Demographic structure and capital accumulation

This paper develops an overlapping-generations (OLG) model to analyze the consequences of demographic structure changes induced by an exogenous shift in the birth rate. We first show that a finite growth rate of the population that maximizes long-run capital per capita exists. Then, we examine the theoretical properties of this growth rate by showing that: (i) it corresponds to the demographic structure such that the average ages of capital holders and workers are equal; (ii) it is associated to an efficient steady state; (iii) it increases with compulsory transfers from younger to older generations. Finally, we explain why standard OLG models do not exhibit such a growth rate.     

On the interaction between risk sharing and capital accumulation in a stochastic OLG model with production

We analyze the interaction between risk sharing and capital accumulation in a stochastic OLG model with production. We give a complete characterization of interim Pareto optimal competitive equilibrium allocations. Furthermore, we provide tests of Pareto optimality/suboptimality based on (risky) rates of return only.     

Consumption habits in an overlapping-generations model

This paper introduces consumption habits in the Blanchard (1985) overlapping-generations model. It shows that steady-state capital and consumption are higher if individuals have habits than otherwise. Moreover, “inward habits” lead to higher steady-state capital and consumption compared to “outward habits.”     

The existence, uniqueness, and optimality of the terminal wealth depletion time in life-cycle models of saving under uncertain lifetime and borrowing constraint

In life-cycle models of saving under uncertain lifetime and borrowing constraint, the consumer's wealth must be depleted before the maximum lifetime. This paper investigates the existence, uniqueness, and optimality of the terminal wealth depletion time. It is proved that the optimal terminal wealth depletion time, if such exists, must be unique. If the equation that determines the optimal terminal wealth depletion has multiple solutions, then the location of the optimal solution will depend on the configuration of the solutions. An optimality test is developed to verify whether a candidate solution for the terminal wealth depletion time is indeed optimal. The paper introduces a method new to economics, the Dubovitskii-Milyutin adjoint equation, to analyze the properties of the optimal control problem.     

Consumption Externalities,Habit Formation and Equilibrium Efficiency*

We analyze the welfare properties of the competitive equilibrium in a capital accumulation model where individual preferences are subject to both habit formation and consumption spillovers. Using an additive specification for preferences, according to which the argument in the utility function is a linear combination of present and past values of own consumption and consumption spillovers, we analyze the circumstances under which these spillovers are a source of inefficiency. It is shown that consumption externalities have to interact with habits in order to generate an inefficient dynamic equilibrium. Finally, we characterize optimal tax policies aimed at restoring efficient decentralized paths.     

Risk capital,private credit,and innovative production

Abstract Although ideas production plays a critical role for growth, there has been only a modicum of research on the role played by financial forces in fostering new inventions. Drawing on Schumpeterian growth theory, this paper tests the roles of risk capital and private credit in stimulating knowledge production. Using panel data for 77 countries over the period 1965–2009, we find that countries with more developed financial systems are more innovative. A stronger patent protection framework, on the other hand, curbs innovative production.     

Human capital accumulation in R&D-based growth models

This paper develops a model that reproduces the essential aspects of the recent ICT-based economy using the framework of endogenous growth theory in which a central role is played by human capital accumulation. In particular, it considers a multi-sectoral growth model in discrete time with infinite horizon, endogenous growth, embodied technological progress, horizontal differentiation and “lab-equipment” specification of R&D, and with human capital accumulation (represented by the fact that households devote a fraction of their time to schooling), in order to take into account the crucial role of the latter when new technologies are present. In this model it is possible to obtain some important results, both analytically and through simulations, either in the case of constant productivity of schooling and in the case in which this productivity is a function of technological progress. The first conclusion is that the productivity of schooling affects the long run growth of the economy, contrary to the productivities of the other sectors, hence in this model human capital accumulation is the true engine of growth. It is then possible to study the reaction of the economy to different types of shocks, and to compare the results with the empirical evidence. The conclusion is that the model is able to reproduce such evidence, suggesting that the interaction between ICT and human capital is one of the drivers of the recent economic performance.     

Growth, habit formation, and catching-up with the Joneses

When habits are introduced multiplicatively in a capital accumulation model, the consumers’ objective function might fail to be concave. In this paper, we provide conditions aimed at guaranteeing the existence of interior solutions to the consumers’ problem. We also characterize the equilibrium path of two growth models with multiplicative habits: the internal habit formation model, where individual habits coincide with own past consumption, and the external habit formation (or catching-up with the Joneses) model, where habits arise from the average past consumption in the economy. We show that the introduction of external habits makes the equilibrium path inefficient. We characterize in this context the optimal tax policy.     

