Do Consumers Learn from Their Own Experiences?

Transcription

1 Do Consumers Learn from Their Own Experiences? Kiichi Tokuoka Abstract It is natural to think that a household may learn from its own experiences and subsequently increase savings. This paper tests empirically the hypothesis that Japanese households learn from their experiences of large expenditure and increase their targets for precautionary savings after such experiences. The results imply that households raise their targets for precautionary savings by 4 5 percent of annual income in response to such experiences. Moreover, data are consistent with the argument that targets for savings affect actual savings. Assuming this holds, the results in this paper suggest that consumers may increase their actual savings following large expenditure. Keywords: Learning, Precautionary savings, Target JEL classification: D12, D83 1. Introduction Despite an abundant and expanding literature on learning in the field of macroeconomic policy, 1 economists have generally not paid sufficient attention to the effects of learning on decision making between consumption and saving. While several recent, mostly empirical studies have begun to examine the effectiveness of formal learning in this sort of decision making, such as through attending retirement seminars, studies on informal learning This paper is based on the research I made while working at the International Monetary Fund. The views expressed in this paper are my own and do not represent those of the Ministry of Finance or the International Monetary Fund. Ministry of Finance, Tokyo, , Japan; Phone ; Fax address: kiichi.tokuoka@gmail.com (Kiichi Tokuoka ) 1 See Evans and Honkapohja (2009) for a comprehensive review of the monetary policy literature. Outside traditional economics, Giuliano and Spilimbergo (2009) have shown that people who grew up during recessions tend to support government redistribution. Preprint submitted to JER March 7, 2015

2 (e.g., learning from one s own and others experiences), in particular empirical ones, remain limited with a few exceptions (for the relevant literature, see Section 2). Undeniably, economists have a good reason for assuming away learning in a savings model in that if we were to seriously consider learning (especially in a heterogeneous agents model), we would need to know the distribution of information to obtain any aggregate implications. This may substantially complicate modeling. It is, however, natural to believe that a household may learn from its own experience and subsequently increase savings. Suppose, for example, a car accident involving catastrophic damage, such that after the owner purchases a replacement vehicle, there is no buffer stock of cash remaining. Following such an event, the owner may learn the need for larger precautionary savings (than at least was the case before), and will then attempt to increase savings. The implications of such informal learning for the aggregate economy may also be quite important, for example, after a sharp increase in unemployment following an economic crisis. Of course, I could test for this type of informal learning by regressing the change in the wealth permanent income ratio on a dummy variable signifying one s experience (e.g., a large expenditure or income shock). However, this test is subject to a serious identification problem in that those who have experienced large expenditure typically reduce savings. 2 Instead, in this analysis I consider the alternative hypothesis that a household may learn from its experience of large expenditures and increase its target for precautionary savings. I empirically test this hypothesis using the Japanese Panel Survey of Consumers (JPSC), which records targets for precautionary savings. Of course, testing this hypothesis is not the same as testing whether one s own large expenditure experience affects saving behavior (updating the target for savings does not necessarily imply a change in behavior); however, at the least, this is a useful step forward in better understanding household saving and consumption decision making. The empirical results support the hypothesis that household perceptions change after experiencing large expenditure, with the estimated coefficients suggesting that in Japan, households raise their targets for precautionary savings by 4 5 percent of (permanent) income after large expenditure. I also 2 In fact, using the same data set as in this analysis, I have estimated that a large expenditure change is likely to reduce actual liquid assets by 5 percent of income. 2

3 find that several alternative hypotheses do not explain these results. For example, I find no support for the competing hypothesis that the persistence of expenditure, such as that arising due to illness, raises the targets for lifecycle savings, and creates positive coefficient estimates. The data are also consistent with the argument that these savings targets affect actual savings. Assuming this holds, the results above imply that households will save more (than others) following large expenditure. The remainder of the paper is structured as follows. Section 2 reviews the related literature. Section 3 considers the theoretical model including learning from large expenditure used to draw the implications for empirical analysis later in the paper. Section 4 presents the econometric model used for the empirical analysis and Section 5 describes the data. Section 6 reports the empirical results, followed by some concluding remarks. 2. Related Literature This paper relates to a stream of literature concerning the role of learning in decision making about consumption and saving. In the area of retirement saving, several authors have studied the role of formal learning, such as through attending seminars (e.g., Lusardi and Mitchell (2007), Lusardi (2005), Bernheim and Garrett (2003), and Duflo and Saez (2003)). However, few studies have addressed informal learning in retirement saving, with just a few exceptions, including Choi et al. (2009), Lusardi (2003), and Owen and Wu (2007). Choi et al. (2009) report that investors who have experienced higher returns from 401(k) accounts tend to accumulate larger 401(k) savings. Lusardi (2003) suggests that consumers who have older siblings learn from them and thus have larger retirement savings. Finally, using the US Health and Retirement Study (HRS) and the Survey of Consumer Finances (SCF), Owen and Wu (2007) examined the qualitative impact of a financial shock on retirement savings, showing that households experiencing financial shocks worry more about the adequacy of their retirement savings. There are already several theoretical studies concerning informal learning in the area of precautionary saving (e.g., Ozak (2014), Howitt and Ozak (2014), Allen and Carroll (2001), and Lettau and Uhlig (1999)). However, empirical work in the area is rather more limited. Among the few exceptions, Tokuoka (2013) reports that one s own saving rate rises if a sibling has experienced unemployment. Experimental results by Ballinger et al. (2003) also suggest that in solving the life-cycle precautionary saving model, later 3

