Factors Affecting the Retirement Effect on Portfolio Choice

Transcription

1 Venture or Safety? Retirement and Portfolio Choice Guodong Chen Tong Yob Nam February 2014 Abstract Common wisdom suggests that, due to reductions in labor income, households should hold more safe assets in their portfolios after retirement. However, few consensus in theoretical studies was reached and little empirical evidence has been provided to evaluate this argument. In this paper, to address this issue, we systematically establish the causal effect of retirement on portfolio choice during the retirement transitions. We find that, on average, retirement causes a jump of percentage points of risky shares in households portfolios after retirement. This discrete jump cannot be reconciled by the existing theoretical studies and posits a "retirement portfolio choice puzzle". Further, we propose and test four factors that could possibly contribute to explain this retirement effect, including 1) shifts in risk tolerance; 2) increases in time spending in tracking risky asset markets; 3) changes in life expectancy; and 4) changes in bequest motives. Among these, we find that the first two channels are more likely to be the driving force for this retirement effect. Keywords: Retirement, Portfolio Choice, Risk Tolerance, Time Spending, Life Expectancy, Bequest Motive JEL Classification: D14, E11, G11, G12 We are very grateful of Sugato Bhattacharya, John Bound, Christopher House, and John Laitner for their insightful comments.we have also benefited from discussions with Charles Brown, Stephan Nagel, Amiyatosh Purnanandam, and Uday Rajan. We also thank participants of the Finance Brown Bag Seminar at Ross School of Business for very helpful comments. All errors remain ours. Department of Economics, University of Michigan, gdchen@umich.edu Department of Economics, University of Michigan, tynam@umich.edu 1

2 1 Introduction As Baby-Boomers are about to join in the aging population, together with increased life expectancy, this trend imposes many challenges for financial sustainability of social security systems. Among these challenges, understanding portfolio choices of retirees, especially in the period of transitions into retirement has draw increasing attention. It is because the portfolio choice of retirees will not only affect their assets compositions and returns but it will also affect other economic decisions such as consumption, pension benefit and so forth. Understanding the portfolio choice is therefore of great importance to help policy makers to better implement and design policies associated with retirement benefit and health care. The common wisdom suggests that when there is a substantial decrease in income after retirement, retirees are expected to reduce their risk portfolio holdings when transiting into retirement, and shift the portfolio composition from risk asset to relatively safe assets. In economic studies, however, it is far beyond to reaching the consensus. From theoretical perspective, though portfolio choice over the life cycle is extensively discussed, the effect of retirement on portfolio choice, so called retirement effects so far, is still ambiguous 1. From empirical perspective, studies about such retirement effect, to the best of our knowledge, are even underexplored 2. To fill the gap in the literature, the goal of this paper is to empirically establish the causal effect of retirement on portfolio choice; and to provide some possible explanations for this causal effect found in data. Modeling and estimating models with endogenous retirement decision pose economic and econometric challenges. To solve this endogeneity problem, we use data from Health Retirement Study (HRS), a national longitudinal survey, and adopt the instrumental variable approach by using two sets of instruments for retirement status: historical expected retirement status and eligibility age indicators of retirement benefits (especially, Social Security benefits). Using these instruments, we find that retirement causes an discrete jump in risky share holdings by percentage points. This increase accounts for one forth increases in risk asset holding provided that the average risky asset holding is 20.2 percentage points in our sample. This finding suggests that there exists positive and sizable retirement effect on portfolio choice, which contradicts against almost all theoretical predictions in existing studies, posing a puzzle in the portfolio choice around retirement 3. In addition, we also find substantial heterogeneous retirement effects across wealth and mortgage. In particular, the retirement effect is mainly from individuals in top one-third wealthy 1 The seminal work by Samuelson (1969) and Merton (1969, 1971) suggests that under frictionless market, retirement status is irrelevant to the portfolio choice. Bodie, Merton, and Samuelson (1992) show that, with nontradable labor income, individuals tend to hold more risky assets at work than that after retirement. Different from above, Viceira (2001) shows that, with large correlation between stock market risk and labor market risk, portfolio can be riskier after retirement than that prior to retirement. A detailed discussion on this stream of literature will be provided later. 2 A partial list includes Heaton and Lucas (2000), Horneff, Maurer, Mitchell, and Stamos (2007), and Addoum (2013). 3 For example, Samuelson (1969) posits that retirement is uncorrelated to the portfolio choice; Bodie, Merton, and Samuelson (1992) predict a decrease in risky asset holdings right after retirement; Cocco, Gomes, and Maenhout (2005) argues for a smooth increase in risky share after retirement. 2

