Equivalent representations of non-exponential discounting models

I characterize the entire class of consumption rules for finite-horizon models in which consumption is proportional to lifetime wealth. Any such rule can be obtained from a preference model with CRRA period utility. In a steady state with constant interest rates, a proportional consumption rule can be derived from a model with time-consistent preferences or from a model with possibly time-inconsistent preferences in which a household continually reoptimizes future utility discounted relative to the present instant. These two preference models will only coincide for the special case when the discount function is exponential. More generally, there will be two distinct yet observationally equivalent preference models. Hyperbolic-like discounting may arise because that is a simpler way for the brain to process a standard exponential discount function after accounting for mortality risk.     

Learning by doing,endogenous discounting and economic development

In this paper, we focus on a growth model where the discount rate is decreasing in capital accumulation and endogenous growth is made possible through learning by doing, knowledge accumulation being a by-product of gross investment. In such a model, the utility function has to be restricted to take positive values implying that the elasticity of marginal utility is lower than one. The presence of endogenous discounting generates a steady-state of stagnation which can be saddle-path stable or unstable depending on the marginal productivity of knowledge. In the case of long run growth, the fact that the elasticity of marginal utility is lower than one implies the existence of two asymptotic balanced growth paths: the one with the higher growth rate being a saddle point while the one with the lower growth rate not being a saddle point. We also study the optimal solution which is characterized by a unique balanced growth path. The policy consists as usual in subsidizing investment in order to internalize the externality.     

On time-consistent policy rules for heterogeneous discounting programs

This article considers a new concept of social optimum for an economy populated by agents with heterogeneous discount factors. It is based upon an approach that constrains decision rules to be temporally consistent: these are stationary and unequivocally ruled by the state variable. For agents who differ only in their discount factors and have equal weights in the planner’s objective, the temporally-consistent optimal solution produces identical consumption for the agents at all time periods. In the long run, the capital stock is determined by a modified golden rule that corresponds to an average-like summation of all discount factors. The general argument is illustrated by various two-agent examples that allow for an explicit determination of the temporally consistent decision rules. Interestingly, this temporally consistent solution can be simply recovered from the characterization of a social planner’s problem with variable discounting and can also be decentralized as a competitive equilibrium through the use of various instruments.     

Management of a capital stock by Strotz's naive planner

The capital management problem posed by R.H. Strotz is analyzed for the case of the ‘naive’ planner who fails to anticipate changes in his own preferences. By imposing progressively stronger restrictions on the primitives of the problem – namely, the discounting function, the utility index function, and the investment technology – the planner's behavior is characterized first as the solution to an ordinary differential equation and then via explicit formulae. Inasmuch as these characterizations leave the discounting function essentially unrestricted, the theory can accommodate, in particular, decision makers who discount time according to the hyperbolic and ‘quasi-hyperbolic’ curves used in applied work and said to be supported by psychological studies. Comparative statics of the model are discussed, as are extensions of the analysis to allow for credit constraints, limited foresight, and partial commitment.     

Discounting models for outcomes over continuous time

Events that occur over a period of time can be described either as sequences of outcomes at discrete times or as functions of outcomes in an interval of time. This paper presents discounting models for events of the latter type. Conditions on preferences are shown to be satisfied if and only if the preferences are represented by a function that is an integral of a discounting function times a scale defined on outcomes at instants of time.     

Characterization of stationary preferences in a continuous time framework

We characterize preference relations on continuous time consumption paths which admit an exponential discounting representation. We provide two theorems as such, one in the cardinal framework and another in the ordinal framework. Our characterizations parallel the known characterizations in discrete time framework. In the cardinal framework, we adopt the axioms of Epstein (1983), which characterize a stationary preference relation in discrete time, and obtain the exponential discounting model as a special case of the discounting model proposed by Uzawa (1968). In the ordinal framework, we adopt the axioms of Bleichrodt et al. (2008) which were proposed to generalize Koopmans’ classical characterization of stationary preferences.     

Simple axioms for countably additive subjective probability

This paper refines Savage’s theory of subjective probability for the case of countably additive beliefs. First, I replace his continuity axioms P6 and P7 with a simple modification of Arrow’s (1970) Monotone Continuity. Second, I relax Savage’s primitives: in my framework, the class of events need not be a σ-algebra, and acts need not have finite or bounded range. By varying the domains of acts and events, I obtain a unique extension of preference that parallels Caratheodory’s unique extension of probability measures. Aside from subjective expected utility, I characterize exponential time discounting in a setting with continuous time and an arbitrary consumption set.     

On existence of optimal programs: The RSS model without concavity assumptions on felicities

In the context of a model due to Robinson, Solow and Srinivasan (the RSS model) with time-dependent felicity functions that are not necessarily concave, we report a theorem on the existence of optimal programs. An extended introduction places our theorem in the context of previous work on the existence question.     

House Price Shocks,Windfall Gains and Hours of Work: British Evidence*

Do workers adjust hours of work in response to capital gains and losses? This paper investigates this question using British panel data on individual employees from 1992 to 2001. It investigates hours of work adjustments to two sources of capital gain: financial windfalls and real housing wealth gains. Significant reductions in hours are found for both men and women in response, in particular, to housing gains. Men appear to increase hours in response to real housing losses, whereas women reduce hours in response to real housing gains. Evidence on hours of work preferences suggests that observed adjustments are only partial responses.     

