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Applied Economics Letters
ISSN: 1350-4851 (Print) 1466-4291 (Online) Journal homepage: http://www.tandfonline.com/loi/rael20
Time preference and savings behaviour
Yoonseok Choi & Jong-soo Han
To cite this article: Yoonseok Choi & Jong-soo Han (2017): Time preference and savings
behaviour, Applied Economics Letters, DOI: 10.1080/13504851.2017.1391989
To link to this article: http://dx.doi.org/10.1080/13504851.2017.1391989
Published online: 24 Oct 2017.
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Download by: [University of Florida]
Date: 25 October 2017, At: 04:58
APPLIED ECONOMICS LETTERS, 2017
https://doi.org/10.1080/13504851.2017.1391989
ARTICLE
Time preference and savings behaviour
Yoonseok Choi
Downloaded by [University of Florida] at 04:58 25 October 2017
a
a
and Jong-soo Hanb
Department of Economics, Korea University, Seoul, Korea; bBusiness Administration, Dankook University, Cheonan-si, Korea
ABSTRACT
KEYWORDS
A number of studies have examined various determinants of savings rate. This article contributes
to this literature by empirically testing whether the time preference (discounting behaviour) is
another important determinant of savings rate. To this end, we estimate the hyperbolic Euler
equation using the generalized method of moments (GMM) to examine whether the short-run
discount factor can account for savings behaviour. The empirical results show that people exhibit
short-run patience (impatience) when savings rate increases (decreases), which is in line with the
theoretical prediction. This result implies that the time preference also plays an important role in
determining savings behaviour. Various sets of instruments and different sample periods do not
reverse the main finding.
Savings rate; hyperbolic
Euler equation; short-run
patience; GMM estimation
I. Introduction
The savings rate is one of the important factors to
foster economic growth because it is an important
source for investment. Earlier studies have examined
various determinants of savings rate by focusing
mostly on economic and demographic factors such
as income, interest rates, age, dependency ratio, fertility rate and life expectancy (e.g. Leff 1969; Doshi
1994; Yasin 2008; among others). However, the role
of time preference has received little attention as a
determinant of savings rate.
The time preference is captured by discounting
behaviour in intertemporal choice problems. In particular, a number of behavioural and experimental
studies have explained a wide range of empirical
observations in the consumption-savings literature
using a particular form of time preference called
hyperbolic discounting.1 Unlike standard exponential discounting, the hyperbolic preference involves
time inconsistency in preferences characterized by
two types of discounting, short- and long-run discount factors. The long-run discount factor is similarly interpreted as the exponential discount factor,
whereas the short-run discount factor is the unique
parameter in the hyperbolic preference that determines people’s short-run impatience. If the short-
JEL CLASSIFICATION
D91; E21
run discount factor is smaller than unity, people
exhibit short-run impatience so that they tend to
increase consumption (instantaneous gratification)
by delaying savings (unpleasant activity). In contrast,
if it is larger than unity, people exhibit short-run
patience so that they tend to save more by reducing
consumption (Krusell, Kuruşçu, and Smith 2002).2
This article provides an added dimension to the
literature by empirically testing whether the time
preference with hyperbolic discounting is another
determinant of savings rate. To this end, we estimate
the hyperbolic Euler equation (HEE) using the
GMM technique to examine whether the short-run
discount factor (degree of short-run patience) can
account for savings behaviour in Korea.
The baseline results show that people exhibit
short-run patience so that they save more by
decreasing consumption in the period of
1970–1987, whereas they become short-run impatient so that they enjoy consumption by reducing
savings in the period of 1988–2014. It implies that
discounting behaviour can explain the transitional
path of savings rate. This finding is robust to various
sets of instruments and different sample periods.
This article proceeds as follows. Section II
describes the HEE, estimation method and data.
CONTACT Jong-soo Han
joshahn@dankook.ac.kr
Business Administration, Dankook University, Cheonan-si, Korea
1
They include substantial drop in consumption at retirement, accumulation of illiquid assets instead of liquid assets, etc. See Laibson (1997; 1998) for more
examples.
2
Krusell, Kuruşçu, and Smith (2002) call hyperbolic preferences quasi-geometric preferences.
© 2017 Informa UK Limited, trading as Taylor & Francis Group
2
Y. CHOI AND J.-S. HAN
Section III presents the empirical results. Section IV
concludes.
The data are taken from Bank of Korea Economic
Statistics System and Korean Statistical Information
Service.