3 households in our sample, while the portfolio choice of bottom one-third poor households are not affected by retirement. Meanwhile, non-mortgage holders have a larger positive retirement effect on portfolio choice than mortgage holders. Motivated by these puzzles, we further propose and test four possible hypotheses separately that may justify such behaviors in reality. 1) Risk tolerance hypothesis states provided that the risk tolerance is negatively correlated with risky asset holding, when the retirement can keep retirees away from income and employment uncertainty and thus decreases the level of risk tolerance of retirees, the corresponding risky asset holding will increase 4. 2) Time spending hypothesis suggests that, more time after retirement that could be allocated on the risky assets like stock can increase the risky asset holding or more utility that can be drawn from additional time working on risky asset could also increase the risk asset holding. 3) Life expectancy hypothesis implies that retirement results in a passive view of life expectancy, it will lead to an increase in risky share of asset holdings. In particular, increase (decrease) in life expectancy may cause an increase (reduction) in savings and consequently decreases (increases) the relative risky shares in the portfolio, as predicted by Cocco and Gomes (2012). 4) Bequest motive hypothesis indicates that retirement weakens the bequest motive and thus reduces individual s risky asset holdings. To be specific, a weaker bequest motive increases the speed of wealth being drawn down and thus decreases the wealth to labor income ratio. In turn, it will potentially result in an increase in risky portfolio choicefollowing (Cocco, Gomes, and Maenhout, 2005). Though our results indicate that all these four explanations can possibly contribute to the retirement effect on portfolio choice, changes in risk tolerance and increase in time spending are the main driving force with robust evidence 5. Our paper is related to two main streams of studies. The first stream discusses household portfolio choice under the life-cycle framework. The seminal papers include Samuelson (1969) and Merton (1969, 1971). From then on, many following up studies emerge into two directions. On the one hand, some researches do not explicitly model the retirement in life-cycle model and generally discuss the portfolio choice over time (Calvet, Campbell, and Sodini, 2009; Campbell, 2006; Heaton and Lucas, 2000). Other studies focus on the effects of demographic changes on the portfolio choice, like age (Ameriks and Zeldes, 2004), health (Rosen and Wu, 2004; Edwards, 2008), or the effects of the experience, like lifetime experience of volatility (Malmendier and Nagel, 2011; Appendino, 2013), expectation of future borrowing constraints (Guiso, Jappelli, and Terlizzese, 1996), optimism on investment decision (Dominitz and Manski, 2007; Puri and Robinson, 2007) and financial literacy (Lusardi and Mitchell, 2007; Van Rooij, Lusardi, and Alessie, 2011). 4 this is consistent to Canner, Mankiw, and Weil (1997), who argue that risk tolerance is negatively correlated to risky asset allocation. 5 Our analysis only captures the net effects from retirement and explanations proposed here are just possibilities. Structurally decomposing contributions from different channels can be an interesting topic for future studies. 3

4 On the other hand, other studies explicitly model retirement, either exogenously (Viceira, 2001; Campbell, Cocco, Gomes, Maenhout, and Viceira, 2001; Cocco, Gomes, and Maenhout, 2005; Gomes and Michaelides, 2005) or endogenously (Bodie, Merton, and Samuelson, 1992; Bodie, Detemple, Otruba, and Walter, 2004; Farhi and Panageas, 2007; Dybvig and Liu, 2010), and extend the discussion on the retirement transitions. For example, Cocco, Gomes, and Maenhout (2005) build up an exogenous retirement model and predict that individuals may smoothly adjust their risk portfolio holdings upwards at retirement. Farhi and Panageas (2007) endogenize an irreversible retirement choice and show a larger portion of risky assets prior to retirement. Among these, Gomes and Michaelides (2005) provide some theoretical predictions that are the closest to our empirical findings. In their paper, they use Epstein-Zin utility function and include a fixed entry cost in risky investment as well as risk aversion heterogeneities in their model. Given this model, they find that with certain parameters, there could be a discrete jump of risky share at exogenous retirement age 65. While Gomes and Michaelides (2005) provide a possible case of the portfolio choice changes close to retirement age, very little is discussed in their paper for this jump. Our paper differs because we will particularly focus on empirically showing this jump in portfolio choice around retirement and discuss possible explanations, accordingly. Addoum (2013) is the most relevant empirical work but it focuses on the relative bargaining power between husband and wife within household. Moreover, the author finds negative retirement effect, which is opposite to our findings. In addition, our paper is also related to the second stream of studies, which concentrate on other aspects of economic behaviors other than portfolio choice around retirement. Some studies discuss the "retirement consumption puzzle", i.e. a downward shift of consumptions at retirement (Modigliani and Brumberg, 1954; Friedman, 1957; Heckman, 1974; Bernheim, Skinner, and Weinberg, 2001; Haider and Stephens Jr, 2007; Battistin, Brugiavini, Rettore, and Weber, 2009) 6. Other studies consider the saving behavior (Papke, 2004), housing (Yogo, 2009), pension and annutization (Brown, 2001), as well as health care (Hurd and McGarry, 1997). Compared to these studies, portfolio choice is under-explored especially from empirical perspectives. Our paper will complement previous studies at this aspect. The remainder of this paper is organized as follows. Section 2 presents our empirical methodology, sketching out our benchmark specification and identification strategy. Section 3 discusses the data issues and our variable definitions. Section 4 presents our main results of the retirement effect on portfolio choice. Section 5 investigates four possible channels in explaining the retirement effect. In addition, We conduct several additional sets of tests to address concerns that our results may be due to confounding effects. These include 1) alternative risky share measure by including IRA account; 2) alternative retirement measure; 3) impact of spouse s retirement status; 4) crisis effect on passive risky asset holdings; 5) high order age, wealth 6 Attanasio (1999) and Hurst (2008) provide excellent reviews on this topic. 4