4 generations perform significantly better thanks to learning from earlier generations. Similarly, through experiments, Brown et al. (2009) find that using social learning, subjects can reach saving decisions that are quite close to being optimal much more quickly. These three studies point to the importance of social learning in precautionary saving. However, while these studies have quantified the importance of learning from others experiences, to my knowledge, no empirical studies in the field of precautionary saving have yet quantified the role of learning from one s own experiences. The purpose of the present analysis is to address this gap in the literature. Outside of the area of learning concerning decision making about consumption and saving, many studies have empirically investigated the role of informal learning in individual investment decisions. For example, Kaustia and Knupfer (2008) find that retail investors who have experienced higher returns from initial public offerings (IPOs) are more likely to participate in future IPOs. More generally, Malmendier and Nagel (2011) conclude that individuals who have experienced generally lower stock market returns throughout their lives tend to invest a smaller proportion of their assets in stocks. Malmendier and Nagel (2011) is consistent with Greenwood and Nagel (2009) in that the latter finds that younger fund managers were more likely to bet on technology stocks during the technology bubble of the late 1990s. 3 Lastly, Kaustia and Knupfer (2012) find that the stock returns experienced by local peers affect the stock market entry decisions of individuals. This work in particular highlights the importance of social learning in investment decisions. In the area of corporate financing, Malmendier and Tate (2005) argue that corporate investment by managers belonging to the Great Depression birth cohort is more sensitive to cash flows, suggesting that based on their experience, they do not see capital markets as a reliable source of corporate funding. In a similar vein, Graham and Narasimhan (2004) find that managers who experienced the Great Depression were also generally more conservative in taking on debt. 3 Similarly, Vissing-Jorgensen (2003) concludes that during the boom of the late 1990s, younger investors with a shorter investment memory held higher expectations of stock returns. 4

5 3. Theoretical Model with Learning This section introduces learning in the standard buffer stock model and runs several simulations. The goal of the exercise is to draw implications for the empirical analysis later in the paper Model description The key difference between the model in this paper and the buffer stock model (Carroll (1997)) is that the present model assumes that households are subject to a negative shock to utility, which forces them to spend more (experience large expenditure), and that they learn from such an event. Begin with the standard buffer stock model (Carroll (1997)). Households then solve the following infinite horizon maximization problem: max E t [ n=0 βn u(c t+n )] where u( ) = 1 ρ /(1 ρ) is a constant relative risk aversion utility function. The budget constraint is: C t M t A t = M t C t M t+1 = RA t + P t+1 θ t+1 (1) P t+1 = GP t ψ t+1, where A t is assets at the end of period t; M t+1 is the sum of the interest rate R multiplied by the end-of-period assets and next-period noncapital income (equal to permanent noncapital income P t+1 multiplied by an iid transitory income shock factor θ t+1 ); and P t+1 is equal to its previous value, multiplied by a growth factor G and a mean one iid shock ψ t+1. The distributions of θ t+1 and ψ t+1 are assumed to be log normal. A key property of the buffer stock model is that each household has a target level for A t /P t (Carroll (1997)). I utilize this property in the analysis in the following subsection. Now, to introduce learning, add a negative utility shock (e.g., due to illness) to the model in the following manner: 1. In period t, the level of utility is u(c t ) with probability (1 p) u(ζc t ) with probability p, 5

6 where ζ < 1 is the discount factor attached to consumption, when households are hit by an iid utility shock (with probability p). 4 Households facing a utility shock spend more (experience large expenditure) to recover utility. 2. The perceived probability of a utility shock (ˆp) evolves according to the following equation: ˆp t = πd t + (1 π)ˆp t 1, where D t is the dummy of a utility shock in year t and π is the weight attached to learning. Under this equation, the unconditional expected value of ˆp is the true probability (p). I assume that the household solves the optimization problem, taking the perceived probability as the actual probability of large expenditure. In the current model, households do not know the true probability of a utility shock and update their perceived probability following a shock (adaptive expectation), but can correctly solve the dynamic stochastic optimization problem given their estimated probabilities. In other words, the model assumes bounded rationality (Evans and McGough (2014)). This contrasts with the earlier theoretical literature on learning in precautionary saving (e.g., Allen and Carroll (2001)) which assumes that households know the true parameters but cannot solve the decision problem optimally (bounded optimality (Evans and McGough (2014))). The means of learning in the current model is, of course, a special case and there are many other possible forms of learning. For example, one could introduce exogenous large expenditure (EX) in equation (1) M t+1 = RA t + P t+1 θ t+1 EX t+1, and assume no utility from EX (following, for example, Hubbard et al. (1995, 1994) who assume no utility from medical expenditures), 5 while the current 4 Even though the shock could be persistent (e.g., illness), for simplicity I assume an iid distribution here as the goal of this part of the analysis is to illustrate how informal learning can potentially affect households perceptions. Introducing the persistence of shocks would not essentially change the mechanism for informal learning from one s own experiences. That said, I empirically investigate the issue of persistent shocks later in the paper. 5 In this setup, where EX captures not only expenditure but also the loss of income, 6

