This work focuses on the impact of uncertainty on savings under bequest form. Specifically, we estimate whether and to what extent income variability does have an effect on post-mortem savings. We approximate the post-mortem savings with the closest dedicated savings, which is savings in term insurance, a lump sum inherited at the death of the subscriber. Furthermore, we test whether the intensity of the income variance or the riskiness of the job type—such as self-employment—matters more in the choice. Our results show that self-employment status is one of the most relevant variables affecting term insurance ownership.
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For later reference, we should also point out that (Jappelli and Pistaferri 2003) showed that in Italy the demand of life insurance does not substantially depend on the tax treatment.
Finally, from a theoretical perspective, it is worth mentioning the use of term insurance to study household consumption in a general equilibrium overlapping generation model by (Hong and Ríos-Rull 2012). (Strawczynski 1999) also proved that wealth segmentation of altruistic individuals between annuities and riskless bond may not be optimal once income uncertainty is introduced in an overlapping generation model.
Note that in the model, the bequest value B appears only in the second period. This does not imply that death insurance can be bought only in the second period. Indeed, such assumption would be unrealistic, since individuals buy such insurance over the lifetime. Here, we are assuming that the final value of B is decided in the last period, while if individuals decide to buy death insurance in the first period, such amount would be included in the savings s.
This framework has also been discussed in (Rust et al. 2005).
Note that, for simplicity, we have assumed β to be equal to 1 and no interest rate. The main conclusions of the model would not change using different settings, although the closed-form solution would become more cumbersome.
It is worth noting that the above closed-form solution for bequest includes also ỹ 2 . This is because B is the actual bequest in the second period, not the expected one. On the other hand, the expected bequest E 1[B] would only contain ȳ 2 and σ 2.
First-order conditions and comparative statics are shown in the Online Appendix A.3.
Data from this survey are also included in the European dataset Household Finance and Consumption Survey (HFCS) and are harmonized following the directives of the Luxembourg Income Study and Luxembourg Wealth Study.
The role of household head is self-stated. He or she is defined as the person who takes financial decisions or the most informed one.
The empirical analysis has been done with Stata 14.
In particular, the first measure has been constructed by computing, in each wave, the variance of the net individual labor income within each household (including incomes from all members of the households, not only the household head and the spouse). On the other hand, the second measure has been derived as follows: in 2012, the variance for each individual across all waves of the net individual labor income; in 2010, the variance across all waves except 2012 of the net individual labor income; in 2008, the variance across all waves except 2012 and 2010 of the net individual labor income, and so on. These two procedures have allowed us to obtain two time-varying indicators, which thus can be used also in a FE model. For both measures, the standard deviation has been divided by 100,000. Our measure of labor income includes all sources of income from employment and self-employment activities, but it does not include pensions and other social transfers, as well as rents and capital gains. The reason behind this choice is that we want to approximate labor income risk associated with the employment status; thus, the last two categories would not fit in this definition. Finally, given the results in (Jappelli and Pistaferri 2003), we feel confident in using net rather than gross income.
Table 1 does not include the individual income over household income ratio, since it is strongly correlated with our definition of variance within family. Results do not change substantially by adding such regressors. Table available upon request.
An additional measure of income risk that we could have used is the subjective one used, among the others, by (Guiso et al. 1992) and (Mastrogiacomo and Alessie 2014). However, in the waves used in our analysis, this kind of question was available only in 2012, thus making it impossible to use a FE estimation, as done in the next section.
For the sake of comparison, we have also estimated a pooled probit. Results do not change substantially: the marginal effect of the household income risk is 0.012 and insignificant, while for the self-employment indicator, the impact is 0.061 and highly significant (compared with Table 1, where the coefficients are 0.021 and 0.084, respectively). Table available upon request.
A detailed description of these controls is available in the Online Appendix A.2.
One advantage of a linear model is that it is straightforward to add fixed effects, and the coefficients can be interpreted as average partial effects. A simple logit or probit model would not allow the inclusion of μ i with only five observations for individuals because of the incidental parameter problem. An alternative approach would have been to estimate a conditional logit model. However, since the distribution of the fixed effects is unknown, it would have not been possible to estimate the average partial effects in this case, but only the effect of the regressors on the log-odds ratio (Wooldridge 2010). Such estimates are available upon request.
