Pension Risk, Retirement Saving and Insurance

Transcription

1 Pension Risk, Retirement Saving and Insurance Luigi Guiso European University Institute and CEPR Tullio Jappelli Università di Napoli Federico II, CEPR and CSEF Mario Padula Università Ca Foscari di Venezia and CSEF 10 Novembre 2008 Abstract We estimate the risk associated with pension benefits in a representative sample of customers of a leading Italian bank. Our survey gives the unique opportunity of measuring such risk, by eliciting for each individual the subjective distribution of the replacement rate upon which social security wealth ultimately depends. We document substantial heterogeneity of pension risk, and then relate it to the allocation of private wealth and the propensity to insure other risks. We focus particularly on the demand for targeted retirement instruments and the demand for health care and casualty insurance. We find that the propensities to enroll in a private pension fund, to invest in life insurance and to own a private health insurance policy are positively associated with the riskiness of social security. Our results lend support to models of investors behavior in which background risk affects investors decisions. Keywords: Pension risk, retirement saving, insurance JEL Classification: H55, E21 Acknowledgments. We are grateful to the Unicredit Group, and particularly to Daniele Fano and Laura Marzorati, for letting us contribute to the design and use of the Unicredit Customer Survey. 1

2 1. Introduction Due to the demographic transitions and the incomplete process of pension reforms citizens of most industrialized countries face considerable uncertainty about their future pension entitlements. The long-term nature of pension arrangements makes it all the more difficult to predict what the pension will look like in the future. As a consequence, prudent individuals should have strong incentives to caution against the risk of curtailing consumption after retirement, and should devote considerable effort in trying to improve the quality of their forecast about future benefits. In this paper we rely on information on the subjective probability distribution of long-term pension benefits that Italian working-age individuals anticipate to be entitled to. We address two issues. First, we quantify the amount of uncertainty about future pensions that individuals face, and single out the most important drivers of measured heterogeneity. The issue helps us understand if people are aware of the risks they face, a necessary condition for them to react to future perceived risks. Second, we investigate if pension risk is related to the demand of retirement saving (life insurance and pension funds) and to the propensity to insure other risks (health and casualty risks). To answer these questions we use the Unicredit Customers Survey (UCS), a random sample of the 2007 Unicredit clientele. The survey elicits the subjective probability distribution of the replacement rate, as well as detailed income, asset and demographic variables. A large literature has investigated the relation between pension wealth and the accumulation of private wealth. Feldstein (1974) and Feldstein and Pellechio (1979) pioneered the analysis of the displacement effect of pension wealth on national saving using U.S. time series and microeconomic data, respectively. Since then, researchers have used individual level data to estimate the displacement effect in the U.S. and other countries imputing pension wealth from legislation, see Gale (1998) and Bernheim (2001). Existing microeconometric evidence suggests that pension wealth crowds out discretionary wealth, but at a rate of considerably less than one-for-one. Other related and influential research looks at how pension wealth affects retirement and labor participation decisions of the elderly, and simulates the effects of policy reforms, see Gruber and Wise 2

3 (1999; 2004). Using Italian survey data, Attanasio and Brugiavini (2003) estimate the displacement effect exploiting changes in pension wealth across cohorts and employment groups induced by the Italian pension reforms. Bottazzi, Jappelli and Padula (2006) study the impact of the Italian pension reforms relying on an estimate of pension wealth based on the expected retirement age and the expected replacement rate, rather than computed from legislation. Rather than using data from legislation or point expectations, in this paper we estimate the respondent-specific probability distributions of replacement rates. On this front, the UCS provides a unique opportunity, because it elicits individual beliefs on pension outcomes, asset allocation and insurance ownership. 1 The subjective distributions allow us to focus on an unexplored issue, i.e. how pension risk affects the demand for retirement saving and the propensity to insure other risks. In particular, people who perceive greater pension risk might choose to increase retirement saving to buffer this additional sources of risk. Empirically, we find that the propensity to enroll in a private pension fund and to invest in life insurance are positively associated with the perceived riskiness of social security. We also find that the propensity to enrol in health insurance plans is higher for those who perceive greater pension risk. Overall, our results lend support to models of investors behavior in which background risk (as measured by pension risk) affects portfolio and insurance decisions (Kimball, 1992; Gollier and Pratt, 1996). The remaining of the paper is organized as follows. Section 2 describes the pension rules in Italy and clarifies the sources of uncertainty of social security benefits. Section 3 presents the data on the respondent-specific subjective distributions of replacement rates and provides descriptive evidence on the extent of heterogeneity in respondents beliefs about pension entitlements. In Section 4 we investigate if people facing higher pension risk (as measured by the standard deviation of the respondent social security risk) 1 Manski (2004) and Dominitz, Manski and Heinz (2003) use the Survey of Economic Expectations (SEE) elicit the subjective distribution of social security benefits with a different method. However, the SEE is telephone interview, with only few demographic variables and no wealth data. 3