7 paper assumes endogenous large expenditure (for recovering from a utility shock). Therefore, I see the current model with learning as an illustration of how learning can potentially increase the target for precautionary savings Estimation using simulation data The buffer stock model (Carroll (1997)) implies that in period t, household i has a target level a i,t for its (precautionary) savings to permanent noncapital income ratio: A i,t/p i,t = a i,t, where A i,t is the target for precautionary savings (level) and P i,t is permanent noncapital income. This implies: (A i,t A i,t 1)/P i,t = a i,t(1 (a i,t 1/a i,t)(p i,t 1 /P i,t )) A i,t/p i,t = a i,t(1 (1/Γ i,t )(1/G i,t )), (2) where Γ i,t a i,t/a i,t 1 and G i,t P i,t /P i,t 1. Theory (Carroll (1997)) implies that a i,t (in the right-hand side of equation (2)) is determined by fundamental parameters including the probability of large expenditure (introduced in the present model), the degree of risk aversion, and the variance of income shocks. In the current model, learning from large expenditure has an impact on the perceived probability of large expenditure, which in turn affects a i,t. Therefore, if we estimate the following equation with simulation data generated by the model, we should find a significant coefficient on the dummy of large expenditure D i,t. 6 A i,t/p i,t = β 0 + β 1 D i,t + β 2 log P i,t + ε i,t. (3) In estimating this equation, following the empirical analysis later (see Section 4), I use lagged actual income Y i 1,t as a proxy for P i,t, and include log the results are similar to those of this paper s model (reported in Table 2). 6 The sign of the coefficient can be either positive or negative, depending on the sign of the term (1 (1/Γ i,t )(1/G i,t )). That said, if (1 (1/Γ i,t )(1/G i,t )) in equation (2) is on average positive, the sign on the coefficient should be positive. This may be the case because the growth rate of permanent income G i,t is likely to be greater than 1 for relatively young households in the JPSC data used in this paper (see Table 3), and the average value of Γ i,t ( a i,t /a i,t 1 ) may be around 1 (which is indeed the case in the current data). 7

8 Table 1: Baseline Parameter Values for Simulation Parameter Description Value Source ρ Coefficient of relative risk aversion 2 Carroll (1997) β Discount factor 0.96 Carroll (1997) G Permanent income growth 1.02 Carroll (1997) R Interest rate 1.02 Carroll (1997) σ ψ Log std. of permanent income shock 0.1 Carroll (1997) σ θ Log std. of transitory income shock 0.1 Carroll (1997) p Probability of large expenditure 0.1 Data (JPSC) π Weight attached to learning 0.05 ζ Consumption discount factor under a utility shock 0.80 permanent income log P i,t (proxied by log Y i,t 1 ) as an independent variable and use log Y i,t 2 as its instrument. I run a simulation with 9,000 households for 200 periods to generate simulation data, and use the last two periods of cross-section data for estimation. Table 1 presents the baseline parameter values for the simulation, of which ρ, β, G, R, σ ψ, and σ θ are from Carroll (1997), 7 and p is from the JPSC data. 8 π and ζ are not from the data or previous literature (I test the robustness of these values below). With the baseline parameter values, the coefficient on D i,t is positive at 0.02 (first column in Table 2). The coefficient varies by changing parameter values, but stays in the range of (rest of the columns). 4. Econometric Model To make empirical analysis, consider the following econometric model: A i,t/p i,t = β 0 + β 1 D i,t + β 2 log P i,t + β 3 Z i,t + ε i,t. (4) This equation is essentially the same as equation (3) but includes demographic variables, cohort dummies, and time dummies (Z i,t ) as additional 7 While Carroll (1997) uses R = 1.00 as the baseline parameter and R = 1.02 as an alternative, I use R = 1.02 as the baseline because R > 1.00 is more realistic. 8 Table 3 indicates that the probability of a large expenditure experience is about 10 percent. 8

