Habit Persistence and Keeping Up with the Joneses:
Evidence from Micro Data
Enrichetta Ravina?
New York University
November 2005
Abstract
This paper provides evidence that habit persistence is an important determinant of household
consumption choices, in a setting that allows for heterogeneity and household-specificinterest
rates. By estimating Euler equations for a representative sample of U.S. credit-card account
holders, I find that the strength of external habit, captured by the fraction of the consumption
of the reference group that enters the utility function, is 0.290, and that the strength of internal
habit, represented by household past consumption, is 0.503. My results are robust to the
inclusion of various measures of economic activity in the regression, tests for the presence of
aggregate shocks, liquidity constraints, precautionary saving motives, and learning. Aggregation
of the Euler equations as a weighted average of individual marginal rates of substitution accounts
for heterogeneity and market incompleteness and preserves the results.
? I would like to thank Debbie Lucas, Kent Daniel, Bill Rogerson and Paola Sapienza for long discussions, support
and guidance. Special thanks go to Donald P. Jacobs and the U.S. credit card company that provided the data. I am
also grateful to Roc Armenter, Paco Buera, Francesco Caselli, John Campbell, Janice Eberly, Martin Eichenbaum,
Mike Fishman, Joel Hasbrouck, Johannes Horner, Ming Hsu, Arvind Krishnamurthy, David Laibson, Ron Laschever,
Martin Lettau, Annamaria Lusardi, Stefan Nagel, John Panzar, Marcin Peski, Karl Schmedders, Christopher Polk,
Matthew Rabin, Marciano Siniscalchi, Mark Seasholes, Costis Skiadas, Annette Vissing-Jorgensen, partecipants at
the Russell Sage Foundation Behavioral Camp 2004, and seminar participants at Kellogg School of Management (Fi-
nance), Northwestern University, Cornell, NYU-Stern, Harvard Business School NOM and Finance groups, Brandeis,
UNC at Chapell Hill, London Business School, Stockholm School of Economics, the FED Board of Governors, the
Western Finance Association 2005 Meeting, the Society of Economic Dynamics 2005 Meeting, the 2005 Econometric
Society World Congress, and the NYU Stern Macro Lunch for valuable discussions and suggestions. Financial support
from the Northwestern University Dissertation Year Fellowship, Banca d?Italia and Fondazione Einaudi is gratefully
acknowledged. All remaining errors are mine. Comments are welcome: eravina@stern.nyu.edu.
The ideas of habit formation and social comparisons in consumption choices have a long history
in economics, dating back to Thorstein Veblen?s 1899 "The Theory of the Leisure Class," and James
Duesenberry?s 1949 "Income, Saving, and the Theory of Consumer Behavior". These studies, and
the many studies written thereafter, postulate that individuals derive utility not only from the
level of their current consumption, but also from how their consumption compares to their own
past consumption (internal habit) and the consumption of the people around them ("Keeping Up
with the Joneses," or external habit).
Habit formation models have proven very successful in providing theoretical explanations of a
variety of dynamic asset pricing phenomena and macroeconomic facts. In the asset pricing litera-
ture, they have been employed to explain the equity premium puzzle (Constantinides (1990), Abel
(1990, 1999), Campbell and Cochrane (1999)), the procyclical variation of stock prices (Campbell
and Shiller (1988)), and the countercyclical variation of stock market volatility (Harvey (1989)). In
the macroeconomics literature, habit persistence frameworks explain business cycle facts (Boldrin,
Christiano and Fisher (2001)), the equity home bias (Shore and White (2002)), savings and growth
(Carroll, Overland and Weil (2000)), and consumption?s response to monetary and other shocks
(Fuhrer (2000)). However, despite these models? impressive track record in simulations with aggre-
gate data, there is only mixed evidence on whether they reflect actual preferences. The empirical
studies that have addressed this question so far have mostly followed the macroeconomists? approach
to aggregate consumption, leaving the micro foundations of the phenomenon largely unexplored.
In this paper, I look into actual household consumption decisions and estimate a log-linearized
Euler equation for a representative sample of U.S. credit-card holders. The estimation equation
incorporates internal and external habit motives, using a setting characterized by uninsurable
income shocks and household-specific interest rates.
My empirical strategy builds on the many studies that examine micro-level consumption and
shows two novel features. First, I exploit the detailed information on the evolution of household
financial variables. I use this information to build a more powerful instrument set, and to directly
control for the e? ect of household-specific interest rates, debt burden, and credit availability. These
controls are valuable in disentangling the e? ect of internal habit from that of liquidity constraints.
They also have the advantage of allowing me to estimate the reaction of consumption to household-
specific interest rates, rather than the risk-free rate most of the previous literature has had to use.
Second, I define and test a more intuitive measure of the external reference point of each household
(HH), the consumption level of the city in which the household lives, measured by city-level sales,
1
rather than the consumption of the entire nation, as in previous studies. To address the potential
endogeneity of city-level consumption in the Euler equation, in addition to using an instrumental
variables approach that exploits lagged information, I show that my results are robust to using
an alternative, strictly exogenous measure of changes in the external reference point, whether
somebody in the city of the household wins the lottery.
To measure consumption, I use a novel panel data set, the Credit Card Panel (CCP), which
consists of 2,674 U.S. credit-card accounts located in California, for the period between the third
quarter of 1999 and the third quarter of 2002. I construct the consumption measure as the sum of all
the credit-card purchases over the quarter for the households that are active credit-card users. My
comparisons with the U.S. Census and the Survey of Consumer Finances show that my sample is
representative of the U.S. population for both demographic characteristics and borrowing behavior.
Moreover, this variable exhibits the characteristics we expect to see in household consumption: a
hump-shapedpathoverthelifecycle,andanincreasingrelationshipwithincome. Althoughit
is far from perfect, this measure of consumption allows me to overcome some of the drawbacks of
previously used data sets, such as the Panel Study of Income Dynamics (PSID), which contains only
information on food consumed both at home and at restaurants, and the Consumer Expenditure
Survey (CEX), which provides a very detailed measure of consumption, but only follows households
up to five quarters, and does not contain any household-specific geographic or detailed financial
information.
I find that the strength of external habit, captured by the consumption of the reference group, is
0.29 (significant at the 5% level), and that the strength of internal habit, represented by household
past consumption, is 0.503 (significant at the 1% level). These coe? cients represent the fraction
of city-level aggregate consumption (or household?s own past consumption) that enters the util-
ity function as the reference level to which the household compares itself. A coe? cient of zero
would imply that a household is not influenced by the consumption of its neighbors (its own past
consumption), and the model would then collapse to the standard one used in the literature. On
the contrary, a coe? cient of one would mean that the household only cares about the way its
consumption compares to the neighbors? (its past own consumption), and not about the absolute
level.
These findings provide micro evidence that supports the theories that explain macroeconomic
and asset pricing phenomena by introducing habit persistence in the utility function. The magni-
tude of the coe? cients is in line with the conclusions of these theories, and points to a large e? ect
2
of habit formation.
Iconfirm my findings by using a battery of robustness checks. To control for the possibility that
city and lagged household-level consumption growth capture the e? ect of some omitted variable, I
repeat the estimations adding to the regression the change in city-level unemployment rate, current
and future state-wide income growth rates, and measures of city housing market conditions. I also
use lottery winnings to measure the change in external reference points. To address the concern that
unobservable aggregate shocks might influence the results, I add time dummies to the regression
and repeat the estimation separately for each major occupation in the data set to address the
concern that such shocks might a? ect di? erent HHs in a di? erent way. I also directly test for the
presence of aggregate shocks following the methods in Runkle (1991), and I detect no aggregate
shock. These results reduce the concern that aggregate shocks influence the findings. All the tests
confirm the economic and statistical significance of the habit persistence coe? cients.
Alternative explanations of the findings include the presence of liquidity constraints, precau-
tionary saving motives, and learning about the household?s income profile. These phenomena, like
internal habit formation, cause consumption to adjust slowly to changes in income, and therefore in-
duce a positive correlation between current and lagged consumption growth rates. Following Zeldes
(1989), I test the habit formation hypothesis against a liquidity constraintsmodelbyre-estimating
the Euler equation on two subsamples of unconstrained and credit-constrained HHs. I perform
further tests by including the lagged growth rate of income and a credit constrained indicator into
the regression. The tests show some evidence of liquidity constraints in addition to those accounted
for by the household-specific borrowing rate, but indicate that these liquidity constraints are not
the cause of the results. The precautionary motive and learning stories have similar implications.
I test them further by adding a measure of consumption uncertainty to the regression. Again, the
tests confirm the validity of the habit persistence interpretation of the evidence.
The results di? er from those in Dynan (2000), who investigates internal habit formation in
annual food consumption using the PSID and reaches negative conclusions. A comparison of the
two methodologies indicates that the main reason for these discrepancies is the instrument set used
in this study, due to the availability of household-specific financial information. I find that once I
drop the financial variables from the instrument set I cannot capture the endogenous variables as
well as before and, most important, that the internal habit coe? cient drops from 0.60 to 0.13.
Finally, I examine the aggregate implications of the micro findings. Following Attanasio and
Weber (1993b) and Brav, Constantinides and Geczy (2002), I estimate an Euler equation on ag-
3
gregate data, which I obtain by taking the weighted average of HHs? marginal rates of substitution
(MRS). This procedure takes into account that due to market incompleteness and liquidity con-
straints, at any point in time the MRS of di? erent HHs are not necessarily the same. I find a habit
persistence coe? cient of 0.515 (significant at the 5% level). On the contrary, an econometrician
who uses the same data to calculate the MRS of a representative agent that consumes per capita
consumption will find no evidence of habit persistence.
The paper is organized as follows. Section 1 contains a brief overview of the related literature.
Section 2 describes the data and compares them to those traditionally used in the literature.
Section 3 presents the Euler equation that guides the estimation, describes my empirical strategy,
and illustrates the results. Section 4 contains various robustness checks, and Section 5 examines
alternative explanations for the results. Section 6 examines the aggregate implications of my micro
findings. Section 8 concludes. An appendix, available upon request, contains detailed information
on my sample selection, the features of the data and the model.
1 Related Literature
This paper is related to three main strands of literature: the empirical asset-pricing studies that
investigate habit formation using a representative agent framework; the micro-consumption liter-
ature, from which I borrow the estimation techniques and the focus on the micro data; and the
many studies that examine the e? ect of social influences on happiness and economic choices.
The papers belonging to the first category vary in the instruments used, the horizon analyzed
and the specifics of the estimation equation. These papers reach mixed conclusions. Eichenbaum,
Hansen, and Singleton (1988) find evidence of habit persistence in leisure choices, but not in
consumption, while Heaton (1995) finds evidence of durability at very short horizons and of habit
persistence at quarterly frequencies. Conversely, Constantinides and Ferson (1991) find support for
habit formation in monthly, quarterly and annual data. More recently, Chen and Ludvigson (2003)
finds support for a non-linear form of internal habit. My paper di? ers from these studies in that it
does not use the abstraction of the representative agent, with all the necessary assumptions related
to market completeness and the types of heterogeneity that such an abstraction involves. Instead, I
test the micro story behind habit formation models. I also analyze the aggregate implications of the
findings from a "micro perspective," which takes into account the e? ect of market incompleteness
and liquidity constraints.
4
My study is related to the micro consumption literature, such as Attanasio and Weber (1995),
and the literature surveyed in Deaton (1992) and Browning and Lusardi (1996), for the estimation
techniques. Within this area of study, my paper also provides new evidence on the importance of
accounting for liquidity constraints in the analysis of household consumption decisions. Thus, my
research is related to the papers of Hayashi (1985a) and Zeldes (1989), and to studies of liquidity
constraints. I also analyze the sensitivity of consumption choices to household-specific interest rates,
and find that, contrary to the conclusions reached previously from the analysis of the risk-free rate,
households do respond to prices. Work in this area includes papers by Attanasio and Weber (1993a
and 1995), Ausubel (1999), Gross and Souleles (2002), and Vissing-Jorgensen (2002). Finally, my
paper also builds on Attanasio and Weber (1993b) in my analysis of the aggregate implications of
the micro findings.
At the intersection of these two areas of study there are a few papers that investigate the
implications of habit formation at the micro level. In addition to Dynan (2000), the other such
studies are Lupton (2003) and Brunnermeier and Nagel (2005). Rather than directly examining
consumption, these papers look at the implications of habit formation for households? stock market
investment. In particular, Lupton (2003) estimates a proxy for the habit level and shows that,
consistent with the theory, the habit level is negatively related to the share of the household
portfolio that is invested in stocks. On the contrary, Brunnermeier and Nagel (2005) analyze the
link between idiosyncratic wealth changes and portfolio allocations and conclude against habit
persistence.
