Hyperbolic Discounting and Consumer Patience During Financial Crises in Korea *

Hyperbolic Discounting and Consumer Patience During Financial Crises in Korea * Yoonseok Choi ** Suffolk University Sunghyun Kim *** Sungkyunkwan University and Suffolk University January 2014 * This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2013S1A5A8024554). ** Department of Economics, Suffolk University, 8 Ashburton Place, Boston, MA, USA. E-mail: ychoi2@suffolk.edu. *** Corresponding Author. Department of Economics, Sungkyunkwan University, Jongno-Gu, Seoul, Korea and Department of Economics, Suffolk University, 8 Ashburton Place, Boston, MA, USA. Tel: 02-760-0421, E-mail: shenrykim@skku.edu. 1

Hyperbolic Discounting and Consumer Patience During Financial Crises in Korea Abstract This paper tests whether consumption pattern in Korea exhibits a time-inconsistent discounting behavior using a quasi-hyperbolic Euler equation estimated by the generalized method of moments (GMM). In particular, we examine whether consumers change their discounting behavior during financial crises in 1997 and 2008. The estimation results show that Korean consumers exhibit a time-inconsistent quasi-hyperbolic discounting behavior during normal times (excluding financial crisis periods) and become more patient in making consumption decisions during financial crises, which can explain an excessive decline in consumption during financial crises. JEL Classification: D9, E2; Key Words: consumption, quasi-hyperbolic discounting, patience, Euler equation, GMM estimation. 2

1. Introduction A number of papers have provided strong empirical evidence on an excessive decline in aggregate consumption during financial crisis periods. 1 However, this evidence is against the consumption smoothing hypothesis of utility-maximizing agents, which implies that consumers should maintain a steady stream of consumption by borrowing in financial markets when they face negative income shocks. This paper attempts to explain an excessive decline in consumption during financial crises by focusing on the role of consumer s discounting behavior, in particular using time-inconsistent quasi-hyperbolic discount function. 2 Many economists have demonstrated that consumers may have different discounting pattern for an immediate future vs. long-run state. 3 This time-inconsistent discounting behavior is formalized as hyperbolic discounting. Under hyperbolic discounting, consumers tend to show both a long-run patience and a short-run preference for instantaneous gratification (self-control problem). The original idea of time-inconsistent consumer behavior belongs to Phelps and Pollak (1968) who formally model a time-inconsistent preference in the context of intergenerational altruism. Laibson (1997) uses the quasihyperbolic discount function to analyze the consumer behavior with dynamically inconsistent preferences. The quasi-hyperbolic discount function is different from the hyperbolic function in terms of the shape but captures the key qualitative property of the hyperbolic function: a faster rate of decline in the short-run than in the long run. 4 1 See, for example, Lee, et al. (2010), Ivaylo, et al. (2011) and Lee (2013). 2 Other factors can explain the lack of consumption smoothing behavior, for example, financial market incompleteness and borrowing constraints. 3 See, for example, Ainslie (1992). Akelof (1991) provides anecdotal evidence to show time-inconsistent preferences and emphasizes that severe procrastination (self-control problems) can occur under naive belief for the future selves. 4 Krusell et al. (2002) use the term quasi-geometric instead of quasi-hyperbolic. 3

In this paper, we first test whether consumers exhibit time-inconsistent quasihyperbolic discounting behavior using the data of Korea. Then, we test if the degree of short-run impatience changes and consumers exhibit an excessive short-run patience during financial crisis periods, which can help to explain a sharp decline in consumption during financial crises. Korea is an ideal candidate for this exercise as Korea recently experienced two financial crises: the Asian Crisis in 1997 and the global financial crisis started in 2008. Figure 1 displays the time series graph of real aggregate consumption of Korea, which exhibits an excessive decline in consumption in Korea during these financial crisis periods. To do this analysis, we construct the Euler equation based on a quasi-hyperbolic discounting, which is called the quasi-hyperbolic Euler equation (QHEE), and estimate the deep parameters of the Euler equation that represent the degree of short-run impatience using the generalized method of moments (GMM) estimation. The GMM technique is widely employed to estimate the Euler equation because it can effectively deal with expectation terms in the nonlinear Euler equation and does not need a specific assumption about the distribution of the economic model considered. We compare the hyperbolic discounting preference parameters in samples with and without crisis periods to test whether there is a significant difference in preference parameters. Estimation results show that consumers in Korea exhibit a time-inconsistent behavior in general but the pattern of inconsistency in consumption behavior changes over time. In particular, consumers exhibit a short-run impatience at normal times (without crises) but they exhibit excessive short-run patience during financial crises, which can explain an excessive decline in consumption during crisis periods. Few papers have tried to empirically estimate the quasi-hyperbolic discounting parameters. Ahumada and Garegnani (2007) estimate the preference parameters to test if 4