9 Table 2: Estimation using Simulation Data (1) (2) (3) (4) (5) (6) (7) Baseline π π ζ ζ β β VARIABLES Params D t (0.000)*** (0.000)*** (0.000)*** (0.000)*** (0.000)*** (0.000)*** (0.000)*** Observations 9,000 9,000 9,000 9,000 9,000 9,000 9,000 R-squared Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Notes: Control variable is log P t. controls. Log permanent income (log P i,t ) is also included. 9 The key variable is D i,t, which is the dummy for whether the household has experienced large expenditure in the past year. If learning works in the real world, we may see a positive coefficient on D i,t, as we have seen in the simulation analysis above. Using an own experience variable in this empirical analysis may involve the omitted variable problem. This is because own experience is likely to be highly correlated with unobservable individually specific factors such as ability and preferences. For example, those who are less able might be more likely to be hit by an accident that leads to large expenditure or an income loss. The problem is that such unobservable factors may not be fully captured by control variables, possibly creating a correlation between the error term and the key dummy (D i,t in this paper). Using the fixed effects estimator (FE) could alleviate this problem. Z i,t consists of the age of the household head (husband); 10 age squared; the number of family members; education dummies; industry dummies; 9 log P i,t is included in the equation as there is empirical evidence that high-permanentincome households save more (Dynan et al. (2004)). 10 I assume that the husband is the head because in more than 90 percent of the households in the data set, the husband s income is higher than that of the wife. 9

10 occupation dummies interacted with the dummy for whether or not the head has regular employment; cohort dummies; and time dummies. Since P i,t is not observable in the data, this paper estimates the equation by replacing P i,t in (4) with lagged actual household total income Y i,t 1. Alternatively, one could use current income Y i,t as a proxy for P i,t. The problem with this approach is that if current income and large expenditure (D i,t ) are negatively correlated (for example, illness may increase expenditure while reducing income), we may see a spurious positive correlation between A i,t/p i,t (proxied by A i,t/y i,t ) and D i,t. I estimate the model mainly by the instrumental variable (IV) method, using log Y i,t 2 as the instrument for log Y i,t 1 (throughout the IV regressions in this paper, I use Y i,t 1 as a proxy for P i,t and log Y i,t 2 as the instrument for log Y i,t 1, unless otherwise noted). 11 The panel structure of the data (discussed below) allows the use of the FE as well. Under the assumption that individually specific unobservable elements such as preferences are time-invariant, 12 the FE corrects the omitted variable problem. 5. Data The data used in the econometric analysis are taken from the JPSC. The JPSC comprises Japanese annual panel data. The initial 1993 survey covered 1,500 women aged In 1997, women aged were added to the sample, and in 2004, women aged were added. Although the JPSC tracks only women (either single or married) as respondents, data on the married women s husbands are also available. The data set offers a rich set of variables, including those related to savings, income, age, education, and employment. In particular, the JPSC asks two questions that are critical for this paper. The first is: How much are your household s target savings for unexpected 11 Equation (4) tells us that the dependent variable should be A i,t /P i,t, but Y i,t 1, which includes a transitory component, is used as a proxy for P i,t. This can be seen as a measurement error problem, and the error term ε i,t picks up the transitory component in Y i,t 1. The correlation between the error term and log Y i,t 1 (proxy for log P i,t ) requires instrumenting log Y i,t Examples of such unobservable elements include preferences, but Z i,t is unlikely to fully control for them. 10

11 expenses such as for illness, disaster, and so on? I interpret this as the target for precautionary savings and use it as A i,t below. 13 The second question is: Which of the following has your household experienced: i) large expenditure; and/or ii) income and/or wealth decline? 14 I use the answer to the second question to construct D i,t. 15 Note that there are several interpretations of large expenditure. For some, large may have been interpreted as meaning large relative to income, while for others, relative to wealth. Unfortunately, the survey cannot identify their interpretations as it asks no follow-up questions. These events could be either expected or unexpected, whereas the theoretical model in Section 3 assumes that the large expenditure event is unexpected (only the probability of the event is known). Consequently, in the empirical analysis in the next section, the coefficient on D i,t estimates the average impact of both expected and unexpected large expenditure events. It is possible that expected large expenditure increases the target for precautionary savings even before the large expenditure event actually occurs (i.e., raising A i,t 1, while lowering A i,t). If so, the estimated coefficient on D i,t may understate the impact of unexpected large expenditure. Actually, in certain cases, it is possible to see if a large expenditure experience is unexpected or not, but the results using large expenditure events that are identified to be unexpected are weak due to the small number of such events (see the next section for details). Before asking about the experience of large expenditure, the JPSC asks whether any of the family members (other than the wife) had experienced adverse events, including: i) an accident or disaster; ii) serious illness; and iii) physical move. If large expenditure follows an accident or disaster, we can interpret such large expenditure is unexpected. If large expenditure follows serious illness, it is not so straightforward to determine if the large expenditure event is unexpected because some illness events may be expected. The next section reports that the re- 13 The intention of this question is to obtain the target for precautionary savings. However, the possibility that misreporting occurs cannot be denied. For example, some households might include expected expenses for education. If so, the responses also incorporate life-cycle savings because, in the pure sense, precautionary savings should cover only savings for unexpected events. The paper will discuss this issue later. 14 The full list of responses includes several other experience (e.g., wife s depression), but they are omitted here because they are not relevant to this paper s hypothesis. 15 The JPSC introduced this question in 1994; it is not in the initial 1993 survey. 11

