GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No.48

Rational Consumers

Kohei Kubota and Mototsugu Fukushige

May 2009; revised June 2011

GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Rational Consumers∗
Kohei Kubota † and Mototsugu Fukushige ‡June 2011
Abstract
The life cycle/permanent income hypothesis (LCPIH) makes two postulates: people
behave with rational expectations, and people do not have self-control problems. If
either or both of these postulates do not apply, we cannot obtain a testable implication of
the LCPIH. We use Japanese panel data that include responses to self-reported andretrospective questions to elicit individual characteristics such as forward-looking
behavior, experience of self-control problems, and use of commitment devices toovercome self-control problems. First, we test the rational expectations hypothesis andfind that it holds for the whole sample. We then test the LCPIH implication and find that
consumption does not change in response to expected income changes, which we
restrict to fit the assumptions of the LCPIH. This result indicates that the LCPIH is aconvincing model to account for the behavior of rational consumers who have rational
expectations and no self-control problems. Our results also imply that responses toself-reported and retrospective questions are not meaningless when eliciting information
on household characteristics.
Keywords: Life cycle/permanent income hypothesis; Excess sensitivity;
Rational expectation; Self-control problems; sophisticated and naïve.
JEL Classification: D12; D91; E21.

∗

We would like to thank Charles Y. Horioka, Hidehiko Ichimura, Fumio Ohtake, Takashi Unayama,Kazuo Yamaguchi and 10th Macro Conference held in December 2008 and 8th Panel Research
Conference held in December 2008 for their helpful comments and suggestions. We gratefully
acknowledge financial support from the Osaka University Global COE program, “Human Behavior
and Socioeconomic Dynamics.” Kubota also acknowledge a grant obtained by the Nihon University
Population Research Institute from the "Academic Frontier" Project for Private Universities
matching fund subsidy 2006-2010 from the Ministry of Education, Culture, Sports, Science andTechnology, Japan and financial support from the Research Fellowships for Young Scientists of theJapan Society for the Promotion of Science (JSPS).
†

Corresponding author: Institute of Social and Economic Research, Osaka University, Mihogaoka
6-1, Ibaraki, Osaka 567-0047 Japan. E-mail address: kohei.kubota09@gmail.com‡
Graduate School of Economics, Osaka University, 1-7, Machikaneyama, Toyonaka, Osaka
560-0043, Japan. E-mail address: mfuku@econ.osaka-u.ac.jp

1. Introduction
Understanding the mechanisms of consumer behavior is fundamental for evaluating themacroeconomic impact of public policy. The life cycle/permanent income hypothesis(LCPIH) is a basic model for describing consumption behavior over time. Therefore,
many economists have conducted empirical analyses to test the LCPIH. Some
researchers have examined the relation between predicted income change andconsumption growth, and found that, if the LCPIH holds, the predicted income change
does not help explain consumption growth. 1 Despite many empirical studies testing the
LCPIH using this method, no consensus on the LCPIH has been reached (Browning andLusardi, 1996; Attanasio, 1999; Attanasio and Weber, 2010; Jappelli and Pistaferri,2010).
In rejecting the LCPIH implication, several hypotheses have been tested,
including liquidity constraints, precautionary motives, inseparability of consumption
and leisure, buffer-stock saving behavior, durability of goods, and habit formation. A
fundamental specification error of an economic model is also candidate to induce theexcess sensitivity.
Our paper focuses on the implicit and defined assumptions of the standard
2
LCPIH. The standard LCPIH assumes that households can construct consumption
plans based on unbiased predictions of future income and that they can execute theirplans. In other words, we focus on two postulates of the LCPIH: (1) households haverational expectations; (2) households do not have self-control problems. If either or bothof these assumptions are not applicable, we cannot obtain a testable implication of the
LCPIH. Moreover, if these assumptions do not describe actual behavior, the economic
model will not explain actual behavior. To construct a more suitable model, we must
know what assumptions are reasonable.
The rational expectations hypothesis (REH) is implicitly and definitely
assumed for any models of dynamic decision making. Some empirical studies havetested REH. For example, Das and van Soest (1999) and Souleles (2004) provided
evidence that shows that agents cannot forecast their future income changes correctly.
Standard models also assume that people do not have self-control problems. In other1

This test, known as the excess sensitivity test, was originally proposed by Flavin (1981). She
modified Hall’s model assuming that income follows an ARMA process and found excess sensitivity,
which means that the response of consumption change to income change is greater than the LCPIH
implies.
2
In this paper, we refer to the standard consumption model as the model proposed by Hall (1978).
Hall assumed that the utility function is additively separable for time and quadratic (which makes theinstantaneous utility function concave), that the interest rate is equivalent to the subjective discountrate, and that there is a perfect capital market. In addition, Hall introduces uncertainty of future
income.

1words, under the LCPIH consumers can execute ex ante optimal consumption plans.
However, many empirical studies have shown that a certain proportion of people doexperience self-control problems. 3 If the assumption of no self-control problems is not
valid, the implication of the LCPIH could be rejected.
The purpose of this paper is to investigate whether the LCPIH, and two
associated postulates, hold for the households in our sample. If the LCPIH holds,
expected income changes should not explain consumption changes for households that
not only precisely predict their future income changes but also execute ex ante optimal
consumption plans. To examine this prediction, we use data from the Preference andLife Satisfaction Survey (PLiSS) conducted as part of a 21st Century Center of Excellent(COE) Program and Global COE Program by Osaka University. 4 The PLiSS is alongitudinal survey conducted from 2004 to 2010 that asks questions about individual
preferences and individual future expectations about income and consumption.
Responses to self-reported and retrospective questions enable us to identify respondents’forward-looking behavior, which is an element of the REH, and characteristics related
to self-control problems. Using these questions, we can identify households whosecharacteristics coincide with the assumptions of the LCPIH. Of course, some concerns
might arise about the usefulness of self-reported or retrospective questions in eliciting
household characteristics. One criticism of the method is the difference between actual
behavior and behavior described in responses. In particular, this criticism is likely toapply to information on individual self-control problems. Although we cannot fully deal
with this issue, we try to provide a robust result by using several kinds of questions.
The excess sensitivity test requires an expectation of income change. We use
subjective expectations of income change, which is a better approach than the
instrumental variable method because it contains richer information that an
econometrician cannot observe (Browning and Lusardi, 1996; Jappelli and Pistaferri,2000). This approach also helps in examining the REH because we can compare actual
incomes with subjective income expectations. Furthermore, the responses to ourquestions on expected income changes are presented as quantitative measures rather
than as qualitative ones and have greater variation than in previous studies such as Das
and van Soest (1999), Jappelli and Pistaferri (2000), and Souleles (2004). Thus, our data

3

Papers examining self-control problems include Frederick, Lowenstein, and O’Donoghue (2002)
and Della Vigna (2009).
4
The full name is the 21st Century Center of Excellence Program titled “Construction of Behavioral
Macrodynamics by Large-scale Survey and Experiments.” This program was supported by the
Ministry of Education, Culture, Sports and Science and Technology since 2003.

2

enable us to implement the REH test and the excess sensitivity test under morefavorable conditions than previous studies. 5
In the first step of our analysis, to examine the REH and detect households forwhich the REH holds, we conduct the REH test (unbiased prediction test) for both thewhole sample and the subsamples, created by dividing the whole sample according toproxies for forward-looking behavior. We find that, in the whole sample, people cancorrectly forecast their future income changes. Furthermore, our results of the REH test
for the subsamples show that people who always make plans before they actually
implement them predict their future incomes more precisely than people who do notmake such plans. This result indicates that our proxies for forward-looking behavior
successfully detect individual characteristics that relate to rational expectations.
In the second step, we examine whether the LCPIH holds for households
whose behavior coincides with the LCPIH assumptions. First, we find that the predicted
growth in income explains the growth in consumption for the whole sample, even whencontrolling for the precautionary saving motive, nonseparability between consumption
and leisure, forecast error potentially arising from short panel data, and the effect ofliquidity constraints. As expected, our results show stronger excess sensitivity for
non-forward-looking households, but weaker excess sensitivity for forward-looking
households that make plans. In addition, using survey questions, we identify not only
the households for which the REH holds but also those that do not have self-control
problems. In this group, we do not observe excess sensitivity. Incrementally, we
implement the excess sensitivity test after dividing the sample into sophisticatedhouseholds and naïve households to investigate the theoretical implications of
O’Donoghue and Rabin (1999). 6 We find that sophisticated households have weaker
excess sensitivity than naïve households. This result supports our hypothesis. If we
confine our sample to the group for which the standard LCPIH is intended, we confirm
that the LCPIH is not rejected. This result implies that the LCPIH is useful for
predicting consumer behavior for rational households and comprehensive as thebenchmark model. Furthermore, our results indicate that responses to self-reported andretrospective questions are not meaningless in eliciting information on households’
characteristics.
The rest of the paper is structured as follows. In Section 2, we survey relevant
literature related to our hypothesis. Section 3 explains the survey and sample data usedin our study. Section 4 provides the empirical model used to examine the REH. Section
5 explains the empirical model used to examine the LCPIH. In Section 6, we report the5Souleles (2004) also implemented the REH test and the excess sensitivity test. However, he usedmatched data to conduct the excess sensitivity test.
6
Whereas sophisticated households are aware of their self-control problems, naïve households arenot. We divide our sample based on responses to self-reported and retrospective questions.