4 increase their demand for private pension funds, life insurance and health insurance. Section 5 concludes. 2. Pension risk in the current regime Until the early nineties, the Italian social security system had high replacement rates (the ratio between first pension benefit and the last salary or income), earningsbased benefits, indexation of pensions to real earnings and cost of living, generous provisions for early retirement, and a large number of social pensions (i.e., old-age income assistance). This resulted in the ratio of pension benefits to GNP reaching almost 16 percent in 1992, the highest value among industrialized countries. The high burden of pension benefits on the state budget prompted several reforms, implemented between 1992 and The main features of the reforms were an increase in retirement age and minimum years of contributions for pension eligibility, abolition of seniority pensions for all those who started working after 1995, and a new formula to compute benefits. 2 As of 2007, pension benefits and eligibility vary according to years of contributions at the end of A defined benefit formula applies to those who had more than 18 years of contributions in 1995 (who have currently more than 30 years of contributions): we term this formula the earnings model and workers to whom this formula applies as the old. A notionally defined contribution model applies to those who entered the labor market after 1995 (the young ), while benefits for those who had less than 18 years of contributions in 1995 (the middle-aged ), are computed according to a pro-rata model. The upper panel of Table 1 summarizes the pension ward formulas. For the old pension benefits are proportional to the average of the last 10 years salary (15 for self-employed), with an accrual rate of 2 percent for each year of 2 Seniority pensions were de-facto re-introduced by the 2004 also for those who started working after 1995, while the 2008 reform, not covered by our sample, has introduced a system of age and seniority called quotas. 4

5 contributions. For the young benefits will be computed according to the formula γτ N 1 0 w t (1 + g) N 1 t, where τ is the contribution rate and g a 5-year moving average of the GDP growth rate. Contributions are proportional to earnings w, capitalized on the basis of a 5-year moving average, and then transformed in flow benefits using an annuitization factor (γ), set by legislators, that depends on retirement age and life expectancy. 3 Since the contribution rate τ is 33 percent for private and public employees and 20 percent for the self-employed, the self-employed will receive substantially lower pensions than employees. For the middle-aged, pensions are earnings-related for working years before 1995, and contributions-related afterwards. The current regime thus features considerable heterogeneity: generous provisions for workers close to retirement, and different contribution rates for employed (private and public) and self-employed. Eligibility rules also vary with the model used for computing pension benefits. For benefits computed with the earnings and pro-rata models, retirement age depends on the year of retirement. Retirement age for those who will retire in 2008 and 2009 is 60 years (61 for self-employed), and a minimum of 35 years of contributions. For those who will retire in retirement age is 61 (62 for self employed), and 62 (63 for selfemployed) for those who retire in 2014 or later. For the contribution model pension eligibility is either 40 years of contribution, or 60 years of age (65 for males), as shown in the lower panel of Table 1. 4 This shows that future pension benefits of Italian workers depend on a wide set of variables, including year of birth, occupation and career earningsprofile. To forecast pension benefits workers must also take into account population aging (reflected in the annuitization factor) and slow growth, which are likely to prompt further reforms. In the paper we focus on the replacement rate, the ratio of the first pension to the last salary, as a synthetic indicator of pension wealth. Even without considering demographic uncertainty and possible changes in future legislation, forecasting one s pension is not an easy task. To assess the sensitivity of the different pension award 3 Currently, γ increases from percent for somebody retiring at 57 to percent for somebody retiring at Ex lege 243 of

6 formulas to variation in features of the income process, we compute pension benefits for an individual under different assumptions of the age-income profile and income uncertainty. Consider first a young worker who entered the labor market after 1995 and earns 15,000 euro from age 25 to 35, 20,000 from age 36 to 45 and 40,000 from age 46 to 65; she will be entitled to a pension of 27,200 euro (a replacement rate of 68 percent). A flatter earnings profile will substantially reduce pensions: with earnings of 15,000 euro from age 25 to 41, 20,000 from age 42 to age 51 and 40,000 from age 52 to 65, the pension will be 23,600 euro (a replacement rate of 59 percent). The example suggests that in the Italian contribution-based system that applies to young workers the shape of the age-earnings profile affects dramatically the replacement rate. Earnings uncertainty also plays a role. One case is that of old employees hit by a negative income shock in the last few years of work. This would reduce their benefits, since these are proportional to the average wage in the last 10 years. But income risk affects pension risk also for younger workers. We posit that income shocks have a permanent and a transitory component and compute by Monte Carlo simulations the standard deviation of pension benefits, drawing with replacement from the income process, and computing benefits for each draw. We find that if the standard deviation of transitory income shocks increases from 0.1 to 0.2, the standard deviation of pension benefits increases from 0.14 to Using the same procedure, we can compare pension risk between old and young workers. Whether pension benefits are more risky for young workers depends on the timing of uncertainty resolution. If uncertainty resolves early on in the individual career, the contribution is more risky than the earnings model. For instance, suppose that in the first 10 years the transitory and permanent income shocks have a standard deviation of 0.1, and that after the first 10 years income is certain (20,000 euro between age and 40,000 euro between 46 and 65). The replacement rate computed with the earnings model has zero standard deviation, because income is certain in the last 30 years of work; in the contribution model the standard deviation is positive, reflecting early years of income uncertainty. 6

