Are asts fungible?Testing the behavioral theory of life-cycle savings
Laurence Levin *
Cornerstone Rearch Suite 250,1000El Camino Real,Menlo Park,CA 94025,USA
Received 7February 1994;received in revid form 14January 1998;accepted 11February 1998Abstract
This paper is an empirical investigation of the behavioral life-cycle savings model.This model posits that lf-control problems caus individuals to depart substantially from rational behavior.I show that this model can explain how the consumption of individuals at or near retirement vary with changes in different types of financial asts.Specifically,consumption spending is nsitive to changes in income and in liquid asts,but not very nsitive to changes in the value of other types of asts such as hous and social curity (even though the value of non-liquid asts is relatively large for most of the houholds in the sample).In general,the evidence prented here favors the Behavioral Life-Cycle Model over the conventional life-cycle model even when liquidity constraints are introduced.#1998Elvier Science B.V .All rights rerved
JEL classi®cation :D91:Intertemporal consumer choice;Life-cycle models and savings;E21:Consumption;Savings
Keywords :Savings;Life-cycle;Behavioral models
1.Introduction
According to the simplest versions of the life-cycle theory,a person's consumption should depend only on the prent value of his wealth.This theory has many implications,the most studied being that individuals should engage in consumption smoothing.However,this implication has been rejected by most empirical studies.1Often the failure Journal of Economic Behavior &Organization V ol.36(1998)
59±83
*Corresponding author.Tel.:+14152398224;e-mail: ,e papers by Flavin (1981),Mankiw (1981),Hall and Mishkin (1982),Hann and Singleton (1983),Courant et al.(1986),Carroll and Summers (1989)and Campbell and Mankiw (1989).An excellent summary of empirical work on the life-cycle hypothesis can be found in Thaler (1990).
0167-2681/98/$19.00#1998Elvier Science B.V .All rights rerved PII S 0167-2681(98)00070-5我心中的宝藏
60L.Levin/J.of Economic Behavior&Org.36(1998)59±83
of the life-cycle model is attributed to the prence of liquidity constraints for significant subts of the population(e Hayashi(1985)or Zeldes(1989)for examples).This paper examines whether the anomalous results can be better explained by an alternative model of savings behavior that takes into account the problem of lf-control.This model is called the behavioral life-cycle model,which was formulated by Shefrin and Thaler (1988).2
To compare the two models,I examine how consumption varies with both the level of wealth and the form that wealth takes.In the simplest life-cycle models,consumption should only depend on an individual's total wealth,in other words,asts should be fungible;receiving$100today should have as much effect on an individual's spending as receiving$100 interest next year,or a$100appreciation of t
he value of his hou.3The behavioral life-cycle model predicts that asts should not be fungible,implying that an individual's consumption decisions will be affected by ast composition as well as total wealth.
The behavioral life-cycle model as developed by Shefrin and Thaler is a simple model of lf-control bad on three ideas.First,individuals are tempted to spend all their resources on current consumption instead of saving for the future.Second,individuals who save,overcome this lf-control problem by investing in a variety of asts that have different levels of temptation associated with them.A historic example of this type of ast was Christmas clubs which were savings plans(usually with low or non-existent interest rates)that did not allow withdrawal unto December.Individuals invested in them to insure they had enough money saved for Christmas prents.Thus,individuals create mental accounts for their different asts causing their marginal propensities to consume from tho asts to vary with the level of temptation associated with each one.Third, tting up the mental accounts implies that individuals engage in`framing';a person's consumption spending not only depends on total wealth but also depends on how that wealth is allocated among asts with differing levels of`temptation.'For example, individuals are more willing to spend asts they have labeled current income than tho they have labeled wealth or tho that they expect in the future.E
sntially,the behavioral life-cycle posits that there are psychological as well as financial transaction costs associated with spending from different types of asts.
This paper contains the first formal empirical tests of the behavioral life-cycle model using a large panel datat such as tho that have been ud to study other models of savings.Previous evidence for the behavioral life-cycle(collected in Thaler,1992)has either come from small surveys of college or MBA students or been garnered from anomalies found in other studies that were not designed to test the behavioral life-cycle model.Although this type of evidence is valuable,it cannot be definitive becau of small sample size or possible bias in studies that were not designed to study behavioral decision making.Testing the behavioral life-cycle model necessitates taking the asrtions of that model and creating empirical tests that distinguish between it and 2This theory can be interpreted as a formalization of an older literature which had rejected some of the implications of permanent income/life-cycle models but found that wealth was still an important element in making consumption decisions.This literature is summarized in Mayer(1972).
3Liquidity constraints and other extensions of the life-cycle model may also cau fungibility to be rejected. See the discussion in Section2.