3

empirical results of the REH test and the excess sensitivity test. Section 7 concludes thepaper.
2. Related literature
We focus on two postulates of the LCPIH: (1) households have rational expectations;(2) households do not have self-control problems. In this section, we survey theliterature relevant to these postulates.
2.1. Rational expectations hypothesis
The REH is postulated not only for the LCPIH but also for any macroeconomic models
that analyze agent’s dynamic decision making. The REH in relation to future incomechanges is often defined as follows:
whereis the expected
income growth rate from t to t+1 expected at t, E is the expectation operator,
the income growth rate from t to t+1, andisis the agent’s information set available att. This equation indicates that agents are forward looking and, on average, correctly
forecast their future income changes.
As the REH is the central assumption in any dynamic model, many studies
have investigated households’ predictions of factors such as the future inflation rate, theinterest rate, and change in income (Pesaran and Weale, 2006). However, there is noestablished consensus on the REH. Although many studies have investigated the REH
using aggregate-level data, only a few papers have examined the REH using
household-level data because of data limitations. As Manski (2004) mentioned,
micro-level data on future expectations are required in order to elicit a household’s
dynamic decision-making mechanism.
Empirical studies of the REH that use household-level data compare thepredicted and actual outcomes. We refer to this method as the unbiased prediction test.
As Chamberlin (1984) and Souleles (2004) pointed out, the unbiased prediction test
raises some concerns in testing the REH. They emphasized that the forecast error could
reject any empirical model testing households’ dynamic decisions. Two types of forecast
error have been identified (Souleles, 2004). The first type arises from data limitations.
According to the LCPIH that assumes the REH, the error term of the Euler equationmust be zero. The conditional expectation of the forecast error will be zero when taking
an average over long periods of time. However, the forecast error will not be zero acrossa large number of households. Furthermore, if the forecast error is the sum of anaggregate shock and of an idiosyncratic shock, then the orthogonal condition fails in ashort panel even if the LCPIH is true. Aggregate shocks could induce a cross-sectionalcorrelation between expected consumption growth and predicted income growth. Someempirical evidence using household-level data indicates that this forecast error issignificant. For example, Das and van Soest (1999) used data from The Dutch
4

Socio-Economic Panel and rejected the REH; their results showed that households tend
to underestimate future income changes.
Systematic heterogeneous forecast errors are the second type of error, and canlead to rejection of the REH even if we can use sufficiently long panel data to test it. In
this respect, Souleles (2004) is a crucial study because he tested the REH using longer
data from The Michigan Survey of Consumer Attitudes and Behavior, which contains
information on households’ expectations about their future income prospects, businessconditions, and prices, among others. His test rejected the REH because of evidence
showing that the forecast errors were correlated with household demographic
characteristics. This result implies that systematic heterogeneity in forecast errors could
be a general problem when testing the LCPIH. If the agent’s characteristics that could
potentially induce systematic forecast errors are correlated with predictions of own
future income changes and consumption behavior, excess sensitivity could beobserved. 7
Another possible explanation for the failure of the REH is bounded rationality,
which has been used broadly since Simon (1955). 8 Furthermore, the rule of thumbcould also cause a rejection of the REH. For example, Campbell and Mankiw (1989;
1990; 1991) assumed rule-of-thumb behavior as current consumption changes depend
on current income changes, and showed that 35%–50% of consumers can be classified
as rule-of-thumb consumers.

2.2. Self-control problems
The standard consumption model assumes that people do not have self-control problems,
which means that they can execute their ex ante optimal consumption plans. However,in the real world, people may struggle with self-control problems in any situation.
Therefore, there are many theoretical approaches to modeling self-control problems, aswell as considerable empirical evidence showing that people experience self-control
problems (Frederick, Lowenstein, and O’Donoghue, 2002; Della Vigna, 2009). In
addition, agents’ awareness of their self-control problems is an important topic because
it relates to aspects of public policy, such as the pension system or bankruptcy rules. It istherefore worthwhile to test whether the assumption of self-control problems is criticalin describing consumption behavior.

7

Overconfidence and propensity to plan might be candidates to cause systematic forecast errors; forexample, see Clark and Friesen (2009) and Ameriks, Caplin, and Leahy (2003).
8
Conlisk (1996) conducted a survey of studies of bounded rationality. The rule of thumb has beenused in a similar way. In the words of Rodepeter and Winter (2000, p. 1), “rule of thumb behavior is
as important aspect of bounded rationality”.

5There are five broad approaches to modeling self-control problems. One
approach assumes that people have present-biased quasi-hyperbolic discounting
preferences (Strotz, 1995; Ainslie, 1992; Laibson, 1997; O’Donoghue and Rabin, 1999).
That is, people put more weight on the present than on the future, leading to dynamic
inconsistency. 9 As this model is simple and tractable, many studies have modified it
and provide empirical evidence based on it. The second approach is the temptation
model, as used in Gul and Pessendorfer (2001); they show that commitment is a usefulmechanism to overcome temptation by restricting the agent’s choice sets. The third
approach is the dual-self model (Thaler and Shefrin, 1981; Fudenberg and Levine,
2006), which analyzes the relationship between two types of self-behavior: an optimalplanner and a myopic doer. The fourth approach to modeling self-control problems
considers self-signaling, which assumes two periods and imperfect knowledge of one’s
own type (Béhabou and Tirole, 2004). The fifth approach examines the agent’s will or
willpower, as in Ozdenoren, Salant, and Silverman (forthcoming); they incorporate
willpower into a basic household’s dynamic decision-making model as a depletable but
renewable resource.
We do not seek to prove these theoretical explanations for self-control
problems, as our purpose is to test the validity of the LCPIH assumption for householdswith rational expectations and no self-control problems—characteristics that coincidewith the standard LCPIH assumptions.
Whether or not people are aware of their self-control problems is also an
important issue. If they are aware of their self-control problems, they should use
commitment devices to work out optimal consumption plans. O’Donoghue and Rabin(1999; 2001) classified households as sophisticated or naïve and discussed the welfare
implications in a quasi-hyperbolic discount model. 10 They showed that sophisticatedhouseholds employ commitment devices to force them to execute their ex ante plans.
Let ut denote the instantaneous utility at time t, Ut the overall utility at time t, and δ the discountfactor. We can write the overall utility as follows: Ut = ut + βδut + 1 + β(δ × δ)ut + 2 + ⋯. In
contrast to the standard model (β = 1), parameter β < 1 induces time-inconsistent preferences, which
implies that households have self-control problems.
10
O’Donoghue and Rabin (2001) classified households as (1) sophisticated, (2) partially naïve, or
9(3) fully naïve. They introduced a person’s beliefs about his or her self-control problems
case of. In the, which means that a self-control problem exists, and where the agent’s belief is, which means the agent is fully aware of his or her self-control problem, the person is called“sophisticated.” In the case of

and where the agent’s belief is, which means theagent is not at all aware of his or her self-control problem, the person is “fully naïve.” They also
introduce a “partially naïve” person, forandprecisely know of his or her self-control problem.

6, which means the person does notNaïve households, by contrast, do not use commitment devices and their ex post
lifetime utility is worse off than the lifetime utility evaluated by the ex ante plan. Someempirical studies have analyzed the effect of commitment devices on decisions ofparticipation and savings, focusing on individual retirement accounts, 401(k) retirementsavings plans, and social security in the case of the United States (Madrian and Shea,
2001; Choi, Laibson, Madrian, and Metrick 2003; Thaler and Benartzi, 2004). However,
sufficient evidence has not been provided to explore the relationship between
consumption behavior and the use of commitment devices.
According to the LCPIH, consumption behavior should not change in response
to expected income changes if households do not have self-control problems. However,consumption behavior could respond to expected income change if households do haveself-control problems. 11 Furthermore, the model proposed by O’Donoghue and Rabin(1999; 2001) predicts that the LCPIH assumption could be rejected for naïve households
that do not prepare a commitment device in advance. Our paper examines thishypothesis using self-reported and retrospective questions that proxy for sophisticatedhouseholds.
3. Data
3.1. Preference and Life Satisfaction Survey
This paper uses micro-level data from the Preference and Life Satisfaction Survey(PLiSS), a panel survey conducted by Osaka University as part of the 21st Century COE
Program and Global COE Program. 12 This survey gathers useful information on
individual preferences and predictions for future income and consumption changes.
With this information on future expectations and longitudinal data, we can jointly test
the rational expectations and excess sensitivity of the same households. The sample
households are selected randomly from across Japan using the Basic Residents
Registration System, thus providing a representative sample of the total Japanese
population. Households were interviewed once a year from February 2004 to 2010. New
households entered the panel in 2006 and 2009.
The annual attrition rate for the panel ranges from 12% to 29% and the sample
size decreases over time. Therefore, the sample for our analysis is an unbalanced panel.
To test the REH and excess sensitivity, we keep observations that contain sufficient
information to obtain the changes in family income and consumption for at least two
successive periods. The sample includes married respondents where either the husband
11

If households have time-inconsistent preferences for immediate costs, they procrastinate in orderto decrease their consumption when their future income is expected to decrease (O’Donoghue andRabin, 1999).
12
The 21st Century COE Program and the Global COE Program are projects conducted by the
Ministry of Education, Culture, Sports and Science and Technology.

7

or the wife is employed. Retired households are excluded from the sample. Aftereliminating observations with missing data, the resulting sample includes 7,128
respondents. The total number of observations is 19,052 and the percentages ofcross-sectional observations in each year of the survey are 16%(2004-05),
12%(2005-06), 16%(2006-07), 14%(2007-08), 13%(2008-09), and 28%(2009-10). 13
The sample used in our analysis follows the same trend for the proportion ofcross-sectional observations as the total sample that includes observations excluded
because of missing values.
[Table 1]
Table 1 shows the basic characteristics of the households in our data set. The
average age of the respondents is 52.68 years. Half of all respondents are female. Halfof all respondents are high school graduates and a quarter of all respondents areuniversity or college graduates.
3.2. Main variables
3.2.1. Income
The PLiSS collects data on income in several ways. We use two income variables: (1)total annual household income and (2) the sum of the monthly incomes of the
respondent and spouse over the course of the year. 14 Although we need the rate ofincome change to test rational expectations, we cannot obtain the precise rate of incomechange using total annual household income because it is a categorical variable. To
mitigate measurement errors arising from basing calculations on a categorical variable,
we also use the monthly income data, which are obtained by asking an open-ended
question. However, using the monthly income data has two limitations. First, themonthly income variable is not total household income. Because the variable for the
expected income growth rate (EGY) asks about total household income, the monthly
income variable is not consistent with EGY. Second, panel data for monthly income areavailable over a shorter period of time than those for the household’s total annual
income, because the monthly income question was added in 2007. Therefore, to obtainrobust results for the rational expectations test, we use two income change ratevariables: GY(1), which is calculated using total annual household income, and GY(2),which is calculated as the sum of the respondent’s and spouse’s monthly incomes overthe course of the year. Both variables, GY(1) and GY(2), show that around half of the13
14

Table A in Appendix 1 provides a brief distribution of observations by year.
The wording of the questions is given in Appendix 2.

