Extending Dynan's methodology (1993), we show that a significant frac tion of the prudence parameter puzzle can be explained by a downward omitted variable bias. Further, the estimated prudence is substantially higher for liquidity-constrained households.

Jeong-Joon Lee

Yasuyuki Sawada

English

Research Papers in Economics

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CIRJE-F-448
The Degree of Precautionary Saving:
A Reexamination
Jeong-Joon Lee
Towson University
Yasuyuki Sawada
University of Tokyo
November 2006The Degree of Precautionary Saving:
A Reexamination¤
Jeong-Joon Lee
Department of Economics
Towson University
Yasuyuki Sawaday
Faculty of Economics
University of Tokyo
November 2006
Abstract
Extending Dynan's methodology (1993), we show that a signi¯cant frac-
tion of the prudence parameter puzzle can be explained by a downward
omitted variable bias. Further, the estimated prudence is substantially
higher for liquidity-constrained households.
JEL Classi¯cation: D12, E21
Keywords: Precautionary saving; Prudence; Liquidity constraints
¤We would like to thank Dirk Krueger and Fabrizo Perri for making their CEX data set
available to us. We are also grateful to Hidehiko Ichimura and an anonymous referee for their
valuable suggestions.
yCorresponding author. Faculty of Economics, University of Tokyo, 7-3-1 Hongo, Bunkyo-
ku, Tokyo 113-0033, Japan. Tel: +81 3 5841 5572; Fax: +81 3 5841 5521. E-mail:
sawada@e.u-tokyo.ac.jp
11 Introduction
Since the seminal work of Dynan (1993, hereafter Dynan), the small estimates
of Kimball's (1990) prudence parameter has been one of the puzzles in the
literature on consumption behavior. While a growing number of theoretical
studies point out the importance of precautionary saving, the existing evidence
suggests that precautionary saving motives may not be empirically important.1
Most of the previous studies overlook the potential omitted variable bias caused
in the consumption Euler equation estimation by liquidity constraints.2
This paper seeks to resolve the puzzle by integrating Dynan's framework
with Zeldes' (1989, hereafter Zeldes) model of liquidity constraints. We show
that estimating prudence without taking into account liquidity constraints could
lead to a nonnegligible omitted variable bias.
2 Precautionary Saving under Liquidity Con-
straints
To examine the precautionary saving motives, we estimate relative prudence,
considering the liquidity constraints. Following Zeldes, we augment the con-
sumption Euler equation,
U0(Ci;t) =
µ
1 + r
1 + ±
¶
Et [U0(Ci;t+1)] + ¸i;t; (1)
where Ci;t is household's consumption, r is interest rate, ± is discount rate,
and Et is the conditional expectation operator. ¸i;t is the Lagrange multiplier
1Dynan found the estimated prudence to be in the range of 0.02 and 0.3 and argued that
this was too low to be consistent with widely accepted beliefs about risk aversion. Merrigan and
Normandin (1996) reported that based on the U.K. data, the estimated prudence would be
between 0.78 and 1.33. Notable studies on precautionary saving include Parker and Preston
(2005), Gourinchas and Parker (2002), and Banks, Blundell, and Brugiavini (2001).
2See Attanasio and Low (2004), Carroll (2001), and Ludvigson and Paxon (2001).
2associated with the liquidity constraint.
Then, using the second-order Taylor approximation of Et[U0(Ci;t+1)] around
Ci;t as in Dynan,
Et
µ
Ci;t+1 ¡ Ci;t
Ci;t
¶
=
1
¾
µ
r ¡ ±
1 + r
¶
+
½
2
Et
"µ
Ci;t+1 ¡ Ci;t
Ci;t
¶2#
+ ~ ¸i;t; (2)
where ¾ is the coe±cient of relative risk aversion, ¡
U
00Ci;t
U0 ; ½ is the coe±cient
of relative prudence, ¡
U
000¢Ci;t
U00 ; and ~ ¸i;t ´
¸i;t
Ci;tU00.
Because ~ ¸ > 0 for the liquidity-constrained households in Equation (2),
Dynan's speci¯cation, which estimates ½ excluding ~ ¸, is subject to the omitted-
variable bias. In fact, people with more ¯nancial wealth are less likely to be
facing a liquidity constraint and might be the ones who are taking bigger risks.3
In this case, corr
µ
~ ¸; Et
·³
Ct¡Ct+1
Ct
´2¸¶
< 0, and the omission would result in
a downward bias of the prudence coe±cient.
3 Data and Estimation
As in Dynan, this study uses the 1985 Consumer Expenditure Survey (CEX)
data.4 We exclude all the observations of household heads below 16 or above 64
years of age and those who did not complete the entire set of four interviews.
We use the ratio of liquidity assets to one month's income as a threshold to
divide our sample. The high-wealth households whose liquid assets exceed their
