Is Stock Investment Contagious among Siblings?

Transcription

1 Is Stock Investment Contagious among Siblings? Kiichi Tokuoka Abstract A household may learn the importance of stock investment from its siblings. Using the probit and logit models, this paper tests empirically the learning hypothesis that a household is more likely to purchase stocks if its siblings have bought stocks, and finds evidence for the hypothesis. The estimates obtained in the analysis imply that a household s probability of stock purchases increases by about 2 percentage points if a sibling has purchased stocks. The positive results are not due to alternative explanations, such as financial support from siblings, common shocks, or unobservable correlations. Keywords: Learning, Siblings, Stock investment JEL classification: G11, D83 I am grateful to Christopher Carroll, Raphael Lam, Yasuhisa Ojima, and those who participated in the seminars at Johns Hopkins University and Tokyo University on learning in financial decisions for helpful comments. This paper is based on the research I started while working at the International Monetary Fund, but the views presented in this paper are those of the author, and should not be attributed to the International Monetary Fund or the Japanese Ministry of Finance. address: [email protected] (Kiichi Tokuoka ) Preprint submitted to Elsevier May 30, 2015

2 1. Introduction A large macroeconomic literature, particularly that concerning monetary policy, has examined the implications of the process whereby agents learn from their own or others experiences. 1 Comparable studies on learning at the micro level appear to lag behind these developments but are gradually catching up in a number of areas including, as discussed below, individual stock investment and saving. With individual stock investment, it is natural to believe that stock investment is contagious a household hears from others about their stock purchases, learns of the potential benefits of stock investment, and subsequently purchases stocks. Such learning could have a large aggregate impact because individuals can potentially learn from a great variety of sources; e.g., relatives, friends, colleagues, and neighbors. In turn, this could lead to herding behavior and might even contribute to the creation of an asset bubble, with sometimes devastating impacts on the economy as a whole. While the idea of learning from others in stock investment is not new, the main contribution of this paper is that it is the first to find direct evidence for learning in stock investment from siblings. 2 Several existing studies have tested and supported the existence of learning in stock investment from one s own experiences (e.g., Malmendier and Nagel (2011)) but not from the experiences of others. Yet other studies have investigated learning about stock trading from local peers (e.g., Hong et al. (2004), Brown et al. (2008)). However, these studies neither define the nature of local peers nor identify precisely from whom one learns the merits of stock market participation. An exception is Li (2014), who reported robust evidence for learning (information sharing) between parents and children but found no evidence for learning in stock investment between siblings. Although his work is indeed a notable contribution to the literature on social learning in stock investment, the existence of inheritances and other financial transfers from parents to children, some of which are perhaps not reported in the survey, may demand careful interpretation of the results. For this reason, I reexamine learning 1 Evans and Honkapohja (2009) provide a comprehensive review of studies on the learning process in monetary policy. 2 Using data on Swedish twins, Calvet and Sodini (2014) find that regressions of the share of risky assets in the portfolio have a lower (adjusted) R-squared for twins communicating more frequently, which suggests that communication is driving stock holdings. 2

3 from siblings with a larger set of independent variables (discussed below) to control for unobservable factors. For this purpose, I use the Panel Study of Income Dynamics (PSID), the structure of which allows us to identify siblings exactly. The estimates obtained in the analysis imply that a household s probability of stock purchases increases by about 2 percentage points if a sibling has purchased stocks. Moreover, I estimate that a household that has decided to purchase stocks on hearing news of a sibling s stock investment will increase stock purchases by as much as 4.5 percent of net worth. Of course, identification is a serious challenge for testing social learning (Manski (1993) and Manski (2000)). However, I find no support for any of the alternative explanations, including financial support from siblings, common shocks, or unobservable correlations. The remainder of the paper is structured as follows. The next section reviews the related literature. Section 3 describes the PSID data, Section 4 presents the econometric model for the empirical analysis, and Section 5 reports the results, followed by the conclusions in the final section. The Appendix introduces a theoretical model with learning in stock investment to provide a potential mechanism for learning from siblings as tested empirically in this paper. 2. Related empirical literature Over the past decade, economists have empirically studied informal learning in individual investment from own and others experiences. In the field of precautionary or retirement saving, a few studies have investigated exactly from whom people learn. Learning in investment from own and others experiences. Several 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 lower stock market returns over their lives tend to invest a smaller proportion of their assets in stocks. Their main contribution is that they controlled for the difficulty faced by Ameriks and Zeldes (2004) in separating cohort effects from the age and time effects on these decisions. Unlike the current paper, 3

4 these studies all investigated learning about individual investment from only one s own experiences, not from the experiences of others. Two strands of literature concern informal learning from others (social learning) about retail stock investment, namely 1) action-based learning and 2) outcome-based learning Action-based learning is a learning mechanism whereby one changes one s behavior on hearing/observing others actions. For instance, Shive (2010) considered action-based learning, finding empirical evidence for the impact of peer actions on stock purchases. Similarly, Ivkovic and Weisbenner (2007) found that neighbors purchases of stocks from an industry increased one s purchases of stocks from the same industry. 4 Other action-based studies include Brown et al. (2008) and Hong et al. (2004). The former reported that individual stock market participation (stock holding) relates to average stock market participation in the community. Similarly, Hong et al. (2004) found that more social households are more likely to hold and invest in stocks. 5 However, these studies do not identify exactly from whom individuals learn about stock investment. A notable exception is Li (2014), who reported evidence for the hypothesis that children are more likely to enter the stock market when parents have started stock investment, but he was unsuccessful in finding evidence for learning in stock investment between siblings. This motivates me to reexamine learning about stock investment from siblings. I also consider whether learning from siblings is action- or outcome-based (as defined below), finding results favoring the former over the latter. 2. Outcome-based learning is a mechanism whereby one changes behavior based on the outcomes of others actions. Empirical work on outcomebased learning in stock investment is limited. 6 A recent example is 3 Related, Bursztyn et al. (2014) studied the impact of social learning in purchases of a financial product designed for a special experiment. 4 In a related vein, Hong et al. (2005) reported that fund managers tend to purchase stocks that other fund managers in the same city have been buying. 5 Related, Heimer (2014) reported that social interaction is associated with active portfolio management. 6 Empirical studies on outcome-based learning in general are also few in number (exceptions include Conley and Udry (2010) and Munshi (2004)), although there are numerous theoretical studies (including Cao et al. (2011) and Banerjee and Fudenberg (2004)). 4