Besides the literature on household-level consumption, asset pricing and macroeconomics, my
paper is related to the literature that studies the implications of interpersonal e? ects and time
nonseparabilities in settings that range from status and conformity (Dupor and Liu (2003), Frank
(2005)), happiness (Luttmer (2005)); criminal behavior and welfare choices (Case and Katz (1991),
Bertrand, Luttmer and Mullainathan (2000)); auto purchases (Grinblatt, Kelohariu and Ikaheimo
(2004)), and stock market participation (Hong, Kubik and Stein (2004)). Among these studies, the
closest work to mine is that of Luttmer (2005) who, using various measures of happiness, illustrates
how people care about relative positions and feel worse o? when others around them earn more.
This result is consistent with the finding in my paper that households care about "keeping up with
the Joneses".
5
2DataDescription
To measure household consumption, I use the CCP panel data set, which comprises 2,674 U.S.
credit-card accounts located in California, for the period between the third quarter of 1999 and
the third quarter of 2002. The data provide information on spending and borrowing patterns,
the evolution of interest rates, and credit availability. The data also give a snapshot of the main
economic and demographic characteristics of the account holder and the zip code of the area in
which he or she lives.1 To measure the external reference point, I link these data to city-level
quarterly retail sales data. To perform robustness checks I conflate the data to Census, BLS and
ACCRA city-level information on median house values and rent, median income, unemployment,
price-level data, and mortgage rates.
Table I describe the definition and sources of the variables. I present summary statistics in
Table II. In constructing the sample, to obtain a more meaningful measure of consumption I exclude
people whose accounts are inactive and those who seldom use their credit cards. Following earlier
studies, I also exclude retired account holders, because modeling their consumption and borrowing
decisions is very complex and requires the consideration of issues such as bequests, failing health
and other factors that are not specific to the scope of this study. Section A of Appendix I provides
a detailed description of the sample selection procedure.
2.1 Demographic and Financial Characteristics
The Credit Card Panel (CCP) is representative of the U.S. population in terms of both demographic
characteristics and borrowing behavior. Section B of Appendix I compares the demographics of the
account holders to those of the U.S. population reported in the 2000 U.S. Census. The Appendix
shows that the distributions of income and age are very alike. The main discrepancy is due to the
fact that HHs in the lower income range, and individuals who are either very young or old, are
under-represented in the credit-card data set. The Survey of Consumer Finances (SCF), which is
the main source of information for assets and liabilities of U.S. households, also shares this feature,
because people in those age categories are less likely to own financial instruments. Finally, my data
set contains information on the occupation of the account holders. However, I note that it is harder
to make a comparison with the Census Bureau figures, given the di? erent classification criteria.
My data set also compares well with the U.S. data on household borrowing behavior. The
1 One of the major U.S. credit card issuers, which wishes to remain anonymous, provided the data set.
6
sample is similar to the SCF on the percentage of people who do not pay their credit-card balance
in full at the end of the month. The SCF estimates this percentage at 44.4%. In my sample it is
45.75%. However, studies such as those by Laibson et al. (2000) and Gross and Souleles (2002)
show that the SCF survey su? ers from under-reporting of debt. One of the specific advantages of my
data set is that it is not a survey. Therefore under-reporting and measurement error in the financial
variables are not an issue. Comparisons with a large multi-issuer credit card data set covering the
period between 1995 and 1998 and used by Gross and Souleles (2002) further confirms that the
CCP correctly represents the level of indebtedness and interest rates faced by the households.
2.2 Credit Card Expenditures as a Measure of Consumption
I measure household consumption as the sum of the purchases and cash advances charged on the
credit card each quarter. I note that my data set contains information on the size and timing of
balance transfers, and that I exclude these quantities from the consumption measure.
Because this sample is representative of the U.S. credit-card accounts, an important question
is whether credit-card expenditures are a good measure of household consumption. Panels A and
B of Figure I show that this measure of consumption exhibits the characteristics we expect to see
in household consumption, a hump-shaped path over the life cycle and an increasing relation with
income.
Credit-card purchases represent an increasing fraction of U.S. consumer spending. Roughly
24% of people purchases in the United States are made by credit cards, retail cards, and debit
cards. Statistics from the Survey of Consumer Finances (SCF) and other sources indicate that in
the year 2000, the average American had five or six credit cards and used them to charge over $1
trillion in purchases, more than he or she spent in cash.2 While these statistics provide support for
using credit-card spending as a measure of consumption, they also raise the issue of whether having
information about one credit card is enough. To address this issue, I build quarterly nondurables
and services expenditures from the CEX, following the criteria in Attanasio and Weber (1995).
Using CEX data, I estimate the amount that the average household spends on credit cards is
between $1,143 and $1,212. In comparison, the average credit-card expenditure in my sample is
approximately $700, which shows that the HHs in my data set make heavy use of this credit card
and therefore provide a good measure of their expenditures. Section C of the Appendix provides
2 Lim, Paul J., and Matthew Benjamin. "Digging Your Way Out of Debt", U.S. News and World Report, (3/19/01);
Gerdes and Walton (2002) and Zinman (2004).
7
details on this calculations.
The main advantage of my data in comparison to the PSID is that they provide a more com-
prehensive measure of consumption than food consumed at home or at restaurants, which has been
proven inadequate for many reasons.3 The CEX negates some of the drawbacks of the PSID by
providing a very detailed measure of overall consumption. However, the CEX only interviews fam-
ilies for up to five quarters, and the survey does not contain any household-specific geographic or
detailed financial information.
Onefeatureofthesedataisthatwecanobserveexpendituresfluctuate on this card even though
they stay relatively stable overall, if the appeal of using this card versus another varies over time.
Information on interest rates and credit line variations, unused portion of the credit line and balance
transfers in and out of the card and time dummies helps to control for such e? ects. Finally, I note
that, despite I don?t have information on the fraction of credit-card purchases related to durables
goods, the presence of goods would bias the results against finding the positive coe? cient implied
by internal habit.
Table III compares the mean and standard deviation of my consumption measure to those of
both micro-level and aggregate data, and shows that these measures are comparable. The statistics
confirm that household consumption is very noisy, with a standard deviation of 2.73 if I use all the
observations down to 0.37 if, like Zeldes (1989), I consider only those cases in which the growth
rate of consumption is between -1.1 and 1.1. I also provide a comparison with the CEX data. Since
these are cross sectional averages, I build the same quantity in my data set. The volatility of my
individual consumption measure is 0.33, compared to 0.06 obtained by Brav et al. (2002) for the
1982-1996 period.
I note that the assumption underlying my estimation is the separability between credit-card
expenditures and the rest of the consumption basket. Macroeconomic models of cash and credit
goods can shed light on the issue of separability.
3 First, food is a necessity, its share of expenditure falls with wealth, and it might not represent well the overall
consumption basket. Moreover, using food as a proxy for total consumption implicitly assumes separability between
food and other commodities, and this has been rejected by numerous studies. In particular, Attanasio and Weber
(1995) analyze the bias induced by using PSID food consumption rather than a more general measure and find it
sizeable. Another problem with the PSID measure of consumption is that the way the question about food expenditure
is posed leaves a lot of space to the interpretation of the timing of the variable making the choice of the correct timing
for the instrumental variables very hard. Finally, Runkle (1991) estimates that up to 76% of the variability of food
expenditure is noise.
8
2.3 City-level Consumption
As the reference group of the household I use the city in which the household is located. My measure
of the consumption of the reference group is city-level quarterly per capita taxable sales, which I
obtain from the California Board of Equalization (BOE). I use this variable because it is a very
comprehensive, natural measure of city-level consumption and it is a good aggregate equivalent to
credit card expenditures. The main categories it excludes are necessities (such as food consumed
at home, prescription medicines, etc.) and sales of goods intended for resale.
Also, retail sales constitute an important component of personal consumption expenditures at
the national level. The National Income and Product Accounts (NIPA) constructs this quantity
from a variety of sources, among which a monthly sample of national retail sales plays a central
role. The measure I use here is not a sample, but the total of all reported taxable sales. Therefore,
it is not influenced by sampling procedures and errors. Table IV presents a comparison of the
summary statistics of aggregate consumption constructed with city-level sales data and personal
consumption expenditures on nondurables and services from NIPA. The two measures compare
very well in their variability and are highly correlated. The main di? erence between them is due
to the fact that NIPA includes housing services.
3 Estimation and Empirical Evidence on the Micro Foundations
of Habit Persistence
Households face uninsurable income shocks and borrowing rates that depend on their asset position
and credit history. Davis, Kubler and Willen (2004) show that disregarding borrowing frictions,
and especially the wedge between borrowing and lending rates, can lead to unrealistic predictions
in terms of the amounts borrowed and the portfolio allocations of the households. Despite this
evidence and due to lack of data, empirical analyses of consumption decisions usually assume that
HHs can borrow and save at the same rate. In this paper I depart from these assumptions. In
Appendix II, I present a standard model of intertemporal choice that incorporates uninsurable
income risk and household-specific borrowing rates. The Euler equation I derive from this model
guides my choice of the variables to consider in the empirical analysis and o? ers a framework for
interpreting the results:
u ci,t = ?E t
h
[u ci,t +1 + ?? E Y u hi,t +2](1 + (R fi,t +1 ? 1)1[Y Hi,t +1])(1 + (R Ci,t ? 1)1[B ]) ? ?u hi,t +1
i
(3.1)
9
where 1[Y Ht +1] is an indicator function that equals one for high realizations of income that will allow
theHHtorepaythecreditcardinfullnextperiod.1[B ] is an indicator function that equals one
if the HH has an unpaid balance in the current period.
These results are intuitive. The household decides how much to consume today versus tomorrow
by weighting future utility and di? erent interest rates against the probability that it will actually
face them. If we disregard for a moment the e? ect of the habit stock, we can see that if the HH
consumes $1 less today it loses u c (c t ) and gains the following: in the next period the HH?s credit-
card balance will be $1 lower, making one more dollar available for consumption, and yielding
autilityofu c (c t +1). In addition to this gain, if the income realization is high enough that the
HH is able to repay the balance in full, the HH will earn the gross risk-free rate on the dollar
moved through time and the utility will be u c (c t +1)R ft +1. If the HH carries a balance, consuming
one dollar less today means that the credit-card balance next period will be R Ct dollars less. The
utility deriving from this intertemporal transfer will be u c (c t +1)R Ct if the HH does not have enough
resources to pay the balance in full in period t+1,andu c (c t +1)R Ct R ft +1 if it does and can invest the
dollar charged on the credit card at the risk-free rate. The presence of the habit stock generates
an additional e? ect because when the HH consumes one dollar less today it increases tomorrow?s
utility not only directly, but also indirectly by decreasing its habit level.
I note that HH income does not enter the Euler equation, since HHs optimize the consumption
path and o? set predicted changes in income with asset transactions, while unanticipated changes
in income are reflected in the error term. This result does not hold for those HHs that are liquidity
constrained. A big advantage of the data set is that I can take the degree of liquidity constraints
into account in my empirical analysis.
My assumptions about HHs? expectations on the evolution of income that are consistent with
(3.1). These assumptions are flexible, and include income processes following ARMA models and
both trend and di? erence stationary income processes.
3.1 Specification and Estimation Strategy
Following Deaton (1992), I can express equation (3.1) as a second-order di? erence equation in u ci,t .
The solution is given by:
u ci,t = ?E t
h
u ci,t +1(1 + (R fi,t +1 ? 1)1[Y Hi,t +1])(1 + (R Ci,t ? 1)1[B ])
i
(3.2)
10
Equation (3.2) holds approximately if the number of lags of consumption entering the habit stock
is small relative to the HH lifetime horizon, and if the HH has static expectations about future
interest rates. The equation holds exactly if the interest rates are constant.
Following the consumption literature, I consider a log-linear version of (3.2):
lnu ci,t =ln? + k +lnu ci,t +1 +ln(1+(R fi,t +1 ? 1)1[Y Hi,t +1]) + ln(1 + (R Ci,t ? 1)1[B ]) + ? i,t +1 (3.3)
where ? i,t +1 contains an expectation error, a multiplicative measurement error in consumption and
preference shocks, and k contains second and possibly higher moments of the variables. As is
traditional in the literature, I assume that these variables are either constant or uncorrelated with
the instruments used in the estimation.
