Optimal education and pensions in an endogenous growth model

In OLG economies with life-cycle saving and exogenous growth, competitive equilibria in general fail to achieve optimality because individuals accumulate amounts of physical capital that differ from the one that maximizes welfare along a balanced growth path (the Golden Rule). With human capital, a second potential source of departure from optimality arises, related to education decisions. We propose to recover the Golden Rule of physical and also human capital accumulation. We characterize the optimal policy to decentralize the Golden Rule balanced growth path when there are no constraints for individuals to finance their education investments, and show that it involves education taxes. Also, when the government subsidizes the repayment of education loans, optimal pensions are positive.     

Undiscounted optimal growth with consumable capital and labor-intensive consumption goods

This paper presents a complete characterization of the optimal policy in a two sector undiscounted growth model. The model is an extension of the Leontief two sector model, which analyzes the optimal allocation of capital and labor to a consumption good sector and an investment good sector. The paper extends this framework to include consumable capital. Thus, the planner has preferences over the consumption good and the consumable capital. Future welfare levels are treated equally as current ones. Geometric techniques are applied to characterize the optimal policy if the consumption good is labor-intensive. The results suggest that if the initial capital stock is above a threshold level, that depends upon the consumption of capital, every optimal program is monotonic, converges to the golden rule stock in a finite number of periods, and undergoes either unemployment or excess capacity of capital.     

On capital accumulation paths in a neoclassical stochastic growth model

Summary. Boldrin and Montrucchio [2] showed that any twice continuously differentiable function could be obtained as the optimal policy function for some value of the discount parameter in a deterministic neoclassical growth model. I extend their result to the stochastic growth model with non-degenerate shocks to preferences or technology. This indicates that one can obtain complex dynamics endogenously in a wide variety of economic models, both under certainty and uncertainty. Further, this result motivates the analysis of convergence of adaptive learning mechanisms to rational expectations in economic models with (potentially) complicated dynamics. Received: June 21, 1996; revised version: October 31, 1996     

Optimal nonlinear income taxation with a finite population

In the standard optimal income taxation problem, tax payments depend only on each consumer's own actions. Piketty [J. Econ. Theory 61 (1993) 23-41] shows that, if one individual's tax schedule depends on others’ actions and the government knows the exact ability distribution, it can implement any undistorted allocation as the unique revelation game outcome. If some individuals misreveal their types, Piketty's mechanism may assign infeasible allocations. We require that tax schedules must balance the government budget for every possible vector of revelations. When individuals reveal their type by simple announcements, all undistorted allocations can be still implemented, even with off-equilibrium feasibility constraints.     

INCOMPLETE FINANCIAL MARKETS,IRREVERSIBILITY OF INVESTMENTS AND FISCAL AND MONETARY POLICY INSTRUMENTS*

In this paper, we analyse the use of fiscal and monetary instruments to improve long‐run welfare when productive investment is irreversible and uncollateralizable and there is no insurance. Only fiat money or government issued bonds provide self‐insurance. We demonstrate that an increase in precautionary savings reduces irreversible productive investment. Hence, subsidies to promote productive but irreversible investment should be financed in such a way that they do not reduce insurance capability. When lump‐sum subsidies are high, a consumption tax is likely to be more redistributive and thus more consumption smoothing than are the other sets of instruments analysed in our model.     

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.      

Facts and distortions in an endogenous growth model with physical capital, human capital and varieties

This article studies a model with physical and human capital accumulation and varieties. The model includes several distortions: duplication effects, spillovers, creative destruction, surplus appropriability, and an erosion effect. We show that the duplication effect in R&D is essential to make the model replicate several stylized facts linked with R&D. We evaluate the distance to the optimal solution, comparing the strength of each distortion.     

Optimal accumulation in a small open economy with technological uncertainty

Summary. This paper analyzes the optimal allocation problem of a small trading country facing an uncertain technology. It is involved in production of many commodities. Differentiability cannot be guaranteed, hence, the Ramsey-Euler condition of optimality needs to be modified. From the optimality criterion, we derive a pair of conditions, which does not require differentiability. If “enough” uncertainty is allowed, the sequence of the distribution functions of investment expenditure converges uniformly to a unique invariant measure. In addition to the weak convergence of the stochastic process of investment expenditure we also have the sequences of the stochastic process of investment expenditure converging weakly. Received: September 8, 1994; revised version: September 25, 1997     

Optimal social security in a dynastic model with human capital externalities,fertility and endogenous growth

In this paper we investigate the optimal scale of pay-as-you-go social security in a dynastic family model with human capital externalities, fertility and endogenous growth. Human capital externalities reduce the return to human capital investment and hence lead to under-investment in human capital and over-reproduction of the population. If the taste for the number of children is sufficiently weak relative to the taste for the welfare of children, social security can be welfare enhancing by reducing fertility and raising human capital investment per child.     

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.     