5 Kaustia and Knupfer (2012), who conclude that positive local stock returns have an impact on individual stock market entry decisions. Social learning in saving behavior. In the field of decision making between saving and consumption an area closely related to individual investment several analyses have examined empirically informal learning from others (social learning). 7 In the area of precautionary saving using experimental results, Ballinger et al. (2003) suggest that in solving the precautionary saving model, later generations learn from earlier generations and perform significantly better. 8 A few studies are more explicit about from whom one could learn. For example, Tokuoka (2013) shows empirically that one s own saving rate may rise if a sibling has been unemployed. In the field of retirement savings, Lusardi (2003) s empirical results suggest that consumers learn from their older siblings and will have larger savings, while Duflo and Saez (2002) find that the decisions of other employees have a positive impact on one s decision to participate in a tax-deferred account plan. By contrast, Beshears et al. (2015) report that information on peers high saving rates actually reduce savings of individuals with low saving rates. Social learning and interactions in other areas. Other empirical works on social learning and interactions cover a wide range of areas. Several studies on other financial decisions exist, including, e.g., group lending (Li et al. (2013)) and purchase of goods (e.g., automobiles (Grinblatt et al. (2008)), movies (Moretti (2011)), lotteries (Mitton et al. (2014)), and even the choice of dishes from a restaurant menu (Cai et al. (2009))). 9 7 In this field, there also exists a literature on informal learning from own experiences (e.g., Choi et al. (2009), Owen and Wu (2007)) and on formal learning about retirement saving, such as through joining seminars (e.g., Lusardi and Mitchell (2007), Lusardi (2005), Bernheim and Garrett (2003), and Duflo and Saez (2003)). 8 For purely theoretical studies on learning in saving, see Howitt and Ozak (2009), Allen and Carroll (2001), and Lettau and Uhlig (1999). 9 Other studies in financial areas include the use of welfare (Bertrand et al. (2000)), the choice of a health plan (Sorensen (2006)), and health insurance enrollment (Liu et al. (2013)). Examples of studies on nonfinancial areas include farming (Conley and Udry (2010), Munshi (2004), Foster and Rosenzweig (1995)), choice of workplace (Bayer et al. (2008)), use of drugs (Kremer and Miguel (2007)), academic performance (Carrell et al. (2009), Zimmerman (2003), Sacerdote (2001)), and criminal activity (Glaeser et al. (1996)). For a comprehensive literature review of social learning, see, e.g., Dahl et al. (2014) and Kaustia and Knupfer (2012). 5

6 3. Data The empirical analysis employs the PSID. This is a panel data set containing data on US households and individuals, and most importantly, it contains data on split-off households formed by household members who moved out of the households interviewed in the original survey in Taking advantage of this data structure, I identify households whose heads are siblings of each other by tracking sons and daughters in the original survey in 1968 (see Tokuoka (2013) for the method of identifying siblings) and include in the empirical analysis only households whose head or spouse was recorded as a son or a daughter in the 1968 survey. The PSID has collected data including household assets every two years since 1999 through to 2011 (representing seven survey waves). As I specify a two-year lag in some of the regression variables, I construct the first wave with the data, the second with the data, and so on. Consequently, the data set used for the empirical analysis comprises six waves. Table 1 details the means of the main variables. For the empirical analysis, I dropped households with zero total family income or negative net worth. As shown, while the household head is generally older in the later waves, the level of total family income (deflated by the 2000 GDP deflator) is relatively stable across years. The share of stocks in net worth is modest at around 5 percent. 10 As I discuss in the next section, the key variable is DP artsib t a dummy variable indicating whether one of the siblings of the household head is participating in the stock market (holding stocks)). 11 Its mean is 20 to 34 percent, but this may appear to be low given that the mean of DP art t the dummy variable identifying whether the household is participating in the stock market (holding stocks) is between 18 and 30 percent. For example, assuming that each household has two siblings (both direct siblings and siblings-inlaw), the mean of DP art t implies that roughly twice 18 to 30 percent (= 36 to 60 percent) of household heads siblings own stocks. The apparently low level of DP artsib t emerges because the data set contains only siblings in the original 1968 PSID survey and does not include siblings born since 10 The table reports the two-year lag because that is the variable used in the empirical analysis. 11 The PSID excludes stocks held in employer-based pensions or IRAs. 6

7 then (furthermore, since 1968, some of the siblings reported in 1968 may have dropped out of the sample). The mean of DP ursib t a dummy variable taking a value of one if a sibling of household i s head or spouse has purchased stocks between years t 2 and t appears similarly low for the same reason. A related but more important data issue is that because of the data structure, the significant effects of learning from siblings reported below comprise a lower bound of the true impact of learning from siblings. As noted already, the data set for the current analysis contains only households whose head or spouse was recorded as a son or a daughter in the 1968 survey. This data structure implies that if the household head (spouse) was a son or a daughter in 1968 and is married, the spouse s (head s) siblings (siblings-in-law for the head (spouse)) are not included in the sample. 12 In other words, roughly half of the siblings cannot be identified, and their data are not available. 13 As a result, the coefficients on sibling-related variables, such as DP ursib t (dummy of siblings stock purchases) and its lag, are effectively subject to the measurement error (missing observation) problem, and thus their coefficients are likely to be biased toward zero. In addition to the data set used for this paper ( ), I could construct an alternative data set containing three survey waves, , , and , because the PSID reported wealth data every five years between 1984 and I use the data set containing data for the period because it is much larger, comprising six survey waves with over 10,000 observations. I cannot combine the alternative data set ( ) with the current data set ( ) because of the difference in the periods (five years in the alternative data set against two years in the current data set). 4. Econometric model This section presents the econometric models used to test the hypothesis of learning from siblings in stock investment but without specifying the mechanism underpinning learning from siblings because there are a number of potential mechanisms. (The Appendix lays out a potential theoretical 12 This is the case unless both head and spouse were recorded in the 1968 survey. 13 For additional details about the data structure, see Tokuoka (2013). 7