The utility function depends not only on the level of current consumption, but also on own past
consumption, the consumption of the reference group and demographic characteristics:
u (c i,t ,H i,t , ? i, h i,t )=u (c i,t ? h i,t ? H i,t )exp(? 0? i,t ) (3.4)
The variable h i,t represents the internal habit stock and depends on the household?s past con-
sumption:
h i,t = ?c i,t ? 1
In this framework, to maintain the marginal utility constant, an increase in past consumption
must be followed by an increase in present consumption, because the habit stock to which con-
sumption is compared is higher. Therefore the HH will try to smooth not only consumption levels,
but also changes. The HH?s consumption will react slowly to changes in permanent income to avoid
the risk of building a habit too quickly. Theoretical papers usually model internal habit formation
by including a large number of consumption lags in the utility function. However, empirical inves-
tigations are usually limited to one lag as adding extra ones would require very long lags of the
instruments to insure exogeneity.
The variable H i,t represents the external habit level. I model it as a function of the consumption
11
ofthecityinwhichtheHHlives:
H i,t = ? 0C i,t + ? ? 1C i,t ? 1 (3.5)
? i,t represents household demographic characteristics. Attanasio and Weber (1993 and 1995)
show that age, family characteristics and labor supply choices are very important explanatory fac-
tors for individual consumption. I condition on the optimal value of these variables by incorporating
them into the utility function in the multiplicative way shown in (3.4):
? i,t = ? 1ag e i,t + ? 2ag e 2i,t + a i + t t + e i,t (3.6)
where a i is an unobservable HH-specifice? ect, t t is a time-varying e? ectthatisconstantacross
HHs, and e i,t an idiosyncratic component orthogonal to the previous two.
I also add to some of the estimations individual characteristics such as the marital status of the
HH?s head, homeownership, income bracket, occupation and, in some specifications, the median
income, house value and unemployment rate in the zip code area of the HH at the end of 1999.
To control for cyclical fluctuations in consumption, I include seasonal dummies in the estimation.
This specification is equivalent to modeling the discount factor as dependent on HH socioeconomic
characteristics and the time and seasonal dummies.
I can rewrite the log-linear Euler equation (3.3) more extensively as:
? ln c i,t = k 1 + ? 0? ln C i,t + ? ? 1? lnC i,t ? 1 + ? ? lnc i,t ? 1 + ? ln(1 + (R fi,t ? 1)Pr[Y Hi,t ])
+? ln(1 + (R Ci,t ? 1 ? 1)1[B ]) + ? 1? ag e i,t + ? 2? ag e 2i,t + Seas.Dummies + ? i,t
(3.7)
where, following Muellbauer (1988) and Dynan (2000), I approximate the expression ln u (c i,t ?
H i,t ? h i,t ) with lnu (c i,t ) ? ln u (H i,t ) ? lnu (h i,t ).4 For simplicity and flexibility, I specify the utility
function to depend linearly on the growth rate of HH and aggregate consumption. This specification
subsumes, among other factors, the isoelastic functional form widely used in the literature. Since
this equation reflects the fundamental dynamics of habit persistence, the results of the estimation
do not constitute only a test of the specific model presented, but also of the general idea of habit
formation. I also note that the estimation takes into account unobserved household heterogeneity
in consumption levels, since the equation is in first di? erences and the HH fixed e? ect a i contained
4 Muellbauer (1988) and Dynan (2000) show that the correlation between this approximation and the exact ex-
pression is higher than 0.90 for reasonable values of the coe? cients.
12
in (3.3) drops out.
The estimation strategy exploits the panel aspect of the data set and the wide cross-sectional
variation in the external reference point faced by households living in di? erent cities. I estimate
the equation by using a GMM procedure with robust standard errors. I treat as endogenous both
household and city-level consumption and the interest rates either because they are simultaneous
or uncertain at the time the HH makes the consumption decision, or because they are a? ected by
measurement error. The instruments I use in the estimation are the second lag of the marginal
tax rate, the city-level unemployment rate, inflation rate, mortgage rate, the state-level disposable
income growth rate, and some individual variables such as lags of the growth rate of debt, amount
charged o? , automatic credit line changes, and a credit constrained indicator. The macroeconomic
literature shows that aggregate and city-level indicators of economic activity are good predictors of
the risk-free rate and city-level consumption growth. The individual variables capture the house-
hold lagged asset position and resources on hand. Table V shows that the autocorrelation in HH
consumption growth rates is negative and consistent with a MA(1) structure that is induced by the
presence of measurement error and taste shocks when true consumption changes are not serially
correlated.5 Therefore, I choose not to use past lags of the consumption growth rate as an instru-
ment. The basic assumption required for identification is that the instruments are uncorrelated
with the preference shocks, measurement error and expectation errors contained in ? i,t . I test this
assumption by performing various tests of overidentifying restrictions, such as the Hansen J test for
the entire instrument set and the di? erence-in-Sargan statistic on the subset of household-specific
instruments. Both tests support the validity of the instruments set.
Finally, the standard errors are robust to arbitrary correlation and heteroskedasticity within
households. However, once the time dummies account for a common aggregate component, I assume
that the errors are uncorrelated across households.
3.2 Empirical Evidence
Table VI reports the main results of my estimation of (3.7). I regress the household consumption
growth on past HH consumption growth, as a measure of internal habit stock, city-level per-capita
consumption and its first lag, as a measure of the external habit level, the household-specific interest
rate, HH demographic characteristics and seasonal dummies. Column I of Table VI estimates
5 Similar values of the autocorrelation coe? cients are obtained by Hayashi (1985b), who analyzes a panel of
Japanese household expenditures.
13
the basic model, and columns II to IV progressively add to the specification family composition,
home ownership and occupation. I correct the standard errors for the non-independence of the
observations within the same household. I also include controls for the evolution of city-level prices
and seasonal dummies in all the regressions.
All versions of the estimates are consistent with the presence of habit formation in household
consumption decisions. The specification reported in column IV of Table VI shows that after con-
trolling for own consumption and demographic and socioeconomic characteristics, the e? ect of
the external habit is significant at the 5% level. This coe? cient captures complementarities in
consumption and represents the fraction of city-level consumption that enters the utility function
as the reference level to which the household compares itself. To meaningfully interpret the quanti-
tative e? ect of this variable, I find it necessary to perform some scaling procedures, since individual
consumption is considerably more volatile than is the city-level one. I scale city-level consumption
by the ratio of the standard deviations of individual and city-level consumption. The strength of
the external habit is 0.29 in the specification reported in Column IV and ranges between 0.258
and 0.295 in the other columns of the table.6 Acoe? cient of zero would imply that the HH is
not influenced by the consumption of its neighbors and the model would collapse to the standard
model used in the literature. A coe? cient of one would mean that the HH cares only about the
way its consumption compares to the neighbors? and not about the absolute level.
The strength of internal habit is also very high: the coe? cient on past household consump-
tion growth is 0.503, which is significant at the 1% level. These findings provide empirical micro
foundations to the theories that explain macroeconomic facts and the equity premium puzzle by
introducing habit persistence in the utility function. Although, market incompleteness and hetero-
geneity don?t permit to compare this coe? cient directly to those in the representative agent models,
it is interesting that the coe? cients are of the same order of magnitude required in Constantinides
(1990) and Campbell and Cochrane (1999) to explain the equity premium puzzle, and in Boldrin
et al. (2001) to explain output persistency.
A natural question is what drives the discrepancy between my findings and Dynan?s (2000).
The di? erences between the two studies are many: the measure of consumption used, food
vs. credit-card expenditures, the annual versus quarterly frequency of observation, the di? erent
6 I note that a variation of this procedure scales ? C i,t by the ratio of the standard deviations of each HH con-
sumption growth rate and its reference group?s consumption growth rate. The external habit coe? cient is slightly
lower, but continues to be statistically significant at the 5% level. Alternatively, I standardize the city-level consump-
tion growth rate and obtain a habit coe? cient with the same statistical significance and an even higher economic
significance than those obtained with the two procedures outlined above.
14
estimation equation, which in her case doesn?t take the variation of the interest rates into account,
and the instrument set. In particular, Dynan uses the second lag of income, hours worked and
job loss as instruments, while I use the second lag of local unemployment rate, the inflation rate,
aggregate income growth rate, mortgage rate, and some individual financial variables. Table VII
presents an attempt to compare the two studies. Columns I, II and III show that neither the annual
frequency nor the HH specific interest rates seem to cause the di? erence, since simply re-estimating
(3.7) with my data annualized or assuming constant interest rates still generates economically and
statistically significant coe? cients on the internal habit parameter. On the contrary, Column IV
shows that excluding the household-specific financial variables from the instrument set, generates a
drop from 0.60 to 0.10 in the internal habit coe? cient, although the coe? cient is still statistically
significant. Panel B of Table VII shows that both the partial R2s and the F tests of the first-
stage regressions are higher and safe from the Stock and Yogo (2002)?s critique when financial
variables are among the instruments. These results indicate that the di? erent findings stem from
the availability of HH specific financial information.
Another result of the paper is my finding that households respond to the price of consumption.
The availability of household-specific borrowing rates and financial information allows to study the
sensitivity of consumption to individual-specific interest rate. Iestimatethattheshort
run elasticity of consumption to the borrowing rate, R C , is -1.876, which is statistically significant
at the 1% level. Previous studies had di? culties in getting precise estimates of this parameter,
as they were forced to use the after tax risk-free rate, which by nature displays very limited cross
sectional variability. The magnitude is consistent with the results of Gross and Souleles (2002),
who estimate that the elasticity of debt, and therefore consumption, to the borrowing rate is -1.3.
The coe? cient on the risk-free rate represents the Elasticity of Intertemporal Substitution
(EIS). The estimates indicate that an increase of one percentage point in the risk free rate leads
on average to an increase of 0.765% in the consumption growth rate. As in most of the literature,
due to the small amount of cross sectional variation exhibited by this variable, I cannot precisely
measure the e? ect. Nevertheless, the value of the coe? cient is very similar to those obtained in
previous studies of individual consumption choices. For some very common specifications of the
utility function the inverse of the EIS constitutes the coe? cient of relative risk aversion. This
variable measures the curvature of the value function, which can be interpreted as the willingness
to substitute consumption across di? erent states of nature. When this is the case the results imply
acoe? cient of risk aversion of 1.31, which is reasonable based on the range of values found by other
15
micro-level studies and surveys.
Consistent with the predictions of economic theory, the coe? cients on age and age squared
indicate that consumption exhibits a hump-shaped path over the life cycle. I include occupa-
tion dummies in the regression, although they are imprecisely measured. Among them, particu-
larly interesting is the positive, although not significant, e? ect on consumption growth of being
self-employed. Since this group can be using the credit card for business related expenses, as a
robustness check I re-estimate all the regressions, this time discarding households headed by a
self-employed individual and find that the results do not change. Column IV also shows that the
e? ect of home ownership and income bracket on consumption growth is negative, although it is so
small as to be almost indistinguishable from zero. I can interpret these findings as mild evidence
of precautionary savings or liquidity constraints: households that own a house or which are in a
higher income bracket have less need to save for a rainy day and they face fewer limitations on the
amount of funds they can borrow. Consequently, they are better able to smooth consumption and,
on average, exhibit a lower consumption growth rate.
The Hansen J statistics of overidentifying restrictions confirms the validity of the instru-
ments in all the specifications. Further, to make sure that the household-specific instruments are
orthogonal to the error term, I compute an additional di? erence-in-Sargan statistic for this group
of instruments. Again, the hypothesis of orthogonality is not rejected. Nonetheless, a too large
instrument set could decrease the power of the overidentifying restrictions tests and also bias the
coe? cients toward the inconsistent ordinary least square estimates. I note that this e? ect would
bias the results against finding habit persistence, because due to measurement error, the OLS coef-
ficients are biased toward zero. In Table VIII, I re-estimate the equation by progressively reducing
the number of instruments, to the point in which the system is just identified. For comparison,
column I reproduces the first column of Table VI. In Column II, I eliminate the marginal tax rate
from the instrument set illustrated above. In Column III I further eliminate the unemployment
rate; in Column IV the inflation rate; in Column V all but one lag of aggregate income; in column
VI the amount charged o? . Finally, in Column VII, I eliminate the automatic credit-line increases.