8

observations of annual family income are nearly zero. 15 The distribution of GY(1) has
more kurtosis than that of GY(2).
3.2.2. Consumption
The PLiSS also collects data on several measures of consumption. For example, thesurvey tracks household expenses for eating at home, household expenses for eating out,
household expenses for durable goods, and primary household expenses excluding
durable goods. We use the primary household expenses excluding durable goods as themeasure of household expenditure. This question is worded as follows:
How much was your entire family’s average monthly expenditure in 2009?
Exclude durable consumer goods purchased such as houses, cars, expensive
electronic products. Also exclude taxes, insurance premiums, and mortgage
interest. Include costs of public utilities and energy bills.
These consumption data offer three advantages. First, excluding expenses fordurable goods eliminates the problem of consumption durability. Second, as this survey
asks for average expenditure, we do not need to account for seasonal fluctuations in
expenditure. Third, these data include expenditure for goods and services, as well as
food-related expenses. By contrast, the Panel Study of Income Dynamics, a well-known
longitudinal panel survey in the United States, only collects data on food expenditure.
Using these data, we calculate the growth rate of consumption (GC). The distribution of
GC shows that GC has more variation than GY(1) and GY(2). 16
3.3.3. Expected income change
The expected income change is a key variable for our paper, because it is used for both
the rational expectations test and the excess sensitivity test. The PLiSS collects the
expected income growth rate (EGY) directly. The wording of the EGY question is asfollows:
By how much do you estimate that the annual earned gross income of yourentire household in 2010 will change compared with the amount in 2009? (1)Increase by more than 9%, (2) Increase by 7%–9%, (3) Increase by 5%–7%,(4) Increase by 3%–5%, (5) Increase by 1%–3%, (6) Increase by less than 1%
or decrease by less than 1%, (7) Decrease by 1%–3%, (8) Decrease by 3%–5%,1516

See Figures A-1 and A-2 in Appendix 3.
See Figure B in Appendix 3.

9(9) Decrease by 5%–7%, (10) Decrease by 7%–9%, (11) Decrease by morethan 9%.
We replace these data categories with the midpoint values of each range. We
also replace the top-code categories with 0.1125 (0.09 × 1.25) and –0.1125, respectively.
The distribution of EGY is shown in Figure 1. It is seen that 11% of the observations arein the top categories. We provide robust results that handle this issue in the test of the
REH.
[Figure 1]
4. Rational expectations test
Many authors have suggested various models to empirically test the REH. We follow
the model used in Das and van Soest (1999). Let
denote the expected income
growth and let

represent actual income growth where i is the household index

and t is the time index (t = 2004, 2005, 2006, 2007, 2008, 2009). Under the REH,
expected income growth would be equal to the realized income growth, on average. To
test this hypothesis, we introduce the following empirical model:.

(1)This is the benchmark model. If the REH holds, we have β = 1 and α = 0.
Next, we add the year dummies, µt, to the empirical model (1) to account for
macroeconomic shocks.

.

(2)

We should note that our data could not identify macro-economic shocks andnon-rational expectations. If the forecast error is not averaged out, the estimatedconstant term and the estimated coefficients of the year dummies are sometimes
significantly different from zero. Thus, our data make it difficult to evaluate theestimated coefficients of the constant term and the year dummies.
10

Empirical model (2) assumes that macro-economic shocks affect allhouseholds’ income changes equally. However, the effects of macro-economic shocks
could differ by socio-economic attributes. For example, the effects of macro-economic
shocks differ between low education and high education individuals. To handle thispoint, we introduce the empirical model (3), which allows for heterogeneous effects
from aggregate shocks. We add the following to the model: a dummy for the interactionof year and respondent age, a dummy for respondent education, and the first lag of thelogarithm of the family income level.

(3)

where s is group index split by age, education, and family income.
We estimate equations (1), (2), and (3) using an ordinary least squares (OLS)
model and a random effects model. We do not estimate using fixed effects because fixed
effects models assume that the estimates of forecast error of income are persistent evenwith short panel data. This assumption is not valid for our aim of detecting thehouseholds for whom the REH holds.
5. Excess sensitivity test
5.1. Euler equation
We introduce the following Euler equation that is commonly used to test the LCPIH.

(4)

where i is the household index,
goods,

is a measure of consumption excluding durable

includes predictable indicators of household preferences such as age,is the real after-tax rate of interest, 1/ρ is the intertemporal elasticity of

substitution, δ is the rate of time preference,is the forecast error.
17

17

is the expectation operator, andEquation (4) is derived assuming that preferences are iso-elastic

The notation of this model follows Jappelli and Pistaferri (2000).

11

and that the distributions of the real interest rate and the consumption growth are jointly
lognormal. Under these assumptions, we have equation (4) as a second-orderapproximation of the first-order condition of the consumer dynamic optimization
problem.
The Euler equation implies that the predicted income change does not help in
explaining consumption growth regardless of whether the income changes arepermanent or temporary. Because the LCPIH predicts that the household will change its
consumption at the time it anticipates its future income change and that this behavior
will apply for both permanent and temporary anticipated income changes. Thisimplication facilitates the testing of the LCPIH. Thus, many studies in the literature add
the predicted income change to the Euler equation and test the relationship between thepredicted income change and consumption growth. 18
5.2. Estimation issues 19
A degree of caution must be used in conducting the excess sensitivity test, even though
this test is simple and convenient. First, obtaining the predicted income change using
panel data is rare. Second, the conditional variance of consumption cannot be observed.
Ludvigson and Paxson (1997) and Carroll (2000) cautioned that omitting theconditional variance would cause serious bias when estimating the Euler equation. Third,
excess sensitivity may result from a failure to control properly for the inseparability of
consumption and leisure. Finally, excess sensitivity may result in a spurious correlation
because of misspecification of the stochastic structure of the forecast error.
5.2.1. Predicting income growth
Testing for excess sensitivity requires that the predicted growth in income be known. To
obtain this variable, three approaches have been proposed: out-of-sample information,
two-sample instrumental variable techniques, and subjective income expectations. The
limitations of these approaches have been discussed in the literature. 20 Using subjective
income expectations is the best approach, because instrumental variable methods can beproblematic if the researcher omits critical information related to the income
expectation. Thus, we use expected family income growth (EGY) obtained from thePLiSS.
5.2.2. The conditional variance of consumption growth18

We should note that the effect of a temporary income change should be smaller than that of apermanent one.
19
The discussion in this subsection largely follows Jappelli and Pistaferri (2000).
20
See, for example, Browning and Lusardi (1996) and Jappelli and Pistaferri (2000).

12

If the utility function shows decreasing risk aversion, prudent households react to the
expected consumption risk, which is the conditional variance of consumption growth inequation (4), by reducing consumption in period t relative to period t+1. As theomission of an expected consumption risk could cause serious bias in the Euler equation
estimates, some studies introduced explicit proxies for the conditional variance ofconsumption growth. For example, Jappelli and Pistaferri (2000) used the conditionalvariance of expected nominal income growth, and Kohara and Horioka (2006) used theconditional variance of expenditure growth excluding durable goods.
We use the conditional variance of expected total family expenditure (VAR).
This variable has at least two advantages compared with the variables used in paststudies. First, expected consumption growth is better than expected income growth interms of rigorously estimating equation (4). Second, the conditional variance ofconsumption growth is an endogenous variable, whereas expected consumption growthis exogenous. Using expected consumption growth requires that endogeneity bias beaccounted for in the model.
5.2.3. Separability of consumption and leisure
If leisure is an argument of the household utility function and if consumption and leisure
are inseparable, then current consumption decisions are affected by predictable changes
in the household labor supply. We use the change in the number of workers inhouseholds (∆WORKER) as a control variable, as also done by Jappelli and Pistaferri(2000). However, this variable can be problematic in that ∆WORKER might besimultaneously determined with the current change in consumption. The ideal control
variable to capture this effect is the expected change in the total hours of work in thehousehold, but our data are not available.
5.2.4. The stochastic structure of the forecast errors
According to the LCPIH, the error term of the Euler equation must be zero. If theforecast error is the sum of an aggregate shock and of an idiosyncratic shock, then theorthogonal condition fails in a short panel even if the LCPIH is true (Chamberlin, 1984;
Souleles, 2004). Aggregate shocks induce a cross-sectional correlation between
expected consumption growth and predicted income growth. The problem is sometimes
handled by including time dummies in the Euler equation. This approach, nevertheless,is restrictive, because it eliminates the possibility that the aggregate shocks are not
evenly distributed among the population.
To capture the individual effect of aggregate shocks on consumption growth,
we explicitly introduce the interaction of year dummies with the forecast error of
consumption change (ERROR), which is calculated by subtracting growth of expected13total family expenditure (EGTC) from growth of total family expenditure including
durables (GTC). 21
The standard Euler equation, for example the model proposed by Hall (1978),implies that consumption is affected only by unpredictable shocks. Therefore, previous
studies usually assume that the disturbance implicitly includes the forecast error of
consumption change (ERROR). In this paper, we explicitly control ERROR to
overcome the forecast error caused by a short panel of unobserved household
characteristics.
5.3. Estimation model
We present an empirical model that addresses the estimation issues discussed above:

(5)

where

denotes the change in family size from period t to t+1,

an age dummy,is the change in number of workers,

isis theconditional variance of expected total family expenditure,is the forecast

error of total family expenditure including durable goods,

is a year dummy, andis the error term with a mean of zero and independently identically distributed.
When the LCPIH holds, previously expected income has no effect on current
expenditure growth. In addition, the standard LCPIH predicts that only permanentmacroeconomic shocks affect consumption change. However, in some cases, temporary
macroeconomic shocks affect temporary consumption Examples are an incomplete
financial market, the presence of liquidity constraints, and a failure of model
specifications.
6. Empirical results
To investigate our hypotheses, we first test the REH for the whole sample and then for
subsamples made by dividing the sample by proxies for forward-looking behavior. We
then conduct the excess sensitivity test for subsamples made by dividing the sample by21

The distributions of GTC and EGC are provided in Figures C-1 and C-2 of Appendix 3,
respectively.