The not-so-secret-agent: Professional monitors,hierarchies and implementation

Abstract. It is well-known that, when agents in an organization possess private information that is unverifiable by an outside party, games where agents simply announce their information can have multiple equilibria that may impede the successful implementation of the organization's objectives. We show that the introduction of a professional monitor (e.g. auditor, regulator, supervisor) can help to destroy the “bad' equilibria when agents have private information but have incomplete info rmation about others' information. Received: 21 May 1998 / Accepted: 26 May 2000     

Habits,Complementarities and Heterogeneity in Alcohol and Tobacco Demand: A Multivariate Dynamic Model*

In this paper we test the existence of forward‐looking behaviour in a multivariate model for alcohol and tobacco consumption. The theoretical framework, based on a dynamic adjustment cost model with forward‐looking behaviour, is enhanced to include the intertemporal interactions between the two goods. The analysis of the within‐period preferences completes the intertemporal model, allowing to evaluate the static substitutability/complementarity relationships. The empirical strategy consists in a two‐step estimation procedure. In a first stage, we obtain the parameters of the demand system, while in a second stage Euler equations are estimated. Results, based on a cohort data set constructed from a series of cross‐sections of the Italian Household Budget Survey, reveal a significant complementarity relationship between alcohol and tobacco. Estimation of the Euler equations does not lead to rejection of the hypothesis of intertemporal dependence, providing evidence for a forward‐looking behaviour in alcohol and tobacco consumption. Moreover, we find significant intertemporal interactions that support the adjustment cost setting in a multivariate model with rational expectations.     

Fiscal policy,entry and capital accumulation: Hump-shaped responses

In this paper we consider the entry and exit of firms in a Ramsey model with capital and an endogenous labour supply. At the firm level, there is a fixed cost combined with increasing marginal cost, which gives a standard U-shaped cost curve with optimal firm size. The costs of entry (exit) are quadratic in the flow of new firms. The number of firms becomes a second state variable and the entry dynamics gives rise to a richer set of dynamics than in the standard case: in particular, there is likely to be a hump shaped response of output to a fiscal shock with maximum effect after impact and before steady-state is reached. Output and capital per firm are also likely to be hump shaped.     

Price uncertainty, saving, and welfare

We analyze how commodity price uncertainty affects saving behavior and welfare in a dynamic model with multiple commodities, portfolio hedging, and a preference structure that disentangles ordinal preferences, attitudes towards risk, and attitudes towards intertemporal substitution. We show that the effect of price uncertainty on savings boils down to knowing (1) hf degree of resistance to intertemporal substitution and (2) the effect that uncertainty has on the certainty-equivalent real interest rate. We also show that, if the certainty-equivalent real interest rate is lower with uncertainty, consumers' welfare is also lower.     

Introduction to internally consistent modeling,aggregation, inference,and policy

This special issue of the Journal of Econometrics honors William A. Barnett’s exceptional contributions to unifying economic theory with rigorous statistical inference to interpret economic data and inform public policy. It is devoted to papers that advance microeconometrics, macroeconometrics, and financial econometrics to build models to interpret evidence.     

Productivity,R&D Spillovers and Educational Attainment*

Economists have long agreed that the local availability of a more qualified workforce generates significant spillovers. This study suggests that these externalities may arise because plants by having access to a more qualified workforce at a regional level, can benefit more from R&D spillovers than those located in areas with less qualified workforce. This hypothesis is tested on a sample of British establishments drawn from the Annual Business Inquiry over the period 1997–2002. The main results are consistent with our expectations that the regional differences in the industry‐level educational attainment of the workforce available to a plant will condition its capability of absorbing R&D spillovers.     

Optimal dividend strategies with time-inconsistent preferences

This paper studies the optimal dividend strategies of an insurance company when the manager has time-inconsistent preferences. We consider the problem for a naive manager and a sophisticated manager, and analytically derive the optimal dividend strategies when claim sizes follow an exponential distribution. Our results show that the manager with time-inconsistent preferences tends to pay out dividends earlier than her time-consistent counterpart and that the sophisticated manager is more inclined to pay out dividends than the naive manager. Furthermore, we extend these results to the case with claim sizes following a mixed exponential distribution, and provide a numerical analysis to reveal the sensitivity of the optimal dividend strategies to changes in the premium, claims and surplus volatility.     

Evaluating intergenerational risks

Climate policies have stochastic consequences that involve a great number of generations. This calls for evaluating social risk (what kind of societies will future people be born into) rather than individual risk (what will happen to people during their own lifetimes). We respond to this call by proposing and axiomatizing probability adjusted rank-discounted critical-level generalized utilitarianism (PARDCLU) through a key axiom ensuring that the social welfare order both is ethical and satisfies first-order stochastic dominance. PARDCLU yields a new useful perspective on intergenerational risks, is ethical in contrast to discounted utilitarianism, and avoids objections that have been raised against other ethical criteria. We show that PARDCLU handles situations with positive probability of human extinction and is linked to decision theory by yielding rank-dependent expected utilitarianism—but with additional structure—in a special case.