5 and 6) placebo tests. These results for robustness checks will be discussed in details in Section 6, and then Section 7 concludes. 2 Empirical Methodology 2.1 Benchmark We estimate the retirement effect on household s portfolio choice. To this end, following a panel regression approach, we consider the benchmark regression as follows: Riskyshare it = β 0 + β 1 HHretire it + γ X it + δ i + η t + ε it (1) where the dependent variable, Riskyshare it, is the household i s risky share at wave t, which is measured as the value of risky assets dividing the value of total financial assets. The key variable of interest, HHretire it, is the household head of household i s retirement status dummy at wave t. X it contain sets of 1) household characteristics; 2) household head s characteristics; and 3) spouse s characteristics, from household i at wave t, under different specifications. The household fixed effects, δ i, capture time-invariant factors that are correlated to risk portfolio choice. η t represents the wave fixed effects and ε it is the time-varying unobserved disturbance. The key coefficient of intereste, β 1, measures the retirement effect on risk portfolio choice we are focusing on. Note that the benchmark specification can tell us the average retirement effect, but it cannot provide enough information to help us distinguish two competing driving sources for the retirement effects. More specifically, we cannot distinguish the effects by 1) those who switch from non-risky-asset buyers to riskyasset buyers after retirement (extensive margin) or 2) those who owned risky assets before and increase their risky asset holdings after retirement (intensive margin). To separate out these two possible driving sources, we conduct two additional exercises. To test the extensive margin effect, we use a stock market participation indicator as the dependent variable to run a panel logistic regression model with a similar setting to Equation (1) (effects of A on B). To test the intensive margin effect, we follow Equation (1) by restricting our sample on households with positive risky shares only to see whether risky asset holders increase their risky share after retirement. 2.2 Identification Strategy To establish the causal effect of retirement, we need to solve the endogeneity problem. Two sources of endogeneity could bias the estimate of the coefficientβ 1 : 1) omitted variable bias and 2) reverse causality. 5

6 More specifically, omitted variable endogeneity occurs when some unobserved factors like preference and life styles will simultaneously affect the retirement decision and portfolio choice. Simultaneous endogeneity occurs when portfolio choice decision can reversely affect retirement decisions. To address the endogeneity issue, we use the instrumental variable approach, which commonly requires two restrictions: 1) relevance restriction which needs that the instrumental variables are correlated to the endogenous variable, household head s retirement status, HHretire it ; 2) exclusion restriction which requires that the instrumental variable we use is uncorrelated to the error term ε it, directly. To satisfy these two restrictions, we consider two sets of instrumental variables for the retirement status. The first instrument we use, following Haider and Stephens Jr (2007), is the subjective expected retirement status. We argue that these self-reported retirement expectations in previous wave are highly correlated to the current actual retirement status 7. In addition, based upon rational expectation argument, information known at time t is uncorrelated with the expectation error between period t and future periods t + 1, t + 2, and so forth, i.e. the instrument is uncorrelated with the error term in Equation (1). The second set of instrumental variables used in this paper are two indicators: 1) whether an individual is aged 62 and above, 2) whether an individual is aged 65 and above, following Bonsang, Adam, and Perelman (2012). We take advantage of the fact that these two age thresholds are minimum age requirements when claiming social security benefits and thus are highly correlated to retirement decisions. To be specific, age 62 is the minimum age at which Social Security benefits can be partially claimed, i.e. early retirement 8, and age 65 is the age at which individuals can claim full Social Security benefits if they retire at that age 9. The first-stage regression regarding to the relevance restriction is also reported in Appendix Table. 3. For the exclusion restriction, we argue that ages are relatively exogenous and are not correlated to the error terms Data Description The data set we use in this paper is the Health and Retirement Study (HRS), a longitudinal survey that collects detailed information of the US population over the age of In particular, we use the RAND HRS Data file, a cleaned and processed version of the HRS data. The data contains 26,000 household observations 7 The first-stage regression in Appendix Table 3 ensures that the subjective retirement expectation is highly predictive of subsequent retirement behavior. 8 75% Social Security benefits can be claimed at age 62 and the proportion is increasing overtime until 65 with eligibility of full Social Security benefit. 9 Note that the normal retirement age is set to increase to age 67 over a 22-year period, which affects people born January 2nd, 1938, and later. 10 If the error term contains factors that affect individuals s life expectancy, the exclusion restriction may not necessarily hold. 11 Although the HRS was designed to represent the all US population over the age of 50, to address the research regarding racial and ethnic disparities, the HRS has oversampled Black and Hispanic populations. In this study, we do not adjust the sample regarding race and ethnicity, rather a subsample with white population only was examined. The results, though not reported, are qualitatively the same as our main results. 6

7 with detailed information on demographics, health, income, wealth and retirement. The main advantage of this data is that it includes 7700 household with at least one respondent born from 1931 to 1941, who had retired or expected to be retired over the survey periods ( ). Our primary sample draws from the waves from 1992 to 2010 to keep observations as large as possible. To make our result comparable to literature, we restrict our sample following four criterions: 1) Households of married couples with the male head aged between 50 and ; 2) samples without reporting as selfemployed; (3) retirement status are known; (4) risky share measure between 0 and 1. The detailed sample selection procedures can be found in Appendix Table Variable Definitions Retirement Status Retirement status is a key determinant in our analysis. To identify the retirement status of each individual, we use the self-reported retirement status in the HRS, which is derived from the question, At this time do you consider yourself to be completely retired, partly retired, or not retired at all? For the main analysis, we classify the respondent who self-reported completely retired as a retiree. As an alternative measure of retirement, we also treat both the completely and the partly retired groups as retirees. In addition to the self-reported retirement status, the HRS provide the labor force status. The labor force status is divided into seven categories: working full-time, working part-time, unemployed, partly retired, retired, disabled, or not in the labor force. We use this labor force status to check the robustness of our result. The advantage of using the labor force status is that we can eliminate the effect of other pre-retirement status. For example, we can distinguish the retiree who was previously unemployed from the retirees who was previously working. Figure 1 shows the portion of retirees by age. As can be seen in the figure, the portion of retirees is increasing rapidly between age 62 to 65, which is closely related to the eligibility age for the social security retirement benefits. Risky Shares We define risky shares as the net value of stocks, mutual funds, and investment trusts divided by total financial assets. Total financial assets are the sum of checking and saving accounts, money market funds, certificates of deposit (CD), government saving bonds, Treasury bills, corporate, municipal, government, and foreign bonds, and other savings subtracted by other debts such as credit card balances, medical debts, and life insurance policy loans. However, financial assets do not include main residence, other real estate, 12 We define the head of households as the member who earns the most over entire survey period. 7