7 Pension benefits are thus sensitive to the income process parameters. To the extent that individuals are uncertain about these parameters, they will also be uncertain about benefits. Pension risk is higher for those who face more income risk, such as the selfemployed, and for the young, if income risk is higher at the beginning of workers careers. Moreover, uncertainty about other variables entering the computation of pension benefits (such as demographic risk and future GDP growth), also affect pension risk. 3. The subjective probability distribution of the replacement rate Research aiming to understand the impact of Social Security policy on labor supply, retirement savings, and other household decisions is hampered by a dearth of empirical evidence on Social Security expectations. In the US, respondents to the Health and Retirement Study (HRS) provide point predictions of the level of their future benefits (Bernheim, 1988; Gustman and Steinmeier, 1999, 2001). Point expectations of the replacement rate are reported also in the UK (Banks and Tanner, 2004) and in Italy (Bottazzi, Jappelli and Padula (2006). So far, uncertainty about benefits has been measured only in Dominitz, Manski, and Heinz (2003), who study probabilistic expectations of social security retirement benefits in the SEE (the Survey of Economic Expectations). SEE respondents of ages were first asked to report the lowest and highest possible levels of their future benefits. The responses to these preliminary questions were then used to set thresholds for up to six probabilistic questions about the level of benefits. Finally, the subjective probabilities elicited from respondent are then used to fit a respondent-specific parametric distribution following the procedure described in Manski (2004). The SEE has only basic demographic information (age, gender, education), and no information on portfolio choice. Therefore, one cannot relate pension subjective probabilities to outcomes such as portfolio choice or the demand for insurance. Furthermore, the SEE is based on telephone interviews, and variables are therefore potentially subject to considerable measurement error. 7

8 In keeping with the British and Italian evidence, in this paper we take as indicator of social security wealth the replacement rate, which in turn depends on the pension award formula and the expected retirement age, rather than the level of benefits Elicitation method To elicit pension expectations in the UCS we follow a similar procedure as in Dominitz, Manski, and Heinz (2003). All employees (1,024 observations) are preliminarily asked to report the minimum (y m ) and the maximum (y M ) value of the replacement rate that will apply to them. Each respondent is then asked to state on a scale between 0 and 100 the probability that the replacement rate will be less than the midpoint between the minimum and the maximum, Prob(y (y m + y M )/2) = π. The exact wording of the questions is reported in the Appendix. To estimate the moments of the subjective distributions of the replacement rate, we assume that the underlying distribution is either uniform or triangular. Based on the range of the distribution and on the subjective probability elicited, we then compute the respondent-specific mean, standard deviation, and coefficient of variation. The formula to compute these statistics are also reported in the Appendix Descriptive statistics Table 2 reports the cross-sectional average and coefficient of variation of the subjective means, medians, standard deviation and coefficient of variation of the respondent-specific subjective distributions of the replacement rate. The cross-sectional mean is 67 percent for both the uniform and triangular distributions, a value that is close to the statutory replacement rate for the average individual in the sample. 5 The median is slightly higher (71 percent), and the standard deviation is about 20 percent. Assuming that the replacement rate distribution is uniform, the average of the respondent-specific 5 Bottazzi, Jappelli and Padula (2006) provide details on the computation of the statutory rate and a comparison between statutory and point expectations of the replacement rates in the SHIW. 8

9 coefficients of variation is 4.3 percent (3.1 using the triangular distribution). The median coefficient of variation is slightly lower (3.4 and 2.4, respectively). While cross-sectional averages are useful statistics to describe the subjective distribution of the average individual, they hide potentially important differences across individuals. In Figure 1 we plot the cross-sectional distribution of the mean and coefficient of variation of the respondent-specific distributions. The figure highlights considerably heterogeneity of responses. For instance, 10 percent of respondents expect a replacement rate of less than 40 percent, while 10 percent expect it to be over 90 percent. As for the coefficient of variation, almost 20 percent of respondents hold point expectations (resulting in a coefficient of variation equal to zero), while for 9.6 percent our estimate of the coefficient of variation is greater than 10. The next step of the analysis is to study if pension expectations are associated with individual characteristics. We are particularly interested in checking if individual subjective probabilities correlate with some of the features of the current pension regime (such as cohort or occupation), and if portfolio choice and the demand for insurance correlate with pension risk Determinants of pension risk Figure 1 presents kernel-smoothed means of the average and coefficient of variation of the respondent-specific replacement rate distributions by education and age. In this figure and in the remaining of the paper we focus on the triangular distributions (results for the uniform are qualitatively similar). The visual impression is that the mean of respondents expectations of the replacement rate increase with age (upper-left panel), while they are not strongly correlated with education (bottom-left panel). In particular, 35-years old workers expect a replacement rate of 63 percent, while workers close to retirement expect a replacement rate of 70 percent or higher. A positive relation between age and the replacement rate agrees with the features of the current pension regime, which grants more generous pensions to workers close to retirement. The coefficient of variation declines substantially during the life cycle (from 4.5 to about 2, upper-right panel), and 9

10 with education (particularly for the first education group, bottom-right panel), signaling that younger workers perceive substantially more risk than workers close to retirement. To dig deeper in the relation between age, education and the subjective distributions in Figure 3 we present kernel-smoothed 0.25, 0.50, and 0.75-quantile regressions of the subjective mean and coefficient of variation by age and education groups. The figure shows that subjective uncertainty about social security benefits is substantial among young persons but decreases with age (upper-right panel), confirming the findings of Dominitz, Manski and Heinz (2003). Even middle-aged workers tend to be rather uncertain about their future benefits. That uncertainty about benefits should decrease with age agrees with intuition, because uncertainty about future labor earnings and the future structure of social security should decrease as retirement nears. In Figure 4 we explore the relation between subjective expectations and occupation, by plotting the mean and coefficient of variation of the respondent-specific distributions by occupation and income deciles. The most notable features are that expected replacement rates don t vary with income (upper-left panel), while the relation between income and the coefficient of variation is non-linear (upper-right panel): uncertainty is greatest at the lowest and highest ends of the income distribution. Furthermore, the figure suggests that professionals and self-employed workers, who are entitled with lower pensions, indeed expect their pensions to be lower (bottom-left panel). They perceive also greater pension risk; given pension award formula, this agrees with the fact that they also face higher income risk Regressions analysis Table 3 relates the mean, standard deviation and coefficient of variation of the respondent-specific replacement rate distributions to demographic characteristics (age, gender, education), occupation (dummies for public employees and self-employed), region of residence and income. Other variables (for instance, sector of occupation) are excluded from the regression because the coefficients were not statistically different from zero. 10