consumers in Argentina show a quasi-hyperbolic discounting pattern using a generalized Euler equation derived by Harris and Laibson (2001). They provide empirical evidence that consumers in Argentina exhibit a hyperbolic discounting after 2002. Collado et al. (2003) use the panel data on household expenditures and show that consumers in Spain exhibit a quasi-hyperbolic discounting behavior using a linearized hyperbolic Euler equation. Angeletos et al. (2001) use a simulation exercise to show that the consumption model with the hyperbolic discount function performs better than that with the exponential discount function. However, none of these papers have tried to connect hyperbolic discounting to changes in consumption behavior during financial crises. This paper consists of six sections. Section 2 provides a detailed explanation of hyperbolic discounting and describes an intertemporal optimization model based on quasihyperbolic discounting. Section 3 derives a testable Euler equation for the GMM estimation. Section 4 presents estimation results and Section 5 provides sensitivity analysis. Section 6 concludes. 2. Model with Quasi-hyperbolic Discounting We first provide a simple illustration of time-inconsistent discount function based on Krusell et al. (2002). 5 In a discrete-time setup with time-additive periodic utility, intertemporal utility V t can be described as follows using two preference parameters, and : = + + + +.. (1) 5 Several other papers have described an equilibrium model with hyperbolic discounting including Akelof (1991), Laibson (1997), Harris and Laibson (2001), and O Donoghue and Rabin (2001). 5

When =1, this intertemporal utility exhibits the standard, time-consistent, exponential preference with discounting factor. However, when 1, there is time inconsistency: in the perspective of the current period t, people perceive the trade-off between the future periods t+1 and t+2 differently from the period between t and t+1. When <1, the intertemporal utility implies excessive short-run impatience: people tend to think that I want to save, just not right now. This case represents the standard self-control problem. 6 When =1 with <1, the intertemporal utility exhibits the same weight on all future events, as described in Akerlof (1991). He argues that, using the procrastination model, some phenomena such as declining savings rates and many personal financial decisions can be explained by this preference. When >1, it means excessive short-run patience: consumers think that I want to consume, just not right now. Figure 2 shows how discount factor changes over time with different values of. In order to test whether consumers exhibit hyperbolic discounting behavior, we need to estimate the value of and from the data. We first derive the optimality condition (Euler equation) from the intertemporal utility maximization problem with quasi-hyperbolic discounting. Then, we derive a testable econometric model based on this maximization problem. We use a buffer-stock model with a quasi-hyperbolic discount function based on Harris and Laibson (2001). A representative agent spends his cash-on-hand 0 to choose a consumption level [0, ] in period t. He also receives a stochastic labor income. The remaining cash-on-hand after consumption is saved for the next period. Saving earns a gross real interest rate. Under these assumptions, a representative agent maximizes the following lifetime expected utility: 6 Lower value of β implies a more serious self-control problem. 6

[ ( ) + ( )] (2) subject to = ( ) +, (3) where 0 and 0 are time preference parameters. Labor income is assumed to be identically and independently distributed. Unlike the standard dynamic optimization problem with a constant discount factor, the model solution with a quasi-hyperbolic discounting involves two value functions: the currentvalue function at time t using a discount factor and the continuation-value function from time t+1 using a discount factor. From these two value functions, we can derive the quasi-hyperbolic Euler equation (QHEE): ( ) =E ( ) + 1 ( ) ( ), (4) where ( ) indicates a marginal utility, ( ) is an equilibrium consumption function, and ( ) implies a marginal propensity to consume (MPC). 7 We assume that ( ) follows a CRRA form,, where is the measure for relative risk aversion. Then, QHEE 7 See Harris and Laibson (2001) for the complete derivation of the quasi-hyperbolic Euler equation. 7