8 vehicles, business, and Individual Retirement Account (IRA) and Keogh plans. For retirees or almost retirees, the IRA assets account for a non-negligible portion of total assets. Additionally, households can use the fund in the IRA to invest in stocks or other risky assets. This risky asset in the IRA can affect the risky investment decision on their financial assets. To consider this effect of stock investment in IRA assets, we use the alternative measure, the combined risky share in financial and IRA assets, which is the weighted sum of risky share in financial assets and risky share in IRA assets. The HRS provides information regarding stock investment in IRA assets since In 2000, 2002 and 2004 surveys, the HRS collects what portion of IRAs invest in stocks in three categories: Mostly or All Stocks, Mostly or All Interest Earning, and Evenly Split. From 2006, the exact portion of stock in IRA assets has been collected. Using this information, we can calculate the stock share in IRA assets and use this information to estimate the total risky share in financial and IRA assets. Because of the limited precise information for IRA accounts prior to 2006, in the main results, we will focus on risky shares definition without IRA. As robustness check, we also report the results by considering IRA account in Section 7. Expected Retirement Status Following Haider and Stephens Jr (2007), we construct an expected retirement status dummy variable. To do so, we first extract the information about expected retirement age of each invididual in the initial wave 1992 and then compare this expected retirement age to the acutual age in the following waves. If an individual s expected retirement age is smaller than the actual age in a given wave, we will define this individual s expected retirement status as "expected to be retired". Alternatively, if his/her expected retirement age is greater than the actual age, we will label the expected retirement status as "expected not to be retired" 13. Age Indicators for 62 and 65 above As discussed in Bonsang, Adam, and Perelman (2012), 62 and 65 are crucial age thresholds for claiming retirement benefits. We treat indicator "age 62 and above" to be 1 if individual s actual age is greater or equal to 62. The other indicator "age 65 and above" is defined following the same vein. Measure of Risk Tolerance Barsky, Juster, Kimball, and Shapiro (1997) included the experimental survey questions regarding risk tolerance into the first wave (1992) of the HRS. They show the positive relationship between estimated risk tolerance and risky behavior of participants including stock investment. The HRS includes these experimental 13 For samples with non-missing observations on this variable, they must appear in wave As a robustness check, we also use the expected retirement age asked in last wave to define an alternative expected retirement indicator. Though not reported here, the results are qualitatively the same. 8

9 questions until 2006, except We use this subjective risk tolerance measure to examine the change in risk tolerance around retirement. Based on the series of questions, the HRS classifies each individual into four different risk tolerance groups: from the least risk tolerant to the most risk tolerant. In addition, from 1998 to 2006, the HRS includes the subdivided 6 risk tolerance group. We use both category 4 and category 6 risk tolerance measure in our analysis. Following Stock Market Stock market participation is costly. To explain the low stock market participation rate in the US, various types of participation cost are considered (Gomes and Michaelides (2003); Vissing-Jorgensen (2002); Paiella (2001)). Time allocation is one type of cost that investors spend to participate in the stock market. After retirement, more time is allocated to leisure and other activities in place of working. We conjecture that reducing working our affects time allocations to stock market and investment decisions. The HRS provide the time allocation to stock market using the following question: How closely do you follow the stock market: very closely, somewhat, or not at all? 14 Based on the answer to this question, we examine whether the degree of following stock market changes around retirement. Life Expectancy The HRS provide the self-reported life expectancy. Self-reported life expectancy is important in two aspects. First, it determines the horizon of lifetime asset allocation problem. The portfolio choice of individuals who expect live longer will be different from the portfolio choice of individuals with shorter life expectancy. Second, the self-reported life expectancy can be a measure of optimism. Puri and Robinson (2007) create a measure of optimism as they compare the self-reported subjective life expectancy to actuarial life expectancy. They show that the more optimistic individuals, who have higher self-expected life expectancy than the standard, are more likely to invest in stocks. We consider the effect of life expectancy on the portfolio choice. The HRS provides two measures of life expectancy: self-reported probability of living to age 75 and self-reported probability of living to age 85. Using these two measures, we test whether the life expectancy matters to change in stock share around retirement. Probability of Leaving Bequest Although there exists some skeptical views regarding the effect of bequest motive on saving decisions (Hurd (1989); Dynan, Skinner, and Zeldes (2002); Cagetti (2003)), it is more common to assume that investors with high bequest motives are likely to save more and this behavior affects an individual s portfolio choice 14 Question about following stock market is available from 2002 survey. 9