The resulting instrument set exactly identifies the system and is comprised of the first available
lag of the mortgage rate, the state-level income growth, the household debt growth rate and the
credit-constrained indicator. Among these variables the instrument that is most relevant for the
prediction of city-level aggregate consumption is the mortgage rate, followed by local unemployment
and inflation rate. The coe? cientonincomegrowthrateisstatisticallysignificant, but extremely
16
small. The results of this test are very encouraging, because the coe? cients on ? C t , ? c t ? 1 and
R C either remain approximately the same or increase slightly, and continue to be statistically sig-
nificant.7 The coe? cient that is most sensitive to the reduction of the instrument set is that on the
risk-free interest rate, which is sometimes negative, even though very close to zero. However, this
coe? cient is very imprecisely measured. Also, I report the R 20 sfromthefirst stage regressions
for Table VI at the bottom. The value of the adjusted R 2s are very good. The F statistic shows
that the coe? cients on the instruments are statistically di? erent from zero and way outside the
critical values indicated by Stock and Yogo (2002) in relation to concerns of weak instruments. The
external habit variable in some of the regressions presents an exception. The value of the F tests
are way outside of the critical interval required by traditional theory, but they are sometimes too
low to dismiss the possibility that the variable is weakly instrumented.
4 Robustness Checks
A central focus of the social interaction literature is finding out why people who belong to the same
group behave similarly. Manski (1993) identifies three distinct reasons why it could happen: the
people in the group face the same shocks, they have similar characteristics, which lead them to
behave similarly, and social interactions. Given the data usually available to the econometrician,
the identification of the mechanisms at work in the various situations is often problematic. De-
spite the use of lagged information to instrument for the contemporaneous city-level consumption
growth rate, there might still be questions about the endogeneity of this variable. To address this
issue, I analyze the e? ect of a strictly exogenous random change in the external reference point of
the household: the event that somebody in the city wins the lottery. I merge the data set with
information about lottery winnings from the California lottery and repeat the estimates reported in
Table VI but now I drop the city-level information from the instrument set, since the city consump-
tion does not enter the estimation equation anymore and use a lottery dummy instead. Table IX
shows that the coe? cient on the lottery dummy is economically and statistically significant across
all the specifications. The other coe? cients are similar to those in Table VI. If we interpret the
lottery dummy as a proxy for the change in the reference points, then the coe? cient indicates that
the fraction of city-level consumption that enters the utility function of the household is approxi-
mately 0.22. The estimation equation also includes the lag of the lottery dummy, which displays
7 These results are not due to a particular choice of which instruments to drop. Results available upon request
show the robustness of the findings to changes in the instrument set.
17
a negative, although not statistically significant, coe? cient. To investigate this aspect further, I
re-estimate all the regressions in Table IX without the lagged dummy. I obtain a coe? cient of 0.13
for the contemporaneous dummy, which is statistically significant at the 5% level. These findings
provide complementary evidence on the e? ect of social comparisons on consumption decisions. I
note that these two measures of the consumption of the external reference group most likely have
e? ect through di? erent mechanisms. In the case of city-level consumption what matters for the HH
is the average of the reference group, while in the case of the lottery, it is the consumption of one
outlier, like the e? ect that the lifestyle of celebrities can have on common people?s consumption.
Another concern is that unobservable aggregate shocks might a? ect the results and generate
biases due to the short time dimension of the panel. In column VI of Table XI, I add time dummies
to the estimation equation to address the case in which I can decompose the shock into economy-
wide and idiosyncratic shocks. However, Mariger and Shaw (1993) show that if these shocks hit
di? erenthouseholdstoadi? erent extent, time dummies do not address the issue. The reason is
that when there is an unexpected shock, HHs make common errors in predicting future income.
As a consequence, surprise changes in income, and therefore consumption today, are correlated
with lagged changes in income (and lagged consumption). In the consumption context the story
could go this way. Suppose everybody expects a recession that does not happen. It is likely that
the lower the predicted income change, the higher will be the surprise. This mechanism generates
a negative correlation between prediction and surprise that goes against finding habit formation.
Nevertheless, I check for the stability of the coe? cients across the major occupations in the data
set, as occupation is one of the main reasons why di? erent economic agents might be a? ected
di? erently by macroeconomic shocks. Table X reports the results. The coe? cient on the internal
habit parameter is statistically significant in five out of six cases and is also very stable, ranging
between 0.425 and 0.546. Following Runkle (1991), I also directly test for the presence of these
aggregate shocks by including year dummies in the regression. I check whether they are valid
instruments by looking at the di? erence in the J statistics from the estimation with and without
these dummies. The di? erence is distributed as a ? 23 and is equal to 7.817. From this evidence
I conclude I cannot reject the null hypothesis of no aggregate shocks. This evidence reduces my
concern that aggregate shocks are the source of the findings.
I further investigate the possibility that the findings are a? ected by an omitted variable problem.
Such problem might causes city-level consumption growth to influence household behavior simply
because it captures some measure of economic activity that helps households predict their income.
18
In other words, I am concerned that the results constitute another facet of the "excess sensitivity"
of consumption to income documented by Flavin (1981), Campbell and Mankiw (1989) and the
many studies thereafter. To exclude this possibility, I add both the current and future growth
rate of income to the Euler equation and perform a horse race between city-level consumption and
income. Unfortunately, my data doesn?t contain household-specific income evolution, and therefore
I use California state income instead. Column I and II of Table XI show that the coe? cient
on the external habit variable is unchanged and significant at the 5% level, while income is not
statistically significant (p-value=0.319 and 0.434, respectively). The first stage regressions exclude
the possibility that this result is due to income being poorly instrumented, since the adjusted R 2 for
the income regression is 0.698. Although it seems reasonable that aggregate income is a better proxy
for individual income than are city sales, perhaps the smaller information contained in the sales is
orthogonal to that contained in aggregate income and therefore relevant in forming expectations.
Encouragingly, Attanasio and Weber (1995) find that once demographic variables and labor choice
are accounted for, individual income doesn?t enter the Euler equation in a significant way. While
indicative, these arguments alone are unconvincing: for example, Lusardi (1996) using micro data
finds evidence of excess sensitivity, so the debate is still open. For this reason, using the PSID, I
directly investigate whether city sales provide any information about household income once state
income is available:
? lnincome indiv idual,it = ? + ? 1? lnI N C OM E state ? lev el,it
+? 2? lnC city ? lev el,it + ? 3ag e i + ? 4ag e 2i + ? it
(4.1)
I also include in the regression dummy variables that capture marital status, occupational
choice, seasonal fluctuations and homeownership. The null hypothesis is that once I control for state
income, the coe? cient on city sales is small and not statistically significant. Table XII confirms
this hypothesis and suggests that the reason why income is not significant in Table IX cannot
be ascribed to the fact that I use state rather than individual income. Some caution should be
exercised in interpreting these results since the time period analyzed spans only from 1997 to 2001.
Nevertheless, the various pieces of evidence presented above, taken together, seem to indicate that
city-level consumption doesn?t proxy for individual income.8 To further control for local economic
activity, in column III and IV of Table XI, I add to the regression the variation in city-level
8 Similar regressions using the growth rate of individual wealth as the dependent variable provide evidence that
city-level consumption doesn?t proxy for this variable either.
19
unemployment rate and median zip code house value and rent: these variables are neither
economically nor statistically significant, while the habit persistence coe? cients are stable and
statistically significant.Again, the result is not driven by poor instruments for city unemployment
rate, since the adjusted R 2 of the first stage regression is 0.84.
In column V of Table XI, I investigate the e? ect of changing the specification and addanextra
lag of household own consumption to the regression. I am interested to see the e? ect ofhow this
simplification on a? ects the estimates, since HH consumption exhibits autocorrelation over time.
The coe? cient on the second lag of HH consumption growth is statistically significant, although
not very big. Most important, the coe? cient on the first lag of consumption growth decreases only
slightly (from 0.503 to 0.453), while the one on city-level consumption actually increases, and the
statistical significance is the same.
Results (available upon request) also indicate that my findings are robust to changes in the
instrument set beyond those reported in Table VIII,andtotheinclusionintheregressionof
various measures of household financial conditions, as the growth rate of debt, and balance transfers
indicators. Column VII of Table XI contains, as an illustrative example, the estimates obtained
by adding the household-specificdebtgrowthrateto the regression, which confirms the
results. I note that the measure of consumption is not a? ected by the presence of balance transfers
on the credit card, because I separately identify and exclude these sums. However, it could be that
HHs that make balance transfers behave di? erently from others in ways that the variables in the
regression cannot control. This robustness test controls for that possibility.
5 Alternative Explanations of the Results
Alternative explanations for my findings include the presence of liquidity constraints, precautionary
saving motives, and learning about one?s own income profile. These phenomena, like internal habit
formation, cause consumption to adjust slowly to predictable changes in income, and therefore
induce positive correlation between current and lagged consumption growth rates.
Liquidity constraints consist in borrowing interest rates that are higher than the lending rates
and quantity constraints on the amount of funds that an HH can borrow. I can control for both of
these aspects in the current setting. One way to test for the presence of liquidity constraints consists
in splitting the sample between unconstrained and credit constrained households. For this purpose,
I build a measure of the tightness of liquidity constraints based on the ratio of unpaid balance to the
20
credit limit. Figure II plots the frequency distribution of this indicator and shows that the majority
of the observations display quite low credit usage, most of the times due to the very high credit limit
they enjoy. Nevertheless, some cases of very high usage and therefore binding credit constraints are
present in the data. Column I and II of Table XIII contain the results of estimating the baseline
regression on subsamples constituted by the lowest and highest quartile of the credit constrained
indicator distribution. The lowest quartile subsample contains the unconstrained HHs for whom
the credit constraint measure is zero; while the highest quartile subsample contains the liquidity
constrained households, for which the measure is above 0.76. If liquidity constraints are the cause
of the correlation between current and lagged household consumption growth rate, I would expect
to see that the past consumption growth rate matters only in the highly constrained subsample.
The estimates indicate that this is not the case.The magnitude of the internal habit coe? cient is
similar and highly significant statistically in both subsamples: 0.565 in the unconstrained sample,
and 0.557 in the liquidity constrained sample. The results are robust to the choice of other cuto?
points. The inclusion of the lagged growth rate of state income in each of the subsample regressions
confirms that income is not economically nor statistically significant (columns III and IV of Table
XIII, respectively). Nevertheless, it slightly decreases the coe? cient on the internal habit parameter
in the unconstrained case and increases it in the constrained one. This result indicates some sign of
liquidity constraints, although they are not strong enough to dismiss the e? ect of habit persistence.
Another interesting result from column I is that keeping up with the Joneses is a phenomenon
typical of higher-income HHs, who are over-represented in the unconstrained group.
Another consequence of binding liquidity constraints is that the HH cannot set the consump-
tion at the optimal level. Therefore I will observe that consumption is too low today relative to
tomorrow, and that the lagged income growth rate is negatively related to current consumption
growth (Zeldes (1989)). Column V of Table XIII shows that when I include the lagged state income
growth rate in the regression, the coe? cient of the internal habit parameter equals 0.502, similar
to 0.503 in the baseline regression, and is statistically significant at the one percent level. On the
contrary, the coe? cient on the income growth rate doesn?t have the expected negative sign and
cannot be statistically distinguished from zero.
I present a further robustness test in Column VI. This test consists of adding the credit-
constrained indicator directly in the regression, where it acts as a proxy of the Lagrange multiplier
on the borrowing constraint. The coe? cient on this variable has the expected sign, although it
is not significantly di? erent than zero. This indicator is increasing in the level of credit line us-
21
age and therefore should display an increasing relationship with the unobserved shadow price of
resources. Since it is not possible to directly test this assertion these results should be considered
only indicative.
All the tests discussed above suggest that the presence of liquidity constraints does not explain
away the results. The precautionary motives story has implications that are very similar to the
liquidity constraints model, and the tests of the significance of lagged income growth and splitting
of the sample contained in column I to V of Table XIII speaks to this alternative as well. HHs
that have low resources available and uncertain future prospects save more and therefore display
a higher growth rate of consumption from one period to the next, much like liquidity constrained
HHs. Following Dynan (1993) and Carroll (1997), I also add the square of household consumption
growth rate to the regression, to capture future household-specific uncertainty. To address Carroll?s
concerns about the validity of group-specific instruments, I include in the instrument set individual
variables proxying for household resources, such as lags of the growth rate of debt, amount charged
o? , automatic credit line changes, and a credit constrained indicator. Column VII of Table XIII
shows that the coe? cient on the square of consumption innovations is neither economically nor
statistically significant and its presence in the regression doesn?t a? ect the estimates of the habit
persistence parameters or the interest rates sensitivities.