11 The estimates in column 1 reveal that women expect, on average, a lower pension, in agreement with their shorter working career and younger retirement age. Older workers also expect a higher replacement rate, owing to the more generous pension award formula (linked to average wages in the 10 or 15 years before retirement) than younger workers (whose pensions is linked to contributions over the entire career). Public employees expect a replacement rate that is 5 percentage points higher than the reference category (private employees), while the self-employed expect a replacement rate of 6 points lower. Residents in the North expect a lower replacement rate, compared to individuals living in the Centre (who expect a replacement rate about 5 percentage points higher), and in the South (6 points higher). In column 2 we add to the set of regressors an index of financial literacy computed from specific survey responses. The index is meant to capture the ability to understand simple financial concepts; financial literacy and formal education (as measured by years of schooling) might affect the ability to process financial information and risk perceptions. To compute the index of financial literacy we define two dummy variables equal to one if respondents answer correctly two questions about the understanding of interest rates and inflation, 6 four dummies that measure ability to rank asset riskiness correctly, 7 and two dummies about the meaning of financial diversification and the ability to rank the diversification of specific portfolios. 8 The resulting index ranges from 0 (no question is answered correctly) to 8 (all correct), with a median of 3. Column 2 shows that people with above average financial literacy and education tend to expect a lower 6 The interest rate question is: Suppose that in the next 6 months interest rate will increase. Do you think it is a good idea to buy today fixed interest rate bonds? The inflation question is: Suppose that a saving account earns an interest rate of 2 percent per year (net of costs). If the annual inflation rate is 2 percent, after two years (with no withdrawals), do you think that you could buy more than you could buy today / less / the same / don t know? 7 We consider if the respondents ranking of asset categories satisfies each of the following inequalities: (a) bonds are at least as risky as transaction accounts; (b) stocks are at least as risky as bonds; (c) equity mutual funds are at least as risky as bond mutual funds; (d) housing is riskier than transaction accounts. 8 The list of portfolios is: 70 percent invested in T-bills and 30 percent in a European equity fund; 70 percent in T-bills, 15 percent in a European equity fund, and 15 percent in 2-3 stocks; 70 percent in T-bills and 30 percent in 2-3 stocks; 70 percent in T-bills and 30 percent in a stock I know well). 11

12 replacement rate. However, only the coefficient of education is statistically different from zero at the 5 percent level, while the coefficient of financial literacy is not statistically different from zero. In columns 3 and 4 the dependent variable is the standard deviation of the respondent-specific subjective distribution of the replacement rate. Pension benefits are more uncertain for the self-employed than for the employees, consistent with their greater income volatility. Perceived pension risk falls with age, in agreement with the descriptive analysis and the finding of Dominitz, Manski and Heinz (2003). The age effect captures the fact that individuals have more incentives to learn about benefits near retirement, but also the fact for workers with more than 30 years of contributions benefits are proportional to earnings in the last years of work, while for younger workers they are linked to capitalized lifetime contributions. Therefore, for the young benefits depend on a broader range of variables, including expectations on GDP growth and demographic risk. Moreover, as we discuss in Section 2, the contribution method potentially amplifies the effect of earnings uncertainty on pension risk. The standard deviation of the replacement rate distribution is negatively associated with the index of financial literacy: increasing the index from 1 to 8 raises pension risk by 0.8 percentage points, about 5 percent of the sample mean. The finding suggests that more financially informed investors are also more aware than pensions are risky. For robustness, in columns 5 and 6 of Table 3 we report regressions where the dependent variable is the coefficient of variation of the replacement rate distribution. The results confirm that perceived pension risk is greater for the self-employed, and smaller near retirement. In this case the coefficients of education, financial literacy and region of residence are not statistically different from zero. Overall, Table 3 documents substantial heterogeneity in the subjective distributions of the replacement rate, and that observable variables, such as age and occupation, are able to account only for some of the observed variability. In the next two sections we investigate if people react to perceived pension risk by focusing on the demand for retirement saving and for insurance. 12

13 4. The demand for retirement saving People who expect a lower social security replacement rate could supplement public pensions by increasing retirement saving. This is a widely investigated link, and relates to the offset between social security and private wealth, an issue which has received a lot of attention since the seminal work of Feldstein (1974). Data on subjective probabilities allow us to estimate the moments of the distribution of the replacement rate and to focus on a related but unexplored issue: does social security risk affect the demand for retirement saving? In particular, people who perceive greater social security risk might choose to increase discretionary retirement saving to buffer this additional sources of risk. Thus, one should expect participation in private pension funds and life insurance the two main vehicles for retirement saving to be negatively associated with the average replacement rate, and positively associated with the riskiness of social security, as measured by the standard deviations of the subjective distributions. 9 From a policy perspectives, understanding the link between pension risk and the demand for retirement saving is quite relevant. Indeed, in the last two decades pension legislation has repeatedly tried to encourage the development of private pension funds and life insurace. Favored fiscal treatments of contributions to life insurance policies have been introduced since 1986, and have been later extended to contributions to private pension plans. More recent policy interventions have been directed at diverting contributions to the severance payment fund towards individual and occupational pension plans. 10 Whether or not such measures have been effective is an open question, though the evidence presented in Jappelli and Pistaferri (2003) suggests that the favored fiscal treatment of life-insurance policies has not induced large reallocations of household 9 In this section we focus on participation in saving plans rather then in wealth amounts, which in the survey are subject to larger measurement errors. 10 The TFR is a severance pay that workers receive at the end of their working life. Starting from the 1 st January 2007 workers can choose to direct TFR contributions to complementary pension plans. 13