10 (Cocco, Gomes, and Maenhout (2005); Rosen and Wu (2004)). To test whether bequest motive changes around retirement and its effect on the portfolio choice, we use the survey question about the probability of leaving bequest. From second wave (1994), HRS surveyed the following question, what are the chances that you [or your (husband/wife/partner)] will leave an inheritance totalling $10, 000 or more?. There are two follow-up questions based on the answer to the first question. If the probability of leaving bequest $10, 000 or more is larger than zero in the first question, they ask What are the chances that you [or your (husband/wife/partner)] will leave an inheritance totalling $100, 000 or more. If the probability is zero, they ask What are the chances that you (and your (spouse/partner)) will leave any inheritance? Using this probability of leaving bequest, we examine the change in bequest motive around the retirement. Other Control Variables We use other demographic characteristics and financial status as control variables. First of all, age is one of the most important demographic characteristics in the portfolio choice. Portfolio choice literature has already emphasized the relationship between age and portfolio choice (Ameriks and Zeldes (2004)). We include age and age squared terms as control variables to distinguish the effect of age from the effect of retirement. In addition to age, other demographic factors such as education and cognitive level (Christelis, Jappelli, and Padula (2010)), health status (Fan and Zhao (2009)), ethnicity (Bellante and Green (2004)), and religion can affect the portfolio choice. We control these characteristics as well as other basic household characteristics including region of residence, size of households, and gender of head (Olsen and Cox (2001)). Classic portfolio theory assumes non-crra utility function and no labor income risk so that optimal portfolio share should be constant regardless income and wealth level (Merton (1969); Samuelson (1969)). However, many studies have shown that level of income and wealth are important factors that affect individual s portfolio decision (Cohn, Lewellen, Lease, and Schlarbaum (1975); Donkers and Van Soest (1999); Guiso, Haliassos, and Jappelli (2003); Peress (2004)). To control the effect of financial status on the portfolio decision, we use income level, wealth level, pension information, and mortgage status as control variables Summary Statistics Table 1 shows the summary statistics by retirement status of household head. 16 Part I of the table presents demographic characteristics and part II summarizes the financial status. Average age of retirees is 9 years older than the average of non-retiree. Retirees are less educated and less healthy than non-retirees. All these differences are statistically significant. In terms of financial status, the average dollar value of total 15 All wealth and income data are deflated by the consumer price index (CPI) into 2000 dollars. 16 In this table, we only report some important variables to our analysis. The detailed summary statistics can be found in the appendix. 10

11 financial wealth of retirees is almost 50 percent larger than the value of non-retirees. On the other hand, after retirement, the income is reduced by 42 percent from $41,000 to $23,800. While most summary statistics correspond to conventional wisdom, the risky share shows the opposite pattern. Stock share in financial asset of retirees is 2.8 percent higher than the stock share of non-retiree, which is almost 15 percent increase of the stock share of non-retiree. This difference in stock share is statistically significant while we cannot find the significant difference in combined stock share in financial and IRA assets between two groups. The subjective measure of risk tolerance is also reported in last two rows, but the difference is not statistically significant. Other risky shares such as stock shares, and stock and other real estate shares in total assets are also higher for retirees compared to non-retirees. To understand the household asset composition in detail, we summarize the value of each asset and its portion in total households wealth in Table 2. Housing asset takes the largest portion of total wealth and the financial asset takes 19.6 percent of total asset, which is the second largest. We also compare the asset composition of retiree and non-retiree. As shown in the table, there is no change in relative importance of each asset before and after retirement. However, the portion of each asset varies. The portions of relatively liquid asset including financial, stock, and IRA assets increase while the portions of illiquid assets such as home equity, transportation, business, and other real estate decrease. In particular, the portion of financial show the largest increase in level and percentage as well. 4 Main Results 4.1 Benchmark Case In this subsection, we will discuss the general pattern of retirement effects we obtained from data. To provide a rough idea of how the portfolio choice differs between retirees and non-retirees across ages, we plot the risky share holding for retirees and non-retirees respectively in Figure 2. It shows that overall retirees hold larger risky shares in their portfolio than non-retirees do. The difference of risky share holding between retirees and non-retirees diverges as the age increases. To further explore retirement effects and control other factors that could also affect portfolio choice, we consider the regression analysis that we described in Section 2. The results are summarized in Table 3. Column 1 provides the estimates using the panel regression. Columns 2 to 4 report the estimates using the different set of instruments 17. Columns 5-8 correspond to Columns 1-4, by adding more control variables of spouse s demographic characteristics, like age, square of age, and self-reported health status. Standard errors are all clustered at household level. From Table 3, we find that the retirement effect is quite striking and robust across different specifications. 17 The first-stage regression results of our instrumental variables are reported in Appendix Table 3. We can observe that all three instrumental variables we use in this paper are,both economically and statistically, significantly correlated to the actual retirement status. 11

12 For the benchmark specification in Column 1, it shows that individuals invest approximately 1.4 percentage points more in risky share, accounting for about 7% of average risky share holdings. Taking into account of the fact that the estimates in Column 1 might be biased due to endogeneity issues, it shows in Columns 2-4 by using the instrumental variables, that the retirement effect increases to about 5.1 percentage points to 7.2 percentage points across different specification, which accounts for almost 25% to 36% of the average risky shares. Those results suggest that there exists a huge impact of retirement status on risky portfolio choices. Beyond the retirement effect, we also find that other control variables exhibit mostly the effects as we expected. Households with more wealth, higher income are investing more in risky assets, which is consistent with predictions from Calvet, Campbell, and Sodini (2009). Older individuals are in general investing less in risky assets over time, though this trend reverses in late ages around 77, consistent to findings in Campbell, Cocco, Gomes, Maenhout, and Viceira (2001) and Cocco, Gomes, and Maenhout (2005). Larger households invest less in risky assets while households with more children have a higher risky share in their portfolios. Though the sign of the coefficient is negative, the self-reported health status does not have any significant impact on risk portfolio choice, which is different from findings in Rosen and Wu (2004), in which health exhibits negative effects on risk portfolio choice. The possible reason for this might be different sampling periods and sample selection rules. In short, we find that retirement causes a discrete jump of individual s portfolio choice. These findings are consistent with some existing theoretical studies (for example, Cocco, Gomes, and Maenhout (2005)), that proportion of risky assets increases after retirement. However, it contradicts against these studies by a discrete jump instead of a smooth adjustment, which posits a puzzle empirically. Analogous to retirement consumption puzzle discussed by Hurst (2008) and others, we call this retirement effect on portfolio choice as a "retirement portfolio choice puzzle". 4.2 Extensive Margin vs. Intensive Margin In this subsection, we further investigate which drives this retirement effect: extensive margin or intensive margin as we defined in Section 2. The HRS data provide rich information to allow us to explore this possibility. To test extensive margin, we first define households as risky asset holders if they hold any positive risky assets, and as non-risky asset holders, otherwise. Though this definition does not distinguish the stock holdings from the mutual fund holdings in detail, it is still a good approximation for households risky asset market participation. Then, we run the panel logit regression with the indicator of risky asset holders as a 12