14

proxies for forward-looking behavior, self-control problems, and use of commitment
devices, which indicates that a household is sophisticated.
6.1. Empirical results of rational expectations test
6.1.1. Benchmark empirical results
Before we present the estimation results for equations (1) and (2), we present visualevidence of the degree of precision in predicting future income. We first show themeans of GY(1), GY(2), and EGY by year in Figure 2. The mean of EGY in 2005 is
expected growth in family income from 2004 to 2005, which is calculated based on
2004 data. While the trend in GY(1) runs parallel to that of EGY until 2007, the meansof GY(1) decrease from 2008. This decrease is intuitively consistent with the effect of
the global financial crisis in those years. The means of GY(2) are in line with those of
GY(1). The similarity of these trends implies that the measurement error of GY(1)might be negligible.
[Figure 2]
To confirm people’s predictions, on average, we provide a forecast error offamily income change in Figure 3. The forecast error is calculated by subtracting theactual family income growth rate from the expected family income growth rate
predicted in the previous period. The expected errors of GY(1) are not statisticallydifferent from zero at the 5% significance level from 2005 to 2007. From 2008 to 2009,
actual family income growth is less than the expected income growth. Based on Figure
2, we conjecture that this negative forecast error arises because of an unexpected
income decrease.
[Figure 3]
Table 2 shows the empirical results of equations (1) and (2). The dependent
variable of models (1) and (2) is GY(1) and the dependent variable of models (3) and(4) is GY(2). As mentioned above, GY(1) might have a measurement error in thecalculation of the growth rate because of the use of a categorical variable. We estimate
models (3) and (4) to address this measurement error using GY(2). However, as GY(2)is a shorter panel, it could be more strongly influenced by a macroeconomic shock than
GY(1). Furthermore, the fact that GY(2) is not total family income is another issue inestimating GY(2). We estimate all models using an OLS model and a random effects
model. The results of the specification test between the OLS and the random effects
models show that OLS is appropriate for estimation; we therefore present the OLS
results.
15

[Table 2]
As can be seen in Table 2, the coefficients of EGY are almost equal to one in
all of the models. These results indicate that EGY is a suitable predictor for futurefamily income. The effects of the year dummies in 2008, 2009, and 2010 are negativeand significant in model (2). These are consistent with the trends shown in Figure 3. The
last row in Table 2 shows the Wald test statistics. The null hypothesis of the Wald test isthat the coefficient of EGY are equal to one, that the coefficients of the dummy
variables for each year are equal to zero, and that the constant term is equal to zero. The
results of the Wald test indicate that the REH does not hold in all models. Our data arefrom a short panel and, as shown in Figures 2 and 3, the macroeconomic conditions
from 2008 to 2010 are unstable. These facts suggest that our results might be influenced
by macroeconomic shocks.
[Table 3]
Next, we estimate equation (3) to address the issue of the forecast error in shortpanel data, and we estimate equation (4), which accounts for group heterogeneous
macroeconomic shocks. The results are presented in Table 3. The coefficients of EGY inmodels (1) and (3) are not statistically different from one. In addition, the magnitudes of
the coefficients are not statistically different from the estimates in Table 2.
EGY is a superior expectation variable to the variables used in previous studies.
The survey question on EGY contained 11 categories to capture the range of income
growth, whereas in previous papers such as Das and van Soest (1999), only fivecategories were used. However, when using a categorical variable, we must attach anarbitrary number to the top codes, and changes in the top-coding number could alter theempirical results. 22
To overcome this problem, we estimate models (2) and (4) in Table 3. The
coefficient of EGY without the top and bottom categories is 0.90, and it is notstatistically different from one. By contrast, in model (4), the coefficient is 0.52 and it isstatistically different from one. As shown in Figures 2 and 3, the macroeconomic
conditions from 2008 to 2010 are unstable. The estimation of GY(2) could likely be
influenced by top-coding because of the shorter panel. For this reason, the results of
GY(1) might be reliable.

22

We estimate several models to attach top (bottom) categories to the following numbers: 0.1 (–0.1),
0.11 (–0.11), 0.12 (–0.12), 0.13 (–0.13). The results are almost the same as those in Tables 2 and 3.

16

As discussed in Section 4, it is difficult to interpret the estimates of the constantterm and the coefficients of the year dummies because our panel data are short and ourempirical model has some strong assumptions. If π = 1 means that the REH holds, ourresults do not reject the hypothesis for our full sample.
6.1.2. Empirical results according to forward-looking behavior
Proxies for forward-looking behavior
As discussed in Section 2.1, the forecast error could provide spurious results for an
unbiased prediction test. To overcome the forecast error problem, we define the REH as
forward-looking behavior with unbiased prediction of own income profile.
Forward-looking agents make decisions based on intertemporal utility maximization. By
contrast, non-forward-looking agents do not look ahead and do not make dynamic
consumption plans. Our definition of the REH requires both conditions.
In this definition, we can separate our sample into a forward-looking group anda non-forward-looking group. We conduct unbiased prediction tests in each group. We
expect that only the group that consists of forward-looking households will predict
future income changes precisely. To detect this behavior in household-level data, we use
two self-reported questions in the PLiSS. The first question directly asks households
about their planning behavior by inviting survey participants to respond to the following
general statement: “I always plan things before I actually do them.” The answer is given
on a five-item scale (“Completely agree” = 5, “Somewhat agree” = 4, “Neither agree
nor disagree” = 3, “Somewhat disagree” = 2, and “Completely disagree” = 1). We callthis variable Always plan. The distribution of the responses is shown in Figure 4. Basedon the responses, we divide the households into two groups. The first group (Yes)
consists of households that choose “4” or “5”; they account for 23% of the observations.
The remaining households make up the second group (No).
[Figure 4]
The second question asks the survey participants about their planning behavior
for after retirement. The question is worded as follows:
Do you have a savings plan for after the household head retires? (If thehousehold head has already retired, do you have a savings plan for the future?)(1) I have a specific plan(2) I have a rough plan.
(3) I do not have a plan now, but I am going to make a plan in the future.
(4) I do not have a plan now, and I am not going to make a plan in the future.
17

The distribution of the responses is shown in Figure 5. It is natural to divide thehouseholds based on whether or not they have made a plan. We set a dummy variable
that takes a value of one if the household chooses “I have a specific plan” or “I have arough plan” and zero otherwise. We call this dummy variable Retirement plan. About
43% of households answered that they had a specific or rough plan (Yes).
[Figure 5]

Empirical results
We use two proxy variables, (A) Always plan and (B) Retirement plan, to identify
individual forward-looking behavior. Table 4 presents the empirical results of the REH
test split by these proxies. Part (A) presents the results of the REH test split according to
Always plan, and (B) gives the results split according to Retirement plan. The empiricalmodel we use is the same as model (2) in Table 3. From part (A), we confirm that thehouseholds that do not have a plan overestimate their future income changes. By
contrast, households with a plan suitably predict their future income changes. However,
the results in part (B) show that the accuracy of prediction behavior does not differ
between the households that have a plan for after retirement and the households that do
not have such a plan. The results in Table 4 partly confirm our hypothesis thatforward-looking households are likely to predict their future income changes more
precisely. A comparison of (A) Always plan with (B) Retirement plan shows that (A)Always plan captures more general forward-looking behavior than (B) Retirement plan.
(B) Retirement plan represents one aspect of forward-looking behavior.
[Table 4]

6.2. Empirical results of the excess sensitivity test
6.2.1. Benchmark empirical results
Table 5 provides the results of the excess sensitivity test. The results for models (1) to(3) use the whole sample and the results for models (4) to (6) exclude
liquidity-constrained households. The results of the F-test and Wu–Hausman test showthat the OLS model with clustered robust standard error is appropriate to be estimatedagainst the fixed effects model and the random effects model.
[Table 5]18