12 sults using the dummy of large expenditure following an accident or disaster are weak. The SCF also asks questions about target savings and the incidence of expenditure, 16 which could allow researchers to conduct a test similar to this paper s test. However, the advantage of the JPSC is that it is a long panel data set and, thus, we can test dynamics in saving behavior, which is not possible with the SCF. In my data set, I have included only married households; restricted the head s (husband) s age to between 20 and 60 to avoid the impact of retirement; and measured financial variables in 1993 prices (using headline CPI). In addition, in each of the regressions below, the top and bottom 1 percent of the dependent variable are trimmed (as the distribution is very wide). The averages of key variables by year in my data set are reported in Table 3. A /Y drops sharply in 2001 and stays lower subsequently. This may be reflecting the change in the question. Until 2000, the JPSC asked For what purposes do you accumulate wealth? Please choose your first, second and third most important objectives, and report the target amount for each. Then, the survey listed 12 types of savings, including retirement savings, precautionary savings, and savings for children s education. In 2001, the JPSC changed the question slightly, and since then it has allowed respondents to report their target for savings for each purpose (not only three). It may be that before 2001, households overreported targets for precautionary savings (relative to 2001 and after) by including savings for other purposes in precautionary savings because they could report only three types of target. Over time, household actual income Y (in 10 thousand yen, deflated with 1993 CPI) rises, and heads (husbands) get older. The average of the key dummy D (dummy of large expenditure experience) is higher in the second half of the sample period, but the reason for this is not clear. The sample size increases over time, reflecting the fact that more women in the sample are married (recall that the JPSC tracks only women as respondents and that this paper restricted the sample to married households). 16 Specifically, since 1995, the SCF has asked About how much do you think you (and your family) need to have in savings for emergencies and other unexpected things that may come up? It also asks the following two questions, which could be used to identify the incidence of expenditure: Did you take out this mortgage to: refinance or rollover an earlier loan, borrow additional money on your home equity, or to do both? ; and, subsequently, For what purpose was the money used? 12

13 Table 3: Average of Key Variables Target for Actual Dummy Head Number Precautionary Income Large Age of Obs Savings to Expenditure Income Ratio (A /Y ) (Y ) (D) Full sample Notes: Observations with the top or bottom 1 percent of A t /Pt (dependent variable in the main specification below) are trimmed. 13

14 6. Results 6.1. Do households raise targets for precautionary savings after large expenditure? Baseline regression results. The results from estimating equation (4) support the hypothesis that households increase their targets for savings following large expenditure. When setting D i,t at 1 if household i has experienced large expenditure over the past year, the coefficient estimated by OLS is positive and significant (first column in Table 4), despite the potential underestimation of the coefficient discussed in Section When using IV, the coefficient on the dummy is somewhat lower, but remains statistically significant (second column), and the results are robust with respect to the choice of instrument. 18 The estimates using the FE and FE+IV are similar to those of IV (third and fourth columns). 19 Throughout these regressions, the size of the coefficients on D i,t is about 4 percent, meaning that if a household experiences large expenditure, its target for precautionary savings rises by 4 percent of annual permanent (household) income. The coefficients are close to the estimates produced by the simulation data (Table 2). When setting the key dummy at 1 if the household has reduced income and/or wealth, the coefficient is weak, although still positive (fifth and sixth columns in the table). This could be because following a negative income shock, some households may learn that their future permanent income has declined and may cut their targets for precautionary savings accordingly. From this point, this paper focuses on the experience of large expenditure. 17 I do not report the OLS results as they are similar to the results of IV, which is my preferred specification. 18 The regression in the first column used log Y i,t 2 as the instrument. The instrument is highly significant with a t-statistic greater than 100 (henceforth I do not report the significance of the instrument, as each instrument is highly significant throughout the analysis). Using a two-year lag as the instrument yields similar results (not reported here). 19 When running the FE+IV, I use log Y i,t 2 log Y i (log Y i is the average of log Y i,t across years) as the instrument for log Y i,t 1 log Y i. The t-statistic of the instrument in the first-stage regression is Below, I report the results for the FE only, and do not report results of FE+IV because they are close to the FE results. More fundamentally, the FE+IV really would not solve the measurement error problem with log Y i,t 1 log Y i, if it existed, as log Y i in (log Y i,t 2 log Y i ) (instrument) includes log Y i,t 1 and thus its measurement error. 14

15 Table 4: Baseline Regressions VARIABLES (1) (2) (3) (4) (5) (6) (7) (8) OLS IV FE FE+IV IV FE IV FE A t /Pt A t /Pt A t /Pt A t /Pt A t /Pt A t /Pt A t /Pt A t /Pt D t (0.012)*** (0.012)*** (0.014)*** (0.015)*** D t (0.019) (0.022) D accdisaster t (0.034) (0.049) Observations 10,352 8,968 10,352 8,968 8,968 10,352 8,968 10,352 R-squared Number of id 1,807 1,542 1,807 1,807 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Notes: Control variables are log P t and Z t. The results are weak when setting the dummy at 1 if household i has experienced large expenditure following an accident or disaster (last two columns in the table). The motivation for this regression is to estimate the impact of large expenditure experiences that are identified to be unexpected. The weak results may be because of the small number of such events. In evidence, while about 1,000 households experience large expenditure, only 7 percent (about 70 households) experience large expenditure following an accident or disaster. Below, I use the original definition of D i,t (large expenditure). The results support the learning hypothesis, even if I split the data into that before 2001 and that after. As discussed in Section 5, the question concerning the target for precautionary savings changed in If I use only the data prior to 2001, the coefficient on the dummy is positive and about the same size as before, but becomes insignificant (first column in Table 5). However, this is probably because of the small sample size (the number of households is only about 1,500 compared to nearly 9,000 in the full sample). Using the data for 2001 and after yields a significant coefficient on the dummy (second column in the table). I now use the full sample and add a new dummy D bf2001 i,t D i,t, which is the large expenditure dummy interacted with the dummy of year < With this additional dummy variable, I obtain a significant coefficient on D i,t and insignificant coefficient 15