13 dependent variable. The result is shown in Column 1 of Table 4. It shows that households are 3.7 percentage points more likely to invest in stock markets after retirement than before. It is statistically significant at 1 To test intensive margin, we first focus on households with positive risky assets only and later, we consider full sample based upon Tobit Model, (i.e. treat the households without risky assets as the truncation points). We report the results with controlling for the spouse s characteristics in Columns 2-6 of Table 4. The results without controlling for the spouse s characteristics exhibit similar pattern. Column 2 reports the panel regression results with the selected sample; Column 3 describes the results using the panel Tobit; Column 4 to Column 6 present IV Tobit results with different sets of instrumental variables. Overall, we can observe that inviduals after retirement tend to increase their potential risky share holdings by 4.8 percentage points in panel regression specification and 5.6 to 12.2 percentage points in different IV specifications. The results indicate that for individuals who own risky assets already, they are also more likely to increase their risky shares in their portfolios after retirement. In other words, increase in intensive margin also contributes to the retirement effect we found in the benchmark results. In short, we find that this retirement effect comes from both effects on extensive margin, i.e. becoming new risky assets buyers, and on intensive margin, i.e. holding more risky shares for risky asset holders, after retirement. We do not try to decompose and quantify each effect in this paper, but it will be an interesting exercise for future studies. 4.3 Heterogeneities As we may expect, the retirement effect might be heterogeneous across different characteristics. In particular, we focus on exploring the potential heterogeneities regarding to 1) wealth; 2) mortgage holding; and 3) pension holding Heterogeneities by Wealth Among all possible characteristics, wealth is more likely to give rise to heterogeneous retirement effect. Intuitively speaking, individuals from households with limited budget can only allocate money to support their livings and may not be able to buy any risky assets, thus the changes in the portfolio choice are less likely to occur after the retirement. In contrast, when individuals from wealthier households are more flexible to allocate money towards different portfolio choices, then the changes in the portfolio choice are more likely to occur after the retirement. In the following context, we will explore the possible heterogeneity across different wealth levels. We split each wave sample evenly by wealth into three groups: high, medium and low. We first plot the 13

14 average risky share by three groups by retirement status across different ages in Figure 3. It shows that for the high wealth group, across different ages, retirees in general have larger risky share holdings than nonretirees do. The medium and low wealth groups do not exhibit any substantial difference between retirees and non-retirees. In addition, we also conduct the regression analyses including both panel regression and IV panel regression as before to examine the heterogeneity across wealth 18. The low wealth group is omitted as the reference group in all specifications. The results are summarized in Table 5. Column 1 represents the result in simple panel regression. It shows that the retirement effect is mainly from high wealth group, where the coefficient on the interaction term of high wealth group indicator and retirement indicator is positive and statistically significant. For medium wealth group and low wealth group, this retirement effect is not evident. The IV results in Column 2 through Column 4 show that not only high wealth group experiences the jump in risky shares around retirement, individuals from medium wealth group are also affected, though less than that of high wealth group. The low wealth group does not present any significant effect on portfolio choice at retirement Heterogeneity by Mortgage Holdings Like wealth, mortgage is also likely to give rise to heterogeneous retirement effects. The idea is that since the mortgage holders need to pay back their mortgage even after retirement, mortgage holders 1) may not have enough money to invest in risky assets and 2) may not be willing to invest more in risky assets to bear more risk. If it is true, we expect that the retirement effect for mortgage holders will be smaller than that for non-mortgage holders. Here we consider two measures to examine the heterogeneous retirement effects. For the first measure, we classify households with any mortgage as mortgage holders and the rest as non-mortgage holders. We define this dummy variable as the first measure of the mortgage holding. For the second measure, we use the natural log of mortgage that is reported in the HRS data, as a continuous measure of mortgage holdings. Table 6 represents the regression regressions similar to Table 5. Columns 1-4 report the results using the first measure and Columns 5-8 report the results using the second measure. It shows that the coefficient of the interaction term between mortgage dummy and retirement status dummy is negative and statistically significant across different specifications. Based upon these coefficients, we calculate that the retirement effect on the risky share holdings for non-mortgage holders is 1.3 percentage points higher in panel regression and 18 When we conduct instrumental variables regression analysis for specifications with retirement-wealth interactions, we instrument these interactions by interactions between our instrumental variables and wealth indicators. Similar settings are adopted for other heterogeneity tests 19 These findings are consistent with our conjecture in the sense that for individuals in the low wealth group, they rarely hold risky assets no matter before or after retirement. In the data, the average risky holding in total portfolio for the low wealth group is just 4.5%. 14