one month's income are likely to be liquidity-unconstrained. Out of the total
1,625 households in our sample, 787 are unconstrained and 838 are constrained.5
Table 1 shows that the liquidity-constrained households are younger, poorer, less
3Rich households with high ¯nancial wealth can be exposed to greater risks.
4Our CEX data set is compiled by Krueger and Perri (2005).
5Dynan used a total of 1,733 households, where 941 were liquidity-constrained and 792
were unconstrained. The discrepancies may be due to the compiled CEX data by Krueger
and Perri (2005).
3educated, less skilled, and have accumulated less ¯nancial assets. In particular,
the unconstrained households are exposed to bigger risks than the constrained
households.6
To obtain the ¯nal speci¯cation, we use an initial income as a proxy for ~ ¸
as in Zeldes. Thus, we get
1
N
N X
t=1
µ
Ci;t+1 ¡ Ci;t
Ci;t
¶
= ¯0 + ¯1
1
N
N X
t=1
µ
Ci;t+1 ¡ Ci;t
Ci;t
¶2
+ ¯2yi;0 + ´i; (3)
where ¯0 = 1
¾
³
r¡±
1+r
´
, ¯1 =
½
2, N represents the number of periods, yi;0 is
the initial income, and ´i is the expectation error. We expect ¯2 < 0 for the
constrained and ¯2 = 0 for the unconstrained. We use the instrumental variable
(IV) technique and control for heterogeneity and time-speci¯c e®ects by using
age and month dummies, respectively.
Table 2 shows the replication results for Dynan's speci¯cation; it con¯rms
the small prudence puzzle. When we include income, as shown in Table 3,
^ ¯2 < 0 and the prudence estimates are uniformly greater than those in Table
2, suggesting that the small prudence puzzle may be a re°ection of the omitted
variable bias.
Finally, we split the sample and estimate the model. As Table 4 presents,
we obtain ^ ¯2 < 0 signi¯cant for the constrained households but ^ ¯2 = 0 for the
unconstrained ones. Moreover, the constrained households have stronger pre-
cautionary saving motives: they behave more prudently than the unconstrained
ones. More importantly, the degree of prudence for the constrained households
(ranging from 0.838 to 1.094) is signi¯cantly larger than that of Dynan (ranging
from 0.14 to 0.166).
However, our estimates are still smaller than the expected size of the pru-
6We reject the equal squared consumption growth between the two groups at the 5% level
of signi¯cance based on a one-tailed test; t = 1.807 and p-value is 0.0354.
4dence that ranges from 2 to 5, which can be computed from the constant relative
risk aversion (CRRA) utility with the coe±cient of relative risk aversion ranging
from 1 to 4. Hence, approximately 14% to 46% of the prudence puzzle can be
attributed to the omitted variable bias.
To check the robustness of our ¯ndings, we conduct sensitivity analyses.
First, we use the wealth-to-income ratio as a proxy ~ ¸. The results from the ¯rst
panel of Table 5 are quite similar to those of the benchmark case in Table 4: the
prudence estimates are still larger than those of Dynan, and we obtain ^ ¯2 < 0
signi¯cant for the constrained households. Second, we use a lower cuto® (the
ratio of liquidity assets to half a month's income) when we split our sample.7
Overall, the qualitative results in the second panel of Table 5 do not change.
In summary, this study shows that adding ~ ¸ and splitting the sample help
to resolve Dynan's small prudence puzzle. Explicitly considering liquidity con-
straints, our results are in line with the approximation bias argued by Ludvigson
and Paxon (2001)8 and the concavity of the consumption function elaborated
by Carroll (2001) and Carroll and Kimball (2006).
4 Conclusion
This study shows that Dynan's prudence estimates are biased downward because
of the omitted shadow value of the liquidity constraints, and the constrained
households have stronger precautionary saving motives.
7Now, 644 households are constrained and 961 are unconstrained. The squared consump-
tion growth is still larger for the unconstrained households: 0.199 vs. 0.162.
8They argued that Dynan's speci¯cation would produce a downward bias in the estimate
of prudence for the less wealthy households.
5References
[1] Attanasio, O. and H. Low, 2004, Estimating Euler equations, Review of
Economic Dynamics, 7, 405{435.
[2] Carroll, C., 2001, Death to the log-linearized consumption Euler equa-
tion! (and very poor health to the second-order approximation), Advances in
Macroeconomics, 1, Article 6.
[3] Carroll, C. and M. Kimball, 2006, Precautionary saving and precautionary