CREDIT CRUNCH AND HOUSEHOLD WELFARE,THE CASE OF THE KOREAN FINANCIAL CRISIS*

We examine how the credit crunch in Korea in the late 1990s affected household behaviour and welfare. Using 1996–1998 household panel data, we estimate a consumption Euler equation, augmented by endogenous credit constraints. Korean households coped with the negative shocks of the 1997 credit crunch by reducing consumption of luxury items while maintaining food, education and health related expenditures. Our results show that, in 1997–1998, during the crisis, the probability of facing credit constraints and the resulting expected welfare loss from the binding constraints increased significantly, suggesting the gravity of the credit crunch at the household level.     

Income taxes, spending composition and long-run growth

The focus of this paper is threefold. First, it reexamines the impact on long-run growth of changes in flat-rate income taxes when a fraction of total government expenditures is used to provide public services that affect the productivity of privately held inputs. Second, for a given tax policy, this paper studies the impact of government expenditure composition on the rate of economic growth. Third, since demographics follow an overlapping generations structure and fiscal policy affects the economy's productivity, the paper features the role of productivity as a means of redistributing income across generations. The economy is analyzed numerically and policy experiments are carried out.     

Strategic intergenerational bequests with stochastic convex production

Summary This note reconsiders the well-known model of strategic bequest/ altruistic growth, but with stochastic production satisfying a strong convexity condition: The probability that the next stock exceeds any given level is concave in investment. Existence of a Markov-stationary equilibrium consumption schedule, which is continuous and with all slopes in [0,1], is established. Under smooth data and interiority assumptions, this schedule is differentiable, and marginal consumption is in (0,1). This property allows for a rigorous and straightforward treatment of the equilibrium characterization problem.The author is grateful to Wolfgang Leininger for helpful discussions on the subject of this paper. This research work was carried out while the author was visiting C.O.R.E., Belgium and the University of Dortmund, Germany. The author wishes to thank both institutions for providing a great work environment as well as financial support from the projects Markets as Games and Marktstruktut und Gesamtwirtschaftliche Entwicklung, respectively.     

Will the consumption externalities' effects in the Ramsey model please stand up?

According to the prior literature, in a Ramsey model, consumption externalities have no impact on steady state behavior, once labor supply is exogenous. In contrast, this paper argues that — in the presence of technical change — consumption externalities always affect steady state behavior, via their impact on the elasticity of marginal utility of consumption.     

On negative time preferences

Survey data show that subjects positively discount both gains and losses but discount gains more heavily than losses. This holds for monetary and non-monetary outcomes. These results do not confirm the findings of two earlier studies about negative time preferences for non-monetary outcomes.     

Consumption smoothing? Livestock,insurance and drought in rural Burkina Faso

This paper explores the extent of consumption smoothing between 1981 and 1985 in rural Burkina Faso. In particular, we examine the extent to which livestock, grain storage and inter-household transfers are used to smooth consumption against income risk. The survey coincided with a period of severe drought, so the results provide direct evidence on the effectiveness of these various insurance mechanisms when they are the most needed. We find evidence of little consumption smoothing. In particular, there is almost no risk sharing, and households rely almost exclusively on self-insurance in the form of adjustments to grain stocks to smooth out consumption. The outcome, however, is far from complete smoothing. Hence the main risk-coping strategies which are hypothesized in the literature (risk sharing and the use of assets as buffer stocks) were not effective during the survey period.     

Growth,unemployment and public capital

Abstract. Existing literature has studied the growth effects of fiscal policy in models with full-employment. The aim of this paper is to study these growth effects in an endogenous growth model with unemployment and compare them with the effects obtained when there is full-employment. To this end, we assume that unemployment arises due to the existence of unions. We also assume that the government finances, by means of income taxes, both public capital and an unemployment benefit. Public capital increases total factor productivity and modifies the elasticity of the labor demand. We show that the effects of fiscal policy on both employment and growth crucially depend on the relation between this elasticity and public capital. We would like to thank Jordi Caballé, Fernando Sánchez, Manuel Santos and an anonymous referee for their helpful comments. Sorolla is grateful for financial support to Spanish Ministry of Education through DGICYT grant SEC2000-0684 and to Generalitat de Catalunya through grant SGR2001-164. Raurich is grateful to Universitat de Girona for financial support through grant 9100075.     