16 on D bf2001 i,t D i,t. This supports combining the two sub data sets before 2001 and after (third and fourth columns in the table). With an alternative estimate for permanent income, the results change little from the baseline results reported in the first three columns in Table 4. For example, the fifth and sixth columns in Table 5 report that the results are similar when using the value of income predicted by Z i,t as an estimate for P i,t (following e.g., Mishra and Paudel (2011) and Bhalla (1980)) and instrumenting the estimate for log P i,t by log Y i,t 2. Similarly, the seventh and eighth columns in the table indicate that when using P i,t estimated using a three-year average (t 1, t, t+1), 20 the results are similar to those reported earlier. Using a five-year average yields very similar results (not reported here). As below, to conserve space, I omit results with an alternative estimate for permanent income, as they do not differ much from the results reported in the tables. The results are also robust using an alternative level specification: 21 A i,t = γ 0 + γ 1 D i,t + γ 2 P i,t + γ 3 Z i,t + ε i,t, (5) where Y i,t (actual income) is used as a proxy for P i,t. Using Y i,t 1 as the instrument of Y i,t, the coefficient on D i,t is about 25 thousand yen and highly significant (the last two columns in Table 5). This is about 4 percent of average annual household income similar to the magnitude of that estimated earlier. Is the increase in the target for savings (A i,t) really because of learning in relation to precautionary saving?. This question is important because the positive coefficient on D i,t could arise from other causes, not just from learning in precautionary saving. First, an increase in borrowing could be driving the positive coefficient on D i,t. If hit by large expenditure needs and the requirement to finance this spending, a household s immediate reaction may be one of the following: i) increase borrowing; ii) reduce assets (e.g., withdraw deposits); or iii) cut back other spending. If the household increases its borrowing (case i), then 20 The idea of estimating P i,t using a multiyear average follows Carroll and Samwick (1998). 21 This level specification may be misspecified. The level specification restricts the coefficient on P i,t to be constant across households, but equation (2) implies that if the coefficient on P i,t is proportional to a i,t, it is heterogeneous across consumers. 16

17 Table 5: Robustness Tests (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) IV IV IV FE IV FE IV FE IV FE A t /Pt A t /Pt A t /Pt A t /Pt A t /Pt A t /Pt A t /Pt A t /Pt A t A t year year Alt Alt Alt Alt LV LV < 2001 >= 2001 Perm Perm Perm Perm Spec Spec VARIABLES Predicted Predicted 3 Yr Av 3 Yr Av Dt (0.042) (0.013)*** (0.013)*** (0.015)*** (0.012)*** (0.013)*** (0.014)*** (0.017)*** (7.6)*** (8.8)*** D bf2001t Dt (0.043) (0.041) Observations 1,481 7,487 8,968 10,352 9,404 11,118 7,093 8,028 9,890 10,652 R-squared Number of id 1,807 1,858 1,479 1,871 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Notes: Control variables are log Pt and Zt. 17

18 it may increase its target for savings for future repayment. Although this channel is not learning, if it works, it could be picked up in its effect on D i,t. However, the coefficient on D i,t changes very little, even after controlling for this possibility, thereby providing no evidence against the learning hypothesis. The first column in Table 6 reports that including new borrowing (in the past year) normalized by P i,t still yields a statistically significant coefficient on D i,t and an insignificant coefficient on the borrowing variable. The results are similar if I use the fixed effects estimator (second column) or the interaction between new borrowing and D i,t (third and fourth columns). Second, persistence of expenditure due to illness could also be a cause of the positive coefficient on D i,t. As noted earlier, the JPSC reports events underlying large expenditure, including i) an accident or disaster; ii) serious illness; and iii) physical move. Of these events, illness could be particularly persistent (e.g., Hubbard et al. (1994)), and thus experience of illness this year could include information about future medical expenditure. For example, if one suffers a certain illness this year, it may shift upward an individual s expectations of lifetime medical expenditure. The significant positive coefficient on the dummy variable found earlier might therefore merely reflect an increase in the target for life-cycle savings. The dependent variable, however, should be interpreted as an increase in the target for precautionary savings because the survey question is How much are your household s target savings for unexpected expenses such as for illness, disaster, and so on?. Still, some respondents could have misinterpreted this question, and accordingly included, at least partly, the target for life-cycle savings in that for precautionary savings. To control for this possibility, I set the dummy variable at 1 when the household experienced large expenditure, but not large expenditure accompanied by serious illness. With the new definition of the dummy to control for this possibility, the results still support the hypothesis of learning in precautionary saving. The coefficient on the dummy remains positive and statistically significant (fifth and sixth columns in the table), suggesting that the significant coefficients earlier do not result from the persistence of medical expenditure. Nonetheless, the experience of expenditure persistence may not be limited to medical expenditure. For example, if a household has a newborn baby this year, it may experience large expenditure on childcare services in subsequent years. In such a case, the household may raise the target for life-cycle savings, which the target for precautionary savings reported in the JPSC could reflect (once again because of the misinterpretation of the survey question pointed 18