II. HEE, method and data
where γ; β and δ denote the measure of relative
risk aversion, short- and long-run discount factors, respectively. Rtþ1 is real gross interest rate,
CðMt Þ denotes equilibrium consumption that is
implicitly a function of cash-on-hand Mt ; and
@CðMtþ1 Þ=@Mtþ1 is marginal propensity to consume. As discussed earlier, people exhibit shortrun impatience (patience) when β<1 ðβ>1Þ: The
model reduces to the standard Euler equation
when β ¼ 1:
To estimate Equation 1, we use the continuously
updating estimator (CUE) proposed by Hansen,
Heaton, and Yaron (1996), arguing that the CUE
performs better than the typical GMM estimator in
small samples. Since the CUE may be sensitive to the
choice of instruments, however, we consider four
different sets of instruments. IV set 1 (IV set 3)
contains the first and second (second and third) lags
of consumption growth rate, APC and real interest
rate.4 IV set 2 (IV set 4) includes the first and second
(second and third) lags of consumption growth rate,
APC, nominal interest rate and inflation rate.5
All the variables are quarterly real per capita
Korean data, ranging from 1970:1 to 2014:4. The
data are final household consumption expenditure,
deposit rate and gross national disposable income.
3
III. Empirical results
Figure 1 displays savings rate in Korea. A noticeable
feature is that savings rate shows two opposite trends
around 1988: it has an upward (downward) trend from
1970 to 1987 (from 1988 to 2014).6 We, therefore, divide
the whole sample into two sub-samples to test whether
the different trends in savings rate can be explained by
discounting behaviour.7 The first (second) sample starts
from 1970:1 to 1987:4 (1988:1 to 2014:4).8 Furthermore,
Figure 1 shows greater volatility of savings rate from
1970 to 1980 (1997 to 2014) in the first (second) sample,
which may affect the estimation results. Hence, we also
consider the sample excluding these periods, ranging
from 1981:1 to 1996:4.
Table 1 presents the empirical results with four different sets of instruments. The left and right sides of
Table 1 indicate the results based on Sample 1
(1970:1 ~ 2014:4) and Sample 2 (1981:1 ~ 1996:4),
respectively. Consider first the results from Sample 1.
For any IV sets, the estimates of the degree of short-run
patience are close to (smaller than) unity in Period 1
(Period 2), with the average value of 1.026 (0.895). The
44
40
36
32
%
Downloaded by [University of Florida] at 04:58 25 October 2017
Harris and Laibson (2001) derive the HEE by incorporating hyperbolic discounting into the buffer stock
model proposed by Carroll (1992).3 Assuming a
typical constant relative risk aversion utility function
1γ
Ct =1 γ; the HEE is given by
@CðMtþ1 Þ γ
γ
Ct ¼ δEt Rtþ1 1 ð1 βÞ
Ctþ1
@Mtþ1
(1)
28
24
20
16
12
1970:1 1975:1 1980:1 1985:1 1990:1 1995:1 2000:1 2005:1 2010:1
Figure 1. Savings rate.
Source: Bank of Korea.
We skip the model description to reduce space. For those who are interested in the model and derivation of the hyperbolic Euler equation (HEE), see Harris
and Laibson (2001).
4
Following Ahumada and Garegnani (2007), we use the average propensity to consume (APC) as a proxy for marginal propensity to consume.
5
Yogo (2004) uses nominal interest rates and inflation as instruments when estimating the Euler equation.
6
Estimates may shift to explain the different trends in savings rate unless variables in the model can account for those trends. The interest rate (APC) in
Equation 1 tracks savings rate positively (negatively), implying that the choice of two samples based on the different trends in savings rate is appropriate.
7
Including any policy change that affects different discounting behaviours in different samples is important. Laibson (1997, 1998) argue that financial
innovation such as credit cards has been a cause of ongoing decline in US savings rate since the 1980s. Hence, we also include data on credit cards (value
of credit card transactions) as an additional variable when estimating the HEE for Period 2. The data are taken from Credit Finance Association of Korea and
converted into the quarterly data using the cubic-match interpolation method. The starting year of data is set at 1990 due to data availability.
8
The savings rate has a peak of 42.5% in 1988:1 and then declines.
APPLIED ECONOMICS LETTERS
3
Table 1. Estimation results.