8 Table 1: Average of key variables year age log total family income (deflated by 2000 GDP deflator) stock share in net worth (two-year lag) dummy male dummy marriage dummy white number of children DP artsibt (dummy siblings stock market participation) DP artt (dummy stock market participation) DP ursibt (dummy siblings stock purchases) DP urt (dummy stock purchases) number of observations 2,160 2,152 2,154 2,119 2,095 1,980 Notes: The sample comprises households whose head or spouse was recorded as a son or a daughter in the original PSID survey in The sample excludes households with zero total family income or negative net worth, and then to avoid the results being affected by extreme observations, households with top and bottom 1 percent of these variables in the distribution are also dropped. The table reports two-year lag of the stock share in net worth because that is the variable used in the empirical analysis later in the paper. 8

9 mechanism for learning from siblings and discusses several other potential mechanisms.) As a first step, following the existing literature, we specify the dummy variable indicating stock market participation (stock holding) as the dependent variable 14 and estimate the following econometric model, using probit and logit models. I take two years as the interval, as the PSID conducts its survey every two years. DP art i,t = β 0 +β 1 DP artsib i,t +β 2 DP artsib i,t 2 +β 3 DP art i,t 2 +β 4 F i,t +β 5 Z i,t. (1) DP art i,t is the dummy of stock market participation (stock holding), taking a value of one if household i owns stocks in year t. DP artsib i,t takes a value of one if a sibling of household i s head or wife is participating in stock market (owning stocks) in year t. DP artsib i,t 2 is the two-year lag of DP artsib i,t. DP art i,t 2 is the two-year lag of DP art i,t. F i,t is the vector of financial variables. Following previous literature examining stock investment decisions, F i,t contains dummies for every 5 percent of the distribution of total family income (19 dummies) and dummies for every 5 percent of the distribution of net worth (19 dummies). 15 Z i,t is the vector of other variables, containing a number of variables standard in the literature, specifically, age, age squared, a dummy variable indicating the sex of the household head, a dummy variable denoting marriage, a dummy variable indicating whether the household head is white, and the number of children in the household (following Carroll and Samwick (1997) who also used the PSID). Other controls in Z i,t are a dummy variable indicating whether the household head has a college degree, five region 14 For example, Hong et al. (2004), Brown et al. (2008), and Malmendier and Nagel (2011) all specified stock market participation as the dependent variable. 15 This is the approach taken by Hong et al. (2004) and other studies took a similar approach (e.g., Brown et al. (2008) created dummies for every percentile of the income distribution). 9

10 dummies identifying household location interacted with time dummies, eight household head occupation dummies, and 12 industry dummies identifying household head employment (not included in Carroll and Samwick (1997)). 16 Using the dummy of stock purchases as the dependent variable is a more direct way of testing the learning effect, as stock market participation (stock holding) is a result of past stock purchases. 17 For this reason, I estimate the following econometric model as a preferred specification: DP ur i,t = β 0 +β 1 DP ursib i,t +β 2 DP ursib i,t 2 +β 3 stockshare i,t 2 +β 4 F i,t +β 5 Z i,t. (2) DP ur i,t takes a value of one if household i has purchased stocks between years t 2 and t. DP ursib i,t takes a value of one if a sibling of household i s head or wife has bought stocks between years t 2 and t. DP ursib i,t 2 is the two-year lag of DP ursib i,t. stockshare i,t 2 is the share of stocks in net worth in year t 2. The definitions of F i,t and Z i,t are the same as above. Either or both β 1 and β 2 equations (1) and (2) will be positive if the learning hypothesis holds. However, even if the hypothesis holds, households may change their asset portfolio only gradually. For example, the presence of transaction costs could lead to a delayed effect. Alternatively, insufficient liquid assets may oblige a household to accumulate liquidity before purchasing 16 The five regions are: northeast, north central, south, west, and others (Alaska and Hawaii). The eight occupation groups are: professional and technical workers; managers (not self-employed); managers (self-employed); clerical and sales workers; craftspersons; operatives and laborers; farmers and farm laborers; and service workers. The 12 industry dummies are: agriculture, forestry, and fishing; mining; construction; manufacturing; transportation, communications, and utilities; wholesale and retail trade; finance, insurance, and real estate; business and repair services; personal services; entertainment and recreation services; professional and related services; and public administration. The occupation and industry groupings are from Carroll and Samwick (1997). 17 Shive (2010) also investigated the learning impact on stock purchases. 10

11 stocks, delaying the purchase of stocks. If any of these delayed effects dominates, then the two-year lag DP artsib i,t 2 or DP ursib i,t 2 may be more important than the current variable (DP artsib i,t or DP ursib i,t ). Learning takes the form of either direct communication or observational learning. The latter takes place if one s observations of other people influence one s own behavior. β 1 or β 2 (if significant) is likely to capture the impact of direct communication because it may be more common for one to hear about siblings stock holdings or purchases than to observe them purchasing stocks online or at a financial institution. I could test learning from other relatives, particularly parents, as done by Li (2014), but that would make the interpretation of the results more difficult. If we include a dummy variable for parents stock market participation or stock purchases as an independent variable, it is likely to correlate with inheritances and other income transfers to their children, some of which may be unobserved in the data. Consider, for example, the case where parents receive capital gains after purchasing stocks and provide an inheritance to their children by tapping some of the gains. If children purchase stocks without reporting these inheritances, this would create an unobserved correlation between parents and children s stock purchase decisions, biasing the empirical estimates. Another example is financial transfers to children in the form of educational expenses for grandchildren. Although the PSID surveys the amount of financial support to someone outside of the household, it is plausible to assume that some educational and other expenses are not reported (as financial support ) in the PSID by respondents, which may create unobserved correlations. Using the dummy variable for siblings can mitigate this problem. 5. Empirical results 5.1. Regression of stock market participation When I estimate the learning impact on stock market participation using equation (1), the results support the learning hypothesis. The first column in Table 2 reports that the coefficient on the dummy of siblings stock market participation DP artsib i,t is insignificant, but this may be because the delayed effect is more important (discussed in Section 4). Indeed, once the two-year lag DP artsib i,t 2 is included in the regression, its coefficient is statistically significant (second column in the table). The coefficient on 11