in (4) becomes 8 = E 1 (1 ) ( ). (5) 3. GMM Estimation of Preference Parameters Estimating the deep parameters in equation (5) enables us to test whether the agents exhibit a hyperbolic discounting or not. From (5), we can derive an econometric model as follows: E δr 1 (1 β) ( ) 1 X =0, (6) where X is a set of instruments. The typical and common way of estimating this type of nonlinear Euler equation is to use GMM estimator first proposed by Hansen (1982) and Hansen and Singleton (1982). In this paper, we use the iterative GMM estimator to estimate equation (6). To capture the heteroskedasticity and autocorrelation, we employ the heteroskedasticity and autocorrelation consistent (HAC) estimator. We employ the Bartlett kernel used by Newey and West (1987) with the fixed bandwidth 4. From the nonlinear estimation of (6), we can derive estimated parameter values for,, and. In order to estimate (6), we need the data for consumption growth rates, real interest rate and the marginal propensity to consume (MPC). Following Ahumada and Garegnani (2007), we use the average propensity to consume (APC) as a proxy variable for 8 The QHEE (nonlinear conditional moment model) derived in (5) can be viewed as an extended version of the nonlinear consumption-capital asset pricing model (C-CAPM). 8

MPC. 9 All the variables are constructed based on quarterly data of final household consumption expenditure, GDP, and nominal and real interest rates (yield on one year monetary stabilization bond), taken from Bank of Korea Economic Statistics System. We set the estimation period from 1987Q1 to 2011Q4. All data are seasonally adjusted. Since the GMM estimation is sensitive to the choice of instruments, we consider various sets of instruments such as lagged variables of consumption growth rate, APC, real interest rate, inflation rate, nominal interest rate, and gross national disposable income. 10 The benchmark instrumental variable (IV) set 1 includes the second to fourth lags of consumption growth rate, APC, inflation, nominal interest rate, and gross national disposable income. We experiment with three more IV sets that have smaller number of instruments. IV set 2 includes consumption growth rate, APC, inflation, and nominal interest rate. IV set 3 has consumption growth rate, APC, real interest rate, and gross national disposable income. Finally, IV set 4 includes consumption growth rate, APC, and real interest rate. 4. Estimation Results Table 1 presents the GMM estimation results of three deep parameters of the model,, and with different sets of instruments (IV sets 1 through 4). For all regressions, we report the estimation results from the two sample periods; sample 1 is for the whole period (1987-2011), whereas sample 2 is for the period excluding two crisis periods (1997-1998 and 2008-2011). 9 Ahumada and Garegnani (2007) tested if people in Argentina have the hyperbolic discount function using the same GMM estimation method with APC. 10 Generally, any variables can be used as instruments if those variables are correlated with endogenous variables but orthogonal to the error term. In the standard Euler equation, lagged endogenous variables such as consumption growth and interest rates are typically used as instruments. Some used more than these two variables. For example, Attanasio and Low (2004) uses lagged consumption growth, income and interest rate as instruments. Yogo (2004) uses nominal interest rates, inflation, consumption growth, and log dividend-price ratio as instruments. The starting lag of the instruments is the second lag to avoid possible time aggregation problem suggested by Hall (1988). 9

We first focus on the value of. When is significantly different from one, then it means that consumers follow a time-inconsistent discounting behavior. The estimated value of in the whole sample period is above 1 with the range of 1.14 1.17 depending on which IV set is used. Table 2 reports the Wald test statistics for the null hypothesis that the estimated is equal to one. The Chi-square test statistics and the P-values show that for IV sets 1 and 3, the estimated is significantly different from one at 10% significance level, whereas these p-values are actually quite close to 5% significance level. For IV sets 2 and 4, the null hypothesis cannot be rejected at 10% level but for IV set 2, the p-value is quite close to the 10% level. Overall, we can safely claim that Korean consumers do not exhibit a traditional exponential discount function, but rather they follow a time-inconsistent preference behavior. However, the fact that is larger than one implies that consumers in Korea exhibit a hyperbolic discounting pattern in an unusual way. Typically, discussion regarding hyperbolic discounting is for the case of <1, where consumers show an excessive shortrun impatience (self-control problem). Consumers in Korea, however, exhibit an excessive short-run patience ( >1) implying that I want to consume, but not right now. The value of (a typical discount factor) is less than 1, ranging from 0.91 0.93, which is consistent with the theory. In order to examine why Korean consumers exhibit excessive short-run patience, we derive the preference parameters from the sample excluding two crisis periods (sample 2 in Table 1). 11 The table shows that the estimated for all the IV sets is less than 1 in the range of 0.95 1. Comparison of the results with and without crisis periods indicates that the excessive short-run patience derived in the whole sample estimation is due to the crisis 11 Ideally, if we can run the regression with crisis periods only, then we can directly compare the estimated parameters. However, the sample periods are too short to give us any significant estimation results. 10

