Quasi-hyperbolic discounting and retirement

Some people have self-control problems regularly. This paper adds endogenous retirement to Laibson’s quasi-hyperbolic discounting savings model [Quarterly Journal of Economics 112 (1997) 443–477]. Earlier selves think that the deciding self tends to retire too early and may save less to induce later retirement. Still earlier selves may think the pre-retirement self does this too much, saving more to induce early retirement. The consumption pattern may be different from that with exponential discounting. Other observational non-equivalence includes the impact of changing mandatory retirement rules or work incentives on savings and a possibly negative marginal propensity to consume out of increased future earnings. Naive agents are briefly considered.     

A direct test of hyperbolic discounting using market asset data

This paper introduces a framework that generalizes exponential discounting in a net present value model by including a quasi-hyperbolic discount parameter in the asset valuation equation. Using observed market asset data, a statistically significant quasi-hyperbolic parameter is obtained, thus rejecting exponential discounting.     

Exponential discounting bias

We address intertemporal utility maximization under a general discount function that nests the exponential discounting and the quasi-hyperbolic discounting cases as particular specifications. Under the suggested framework, the representative agent adopts, at some initial date, an optimal behavior that shapes her consumption trajectory over time. This agent desires to take a constant discount rate to approach the optimization problem, but bounded rationality, under the form of a present bias, deviates the individual from the intended goal. As a result, decreasing impatience will end up dominating the agent’s behavior. The individual will not be aware of her own time inconsistency and, therefore, she will not revise her plans as time elapses, what makes the problem relatively simple to address from a computational point of view. The general discounting framework is used to approach a standard optimal growth model in discrete time. Transitional dynamics and stability properties of the corresponding dynamic setup are studied. An extension of the standard utility maximization model to the case of habit persistence is also considered.     

Quasi-hyperbolic preferences and retirement: A comment

Diamond and Koszegi [Diamond, P. and Koszegi, B. (2003), “Quasi-Hyperbolic Preferences and Retirement,” Journal of Public Economics, 87: 1839–1972] have argued that quasi-hyperbolic discounting can cause dynamic inconsistency in planning when to retire as well as in consumption plans. This comment shows that in a simple model with such preferences, retirement plans are never time-inconsistent, as these same preferences keep savings too low for individuals to ever be able to afford unplanned early retirement. Although only a simple example is presented here to demonstrate the point, this insight suggests the application of ordiamond03's framework should be reconsidered. The model presented needs to be extended to find robust general conclusions.     

Patience auctions: the impact of time vs. money bidding on elicited discount rates

We introduce, test, and compare two auction-based methods for eliciting discount rates. In these “patience auctions”, participants bid the smallest future sum they would prefer -or- the longest time they would wait for a reward, rather than receive a smaller, immediate payoff. The most patient bidder receives the delayed reward; all others receive the immediate payoff. These auctions allow us to compare discounting when participants’ attention is focused on the temporal versus monetary dimension of delayed rewards. We find that the estimated parameters in the three most commonly used discount functions (exponential, hyperbolic, and quasi-hyperbolic) differ across these two bidding methods (time-bids vs. money-bids). Specifically, our participants tend to show more impatience under time-bids. Furthermore, we find that people are more likely to exhibit exponential (as opposed to hyperbolic) discounting and exhibit less present bias under time-bids, compared to money-bids. To our knowledge, this paper is the first to directly compare time versus money preference elicitations, within the same subjects, using an incentive-compatible mechanism.     

Hyperbolic discounting and the time-consistent solution of three canonical environmental problems

In this paper I propose a time-consistent method of discounting hyperbolically and apply it to three canonical environmental problems: (i) optimal renewable resource use, (ii) the tragedy of the commons, and (iii) economic growth and pollution. I show that, irrespective of potentially high initial discount rates, time-consistent hyperbolic discounting leads always to a steady state of maximum yield, or, if the environment enters the utility function, a steady state where the Green Golden Rule applies. While (asymptotic) extinction is a real threat under exponential discounting it is impossible under time-consistent hyperbolic discounting. This result is also confirmed for open-access resources. In a model of economic growth and pollution, hyperbolic discounting establishes the Golden Rule of capital accumulation and the modified Green Golden Rule.     

Hyperbolic discounting and the standard model: Eliciting discount functions

Experiments on static intertemporal choice find evidence of particularly extreme impatience toward immediate rewards. While this is often taken as support for hyperbolic discounting, it could also arise because the most likely participants in experiments may be those with the most immediate need for money. We conduct a calibration exercise and find that the extreme impatience observed in experiments can be accommodated by a standard exponential discounting model with no discounting and expectation of a ‘small’ increase in the base consumption level. The calibration uses existing estimates of curvature of utility.     

Precautionary retirement and precautionary saving

The paper analyzes the lifetime utility maximization problem of an agent who chooses her saving and timing of retirement in the presence of labor income risk in a simple setting where a pure redistributive pension scheme is in place. In this context, a precautionary motive for retirement, which pushes old workers to replace an uncertain labor income with certain pension payments, and to retire early is identified. The conditions for precautionary retirement and saving to arise are then characterized and interpreted in two settings. In the first setting, utility only depends on income, and a sufficiently low level of absolute prudence is necessary for precautionary retirement. A sufficiently high level is necessary however for precautionary saving, which can coexist with precautionary retirement only for intermediate values of absolute prudence. In the second setting, agent utility also depends on leisure, and three conditions allow the precautionary motive for retirement and saving to jointly operate: prudence, an index of absolute prudence sufficiently low and cross-prudence in leisure.     

