimal monetary and fiscal policies within the framework of an overlapping generations model with cash-in-advance constraints. We first characterize the intertemporal equilibrium. Then we show how to decentralize the optimal growth path using available policy instruments (i.e., labor income and capital taxes, public debt, money supply). Between the four instruments: wages and capital taxes, debt and monetary policy, one is redundant among the three last which implies that the Friedman Rule is only a special case.     

Cash-in-advance constraint,optimal monetary policy,and human capital accumulation

This paper investigates optimal monetary policy in an overlapping-generations model with endogenous growth fueled by the accumulation of human capital and under a cash-in-advance constraint. We consider the case where the government finances public education fully by seigniorage. Three main results are obtained. First, there exists an optimal money growth rate that maximizes the economic growth rate along the steady growth path. Second, on this path, the Laffer curve of seigniorage takes the maximum. Finally, the money growth rate for maximizing seigniorage along the steady growth path, which also leads to maximization of the economic growth rate, is lower than that for maximizing seigniorage in the present period.     

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.