The latter test also addresses the hypothesis that consumption reacts slowly to expected income
changes because the HH learns whether the change is permanent or temporary. To the extent that
more volatile consumption indicates more uncertain income and thus more scope for learning,we
should expect higher consumption growth rates for HHs with more volatile ? c it .ColumnVIIshows
that the data do not bear out this hypothesis.
6 Aggregate Implications of the Micro Findings
In addition to characterizing household preferences, does habit persistence matter in the aggregate?
And can the representative agent model capture this phenomenon? I investigate this issue by
aggregating the micro data, with the caveat that, given the relatively short time dimension of the
panel, the results are only suggestive.
Leaving aside the statistical problems of the per-capita-consumption series (Wilcox (1992),
Dynan (2000)), the representative agent framework does not capture heterogenous information
sets, finite lives, and liquidity constraints. These factors cause the marginal rate of substitution
22
(MRS) to di? er across agents and, unless very restrictive conditions are met, the estimates of the
preference parameters obtained with such models can be severely biased. While in the theory, there
are contrasting conclusions on whether these biases arise, the empirical work on aggregation issues
unanimously indicates the crucial importance of accounting for heterogeneity. Brav et al. (2002)
show that in order to obtain plausible asset pricing implications the stochastic discount factor needs
to be constructed as a weighted average of individual MRS. Attanasio and Weber (1993) illustrate
how correct aggregation matters for estimating the EIS and the excess sensitivity of consumption
to income.9
Exploiting the household-level data, I can estimate the Euler equations using a weighted average
of the individual MRS that takes heterogeneity and non linearities into account:
? 1N
NX
i =1
(ln c i,t )=? + ? ? 1N
NX
i =1
(ln c i,t ? 1)+R ft + ? t (6.1)
but also using the per capita MRS, as in the representative agent framework:
? ln
?
1
N
NX
i =1
c i,t
!
= ? + ? ? ln
?
1
N
NX
i =1
c i,t ? 1
!
+ R ft + ? t (6.2)
where c i,t is household consumption, and R ft is the risk-free rate.10
Table XIV contains the estimates from (6.1) and (6.2). As in the micro-level regressions,
household consumption and the risk free rate are treated as endogenous and instrumented with
the second lag of income growth rate, average mortgage rate, and unemployment rate. Column I
shows that when estimating the per capita regression (6.2) there is no evidence of habit persistence:
the coe? cient on past consumption growth rate is actually negative, albeit not statistically di? erent
from zero. Columns II and III illustrate that the estimates display signs of excess sensitivity of
consumption to income. A di? erent picture arises when the properly aggregated quantities are used.
Column IV reports the results of the estimation of (6.1). The habit persistence coe? cient is now
equal to 0.515 and it is statistically significant at the 5% level. This number is quite sizeable, and
9 In the theoretical literature, Mankiw (1986) and Constantinides and Du? e (1996) show that in the presence of
idiosyncratic income shocks the Euler equations don?t depend only on the growth rate of consumption, but also on its
cross sectional variability. On the contrary, Krusell and Smith (1998), show, using calibrations, that in a setting with
transitory idiosyncratic income shocks the mean of the wealth distribution is enough to describe the macroeconomic
aggregates.
10Since, by definition, the representative agent framework is populated only by one consumer, the di? erence between
internal and external reference point dissipates and only the dependence of current consumption growth on last period
growth can be tested.
23
suggests that, once the correct measure of consumption is used, there is evidence of habit formation
also at the aggregate level. Tests of excess sensitivity, reported in Columns V and VI, display no
sign of it, using either the contemporaneous or lagged income growth rate. The Hansen J statistic
indicates that the overidentifying restrictions don?t reject the model, but has low power, due to
the relatively big number of instruments in comparison to the number of observations available. I
have therefore performed some robustness checks by changing the instrument set and found that
the habit persistence coe? cient is relatively stable when the properly aggregated measure is used,
while it varies from -0.8 to 0.15, and it is never significant, when per capita consumption is analyzed.
Although the short time period analyzed makes these findings only indicative, it is striking
that they show a big discrepancy between the two procedures. What are the reasons for this
di? erence? Attanasio and Weber (1993) show that, for any distribution of consumption growth,
the di? erence between ? 1N PNi =1 (lnc i,t ) and ? ln
?
1
N
PN
i =1 c i,t
?
represents the change in the Theil?s
measure of entropy and can be approximated by the first four central moments of the cross sectional
distribution:
? Theil = ? E i lnc i,t ? ? ln (E i c i,t )=? ln
?
1+12? 2,t + 16? 3,t + 124? 4,t
?
+ e (6.3)
where ? k,t represents the kth central moment and e is an approximation residual. If the cross
sectional moments of consumption growth rates change over time, the two measures will move in
an asynchronous way and the per capita regression will be biased. Figure III, panel A, shows
the evolution of E i ln c i,t and ln (E i c i,t ) over time. As the economy slows down, both measures of
aggregate consumption fall, but the di? erence between them widens. Fig. III, panel B, confirms
that the two series not only diverge in levels, but have also di? erent growth rates, which causes
marginal utilities to di? er. To further investigate the origins of the di? erences, Figure IV plots
each of the higher moments of the cross sectional distribution of household consumption included
in (6.3): the cross sectional standard deviation of consumption growth displays a strong seasonal
pattern (Panel A), the skewness is always positive and tends to increase as time passes and the
economy gets deeper into recession (Panel B), and the distribution evolves from fairly flat to quite
peaked (Panel C). Following Attanasio and Weber (1993b), Abel and Eberly (2002), columns VII
to IX of Table XIV report the results of adding to the regression cross sectional standard deviation,
the skewness and the kurtosis, respectively, to see whether this reduces the bias. The estimates
indicate that adding these moments strongly improves the significance of the EIS, but has no
24
e? ect on uncovering the habit persistence revealed by the micro data. These results suggest that
omitted demographic variables and other measures of heterogeneity also play a very important
role. Unfortunately, it is not possible to check directly the e? ects of omitting these variables in the
aggregate regression.
7Conclusions
In this paper I use a novel data set on the credit-card expenditures of a representative sample of
U.S. households to investigate whether household preferences exhibit habit formation.
The estimation results provide support for this hypothesis: I find that the strength of the exter-
nal habit, captured by the fraction of the consumption of the reference group that enters the utility
function, is 0.290; while the strength of internal habit, represented by household past consumption,
is 0.503. My results are robust to the inclusion of various measures of economic activity in the
regression, tests for the presence of aggregate shocks, liquidity constraints, precautionary saving
motives, and learning. The results are also confirmed by the use of lottery winnings in the city
as an independent exogenous measure of the change in the reference point. Another result is the
finding that households respond to the price of consumption. I estimate the short run elasticity of
consumption to the borrowing rate at -1.876, which is statistically significant at the 1% level.
An open issue is whether the results generalize to a more comprehensive measure of consump-
tion. Unfortunately, there are no statistics available on the type of goods bought with credit cards,
so I am unable to check whether these HHs are more likely to exhibit habit formation or to display
status. And yet, the analysis in Section 2 shows that this measure of consumption displays the same
features that we would expect to see in overall consumption. Further the statistics on payment
methods illustrate the exponential pervasiveness of credit-card payments.
Another question is whether we can distinguish internal habit formation from adjustment costs.
Gabaix and Laibson (2002) build a model based on adjustment costs. Their model shows aggregate
implications that are observationally equivalent to habit persistence. The individual behavior be-
hind these dynamics is however one of infrequent adjustments that in the micro data would generate
a negative, rather than a positive, coe? cient on the lagged consumption growth. Nevertheless, it
is always possible to model the adjustment costs in a di? erent way and develop a setting that is
observationally equivalent to internal habit. For example, quadratic adjustment costs would gen-
erate these results. However, while this type of adjustment costs is intuitively appealing for firms
25
making capital investments, it is not clear why a consumer should face psychological or physical
costs that would induce her to buy something in installments of increasing amounts over time. On
the contrary, search costs and the cost of processing information or paying attention would lead to
a framework similar to that of Gabaix and Laibson (2002).11 While these remarks are suggestive,
one would like to directly test this hypothesis; unfortunately, very detailed data on good purchased
and possibly survey evidence would be necessary to address this question.
Finally and most important, these findings provide micro evidence in support of the theories
that explain macroeconomic and asset pricing phenomena by introducing habit persistence in the
utility function. Most of this work is based on a representative agent framework, and although a
direct parallel between the magnitude of the coe? cients cannot be made, my findings are line with
those the theoretical models require for habit persistence to explain the macroeconomic and asset
pricing phenomena in question. However, most important for policy making, and to understand
what drives consumption, saving and financial investments decisions, is that these preferences are
not the artifact of aggregation, but rather a feature of the decision making by the households in
the economy. The results in this paper suggest that this is the case. A related question is whether
these phenomena matter in the aggregate. Section 6 indicates that, once I aggregate individual
consumption choices properly, and take into account heterogeneity and nonlinearity of marginal
utility, habit persistence is present at the aggregate level as well. Theoretical investigation of the
aggregate implications of heterogenous households exhibiting habit persistence and facing liquidity
constraints is an important task for future research.
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29
Fig. I
Panel A
Panel B
Fig. I ? Plot of average quarterly credit-card expenditures against age (Panel A) and income
bracket (Panel B).
Consumption over the life cycle
0
200
400
600
800
1000
1200
1400
1600
18 28 38 48 58 68 78 88 98
Age
Quarterly Consumption
Relationship between Consumption and Income
380
480
580
680
780
880
980
1080
0246810
Income Bracket
Quarterly Consumptio
n
Fig II
Fig . II ? Frequency distribution of the credit-constrained indicator. This variable is calculated as
the ratio between unpaid balance and credit line.
Distribution of credit usage
58.21%
6.77% 3.93%
2.98% 2.85% 2.53% 2.80% 3.17% 3.37%
7.23% 6.16%
0%
10 %
20%
30%
40%
50%
60%
70%
<0.10
0.10-0.20
0.20-0.30
0.30-0.40
0.40-0.50
0.50-0.60
0.60-0.70
0.70-0.80
0.80-0.90
0.90-1.00
>1.00
Credit-Constrained Indicator
Fig. III
Panel A
Correctly aggregated and per-capita aggregate consumption
0
1
2
3
4
5
6
7
8
qdate
1999q4
2000q1
2000q2
2000q3
2000q4
2001q1
2001q2
2001q3
2001q4
2002q1
2002q2
Panel B
Growth rates of correctly aggregated and per-capita aggregate consumption
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
1.20
qdate
1999q4
2000q1
2000q2
2000q3
2000q4
2001q1
2001q2
2001q3
2001q4
2002q1
2002q2
2002q3
Fig. III ? Aggregate consumption series, constructed from the credit card data. The blue line
represents the correctly aggregated variable, as in (7.1), and the pink line represents per-capita
consumption, as in (7.2).
Fig. IV
Evolution of standard deviation, skewness and kurtosis of the cross sectional distribution of
household consumption growth rates
Evolution of the cross sectional standard deviation of
household consumption growth
400
500
600
700
800
900
1000
qdate
1999q4
2000q1
2000q2
2000q3
2000q4
2001q1
2001q2
2001q3
2001q4
2002q1
2002q2
2002q3
Evolution of the cross sectional skewness of
household consumption growth
0.00
0.50
1.00
1.50
2.00
2.50
3.00
qdate
1999q4
2000q1
2000q2
2000q3
2000q4
2001q1
2001q2
2001q3
2001q4
2002q1
2002q2
2002q3
Evolution of the cross sectional kurtosis of household
consumption growth
0.00
1.00
2.00
3.00
4.00
5.00
6.00
qdate
1999q4
2000q1
2000q2
2000q3
2000q4
2001q1
2001q2
2001q3
2001q4
2002q1
2002q2
2002q3
Table I
Data Sources and Variables Description
Variable Description Source
? cit Household consumption growth rate
Amount charged on the credit cardduring the quarter for purchases and
cash advances. I construct growth rates by taking the difference in the
logarithms of this variable between time t and (t-1)
Credit card data set
? Cjt External Reference Point: Citi-level consumption growth rate
city level quarterly taxable sales, defined as "the dollar amount of
California retail transactions, excluding those transactions specifically
exempt from the California Sales and Use tax". This measure excludes
prescription medicines, sales of nontaxable items such as some food
products consumed at home and prescription medicines, and taxable
transactions disclosed by BOE audits. A detail description is available
in "Publication Number 61, Sales and Use Taxes: Exemptions and
Exclusions" (March 2003). People not living in a city are associated to
the nearest one by geographic matching based on distance between zip
code's centroids. The average distance between the centroids of the
originating and matching point for HHs not living in a city is 1.1
miles, while the median is 0.4 miles. I construct per capita sales by
dividing this quantity by the city population available from Current
Population Survey at annual intervals.