12 DP artsib t 2 implies that if a sibling owned stocks in year t 2, the probability of household holdings increases by 2.1 percentage points in year t. The results are similar using the logit model (third column in the table) or OLS (last column in the table) Baseline regression of stock purchases Now turn to the preferred specification (equation (2)) and estimate the learning impact on stock purchases. The results support the hypothesis of learning from siblings in stock purchases. The first column in Table 3 shows that by running the probit model, the coefficient on the lagged dummy of siblings stock purchases DP ursib t 2 is 0.15 and statistically significant. The positive, but weaker, coefficient on DP ursib t (compared with DP ursib t 2 ) is consistent with the existence of the delayed effect. The coefficient on DP ursib t 2 implies that if a sibling purchased stocks between years t 4 and t 2, the probability of a household purchasing stocks rises by 1.6 percentage points in the subsequent two-year period (between years t 2 and t). 19 The results using the logit model are similarly strong (second column in the table). These positive results contrast with those of Li (2014), who also used the PSID but did not find evidence for learning in stock investment from siblings. The difference may reflect the following. The empirical analysis in the current paper includes only households whose head or spouse was a son or a daughter in the 1968 survey, mitigating the measurement error (missing observation) problem, which Li (2014) faced. 20 Unlike the current paper, he used all the households whose head or spouse has a parent, child, or sibling in the PSID (in other words, he used both parents and children in the 1968 original survey). While the total sample size of his data set is larger than that of 18 Henceforth, the current paper omits the OLS regression results, but the results are similar to the probit and logit results reported below. 19 This in fact may be an underestimate of the cumulative impact of siblings stock purchases because it measures only the lagged impact. The coefficient on DP ursib t (first column in Table 3) infers that if a sibling purchases stocks, the probability of household i purchasing stocks increases by 0.2 percentage points. 20 As discussed in Section 3, the analysis in this paper still faces the measurement error problem, but that does not undermine the significant results so far because the measurement error problem is likely to bias the coefficients downward. 12

13 Table 2: Regression of stock market participation VARIABLES (1) (2) (3) (4) probit probit logit OLS DP artt DP artt DP artt DP artt DP artsibt (dummy of sibling stock market participation) (0.033) (0.043) (0.078) (0.0094) DP artsibt 2 (lagged dummy of sibling stock market participation) (0.043)* (0.076)** (0.0094)** DP artt 2 (dummy of stock market participation) (0.033)*** (0.033)*** (0.057)*** (0.013)*** age (0.020)*** (0.020)*** (0.035)*** (0.0043)** age 2 / e e e-07 (1.9e-06)*** (1.9e-06)*** (3.5e-06)*** (4.2e-07)** dummy male (0.066) (0.066) (0.12) (0.010) dummy marriage (0.056) (0.056) (0.10) (0.011) dummy white (0.043)*** (0.043)*** (0.080)*** (0.0070)*** dummy college degree (0.037)*** (0.037)*** (0.066)*** (0.0090)*** number of children (0.017) (0.017) (0.031) (0.0033) Observations 12,660 12,660 12,660 12,660 R-squared Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Notes: The sample comprises households whose head or spouse was recorded as a son or a daughter in the original PSID survey in The sample excludes households with zero total family income or negative net worth, and then to avoid the empirical analysis being affected by extreme observations, households with top and bottom 1 percent of these variables in the distribution are also dropped. The dependent variable is DP artt (dummy of stock market participation (stock holding)). The independent variables not shown in the table are dummies for every 5 percent of the distribution of total family income (19 dummies), dummies for every 5 percent of the distribution of net worth (19 dummies), the five region dummies interacted with the time dummies, the eight occupation dummies, and the 12 industry dummies. 13

14 Table 3: Baseline regression of stock purchases VARIABLES (1) (2) (3) (4) (5) (6) (7) (8) probit logit probit logit probit logit probit logit DP urt DP urt DP urt DP urt DP urt DP urt DNetP urt DNetP urt DP ursibt (dummy of sibling stock purchases) (0.058) (0.11) (0.058) (0.11) DP ursib t 2 (lagged dummy of sibling stock purchases) (0.053)*** (0.100)*** (0.053)*** (0.100)*** DP urorsellsibt (dummy of sibling stock purchases or sales) (0.053) (0.100) DP urorsellsib t 2 (lagged dummy of sibling stock purchases or sales) (0.050)*** (0.094)*** DSellSibt (dummy of sibling stock sales) (0.086) (0.16) DSellSib t 2 (lagged dummy of sibling stock sales) (0.087) (0.16) Observations 12,623 12,623 12,623 12,623 12,623 12,623 12,623 12,623 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Notes: The sample comprises households whose head or spouse was recorded as a son or a daughter in the original PSID survey in The sample excludes households with zero total family income or negative net worth, and then to avoid the empirical analysis being affected by extreme observations, households with top and bottom 1 percent of these variables in the distribution are also dropped. The dependent variable is DP urt (dummy of stock purchases) or DNetP urt (dummy of net stock purchases). The independent variables not shown in the table are stockshare t 2 (lagged stock share in net worth), dummies for every 5 percent of the distribution of total family income (19 dummies), dummies for every 5 percent of the distribution of net worth (19 dummies), and Zt (defined in Section 4). 14

15 the current paper, if researchers focus on siblings, his sample selection creates the measurement error problem, making it more difficult to find a significant learning (information sharing) effect from siblings. Li (2014) reported that only half of the households in his sample are households whose heads have siblings in the sample (i.e., the household head or spouse was a son or a daughter in the 1968 survey). The remaining households do not have siblings in the data set, with zero (missing) values for sibling-related variables. This paper included more controls than Li (2014). For instance, following the previous literature, the current paper included the dummies for every 5 percent of the distribution of net worth (19 dummies), five region dummies interacted with time dummies, eight household head occupation dummies, and 12 industry dummies, which may help to capture household characteristics better (Li (2014) did not include these variables in his regressions). 21 A household may purchase stocks if it hears from its siblings about their stock transactions in general, not just stock purchases. Using the dummy for siblings stock transactions (either purchases or sales) DP urorsellsib t 2, its coefficient is slightly lower (third and fourth columns in Table 3), suggesting that siblings sales of stocks do not impact much on the household s decision on whether to purchase stocks. Indeed, if I use the dummy for siblings stock sales DSellSib t 2, its coefficient is positive but becomes insignificant (last two columns in the table). The results are robust with respect to an alternative dependent variable. Specifying the dummy variable denoting net purchases (stock purchases minus sales) DNetP ur t as the dependent variable also yields strong results (last two columns in Table 3) Possible alternative explanations In a general context, Manski (2000) pointed out that social learning is difficult to distinguish from other forces because the results may be subject to 21 Furthermore, to control for preferences, the analysis later in this paper added dummies indicating the household head s health conditions, whether the household head is now smoking or has ever smoked, and the number of cigarettes that the household head smokes per day. 15

