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Journal ArticleDOI

A dynamic model of altruistically-motivated transfers

01 Apr 2014-Review of Economic Dynamics (Academic Press)-Vol. 17, Iss: 2, pp 303-328
TL;DR: In this article, a dynamic Markovian game of two infinitely-lived altruistic agents without commitment is studied, where players can save, consume and give transfers to each other.
About: This article is published in Review of Economic Dynamics.The article was published on 2014-04-01 and is currently open access. It has received 23 citations till now.

Summary (3 min read)

1 Introduction

  • There are many economic situation in which inter-vivos transfers flow – potentially both ways – between two agents who are altruistically linked.
  • In recent decades, panel data sets such as the Health and Retirement Study (HRS) and the Panel Study of Income Dynamics (PSID) have become available, which contain information on both monetary and non-monetary transfers between households and the economic situation of the involved parties.
  • Soon-to-be recipients of transfers fail to fully internalize the burden of transfers on donors; potential donors don’t want to induce poorer family members to act imprudently by building up too many assets and thus creating expectations of large transfers.

2 Empirical facts

  • Much of the empirical literature has focused on three types of intergenerational transfers: co-residence, time assistance and financial transfers.
  • In the past 20 years researchers in economics and sociology have uncovered empirical magnitudes and patterns regarding financial transfers within the family, mainly focusing on parents and their children.
  • Gale & Scholz (1994) provide additional evidence that transfers are large relative to bequests.
  • Similarly, McGarry & Schoeni (1995) document that roughly 30% of parents in their fifties transfer cash of at least $500 to their children, while 9% provide transfers to at least one parent.
  • Lastly, while bequest are usually distributed equally among children, intervivos transfers are targeted toward liquidity-constrained children.

3.1 Setting

  • There are two agents in the economy who are infinitelylived.
  • The authors will denote variables for the first agent, whom they will refer to as “she”, as plain lower-case letters, e.g. ct. Variables referring to the second agent, whom they they will call “he”, are denoted with prime-superscripts, e.g. c′t.
  • The following special cases are of interest:.
  • The strategy of the analysis will be the following: First, the authors discuss the firstorder conditions in regions where no transfers flow (subsection 3.2).
  • The authors then characterize the optimal transfer decision when no agent is constrained and derive conditions under which no transfers flow (subsection 3.3).

3.2 No-transfer region: Euler equations

  • Suppose that the authors know her value function V (k, k′).
  • She has to trade off immediate gains from current consumption, which are captured in u(c), against the gains from saving, which are encoded in the behavior of the value function in the k-direction, as the authors will see in a moment.
  • The authors conclude that altruistic-strategic considerations induce an extra disincentive to save.
  • Note that (6) is not an autonomous system of ordinary differential equations, i.e. the authors cannot take values (Vk, Vk′ , Wk, Wk′) at some final point (kT , k ′ T ) and then solve the system (6) backward.

3.3 Transfer decision

  • So far, the authors have assumed that transfers are zero.
  • The intuition for this result is just as before: Consumption is a flow variable and does not affect stock variables significantly in the short run.
  • Another insight the authors glean from (7) is that the optimal transfer policy is of the bang-bang type:.
  • As mentioned before, the authors will adopt the following strategy:.
  • First, the authors guess that transfers only flow when the recipient is broke and determine the transfer motive at the limit when k′ → 0 (see section 3.4).
  • This multiplies λ > 0, which the authors are familiar with from the Euler equations.

3.4 Region where one player is bankrupt

  • The authors will now consider the case where one player, say she, is bankrupt.
  • Then consider the hyperplane approximating V in the point (0, k′) which is described by V (0, k′)+V limk (0, k ′)∆k+V limk′ (0, k ′)∆k′ where the superscript lim indicates that the authors use the limiting values of the derivatives coming from the inside.
  • The second line says that the authors must add flow utility in this instant and discount the value function since bankruptcy is postponed for a little.
  • Note now, however, that again consumption is optimally chosen, and that the authors must have u′(clim0 ) =.
  • V lim k if the agent behaves optimally.