14 portfolios towards these assets. Here, we address a different question, i.e. whether the riskiness of public pensions stimulates the demand for discretionary retirement saving Descriptive analysis Figure 5 plots the fraction of individuals with private pension funds, life insurance, health and casualty insurance against the average replacement rate. The graph detects a negative relation between pension funds and the replacement rate (upper-left graph): people who expect a relatively low public pension (the mean of their replacement rate distribution is 70 percent or less) exhibit a greater propensity to invest in private pension funds (about 25 percent). And among those who expect a replacement rate of 80 percent or higher, the proportion of with pension funds is only 10 percent. For life insurance the relation is essentially flat (upper-right panel). The relation with pension risk is plotted in Figure 6. The upper-left panel shows that among those who perceive public pensions as relatively safe (a coefficient of variation of 4 percent or less) participation in pension funds is considerably lower (15 percent) than among those who perceive higher risk (participation of 20 percent for those with coefficient of variation greater than 6 percent). On the other hand, life insurance seems to be only weakly related to pension risk (upper-right graph) Regression analysis We focus first on the demand for targeted retirement saving, and relate the probability of ownership of private pension funds and life insurance to the subjective mean and standard deviation of the replacement rate distribution. The probit regressions in Table 5 control also for demographic variables (age, gender, education), employment (two dummies for public sector employees and self-employed), region of residence, 14

15 income, and a dummy for risk aversion. 11 In the table we report marginal effects and the associated standard errors. The estimates in column 1 indicate that the probability of having a private pension fund is negatively related to age, is lower in the South and for investors with relatively high risk aversion, and increases with income and education (although the latter two coefficients are not statistically different from zero). While the expected replacement rate is not correlated with ownership of private pension funds, the relation with the standard deviation of the replacement rate distribution is positive and precisely estimated. The effect is also sizable: a two-point increase in the standard deviation (equivalent to the average of the standard deviation of the subjective distributions) is associated with a 5- percentage points increase in private pension funds ownership. In the other columns of Table 4 we add dummies for level of financial wealth, we control also for the mean and standard deviation of the subjective distribution of retirement age, 12 and for the index of financial literacy described in Section 3. While none of these additional variables is associated with pension funds ownership, the coefficient of the standard deviation of the replacement rate distribution is hardly affected in magnitude and significance. Table 5 repeats the estimation for ownership of life insurance. Here we find that the self-employed are more likely to have life insurance, and that the coefficient of our indicator for risk aversion is negative. The standard deviation of the replacement rate distribution is positively associated with life insurance. 11 The dummy is based on the following question: In managing your financial investment, you think you are a person that is interested in investments that offer the possibility of: (1) a high return, with a high risk of loosing the capital; (2) a good return, and reasonable safety; (3) a moderate return, but at the same time a good degree of safety; (4) a low return, without any risk of loosing the capital. The risk aversion dummy is defined as (3) or (4). 12 People are asked to provide the minimum and maximum values of expected retirement age, and the probability that it will be greater than the mid-point of the range. We apply the same procedure used for replacement rates to estimate the respondent-specific subjective distributions of retirement age. 15

16 5. The demand for insurance Individuals who expect pensions to be risky should tend to protect themselves from other sources of risk. Accordingly, in this section we look at the demand for health and casualty insurance, on the expectation that the propensity to insure is negatively related to pension risk, as measured again by the standard deviation of the replacement rate distribution. The descriptive analysis in Figures 5 and 6 lends some support to the hypothesis that pension expectations affect the demand for insurance. In Figure 5 (lower panels) we see a negative relation between participation in health or casualty insurance and the average replacement rate. In Figure 6 the proportion of individuals with health insurance is around 20 percent for those who perceive relatively small pension risk, and around 30 percent for those with above average coefficient of variation of the replacement rate. The regression results reported in Table 6 confirms a negative association between the average replacement rate and the propensity to hold health insurance. The effect of the standard deviation of replacement rate is positive, suggesting that those who perceive pensions to be risky are more willing to insure against health risks. We also find that the demand for health insurance is positively associated with education, income and selfemployment. In Table 6 we also find that health insurance is positively related to age, self-employment, and income, and that residents of the South or Central Italy have a lower probability of having health insurance. Controlling for financial wealth, the index of financial literacy and the respondent-specific mean and standard deviation of the retirement age distribution does not change the results. Finally, in Table 7 we focus on casualty insurance. Some of the patterns are similar to health insurance: education, self-employment and income are positively associated with the probability of having casualty insurance. In this case, the coefficient of pension risk is negative, lending some support to the hypothesis that pension risk prompts people to insure more against risks that can be avoided, but not statistically different from zero. 16

