An essay on the Life Cycle: Characterizing intertemporal behavior with uncertainty,human capital,taxes, durables,imperfect capital markets,and non-separable preferences

This paper formulates a general characterization of a household's portfolio choice and savings behavior in an environment with uncertain future interest rates, prices, wages, and factors influencing tastes. Savings may be invested in three types of assets: financial assets; human capital, which is non-tradable; and consumer durables, in which investment may be partially irreversible. Risk-return relations determine the optimal allocation of resources across assets at a point in time. The optimal intertemporal allocation of resources is determined by a restriction on the planned growth rate for the marginal utility of after-tax wealth, where growth rates depend on rates of time preference and measures of long-term riskless rates of interest. Given special assumptions, this marginal utility follows a martingale process as a consequence of optimizing behavior. Pricing formulae are developed for evaluating shifts in uncertain future income, wage, and price profiles. The relations characterizing portfolio and savings behavior presented here do not rely on particular distributional assumptions; they account for all forms of uncertainty including wage uncertainty induced by human capital investment; they allow for the non-marketability of assets; and the main results apply for very general functional form assumptions for preferences. In later sections, results are extended to incorporate income taxes and to account for a wide variety of imperfections in asset markets.     

Rational habit formation

This paper discusses consumer demand under rational habit formation. If consumer tastes change endogenously through habit stocks depending on past consumption, the rational consumer will make allowance of the future habit forming effects of current consumption. A model with rational habit formation is made formally equivalent to an intertemporal consumer model without habit formation by redefining the cost of consumption and wealth. The cost of consumption is obtained by adding the cost of future induced consumption to the rental price of the commodity. The extended wealth concept is obtained by subtracting the cost of the initial stocks of habits and the cost of future physically necessary consumption from wealth. The paper also investigates the implication of rational habit formation for constructing one period cost of living indices.     

Excess supply equilibria

This paper addresses a fundamental problem in economic theory: How can there be equilibria of the economic system where some commodity is in excess supply, yet that commodity's relative price shows no tendency to fall? Of course, the principal example of such a phenomenon is an economy experiencing a prolonged period of involuntary unemployment of the labor force during which there is no significant change in the real wage.In the following pages, I shall describe a two-commodity, general equilibrium model that has a continuum of unemployment equilibria, one for any given unemployment rate. The important feature of this model is that workers establish their wage rates in an attempt to maximize expected utility. The information upon which these wage setting decisions are based is provided by actual labor market transactions.Despite the voluntary nature of the wage setting decision, I shall argue that each equilibrium of this economy exhibits involuntary unemployment in the Keynesian sense. For there will always be another equilibrium with a lower real wage, a higher level of employment, and at which (at least when workers are risk neutral) each worker achieves a higher level of expected utility.     

Growth, Environment and Uncertain Future Preferences

The attitude of future generations towards environmental assets may well be different from ours, and it is necessary to take into account thispossibility explicitly in the current debate about environmental policy. The question we are addressing here is: should uncertainty about futurepreferences lead to a more conservative attitude towards environment?Previous literature shows that it is the case when society expects that onaverage future preferences will be more in favor of environment than ours,but this result relies heavily on the assumption of a separability betweenconsumption and environmental quality in the utility function. We show thatthings are less simple when preferences are non-separable: the attitude ofthe society now depends not only on the expectation of the change inpreferences but also on the characteristics of the economy (impatience,intertemporal flexibility, natural capacities of regeneration of theenvironment, relative preference for the environment), on its history(initial level of the environmental quality) and on the date at whichpreferences are expected to change (near or far future).     

To defer or not defer? UK state pension and work decisions in a lifecycle model

The UK state pension (which depends only on age) includes an option to defer take up which yields either a subsequent lump sum or higher weekly pension. We analyse the joint decisions on pension deferral and intertemporal labour supply/participation in a lifecycle setting. We show that deferral is purely a financial decision, but the impact of deferral on work decisions depends on preferences, wage rates, non-labour income and initial wealth. To exactly characterize this, we use a quasilinear utility function and provide calibrated simulations. We also discuss the choice between a lump sum or increased weekly pension.     

Intertemporal Consumption Smoothing and Capital Mobility: Evidence from Australia

This paper examines the optimality of international capital flows to Australia, a persistent net importer of capital, during its post‐capital controls period 1984–99. The evolution of Australia’s current account balance is compared against a benchmark derived from an optimising model of intertemporal consumption smoothing. The consumption‐smoothing approach to the determination of the current account implies that international capital flows act as a buffer to smooth aggregate consumption in the face of temporary shocks to the economic fundamentals: changes in national cash flow (that is, changes in the level of output, investment or government spending). It is found that in the early 1990s a structural break occurred in the relationship between consumption and national cash flow, which coincides with a switch from debt‐financing to equity‐financing of the current account deficit. In the decade of the 1990s following this structural break (and unlike the decade of the 1980s which preceded this break), international capital flows to Australia implied a path for consumption which was broadly consistent with expected‐utility maximisation under the consumption‐smoothing model of the current account.     