15 2.3-3 percentage point higher in the IV setting than that for mortgage holders. Similar patterns can be found by using the second measure and we omit the detailed discussion for brevity Heterogeneity by Pension Holdings Like mortgage, pension is another factor that could also lead to the heterogeneous retirement effects. The reason is that pension provides a constant benefit flows at a monthly base in comparison to social security, which provides a lumpy return at age 62 (75 Here we consider one measure to examine the heterogeneity retirement effect across pension holding. We classify households as pension holders if they report any type pattern benefit and the rest as non-pension holders 20. Still we interact the pension dummy with retirement status as an additional variable. The results are reported in Table 7. It shows that there is no significant difference between pension holders and nonpension holders 21. As a final remark, ideally, we can also explore the heterogeneity across different pension schemes. However, since there is limited information in HRS, we will leave this for future study. 5 Possible Explanations The previous section has established the striking retirement effect, that is, there exists a large effect of retirement on households risky assets investment. This result is very robust across different specifications and cannot be explained by existing theories. To further explore this retirement effect, in this section, we will propose and test four possible channels that could possibly explain such retirement effect. As one caveat, here we do not exhaust all possible cases, so that one should treat these four channels as possible channels rather than exclusive explanations Changes in Risk Tolerance Many factors, like age, wealth, health status, can affect risk tolerance. Now, provided that risky tolerance is positively correlated to risky asset holding(canner, Mankiw, and Weil, 1997), when retirement itself increases the risk tolerance, as a consequence, the increased risk tolerance boosts the chance that individuals would invest more in risky assets. More specifically, before retirement, individuals encounter many other uncertainties, including employment uncertainty, labor income uncertainty, and so forth. Then, they would have lower risk tolerance and then maintain lower risky assets holdings. In contrast, after retirement, those 20 From our definition, pension holder indicator is time invariant, thus is automatically dropped out in our panel regression. 21 This is also an evidence that the retirement effect is not driven by differences in post-retirement income flows due to different retirement benefit schemes. 22 For example, tax concerns might be another possible channel, which we do not discuss here due to data limitation. 15

16 work-related uncertainties disappear, thus they would be more risk tolerant and invest more in risky assets. To test this risk tolerance hypothesis, we employ a risk tolerance measure proposed by Barsky, Juster, Kimball, and Shapiro (1997). This measure is defined following from a series of hypothetical questions about job choices between a job with a certain wage level and jobs with diverse wage uncertainties, and is constructed in two ways: a categorical variable from 1 to 4 and a categorical one from 1 to Note that the smaller the number is, the more risk tolerant the households are. Given this measure, we consider the ordered logit regression and panel regression, respectively. The results of ordered logit regression are reported in Column 1 and 3 and the results of panel regression and represent the results in Column 2 and 3 in Table 8. Across all specifications using different measures, it shows that households have a higher risk tolerance after retirement than that before retirement. 5.2 Time Spending Next, we consider another factor associated with the retirement that could drive the retirement effect. As we know that after retirement, individuals would have more time to be allocated to keep track of the risky asset markets than before and would also possibly enjoy the trading process of risky assets. If it is the case, individuals would invest more risky assets once they have more time after retirement. To test this hypothesis, we will use one measure of tracking stock market in HRS. This measure is drawn from one question in HRS "how closely do you track the stock market: very closely, somewhat closely and never". The value of this measure is assigned as 1, 2 and 3 respectively. In other words, a smaller number means more closeness. We still use the ordered logit regression and the results in Column 5 of Table 8. We find that retirement does increase the closeness how people track the stock market, which supports the time spending hypothesis. 5.3 Life Expectancy As suggested by Cocco and Gomes (2012), when individuals have longer life expectancy, they will allocate more of their assets into saving, switching their portfolio towards a lower risk. However, the effect of retirement on the life expectancy varies with respect to individuals optimism. Optimistic individuals may expect a longer life once they stop working and enjoy life more freely, thus increasing their saving rather than risky assets. On the other hand, pessimistic individuals may expect to have a shorter life expectancy and may be less capable after retirement, thus decrease their saving and buy more risky assets. 23 In the HRS, individuals who were surveyed about these job choice questions to measure risk tolerance are mostly below 65, which makes our samples only with about 15% above 65 for four-category risk measure and 19% above 65 for six-category risk measure. 16

17 To see whether the retirement effect could happen through the changes in life expectancy, we examine on average whether the retirement decreases the life expectancy across different levels of optimisms. Here we use the self-reported probability of living to age 75 and 85 as subject life expectancy to test this hypothesis. The results are represented in Columns 6 and 7 of Table 8. It shows that on average, individuals tend to perceive a lower life expectancy after retirement. In particular, the retirement decreases the life expectancy 1.2 percent probability to live to age 75 and decreases 5.3percent probability to live to age 85. This result supports that the retirement effect could come from the decreasing in life expectancy perceived by retirees. 5.4 Bequest Motives We may also expect that the retirement could also weaken the bequest motives and in turn weaker bequest motives increase the chance that households invest more risky asset holding 24. Imagine that when individuals are at work, they may consider themselves more capable and stronger, thus having a stronger bequest motive. Once getting retired, individuals feel sudden loss of their labor income and may treat themselves not as strong or capable as before. Therefore, they may think more about themselves and weaken their bequest motive. If this is true, changes in bequest motive can be another possible explanation for the retirement effect. Bequest motives in HRS are measured using a sequence of questions. Started with $10K, individuals were asked whether they intend to leave a bequest of this amount with what probability. If zero probability, then individuals will be asked whether they will intend to leave any bequest. If any positive probability, individuals will be further asked whether they will intend to leave $100K or above with what probability. We treat each question as a different measure of bequest motives. We regress these three measures of bequest motives on the retirement. The results are shown in Columns 8 to 10 of Table 8. It shows that though they are not statistically significant except for the leaving any, a relatively weaker bequest motive is found after retirement. It suggests that though the evidence is relatively weak, a weaker bequest motive is also a possible channel that leads to an increase of the risky share holding after retirement. 6 Robustness 6.1 Alternative Risky Share Definition In the previous sections, we focus on the risky share defined by the ratio of risky assets (stocks and mutual funds) and total financial assets, where the financial assets do not include retirement accounts. One may 24 Cocco, Gomes, and Maenhout (2005) justify that people with stronger bequest draws down their wealth more slowly and in turn results in a lower risky share. 17

