SAVINGS AND PERSONAL DISCOUNT RATES IN A MATCHED SAVINGS PROGRAM FOR LOW‐INCOME FAMILIES

The ability to save for future needs is critical to family well‐being and is especially challenging for low‐income families with little extra income and limited access to institutional structures like employment‐based retirement funds or low cost savings mechanisms. Many nonprofits and governments have created new savings vehicles to fill this void. The ability of families to succeed in these programs may depend on their personal discount rates (time preferences). In this paper, we use survey data from a matched savings program and factor analysis to characterize family time preferences in order to predict their influence on savings levels. We find that a single latent factor describing the level of discount rates (rather than other dimensions of time or amount inconsistency) best describes family differences and is significantly related to the ability of families to save within the program. (JEL D91, I30)     

Hyperbolic Discounting,Borrowing Aversion and Debt Holding

Analysis of an original Internet‐based survey reveals that debt holding is related to time discounting through: (i) present bias, measured by the degree of declining impatience in the generalized hyperbolic discount function; (ii) borrowing aversion, captured by a sign effect in that future losses are discounted at lower rates than future gains; and (iii) impatience, measured by the overall discount rate. Hyperbolic respondents are classified naïve if their answers reveal them to be time‐inconsistent procrastinators, and otherwise sophisticated. Naïve respondents with more steeply declining impatience are more likely to be debtors. The sign effect relates negatively to borrowing. Survey responses indicative of high or declining impatience are associated with credit card borrowing and other overborrowing indicators.     

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.     

Conditions for Sustainable Optimal Economic Development

This paper shows that, for dynamic optimizing economies with different types of natural resource, environmental, and human‐made capital stocks, a necessary and sufficient condition for permanently sustaining an optimal utility/consumption level is the stationarity of the current‐value Hamiltonian. For economies whose development is not exogenously and directly affected by time (i.e., time‐autonomous economies), this stationarity condition generalizes Dixit et al.’s (1980 ) “zero‐net‐aggregate‐investment” rule of sustain‐ability, which in turn generalizes Solow‐Hartwick’s sustainability rule. For non‐autonomous economies, the stationarity condition is not generally fulfilled, and the current‐value Hamiltonian under (over) estimates the true welfare level by an amount equal to the discounted value of the net “pure time effect.” For the non‐autonomous case of a time‐dependent utility discount rate, a general condition on the discount rate function (of which the hyperbolic discount rate function is a special case) upholds the results obtained for autonomous cases. The paper concludes with a discussion of policies that promote both optimality and sustainability objectives.     

Empirical and public choice evidence for hyperbolic social discount rates and the implications for intergenerational discounting

The derivation of the correct discount rate for intergenerational projects in Cost Benefit Analysis is particularly contentious. Public choice has resulted in lower discretionary exponential discount rates for many intergenerational projects in Britain and the USA. This is shown to be strong indirect evidence that the true social discount rate may be a hyperbolic (rather than an exponential) function. There is also empirical evidence for this hypothesis. The hyperbolic nature of discounting is also a standard finding in the behavioural sciences. For intergenerational time frames hyperbolic discount rates should be employed together with exponential discount rates in cost-benefit sensitivity analyses.Sincere thanks to Maureen Cropper and Paul Portney for supplying their survey results and to Elaine Barrow and Phillip Judge for graphics assistance. Two anonymous referees also provided valuable comments.     

Equilibrium without prices: A central issue in pareto’smanuale

Pareto in hisManuale asserts that the price concept is inessential for the notion of equilibrium. This view deeply contrasts with the Arrow-Debreu’s dominant approach of Walrasian derivation. This identifies general equilibrium with a system of prices at which the decentralized choices of economic agents match. In this paper the author justifies and gives substance to the Paretian point of view. The differential merit of the Paretian approach is its independence of assumptions of price taking and of convexity in preferences and in production possibility sets. These assumptions are necessary, in the walrasian framework, only to maintain the centrality of prices, but they clash against the request of realism. (JEL:BOO, D51, D60)     

Patience among children

Recent policy initiatives offer cash payments to children (and often their families) to induce better health and educational choices. These policies implicitly assume that children are especially impatient (i.e., have high discount rates); however, little is known about the nature of children's patience, how it varies across children, and whether children can even make rational inter-temporal choices. This paper examines the inter-temporal choices of 5- to 16-year-old children in an artefactual field experiment. We examine their choices between varying levels of compensation received in 2 or 4 months in the future and in 0 or 2 months in the future. We find that children's choices are consistent with hyperbolic discounting, boys are less patient than girls, older children are more patient and that mathematical achievement test scores, private schooling and parent's patience are not correlated with children's patience. We also find that although more than 25% of children do not make rational inter-temporal choices within a single two-period time frame, we cannot find variables that explain this behavior other than age and standardized mathematical achievement test scores.     