16 the correlated effects (unobservable correlation) problem. Researchers typically address this problem, by including additional control variables, finding exogenous variables, or using the fixed effects estimator or the instrumental variable estimator. In the current context, one might argue that the positive coefficients for DP ursib t 2 may result from the existence of financial support, common shocks, or unobservable correlations. As detailed below, by including additional controls or using the fixed effects estimator, I find no evidence supporting any of these explanations. Financial support. If a sibling has purchased stocks and makes profits, the household head may obtain financial support from a sibling and subsequently purchase stocks with the additional cash offered by the sibling. To control for this possibility, I include a dummy variable DP urf insupportsib t 2 that takes a value of one if the key dummy DP ursib t 2 = 1 and a sibling provided support to others (between years t 4 and t 2). 22 Even with this additional control, the coefficient on DP ursib t 2 remains statistically significant (first and second columns of Table 4). Another way of controlling for this possibility is to include a dummy variable DP urp rofitssib t 2 that takes a value of one if a sibling has purchased stocks between years t 2 and t (DP ursib t 2 = 1) and made profits from the stock investment. The estimated coefficient on DP urp rofitssib t 2 is insignificant, while the coefficient on DP ursib t 2 remains significant (third and fourth columns of Table 4), providing no evidence for the impact of financial support (when a sibling makes profits from stock investment). The results are similar when including the dummy, which takes a value of one when DP ursib t 2 = 1 and returns from stocks have been in excess of 10 percent (not reported here). 23 These negative (although insignificant) coefficients on the dummy also do not support the outcome-based learning or selective communication theorized by Han and Hirshleifer (2013). Selective communication is a form of communication where investors are more likely to discuss their outcome of investment if they have made profitable investment. As a result, people tend to invest more in stocks if the stock performance of their local peers is 22 The PSID reports only the total amount of financial support, which includes not only support to a sibling but also other kinds of support (e.g., support for elderly parents). 23 Using an alternative threshold (e.g., 25 percent) gives similar results. 16

17 Table 4: Testing alternative explanations (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) probit logit probit logit probit logit probit logit FE logit FE probit logit DP urt DP urt DP urt DP urt DP urt DP urt DP urt DP urt DP urt DP urt DP urt DP urt VARIABLES with prefs with prefs DP ursibt (0.057) (0.11) (0.058) (0.11) (0.058) (0.11) (0.058) (0.11) (0.15) (0.0095) (0.058) (0.11) DP ursib t (0.057)*** (0.11)*** (0.074)*** (0.14)*** (0.054)*** (0.10)*** (0.054)*** (0.10)*** (0.14)** (0.0090)** (0.054)*** (0.100)*** DP urf insupportsib t (0.12) (0.22) DP urp rofitssib t (0.091) (0.17) DP ursameindsib t (0.31) (0.62) DP ursameoccupationsib t (0.32) (0.63) Observations 12,623 12,623 12,623 12,623 12,623 12,623 12,623 12,623 2,984 12,660 12,623 12,623 R-squared Number of id 546 2,845 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Notes: The sample comprises households whose head or spouse was recorded as a son or a daughter in the original PSID survey in The sample excludes households with zero total family income or negative net worth, and then to avoid the empirical analysis being affected by extreme observations, households with top and bottom 1 percent of these variables in the distribution are also dropped. The dependent variable is DP urt (dummy of stock purchases). The independent variables not shown in the table are stockshare t 2 (lagged stock share in net worth), dummies for every 5 percent of the distribution of total family income (19 dummies), dummies for every 5 percent of the distribution of net worth (19 dummies), and Zt (defined in Section 4). 17

18 more favorable, and such a communication should help produce positive coefficients for the dummy variable. While Kaustia and Knupfer (2012) found results consistent with the existence of selective communication, the results in the current paper do not, suggesting that siblings discuss stock market experiences regardless of investment performance, thereby eliminating the effect of selective communication. Common shocks. The positive coefficients on the dummy of siblings stock purchases (DP ursib t 2 ) could be due to common shocks across siblings, although the industry, occupation, and region dummies already included in the regression should control for common shocks to some extent. For example, siblings may be more likely to work in the same company, and as a result face the same labor income shocks or the same capital income shocks if both of them own the company s stock. To control for this possibility, I include a dummy variable DP ursameindsib t 2 that takes a value of one if DP ursib t 2 = 1 and the household head and sibling work in the same industry. 24 With this dummy, the coefficient on DP ursib t 2 does not change much and remains significant (fifth and sixth columns). Similarly, after controlling for common occupation shocks, the coefficient on DP ursib t 2 = 1 remains significant (seventh and ninth columns). Controlling for geographically common shocks gives similar results (not reported here, but see subsection 5.4). Unobservable correlation. The positive results could also arise from unobservable correlation, specifically the correlation of preferences between siblings. The fixed effects (FE) logit model controls for household-specific unobservable factors, such as preferences, assuming that they are time-invariant. The disadvantage of the FE logit model is that it uses only observations with a change in the state (either (DP ur t, DP ur t 2 ) = (1, 0) or (DP ur t, DP ur t 2 ) = (0, 1)), losing much of the information in the data (Wooldridge (2001)). The ninth column of Table 4 reports that using the FE logit model, the coefficient on DP ursib t 2 remains significant, providing evidence against unobservable correlation between siblings. The linear FE model also gives strong results (10th column). Similarly, the last two columns in the table report that the coefficient on DP ursib t 2 = 1 is significant, even with additional independent variables controlling for unobservable preferences dummies indicating the household 24 The PSID cannot identify which respondents work. 18