17 6. Conclusions In this paper we use the Unicredit Survey (UCS), a representative sample of the clientele of a leading Italian banking group, to elicit information on the respondentspecific distribution of the replacement rate. We characterize the distribution by focusing on the means and standard deviations of the individual distributions. The survey contains not only data on subjective probabilities, but also detailed demographic characteristics of respondents, income, wealth, proxies for risk aversion, and questions to compute an index of financial literacy. Therefore the survey offers the unique opportunity to conduct a systematic exploration on how perceived pension risk correlates with individual characteristics and on how it condition people decisions. On average, we find that the expected replacement rate is close to the statutory value. But average hide important differences across individuals. In particular, we find that the expected replacement rate is higher for older people and lower for the selfemployed, confirming previous evidence consistent with the current rules of the social security system. Pension risk, as measured by the standard deviation of the subjective distributions of the replacement rate, falls when people approach retirement, it is lower for public employees (relative to private employees), and higher self-employed (again, relative to private employees). Financial literacy is also positively associated with pension risk. In the second part of the paper we relate pension risk to the demand for retirement saving, health and casualty insurance. In particular, we study if the demand for retirement saving is negatively related to the expectation of a higher pension, and if people who experience greater public pension risk also choose to increase private retirement saving. Confirming both hypotheses, we find that private pension funds ownership is negatively associated with the average replacement rate and positively associated with the standard deviation of the replacement rate distribution. We also find that the demand for health insurance is positively related to pension risk, while we detect no link for casualty insurance. 17

18 Overall, the evidence implies that heterogeneity in perceived pension risk is not entirely explained by socio-demographic variables (such as age, income and occupation), suggesting that eliciting subjecting pension expectations is crucial to understanding people beliefs. The results also suggest that pension risk is, potentially, a major determinant of the demand for private pension funds, life insurance and health insurance. 18

19 References Bernheim, B. Douglas (1988), Social Security Benefits: An Empirical Study of Expectations and Realizations, Issues in Contemporary Retirement, R.R Campbell and E. Lazear eds. Stanford: Hoover Institution. Bernheim, Douglas (1990), The Timing of Retirement: a Comparison of Expectations and Realizations, in The Economics of Aging, David Wise ed. Chicago: The University of Chicago Press. Bottazzi, Renata, Tullio Jappelli and Mario Padula (2006), Retirement expectations, pension reforms, and their impact on private wealth accumulation, Journal of Public Economics 90, Bottazzi, Renata, Tullio Jappelli and Mario Padula (2008), Pension Reforms and the Allocation of Retirement Saving, in progress. Disney, Richard, and Sarah Tanner (1999), What Can We Learn from Retirement Expectations Data?, IFS Working Paper n. W99/17. London: Institute for Fiscal Studies. Dominitz, Jeff, Charles Manski, and Jordan Heinz (2002), Social Security Expectations and Retirement Savings Decisions, NBER Working Paper n Feldstein, Martin (1974), Social Security, Induced Retirement and Aggregate Capital Accumulation, Journal of Political Economy 82, Feldstein, Martin, and Anthony Pellechio (1979), Social Security and Household Accumulation: New Microeconometric Evidence, Review of Economics and Statistics 61, Gale, William G. (1998), The Effect of Pension Wealth on Household Wealth: a Reevaluation of Theory and Evidence, Journal of Political Economy 106, Gollier Christian, and John W. Pratt (1996), Risk Vulnerability and the Tempering Effect of Background Risk, Econometrica 4, Gruber, Jonathan, and David A. Wise (1999), Social Security and Retirement Around the World. Chicago: The University of Chicago Press. Gruber, Jonathan, and David A. Wise (2004), Social Security Programs and Retirement Around the World: Micro Estimation. Chicago: The University of Chicago Press. 19

20 Gustman, Alan L., and Thomas L. Steinmeier (1989), An Analysis of Pension Benefit Formulas, Pension Wealth and Incentives from Pensions, Research in Labor Economics 10, Gustman, Alan L., and Thomas L. Steinmeier (2005), Imperfect Knowledge, Retirement and Saving, Industrial Relations 44, Hurd, Michael D., and Kathleen McGarry (1995), Evaluation of the Subjective Probabilities of Survival in the Health and Retirement Study, Journal of Human Resources 30, Kimball, Miles (1992), Precautionary Motives for Holding Assets, in John Eatwell, Murray Milgate and Peter Newman (Eds.) The New Palgrave Dictionary of Money and Finance. London: MacMillan. Lusardi, Annamaria, (1999), Information, Expectations and Saving for Retirement, in Behavioral Dimensions of Retirement Economics, Henry Aaron ed. Washington: Brookings. Manski, Charles (2004), Measuring Expectations, Econometrica 72, Mitchell, Olivia (1988), Worker Knowledge of Pensions Provisions, Journal of Labor Economics 6,

21 Figure 1 Average and coefficient of variation of the replacement rate distribution Fraction Uniform distribution Average Fraction Uniform distribution Coefficient of variation (%) Fraction Triangular distribution Average Fraction Triangular distribution Coefficient of variation (%) 21

22 Figure 2 The replacement rate distribution, by age and education Average of replacement rate Age C.v. of replacement rate (%) Age Average of replacement rate Education C.v. of replacement rate (%) Education 22

23 Figure 3 Quantiles of the mean and coefficient of variation of the replacement rate distribution, by age and education Quantiles of subjective mean Quantiles of subjective C.v Age 0.25 quantile 0.50 quantile 0.75 quantile Age 0.25 quantile 0.50 quantile 0.75 quantile Quantiles of subjective mean Quantiles of subjective C.v Education 0.25 quantile 0.50 quantile 0.75 quantile Education 0.25 quantile 0.50 quantile 0.75 quantile 23

24 Figure 4 The replacement rate distribution, by income and occupation Average of replacement rate Income decile C.v. of replacement rate (%) Income decile Average of replacement rate Blu collar White collar Manager Professional Self-employed C.v. of replacement rate (%) Blu collar White collar Manager Professional Self-employed 24