Nontraded Goods and the Current Account

This paper investigates trade balance and current account behavior in response to various shocks when the economy produces and consumes both traded and nontraded goods. Previous analyses of these problems have interpreted current account behavior in terms of tension between parameters that measure intratemporal and intertemporal elasticity, respectively. This paper provides a simple general criterion for whether trade and current account behavior is "perverse" vis-à-vis the standard one-good model results: behavior is perverse if and only if traded and nontraded goods are Edgeworth complements; that is, if the cross-partial of the instantaneous utility function is positive.     

On the optimality and sustainability of Turkey’s current account

We analyze Turkey’s current account optimality and sustainability between 1992 and 2004. Using the intertemporal benchmark model for Turkey’s current account we test for its intertemporal solvency. Based on traditional and alternative tests (which account for persistence in the current account), we conclude that Turkey breached the intertemporal solvency condition in the sample period. In addition, stationarity tests of the deviation between actual and optimal net external liabilities series confirm that Turkey’s current account deficit was unsustainable for that period. However, further econometric investigation and analysis of reforms causes us to question our conclusions of non-optimality and unsustainability of the Turkish current account for the latter part of the period. We are indebted to two anonymous referees for insightful comments and suggestions. We would also like to thank seminar participants at Middle Eastern Technical University, Ankara, Turkey, for comments on an earlier version of this paper. Responsibility for all errors remains with the authors.     

Testable implications of subjective expected utility theory

I show that the predictive content of the hypothesis of subjective expected utility maximization critically depends on what the analyst knows about the details of the problem a particular decision maker faces. When the analyst does not know anything about the agent's payoffs or beliefs and can only observe the sequence of actions taken by the decision maker any arbitrary sequence of actions can be implemented as the choice of an agent that solves some intertemporal utility maximization problem under uncertainty.     

Testable implications of subjective expected utility theory

I show that the predictive content of the hypothesis of subjective expected utility maximization critically depends on what the analyst knows about the details of the problem a particular decision maker faces. When the analyst does not know anything about the agent's payoffs or beliefs and can only observe the sequence of actions taken by the decision maker any arbitrary sequence of actions can be implemented as the choice of an agent that solves some intertemporal utility maximization problem under uncertainty.     

A Model of Endogenous Nontradability and its Implications for the Current Account*

This paper studies how nontraded goods limit the ability of a country to finance current account deficits. It uses an intertemporal model of the current account for a small open economy where goods are endogenously nontraded due to explicit trade costs. The economy has an endowment of two goods with differing trade costs, either of which can be traded or nontraded in equilibrium. The model implies that current account deficits impose a cost, in the form of raising the effective interest rate in the country. The findings differ from some recent studies: first, in that the interest rate rises even for countries with modest current account deficits; secondly, the interest rate cost eventually reaches an upper bound as current account deficits grow, and progressively more nontraded goods become traded to service the debt. Panel regression analysis of interest rate and current account data is consistent with our conclusions.     

Optimal supervision with moral hazard

This paper adopts the principal–supervisor–agent hierarchy model pioneered by Tirole [Tirole, J., 1986. Hierarchies and bureaucracies: on the role of collusion in organizations. Journal of Law, Economics and Organization 2, 181–214] to analyze the optimal architecture of supervision. We consider a principal who encounters a double moral hazard problem. In particular, we examine the endogenously determined supervisory effort and the possibility of untruthful revelation of supervisor's message. The degree of accuracy for this endogenously chosen information architecture hinges upon the supervisory technology, the supervisor's reservation utility and the agent's production technology. Besides, though the principal's welfare would be lowered when the possibility of untruthful revelation is taken into account, we find that his desired supervisory effort level may be enhanced instead.     

A Tradable Permit System in an Intertemporal Economy

It is known that in an intertemporal competitive economy, a tradable permit system may not achieve efficiency without setting appropriate permit interest rates (i.e., rewards for holding permits). To find the rates, however, we need to know in advance the path of efficient permit prices, which is difficult to obtain. This study intends to solve this problem in two ways. First, we analyze a special case in which the permit interest rates are given by a simple rule. For example, if the marginal abatement cost of pollution emission is constant, then the appropriate rate is to equal the monetary interest rate. As is the case for global warming, if the damage is caused in the future far beyond the planning period of the environmental program, the appropriate rate coincides with the marginal self-recovery of environmental stock under certain conditions. As a second approach, we propose a tradable permit system with a permit bank, as a mechanism by which the permit interest rates are generated endogenously without governmental intervention other than the issuance of permits. However, we also show that this approach raises the problem of indeterminacy of the equilibrium.     