L.Levin/J.of Economic Behavior&Org.36(1998)59±8361 conventional models of life-cycle savings.It also requires building an econometric model that controls for the bias inherent in examining consumption data.
Another novel feature of this paper is that many goods are ud to study consumption. In previous empirical studies of consumption only food spending is ud becau it is the only category of consumption included in the PSID and other commonly ud datats.In this paper,I u the Retirement History Survey which contains information on how much is spent on ten different goods.This creates an opportunity to investigate how spending patterns differ between goods.
In the next ction,I derive four testable differences between the behavioral and conventional life-cycle models.The first two tests are straightforward comparisons of the marginal propensity to consume(MPC)out of different types of asts.The third test examines whether liquidity constraints are causing the obrved differences in asts' MPC and is derived from differences between the two models on the effect of liquidity constraints.Esntially this test examines whether liquidity constraints occur becau of an inability to liquify certain asts or becau of large psychological or financial transaction costs in doing so.The final test is an examination of whether transaction costs em to be financial or psychological in nature.This test is derived by looking for evidence of framing
in consumption.For a conventional life-cycle model individual,the propensity to consume a particular good out of any ast will depend only on the good's wealth elasticity and possible financial transaction costs.However,if an individual acts according to the behavioral life-cycle model,then the form wealth takes affects the type of wealth the individual consumes.In other words,the psychological cost of using an ast to finance the consumption of a particular good is a function of that good's attributes.In this ca the propensity to consume a particular good out of a particular ast will depend on the attributes of both the good and the ast.4
In Section3,the data and the statistical methods are discusd.Section4contains the empirical results,and Section5is the conclusion.
The results of this paper provide strong evidence against asts being fungible.For many individuals consumption does not em to be very nsitive to changes in their wealth portfolios.Further,asts'marginal propensities to consume are very different and show strong evidence in favor of the prence of large transaction costs.Finally,the behavior of liquidity constrained individuals is consistent with the expected effects from framing.In general then,this paper finds strong evidence in favor of the behavioral life-cycle model in comparison to the conventional life-cycle model.
2.Modelling consumption expenditures
2.1.Framework
In this ction a simple framework is introduced in order to formalize tests of the differences between the behavioral and conventional life-cycle models.To establish the
4Although this implication of the behavioral life-cycle theory is not explicitly discusd by Shefrin and Thaler (1988),Shefrin and Thaler have derived this result in an unpublished mimeo,Shefrin and Thaler(1981).
framework,compare the expenditure function of a conventional life-cycle individual(E L) to one who acts in a behavioral manner(E B),both with income(Y)and K different types of asts(A1-A K).
In the simplest model,a conventional life-cycle individual's expenditures will only be a function of his total resources.The individual's total resources(W)are the sum of his asts plus the capitalized value of his permanent income which can be written as Y where is
T
t 1
1ÁP t
1 r t
耳朵痛什么原因(1)
where P t survival probability,r interest rate,T time horizon.
Thus the total resources of an individual are:W Y ÆA i.Therefore,the conventional life-cycle individual's expenditure function for the g th good can be written as
E L g E L g W E L g Y
K
k 1A k
23
(2) For a behavioral life-cycle individual,consumption will depend not only on his total resources but also on how tho resources are split up between different types of asts. Thus the expenditure fun
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ction for a behavioral life-cycle individual will be
E B g E B g Y Y A1Y A2Y
哲理性F F F Y A k (3) In this ca,there is no single aggregate that an individual us when making an expenditure decision.From the expenditure functions one can easily derive the marginal propensity to consume(MPC)out of a given ast.For a conventional life-cycle saver the marginal propensity to consume out of any ast(i or j)is
d E L g d A i
d E L g
d A j
d E L g
d W
and
d E L g
d Y
d E L g
d W
(4)
For income this formulation assumes that income is permanent income.If changes in income were completely transitory then the MPC of income would equal the MPC of wealth.Thus,the value of the MPC from an addition to income relative to the MPC from an addition to wealth will range between the MPC of wealth(if the income change is transitory)and(if the income change is permanent)and will depend on how permanent the change in income is.Note that the MPC from income will never be greater than !For a behavioral saver the marginal propensity to consume out of an ast will be
d E B g d A i b
d E B g
d A j
bÁÁÁb
d E B g
d A K
and
d E B g
d Y
b
d E B g
A1
(5)
where the asts are arranged in descending orders of temptation or liquidity(A1is more tempting than A2etc.);further,even if Y is transitory,its high temptation level will cau its MPC to be higher then the MPC of an equivalent change in wealth.