19 out earlier). However, even if I control for the possibility of persistent large expenditure generally, the results continue to support the hypothesis of informal learning. Specifically, I set the dummy variable at 1 if a household experiences large expenditure in year t but not in year t+1. With this definition of the dummy, the coefficient is statistically significant (the last two columns in the table). The results are similar even when I set the dummy variable at 1 if a household experiences large expenditure in year t but not in year t + 1 or t + 2 (results not reported here). 22 Heterogeneous response to large expenditure. A household may learn more if it has experienced large expenditure multiple times. To test this hypothesis, I specify the two-year difference of the target for precautionary savings normalized by permanent income ( 2 A i,t/p i,t ) as the dependent variable, and include the dummy D twice i,t, which is 1 if D i,t 1 = 1 and D i,t = 1. As a control, include D atleastonce i,t, which is 1 if either D i,t 1 = 1 or D i,t = 1. With this specification, D twice i,t measures the impact of multiple large expenditure experiences. It turns out that the coefficient on this dummy is statistically insignificant, although positive as predicted (first two columns in Table 7), providing little evidence for the hypothesis. The response to a large expenditure shock might be weaker for those safeguarded by insurance. We can test this hypothesis by including an interaction dummy (D inscont i,t 1 D i,t ), which is 1 if a household has contributed to insurance (not including funded type) over the past year and D i,t = 1. The results provide little support to this hypothesis, with a negative (as predicted) but insignificant coefficient on this dummy (third and fourth columns in the table). The response to a large expenditure shock could also be heterogeneous across wealth and income levels. If the level of wealth is low, a household may feel more pain from large expenditure because it may have to cut back other spending (if facing a borrowing constraint). If so, such a household may learn the importance of precautionary savings more acutely and increase its target for precautionary savings more than do other households. To examine this hypothesis, consider an interaction dummy D zeroassets i,t 1 D i,t, which is 22 The motivation behind this definition of the dummy is to exclude persistency more broadly because experiencing large expenditure in years t and t + 2 may reflect weak persistency. 19

20 Table 6: Testing Learning in Precautionary Saving (1) (2) (3) (4) (5) (6) (7) (8) IV FE IV FE IV FE IV FE VARIABLES A t /Pt A t /Pt A t /Pt A t /Pt A t /Pt A t /Pt A t /Pt A t /Pt Dt (0.012)*** (0.014)*** (0.013)*** (0.014)*** new borrowt/pt (0.033) (0.021) (new borrowt/pt) Dt (0.022) (0.024) D ex illnesst (0.013)*** (0.015)** D no persistencet (0.014)*** (0.015)*** Observations 8,968 10,352 8,968 10,352 8,968 10,352 8,968 10,352 R-squared Number of id 1,807 1,807 1,807 1,807 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Notes: Each additional variable related to new borrowing during the past year is instrumented by its numerator. The control variables are log Pt and Zt. 20

21 1 if the level of liquid assets was zero a year ago and D i,t = 1 (as before, the dummy of large expenditure experience during the past year). The fifth and sixth columns in Table 7 report that contrary to expectations, the coefficient on this dummy is negative and statistically significant at the 10 percent level. The size of the negative coefficients on the interaction dummy suggests that for low-wealth households, large expenditure appears to have no impact on the target for precautionary savings. The coefficient is between 0.05 and 0.07 and roughly offsets the coefficient on D i,t. Many low-wealth households may be behaving as rule-of-thumb consumers (Campbell and Mankiw (1989)), consuming whatever they have earned. For such consumers, the target for precautionary savings could be less relevant, and their target may not be very responsive to any event, including large expenditure. To see this more clearly, replace the main dummy D i,t with an interaction dummy D posassets i,t 1 D i,t, which is 1 if a household had positive liquid assets a year ago and D i,t = 1. With this specification, the coefficient on D zeroassets i,t 1 D i,t measures the impact of large expenditure for households with zero liquid assets. The seventh and eighth columns in the table confirm that the coefficient on D zeroassets i,t 1 D i,t is statistically insignificant, which is consistent with the argument that for low-wealth households, large expenditure has no impact on the target for precautionary savings. The results do not change much from those reported in the fifth and sixth columns, when setting the dummy variable at 1 if the level of liquid assets was less than 10 percent of income a year ago and interacting it with D i,t (ninth column). 23 When the dummy is set at 1 if the level of liquid assets was in the bottom 10 percent of the population and interacted with D i,t, the size of the coefficient is similar to those reported so far, but the coefficient is statistically insignificant (tenth column). The response to large expenditure, on the other hand, does not appear to be heterogeneous across income levels. The last column in the table provides the results including the additional dummy, which is 1 if the income level is in the bottom 10 percent of the population and D i,t = 1. The coefficient on the additional dummy is not significantly different from zero. 23 Changing the wealth threshold (e.g., to 20 percent of income) does not change the results. 21

