Why Do Some Households Save So Little? A Rational Explanation

This paper offers an explanation for the puzzle of low wealth holdings among a significant fraction of the elderly. Instead of invoking irrational, nonrational, or nonoptimal behavior to resolve the puzzle, it is shown that widespread low wealth holdings are consistent with a rational life-cycle model of saving with uncertain lifetime and borrowing constraint. When there is uncertainty about the length of life, it is optimal for some individuals to save little and exhaust their wealth early. The characteristics of these individuals are derived. The simulation results support that the model can account for low wealth holdings as well as early terminal wealth depletion. The analysis also rejects the common perception that uncertain lifetime reduces dissaving. Journal of Economic Literature Classification Numbers: D11, D91, E21, I12, J14.     

The Dynamic Effects of Social Security on Individual Consumption, Wealth and Welfare

This paper presents a theoretical investigation of the dynamic effects of social security on individual consumption, wealth and welfare. The framework of analysis is Yaari's (1965) life–cycle model of saving with uncertain lifetime and borrowing constraint. A simple uniform social security system as well as an actuarially fair and fully funded social security system is considered. The presence of terminal wealth depletion is shown to play a pivotal role not only in the derivation of the results but also in the outcome of the analysis.     

Nonseparable preferences and optimal social security systems

In this paper, we consider economies in which agents are privately informed about their skills, which evolve stochastically over time. We require agents' preferences to be weakly separable between the lifetime paths of consumption and labor. However, we allow for intertemporal nonseparabilities in preferences like habit formation. In this environment, we derive a generalized version of the Inverse Euler Equation and use it to show that intertemporal wedges characterizing optimal allocations of consumption can be strictly negative. We also show that preference nonseparabilities imply that optimal differentiable asset income taxes are necessarily retrospective in nature. We show that under weak conditions, it is possible to implement a socially optimal allocation using a social security system in which taxes on wealth are linear, and taxes/transfers are history-dependent only at retirement. The average asset income tax in this system is zero.     

A model of collateral, investment, and adverse selection

This paper characterizes the relationship between entrepreneurial wealth and aggregate investment under adverse selection. Its main finding is that such a relationship need not be monotonic. In particular, three results emerge from the analysis: (i) pooling equilibria, in which investment is independent of entrepreneurial wealth, are more likely to arise when entrepreneurial wealth is relatively low; (ii) separating equilibria, in which investment is increasing in entrepreneurial wealth, are most likely to arise when entrepreneurial wealth is relatively high and; (iii) for a given interest rate, an increase in entrepreneurial wealth may generate a discontinuous fall in investment.     

Elementary results on solutions to the bellman equation of dynamic programming: existence,uniqueness, and convergence

We establish some elementary results on solutions to the Bellman equation without introducing any topological assumption. Under a small number of conditions, we show that the Bellman equation has a unique solution in a certain set, that this solution is the value function, and that the value function can be computed by value iteration with an appropriate initial condition. In addition, we show that the value function can be computed by the same procedure under alternative conditions. We apply our results to two optimal growth models: one with a discontinuous production function and the other with “roughly increasing” returns.     

Growth Optimal Investment Strategy: The Impact of Reallocation Frequency and Heavy Tails

The strategy to maximize the long‐term growth rate of final wealth (maximum expected log strategy, maximum geometric mean strategy, Kelly criterion) is based on probability theoretic underpinnings and has asymptotic optimality properties. This article reviews the allocation of wealth in a two‐asset economy with one risky asset and a risk‐free asset. It is also shown that the optimal fraction to be invested in the risky asset (i) depends on the length of the basic return period and (ii) is lower for heavy‐tailed log returns than for light‐tailed log returns.     

Repeated moral hazard with effort persistence

I study a problem of repeated moral hazard where the effect of effort is persistent over time: each period's outcome distribution is a function of a geometrically distributed lag of past efforts. I show that when the utility of the agent is linear in effort, a simple rearrangement of terms in his lifetime utility translates this problem into a related standard repeated moral hazard. The solutions for consumption in the two problems are observationally equivalent, implying that the main properties of the optimal contract remain unchanged with persistence. For illustration, I present the computed solution of an example.     