Recursive smooth ambiguity preferences

This paper axiomatizes an intertemporal version of the Smooth Ambiguity decision model developed in [P. Klibanoff, M. Marinacci, S. Mukerji, A smooth model of decision making under ambiguity, Econometrica 73 (6) (2005) 1849-1892]. A key feature of the model is that it achieves a separation between ambiguity, identified as a characteristic of the decision maker's subjective beliefs, and ambiguity attitude, a characteristic of the decision maker's tastes. In applications one may thus specify/vary these two characteristics independent of each other, thereby facilitating richer comparative statics and modeling flexibility than possible under other models which accommodate ambiguity sensitive preferences. Another key feature is that the preferences are dynamically consistent and have a recursive representation. Therefore techniques of dynamic programming can be applied when using this model.     

ECONOMIC MODELLING OF SUICIDE UNDER INCOME UNCERTAINTY: FOR BETTER UNDERSTANDING OF MIDDLE‐AGED SUICIDE*

This paper formalises an individual's decision about suicide within a framework of lifetime utility maximisation models. This is in line with the literature on economic modelling of suicide. The novelty of the paper is to take into account income uncertainty. Income uncertainty reduces a risk‐averse individual's expected utility, making them more likely to commit suicide. On the other hand, income uncertainty creates a value to postponing suicide even when their income gets sufficiently low. This is because income uncertainty means that if things go well, they will get higher income in the future. Thus, income uncertainty has two opposite effects on suicidal behaviour. The main objective of this paper is to construct an economic model of suicide for investigating net impacts of income uncertainty on suicidal behaviour. For this purpose, it is assumed that the wage evolves according to a stochastic process. Then, the threshold wage, below which an individual commits suicide, is derived as a function of the parameters of the stochastic process assumed for the wage evolution. Impacts of changes in these parameters on the threshold wage are calculated. With the result, the paper shows how income uncertainty affects suicidal behaviour.     

The Skill Premium, Technological Change and Appropriability

This paper demonstrates that an increase in the relative supply of educated workers generates a structural change in the production structure towards a knowledge-intensive production process. This structural shift may ultimately lead to an increase in the return to educated labor despite the increase in their supply. The paper argues that the steady increase in the supply of educated workers that most Western economies have experienced in recent decades may be viewed as the driving force behind the observed pattern of wage inequality. In particular, the paper demonstrates that if firms can appropriate a sufficient share of the intertemporal return from knowledge generating activities of their labor force, a gradual increase in the supply of skilled workers would generate only a temporary reduction in the skill premium followed by a permanent increase in the return to skill.     

The Relation between Real Wage Rates and Employment: An Intertemporal General- Equilibrium Analysis

Abstract. The paper studies the relation between real wage rates and employment in an intertemporal model in which expectations of subsequent real wage rates affect equilibrium capital investments and equilibrium interest rates in previous periods. Whether the wage–employment tradeoff is more favourable or less favourable in this model than in the static model with given capital depends on whether there is relatively more substitution in consumption or in production, or, more precisely, whether the elasticity of substitution in production is less than or greater than the inverse of the elasticity of marginal utility in consumption.     

Certainty Independence and the Separation of Utility and Beliefs

Economists often operate under an implicit assumption that the tastes of a decision maker are quite stable, while his beliefs change with the availability of new information. We show that for a general class of preferences, a separation of a key component of tastes, the utility function, from the other components of the representation is possible only if the decision maker's preferences satisfy a mild but not completely innocuous condition, called ‘certainty independence’. We also outline the axiomatic characterization of the preferences that obtain such separation, which are a subset of the biseparable preferences.     

Present bias and the inefficiency of the centralized economy: The role of the elasticity of intertemporal substitution

We analyze an endogenous growth model considering agents with an isoelastic utility. Preferences are characterized by a utility affected by a negative externality, and a level of impatience which decays with the time distance from the present. Agents who cannot commit the actions of their future selves, play a game against them. The stationary equilibrium of this game defines a balanced growth path with a slower growth when played by subsequent central planners than when played by decision makers in the market economy. First, we prove that the fast growing market economy implies higher welfare if the negative externality is small, while the centralized economy is welfare improving above a given threshold for the externality (obtained for a specific family of non-constant discount functions). Secondly, we observe that this threshold increases with the elasticity of intertemporal substitution in consumption. Therefore, the greater this elasticity the more likely it is that the externality lies below this threshold, where policy interventions would not be adequate. Finally, as one would expect, the range of values of the externality for which the market equilibrium provides higher welfare widens the more different from constant discounting time preferences are, due either to a wider range of variation for the instantaneous discount rates or because these decay more slowly.     

Gift Exchange and the Business Cycle: The Fair Wage Strikes Back

We extend the benchmark real business cycle model amending technology for fair wage considerations. Effort depends on current, alternative, and past wages. Past wages are treated as the worker's past wages (personal norm) or as the past wages of the society (social norm). This last model reproduces the high variability of employment, the low variability of wages, and the low wage–employment correlation without requiring a second source of impulsions. Wages and employment dynamics are adequately captured when norms adjust slowly to the environment. Fair wages are thus useful to solve the business cycle puzzle when we allow for intertemporal wage comparisons. Journal of Economic Literature Classification Number: E24