25 Figure 5 Retirement saving, health insurance and the replacement rate distribution Pension funds Average of replacement rate Life insurance Average of replacement rate Health insurance Casualty insurance Average of replacement rate Average of replacement rate 25

26 Figure 6 Retirement saving, health insurance and the coefficient of variation of the replacement rate distribution Pension funds Life insurance C.v. of replacement rate (%) C.v. of replacement rate (%) Health insurance Casualty insurance C.v. of replacement rate (%) C.v. of replacement rate (%) 26

27 Table 1 Pension award formula Pension award formula Private sector Public sector Self-employed Old 2% years of contribution 2% years of 2% years of average of last 10 years of earnings contribution average contribution of last 10 years of average of last 15 earnings years of earnings. Middle-aged Earnings model before 1995, contribution model after Young Contributions (33% of gross wage for employees and 20% for self-employed) are capitalized on the basis of 5-years moving average of GDP growth. The capitalized sum is then multiplied by a coefficient that varies by retirement age, taking into account life expectancy. Eligibility rules Seniority pensions Old age pensions Minimum years of contribution Retirement age Old and Middle-aged retiring in Private employees Public employees Selfemployed After Young (60) 65 (60) 65 (60) Note. Old, middle-aged and young refer, respectively, to workers with more than 18 years of contributions in 1995, less than 18 years of contribution in 1995, and who started working in In parentheses the retirement age for females. Table 2 Cross-sectional statistics of the subjective replacement rate distribution Mean Median Standard deviation Coefficient of variation Minimum Maximum Cross-sectional average Uniform Triangular Cross-sectional coefficient of variation Uniform Triangular Note. The table reports the cross-sectional mean and median of the subjective mean, standard deviation and coefficient of variation of the replacement rate distribution. 27

28 Table 3 Determinants of the replacement rate distribution Mean Standard deviation Coefficient of variation (1) (2) (3) (4) (5) (6) Male (1.452) (1.454) (0.122) (0.122) (0.245) (0.245) Age (0.060)*** (0.060)*** (0.005)*** (0.005)*** (0.010)*** (0.010)*** Education (0.181)* (0.182)* (0.015) (0.015) (0.031) (0.031) Public sector (1.484)*** (1.485)*** (0.125)** (0.124)** (0.250)*** (0.250)*** Self-employed (1.556)*** (1.556)*** (0.131)* (0.130)** (0.262)*** (0.262)*** Resident in the Centre (1.516)*** (1.519)*** (0.127)** (0.127)** (0.256) (0.256) Resident in the South (1.501)*** (1.502)*** (0.126) (0.126) (0.253) (0.253) Log income (0.916) (0.918) (0.077) (0.077) (0.154) (0.155) Index of financial literacy (0.435) (0.036)*** (0.073) Constant (9.454)*** (9.478)*** (0.793)*** (0.792)*** (1.594)** (1.596)* Observations R-squared Note. Standard errors are reported in parentheses. Three stars indicate statistically significance at the 0.1% confidence level, two stars at the 1%, one star at the 5% level. 28

29 Table 4 Probability of investing in pension funds (1) (2) (3) (4) Age (0.001)* (0.001) (0.002)* (0.001) Male (0.032) (0.032) (0.032) (0.032) Education (0.004) (0.004) (0.004)* (0.004) High risk aversion (0.031)*** (0.031)*** (0.031)*** (0.031)*** Public sector (0.033) (0.033) (0.033) (0.033) Self-employed (0.035) (0.035) (0.036) (0.035) Resident in the Centre (0.032) (0.032) (0.032) (0.032) Resident in the South (0.030)*** (0.030)*** (0.030)*** (0.030)*** Log income (0.021) (0.022) (0.022) (0.022) Replacement rate (average) (0.001) (0.001) (0.001) (0.001) Replacement rate (s.d.) (0.011)** (0.011)** (0.011)** (0.011)** Financial wealth (0.041) (0.041) (0.041) Financial wealth (0.042) (0.042) (0.042) Financial wealth (0.048) (0.048) (0.048) Financial wealth (0.045) (0.046) (0.045) Financial wealth > (0.061) (0.062) (0.060) Retirement age (average) (0.003) Retirement age (s.d.) (0.025) Index of financial literacy (0.010) Observations Note. The table reports marginal effects. Asymptotic standard errors are reported in parentheses. Three stars indicate statistically significance at the 0.1% confidence level, two stars at the 1%, one star at the 5% level. 29

30 Table 5 Probability of investing in life insurance (1) (2) (3) (4) Age (0.002) (0.002) (0.002) (0.002) Male (0.038) (0.038) (0.039) (0.039) Education (0.005) (0.005) (0.005)* (0.005) High risk aversion (0.040)*** (0.040)*** (0.040)*** (0.040)*** Public sector (0.038) (0.038) (0.038) (0.038) Self-employed (0.042)* (0.042)* (0.042)* (0.043)* Resident in the Centre (0.039) (0.038) (0.038) (0.039) Resident in the South (0.038) (0.038) (0.038) (0.038) Log income (0.024) (0.024) (0.024) (0.024) Replacement rate (average) (0.001) (0.001) (0.001) (0.001) Replacement rate (s.d.) (0.013)* (0.013)* (0.013)* (0.013) Financial wealth (0.050) (0.050) (0.050) Financial wealth (0.050) (0.051) (0.050) Financial wealth (0.056) (0.057) (0.057) Financial wealth (0.064)* (0.064)* (0.063) Financial wealth > (0.071) (0.072) (0.069)* Index of financial literacy (0.012)*** Retirement age (average) (0.003) Retirement age (s.d.) (0.024) Observations Note. The table reports marginal effects. Asymptotic standard errors are reported in parentheses. Three stars indicate statistically significance at the 0.1% confidence level, two stars at the 1%, one star at the 5% level. 30