财富积累、习惯、偏好改变、不确定性与家庭消费决策

在本文中,我们建立了一个相当一般的分析家庭消费与储蓄跨期优化决策问题的理论框架。使用综合了家庭的当期消费、消费习惯、财富积累、偏好改变多种作用影响的效用函数,在家庭劳动收入具有不确定性的情况下,我们导出了家庭消费与储蓄跨期优化决策问题的闭式解,给出了家庭消费函数和欧拉方程的解析式。使用中国农村居民的住户调查数据对理论模型中导出的欧拉方程进行估计的结果表明,除了收入和家庭财富以外,消费习惯和预防性储蓄动机确实也都是影响我国农村居民家庭的消费与储蓄决策的重要因素。     

Spillovers,subsidies, and second‐best socially optimal R&D

This paper provides a thorough second‐best welfare analysis of the standard two‐stage model of R&D/product market competition with R&D spillovers. The planner's solution is compared to the standard non‐cooperative scenario, the R&D cartel, and the cartelized research joint venture (or joint lab). We introduce the notion of a social joint lab, as a way for the planner to avoid wasteful R&D duplication. With no spillovers, the non‐cooperative scenario, the joint lab, and the second‐best planner's solutions coincide. However, with spillovers, all three scenarios yield R&D investments that fall short of the socially optimal level. To shed light on the role of the spillover level on these comparisons, we observe that the gaps between the market outcomes and the planners solutions widen as the spillover parameter increases. Finally, we establish that a social planner and a social joint lab solutions may be achieved starting from any of the three scenarios by offering firms respective suitably weighted quadratic R&D subsidization schedules.     

Optimal Investment Strategy in Safe-region on Consumption and Portfolio Problem

This paper investigates an optimal investment strategy on consumption and portfolio problem, in which the investor must withdraw funds continuously at a given rate. By analyzing the evolving process of wealth, we give the definition of safe-region for investment. Moreover, in order to obtain the target wealth as quickly as possible, using Bellman dynamic programming principle, we get the optimal investment strategy and corresponding necessary expected time. At last we give some numerical computations for a set of different parameters.     

On the solution of a stochastic optimal growth model

This note discusses a stochastic optimal growth model in which the optimal paths can be obtained by a simple direct argument. The structural characteristics of the model are the infinite horizon, the form of the instantaneous utility function, and uncertainty as a Wiener process in a linear production constraint. The note explains that, for optimality, at each point in time a formally identical problem must be solved. This implies that the optimal saving ratio must be constant.A proof, employing the rules of stochastic calculus, that the ensuing paths are the unique globally optimal paths is also given.We are very grateful to two referees of this journal for their invaluable comments and suggestions.     

理性预期、完全时间一致性与最优利率规则——一个基于无穷远视角的分析

本文以基准的线性理性预期模型为框架,在对无穷远视角的观点赋予新的解释的基础上,分析比较了利率规则的全局最优解SG、条件承诺最优解SCC、相机抉择最优解SD、时间一致性最优解STP和完全时间一致性最优解SFTP这五种形式的最优解的优劣性.我们发现,虽然SG(丫)SCC(丫)SD((丫)表示"较优于"或"较强于"),但SG和SCC是时间不一致性解,它们最终会退化为SD的形式;又因为STP是SCC的上确界,因而也未必绝对优于SD;最后,SFTP相对于SD是占优解,它等价于在STP的基础上规定社会贴现因子等于1,它所对应的均衡符合时间一致性均衡,是稳态均衡的本质内涵,它相当于在原有的线性理性预期模型框架内增加了两类约束条件,同时随机非稳态社会损失福利函数也相应地转变为随机稳态社会损失福利函数.     

Do the Rich Save More in Japan? Evidence Based on two Micro Data Sets for the 2000s

Using two household surveys, this paper investigates whether the saving rates of richer households are higher than those of poorer households in Japan. We construct a number of proxies for lifetime wealth, including those original to this study, and find marginally positive correlations between saving rates and lifetime wealth for working age households. We further find that the relationship between saving rates and lifetime wealth differs depending on the life stage of individual households. Older households with higher lifetime wealth appear to be dissaving to some extent, which is more or less consistent with the lifecycle model of consumption.     

Wealth Accounting,Exhaustible Resources and Social Welfare

The empirical literature on natural resource accounting uses methods which implicitly or explicitly entail measuring changes in total resource asset value when an exhaustible resource is depleted. In contrast, the growth theoretic literature on saving, social welfare and sustainable development is built upon a central finding, that the change in real wealth (as measured by net or ‘genuine’ saving) is proportional to the change in social welfare. We show that the change in total wealth exceeds the change in real wealth in optimal and non-optimal models of resource-extracting economies. This suggests that the change in social welfare is over-estimated when the change in total resource asset value is used as the measure of depletion. A simple empirical exercise, using World Bank data on ‘adjusted net saving’, reinforces the results from theory.     