4 The planner’s problem

  • It is also straighforward how the planner must allocate resources intratemporally in any instant:.
  • This gives us c′t as a function of ct, and the authors can see that the problem has collapsed to a selfish savings problem with a different objective function; to see this, plug c′t into the objective (9).
  • The authors also see from the intratemporal optimally condition (10) that efficiency holds when one agent is bankrupt.
  • This makes sense since the allocation is in this case is effectively chosen by the rich agent in equilibrium.
  • This is due to the altruisticstrategic distortions that were discussed in section 3.2.

5 A symmetric example with homogeneity in

  • This section demonstrates per example how the model can be solved.
  • Preferences are represented by a logarithmic utility function, there is no uncertainty, households are endowed with some initial wealth and they save through a risk-free asset with constant return, also known as The setting is simple.
  • This requires initial conditions which the authors find in two steps.
  • First, consider the case in which one of the households is broke.
  • In this case the authors can find closedform solutions of the value functions.

5.1 One Household Broke

  • Consider the situation in which only she has wealth and he has none.
  • Intuitively, since he has neither income nor savings his marginal utility explodes, which induces her to transfer wealth until her marginal utility is equal to the weighted marginal utility of him.
  • Then his consumption is proportional to hers with the proportionality factor equal to α.
  • Her value function then takes on the simple form: V = A + Bln(K0), which confirms the guess of the consumption policy above.
  • The difference in the two value functions is only due to the constant term ln(α) which is multiplied by α for agent one.

5.2 No Household Broke

  • Finding a general form for the value function will be useful when computing the system of PDE’s.
  • What the authors are after are, of course, optimal consumption policies.
  • Here the authors will make use of the case when she is broke, namely, when p=0.
  • With the first condition the authors can back out clim0 – her limiting consumption – and with the second Wk – his cross-derivative.
  • For the second PDE the authors note that: From equation (14) they get that:.

7 Conclusions

  • This paper provides a dynamic model of voluntary transfers with two-sided altruism in a Markov-perfect setting.
  • The continuous-time setting allows us to neglect certain second-order effects and provides additional tractability.
  • The authors show that the equilibrium allocation is not Pareto-efficient because agents’ savings decisions are distorted by altruistic-strategic considerations.
  • Agents have an extra disincentive to save since they fear that their relatives react by overspending in reliance on their larger resources.

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Citations
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Journal ArticleDOI
TL;DR: In this article, the authors recast the Aiyagari-Bewley-Huggett model of income and wealth distribution in continuous time, and proved that there is a unique stationary equilibrium if the intertemporal elasticity of substitution is weakly greater than one.
Abstract: We recast the Aiyagari-Bewley-Huggett model of income and wealth distribution in continuous time. This workhorse model – as well as heterogeneous agent models more generally – then boils down to a system of partial differential equations, a fact we take advantage of to make two types of contributions. First, a number of new theoretical results: (i) an analytic characterization of the consumption and saving behavior of the poor, particularly their marginal propensities to consume; (ii) a closed-form solution for the wealth distribution in a special case with two income types; (iii) a proof that there is a unique stationary equilibrium if the intertemporal elasticity of substitution is weakly greater than one; (iv) characterization of “soft” borrowing constraints. Second, we develop a simple, efficient and portable algorithm for numerically solving for equilibria in a wide class of heterogeneous agent models, including – but not limited to – the Aiyagari-Bewley-Huggett model.