First, we confirm the results for the whole sample. The coefficient of EGY is0.36 and is significant at the 5% level in model (1). The magnitudes of excess
sensitivity are fairly consistent with previous studies. The coefficient of ∆FAMILY is
positive and significant. The coefficient of the proxy for consumption risk, VAR, andthe coefficient of ∆WORKER are not significant. These results imply that theassumption of separability of leisure and consumption is valid, and a precautionarysaving theory is rejected. These results are consistent with Jappelli and Pistaferri (2000).
As discussed in Sections 2.1 and 5.2, the forecast error could induce a bias in testing
any dynamic model that assumes the REH. To address this issue, we add ERROR tomodel (1). 23 Whereas the standard consumption model, proposed by Hall (1978),indicates that forecast errors of consumption affect consumption change, the results formodel (2) show that the coefficients of ERROR are significant at the 5% level only in2008 and 2010. This result might arise because of working formal or informal insurance
mechanisms.
Under liquidity constraints, the responses of consumption to predicted incomechanges should be asymmetric (Altonji and Siow, 1987). If liquidity constraints cause
excess sensitivity, only the coefficient of expected income up (EGY_up) should bepositive and significant. Under the LCPIH, while liquidity-constrained households who
decrease their consumption in response to anticipated income declines, they cannot
increase it by responding to anticipated income increases because they face liquidity
constraints. Model (3) in Table 5 presents the results of the asymmetric model. We findthat the coefficient of EGY_up is 0.63 and significant, whereas that of EGY_down is0.25 and not significant. The response to increasing predicted income change is larger
than the response to decreasing predicted income change. This result indicates thatliquidity constraints cause excess sensitivity. This result also suggests thatrule-of-thumb behavior is not the main cause of the excess sensitivity because theresponses of EGY_up and EGY_down to consumption are not of the same magnitude(Flavin, 1985).
Furthermore, to check the robustness of the liquidity-constraints results, we
provide the results for the subsample that excludes liquidity-constrained households. We
identify liquidity-constrained households using the following question: “Have you ever
had a loan application rejected (excluding housing loans)?” We define a household asliquidity constrained if the respondent answers “Yes” to this question. Seven percent ofhouseholds are thus defined as liquidity constrained. This proportion is slightly less thanthat in Kohara and Horioka (2006), who find that 8%–15% of young married Japanesehouseholds are liquidity constrained. We can identify two possible reasons for the
23

ERROR is calculated by subtracting growth of expected total family expenditure (EGTC) fromgrowth of total family expenditure including durables (GTC).

19slightly smaller proportion in our study. First, Kohara and Horioka use a sample ofyoung married Japanese households, whereas our sample represents a wider age
distribution of Japanese households. Second, our proxy variable underestimates thenumber of liquidity-constrained households. Our classification of liquidity constraints
has the following limitations. First, we assume that the economic status of households
has not changed since their loan applications were rejected. Second, we do not take into
account the households who could potentially be rejected for loan applications.
For models (4) to (6) in Table 5, we provide the results whenliquidity-constrained households are excluded. The results for models (4) and (5) showthat the coefficients of EGY are significant at the 5% level. In model (6), we confirm
that the coefficients of EGY_up and EGY_down are not significant. This result isalmost the same as that for model (3). These results imply that factors apart fromliquidity constraints induce co-movements between consumption change and expected
income change.
6.2.2. Empirical results by forward-looking behavior
Proxies for forward-looking behavior
As discussed in Section 2.1, we test the LCPIH for households for which the REH holds.
To examine this, we conduct the excess sensitivity test on groups divided according totheir responses to proxies for forward-looking behavior. We use (A) Always plan and(B) Retirement plan. The results of the REH test in Table 4 indicate that Always plan
could also serve as a good proxy for whether REH holds or not.
Empirical results
Table 6 presents the empirical results of the excess sensitivity test for the sample
divided according to forward-looking behavior. Panel A contains the empirical results
for the whole sample, and panel B contains those for the subsample ofliquidity-unconstrained households. Part (A) provides the results divided according to
Always plan, and part (B) gives the results divided according to Retirement plan.
[Table 6]
Except for the results in part (A), the consumption of households that haveforward-looking behavior does not respond to anticipated income change. By contrast,
we find excess sensitivity for households that are likely not to make a plan. Especiallyin part (A), the coefficient of EGY for the households that answered “No” is larger thanthat for households that answered “Yes” and is significant even though the sample for“No” is smaller than that for “Yes”. Furthermore, these results do not change even if we
exclude liquidity-constrained households. These results indicate that a consumption
20

behavior consistent with the LCPIH relates to the characteristics of forward-looking
behavior, which is a proxy for upholding the REH in this paper. Thus, we confirm that
the LCPIH assumption is not rejected if we limit our sample; this is consistent with the
LCPIH assumption in terms of the REH.
6.2.3. Self-control problems
Measuring self-control problems
Self-control problems are the main reason for the rejection of the LCPIH, as manystudies have pointed out. To elicit self-control problems, we use three questions in the
PLiSS. The first question is answered on a five-item scale, as with Always plan. The
statement is as follows:
When I have something I want, I cannot bear not buying it.
We call this response Cannot bear not buying. It contains characteristics ofimpulsiveness. The distribution of this response is shown in Figure 6. As for Always
plan, we divide the households into two groups. We classify households as having
self-control problems if they agree or somewhat agree with Cannot bear not buying;such households account for 21% of the sample.
[Figure 6]
The second question is answered on the same five-item scale as Cannot bear
not buying. It is worded as follows:
Even if I make plans, I end up procrastinating.
We call this response End up procrastinating. The distribution of this response is shownin Figure 7. The distribution of End up procrastinating has more symmetry than that of
Cannot bear not buying. End up procrastinating is also divided into two groups; 32% of
the sample answer “Yes” for End up procrastinating.
[Figure 7]
The final proxy variable for self-control problems consists of two questions inrelation to completion of homework: (1) “When did you plan to do your assignments?”(Plan); (2) “When did you do your assignments?” (Actual). 24 The responses to and24

The full wordings of these questions are given in Appendix 2.

21

distribution of these questions are in Figure 8. As shown for the Plan responses in
Figure 8, the proportion of those who answered “Got it done right away” was thehighest. By contrast, for the Actual responses, which indicate the reality of theassignment completion, more than 40% of households answered that they “Got it doneat the last minute”. These responses show that many households intended to do theirassignments almost right away, but they ended up procrastinating. We use the responses
to these questions to divide the sample into three groups: (1) can execute the plan (No);(2) cannot execute the plan (Yes); and (3) did not make any plans (Not plan). “No”
refers to households finished their assignments earlier than they planned, and “Yes” isfor households that could not finish their assignments earlier than they planned. “Notplan” is used for households that answered that “I didn’t make any plans”. We call thisvariable Cannot execute plan. About 35% of households are in the group “can executethe plan” (No) and 58% of households are in the group “cannot execute the plan” (Yes).
In each proxy for self-control problems, we confirm that the majority of households
have a self-control problem.
[Figure 8]
Empirical results
Table 7 presents the empirical results of the excess sensitivity test divided according tothree proxy variables: (I) Cannot bear not buying; (II) End up procrastinating; (III)Cannot execute plan. All results provide evidence that the coefficients of EGY are
positive and significant for households with self-control problems. By contrast, the
LCPIH implication is not rejected for households without self-control problems.
Furthermore, the broad results are unchanged even if we eliminate theliquidity-constrained sample. These results imply that, if we focus on households
without self-control problems, which the standard consumption model assumes, the
LCPIH implication is not violated. The results also suggest that self-control might be a
critical factor in inducing excess sensitivity.
[Table 7]
6.2.4. Results of excess sensitivity test for the subsample that is consistent with the
LCPIH assumptions
In Sections 6.2.2 and 6.2.3, we examined the LCPIH implication in households forwhich the REH holds and that do not have self-control problems, respectively. As
expected, the results in Tables 6 and 7 show that the LCPIH holds for the subsample inwhich the LCPIH assumptions are valid. In this subsection, we conduct the excess
sensitivity test jointly considering both postulates.
22

[Table 8]
Table 8 presents the results of the excess sensitivity test according to proxies
both for forward-looking behavior and for having self-control problems. To identify theeffects of liquidity constraints and violation of LCPIH assumptions, we exclude
liquidity-constrained households. 25 The columns are divided according to proxies that
uphold the REH: (A) Always plan and (B) Retirement plan. The rows are divided byproxies for having self-control problems: (I) Cannot bear not buying; (II) End up
procrastinating; and (III) Cannot execute plan. Thus, we make six combinations using
these two types of proxies. Our focus is on the upper-left coefficients of EGY in eachcombination; these are consistent with the LCPIH assumption that households haverational expectations and no self-control problems.
We estimate the same model as model (5) in Table 5 using OLS in each cell.
Clustered robust standard errors are in parentheses and the numbers of observations andthe proportions of observations are in brackets. For example, we can see the distributionof our sample using (A) Always plan and (I) Cannot bear not buying, which tells us that
58% of households enter both “Yes” for (A) and “No” for (I). The proportion ofhouseholds that answer that they do not plan and can bear not buying is 22%, whereas
7% of households answer that they both do not plan and cannot bear not buying. In eachcombination, the proportion of rational consumers ranges from 18% to 58%, which isfairly larger than in other cells.
We confirm that, for each result divided by proxies, excess sensitivity is notobserved for the subsample that is consistent with the LCPIH assumptions. Furthermore,conditioning each proxy for forward-looking behavior, we find that the magnitudes ofexcess sensitivity are larger for households who answer that they are facing self-control
problems. The results suggest that self-control problems might matter more than thevalidity of the REH. This result is convincing, considering the finding that the REH
holds for the whole sample.
6.2.5. Sophisticated and naïve households
Measuring sophisticated and naïve households
As discussed in Section 2.2, people with self-control problems can be classified as
sophisticated or naïve. We define sophisticated households as those that use
commitment devices to execute ex ante plans, and naïve households as those that do notuse commitment devices because they are not aware of their self-control problems. To

25

Results for the whole sample are given in Table B in Appendix 4.