19 head s health conditions (excellent, very good, good, or fair), whether the household head is now smoking or has ever smoked, and the number of cigarettes the household head smokes per day Communication The learning effect could be greater if a household hears about its siblings stock purchases multiple times, and if a household s head/wife and their siblings communicate more frequently (e.g., if they live nearby or their ages are close). Some of the results in this subsection are consistent with the hypothesis that the learning impact is stronger if a household hears about its siblings stock purchases more than once Multiple news of stock purchases To test the hypothesis that the learning impact is greater if a household hears about its siblings stock purchases multiple times, include the dummy DP ursibmultiple which is one if DP ursib t 2 = 1 and its lag DP ursib t 4 = 1. With this additional dummy, its coefficient is positive but slightly below the 10 percent significance level (first column of Table 5). The coefficient turns significant at the 10 pecent when running the logit model (second column in the table). This serves as some additional support for the social learning hypothesis because under alternative explanations, such as common shocks, communication is not relevant Frequency of communication State. The sign on the key dummy is consistent with the hypothesis that the learning impact is stronger if siblings live nearby and communicate more frequently, but the results are not strong. Specifically, when I set the dummy variable DP ursamestatesib t 2 at one if DP ursib t 2 = 1 and a household head and their sibling live in the same state, the estimated coefficient is positive, although not statistically significant (third and fourth columns of Table 5). The insignificant, although positive, coefficient suggests that communication devices such as phones and allow people to communicate anytime they like and may be weakening the impact of physical distance on the frequency of communication. 25 Barsky et al. (1997) report that (measured) risk tolerance is related to risky behaviors such as smoking. 19

20 Table 5: Testing communication (1) (2) (3) (4) (5) (6) probit logit probit logit probit logit DP ur t DP ur t DP ur t DP ur t DP ur t DP ur t VARIABLES with prefs with prefs with prefs with prefs with prefs with prefs DP ursib t (0.058) (0.11) (0.058) (0.11) (0.058) (0.11) DP ursib t (0.064) (0.12) (0.060)** (0.11)** (0.063)** (0.12)** DP ursibm ultiple (0.092) (0.17)* DP ursamestatesib t (0.097) (0.18) DP urcloseagesib t (0.090) (0.17) Observations 12,623 12,623 12,623 12,623 12,623 12,623 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Notes: The sample comprises households whose head or spouse was recorded as a son or a daughter in the original PSID survey in The sample excludes households with zero total family income or negative net worth, and then to avoid the empirical analysis being affected by extreme observations, households with top and bottom 1 percent of these variables in the distribution are also dropped. The dependent variable is DP ur t (dummy of stock purchases). The independent variables not shown in the table are stockshare t 2 (lagged stock share in net worth), dummies for every 5 percent of the distribution of total family income (19 dummies), dummies for every 5 percent of the distribution of net worth (19 dummies), and Z t (defined in Section 4). 20

21 An alternative interpretation of the results could be that the additional dummy is capturing a variety of state common shocks (e.g., common shocks to income and stock returns and local media rumors/reports) not fully controlled for by the variables already included in the regression. Given this interpretation, the positive coefficients on DP ursib t 2 = 1 reported here (third and fourth columns in the table) provide additional evidence against the argument that the significant coefficient on DP ursib t 2 results from common shocks. Age. If siblings ages are close, they may also communicate more often because of a smaller mental gap, but the results do not support this hypothesis either. When setting the dummy DP urcloseagesib t 2 at one if DP ursib t 2 = 1 and the age difference between the head of a household and the head of their sibling s household (that has purchased stocks) is two years or less, its coefficient is insignificant (last two columns of Table 5). The results are similarly weak, when setting the dummy at one if DP ursib t 2 = 1 and the ages of the household head and the head of their sibling s household are the same (results not reported in the table). These results are consistent with the view that the age difference does not affect the frequency of communication between siblings Testing heterogeneity This subsection investigates potential heterogeneous learning effects from siblings, resulting from retirement and household assets holdings Retirement and age Once retired, the household head may lose their appetite for risky assets, including stocks, because there is no longer access to labor income and the capacity to absorb shocks to assets is now less. To investigate this possibility, I include a dummy variable DP urretiredsib t 2 that takes a value of one if DP ursib t 2 = 1 and the head of the household has already retired. The results do not support the retirement effect. As expected, the estimated coefficient on the dummy is negative but insignificant (first and second columns of Table 6). If I set the value of the dummy variable DP urageov55sib t 2 at one when the age of the household head is 55 years 21

22 Table 6: Testing heterogeneity (1) (2) (3) (4) (5) (6) (7) (8) probit logit probit logit probit logit probit logit DP ur t DP ur t DP ur t DP ur t DP ur t DP ur t DP ur t DP ur t VARIABLES with prefs with prefs with prefs with prefs with prefs with prefs with prefs with prefs DP ursib t (0.058) (0.11) (0.058) (0.11) (0.059) (0.11) (0.058) (0.11) DP ursib t (0.054)*** (0.10)*** (0.056)*** (0.10)*** (0.062)*** (0.11)*** (0.054)*** (0.10)*** DP urretiredsib t (0.25) (0.49) DP urageov55sib t (0.15) (0.29) DP urnostocksib t (0.11)*** (0.21)*** DP urlwlq25p ctincsib t (0.23) (0.48) Observations 12,623 12,623 12,623 12,623 12,623 12,623 12,623 12,623 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Notes: The sample comprises households whose head or spouse was recorded as a son or a daughter in the original PSID survey in The sample excludes households with zero total family income or negative net worth, and then to avoid the empirical analysis being affected by extreme observations, households with top and bottom 1 percent of these variables in the distribution are also dropped. The dependent variable is DP ur t (dummy of stock purchases). The independent variables not shown in the table are stockshare t 2 (lagged stock share in net worth), dummies for every 5 percent of the distribution of total family income (19 dummies), dummies for every 5 percent of the distribution of net worth (19 dummies), and Z t (defined in Section 4). or higher, 26 the results are similarly weak (third and fourth columns of Table 6) Zero stock holdings When households do not hold stocks, the impact of their siblings stock purchases on their own stock investments could be either weaker or stronger. If households do not own stocks because they know a lot about stock investment but are not interested in investing in stocks, then news from siblings about stock purchases should not matter. On the other hand, if households do not have stocks just because they do not know about the merits of stock investment, they may start purchasing stocks once they hear that their siblings have bought stocks. The results support the former account that households holding no stocks are not very interested in stock investment. When setting the dummy DP urnostocksib t 2 at one if DP ursib t 2 = 1 but the household did not own stocks in year t 2, its coefficient is negative and significant (fifth and sixth columns of Table 6). 26 Ameriks and Zeldes (2004) report that the share of stocks in household portfolios declines after the age of 55 years when controlling for other factors. 22