62 citations

Journal ArticleDOI
TL;DR: In this paper, a dynamic non-cooperative framework for long-term care (LTC) decisions of families and use it to evaluate LTC policy options for the U.S. is proposed.
Abstract: We propose a dynamic non-cooperative framework for long-term-care (LTC) decisions of families and use it to evaluate LTC policy options for the U.S. We first document the importance of informal caregiving and economic determinants of care arrangements. We then build a heterogeneous-agents model with imperfectly-altruistic overlapping generations to account for the patterns we find. A key innovation is the availability of informal care (IC), which is determined through intra-family bargaining. This opens up a new margin in response to policy and allows for informal insurance through home-production of care. Our calibrated model captures the observed care arrangements well. We study the implications of non-means-tested IC and formal care (FC) subsidies as well as changes to means-tested Medicaid. We find that IC responds strongly to these policies. An IC subsidy substantially reduces reliance on Medicaid, while the reduction of tax revenues due to lower labour supply by caregivers is modest. There are large welfare gains from a combination of IC and FC subsidies, even when combined with a reduction of the Medicaid program.

53 citations


Cites background or methods from "A dynamic model of altruistically-m..."

  • ...Bick (2015) also finds negative aggregate welfare effects of family-child-care subsidies. Erosa et al. (2010) study the effects of parental-leave policies in a model with search frictions and job-specific human capital....

    [...]

  • ...As in Barczyk & Kredler (2014a), we find that in equi- librium V i ai > V i aj throughout the state space, i.e. each generation prefers that an additional dollar of wealth be given to themselves than to the other....

    [...]

  • ...If the unconstrained policy is not feasible, the child will choose a transfer such that the constraintck + gk = w binds since the payoff is strictly concave (again, see Barczyk & Kredler, 2014a)....

    [...]

  • ...Sinceucc(⋅) 0, the optimal consumption choice in the final stage of the gameis as in Barczyk & Kredler (2014a), except for when the parent is in MA: ci = ⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩ (uc)−1(V iai) if ai > 0, cma if i = p andm = 1, min{(uc)−1(V iai), yi4} otherwise....

    [...]

  • ...When making Barczyk’s estimates comparable to log-utility using the method proposed by Barczyk & Kredler (2014a), his altruism measures turn to √ αp = 0.53 and √ αk = 0.35....

    [...]

Journal ArticleDOI
TL;DR: This article analyzed the determinants of college enrolment and the changes in these determinants over time and found that 24 percent of all households are financially constrained in their college decision and that these constraints become more severe over time.
Abstract: In this paper, I analyze the determinants of college enrolment and the changes in these determinants over time. I propose a quantitative life‐cycle model with college enrolment. Altruistic parents provide financial support to their children. Using counterfactual experiments, I find that 24 percent of all households are financially constrained in their college decision. Constraints become more severe over time. I show that my model is consistent with a narrow college enrolment gap between students from rich and poor families, as previously reported in the empirical literature. The estimation of enrolment gaps is a popular reduced‐form approach for measuring the fraction of constrained households. My results suggest that these reduced‐form estimates are misleading, and that a structural model of parental transfers is needed to correctly identify constrained households. Further, I show that parental transfers are an important driver behind the changing role of family income as a determinant of college entry, a fact that is well documented for the US economy.

30 citations


Cites background from "A dynamic model of altruistically-m..."

  • ...The result that binding liquidity constraints trigger transfers holds even if there is no commitment and parents and children play a dynamic game (Barczyk and Kredler (2010)). There is indeed ample empirical evidence for the fact that households that are subject to binding borrowing constraints are more likely to receive transfers (see e.g. Cox (1990))....

    [...]

  • ...The result that binding liquidity constraints trigger transfers holds even if there is no commitment and parents and children play a dynamic game (Barczyk and Kredler (2010))....

    [...]