23

identify sophisticated and naïve households, we use (1) Have cash and (2) Use
incentives to finish assignments.
The first proxy is identified using the question on whether a household has cash
savings. If a household is sophisticated and aware of its self-control problems in relation
to overconsumption, it would not have unnecessary cash at hand. Therefore,sophisticated households should not have cash savings. We construct a dummy variable
called Have cash, which takes a value of one if the household has cash (Yes) and zerootherwise. The proportion of sophisticated households is 74%.
The second proxy variable, Use incentives to finish assignments, is constructedusing the following retrospective question called Types of incentives:
As a child, what types of incentives did you use to finish yourassignments on time?
(Select all options if you apply)
The response options for this question and the proportions of responses are given in
Figure 9. As the figure shows, nearly half of the respondents answered “I did not follow
any specific regimen”. About 20% of respondents answered “I put a homework
schedule in a place where I would see it” and “4. I tried to sit at my desk at the sametime each day”.
[Figure 9]
If respondents are sophisticated, they should have executed their ex ante
homework schedules using some commitment devices. We estimate a probit model todetermine which choices of Types of incentives contribute to the execution. From
Cannot execute plan, we can identify respondents who acuallyexecuted their schedule.
We use this as the dependent variable, Cannot execute plan, which takes a value of one
if the response is “Yes” and zero if it is “No”. The independent variables are choices ofTypes of incentives, age dummy, and female dummy. Table C in Appendix 5 shows themarginal effects estimated by the probit model. The coefficients of the variables “I put ahomework schedule in a place where I would see it” and “I tried to sit at my desk at thesame time each day” are positive and significant at the 1% level. Our results suggestthat other incentives do not contribute to overcoming self-control problems. Therefore,
we construct a proxy variable for sophisticated households, Use incentives to finish
assignments, that takes a value of one if respondents selected “I put a homework
schedule in a place where I would see it” or “I tried to sit at my desk at the same timeeach day” and zero otherwise. According to the variable Use incentives to finish
assignments, 38% of households are sophisticated.
24Note that our proxies catch only one aspect of the characteristics ofsophisticated households. However, few empirical studies have examined consumption
behavior taking into account self-control problems. Therefore, despite the limitations ofour proxies, we believe that our new evidence on personal behavioral aspects
contributes to refining consumption theory.
Empirical results
Economic theory predicts that the consumption of the sophisticated households will not
respond to expected income changes because such households use commitment devices
to overcome their self-control problems (O’Donoghue and Rabin, 1999; 2001). Panel A
in Table 9 shows the result using Not have cash and Panel B provides the results using
Not use incentives to finish assignments. We exclude liquidity-constrained households
from Table 9. 26
As expected, the results of the whole sample in both Panels A and B show thatthe coefficient of EGY is positive and significant at the 1% level for naïve households
that do not use commitment devices, but it is not significant for sophisticatedhouseholds that use commitment devices. The results split by (I) Cannot bear notbuying show that the excess sensitivity is not observed in the households who use acommitment device. The results in Panel B for (II) End up procrastinating and (III)Cannot execute plan show that excess sensitivity does not exist for sophisticatedhouseholds but does exist for naïve households. From the results in Panel A for (II) and(III), we find that the consumption of sophisticated households responds to expected
income changes. However, the magnitudes of the responses of sophisticated households
are smaller than those of naïve households.
[Table 9]
Our results are generally consistent with our hypothesis that the LCPIH
implication is not rejected for sophisticated households because they use commitment
devices. Although our proxies represent narrow aspects of the behavior of sophisticatedhouseholds, our results show that the consumption behavior of sophisticated households
is different from that of naïve households.
7. Conclusions
In this paper, we examine whether the LCPIH holds for households whose behavior isconsistent with the assumptions of the LCPIH. In particular, we focus on the following
26

The results for the whole sample, given in Table D in Appendix 6, are almost the same as thoseshown in Table 9.

25

two postulates: (1) people have rational expectations; and (2) households do not haveself-control problems. These are implicitly assumed in the standard LCPIH. We use
Japanese panel data from the PLiSS, which has two advantages for conducting theexcess sensitivity test and for detecting the preferences of households in relation to the
LCPIH assumptions. The first advantage is that the PLiSS data make it possible toprocure subjective expectations of income growth rate, which are valuable not only to
conduct the excess sensitivity test but also to test the REH. The second advantage is that
the PLiSS contains several self-reported and retrospective questions to elicit individuals’
characteristics concerning such aspects as forward-looking behavior, self-control
problems, and the use of commitment devices.
First, to examine whether the REH holds for our sample, we regress the actual
income changes on expected income changes (unbiased prediction test). Our results of
the REH test show that the REH holds for the whole sample. Although some previous
studies provide evidence of the rejection of the REH, our results show that the REH is
not an irrelevant assumption in any dynamic decision-making model. We also find that,as expected, the households that have forward-looking behavior can predict their future
income changes, whereas households that do not have forward-looking behavior cannot.
This result indicates that our proxies are successful and useful in eliciting characteristics
related to the REH.
Next, we test the LCPIH implication and find that the LCPIH implication isrejected in the sense that excess sensitivity exists both for the whole sample and for the
subsample of liquidity-unconstrained households. To test our hypothesis, we usedself-reported and retrospective questions to identify households for which the REH
holds and that do not have self-control problems. Our results show that the LCPIH
implication is not rejected for households whose behavior is consistent with the LCPIH
assumptions. Furthermore, we confirmed that excess sensitivity becomes larger fornaïve households than for sophisticated ones. As the LCPIH predicts, if the assumptionsof the LCPIH are satisfied, then the LCPIH implication is not violated.
Our results are consistent with the theoretical predictions. Thus, our results
imply that LCPIH is reasonable benchmark model to describe consumption behavior.
Furthermore, our results using several proxy variables indicate that responses toself-reported and retrospective questions are not meaningless when eliciting
characteristics of households.
Finally, we review some limitations of our analyses and discuss directions for
future research. First, even though we use several self-reported and retrospective
questions to provide robust results, the data might not allow us to obtain completely
convincing results. A particular issue when using self-reported questions about
self-control problems is the potential inconsistency between the behavior described in
the responses and actual behavior. We hope to overcome these limitations in future26

research, for example, by comparing survey data and experimental data. Second, we do
not analyze the causation between survey responses and behavior. We implicitly assume
that people respond to survey questions according to their behavior. However, survey
responses could influence household’s behavior. Finally, our paper assumes that thepreferences are time-invariant. However, some papers have shown the possibility that
preferences can change over time. The analysis of causation is also left for future
research. We hope that future research will overcome these limitations.

27

Appendix 1. Distribution of observations by year
[Table A]

Appendix 2. Survey questions on income
GY(1)
1
2
3
4
5
6

Less than 1,000,000 yen
1,000,000 to less than 2,000,000 yen
2,000,000 to less than 4,000,000 yen
4,000,000 to less than 6,000,000 yen
6,000,000 to less than 8,000,000 yen
8,000,000 to less than 10,000,000 yen

7
8
9
10
11
12

10,000,000 to less than 12,000,000 yen
12,000,000 to less than 14,000,000 yen
14,000,000 to less than 16,000,000 yen
16,000,000 to less than 18,000,000 yen
18,000,000 to less than 20,000,000 yen
More than 20,000,000 yen

GY(2)Approximately how much was your and your spouse’s salary for 2009 (including
business income if you are self-employed)?
You: Salary per month _____ _____ _____ yenYour spouse: Salary per month _____ _____ _____ yen
Plan
Thinking about when you were a child and you were given an assignment in school,
when did you usually do the assignment?
Tended to get it done toward the
1 Got it done right away
4
end
Tended to get it done early, before the due
2
5 Got it done at the last minutedate
3 Worked on it daily up until the due date
ActualThinking about when you were a child and you were given an assignment in school,
when did you plan to do your assignment?
I planned to get it done rather toward the1 I planned to get it done right away4end
I planned to get it done rather early,
2
5 I planned to get it done at the last minute
before the due dateI planned to work on it daily up until
3
I didn't make any plansthe due date28

Appendix 3. Distribution of GY(1), GY(2), GC, GTC, and EGC[Figure A-1]
[Figure A-2]
[Figure B][Figure C-1]
[Figure C-2]

Appendix 4. Excess sensitivity test by forward-looking behavior and self-control
problems (whole sample)[Table B]

Appendix 5. Empirical results of Cannot execute plan and Types of incentives[Table C]

Appendix 6. Empirical results of Sophisticated vs. naïve households (whole sample)[Table D]29

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32

Table 1. Descriptive statistics
Mean S.D. Min Max
0.51 0.50 0.00 1.00
52.68 11.30 24.00 77.00
0.01 0.11 0.00 1.00
0.04 0.20 0.00 1.00
0.09 0.29 0.00 1.00
0.12 0.33 0.00 1.00
0.14 0.35 0.00 1.00
0.14 0.35 0.00 1.00
0.15 0.36 0.00 1.00
0.13 0.33 0.00 1.00
0.18 0.38 0.00 1.00

Female dummy
Age
–≦29
30–34
35–39
40–44
45–49
50–54
55–59
60–64
65+
Education level
Junior high school
0.11 0.31 0.00 1.00
High school
0.49 0.50 0.00 1.00
Some college
0.16 0.36 0.00 1.00
University/College
0.25 0.43 0.00 1.00
IncomeGY(1): Family’s total annual income change rate
–0.02 0.41 –3.91 3.40
GY(2): Sum of respondent’s and spouse’s–0.03 0.32 –2.71 2.40
monthly income change rate
Expenditure
GC: Family’s expenditure change rate without durables –0.02 0.68 –3.87 4.25
GTC: Family’s total expenditure change rate
0.01 0.05 –0.11 0.11
Expectation variable
EGY: Family’s expected total income change rate
–0.01 0.04 –0.11 0.11
EGTC: Family’s expected total expenditure change rate
0.01 0.05 –0.11 0.11
–0.04 0.59 –6.00 5.00
∆FAMILY: Change in family size
–0.01 0.36 –1.00 1.00
∆WORKER: Change in number of workers
0.21 0.26 0.00 2.53
VAR: Variance of EGTC×100
Liquidity-constraint dummy
0.07 0.26 0.00 1.00
Note: Number of observations is 7,128 except for GY(2), with 2,859 observations.