wealth, in S. Durlauf and L. Blume, eds., The New Palgrave Dictionary of
Economics, 2nd ed.
[4] Dynan, K., 1993, How prudent are consumers? Journal of Political Economy,
101, 1104{1113.
[5] Gourinchas, P. and J. Parker, 2002, Consumption over the life cycle, Econo-
metrica, 70, 47{89.
[6] Kimball, M., 1990, Precautionary saving in the small and in the large, Econo-
metrica, 58, 53{73.
[7] Krueger, D. and F. Perri, 2005, Does income inequality lead to consumption
inequality? Evidence and theory, Review of Economic Studies, 73, 163{193.
[8] Ludvigson, S. and C. Paxon, 2001, Approximation bias in linearized Euler
equations, Review of Economics and Statistics, 83, 242{256.
[9] Merrigan, P. and M. Mornandin, 1996, Precautionary saving motives: An
assessment from UK time series of cross-sections, The Economic Journal, 106,
1193{1208.
[10] Parker, J. and B. Preston, 2005, Precautionary saving and consumption
°uctuations, American Economic Review, 95, 1119{1143.
6[11] Zeldes, S., 1989, Consumption and liquidity constraints: An empirical in-
vestigation, Journal of Political Economy, 97, 305{346.
7Table 1: Descriptive Statistics
All C Un-C
Variables mean mean mean
Agea 41.1 39.9 42.3
(11.3) (11.2) (11.7)
Educationa 83.3 78.6 88.2
(%)
Occupationa 24.9 18.0 32.4
(%)
Consumptionb 7,020 6,112 7,989
(3,468) (2,797) (3,833)
(Consumption Growth)2 0.184 0.157 0.212
(0.608) (0.305) (0.814)
Incomeb 15,622 13,873 17,486
(10,965) (9,468) (12,092)
Financial Assetsb 6,467 315 13,019
(16,175) (458) (21,378)
Total Wealthb 42,661 30,490 55,622
(54,980) (44,527) (61,711)
Sample size 1625 838 787
Standard deviations are in parentheses. C denotes constrained households and Un-C, uncon-
strained households. a represents the head and b, the households. Education is measured as
the percentage of people in the sample that have studied at least till high school; and occu-
pation, as the percentage of people in the sample who are engaged in managerial/professional
occupations. Consumption and income measures (in 1982{84 constant dollars per adult equiv-
alent) are nondurable expenditures and after-tax income, respectively, as de¯ned in Krueger
and Perri (2005). Total Wealth (in 1982{84 constant dollars per adult equivalent) includes
¯nancial assets and property.
8Table 2: Dynan's Speci¯cations
Instrumental Variables (IV) (1) (2) (3) (4)
Educationa 0.214 0.226 0.228 0.074
Occupationa 0.866 0.701 .. ..
Earnersa 0.406 0.879 0.367 0.852
Propertya 0.018 0.177 0.021 0.237
Financial Assetsa 0.000 .. 0.000 ..
First stage R2 0.076 0.049 0.073 0.044
(Consumption Growth)2 0.141 0.204 0.137 0.225
(0.025)*** (0.045)*** (0.026)*** (0.059)***
Implied Prudence 0.282 0.408 0.274 0.450
(0.050)*** (0.090)*** (0.052)*** (0.118)***
Over IDb 0.515 0.615 0.142 0.233
Standard errors are in parentheses. Age dummies (not reported here) are included to control
for life-cycle e®ects. Month dummies (not reported here) are included to control for time-
speci¯c e®ects. a represents the p-values of the F-tests from the ¯rst stage estimations and
b, the over-identi¯cation tests based on Sargan F-tests. *** indicates signi¯cance at the 1%
level; **, at the 5% level; and *, at the 10% level.
9Table 3: Speci¯cations with Liquidity Constraints
IV (1) (2) (3) (4)
First ¡ stage R2 0.077 0.049 0.074 0.044
(Consumption Growth)2 0.149 0.213 0.943 0.241
(0.024)*** (0.046)*** (0.025)*** (0.061)***
Implied Prudence 0.298 0.426 0.292 0.482
(0.048)*** (0.092)*** (0.050)* (0.122)***
Income {2.155 {2.230 {2.147 {2.435
(1.138)* (1.148)** (1.140)* (1.190)**
Over IDa 0.600 0.731 0.191 0.381
Standard errors are in parentheses. IV (1) includes education, occupation, the number of
earners, property, and ¯nancial assets; IV (2), education, occupation, the number of earners,
and property; IV (3), education, the number of earners, property, and ¯nancial assets; and IV
(4), education, the number of earners, and property. Age and month dummies (not reported
here) are included to control for life-cycle e®ects and time-speci¯c e®ects, respectively. a
represents the over-identi¯cation tests based on Sargan F-tests. *** indicates signi¯cance at
the 1% level; **, at the 5% level; and *, at the 10% level.
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12

"The Degree of Precautionary Saving: A Reexamination"

http://www.cirje.e.u-tokyo.ac.jp/research/dp/2006/2006cf448.pdf

"The Degree of Precautionary Saving: A Reexamination"

Abstract

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