ReportDOI
Corina Boar1
TL;DR: This paper showed that parents accumulate savings to insure their children against income risk, and they refer to these as dynastic precautionary savings, and analyzed the implications of such saving in a quantitative model of altruistically linked overlapping generations.
Abstract: This paper demonstrates that parents accumulate savings to insure their children against income risk. I refer to these as dynastic precautionary savings. Using a sample of matched parent-child pairs from the Panel Study of Income Dynamics, I test for dynastic precautionary savings by examining the response of parental consumption to the child’s permanent income uncertainty. I exploit variation in permanent income risk across age and industry-occupation groups to confirm that higher uncertainty in the child’s permanent income depresses parental consumption. In particular, I find that the elasticity of parental consumption to child’s permanent income risk ranges between -0.08 and -0.06, and is of similar magnitude to the elasticity of parental consumption to own income risk. Motivated by the empirical evidence, I analyze the implications of dynastic precautionary saving in a quantitative model of altruistically linked overlapping generations. I use the model to (i) examine the size and timing of inter-vivos transfers and bequest, (ii) perform counterfactual experiments to isolate the contribution of dynastic precautionary savings to wealth accumulation and intergenerational transfers, and (iii) assess the effect of two policy proposals that can affect parents’ incentives to engage in dynastic precautionary savings: universal basic income and guaranteed minimum income. Lastly, I explore the implications of strategic interactions between parents and children for parents’ precautionary and dynastic precautionary behavior.

23 citations

Posted Content
TL;DR: In this article, the authors studied the asymmetry of information and transfers within a unique data set of 712 extended family networks from Tanzania and developed a static model of asymmetric information that contrasts altruism, pressure and exchange as motives to transfer.
Abstract: This paper studies asymmetry of information and transfers within a unique data set of 712 extended family networks from Tanzania. Using cross-reports on asset holdings, we construct measures of misperception of income among all pairs of households belonging to the same network. We show that there is significant asymmetry of information and no evidence of major systematic over-evaluation or under-evaluation of income in our data, although there is a slight over-evaluation on the part of migrants regarding non-migrants. We develop a static model of asymmetric information that contrasts altruism, pressure and exchange as motives to transfer. The model makes predictions about the correlations between misperceptions and transfers under these competing explanations. Testing these predictions in the data gives support to the model of transfers under pressure or an exchange motive with the recipient holding all the bargaining power.

21 citations

References
More filters
Journal ArticleDOI
TL;DR: In this article, the authors consider the effects of different types of intergenerational transfer schemes on the stock of public debt in the context of an overlapping-generations model and show that finite lives will not be relevant to the capitalization of future tax liabilities so long as current generations are connected to future generations by a chain of operative inter-generational transfers.
Abstract: The assumption that government bonds are perceived as net wealth by the private sector is crucial in demonstrating real effects of shifts in the stock of public debt. In particular, the standard effects of "expansionary" fiscal policy on aggregate demand hinge on this assumption. Government bonds will be perceived as net wealth only if their value exceeds the capitalized value of the implied stream of future tax liabilities. This paper considers the effects on bond values and tax capitalization of finite lives, imperfect private capital markets, a government monopoly in the production of bond "liquidity services," and uncertainty about future tax obligations. It is shown within the context of an overlapping-generations model that finite lives will not be relevant to the capitalization of future tax liabilities so long as current generations are connected to future generations by a chain of operative intergenerational transfers (either in the direction from old to young or in the direction from young to old). Applications of this result to social security and to other types of imposed intergenerational transfer schemes are also noted. In the presence of imperfect private capital markets, government debt issue will increase net wealth if the government is more efficient, at the margin, than the private market in carrying out the loan process. Similarly, if the government has monopoly power in the production of bond "liquidity services," then public debt issue will raise net wealth. Finally, the existence of uncertainty with respect to individual future tax liabilities implies that public debt issue may increase the overall risk contained in household balance sheets and thereby effectively reduce household wealth.(This abstract was borrowed from another version of this item.)