A comparison of national saving rates in the UK, US and Italy

We develop the approach of Gokhale, Kotlikoff and Sabelhaus [1996. Understanding the postwar decline in US saving: A cohort analysis. Brookings Papers on Economic Activity 0, 315-390], based on the life-cycle model of savings, to decompose the differences in the national saving rates between the UK, US and Italy. Our work suggests that the US saving rate is lower principally because Americans on average retire later. In contrast, the Italian saving rate is higher predominantly because Italians are credit constrained, particularly when young. We also found that demography and the different tax and benefit systems are able to explain little of the cross-sectional differences in saving rates. The study accounts for the possible importance of inter-generational private transfers in determining saving rates.     

Over-savings and hyperbolic discounting

Hyperbolic discounting models are widely seen as implying that consumers do not save enough, in accordance with the observed low rates of savings of some households. This paper qualifies this view by showing that hyperbolic consumers may ‘oversave’ in the short run. The result extends to uncertainty on future income and does not depend on whether preferences are present-biased or future-biased. A generalized comparative statics analysis of self-control is introduced, and its relationship to the analysis of uncertainty on discount factors is emphasized.     

Credit market imperfections, income distribution, and capital accumulation

Summary. This paper builds a model in which the distribution of income matters for capital formation, and uses it to analyze the effects of a simple policy intended to create a more equal distribution of income on the severity of certain credit market imperfections and, through this channel, capital accumulation. A neoclassical growth model is developed in which some capital investment must be externally financed, and external finance is subject to a standard costly state verification (CSV) problem. In particular, some fraction of the population is capitalists, who have access to risky but high return capital production technologies. Successful capitalists leave bequests to their offspring, thereby permitting them to internally finance some fraction of their own investment projects. However some external finance is also required. This is provided by workers who save out of labor income. As is well known, the greater the capability of capitalists to provide internal finance, the less severe is the CSV problem. Thus bequests mitigate credit market frictions and, in that sense, promote financial market efficiency and capital accumulation. However, they also perpetrate income inequality. The structure is used to show that a policy that taxes the bequests of capitalists, and transfers the proceeds to workers, necessarily reduces the steady state capital stock. Indeed, when this effect is sufficiently strong, these redistributive tax/transfer schemes can reduce the total (wage plus transfer) incomes of workers, as well as their welfare. Thus some simple policies intended to redistribute income can be highly counterproductive.Received: June 3, 1996; revised version: February 4, 1997This revised version was published online in February 2005 with corrections to the cover date.     

On Ramseyʼs conjecture

Studying a one-sector economy populated by finitely many heterogeneous households that are subject to no-borrowing constraints, we confirm a conjecture by Frank P. Ramsey according to which, in the long run, society would be divided into the set of patient households who own the entire capital stock and impatient ones without any physical wealth. More specifically, we prove (i) that there exists a unique steady state equilibrium that is globally asymptotically stable and (ii) that along every equilibrium the most patient household owns the entire capital of the economy after some finite time. Furthermore, we prove that despite the presence of the no-borrowing constraints all equilibria are efficient. Our results are derived for the continuous-time formulation of the model that was originally used by Ramsey, and they stand in stark contrast to results that – over the last three decades – have been found in the discrete-time version of the model.     

Estate taxes, consumption externalities, and altruism

We study how the introduction of consumption externalities affects the optimality of the dynamic equilibrium in an economy displaying dynastic altruism. When the bequest motive is inoperative consumption externalities affect the intertemporal margin between young and old consumption and thus modify the intertemporal path of aggregate consumption and capital. The optimal tax policy that solves this intertemporal suboptimality consists of a tax on capital income and a pay-as-you-go social security system. The latter solves the excess of capital accumulation due to the inoperativeness of the bequest motive and the former solves the suboptimal allocation of consumption due to consumption externalities. When the bequest motive is operative consumption externalities only cause an intratemporal misallocation of consumption but do not affect the optimality of the capital stock level. This suboptimal allocation of consumption implies in turn that the path of bequest deviates also from optimality. The optimal tax policy in this case consists of an estate tax and a capital income tax.