State Board of
Equalization (BOE)
Financial Variables
RCit Household-specific Borrowing Rate
Interest charged on the debt outstanding on the credit card, calculated
by taking the ratio of the total charges incurred in a period (finance
charges, late charges and over the limit charges) to the balance
outstanding.. It is different from the stated APR, because it takes into
account compounding and the effective period of time over which the
money is borrowed. This results in a more accurate measure of the cost
of borrowing
Credit card data set
Rft Risk Free Rate
3-month T-bill rate. It represents the risk free at which the HHs are
supposed to invest the funds that are left after paying the balance on
the credit card.
Federal Reserve
Bank of St. Louis
(FRED)
Credit constrained
indicatorit
Ratio of debt outstanding to credit limit.It captures credit availability Credit card data set
? debtit Household-specific Debt Growth Rate
Amount of the credit card balance unpaid and on which the HH is
charged interest. Two measures of debt are considered: debt, which
represents the overall debt on the card, including balance transfers
from other cards. And debt2, which excludes balance transfers and
assumes that of any debt outstanding the HH first repays the newly
generated debt and only after that the one transferred from other cards.
Credit card data set
? credit_lineit Household total credit limit on the card Credit card data set
? charged_offit Amount charged off.
Amount of debt outstanding that the credit card issuer will not be able
to recoup and thus writes down as a loss on the account. The reason is
bankruptcy, both formally recognized by a court or informal.
According to this measure 2.68% of the observations have a positive
amount charged off, corresponding to 0.92% of the HHs.
Credit card data set
Balance Transferit Amount of debt outstanding on another credit card and transferred to
this one, or transferred from this card to another. The total number of
balance transfers is 562, equal to 1.6% of the observations. The
measure of consumption doesn't include balance transfers.
Credit card data set
Demographic Variables
Age Age of the main account holder as of July 1999. Credit card data set
Marit_status Dummy variable equal to one if the main account holder is married as
of July 1999
Credit card data set
Homeowner Dummy variable equal to one if the HH owns the house it lives in. Credit card data set
Income bracket Income category the HH belongs to Credit card data set
Occupation dummies dummy variables indicating the occupation of the primary card holder Credit card data set
Self_empl Dummy variable equal to one if the HH head is self-employed. Credit card data set
Marginal Tax Rate Marginal tax rate faced by a family or single individual in a given
income bracket
Internal Revenue
Service (IRS)
Zip Code-Level Economic Variables
Median House Value Median value of the house for a specific sample of owner-occupied
houses in the 2000 U.S. Census. The value is the respondent's estimate
of how much the property would sell for if it were for sale.
2000 U.S. Census
Median Rent Median rent asked in the zip code area. No adjustment is made for the
inclusion of utilities and fuel.
2000 U.S. Census
City-Level Economic Variables
Mortgage Ratet Average mortgage rate faced by people living in the city in a given
quarter.
American Chamber
of Commerce
Research Association
(ACCRA)
? ln U_ratet Quarterly average of the monthly MSA level unemployment rate Bureau of Labor
Statistics (BLS)
Inflation Ratet All Urban Consumers Price Index, base 182:84, not seasonally
adjusted. The quantities are deflated using the BLS Consumer
Price Index of the MSA to which they belong (Los Angeles, San
Francisco-San Jose or the index for the West Region ).
Bureau of Labor
Statistics (BLS)
Lottery Dummy variable equal to one if the HH lives in a city in which there
has been a lottery winning in that quarter
California Lottery
Prop. annuity fraction of the winners who opt to receive the prize in installments,
rather than in a lump-sum payment
California Lottery
Total winnings Total $ winnings in the city where the HH lives, in a given quarter California Lottery
State-Level Economic Variables
? lnincomet Growth rate of quarterly per-capita disposable income in current
dollars
California
Department of
Finance
Table II
Summary Statistics
Mean Median Std. Dev.
Individual Consumption 701.19 114.92 1596.92
growth rate -0.12 0.00 2.73
Aggregate Consumption 2367.22 2239.58 975.53
growth rate 0.01 0.03 0.19
RCit 16.95%0.00%114.65%
Rf 3.88%4.42%1.71%
Inflation rate 0.79% 0.87% 0.46%
DEMOGRAPHIC VARIABLES
Age 46 45 15
Marital Status (% married) 44.76%
Home Owner (%) 74.88%
Marginal Tax Rate 28.44% 28.00% 7.37%
CHARACTERISTICS of the
CONTRACT
Unpaid balance $1,060.05 $0.00 $2,048.60
Credit Line $8,823.51 $10,000.00 $3,733.95
Charged Off $152.33 $0.00 $1,058.07
dummy 0.027 0.000 0.160
Credit-Constrained Indicator 0.33 0.07 0.41
Balance Transfers $132.64 $0.00 $1,004.97
dummy 0.016 0 0.126
ZIP CODE-LEVEL DATA
Median House Value $258,980.80 $222,700.00 $146,479.10
Median Income $54,618.55 $50,825.00 $19,602.71
Rent $791.10 $752.00 $245.95
Unemployment Rate 6.33% 5.49% 3.62%
CITY-LEVEL DATA
Mortgage Rate 7.32% 7.21% 0.59%
Unemployment rate 5.07% 4.43% 3.22%
Lottery 0.0501906 00.2183412
Prop. Annuity 0.0021785 0 0.0466238
Total winnings 156133.4 0 3095676
STATE-LEVEL DATA
Personal Income $26,792.17 $26,906.59 $895.74
Table III
Mean and Std. Dev. of Individual Consumption
In this Table I compare the mean and standard deviation of my measure of consumption to data from the
publicly available data sets traditionally used in the literature: the Panel Study of Income Dynamics (PSID),
the Consumer Expenditure Survey (CEX) and aggregate data.
Credit Card Panel Comparison data set
Mean Std.Dev. Mean Std.Dev.
Individual Data
All -0.120 2.730
-3.3/3.3 0.005 0.870
-1.1/1.1 -0.002 0.368 0.000 0.32*
Cross Sectional Data
All 0.014 0.330 -0.01* 0.06*
Aggregate Data
All 0.000 0.013 0.003*** 0.009***
* Comparison data set: PSID, data from Zeldes (1989)
* Comparison data set: CEX, data from Brav et al. (2002)
* Comparison data set: aggregate data, from Constantinides et al. (1991)
Table IV
Aggregate Local Consumption
Comparison with NIPA Aggregate Consumption
In this table I compare the city-level sales data that I use to construct the measure of the external reference
point to the aggregate data traditionally used in the literature: the aggregate consumption from the National
Income and Product Accounts (NIPA). The main difference between the two measures is the lack of
housing services in the California aggregate sales.
California
Aggregate Sales
Non-durables
and Services
(NIPA)
Mean 3674.3945659.72
Median 3669.729 5737
Std. Dev. 402.2181 404.1349
Correlation Coefficient 0.8583
For a definition of the California aggregate sales see Table I
Table V
Autocorrelations of Household Consumption
? ct ? ct-1 ? ct-2 ? ct-3
? ct 1
? ct-1 -0.3863 1
? ct-2 -0.0281 -0.3866 1
? ct-3 -0.0212 -0.0317 -0.3914 1
Table VI
Basic Estimation
In this Table I present the results of the estimation of the Euler equation:
? lnci,t=k1+? 0? lnCi,t+? -1? lnCi,t-1+?? lnci,t-1+? ln(1+(Ri,tf-1)Pr[Yi,tH]) +? ln(1+( Ri,tC 1)1[B])+? 1? agei,t+? 2? agei,t+? i,t
Column I estimates the basic model, while columns II to IV progressively add to the specification family composition,
home ownership and occupation.
The standard errors are corrected for the non-independence of the observations within the same household. In addition,
controls for the evolution of city-level prices and seasonal dummies are included in all the regressions.
(I) (II) (III) (IV)
RCt -1.727*** -1.845*** -1.842*** -1.876***
(0.000) (0.000) (0.000) (0.000)
Rft 0.448 0.770 0.765 0.824
(0.537) (0.381) (0.384) (0.349)
? Ct 0.258*** 0.295** 0.294** 0.290**
(0.005) (0.024) (0.024) (0.026)
? ct-1 0.530*** 0.501*** 0.502*** 0.503***
(0.000) (0.000) (0.000) (0.000)
? Ct-1 0.007 0.014 0.014 0.013
(0.195) (0.176) (0.176) (0.189)
Age 0.004 0.004 0.004
(0.334) (0.363) (0.305)
Age2 -0.000 -0.000 -0.000
(0.141) (0.152) (0.127)
marital status 0.022 0.023 0.023
(0.399) (0.375) (0.386)
homeowner -0.018 -0.017 -0.017
(0.656) (0.676) (0.668)
income bracket -0.003 -0.004 -0.002
(0.524) (0.470) (0.705)
self_empl 0.085 0.071
(0.158) (0.252)
Occupation dummies Yes
Seasonal dummies Yes Yes Yes Yes
# Households 2220 1432 1432 1432
Hansen J statistic 8.725 7.712 7.730 7.853
(pvalue) 0.463 0.441 0.562 0.441
C statistic+ 1.021 3.748 3.761 3.747
(pvalue) 0.907 0.563 0.439 0.549
Adj. R-squared 0.214 0.226 0.226 0.225
Robust p values in parentheses
* significant at 10%; ** significant at 5%; *** significant at 1%
+ Instruments tested: lags of debt outstanding, amount charged off, change in credit line and credit constraints
measure.
A description of the variables is reported in Table I.
Instrument set: marginal tax rate, the local unemployment rate, the inflation rate, aggregate disposable income
growth rate, mortgage rate, and some individual variables such as lags of the growth rate of debt, amount
charged off, automatic credit line changes, and a credit constrained indicator.
First Stage Regressions
(I) (II) (III) (IV) Adj. R2 Adj. R2 Adj. R2 Adj. R2
RCt 0.0635 0.0602 0.0605 0.0618
Rft 0.9543 0.9543 0.9543 0.9543
? Ct 0.2351 0.3666 0.3666 0.3661
? ct-1 0.0281 0.0282 0.0281 0.028
p-value p-value p-value p-value
RCt 0.0000 0.0000 0.0000 0.0000
Rft 0.0000 0.0000 0.0000 0.0000
? Ct 0.0000 0.0000 0.0000 0.0000
? ct-1 0.0000 0.0000 0.0000 0.0000
Table VII
Comparison with Dynan (2000)
This Table illustrates the comparison between my results and Dynan (2000). In particular, I re-estimate the same
regression as in Col (V) of Table VI using an annualized measure of credit card consumption and of the other variables:
? lnci,t=k1+? 0? lnCi,t+? -1? lnCi,t-1+?? lnci,t-1+? ln(1+(Ri,tf-1)Pr[Yi,tH]) + ? ln(1+( Ri,tC -1)1[B])+? 1? agei,t+? 2? agei,t+? i,t
Col (I) presents the baseline estimation; Col (II) investigates the effect of estimating the above regression without the
external habit, as Dynan?s estimation doesn?t contain this variable. Col (III) drops the HH-specific financial variables
from the instrument set; while Col (IV) drops the interest rate from the estimation equation, as Dynan considers an
Euler equation with constant interest rates. The standard errors are corrected for the non-independence of the
observations within the same household. In addition, controls for the evolution of city-level prices and seasonal
dummies are included in all the regressions.