22 Table 7: Testing Heterogeneity (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) IV FE IV FE IV FE IV FE IV IV IV VARIABLES 2A t /P t 2A t /P t A t /P t A t /P t A t /P t A t /P t A t /P t A t /P t A t /P t A t /P t A t /P t D twicet (0.029) (0.045) D atleastoncet (0.016)*** (0.019)*** Dt (0.021)*** (0.024)*** (0.013)*** (0.016)*** (0.014)*** (0.013)*** (0.013)*** D inscont t 1 Dt (0.025) (0.028) D zeroassets t 1 Dt (0.031)* (0.037)* (0.029) (0.034) D zeroassets t (0.010) (0.018) (0.010) (0.018) D posassets t 1 Dt (0.013)*** (0.016)*** D lowassets 10pct t 1 Dt (0.026)* D lowassets 10pct t (0.008) D lowasset bottom10pct t 1 Dt (0.035) D lowasset bottom10pct t (0.012) D lowincome bottom10pct t 1 Dt (0.051) D lowincome bottom10pct t (0.020) Observations 7,848 8,438 8,968 10,352 8,968 10,352 8,968 10,352 8,968 8,968 8,968 R-squared Number of id 1,530 1,807 1,807 1,807 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Notes: Control variables are log Pt and Zt. 22

23 6.2. Do targets for savings affect actual savings? Although the above results generally support the hypothesis that households that experience a large expenditure increase their savings targets, they do not explain whether households change their behavior after such a shock. We can shed some light on this question by examining the relation between actual and target savings Relevance of fatalism Before investigating the relation between actual savings and the target for savings, I need to examine the relevance of fatalism in the context of the current analysis. Wu (2005) argues that if an individual has fatalistic tendencies, they believe that current and past actions have limited or no effect on determining future outcomes. 25 More specifically, he finds that those who think that luck has played an important role in determining their current financial status are more likely to have a shortfall in savings. If households become fatalistic following large expenditure, an increase in the target because of large expenditure may not increase actual savings. It is then possible that following large expenditure, households recognize the greater need for savings (and increase the target for savings), but at the same time, become fatalistic and reduce savings (or do not increase them at all). To test if households become fatalistic because of large expenditure, it would be ideal to estimate the following equation: Measure of fatalism i,t = β 0 + β 1 D i,t + β 2 log P i,t + β 3 Z i,t + ε i,t, (6) where D i,t is a dummy variable indicating large expenditure, log P i,t is log permanent income as proxied by actual income, and Z i,t is a vector of demographic variables, cohort dummies, and time dummies. Unfortunately, it is difficult to obtain a good measure of fatalism (or lack of fatalism) in the JPSC. For this reason, as the dependent variable in equation (6), I include a dummy variable that is 1 if a household wishes to enroll a child in college. The notion behind this is that if a household wishes 24 As discussed in the Introduction, investigating the correlation between actual savings and expenditure is not sufficient for this purpose. 25 From a theoretical perspective, Kremer (1996) presents an economic model explaining how the increased risk of HIV could make highly sexually active individuals fatalistic, and thus paradoxically lead them to increase their already high level of sexual activity. 23

24 Table 8: Testing the Relevance of Fatalism (1) (2) (3) VARIABLES Probit Probit Logit D t (0.047)** D ex education t (0.073) (0.125) Observations 10,544 10,544 10,544 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Notes: Control variables are Z t. a child to enter college, it suggests that it believes a certain decision will make a difference in the child s life. Although not perfect, this belief should then reflect a lack of fatalism. The results imply that a household s wish to enroll a child in college is unaffected by large expenditure experience. The first column in Table 8 reports that when using the probit model, the coefficient on the large expenditure dummy (D i,t ) is positive and statistically significant. However, the positive coefficient could also reflect large expenditure on children s education. For example, parents who have spent large sums of money on their child s education are more likely to hope their child will also enter college. Indeed, once I set the dummy at 1 when the household has experienced large expenditure excluding educational expenses, the coefficient remains positive, but becomes insignificant (second column in the table). A logit model provides similarly weak results (third column). Of course, this paper s finding is merely that large expenditure experience does not affect a household s wish to enroll a child in college, nothing more. Moreover, both fatalistic and nonfatalistic households might want their child to enroll in a college. If so, the coefficient on D i,t would not really measure the impact of large expenditure on fatalism. That said, we could at least say that given the potential link between fatalism and a household s attitude toward its child s education, the analysis thus far has not found evidence for the impact of large expenditure on fatalism. 24