Variety of products,public capital,and endogenous growth

This paper develops an extension of the endogenous growth model with variety expansion presented in Romer [Romer, P.M., 1990. Endogenous technical change, Journal of Political Economy 98, part 2, S71–S102] by considering public capital accumulation. Characterizing the transitional dynamics, the growth rate of consumption traces (and available number of intermediate goods also might trace) an S-shaped converging path to the equilibrium growth rate, similar to a logistic growth curve, if the intensity of public capital is sufficiently high. We also show that public investment enhances economic growth because it stimulates demand for intermediate goods and raises the market interest rate.     

Duplication externalities in an endogenous growth model with physical capital,human capital,and R&D

This paper devises an endogenous growth model with physical capital, human capital and product variety. Differently to previous works, innovation is subject to externalities associated to the duplication of research effort, as well as to R&D spillovers. We provide conditions for the existence of a unique feasible steady-state equilibrium with positive long-run growth. For appropriate parameter values, the transitional dynamics of the model is represented by a two-dimensional stable manifold. Numerical simulations show that the incorporation of duplication externalities significantly increases the ability of the model to fit the observed data.     

Optimal contracting with dynastic altruism: Family size and per capita consumption

We use a Barro–Becker model of endogenous fertility, in which parents are subject to idiosyncratic shocks that are private information (either to labor productivity or taste for leisure), to study the efficient degree of consumption inequality in the long run. The planner uses the trade-off between family size and future consumption and leisure, to provide incentives for workers to reveal their shocks. We show that in this environment, the optimal dynamic contract no longer features immiseration in consumption. We also discuss the implications of the model on the long run properties of family size in the optimal contract and show that the long run trend in dynasty size can be either positive or negative depending on parameters.     

Optimal redistributive taxation with both extensive and intensive responses

We study optimal income taxation when labor supply reacts along the intensive and extensive margins. Individuals are heterogeneous across two unobserved dimensions: their skill and disutility of participation. We develop a new method to analytically derive conditions under which optimal marginal tax rates are non-negative everywhere. It is typically optimal to provide a distinct level of transfer to the non-employed and to workers with negligible earnings. Numerical simulations illustrate these properties for the US. We also apply our method to sign output distortions in other adverse selection frameworks with random participation, namely the monopoly nonlinear pricing and the regulatory monopoly problems.     

Optimal risk sharing with background risk

This paper examines qualitative properties of efficient insurance contracts in the presence of background risk. In order to get results for all strictly risk-averse expected utility maximizers, the concept of “stochastic increasingness” is used. Different assumptions on the stochastic dependence between the insurable and uninsurable risk lead to different qualitative properties of the efficient contracts. The new results obtained under hypotheses of dependent risks are compared to classical results in the absence of background risk or to the case of independent risks. The theory is further generalized to nonexpected utility maximizers.     

Dynamic inconsistency and non-preferential taxation of foreign capital

When capital is sunk after it is invested, a host government facing heterogeneous foreign investors has a strong incentive to reduce preferential taxes over time in order to attract less eager investors while fully expropriating past investors. This induces investors to wait rather than invest in the initial period, and leads to loss of tax revenue. This dynamic inconsistency problem is resolved if the host government commits to non-preferential taxation in each period even if it does not commit to future tax rates.     

Optimal taxation in the extensive model

We study optimal taxation under extensive preferences: the agents? utilities are constant for positive actions up to a maximal productivity level. Utilities may be discontinuous at the origin, reflecting fixed costs of participation. Allowing for general distributions of work opportunity costs and productivity and for income effects, we characterize optimal, incentive-compatible tax schedules. We then give sufficient conditions for society to desire redistribution. When these conditions hold, upward distortions of the financial incentives to work can only occur for low-skilled workers. Such upwards distortions are indeed always present when the fixed participation costs are pecuniary.     

Consumption externalities, production externalities, and efficient capital accumulation under time non-separable preferences

The effects of consumption and production externalities on economic performance under time non-separable preferences are examined both theoretically and numerically. We show that a consumption externality alone has long-run distortionary effects if and only if labor is supplied elastically. With fixed labor supply, it has only transitional distortionary effects. Production externalities always generate long-run distortions, irrespective of labor supply. The optimal tax structure to correct for the distortions is characterized. We compare the implications of this model with those obtained when the consumption externality is contemporaneous. While some of the long-run effects are robust, there are also important qualitative and quantitative differences, particularly along transitional paths.     

A note on work–leisure choice, human capital accumulation, and endogenous growth

The growth model of Lucas [Lucas Jr., R.E., 1988. On the mechanics of economic development. Journal of Monetary Economics 22 (1), 3–42] is enriched with people having the opportunity to optimally allocate a fraction of their time to non-productive activities (‘leisure’). It is found that the chosen amount of leisure reduces the steady-state rate of growth of per capita output. This implies that the association between income and welfare may not be as strong as it is usually assumed to be. The optimal allocation of time among activities depends on some of the parameters and the marginal product of physical capital per capita.