(I) (II) (III) (IV)
RCt -0.076 -0.116 -2.100
(0.487) (0.246) (0.352)
? Ct 0.110 0.985*** 1.055***
(0.931) (0.000) (0.000)
? ct-1 0.602 0.662*** 0.139** 0.109
(0.422) (0.000) (0.048) (0.179)
Age -0.001 -0.001 0.000 0.007
(0.837) (0.622) (0.910) (0.367)
Age2 0.000 0.000 -0.000 -0.000
(0.829) (0.584) (0.872) (0.346)
marital status 0.006 -0.000 0.010 0.045
(0.740) (0.974) (0.529) (0.273)
self_empl -0.031 -0.031 -0.038 -0.014
(0.519) (0.151) (0.290) (0.839)
homeowner -0.001 -0.005 0.006 -0.035
(0.964) (0.790) (0.815) (0.539)
income bracket -0.002 -0.001 -0.003 -0.008
(0.559) (0.539) (0.439) (0.287)
Occupation dummies Yes Yes Yes Yes
Seasonal dummies Yes Yes Yes Yes
# Households 1330 1450 1336 1336
Hansen J statistic 29.145 29.067 1.616
(p-value) 0.060 0.204
Adj. R-squared -0.490 0.712 0.441 0.386
Robust p values in parentheses
* significant at 10%; ** significant at 5%; *** significant at 1%
A description of the variables is reported in Table I.
Instrument Set: second lag of local unemployment rate, the inflation rate, aggregate income growth rate,
mortgage rate, household-specific debt growth rate and credit-constrained indicator.
First stage Regressions Regressions
Variable Column Partial R2 F test P-value
RCt 0.0846 130.9 0.0000
? Ct 0.14 230.61 0.0000
? ct-1
(I)
0.1587 267.17 0.0000
RCt 0.0768 126.08 0.0000
? ct-1
(II)
0.162 292.84 0.0000
RCt 0.0014 3.89 0.0086
? Ct 0.0744 226.34 0.0000
? ct-1
(III)
0.0814 249.38 0.0000
? Ct 0.0744 226.34 0.0000
? ct-1
(IV)
0.0814 249.38 0.0000
Table VIII
Effect of a smaller IV set
In this table I perform the same regressions as in Column I of Table VI with a progressively smaller instrument set. The
instruments used in the estimation in the paper are: marginal tax rate, various lags of local unemployment rate, inflation
rate, aggregate disposable income growth rate, mortgage rate, and some individual variables such as lags of the growth
rate of debt, amount charged off, automatic credit line changes, and credit constrained indicator.
In Column II, I eliminate the marginal tax rate from the IV set illustrated above. In Column III I further eliminate the
unemployment rate; in Column IV the inflation rate; in Column V all but one lags of aggregate income; in column VI
the amount charged off; finally, in Column VII, I eliminate the credit line increases. The IV set I am left with exactly
identifies the system and is composed by the first available lag of mortgage rate, aggregate income growth, household
debt growth rate and credit constrained indicator.
The results show that restricting the IV set doesn?t change the coefficients on ? Ct and ? ct-1, or their significance. The
coefficient that is most sensitive to the shrinking of the IV set is that on the risk free interest rate, which happens
sometimes to be negative, even though very close to zero and very imprecisely measured.
(I) (II) (III) (IV) (V) (VI) (VII)
RCt -1.727*** -1.743*** -1.742*** -1.750*** -1.738*** -1.752*** -1.568***
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
Rft 0.448 0.408 -0.002 0.362 -0.009 -0.024 0.322
(0.537) (0.576) (0.998) (0.670) (0.992) (0.981) (0.762)
? Ct 0.258*** 0.266*** 0.370*** 0.283** 0.354** 0.352** 0.365**
(0.005) (0.004) (0.001) (0.036) (0.031) (0.034) (0.029)
? ct-1 0.530*** 0.527*** 0.530*** 0.529*** 0.526*** 0.523*** 0.575***
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
? Ct-1 0.007 0.007 0.010* 0.007 0.009 0.009 0.010
(0.195) (0.202) (0.083) (0.247) (0.190) (0.215) (0.188)
# of Households 2220 2220 2220 2220 2220 2220 2220
Hansen J statistic 8.725 8.292 3.322 2.286 0.819 0.816 -
(p-value) 0.463 0.405 0.650 0.683 0.664 0.366 -
Adj. R-squared 0.214 0.211 0.158 0.203 0.168 0.169 0.156
Robust p values in parentheses
* significant at 10%; ** significant at 5%; *** significant at 1%
Table IX
External Reference Shifts measured by Lottery Winnings
In Column (I) to (IV) of this Table, I reproduce the estimations in Table VI, using lottery winnings dummies instead
than the city consumption. I estimate the following Euler equation:
? lnci,t=k1+? 0Lottery+? -1Lottery_lagged+?? lnci,t-1+? ln(1+(Ri,tf-1)Pr[Yi,tH]) +? ln(1+( Ri,tC 1)1[B])+? 1? agei,t+? 2? agei,t+? i,t
In Column (V), I repeat the regression in Column (I), adding some additional controls about the lottery event: the
fraction of winners opting for annuity payments and total winnings in the city in the given quarter.
The standard errors are corrected for the non-independence of the observations within the same household. In addition,
controls for the evolution of city-level prices and seasonal dummies are included in all the regressions.
(I) (II) (III) (IV) (V)
RCt -1.664*** -1.854*** -1.856*** -1.867*** -1.863***
(0.000) (0.000) (0.000) (0.000) (0.000)
Rft 1.508*** 1.929*** 1.934*** 1.955*** 1.949***
(0.001) (0.001) (0.001) (0.001) (0.001)
Lottery 0.136* 0.229** 0.228** 0.229** 0.210**
(0.087) (0.025) (0.026) (0.025) (0.040)
? ct-1 0.548*** 0.537*** 0.537*** 0.538*** 0.539***
(0.000) (0.000) (0.000) (0.000) (0.000)
Lottery_lagged -0.093 -0.164 -0.165 -0.165 -0.156
(0.259) (0.128) (0.125) (0.124) (0.146)
Age 0.004* 0.004* 0.005* 0.005*
(0.070) (0.084) (0.054) (0.054)
Age2 -0.000** -0.000** -0.000*** -0.000***
(0.012) (0.014) (0.009) (0.009)
marital status 0.020 0.021 0.021 0.022
(0.188) (0.173) (0.167) (0.160)
homeowner -0.005 -0.003 -0.004 -0.004
(0.852) (0.908) (0.896) (0.893)
income bracket -0.006 -0.006 -0.006 -0.006
(0.120) (0.101) (0.122) (0.114)
self_empl 0.078** 0.066* 0.066*
(0.043) (0.093) (0.098)
Total winnings 0.000
(0.497)
Prop. annuity -0.245
(0.598)
Occupation dummies Yes Yes
Seasonal dummies Yes Yes Yes Yes Yes
# of Households 24066 15435 15435 15435 15435
Hansen J statistic 9.650 6.737 6.647 6.929 6.918
(p-value) 0.140 0.241 0.248 0.924 0.912
C statistic* 3.214 0.565 0.628 0.476 0.532
(p-value) 0.360 0.904 0.890 0.226 0.227
Adj. R-squared 0.270 0.268 0.268 0.267 0.267
Robust p values in parentheses
* significant at 10%; ** significant at 5%; *** significant at 1%
+ Instruments tested: lags of debt outstanding, amount charged off, change in credit line and credit
constraints measure.
A description of the variables is reported in Table I.
Instrument set: marginal tax rate, aggregate disposable income growth rate and some individual
variables such as lags of the growth rate of debt, amount charged off, automatic credit line
changes, and a credit constrained indicator.
First Stage Regressions
(I) (II) (III) (IV)
Adj. R2 Adj. R2 Adj. R2 Adj. R2
RCt 0.0651 0.0538 0.0566 0.056
Rft 0.9537 0.9536 0.9536 0.9536
? ct-1 0.0247 0.0220 0.0220 0.0221
p-value p-value p-value p-value
RCt 0.0000 0.0000 0.0000 0.0000
Rft 0.0000 0.0000 0.0000 0.0000
? ct-1 0.0000 0.0000 0.0000 0.0000
Table X
Estimations by Occupation
In this Table I reproduce the regression in Column (IV) of Table VI, separately for each of the main occupations in the
data set. The purpose is to control for the stability of the internal habit coefficient across occupations. This can help
address the concern that unobservable aggregate shocks that affect different HHs differently might cause the findings.
The estimation equation is:
? lnci,t=k1+? 0? lnCi,t+? -1? lnCi,t-1+?? lnci,t-1+? ln(1+(Ri,tf-1)Pr[Yi,tH]) +? ln(1+( Ri,tC 1)1[B])+? 1? agei,t+? 2? agei,t+? i,t
Column I estimates the model for a generic group that didn?t specify the occupation, Col. (II) for administrative and
staff, Col. (III) for white collars, Col (IV) for blue collars, Col. (V) for people holding technical jobs, and Col. (VI) for
self-employed. The Appendix contains a more detailed description of these occupations.
The standard errors are corrected for the non-independence of the observations within the same household. In addition,
controls for the evolution of city-level prices and seasonal dummies are included in all the regressions.
(I) (II) (III) (IV) (V) (VI)
RCt -1.906*** -2.532** -1.379 -2.474 -1.191** -1.139
(0.002) (0.022) (0.414) (0.198) (0.037) (0.462)
Rft -0.547 2.600 5.209 1.443 0.491 -6.713
(0.701) (0.341) (0.204) (0.829) (0.830) (0.371)
? Ct 0.434** 0.677 -0.100 0.121 0.302 -0.005
(0.044) (0.131) (0.822) (0.912) (0.125) (0.995)
? ct-1 0.497*** 0.546*** 0.197 0.446* 0.502*** 0.425**
(0.000) (0.000) (0.318) (0.086) (0.000) (0.016)
? Ct-1 0.151 0.136 0.436 3.013 0.405*** 0.965
(0.468) (0.944) (0.871) (0.447) (0.004) (0.784)
Age 0.008 0.009 0.008 -0.038 -0.017 0.023
(0.196) (0.606) (0.767) (0.370) (0.130) (0.384)
Age2 -0.000* -0.000 -0.000 0.000 0.000 -0.000
(0.090) (0.530) (0.710) (0.487) (0.111) (0.273)
marital status 0.016 -0.148 0.024 0.214 0.095 0.059
(0.652) (0.145) (0.864) (0.384) (0.267) (0.565)
homeowner -0.079 -0.232 0.125 0.222 0.008 -0.001
(0.142) (0.250) (0.483) (0.424) (0.927) (0.996)
#of Households 722 160 66 80 265 50
Hansen J statistic 2.414 3.344 6.694 4.873 3.341 2.638
(p-value) 0.660 0.502 0.375 0.301 0.638 0.942
C statistic 1.040 1.427 1.961 3.095 0.898 0.120
(p-value) 0.594 0.490 0.153 0.213 0.502 0.620
Adj. R-squared 0.156 0.259 0.175 0.169 0.121 0.243
Robust p values in parentheses
* significant at 10%; ** significant at 5%; *** significant at 1%
Table XI
Robustness Checks
In this Table I analyze the robustness of the results to the inclusion of various measures of economic activity to the
regression: the state-level income growth rate (Col (I)), the lead of the state-level income growth rate (Col (II)),
change in city-level unemployment rates (Col (III)), housing market conditions (Col. (IV)). I also check the effect of
adding an extra lag of the consumption growth rate (Col. (V)), year dummies to control for aggregate shocks (Col.
VI)), and the growth of household debt (Col. (VII)).
The standard errors are corrected for the non-independence of the observations within the same household. In addition,
controls for the evolution of city-level prices and seasonal dummies are included in all the regressions.