31 Table 6 Probability of having health insurance (1) (2) (3) (4) (0.001) (0.001) (0.001) (0.001) Male (0.034) (0.034) (0.035) (0.035) Education (0.004)*** (0.004)*** (0.005)*** (0.004)*** High risk aversion (0.040) (0.041) (0.041) (0.041) Public sector (0.035) (0.035) (0.035) (0.035) Self-employed (0.042)*** (0.042)*** (0.042)*** (0.042)*** Resident in the Centre (0.032)** (0.032)** (0.032)** (0.032)** Resident in the South (0.033) (0.033) (0.033) (0.033) Log income (0.021)*** (0.021)*** (0.021)*** (0.021)*** Replacement rate (average) (0.001)* (0.001)** (0.001)** (0.001)* Replacement rate (s.d.) (0.011)*** (0.011)*** (0.011)*** (0.011)*** Financial wealth (0.044) (0.044) (0.044) Financial wealth (0.045) (0.045) (0.044) Financial wealth (0.056) (0.056) (0.056) Financial wealth (0.057) (0.058) (0.057) Financial wealth > (0.076) (0.076) (0.075) Index of financial literacy (0.010) Retirement age (average) (0.003) Retirement age (s.d.) (0.022) Observations Note. The table reports marginal effects. Asymptotic standard errors are reported in parentheses. Three stars indicate statistically significance at the 0.1% confidence level, two stars at the 1%, one star at the 5% level. 31

32 Table 7 Probability of having casualty insurance (1) (2) (3) (4) Age (0.002) (0.002) (0.002) (0.002) Male (0.037)*** (0.038)*** (0.038)** (0.038)*** Education (0.005)** (0.005)** (0.005)** (0.005)** High risk aversion (0.046)* (0.046)* (0.046)* (0.046)* Public sector (0.043) (0.043) (0.043) (0.043) Self-employed (0.046)*** (0.046)*** (0.046)*** (0.046)*** Resident in the Centre (0.043) (0.043) (0.043) (0.043) Resident in the South (0.040)* (0.040)* (0.041)* (0.041)* Log income (0.026)*** (0.026)*** (0.026)*** (0.026)*** Replacement rate (average) (0.001)*** (0.001)*** (0.001)*** (0.001)*** Replacement rate (s.d.) (0.014) (0.014) (0.014) (0.014) Financial wealth (0.050) (0.050) (0.050) Financial wealth (0.054) (0.054) (0.054) Financial wealth (0.059) (0.059) (0.059) Financial wealth (0.063) (0.063) (0.063) Financial wealth > (0.089) (0.088) (0.089) Index of financial literacy (0.012) Retirement age (average) (0.003) Retirement age (s.d.) (0.026) Observations Note. The table reports marginal effects. Asymptotic standard errors are reported in parentheses. Three stars indicate statistically significance at the 0.1% confidence level, two stars at the 1%, one star at the 5% level. 32

33 Appendix 1. The wording of the questions The UCS asks three questions to elicit the subjective probability distribution of the replacement rate. All employees and self-employed are asked to report the minimum (y m ) and the maximum (y M ) replacement rate he or she expects after retirement, and the probability that the replacement rate is less than the midpoint of the support of the distribution, Prob(y (y m + y M )/2) = π. The exact wording of the survey questions is provided below. All respondents are first asked: Think about when you will retire, and consider only the public pension (that is, exclude private pensions, if you have one). (a) (b) (c) At the time of retirement, what is the minimum fraction of labor income that you expect to receive? And what is the maximum value? What are the chances that your pension will be greater than X (where X is computed by the interviewer as (a+b)/2? In other words, if you were to assign a score between 0 and 100 to the chance that the fraction will be greater than X, what score would you assign? ( 0 if you are certain to receive a pension greater than X, 100 if you are certain to receive a pension less than X). The following table is shown to the respondent: I am sure I will earn more than X I am sure I will earn less than X 2. The subjective probability distribution of the replacement rate Let s indicate with f(y) the distribution of the replacement rate for each individual. The survey provides information on the support of the distribution [y m, y M ] and on the probability mass to the left of the mid-point of the support, Prob(y (y m +y M )/2) = π. Knowing the support of the distribution, we can express the expected value and variance of y as: y M E ( y) = yf ( y) dy 2 y M ym 2 Var ( y) = y f ( y) dy y f ( y) dy. ym ym y m 33

34 We consider two assumptions concerning f(y). The first is that y is uniformly distributed over each of the two intervals [y m, (y m +y M )/2] and ((y m +y M )/2, y M ]. If π=0.5 the distribution collapses to a single uniform distribution defined in the interval [y m, y M ]. A second possibility is to assume that the distribution is triangular over the same two intervals; if π=0.5 the distribution again collapses to a single triangular distribution over the interval [y m, y M ]. Note that in both cases E(y) and Var(y) depend only on the three known parameters, y m, y M, and π. The triangular distribution is a more plausible description of the probability distribution of the replacement rate, because outcomes further away from the mid-point receive less weight. Figures A1 and A2 show the p.d.f. under the uniform and the triangular assumptions. 34

35 Figure A1 Uniform distribution Figure A2 The triangular distribution 35