Sample 1 (1970:1 ~ 2014:4)
IV set 1
Period 1
Period 2
IV set 2
Period 1
Period 2
IV set 3
Period 1
Period 2
IV set 4
Period 1
Downloaded by [University of Florida] at 04:58 25 October 2017
Period 2
Sample 2 (1981:1 ~ 1996:4)
δ
β
γ
J-stat (p-value)
δ
β
γ
J-stat (p-value)
0.966***
(0.017)
1.060***
(0.033)
1.025***
(0.030)
0.881***
(0.059)
1.883***
(0.280)
0.347***
(0.103)
2.140
(0.709)
4.703
(0.582)
0.910***
(0.047)
1.062***
(0.056)
1.185***
(0.102)
0.837***
(0.093)
0.426**
(0.191)
1.070***
(0.264)
1.003
(0.909)
4.146
(0.656)
0.992***
(0.016)
1.045***
(0.017)
1.005***
(0.026)
0.918***
(0.031)
0.277**
(0.126)
0.159
(0.098)
3.581
(0.733)
2.790
(0.946)
0.904***
(0.038)
1.050***
(0.034)
1.200***
(0.082)
0.859***
(0.054)
0.444***
(0.114)
1.011***
(0.207)
1.000
(0.985)
4.342
(0.825)
0.971***
(0.016)
1.068***
(0.070)
1.045***
(0.029)
0.892***
(0.119)
0.328**
(0.158)
0.662
(0.697)
2.352
(0.671)
4.167
(0.243)
0.910***
(0.046)
1.091***
(0.060)
1.185***
(0.103)
0.795***
(0.100)
0.435
(0.334)
1.181**
(0.190)
1.000
(0.909)
3.061
(0.801)
0.979***
(0.015)
1.063***
(0.036)
1.028***
(0.025)
0.888***
(0.063)
0.388**
(0.177)
0.382***
(0.079)
3.681
(0.719)
2.482
(0.478)
0.946***
(0.033)
1.041***
(0.086)
1.101***
(0.069)
0.879***
(0.156)
0.411*
(0.218)
1.388***
(0.198)
2.850
(0.827)
5.326
(0.722)
Notes: ***, ** and * denote 1%, 5% and 10% significance levels.
Numbers in parenthesis denote SEs.
Period 1 (Period 2) on the left side ranges from 1970:1 to 1987:4 (1990:1 to 2014:4), whereas Period 1 (Period 2) on the right side spans from 1981:1 to
1987:4 (1990:1 to 1996:4).
Wald test in Table 2 corroborates these results. For
Period 2, we can reject the null hypothesis that β ¼ 1
at 5% and 10% significance levels for all IV sets, aside
from IV set 3. However, the null hypothesis is not
rejected for all IV sets of Period 1.
These results suggest that people in Korea exhibit
short-run patience (impatience) in Period 1 (2) so that
they save more (less) by reducing (increasing) consumption, resulting in an increase (decrease) in savings rate. It
implies that the time preference (short-run discount
factor) can explain savings behaviour in Korea.
Next, consider the results from Sample 2 to check
whether greater volatility of savings rate changes the
baseline results. The average estimate of short-run
patience in Period 1 (Period 2) is 1.168 (0.842). This
result is also confirmed by the test in Table 2: we
reject the null hypothesis at all significance levels for
Periods 1 and 2, except for IV set 4. The overall
Table 2. Wald test for the short-run discount factor.
Sample 1 (1970:1 ~ 2014:4)
Period 1
IV set 1
IV set 2
IV set 3
IV set 4
Period 2
IV set 1
IV set 2
IV set 3
IV set 4
Sample 2 (1981:1 ~ 1996:4)
Statistic
p-Value
Statistic
p-Value
0.693
0.037
2.373
1.212
0.404
0.846
0.123
0.270
3.251
5.949
3.238
2.133
0.071
0.014
0.071
0.144
3.975
6.604
0.809
3.035
0.046
0.010
0.368
0.081
3.024
6.653
4.090
0.593
0.082
0.009
0.043
0.441
Notes: IV sets 1, 2, 3 and 4 are identical to those in Table 1.
result suggests that greater volatility of savings rate
has little impact on the baseline results.
In addition to the short-run discount factor (main
focus in this article), we also obtain the estimates of
other deep parameters. The results from Sample 1
show that most estimates of the risk aversion θ are
significant, with the average value of 0.719 (0.388) for
Period 1 (Period 2). All the estimates of long-run
discount factor δ are significant at 1% significance
level and its value is close to unity. Since we use the
GMM technique, we can test the overall performance
of the model using J-statistic. Table 1 shows that we
do not reject the null hypothesis that over-identifying
restrictions are satisfied, implying that the moment
conditions are correctly specified.
IV. Conclusion
In this article, we estimate the HEE using the CUE to
empirically test whether the time preference is also an
important determinant of savings rate. The estimation
results show that people exhibit short-run patience
(impatience) when savings rate increases (decreases),
implying that savings behaviour can be well explained
by the time preference (short-run discount factor) in
Korea. The main finding is robust to various sets of
instruments and different sample periods. The overall
result implies that implementing an appropriate policy
(e.g. tax incentives for savings) that can change people’s
4
Y. CHOI AND J.-S. HAN
discounting behaviour can increase savings rate.
Possible future research would be to test whether the
empirical finding in this article holds for other countries
with different savings behaviour.
Disclosure statement
No potential conflict of interest was reported by the authors.
ORCID
Yoonseok Choi
http://orcid.org/0000-0003-4980-5101
Downloaded by [University of Florida] at 04:58 25 October 2017
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