33

Table 2. The REH test
Dependent variable

GY(1)
(1)
1.15***(0.13)

GY(2)

(2)
(3)
(4)
EGY
1.16***
0.98***
1.02***(0.13)(0.15)(0.15)YD2006–0.03(0.02)YD2007–0.01(0.02)YD2008–0.05**(0.02)YD2009–0.06***–0.03(0.02)(0.02)YD2010–0.03*
0.01(0.02)(0.01)
Constant–0.01***
0.02–0.02***–0.01(0.00)(0.02)(0.01)(0.01)
F-test statistics
0.66
0.67
0.91
0.91
Wu–Hausman test statistics
0.67
2.58
5.83
7.96
Wald test statistics
6.32
4.26
5.95
4.82
Note: The numbers of observations (households) in models (1) and (2) are 7,128 (2,857)
and those in models (3) and (4) are 2,859 (1,934). All models are estimated using OLS
because the results of the specification test indicate that OLS is sufficient for estimation
against the fixed effects model and the random effects model. Clustered robust standard
errors are in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10%
level, respectively. The null hypothesis of the F-test is that the individual fixed effects
are all zero. The null hypothesis of the Wu–Hausman test is that individual effects are
not correlated with explanatory variables. The null hypothesis of the Wald test is that thecoefficient of EGY is equal to one, the coefficients of indicator variables for each year
are equal to zero, and the constant term is equal to zero.

34

Table 3. The REH test allowing for heterogeneous macroeconomic shocks and measurement errors
Dependent variable

GY(1)
(1)
1.17***(0.12)EGY
EGY without top and bottom categories

GY(2)
(2)

(3)
0.88***(0.14)(4)

0.90***
0.52**(0.20)(0.23)
Dummy variable for top category of EGY
0.09**
0.07**(0.03)(0.04)
Dummy variable for bottom category of EGY–0.17***–0.14***(0.02)(0.03)
Yes
Yes
Yes
Yes
Year dummies × Age dummies
Yes
Yes
Yes
Yes
Year dummies × Education level dummies
Yes
Yes
Yes
Yes
Year dummies × 1st lag of family income
Constant
Yes
Yes
Yes
Yes
F-test statistics
2.10
2.10
2.64
2.65
Wu–Hausman test statistics
2591.37 2354.40
942.64945.40Wald test statistics
69.75
71.72
24.69
25.11
Note: The numbers of observations (households) in models (1) and (2) are 7,128 (2,857)
and those in models (3) and (4) are 2,859 (1,934). All models are estimated using OLS
because the results of the specification test indicate that OLS is sufficient for estimation
against the fixed effects model and the random effects model. Clustered robust standard
errors are in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10%
level, respectively. The null hypothesis of the F-test is that the individual fixed effects
are all zero. The null hypothesis of the Wu–Hausman test is that individual effects are
not correlated with explanatory variables. The null hypothesis of the Wald test is that thecoefficient of EGY is equal to one, the coefficients of indicator variables for each year
are equal to zero, and the constant term is equal to zero.

35

Table 4. The REH test by proxies for forward-looking behavior(A) Always plan(B) Retirement plan
Yes
No
Yes
No
(1)
(2)
(3)
(4)
EGY without top and bottom categories
1.01***
0.62*
0.87*** 0.91***(0.24)(0.35)(0.29)(0.27)
Dummy variable for top category of EGY
0.11***–0.01
0.10***
0.06(0.04)(0.07)(0.04)(0.06)
Dummy variable for bottom category of EGY –0.17*** –0.17***–0.20*** –0.15***(0.02)(0.04)(0.03)(0.03)
Year dummies
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Year dummies × Age dummies
Yes
Yes
Yes
Yes
Year dummies × Education level dummies
Yes
Yes
Yes
Yes
Year dummies × 1st lag of family income
Constant
Yes
Yes
Yes
Yes
Number of observations
5089
2039
3121
4007
Number of households (clusters)
2036
821
1240
1617
Proportion of observations
29%
71%
56%
44%
Note: All models are estimated using OLS because the results of the specification test
indicate that OLS is sufficient for estimation against the fixed effects model and therandom effects model. Clustered robust standard errors are in parentheses. ***, **, and* indicate significance at the 1%, 5%, and 10% level, respectively. The null hypothesisof the F-test is that the individual fixed effects are all zero. The null hypothesis of the
Wu-Hausman test is that individual effects are not correlated with explanatory variables.
The null hypothesis of the Wald test is that the coefficient of EGY is equal to one, thecoefficients of indicator variables for each year are equal to zero, and the coefficient of
the constant term is equal to zero.

36

Table 5. The excess sensitivity test
Liquidity-unconstrainedhouseholds
(1)
(2)
(3)
(4)
(5)
(6)
EGY
0.36** 0.38**
0.37** 0.39**(0.16)(0.16)(0.17)(0.17)
EGY_up0.63**
0.54(0.32)(0.33)
EGY_down
0.25
0.32(0.23)(0.24)
–0.59
–0.58
–0.43
–0.43
ERROR×YD2005(0.45)(0.45)(0.46)(0.46)
–0.49
–0.49
–0.56
–0.55
ERROR×YD2006(0.42)(0.42)(0.43)(0.43)
0.48
0.48
0.66
0.67
ERROR×YD2007(0.42)(0.42)(0.44)(0.44)
0.70** 0.70**
0.57
0.57
ERROR×YD2008(0.35)(0.35)(0.37)(0.37)
0.23
0.24
0.36
0.36
ERROR×YD2009(0.31)(0.31)(0.32)(0.32)
0.45** 0.46**
0.36
0.36
ERROR×YD2010(0.23)(0.23)(0.24)(0.24)
0.06*** 0.06*** 0.06***
0.06*** 0.06*** 0.06***∆FAMILY(0.02)(0.02)(0.02)(0.02)(0.02)(0.02)
0.00
0.00
0.00
0.00
0.00
0.00
∆WORKER(0.02)(0.02)(0.02)(0.03)(0.03)(0.03)
VAR
–0.03
–0.04
–0.04
–0.01
–0.01
–0.02
(0.03)(0.03)(0.03)(0.03)(0.03)(0.03)
F-test statistics
0.61
0.61
0.61
0.62
0.62
0.62
Wu-Hausman test statistics
3.04
6.84
7.15
2.69
6.04
6.72
Note: The numbers of observations (households) in models (1) and (2) are 7,128 (2,857)
and those in models (3) and (4) are 6,609 (2,690). The dependent variable is GC. All
models are estimated using OLS because the results of the specification test indicatethat OLS is sufficient for estimation against the fixed effects model and the random
effects model. Clustered robust standard errors are in parentheses. ***, **, and *indicate significance at the 1%, 5%, and 10% level, respectively. The null hypothesis of
Whole sample

37

the F-test is that the individual fixed effects are all zero. The null hypothesis of theHausman test is that individual effects are not correlated with explanatory variables.

38

Table 6. Excess sensitivity test according to proxies for forward-looking behavior(A) Always plan
Yes
No
(1)
(2)

(B) Retirement plan
Yes
No
(3)
(4)

Panel A. Whole sample (Obs.: 7,128)
EGY
0.37*
0.44*
0.33
0.45*
(0.20)(0.25)(0.23)(0.23)
Observations
5089
2039
3121
4007
Proportion of observations
71%
29%
44%
56%
Panel B. Liquidity unconstrained (Obs.: 6,609)
EGY
0.35
0.53**
0.34
0.46*(0.22)(0.27)(0.24)(0.25)
Observations
4734
1875
2952
3657
Proportion of observations
72%
28%
45%
55%
Note: All estimates also include interaction of ERROR with year dummies, ∆FAMILY,∆WORKER, VAR, age dummies, year dummies, and constant term. All models are
estimated using OLS because the results of the specification test indicate that OLS issufficient for estimation against the fixed effects model and the random effects model.
Clustered robust standard errors are in parentheses. ***, **, and * indicate significanceat the 1%, 5%, and 10% level, respectively.

39

Table 7. Excess sensitivity test by proxies for self-control problems(I) Cannot bear notbuyingNo

Yes(II) End up
procrastinating(III) Cannot execute plan

No

No

Yes

Yes

Not
plan
(7)

(1)
(2)
(3)
(4)
(5)
(6)
Panel A. Whole sample (Obs.: 7,128)
EGY
0.26
0.67*
0.17
0.81***–0.05 0.67***–0.09(0.18)(0.37)(0.19)(0.29)(0.28)(0.21)(0.66)
Observations
5654
1474
4829
2299
2476
4130
522
Proportion of obs.
79%
21%
68%
32%
35%
58%
7%
Panel B. Liquidity unconstrained (Obs.: 6,609)
EGY
0.26
0.73*
0.18
0.85***–0.10 0.69***
0.13(0.19)(0.39)(0.21)(0.31)(0.29)(0.22)(0.68)
Observations
5253
1356
4519
2090
2302
3824
483
Proportion of obs.
79%
21%
68%
32%
35%
58%
7%
Note: All estimates are OLS for the results of the specification test. All estimates also
include interaction of ERROR with year dummies, ∆FAMILY, ∆WORKER, VAR, age
dummies, year dummies, and constant term. Clustered robust standard errors are inparentheses. ***, **, and * indicate significance at the 1%, 5% and 10% level,
respectively.