62L.Levin/J.of Economic Behavior&Org.36(1998)59±83
L.Levin/J.of Economic Behavior&Org.36(1998)59±8363 2.2.Test1(Comparing the MPC from income to the MPC from wealth)
The first test derives from comparing Eq.(4)to Eq.(5).This test consists of examining the nsitivity of consumption to income relative to wealth.According to behavioral life-cycle theory,spending should be very nsitive to income and much less nsitive to wealth.Thus if the behavioral theory is right,a regression of consumption against income and other asts should find that income is usually significantly related to consumption, while other asts may not be.Further,if the conventional theory holds,the ratio of the MPC of permanent income to the MPC of wealth should equal,the capitalized value of a $1worth of permanent income;if the behavioral theory is correct this ratio will be larger than.
2.3.Test2(Testing for the equality of different asts'MPC)
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The cond test also directly follows from the framework developed above.This test compares the MPCs of different asts.If individuals are conventional life-cycle savers then the MPCs of the different asts should be equal.In other words asts should be perfect substitutes.However,if individuals are behavioral life-cycle savers then the MPC of different asts will not be the same and should,instead,be a function of the level of temptation associated with the particular ast.Thus,this test consists of examining whether or not the MPCs are equal.
2.4.Test3(Testing for liquidity constraints)
Obviously there are explanations other than the behavioral life-cycle hypothesis that predict Tests1and2would fail.The addition of liquidity constraints to the simplest convention would,by themlves,cau asts to not be fungible.If individuals cannot borrow against some of their asts then even the conventional life-cycle model will predict that less liquid asts will have lower marginal propensities to consume.The third test compares the MPC of different ast types for constrained and unconstrained individuals.The idea behind this test is that in a conventional life-cycle model liquidity constraints are externally impod by market imperfections which limit the ability to borrow against future income whereas in the behavioral life-cycle model,liquidity constraints may also be internally impod by the consumer.The testable difference between internal and extern
al liquidity constraints is that if the constraint is external,the value of an illiquid ast will affect consumption as long as other more liquid asts are still being held(since an increa in this ast just adds to general wealth)but will cea to affect consumption when tho more liquid asts are depleted,since then the liquidity constraint will be binding.The opposite result holds when the liquidity constraint is internally impod.As long as more tempting asts have not been exhausted,the value of the less tempting ast will not affect the decision on how much to consume.Instead a less tempting ast will be consumed only after more tempting asts are exhausted.
To formalize this test,assume there are two asts denoted A1and A2.A1is a liquid ast(for example,the value of a checking account)while A2is an ast that is less
liquid(for example,a hou)that will eventually be liquidated.For a conventional life-cycle individual,the value of A2will only affect consumption when the liquidity constraint is not binding.This occurs when the value of A1is large.If the value of A1is small the individual is liquidity constrained causing an increa in A2to have no effect on consumption since there is no way the individual can access it.In our example,if a person who is not liquidity constrained(a lot of money in his bank account)finds that his hou has doubled in price then his consumption will increa.However,if he is liquidity constrained then the increa in the value of his hou will not change his consumption exp
enditures becau he cannot borrow against it.
向政府申请资金报告Formally then his consumption expenditures will follow this pattern
生产现场d E L d A2
黑色的图片全黑
A1)0
b0and
d E L
d A2
A1%0
0(6)
Two implications of the behavioral life-cycle model predict that the effects of liquidity constraints will be completely different from tho described in Eq.(6).First,as discusd earlier,the liquidity constraints of a behavioral life-cycle individual are internally impod in addition to being externally f
orced upon him by imperfections in the capital market.In this ca a less liquid or tempting ast(A2)will only affect his consumption when other more tempting asts(A1)are depleted and he needs to u it. For example,an increa in the value of a hou only affects consumption when another less tempting ast is exhausted.If there is plenty of liquid wealth available,a change in the value of the hou will not alter the individual's consumption decision becau the value of the hou does not enter into his decision making process.However,if the person is strapped for cash then he will want to dip into tho less liquid asts.Since the constrained individual is(at least implicitly)using tho asts,the components of his decision making process will now include them.In this ca,a change in the value of the asts will affect his consumption pattern.Second,if the behavioral life-cycle model is true then individuals who adopt the rules of behavior suggested by it will be more successful at saving than tho who do not.In this ca the individuals who are least tempted to u illiquid asts to support consumption will be the individuals with relatively larger savings.Thus even after controlling for an individual's initial resources (through a fixed effect or other econometric controls-e below)we will find a differential respon to an exogenous change in a particular ast's value between the group that looks liquidity constrained and the group that does not.Formally,both the reasons imply that a behavioral life-cycle individual's consumption will follow this pattern
d E L d A2
A1)0
0and
d E L
d A2
A1%0
b0(7)
Thus the conventional life-cycle theory and the behavioral life-cycle theory have strongly contrasting and testable implications about the effects of liquidity constraints on consumption behavior.
64L.Levin/J.of Economic Behavior&Org.36(1998)59±83