5,762 citations

Book
18 Dec 1997
TL;DR: In this paper, the main ideas on a model problem with continuous viscosity solutions of Hamilton-Jacobi equations are discussed. But the main idea of the main solutions is not discussed.
Abstract: Preface.- Basic notations.- Outline of the main ideas on a model problem.- Continuous viscosity solutions of Hamilton-Jacobi equations.- Optimal control problems with continuous value functions: unrestricted state space.- Optimal control problems with continuous value functions: restricted state space.- Discontinuous viscosity solutions and applications.- Approximation and perturbation problems.- Asymptotic problems.- Differential Games.- Numerical solution of Dynamic Programming.- Nonlinear H-infinity control by Pierpaolo Soravia.- Bibliography.- Index

2,747 citations

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TL;DR: In this article, the authors focus on avoidable moral hazard and offer one explanation for limited insurance markets, for closely held firms, and for seemingly simple as opposed to contingent forms of debt.

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"A dynamic model of altruistically-m..." refers background in this paper

  • ...Consider, for example, the theories of risk-sharing under limited commitment (Kocherlakota, 1996), exogenously incomplete markets and costs of state verification (Townsend, 1979): In all of these frameworks, since agents are ultimately selfish, one would never observe transfers to agents who are unable to reciprocate....

    [...]

ReportDOI
TL;DR: In this paper, a general treatment of social interactions into the modern theory of consumer demand is presented, where various characteristics of different persons are assumed to affect the utility functions of some persons, and the behavioral implications are systematically explored.
Abstract: This essay incorporates a general treatment of social interactions into the modern theory of consumer demand. Section 1 introduces the topic and explores some of the existing perspectives on social interactions and their importance in the basic structure of wants. In Section 2, various characteristics of different persons are assumed to affect the utility functions of some persons, and the behavioral implications are systematically explored. Section 3 develops further implications and applications in the context of analyzing intra-family relations, charitable behavior, merit goods and multi-persons interactions, and envy and hatred. The variety and significance of these applications is persuasive testimony not only to the importance of social interactions, but also to the feasibility of incorporating them into a rigorous analysis.

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Journal ArticleDOI
TL;DR: In this article, the authors examined viscosity solutions of Hamilton-Jacobi equations, and proved the existence assertions by expanding on the arguments in the introduction concerning the relationship of the vanishing-viscosity method and the notion of viscoity solutions.
Abstract: Publisher Summary This chapter examines viscosity solutions of Hamilton–Jacobi equations. The ability to formulate an existence and uniqueness result for generality requires the ability to discuss non differential solutions of the equation, and this has not been possible before. However, the existence assertions can be proved by expanding on the arguments in the introduction concerning the relationship of the vanishing viscosity method and the notion of viscosity solutions, so users can adapt known methods here. The uniqueness is then the main new point.

2,407 citations

Frequently Asked Questions (8)
Q1. What have the authors contributed in "A dynamic model of altruistically-motivated transfers" ?

In this paper, the authors developed a dynamic theory of voluntary transfers in a Markov-perfect setting with two infinitely-lived agents who are imperfectly altruistic. 

Furthermore, the model has predictions on savings decisions that the authors plan to test in future versions of the paper. The authors also plan to assess the quantitative implications of their theory in computational examples. In future work, the authors plan to use their model as a building block for a dynamic theory on long-term-care decisions in order to evaluate different policy proposals. 

Soldo & Hill (1995) find that in the Health and Retirement Study about 40% gave financial assistance to a child of at least $500. 

While their model is capable of accomodating a variety of transfers, it is most naturally interpreted when considering transfers in terms of money. 

More recently Berry (2008), using the Health and Retirement Study, finds that inter-vivos financial assistance goes to the economically most disadvantaged children. 

To equalize the two margins, the following must hold:u′(ct) + ηα ′u′(c′t) = ηu ′(c′t) + αu ′(ct)]∀t,Plugging in yieldsu′(ct) = η + α1 + α′η u′(c′t) ∀t (10)This gives us c′t as a function of ct, and the authors can see that the problem has collapsed to a selfish savings problem with a different objective function; to see this, plug c′t into the objective (9). 

The authors find that transfers are especially likely when the recipient is liquidityconstrained, which is in line with results from the empirical literature. 

This is a considerable simplification of the problem, which does not arise in the analogous discretetime problem; it occurs because immediate strategic considerations turn out to be of second order.