40

Table 8. Excess sensitivity test by proxies for forward-looking behavior and self-control
problems (excluding liquidity-constrained households)(A) Always plan(B) Retirement plan
Yes
No

Yes
No
(I) Cannot bear not buying
No
0.18
0.50
0.19
0.38
(0.24)(0.31)(0.25)(0.28)[3812, 58%]
[1441, 22%][2462, 37%][2791, 42%]
Yes
0.78
0.53
0.81
0.65
(0.49)(0.61)(0.65)(0.50)[922, 14%][434, 7%][490, 7%][866, 13%](II) End up procrastinating
No
0.23
0.06
–0.01
0.50*
(0.25)(0.35)(0.28)(0.30)[3497, 53%][1022, 15%][2130, 32%]
[2389, 36%]Yes
0.60
1.18***
1.27***
0.55(0.43)(0.40)(0.45)(0.45)[1237, 19%]
[853, 13%][822, 12%][1268, 19%]
(III) Cannot execute plan
No
–0.28
0.27
–0.45
0.31
(0.34)(0.54)(0.39)(0.43)[1793, 29%]
[509, 8%][1116, 18%][1186, 19%]Yes
0.87***
0.42
1.02***
0.39(0.29)(0.32)(0.32)(0.32)[2607, 23%][1217, 20%][1620, 26%]
[2204, 36%]
Note: All estimates also include interaction of ERROR with year dummies, ∆FAMILY,∆WORKER, VAR, age dummies, year dummies, and constant term. All estimates are
OLS for the results of the specification test. Clustered robust standard errors are inparentheses. The numbers of observations and the proportions of observations are inbrackets. ***, **, and * indicate significance at the 1%, 5%, and 10% level,
respectively.

41

Table 9. Sophisticated vs. naïve households (excluding liquidity-constrained households)
Whole sample(1)
Panel A. Not have cashNaïve (Obs.: 1,714)
EGY
Proportion of obs.
Sophisticated (Obs.: 4,895)
EGY

0.83***(0.32)
100%(I) Cannot bear not buying
No
Yes
(2)
(3)

0.60*
(0.33)
79%

1.09(0.84)
21%(II) End up procrastinating
No
Yes
(4)
(5)

0.55
(0.36)
69%

1.46**(0.63)
31%(III) Cannot execute planNo
Yes
Not plan
(6)
(7)
(8)

0.14 1.20***(0.55)(0.39)
36%
60%

5.24*
(2.80)
5%

0.23
0.14
0.52
0.05
0.65*
–0.19 0.53**–0.25(0.20)(0.23)(0.44)(0.25)(0.36)(0.34)(0.27)(0.71)
Proportion of obs.
100%
80%
20%
68%
32%
35%
57%
8%
Panel B. Not use incentives to finish assignmentsNaïve (Obs.: 4,127)EGY
0.54**
0.39
0.84*
0.40
0.85**
0.12 0.77***
0.14(0.21)(0.24)(0.46)(0.26)(0.38)(0.37)(0.28)(0.71)
Proportion of obs.
100%
78%
22%
66%
34%
29%
60%
11%
Sophisticated (Obs.: 2,482)
EGY
0.09
0.04
0.22
–0.23
0.84
–0.35
0.42
(0.29)(0.31)(0.77)(0.34)(0.55)(0.44)(0.38)
Proportion of obs.
100%
82%
18%
72%
28%
44%
55%
1%
Note: All estimates also include interaction of ERROR with year dummies, ∆FAMILY, ∆WORKER, VAR, age dummies, year dummies,
and constant term. All estimates are OLS for the results of the specification test. Clustered robust standard errors are in parentheses. ***,**, and * indicate significance at the 1%, 5%, and 10% level, respectively. Results are omitted for the sophisticated group for (III) in
Panel B because the sample size was not large enough to obtain robust estimates.

42

Table A. Distribution of observations by year
04–05 05–06 06–07 07–08 08–09 09–10 Total Total obs.
Our sample
10% 10% 15% 16% 16% 33% 100%
7,128
Total sample 16% 12% 16% 14% 13% 28% 100%
19,052
Note: Total sample indicates the number of households that responded in at least twoconsecutive periods.

43

Table B. Excess sensitivity test by forward-looking behavior and self-control problems(whole sample)(A) Always plan(B) Retirement plan
Yes
No
Yes
No
(I) Cannot bear not buying
No
0.23
0.40
0.18
0.38
(0.22)(0.29)(0.24)(0.27)[4103, 58%]
[1551, 22%][2593, 36%][3061, 43%]
Yes
0.69
0.59
0.73
0.63
(0.47)(0.55)(0.61)(0.46)[986, 14%][488, 7%][528, 7%][946, 13%](II) End up procrastinating
No
0.23
0.05
–0.03
0.47*
(0.23)(0.33)(0.27)(0.28)[3749, 53%][1080, 15%][2235, 31%][2594, 36%]Yes
0.66
0.93**
1.26***
0.54(0.42)(0.38)(0.42)(0.42)[1340, 19%]
[959, 13%][886, 12%][1413, 20%]
(III) Cannot execute plan
No
–0.22
0.30
–0.31
0.25
(0.33)(0.52)(0.36)(0.43)[1932, 29%][544, 8%][1189, 18%]
[1287, 19%]Yes
0.84***
0.37
0.97***
0.41(0.27)(0.30)(0.31)(0.29)[2804, 42%][1326, 20%][1709, 26%]
[2421, 37%]
Note: All estimates also include interaction of ERROR with year dummies, ∆FAMILY,∆WORKER, VAR, age dummies, year dummies, and constant term. All estimates are
OLS for the results of the specification test. Clustered robust standard errors are inparentheses. The numbers of observations and the proportion of observations are inbrackets. ***, **, and * indicate significance at the 1%, 5%, and 10% level,
respectively.

44

Table C. Cannot execute plan and Types of incentives
Types of incentives
1. I did my homework with my friends and–0.002 (0.044)
made it a competition to see who could do a better job.
2. I asked my parents to give me a reward
0.086 (0.192)
for completing my homework.
3. I put a homework schedule in a place where I would see it. 0.113 (0.035) ***4. I tried to sit at my desk at the same time each day.
0.190 (0.034) ***5. I used other creative methods for completing my–0.034 (0.071)
homework.
6. I did not follow any specific regimen.
Reference
Female dummy
0.008 (0.028)
Age dummies
Yes
Observations
1275
Log likelihood–796
Note: Dependent variable is Cannot execute plan, which takes a value of one if the
response is “Yes” and zero if “No”. The coefficients are marginal effects estimated by
the probit model. Robust standard errors are in parentheses. *** indicates significanceat the 1% level.

45

Table D. Sophisticated vs. naïve households (whole sample)
Whole sample
Panel A. Not have cashNaïve (Obs.: 1,849)
EGY
Proportion of obs.
Sophisticated (Obs.: 5,279)
EGY

0.96***(0.32)
100%(I) Cannot bear not buyingNoYes

0.80**(0.34)
79%

0.89(0.83)
21%(I) End up procrastinating
No
Yes

0.65*
(0.35)
69%

1.59**(0.65)
31%(III) Cannot execute planNo
Yes
Not plan

0.56 1.13***(0.60)(0.36)
36%
60%

3.89
(2.71)
5%

0.18
0.08
0.49
0.02
0.56*
–0.25 0.50**–0.25(0.19)(0.22)(0.40)(0.23)(0.32)(0.32)(0.25)(0.68)
Proportion of obs.
100%
79%
21%
67%
33%
34%
57%
8%
Panel B. Not use incentives to finish assignmentsNaïve (Obs.: 4,454)
EGY
0.52**
0.39*
0.81*
0.33
0.89**
0.24 0.71***–0.16(0.20)(0.24)(0.43)(0.25)(0.36)(0.38)(0.26)(0.69)
Proportion of obs.
100%
77%
23%
65%
35%
29%
60%
11%
Sophisticated (Obs.: 2,674)
EGY
0.11
0.07
0.21
–0.11
0.55
–0.41
0.49 16.59***(0.27)(0.29)(0.69)(0.32)(0.51)(0.42)(0.35)(1.63)
Proportion of obs.
100%
82%
18%
72%
28%
44%
55%
1%
Note: All estimates also include interaction of ERROR with year dummies, ∆FAMILY, ∆WORKER, VAR, age dummies, year dummies,
and constant term. All estimates are OLS for the results of the specification test. Clustered robust standard errors are in parentheses. ***,**, and * indicate significance at the 1%, 5% and 10% level, respectively.

46

0

.1

Fraction
.2

.3

.4

Figure 1. Distribution of expectation of income growth rate (EGY)

-.12

-.1

-.08

-.06

-.04

-.02

47

0

.02

.04

.06

.08

.1

-.05

-.04

-.03

-.02

-.01

0

.01

Figure 2. Means of GY(1), GY(2), and EGY

2005

2008

2007

2006
GY(1)

GY(2)

48

2009
EGY

2010

-.08

-.06

-.04

-.02

0

.02

.04

.06

Figure 3. Forecast error of family income change

2005

2006

2007

2008

Forecast error of GY(1)

49

2009
Forecast error of GY(2)2010

Figure 4. Distribution of proxy for forward-looking (Always plan)50

Figure 5. Distribution of proxy for forward-looking (Retirement plan)

51

Figure 6. Distribution of proxy for self-control problems (Cannot bear not buying)52

Figure 7. Distribution of proxy for self-control problems (End up procrastinating)53

Figure 8. Distribution of proxy for self-control problems (Assignment plans and their
execution)

54

Figure 9. Distribution of using commitment devices (Use of incentives to finish
homework)

55

0

.1

.2

Fraction
.3

.4

.5

Figure A-1. Distribution of income growth rate (GY(1))

-4

-3

-2

-1

0

56

1

2

3

4

0

.1

.2

Fraction
.3

.4

.5

Figure A-2. Distribution of income growth rate (GY(2))

-3

-2

-1

0

57

1

2

3

0

.05

.1

Fraction
.15

.2

.25

Figure B. Distribution of consumption growth rate (GC)

-4

-3

-2

-1

0

58

1

2

3

4

5

0

.1

Fraction.2.3

Figure C-1. Distribution of total consumption growth rate (GTC)

-.12

-.1

-.08

-.06

-.04

-.02

59

0

.02

.04

.06

.08

.1

0

.1

Fraction.2.3

Figure C-2. Distribution of expectation of consumption growth rate (EGTC)

-.12

-.1

-.08

-.06

-.04

-.02

60

0

.02

.04

.06

.08

.1