18 argue that when making portfolio choice decisions, individuals will not only take their non-retirement financial assets into account, but they will also consider the retirement account, together as their total assets. To address this concern, we use an alternative risky share measure by including the IRA account and its respective portion in stocks. This new risky share measure is defined as (stocks + mutual funds + IRA stocks)/ (financial assets+ira) 25. The new results are summarized in Table 9. It shows that the retirement effect maintains and this effect is quantitatively similar to the results using our initial risky share definition. In other words, our results are robust to risk portfolio measure both with and without taking into account the retirement account. 6.2 Alternative Retirement Definition In the previous sections, we use self-reported retirement status and only treat individuals to be retired if they report "fully-retired". Although there is no formal verification about an individual s retirement, there are a set of alternative measures that can be used for robustness check. For the robustness check, we first keep the measure we used in the previous section. Then we define a new retirement status by including both fully-retired and partially- retired individuals as retirees. In addition, we use an additional question regarding the labor force participation to define the retirement status. More specifically, this question is "what is your current labor force status: working, unemployment, not in labor market, disabled, partially retired, fully retired?". To define the retirement status, we exclude individuals who are either "not in labor market" or "disabled" from our sample. Similar to the definitions using the self-report retirement status question, we define one measure of retirement status if one reports labor force participation as "fully-retired" and in addition, we define another measure of retirement status if one reports labor force participation as either "fully retired" or "partially retired". The results using these four measures are reported in Table 10. It shows that the retirement effect is robust across different retirement status definitions. 6.3 Spouse s Retirement Status Another concern about retirement effect stems from the fact that men and women differ with respect to their risk aversion and consequently investment decisions(barber and Odean, 2001; Addoum, 2013). To address this concern, we estimate the retirement effect by incorporating both male household heads retirement status and their spouses retirement status. In table 11, it shows that the positive retirement effect is only driven by the household head s retirement status. The spouse s retirement in general does not contribute to portfolio 25 Since the HRS only includes IRA account information since 2000, and only precise asset allocation information from wave 2006 samples using the new risky share measure will be much smaller than our original definition. 18

19 choice Passive Holdings The idea of passive holding is that when the stock market crash and stock price declines sharply, individuals with stock holding might be trapped by this deep falling and will be reluctant to sell their stocks at a lowest price. When this happens at the same time of retirement, we may misinterpret this passive holding as the retirement effect. We would argue that the wave fixed-effects included in our regression would deal with this issue. In addition, we also conduct subsample regressions which drop the observation in Waves 2008 to 2010 to avoid the potential effect caused by the crisis. In Table 12, the results do not show any significant difference from those obtained by using the full sample, which suggests that the retirement effect is not driven by the crisis High Order Effects in Age, Income and Wealth Age, income and wealth may affect the risky share holding nonlinearly. Though we controlled age in both linear and square terms, and income and wealth in log terms, it might not be sufficient. To explicitly exclude this possibility, we use different specifications to add further higher order terms in our regression by having age, age square, age cubic and age quadratic terms, and log of income, log of wealth and their square terms respectively. As shown in Table 13, after controlling these high order terms, our retirement effect still maintains. 6.6 Placebo Test In HRS data, since individuals retirement information can be constructed only using self-reported question, there might be some potential reporting errors. More specifically, imagine that when individuals tend to misreport their retirement status following a certain way, the retirement effect we obtained in the previous section might be driven by some unobserved factors that also determine the reported retirement status rather than actual retirement. To address this issue, we conduct some placebo tests. To this end, we artificially create fixed retirement ages from 62 to 70, above which people will be labeled as "retirees". The results are reported in Table 14. We find that this "artificial" retirement is only effective in the setting with age 65, which is the minimum legal age for full retirement benefit, and age 66, which is age at which individuals get 26 In the instrumental variable estimations, we construct spouse s expected retirement status and age indicators as IVs for spouse s retirement status in the same spirit as instruments defined for household head s retirement status. 27 In some specifications in Table 10, spouse s retirement even leads to a negative effect. These results also indicate potential gender differences in portfolio choice during the transition into retirement, which was evaluated by Addoum (2013). 28 For the internet bubble crisis during early 2000, we also conduct a similar subsample test by restricting our sample up to wave The results are qualitatively similar. 19

20 retired the most. The placebo tests in Table 13 indicate that our results are not driven by other potential factors and thus indirectly support our main findings of the retirement effect on the portfolio choice. 7 Conclusion To sum up, our paper first establishes the positive causal effect of the retirement on risky asset holdings, after correcting the endogeneity bias associated with the retirement status. We find that the retirement leads to approximately percentage point increase in the risky shares of household s portfolio holdings. We also find that the retirement effect exhibits a sizable jump. These results support positive increase pattern of risky asset holding over time periods as predicted by a stream of theories but is not consistent with the smoothed transition pattern as suggested by these theories 29. To further explore this retirement effect, we then propose and test four possible hypotheses that could explain this sizable shift due to retirement. We show that this retirement effect can be associated with four possible scenarios: 1) higher risk tolerance, 2) more time to track risky asset markets, 3) shorter life expectancy, and 4) lower bequest motives, first two of which are stronger and more robust. One caveat is that we cannot distinguish these scenarios simultaneously. There are four possible directions that we will explore for our further work. First, we will develop a sensible theoretical model that could explain this empirical puzzle. Second, as the retirement is associated with decreased income risk, it is also worth discussing how the decrease in income risk affects the portfolio choice. Thirdly, we try to find the richer data that could allow us to distinguish four channels proposed above simultaneously. Finally, here we only consider the contemporaneous retirement effect and we will try to examine retirement effects in a longer time horizon. 29 This stream of literature includes Viceira (2001), Cocco, Gomes, and Maenhout (2005), Gomes and Michaelides (2005) and Cocco and Gomes (2012). 20