periods. Without those periods, consumers exhibit a slightly impatient behavior in the shortrun. These results indicate that during the crisis periods, consumers become excessively patient in the short run, which can explain a sharp decline in consumption during the crisis periods. Another observation in the regression without crisis periods is that the estimated value of is very close to 1. The fact that <1 and close to 1 implies that consumers may have the Akerlof-type discount function, which is characterized by procrastinating behavior (a type of self-control problem). The Akerlof-type discount function implies that consumers tend to prefer today s gratification more than any gratification in the future. All the estimates of and are significant at the 1% level. However, the estimates for the risk aversion parameter ( ) are significant at the 1% level only in some cases. The J-statistics is a criterion on the validity of the over-identifying restrictions of GMM. All of the P-values in Table 1 imply that the null hypothesis that the moment conditions are valid cannot be rejected. 5. Sensitivity Analysis For robustness check, we perform two exercises: (1) use the Andrews (1991) s automatic bandwidth selection method instead of the Newey-West fixed bandwidth; and (2) use the continuously updating estimator (CUE) instead of iterative estimator in GMM estimation. Since our sample size is relatively small and the model we use in this paper is nonlinear, we employ the continuously updating estimator developed by Hansen et al. (1996). They find that CUE estimator is likely to provide better performance than the iterative GMM in small samples even though the statistical properties of these two estimators are equivalent asymptotically. 11

Table 3 displays the estimation results using the Andrew s automatic bandwidth and Table 4 shows the results from the CUE. The overall observation from these two tables suggests that the baseline results are fairly robust. The estimated values of are highly significant at the one percent level. The estimated values from the whole sample period in Tables 3 and 4 are in the range of 1.15 ~ 1.18 and 1.16 ~ 1.23, respectively. In the sample without two crisis periods, the estimated is in the range of 0.95 ~ 0.99 and 0.96 ~ 0.99, respectively. These results confirm the same conclusion as in the baseline case that Korean consumers become more patient during crisis periods. In addition, other estimated parameters such as the original discount factor (δ), risk aversion parameter ( ) and J-statistics also do not exhibit much difference from the baseline case, which implies that the results are immune to the choice of bandwidth or the type of estimator. 6. Conclusion This paper examines how consumers discounting behavior changes during financial crisis periods by estimating the preference parameters in the quasi-hyperbolic discounting function in Korea using the GMM estimation. The regression results demonstrate that changes in consumer s discounting behavior can explain the excessive decline in aggregate consumption during crisis periods. Consumers become more patient during crisis periods and postpone their consumption to the future periods. Identifying specific reasons why consumers become more patient during crisis periods requires further research: Uncertainties about the length or scope of recession may make consumers become more patient and postpone consumption. The results in this paper also imply that in order to prevent the sharp decline in consumption during financial crises, governments should provide policy measures to affect discounting behavior of consumers and make consumers less patient. 12

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Table 1. GMM estimation results of deep parameters Newey-West bandwidth with lag length 4) J-statistics (P-value) IV set 1 Sample 1 0.911*** (0.041) 1.170*** (0.091) 0.499*** (0.129) 8.275 (0.825) Sample 2 1.006*** (0.019) 0.988*** (0.035) 0.008 (0.084) 8.673 (0.797) IV set 2 Sample 1 0.913*** (0.047) Sample 2 0.999*** (0.026) 1.165*** (0.103) 0.998*** (0.047) 0.496*** (0.128) 0.131 (0.125) 7.432 (0.684) 7.758 (0.652) IV set 3 Sample 1 0.915*** (0.040) Sample 2 1.030*** (0.023) 1.163*** (0.088) 0.954*** (0.041) 0.468*** (0.120) 0.379*** (0.061) 7.717 (0.656) 5.715 (0.838) IV set 4 Sample 1 0.925*** (0.045) Sample 2 1.007*** (0.024) 1.141*** (0.097) 0.990*** (0.042) 0.460*** (0.117) 0.106 (0.131) 5.945 (0.546) 4.099 (0.768) Note: 1. ***, ** and * denote 1%, 5% and 10% significance levels. 2. Sets of instruments IV set 1: consumption growth rate, APC, inflation, nominal interest rate, gross national disposable income. IV set 2: consumption growth rate, APC, inflation, nominal interest rate. IV set 3: consumption growth rate, APC, real interest rate, gross national disposable income. IV set 4: consumption growth rate, APC, real interest rate. 3. Samples 1 and 2 indicate the whole sample period and period without two crises (97-98 and 08-11), respectively. 15