Discounting the Distant Future: An Experimental Investigation

We use a laboratory experiment to elicit discount rates over a 20-year time horizon using government savings bonds as a payment vehicle. When using a constant (exponential) discount rate function, we find an implied average discount rate of 4.9 %, which is much lower than has been found in previous experimental studies that used time horizons of days or months. However, we also find strong support for non-constant, declining discount rates for longer time horizons, with an extrapolated implied annual discount rate approaching 0.5 % in 100 years. There is heterogeneity in discount rates and risk preferences in that people with more optimistic beliefs about technological progress have higher discount rates. These findings contribute to the debate over the appropriate discount rate to use in comparing the long-term benefits of climate change mitigation to the more immediate costs.     

A Joint Latent-Class Model: Combining Likert-Scale Preference Statements With Choice Data to Harvest Preference Heterogeneity

In addition to choice questions (revealed and stated choices), preference surveys typically include other questions that provide information about preferences. Preference-statement data include questions on the importance of different attributes of a good or the extent of agreement with a particular statement. The intent of this paper is to model and jointly estimate preference heterogeneity using stated-preference choice data and preference-statement data. The starting point for this analysis is the belief that the individual has preferences, and both his/her choices and preference statements are manifestations of those preferences. Our modeling contribution is linking the choice data and preference-statement data in a latent-class framework. Estimation is straightforward using the E-M algorithm, even though our model has hundreds of preference parameters. Our estimates demonstrate that: (1) within a preference class, the importance anglers associate with different Green Bay site characteristics is in accordance with their responses to the preference statements; (2) estimated across-class utility parameters for fishing Green Bay are affected by the preference-statement data; (3) estimated across-class preference-statement response probabilities are affected by the inclusion of the choice data; and (4) both data sets influence the number of classes and the probability of belonging to a class as a function of the individual’s type.     

SOCIAL NORMS,LOCAL INTERACTION,AND NEIGHBORHOOD PLANNING*

This article examines optimal social linkage when each individual's repeated interaction with each of his neighbors creates spillovers. Each individual's discount factor is randomly determined. A planner chooses a local interaction network or neighborhood design before the discount factors are realized. Each individual then plays a repeated Prisoner's Dilemma game with his neighbors. A local trigger strategy equilibrium (LTSE) describes an equilibrium in which each individual conditions his cooperation on the cooperation of at least one “acceptable” group of neighbors. Our main results demonstrate a basic trade‐off in the design problem between suboptimal punishment and social conflict. Potentially suboptimal punishment arises in designs with local interactions since in this case monitoring is imperfect. Owing to the heterogeneity of discount factors, however, greater social conflict may arise in more connected networks. When individuals' discount factors are known to the planner, the optimal design exhibits a cooperative “core” and an uncooperative “fringe.”“Uncooperative” (impatient) types are connected to cooperative ones who tolerate their free riding so that social conflict is kept to a minimum. By contrast, when the planner knows only the ex ante distribution over individual discount factors, then in some cases the optimal design partitions individuals into maximally connected cliques (e.g., cul‐de‐sacs), whereas in other cases incomplete graphs with small overlap (e.g., grids) are possible.     

THE OPTIMAL LISTING STRATEGIES IN ONLINE AUCTIONS

This article proposes a unified framework to completely characterize the seller's optimal listing strategy in the online auction as a function of her rate of time impatience. Specifically, the fixed‐price listing, the regular auction, and the buy‐it‐now (BIN) auction are each a solution of the seller's single optimization problem under different values of the rate of intertemporal discount: The perfectly patient seller adopts the regular auction, the sellers with a medium range of time impatience adopt the BIN auction, and the most impatient of sellers adopt the fixed‐price listing. Moreover, under mild conditions, the reverse price is inversely related to the value of the seller's discount factor, either within or across formats. This in turn implies that the posted price in the fixed‐price sale is greater than the reserve price of the BIN auction, followed by that of the regular auction. These predictions offer clear empirical implications.     

On the determinants of household debt maturity choice

This article jointly analyses a behavioural and a cultural concept to explain household debt portfolio choice. The behavioural approach explores the role of time preferences on household debt maturity in a theoretical model and a numerical analysis. We derive a positive relationship between the long-term discount factor δ and the optimal maturity of household loans. The cultural approach examines whether national culture is a reasonable predictor for household debt maturity. We show that culture is an important factor for households’ borrowing decisions and has even more predictive power than time preferences. Countries with higher scores on the Hofstede dimension of long-term orientation tend to have shorter household debt maturity. Time preferences incur a primarily mediating role, because the effect of national culture on the borrowing decision is reduced, as the long-term discount factor δ increases.     

Do China's people favour redistribution? Evidence from an incentivized experiment

From 1949, China's leaders brought their country through three decades of income and wealth compression, which was followed by more than three decades of sharply rising inequality. What preferences do China's people hold regarding what price (if any) is worth paying for greater equality? We conduct a laboratory decision‐making experiment mimicking aspects of a macro‐political–economic environment, using Chinese undergraduate student subjects. We find that our subjects have qualitatively similar tastes for equality as their counterparts in parallel US and European experiments; for example, most are willing to sacrifice some payment for more equality of earnings among other participants, and their willingness to do this is stronger when inequalities originate randomly versus based on performance. Considering the cases permitting direct comparison between Chinese and US subjects’ choices, redistributive choices tend to be a bit higher in China if the participant pays no direct cost and a bit lower if he or she pays such a cost, but the two distributions of decisions differ significantly in under 14% of conditions. Survey data too suggests preferences for a more equal income distribution in China than in other East Asian countries, suggesting a possible impact of the Chinese Communist Party dominance in education and media.     