(I) (II) (III) (IV) (V) (VI) (VII)
RCt -1.878*** -1.862*** -1.871*** -1.833*** -2.054*** -1.849*** -1.322***
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.005)
Rft 2.116 1.213 0.550 0.711 0.266 3.113 0.189
(0.174) (0.230) (0.527) (0.432) (0.777) (0.548) (0.835)
? Ct 0.271** 0.268** 0.442** 0.290** 0.311** 0.266** 0.295**
(0.037) (0.045) (0.016) (0.030) (0.020) (0.039) (0.024)
? ct-1 0.501*** 0.507*** 0.509*** 0.503*** 0.453*** 0.508*** 0.445***
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
? Ct-1 0.014 0.012 0.021 0.014 0.016 0.013 0.014
(0.164) (0.251) (0.107) (0.184) (0.105) (0.234) (0.161)
Age -0.000 -0.000 -0.000 -0.004 -0.000 -0.000 0.004
(0.109) (0.135) (0.188) (0.324) (0.261) (0.150) (0.419)
Age2 0.023 0.025 0.021 0.000 0.027 0.025 -0.000
(0.375) (0.360) (0.466) (0.138) (0.348) (0.366) (0.199)
Marit_status -0.014 -0.015 -0.028 0.026 -0.039 -0.014 0.023
(0.724) (0.708) (0.498) (0.336) (0.361) (0.722) (0.401)
Homeowner -0.002 -0.002 -0.003 -0.012 -0.000 -0.002 -0.025
(0.692) (0.712) (0.650) (0.767) (0.956) (0.701) (0.538)
Income bracket 0.068 0.072 0.080 -0.004 0.092 0.071 -0.002
(0.262) (0.248) (0.201) (0.466) (0.158) (0.248) (0.764)
Self_empl -1.878*** -1.862*** -1.871*** 0.065 -2.054*** -1.849*** 0.057
(0.000) (0.000) (0.000) (0.288) (0.000) (0.000) (0.331)
Occupation dummies Yes Yes Yes Yes Yes Yes Yes
? lnincome 0.020
(0.319)
? lnincome _lead 0.012
(0.434)
? ln U_rate -0.003
(0.465)
Median House Value 0.000
(0.705)
Rent 0.000
(0.544)
(? ct)2 -0.013
(0.527)
? ct-2 0.170***
(0.000)
? lndebtt -0.157*
(0.060)
Year dummies Yes
Seasonal dummies Yes Yes Yes Yes Yes Yes Yes
# Households 1432 1432 1432 1432 1432 1432 1432
Hansen J statistic 6.986 7.245 4.546 7.890 12.705 5.397 9.695
(p-value) 0.538 0.524 0.576 0.545 0.176 0.524 0.287
C statistic+ 5.224 3.204 2.892 3.933 5.665 3.204 2.487
(p-value) 0.265 0.510 0.715 0.415 0.226 0.798 0.647
Adj. R-squared 0.230 0.231 0.176 0.219 0.249 0.232 0.264
Robust p values in parentheses
* significant at 10%; ** significant at 5%; *** significant at 1%
+ Instruments tested: lags of debt outstanding, amount charged off, change in credit line and credit constraints measure.
A description of the variables is reported in Table I.
Instrument set: marginal tax rate, the local unemployment rate, the inflation rate, aggregate disposable income growth rate, mortgage rate, and some
individual variables such as lags of the growth rate of debt, amount charged off, automatic credit line changes, and a credit constrained indicator.
Table XII
Does Local Aggregate Consumption Proxy for Individual Income?
In order to answer this question I use household-level data from the PSID, in which individual income is provided.1 I
investigate whether local aggregate consumption provides any information about household income once aggregate
income is available. The regression is the following:
? lnincomeindividual, it= ? + ? 1? lnINCOMEaggregate, it + ? 2? lnCcitylevel, it + ? 3agei+ ? 4age2i+? it
Dummy variables capturing marital status, occupational choice, seasonal fluctuations and whether the individual owns the house in
which he lives are included in some of the regressions as well.
The null hypothesis is that once we control for aggregate income, the coefficient on aggregate consumption is small
and statistically insignificant. The results below confirm this hypothesis and suggest that aggregate consumption
doesn?t proxy for individual income.
I have also tried the above regression using the growth rate of future HH income as the dependent variable. The results
are presented in columns IV to VI and show that neither aggregate income nor consumption are good predictors of
future individual income. The regression is the following:
? lnincome_leadindividual, it+1= ? + ? 1? lnINCOMEaggregate, it + ? 2? lnCaggregate, it + ? 3agei+ ? 4 age2i +? it
Notice should be given to the fact that the time period analyzed is not very long, spanning from 1997 to 2001.
Unfortunately a longer time series of city-level consumption is not available.
Dependent Variable ? lnincomeindividual, it ? lnincome_leadindividual, it+1
(I) (II) (III) (IV) (V) (VI)
? lnC 0.045 0.066 0.051 0.093 0.057 0.053
(0.550) (0.377) (0.492) (0.290) (0.474) (0.508)
? lnINCOME 2.697*** 2.660*** 2.887*** -0.674 -0.334 -0.525
(0.009) (0.009) (0.005) (0.726) (0.849) (0.768)
Age -0.018** -0.023*** -0.026*** 0.001 -0.000 -0.002
(0.041) (0.010) (0.005) (0.940) (0.967) (0.886)
Age2 0.000* 0.000** 0.000*** -0.000 0.000 0.000
(0.075) (0.022) (0.006) (0.989) (0.915) (0.818)
Marital status -0.057 -0.076 -0.072 -0.077 -0.094 -0.112*
(0.241) (0.144) (0.172) (0.243) (0.153) (0.098)
Homeowner dummy Yes Yes Yes Yes
Occupation dummies Yes Yes
Observations 921 891 891 426 413 413
R-squared 0.017 0.022 0.036 0.019 0.017 0.027
p values in parentheses
* significant at 10%; ** significant at 5%; *** significant at 1%
Sample: households in the PSID living in California. Time span: 1997 to 2001.2
Variables description and definitions: ? lnincomeindividual, it is the quarterly growth rate of household total income; ? lnINC is the
quarterly growth rate of aggregate California per capita income (Source: California DOF); ? lnC is the quarterly growth rate of city-
level aggregate taxable sales and constitutes my measure of aggregate consumption (Source: California DOF); Age is the age of the
head of the household; Marital status is a dummy equal to 1 if the head of the HH is married and 0 otherwise; the Homeowner
dummy equals 1 if the HH owns the house in which it lives and 0 otherwise; the Occupational dummies are dummies that categorize
HH heads in main occupational areas and are built to be as similar as possible to those used in the rest of the paper.
1Unfortunately, this dataset doesn?t contain a good measure of consumption; for other drawbacks of the PSID see Section 3.2.
2 This is the period for which data on taxable sales are available on the California Department of Finance website.
Table XIII
Alternative Explanations: Liquidity Constraints and Precautionary Saving Motives
This Table contains tests of the habit persistence hypothesis against the liquidity constraint and precautionary
saving motive alternatives. The baseline regression to which the results are compared is:
? lnci,t=k1+? 0? lnCi,t+? -1? lnCi,t-1+?? lnci,t-1+? ln(1+(Ri,tf-1)Pr[Yi,tH]) +? ln(1+( Ri,tC -1)1[B])+? 1? agei,t+? 2? agei,t+? i,t
Col. (I) and (II) re-estimate the regression on two sub-samples of unconstrained and credit constrained HHs;
col (III) and (IV) perform the same regression as (I) and (II) adding the lag of income growth rate. Col (V)
adds the lagged growth rate of income to the regression; Col (VI) adds a credit constrained indicator. Col
(VII) adds the square of consumption growth to the regression.
The standard errors are corrected for the non-independence of the observations within the same household. In
addition, controls for the evolution of city-level prices and seasonal dummies are included in all the
regressions.
(I) (II) (III) (IV) (V) (VI) (VII)
RCt 1.788 -1.109 -0.141 -2.395 -1.879*** -0.603 -1.695***
(0.390) (0.829) (0.939) (0.638) (0.000) (0.423) (0.000)
Rft -2.313 3.906 -6.201* 7.733 0.414 0.161 1.543
(0.556) (0.350) (0.099) (0.124) (0.694) (0.870) (0.287)
? Ct 0.644** 0.186 0.267 0.233 0.274** 0.240* 0.290**
(0.035) (0.674) (0.392) (0.598) (0.035) (0.063) (0.024)
? ct-1 0.565*** 0.557*** 0.416*** 0.693*** 0.502*** 0.498*** 0.504***
(0.000) (0.007) (0.005) (0.002) (0.000) (0.000) (0.000)
? lnincomet-1 0.081** -0.076 0.012
(0.048) (0.124) (0.473)
? Ct-1 0.023 -0.362*** 0.016 -0.396*** 0.014 0.011 0.014
(0.307) (0.005) (0.269) (0.003) (0.165) (0.253) (0.184)
Age -0.015 0.001 -0.006 0.006 0.005 0.001 0.004
(0.241) (0.963) (0.596) (0.708) (0.276) (0.900) (0.339)
Age2 0.000 0.000 0.000 -0.000 -0.000 -0.000 -0.000
(0.384) (0.968) (0.842) (0.736) (0.111) (0.775) (0.149)
Marit_status 0.026 -0.048 0.009 -0.038 0.023 0.012 0.026
(0.759) (0.490) (0.902) (0.590) (0.372) (0.623) (0.372)
Homeowner -0.072 -0.148 -0.021 -0.159 -0.015 0.007 -0.017
(0.529) (0.247) (0.840) (0.236) (0.713) (0.839) (0.691)
Income bracket 0.015 0.027* 0.008 0.024 -0.002 0.001 -0.003
(0.437) (0.094) (0.585) (0.173) (0.698) (0.822) (0.653)
Self_empl -0.188 0.243 -0.031 0.287 0.068 0.063 0.067
(0.473) (0.347) (0.885) (0.271) (0.266) (0.177) (0.296)
Credit constr. indic. 0.062
(0.327)
(? ct)2 -0.013
(0.527)
Occupation dummies Yes Yes Yes Yes Yes Yes Yes
Seasonal dummies Yes Yes Yes Yes Yes Yes Yes
# Obs 773 347 773 347 1432 1432 1432
Hansen J statistic 5.400 3.298 3.780 1.028 7.491 7.426 7.567
(p-value) 0.483 0.654 0.779 0.906 0.485 0.406 0.472
C statistic 0.493 0.000 0.079 0.002 5.174 2.911 3.540
(p-value) 0.249 0.990 0.286 0.966 0.270 0.491 0.477
Adj. R-squared 0.229 0.282 0.165 0.240 0.230 0.255 0.233
Robust p values in parentheses
* significant at 10%; ** significant at 5%; *** significant at 1%
A description of the variables is reported in Table I.
Instrument set: marginal tax rate, the local unemployment rate, the inflation rate, aggregate disposable income growth rate, mortgage rate, and some
individual variables such as lags of the growth rate of debt, amount charged off, automatic credit line changes, and a credit constrained indicator.
Table XIV
Aggregate Consumption Regressions
This Table investigates the aggregate implications of household level consumption choices. Columns (I), (II), and
(III) present the results of estimating an aggregate Euler equation based on per capita consumption: (a) ? ln? ci,t=
? +? ? ln? ci,t-1 + Rft + ? t. Columns (IV), (V), and (VI) presents the results of estimating the same Euler equation using
correctly aggregated data: (b) ?? lnci,t= ? +? ?? lnci,t-1 + Rft + ? t. Finally, Columns (VII), (VIII), and (IX) illustrate the
effect of adding moments of the cross sectional distribution of consumption growth rates to regression.
The standard errors are corrected for the non-independence of the observations within the same household. In
addition, controls for the evolution of city-level prices and seasonal dummies are included in all the regressions.
Per-capita Consumption
Aggregation Method
Correct Aggregation
Method
Per-capita Consumption
Aggregation Method plus
Moments
Dependent variable ? ln? ct ?? lnct ? ln? ct
(I) (II) (III) (IV) (V) (VI) (VII) (VIII) (IX)
Rft 1.361 1.468 0.872 -0.112 -0.018 -0.042 2.401* 1.454** 1.444**
(0.186) (0.144) (0.190) (0.818) (0.974) (0.926) (0.064) (0.038) (0.040)
? ln? ci,t-1 -0.685 -0.739 -0.494 0.139 -0.791** 0.233
(0.205) (0.191) (0.164) (0.942) (0.033) (0.704)
?? lnci,t-1 0.515** 0.727** 0.538*
(0.042) (0.039) (0.089)
? lnincomet 0.002 -0.131
(0.996) (0.404)
? lnincomet-1 0.471* 0.147
(0.061) (0.344)
? stddev/2 36.669
(0.489)
? skewness/6 2.278
(0.571)
? kurtosis/24 -4.954
(0.116)
Time dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes
# Obs 10 10 10 10 10 10 10 10 10
Hansen J statistic 2.244 2.061 4.108 2.286 1.213 1.210 0.002 3.532 0.370
(p-value) 0.326 0.151 0.043 0.319 0.271 0.271 0.965 0.060 0.543
Adj. R-squared 0.380 0.363 0.685 0.285 0.009 0.170 -.241 0.479 0.174
Robust
* significant at 10%; ** significant at 5%; *** significant at 1%
A description of the variables is reported in Table I. ? stddev, ? skewness, and ? kurtosis are the standard deviation,
skewness and kurtosis of the cross sectional distribution of consumption.
Instrument set: second lag of aggregated city-level sales, income growth rate, average mortgage rate, and
unemployment rate.