23 The other side of these results is that households that already own stocks are more likely to purchase stocks on hearing of their siblings stock purchases Liquidity A household may not purchase stocks if its liquidity level is low. 27 To test the effect of liquidity on stock purchases, I include a dummy variable DP urlwlq25p ctincsib t 2 that takes a value of one if DP ursib t 2 =1 and the level of household net worth in year t 2 is less than 25 percent of household annual income. The results do not support the liquidity effect. The coefficient on the dummy is insignificant (last two columns of Table 6). Setting the dummy variable at one for an alternative liquidity threshold (e.g., at 10 percent of annual income) does not support the liquidity effect either (results not reported in the table) Quantitative impact of learning This subsection estimates the quantitative impact of siblings stock purchases on a household s own stock purchases. Specifically, I estimate the following equation: stockpurchase i,t = β 0 +β 1 DP ursib i,t +β 2 DP ursib i,t 2 +β 3 stockshare i,t 2 +β 4 F i,t +β 5 Z i,t, (3) where stockpurchase i,t is the amount of stock purchases between years t 2 and t as a percentage of net worth in year t 2. The remaining variables are the same as before. The (significant) coefficient on DP ursib t 2 means that on average, a household purchases stocks amounting to 0.07 percent of net worth, if its sibling has purchased stocks (first column of Table 7). This may look small, but given that the probability impact of a sibling s stock purchases is 1.6 percentage points (reported in subsection 5.2), households that have decided to purchase stocks (after learning from siblings) can be estimated to purchase stocks worth as much as 0.07/(1.6/100) = 4.5 percent of net worth. This is large relative to the average stock holdings at about 5 percent of net worth (reported in Table 1). 27 Wachter and Yogo (2010) report that in the US data, the share of risky assets in portfolios is lower for households with lower net worth. Guiso et al. (2000) report a 23

24 Table 7: Quantitative impact of learning (1) (2) OLS FE stockpurchase t stockpurchase t in % net worth in % net worth VARIABLES with prefs with prefs DP ursib t (0.031)** (0.028)** Observations 12,376 12,376 R-squared Number of id 2,836 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Notes: The sample comprises households whose head or spouse was recorded as a son or a daughter in the original PSID survey in The sample excludes households with zero total family income or negative net worth, and then to avoid the empirical analysis being affected by extreme observations, households with top and bottom 1 percent of these variables in the distribution are also dropped. The dependent variable is the amount of stock purchases between years t 2 and t as a percentage of net worth in year t 2 (the top and bottom 1 percent of the dependent variable are trimmed to prevent the empirical analysis being affected by extreme values). The independent variables not shown in the table are DP ursib t (dummy of siblings stock purchases), stockshare t 2 (lagged stock share in net worth), dummies for every 5 percent of the distribution of total family income (19 dummies), dummies for every 5 percent of the distribution of net worth (19 dummies), and Z t (defined in Section 4). 24

25 6. Conclusions This paper finds empirical evidence for learning from siblings in stock investment, with the estimates implying that a household s probability of stock purchases rises by about 2 percentage points if its sibling has purchased stocks. I find no evidence for any of the alternative explanations, including the existence of financial support, common shocks, or unobservable correlations. As siblings are likely not the sole source of knowledge about stock investment, an area for future research could be examining other potential sources of learning. For example, one could investigate learning from other relatives, friends, the media, and professional forecasters, so long as data allowing such analysis exists. Another avenue for future research would be building and fine-tuning the theoretical model of learning in stock investment to replicate more closely the investment behavior observed in the data (the Appendix of the current paper takes a first step by presenting a potential mechanism behind learning in stock investment from siblings). similar pattern for the United Kingdom, the Netherlands, Germany, and Italy. 25

26 Appendix A. Appendix: Illustrative theoretical example with learning This appendix considers the standard buffer stock model with both riskfree and risky assets (stocks) and introduces in the model a form of learning from siblings in stock investment. The appendix runs simulations with the model, and using the simulation data, estimates the impact of learning. The aim of the estimation is to present a potential mechanism behind social learning tested empirically in the main text. There are many potential forms of learning in stock investment (as discussed below). Thus, I would not argue that the current form is the sole mechanism but rather see the learning mechanism introduced in this appendix as an illustrative example that shows how learning from siblings (and more generally, from others) could increase stock purchases. Appendix A.1. Model description Start with the standard buffer stock model (Carroll (1997)) that maximizes the sum of discounted values of utility from consumption: [ ] max E t (β(1 D)) n u(c t+n ) n=0 where u( ) = 1 ρ /(1 ρ) is a constant relative risk aversion utility function, β is the discount factor, and D is the probability of death (the model introduces accidental death). The budget constraint is: C t M t A t = M t C t M t+1 = R t /(1 D)A t + P t+1 θ t+1 R t = (1 ς t )RF ree + ς t R t, where A t is assets at the end of year t and M t+1 is the sum of the effective interest rate R t /(1 D) multiplied by the end-of-year assets and next-year noncapital income (equal to permanent noncapital income P t+1 multiplied by a log-normally distributed iid transitory income shock factor θ t+1 ). P t+1 is assumed to be constant at P over time. The interest rate R t is boosted by 1/(1 D) because of a wealth redistribution scheme where the wealth of those who die is distributed among survivors 26