THE ACCUMULATION OF HOUSEHOLD WEALTH OVER THE LIFE-CYCLE: A MICRODATA ANALYSIS*

In this paper, I investigate the validity of the Modigliani-Brumberg (M-B) model as an explanation of the variation of wealth holdings among households. The model as such, even with the inclusion of estimates of household lifetime earnings, explains only a minute portion of the variation in household wealth. Indeed, for certain groups such as non-white, rural residents, and the low educated, the coefficients of the regression model are insignificant. Moreover, when the top wealth holders are removed from the sample and when non-cash financial and business assets are eliminated from the household portfolios, the explanatory power of the M-B model increases markedly. Essentially, the validity of life-cycle wealth accumulation models must be restricted to the white, urban, educated middle classes and their accumulation of housing, durables, and cash. The rich have very different motives for saving and very different sources of saving, while the poor do not earn sufficient income over their lifetime to accumulate any non-negligible wealth.     

Social status pursuit,distribution of bequests and inequality

The quest for social status modifies lifetime decisions and as a consequence, the trajectory of the overall economy. Focusing on the relative wealth dimension of social status, we build a two-period overlapping generations model with heterogeneous agents to investigate the effects of status quest on the evolution of bequest distribution and household inequality. We show that the bequest motive and the concern for social status not only increase the stationary level of capital but also enhance the household equality.     

Optimal emission-extraction policy in a world of scarcity and irreversibility

This paper extends the classical exhaustible-resource/stock-pollution model with irreversibility of pollution decay, meaning that after reaching some threshold there is no decay of the pollution stock. Within this framework, we answer the question how the potential irreversibility of pollution affects the extraction path. We investigate the conditions under which the economy will optimally adopt a reversible policy, and when it is optimal to enter the irreversible region. In the case of irreversibility it may be optimal to leave a positive amount of resource in the ground forever. As far as the optimal extraction/emission policy is concerned, several types of solutions may arise, including solutions where the economy stays at the threshold for a while. Given that different programs may satisfy the first order conditions for optimality, we further investigate when each of these is optimal. We show that it is never optimal for the economy to stay at the threshold for a while before entering the irreversible region. The optimality analysis is then illustrated by means of a calibrated example. To sum up, for any pollution level, we can identify a critical resource stock such that there exist multiple optima i.e. a reversible and an irreversible policy that yield exactly the same present value. For any resource stock below this critical value, the optimal policy is reversible whereas with large enough resources, irreversible policies outperform reversible programs.     

Optimal emission-extraction policy in a world of scarcity and irreversibility

This paper extends the classical exhaustible-resource/stock-pollution model with irreversibility of pollution decay, meaning that after reaching some threshold there is no decay of the pollution stock. Within this framework, we answer the question how the potential irreversibility of pollution affects the extraction path. We investigate the conditions under which the economy will optimally adopt a reversible policy, and when it is optimal to enter the irreversible region. In the case of irreversibility it may be optimal to leave a positive amount of resource in the ground forever. As far as the optimal extraction/emission policy is concerned, several types of solutions may arise, including solutions where the economy stays at the threshold for a while. Given that different programs may satisfy the first order conditions for optimality, we further investigate when each of these is optimal. We show that it is never optimal for the economy to stay at the threshold for a while before entering the irreversible region. The optimality analysis is then illustrated by means of a calibrated example. To sum up, for any pollution level, we can identify a critical resource stock such that there exist multiple optima i.e. a reversible and an irreversible policy that yield exactly the same present value. For any resource stock below this critical value, the optimal policy is reversible whereas with large enough resources, irreversible policies outperform reversible programs.     

Do dropouts drop out too soon? Wealth,health and happiness from compulsory schooling

This paper uses compulsory schooling laws to evaluate high school dropout decisions. The main empirical result is that lifetime wealth increases by about 15% with an extra year of compulsory schooling. Students compelled to stay in school are also less likely to report being in poor health, unemployed, and unhappy. The main conclusion is that high school aversion alone is unlikely to explain why dropouts forgo substantial gains to lifetime wealth. The results are more consistent with the possibility that adolescents ignore or heavily discount future consequences when deciding to drop out of school. If teenagers are myopic, making school compulsory or offering incentives to stay in school may help improve lifetime outcomes.     

A model with endogenously determined cycles, discounting and growth

Summary. This article reexamines the role of consumption in growth and emphasises the external effects of aggregate consumption, viewed as consumption standards, as an additional impediment in the growth process. These external effects raise the productivity of the individuals and are positively related to their valuation of the future. Conditions are established under which this results in a marginal value of wealth that is an increasing function of consumption. This brings new types of multiple steady states, local indeterminacies and cyclical motions. Imposing extra homogeneity restrictions, balanced growth solutions with endogenous impatience emerge. The possibility of multiple convergent paths is univocally related to endogenous discount effects. A comparison with a benchmark planning economy indicates an excessive value for the rate of time preference and emphasises its insufficient adaptation to future utility in a stationary setting. Discrepancies along the transition path that rest on endogenous impatience versus fixed discount appear in a non-stationary environment when the competitive balanced growth solution is indeterminate. Received: May 5, 1996; revised version: May 19, 1997