社会养老保险与退休年龄选择*——基于CFPS2010的微观经验证据

随着我国预期寿命的增加与社会养老保险金负担的上升,延迟退休已经成为必然选择。而作为重要的家庭决策,退休行为如何受到养老保险的影响值得研究。本文采用2010年中国家庭追踪调查数据（CFPS）,通过Probit模型和工具变量法实证分析了养老保险对中老年劳动者实际退休年龄选择的影响。结果表明,在控制了各类家庭异质性因素之后,养老保险对劳动者的提前退休具有显著的正向激励,同时显著降低了延迟退休概率。本文以代际居住情况衡量家庭养老行为,发现对于家庭养老影响较强的样本而言,养老保险的退休激励作用并不明显;反之,如果劳动者选择不与子女共同居住,养老保险就可能显著地影响其实际退休行为。     

The Design of Pension Pay Out Options When the Health Status during Retirement Is Uncertain

This paper examines the optimal design of pension plans when the health status during retirement is uncertain. Assuming that the health status affects both life expectancy and the marginal utility of consumption, choice between a lump-sum payment and an annuity can be welfare-enhancing if the health status is not observable by pension plan providers. This result holds if the marginal utility of consumption and life expectancy are negatively correlated. On equity grounds, a lump-sum option can be justified even if the marginal utility of consumption is independent of life expectancy.     

A folk theorem for repeated games with unequal discounting

We introduce a “dynamic non-equivalent utilities” (DNEU) condition and the notion of dynamic player-specific punishments for a general repeated game with unequal discounting, both naturally generalizing the stationary counterparts in Abreu et al. (1994). We show that if the DNEU condition, i.e., no pair of players have equivalent utility functions in the repeated game, is satisfied, then any feasible and strictly sequentially individually rational payoff sequence allows dynamic player-specific punishments. Using this result, we prove a folk theorem for unequal discounting repeated games that satisfy the DNEU condition.     

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.     

运营商利用消费者的上瘾行为定价了吗-来自中国网络游戏产业的经验证据

本文基于30款收费网络游戏玩家的样本数据,对我国收费网络游戏运营商是否在制定游戏价格时利用了玩家的上瘾行为牟利的问题进行了初步的实证研究,并对每款游戏玩家的长期折现因子和短期折现因子进行了探索性的校准讨论,进而对各款游戏玩家的行为类型进行了辨别。经验分析结果初步显示,收费网络游戏运营商主要以垄断定价方式利用了玩家的上瘾行为来牟利,而大部分游戏的玩家为理性消费者,一小部分玩家存在自我约束问题且更可能为心理成熟型消费者。最后,根据实证与理论研究结果对我国网络游戏产业发展的规制政策提出了尝试性的建议。     

Quasi-stationary cardinal utility and present bias

This note gives an axiomatic foundation for utility exhibiting quasi-geometric discounting. In addition, it introduces a wider class of utility functions satisfying weakened stationarity, called quasi-stationary utility. Both are established as von Neumann-Morgenstern utility indices in a model of risk preference.     

“Economics and Psychology”? The Case of Hyperbolic Discounting*

The article questions the methodology of “economics and psychology” in its focus on the case of hyperbolic discounting. Using some experimental results, I argue that the same type of evidence, which rejects the standard constant discount utility functions, can just as easily reject hyperbolic discounting as well. Furthermore, a decision‐making procedure based on similarity relations better explains the observations and is more intuitive. The article concludes that combining “economics and psychology” requires opening the black box of decision makers instead of modifying functional forms.     

Utility Functions whose Parameters depend on Initial Wealth

Conventional one-period utility functions in Economics assume that initial wealth only enters preferences through the definition of final wealth. Consequently, those utility functions most utilized (i.e., exponential and quadratic) have implausible risk characteristics. The authors characterize a new class of utility function whose risk parameters depend upon initial wealth and obtain several desirable results. In particular, investors with quadratic and exponential utility functions can have decreasing risk aversion, and risky assets in a quadratic utility multi-asset environment do not have to be inferior as implied by the traditional framework.     

The dynamics of distributive politics

We study dynamic committee bargaining over an infinite horizon with discounting. In each period, a committee proposal is generated by a random recognition rule, the committee chooses between the proposal and a status quo by majority rule, and the voting outcome in period t becomes the status quo in period t + 1. We study symmetric Markov equilibria of the resulting game and conduct an experiment to test hypotheses generated by the theory for pure distributional (divide-the-dollar) environments. In particular, we investigate the effects of concavity in the utility functions, the existence of a Condorcet winning alternative, and the discount factor (committee “impatience”). We report several new findings. Voting behavior is selfish and myopic. Status quo outcomes have great inertia. There are strong treatment effects that are in the direction predicted by the Markov equilibrium. We find significant evidence of concave utility functions.     

Efficient Timing of Retirement

This study introduces a retirement decision into the classic Merton model. A familiar result is that you should retire if and when the marginal utility of another year's wages is equal to the disutility of work. A new result is that at the point of retirement your exposure to risky assets should not jump. Under power utility and constant time preference, the retirement timing problem has a closed form solution; the nine inputs to the formula in question give rise to nine comparative-static results on retirement timing. Further specialization of preferences, to log consumption utility and zero time preference, reduces the required number of inputs to four. Journal of Economic Literature Classification Numbers: E21, G11, J26.