27 (Blanchard (1985)). R t is the weighted average of the returns from risk-free assets (deposits) RF ree and those from stocks R t. R t is log-normally distributed and its mean equals RF ree plus risk premium R t. ς t is the share of stocks in total asset holdings. Now introduce learning in this model, in the following manner: Each household starts life with an underestimated perceived value of risk premium ˆR t = (1 δ) R, where (1 δ) < 1 and R is the true value of risk premium. In each year, one or more siblings of a household purchase stocks with probability p. Given the event of its siblings stock purchases, the household hears from them about the investment, learns the potential benefits of stock investment, and updates its perceived value of risk premium to the true value R with probability λ. The perceived value stays at this level until the end of the life (learning has a permanent impact until death). The household solves the dynamic optimization problem by taking the perceived value of risk premium ˆR t as the true value. Appendix A.2. Estimation using simulation data This subsection runs simulations for 200 years, and using the last year of the simulation data (and the data on lagged variables), estimate the impact of learning. 28 Specifically, following the preferred econometric model presented later in Section 4 (equation (2)) and used for the empirical analysis in Section 5, I estimate the equation below using the probit and logit models. DP ur i,t = β 0 +β 1 DP ursib i,t +β 2 DP ursib i,t 2 +β 3 stockshare i,t 2 +β 4 F i,t +β 5 Z i,t. DP ur i,t takes a value of one if household i has purchased stocks between years t 2 and t. DP ursib i,t takes a value of one if a sibling of household i has purchased stocks between years t 2 and t. 28 When running simulations, those who are deceased are replaced by newborns with zero assets and ˆR t = (1 δ) R. 27

28 Table A.8: Parameter values Parameter Description Value Source ρ Coefficient of relative risk aversion 10 Cocco et al. (2005) β Discount factor 0.96 Cocco et al. (2005) σ θ Log std. of transitory income shock /2 Cocco et al. (2005) RF ree Return from risk free asset 1.02 Cocco et al. (2005) R True value of risk premium 0.04 Cocco et al. (2005) σ R Log std. of returns from stocks Cocco et al. (2005) D Probability of death 1/60 (Average life expectancy is 60 yrs) δ Underestimation ratio of risk premium 0.5 p Prob of siblings stock purchases 0.05 λ Prob of those who update risk premium 0.2 DP ursib i,t 2 is the two-year lag of DP ursib i,t. 29 stockshare i,t 2 is the share of stocks in total assets in year t 2. F i,t is the vector of dummies for every 5 percent of the distribution of income (19 dummies) and dummies for every 5 percent of the distribution of net worth (19 dummies). Z i,t is the vector of age and age squared. The parameter values are summarized in Table A.8. The first six values in the table (from ρ to σ R ) are all from Cocco et al. (2005) who also calibrated an extended version of the buffer stock model (Carroll (1997)). 30 The results confirm that the coefficient on DP ursib i,t captures the learning effect. The first two columns of Table A.9 report that the coefficient on DP ursib i,t is positive and significant in most cases. The coefficient on DP ursib i,t in the first column implies that a household s probability of stock 29 DP ursib i,t 2 is included to imitate the econometric model in Section 4 for empirical analysis. 30 The relative risk aversion coefficient ρ may appear high, but Cocco et al. (2005) argued that this was an upper bound value considered reasonable by Mehra and Prescott (1985). Indeed, due to the well-known equity premium puzzle, a relatively high ρ is required to generate a portfolio structure with stock holdings that are less than 100 percent of total assets. 28

29 purchases rises by about 7.2 percentage points if a sibling has purchased stocks. The coefficient on DP ursib i,t varies somewhat but remains positive and significant across alternative parameter values (third to last columns in the table). DP ursib i,t 2 is insignificant, providing no evidence for the delayed effect of learning. In the real world, as households may change their asset portfolios only gradually (for a detailed discussion, see Section 4), the delayed effect may exist, which the empirical analysis in the main text indeed confirms. Table A.9: Estimation results using simulation data VARIABLES (1) (2) (3) (4) (5) (6) (7) probit logit probit probit probit probit probit baseline params baseline params δ p p λ λ DP ursib t (0.03)*** (0.05)*** (0.03) (0.03)*** (0.04)*** (0.03)*** (0.03)** DP ursib t (0.03) (0.05) (0.03) (0.03) (0.04) (0.03) (0.03) stockshare t (0.06)*** (0.11)*** (0.16)** (0.06)*** (0.07)*** (0.06)*** (0.07)*** age (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)** age 2 / (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)** Observations 28,061 28,061 28,044 28,036 28,052 28,049 28,051 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Notes: The dependent variable is DP ur t (dummy of stock purchases). The independent variables not shown in the table are dummies for every 5 percent of the distribution of income (19 dummies) and dummies for every 5 percent of the distribution of net worth (19 dummies). Now to examine the quantitative impact of learning, follow the approach taken in the empirical analysis (equation (3)) and estimate the equation below: stockpurchase i,t = β 0 +β 1 DP ursib i,t +β 2 DP ursib i,t 2 +β 3 stockshare i,t 2 +β 4 F i,t +β 5 Z i,t, where stockpurchase i,t is the amount of stock purchases between years t 2 and t as a percentage of total assets in year t 2. The definitions of DP ursib i,t, DP ursib i,t 2, stockshare i,t 2, F i,t, and Z i,t are the same as before. The first column of Table A.10 reports that a household purchases stocks amounting to 4.5 percent of total assets, if its sibling has purchased stocks over the past two years. The rest of the columns in the table reports that the coefficient does not change enormously with alternative parameter values. 29

30 Table A.10: Estimation of quantitative impact using simulation data VARIABLES (1) (2) (3) (4) (5) (6) OLS OLS OLS OLS OLS OLS stockpurchase t stockpurchase t stockpurchase t stockpurchase t stockpurchase t stockpurchase t in % assets in % assets in % assets in % assets in % assets in % assets baseline params δ p p λ λ DP ursib t (0.75)*** (0.92)** (0.68)*** (1.08)*** (0.78)*** (0.85)* Observations 28,061 28,044 28,036 28,052 28,049 28,051 R-squared Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Notes: The dependent variable is the stock share in percent of total assets. The independent variables not shown in the table are DP ursib t 2, stockshare t 2 (lagged stock share in net worth), dummies for every 5 percent of the distribution of income (19 dummies) dummies for every 5 percent of the distribution of net worth (19 dummies), age, and age squared divided by 100. The learning impact on stock purchases is estimated to be several percent of total assets. The form of learning considered above is, of course, a special case. There are many other possible forms of learning. For example, unlike the current model which assumes a permanent learning impact, the learning impact could diminish over time (i.e., one may forget past events). In addition, one may learn and update the variance of stock returns, instead of risk premium. Thus, I see the form of learning assumed in this appendix as an example to illustrate the point that learning from siblings (and more generally, from others) could stimulate stock investment. 30

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