Table 2. Test for the time-inconsistent discount parameter Wald test with the null hypothesis =1, with whole sample period) Statistic (Chi-square) P-value IV Set 1 3.466* 0.062 IV Set 2 2.545 0.110 IV Set 3 3.403* 0.065 IV Set 4 2.136 0.143 Note: ***, ** and * denote 1%, 5% and 10% significance levels. 16

Table 3. Robustness check using Andrews automatic bandwidth selection method J-statistics (P-value) IV set 1 Sample 1 0.921*** (0.056) 1.150*** (0.121) 0.431*** (0.137) 11.207 (0.593) Sample 2 1.030*** (0.024) 0.946*** (0.042) 0.001 (0.097) 8.367 (0.818) IV set 2 Sample 1 0.913*** (0.064) Sample 2 1.008*** (0.037) 1.167*** (0.142) 0.982*** (0.065) 0.475*** (0.167) 0.148 (0.151) 6.019 (0.813) 7.162 (0.710) IV set 3 Sample 1 0.906*** (0.053) Sample 2 1.032*** (0.029) 1.183*** (0.119) 0.951*** (0.051) 0.431*** (0.157) 0.370*** (0.069) 7.887 (0.639) 6.240 (0.794) IV set 4 Sample 1 0.914*** (0.061) Sample 2 1.007*** (0.027) 1.165*** (0.135) 0.989*** (0.049) 0.437*** (0.162) 0.087 (0.132) 5.242 (0.630) 4.068 (0.771) Note: 1. ***, ** and * denote 1%, 5% and 10% significance levels. 2. Sets of instruments IV set 1: consumption growth rate, APC, inflation, nominal interest rate, gross national disposable income. IV set 2: consumption growth rate, APC, inflation, nominal interest rate. IV set 3: consumption growth rate, APC, real interest rate, gross national disposable income. IV set 4: consumption growth rate, APC, real interest rate. 3. Samples 1 and 2 indicate the whole sample period and period without two crises (97-98 and 08-11), respectively. 17

Table 4. Robustness check using GMM based on continuous updating estimator (CUE) J-statistics (P-value) IV set 1 Sample 1 0.913*** (0.040) 1.167*** (0.089) 0.468*** (0.120) 8.236 (0.827) Sample 2 1.024*** (0.019) 0.955*** (0.034) 0.064 (0.092) 8.595 (0.802) IV set 2 Sample 1 0.886*** (0.049) Sample 2 1.005*** (0.029) 1.226*** (0.115) 0.986*** (0.051) 0.528*** (0.140) 0.194 (0.138) 7.337 (0.693) 7.657 (0.662) IV set 3 Sample 1 0.917*** (0.039) Sample 2 1.015*** (0.022) 1.158*** (0.086) 0.974*** (0.038) 0.445*** (0.114) 0.113 (0.093) 7.696 (0.658) 5.100 (0.884) IV set 4 Sample 1 0.906*** (0.049) Sample 2 1.006*** (0.024) 1.182*** (0.110) 0.992*** (0.043) 0.527*** (0.139) 0.125 (0.134) 5.787 (0.564) 4.091 (0.769) Note: 1. ***, ** and * denote 1%, 5% and 10% significance levels. 2. Sets of instruments IV set 1: consumption growth rate, APC, inflation, nominal interest rate, gross national disposable income. IV set 2: consumption growth rate, APC, inflation, nominal interest rate. IV set 3: consumption growth rate, APC, real interest rate, gross national disposable income. IV set 4: consumption growth rate, APC, real interest rate. 3. Samples 1 and 2 indicate the whole sample period and period without two crises (97-98 and 08-11), respectively. 18

Figure 1. Quarterly real aggregate consumption in Korea 160,000 140,000 120,000 Billion Won 100,000 80,000 60,000 40,000 20,000 0 1987 Q1 1988 Q1 1989 Q1 1990 Q1 1991 Q1 1992 Q1 1993 Q1 1994 Q1 1995 Q1 1996 Q1 1997 Q1 1998 Q1 1999 Q1 2000 Q1 2001 Q1 2002 Q1 2003 Q1 2004 Q1 2005 Q1 2006 Q1 2007 Q1 2008 Q1 2009 Q1 2010 Q1 2011 Q1 19

Figure 2. Quasi-hyperbolic discounting with different values of Discounting function β>1 1 β<1 β=1 0 1 2 3 4 5 6 7 8 9 10 t (time) Source) Krusell et al. (2002) 20