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. Submit your article to this journal View related articles View Crossmark data Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=rael20 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 References Ahumada, H. A., and M. L. Garegnani. 2007. “Testing Hyperbolic Discounting in Consumer Decisions: Evidence for Argentina.” Economics Letters 95: 146–150. doi:10.1016/j.econlet.2006.09.026. Carroll, C. 1992. “The Buffer-stock Theory Of Saving.” Some Macroeconomic Evidence". Brookings Papers On Economic Activity 2: 61–135. doi: 10.2307/2534582. Doshi, K. 1994. “Determinants of the Saving Rate: An International Comparison.” Contemporary Economic Policy 12: 37–45. doi:10.1111/coep.1994.12.issue-1. Hansen, L. P., J. Heaton, and A. Yaron. 1996. “Finite-Sample Properties of Some Alternative GMM Estimators.” Journal of Business and Economic Statistics 14: 262–280. doi: 10.2307/1392442. Harris, C., and D. Laibson. 2001. “Dynamic Choice of Hyperbolic Consumers.” Econometrica 69: 935–957. doi:10.1111/1468-0262.00225. Krusell, P., B. Kuruşçu, and A. A. Smith. 2002. “Equilibrium Welfare and Government Policy with Quasi-Geometric Discounting.” Journal of Economic Theory 105: 42–72. doi:10.1006/jeth.2001.2888. Laibson, D. 1997. “Gold Eggs and Hyperbolic Discounting.” Quarterly Journal of Economics 112: 443–477. doi:10.1162/ 003355397555253. Laibson, D. 1998. “Life-Cycle Consumption and Hyperbolic Discount Functions.” European Economic Review 42: 861–871. doi:10.1016/S0014-2921(97) 00132-3. Leff, N. 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