TURNPIKE PROPERTIES OF A MONEY‐IN‐THE‐UTILITY‐FUNCTION MODEL*

This study establishes the global stability of a long‐run stationary state in a money‐in‐the‐utility‐function model. The major finding is that the constant money supply rule results in a stable allocation and price system if consumers discount their future utilities sufficiently weakly. Nominal and real interest rates will be in the neighbourhood of the inverse of the consumers’ discount factor β^‐1.     

Policy Effects in Hyperbolic vs. Exponential Models of Consumption and Retirement

This paper constructs a structural retirement model with hyperbolic preferences and uses it to estimate the effect of several potential Social Security policy changes. Estimated effects of policies are compared using two models, one with hyperbolic preferences and one with standard exponential preferences. Sophisticated hyperbolic discounters may accumulate substantial amounts of wealth for retirement. We find it is frequently difficult to distinguish empirically between models with the two types of preferences on the basis of asset accumulation paths or consumption paths around the period of retirement. Simulations suggest that, despite the much higher initial time preference rate, individuals with hyperbolic preferences may actually value a real annuity more than individuals with exponential preferences who have accumulated roughly equal amounts of assets. This appears to be especially true for individuals with relatively high time preference rates or who have low assets for whatever reason. This affects the tradeoff between current benefits and future benefits on which many of the retirement incentives of the Social Security system rest.Simulations involving increasing the early entitlement age and increasing the delayed retirement credit do not show a great deal of difference whether exponential or hyperbolic preferences are used, but simulations for eliminating the earnings test show a non-trivially greater effect when exponential preferences are used.     

The Effect of Tax Convexity on Corporate Investment Decisions and Tax Burdens

This paper examines the effect of convexity in the corporate tax schedule on corporate investment decisions and tax burdens. Using a contingent‐claims model, we show that greater tax convexity results in (i) earlier exit, (ii) delayed investment (except for small entry cost), and (iii) reduced corporate risk taking (except for small entry cost and unfavorable operating conditions). Also, the effective tax burden is an increasing function of tax convexity. The convexity of the tax schedule has a nontrivial impact on corporate investment decisions and investment levels. These results are relevant for economic growth, which depends (at least partly) on investment levels, and tax policy makers should be aware of these effects when making adjustments that might impact the convexity of the corporate tax schedule.     

Technology and Cartel Stability under Vertical Differentiation

The interplay between R&D activity and cartel stability is investigated in a vertical differentiation framework with convex costs. The behaviour of firms' critical discount factors as the curvature of the cost function varies is investigated, considering either price- or quantity-setting behaviour. In order to stabilize collusion, firms are better off playing à la Cournot and supplying the non-cooperative qualities. There emerges a tradeoff between the reduction of the convexity of the cost function and the associated increase in marginal cost. The decision to carry out joint or independent ventures in research is also investigated, showing that such a decision is non-monotone in intertemporal discounting. Policy measures are then briefly discussed.     

Compensation Convexity without Utility Restriction

We develop an optimal contract model on the use of stock options for chief executive officer compensation under the Mirrlees–Rogerson moral hazard framework. We find that convexity, as know as, the use of stock options, can arise with a broader range of agent utility functions than allowed by Hemmer et al. ( 2000 ). We characterise the necessary conditions regarding the behaviour of the agent's marginal risk tolerance for both the concavity and convexity cases of the likelihood‐ratio function. We find stock options need to be used more intensively, when the agent displays a higher marginal risk tolerance and when the realised task output is higher.     

Discount functions and self-control problems

In this paper we propose a new strategy for comparing the behavior of a hyperbolic discounter who possesses self-control problems to an exponential discounter who does not. Our strategy controls for inherent differences in overall levels of impatience across discount functions, which thereby allows us to isolate the pure effect of self-control problems. We argue that self-control problems, in their pure form as we identify them, can have a very surprising effect on intertemporal choices. Our method reveals that differences in decision making that could be attributed to self-control problems are at least partly (and perhaps entirely) just an artifact of an uncontrolled comparison.     

Developments in discounting: With special reference to future health events

Research on time preferences and discounting has two main motivations: to inform decision making by providing a basis for the comparison of future costs and benefits; to explain the influence of the future on current behaviour. This paper introduces the wide range of discount functions which have been advocated in addition to the standard constant rate exponential model. The different approaches taken to estimating the parameters of the discount function are reviewed. The issues raised by discounting in the longer term are discussed. Particular attention is given to time preferences with respect to future health events which have for a number of reasons been a fruitful area for research on time preferences. Specifically the paper examines: the distinctive issues raised when discounting future health events; the methods which have been used to discount health events; the relationship between time preferences and health-affecting behaviour.