One may claim that our dependent variable is equal to one if an individual owns a term insurance at a certain point in time, not if he or she has bought such a financial product in the time period considered. Therefore, it would be possible to claim that income risk may actually affect the probability of buying a term insurance but not the probability of holding such insurance. This may be true for the OLS estimates. However, the FE estimator is a within estimator: it exploits only the variation over time within individuals. As a result, if income risks were indeed pivotal in the term insurance demand function, the FE estimate should be significant, since it would capture exactly the variables that induce an individual to move from not owning a term insurance in a specific wave to owning the insurance in the next wave (or vice versa). Since we do not find such an effect, our results are robust to this argument.
This is also consistent with the finding of (Rampini and Viswanathan 2016) that lower risk managements among constrained households make them more vulnerable to shocks.
We have also tried to include in the FE specification the age of the household head’s spouse and its squared term. If the household head did not have a spouse, we have tried either to impute zero age to those observations or to consider only households with a spouse. In both cases—and for both income risk measurements—the main results do not change, and the coefficients of these new regressors are not statistically significant, probably because of the high correlation with the age of the household head.
A similar result is obtained if we drop these two regressors and include “Have a son or a daughter” in the specification. However, in the FE regression with income variance within family, the coefficient of such offspring variable is positive with a p value of 0.11.
In fact, the probability of transitioning from not having a child to having one is only 16%.
One of the drawbacks of the linear probability model is that the estimates can be larger than one, which may seem counterintuitive, since probabilities are bounded between zero and one. However, the interpretation can be simple once we take that into account: if an individual shift from being an employee to a self-employed individual, ceteris paribus, the probability of buying a term insurance during the transition is equal to one.
Even if the coefficient of self-employment status is positive, both in the FE and FE-IV cases, the latter is much larger in magnitude. This is unfortunately a typical result when instrumenting a dummy variable with another dummy variable.
We have also tried to use whether the mother used to be a self-employed individual as an instrument. The Hansen p values are still large (although smaller than with the father self-employed), but the instrument is much weaker. The same conclusion can be derived for father self-employed interacted with age or age squared of the respondent. Tables available upon request.
Option endog() of the command xtivreg2.
We also tried to add the interaction between father self-employed and average self-employment rate as an instrument, but the estimates were less precise. Moreover, IV estimates should typically be interpreted as local average treatment effects (LATE) or as weighted LATE in case of multiple instruments. Therefore, adding more instruments makes it more difficult to understand which is the relevant subpopulation for which we estimate the average treatment effect.
All tables for this section are reported in the Online Appendix.
We have also reestimated the FE specification with the IV for self-employment status for this subsample. The coefficient of self-employment is again positive and significant at a 5% level, while income risk is insignificant. Nevertheless, both regressors became insignificant when we reestimated the FE specification with the IV both for self-employment status and income risk.
Table A4 shows the estimation results when income risk is measured by the variance of individual income over time.
The same conclusions can be obtained from the FE and IV specifications.
This result is also important since one may argue that measurement errors could be higher among self-employed individuals, since they are typically more reluctant to disclose their income and wealth. Using the interviewer’s evaluation, we are able to drop all unreliable observations. If it were indeed true that data on self-employed individuals were noisier, this strategy would simply take this into account by excluding more self-employed individuals rather than employed, retired, or inactive individuals.
This is also consistent with the findings of (Kung and Fang 2012).
The same conclusions can be obtained from the FE and IV specification.
The same conclusions can be obtained from the FE and IV specification.
These weights are computed separately in each wave; thus, it is not possible to use them with the FE estimators.
If household wealth was zero, while individual income was positive, such ratio was set equal to individual income. We also tried to set to missing or to one of the ratio for those (few) observations. Results do not change substantially. Tables available upon request.
A similar concern can be raised about the “not employed” indicator, since occupational status is endogenous and we have instrumented only for self-employment status. A possible solution could be to pool together employees, inactive, and retirees as a comparison group, i.e., to drop the dummy variable “not employed”. In such specifications, the coefficient of self-employed is still positive and significant, while income risk remains insignificant. Tables available upon request.
We have considered as self-employed without employees individuals who worked as freelancers (libero professionista), artisan (artigiano), or business owners without employees (lavoratore autonomo). On the other hand, we have considered self-employed with employees business owners with employees (imprenditore individuale), owners or members of family businesses (titolare o coadiuvante di impresa familiare), and partners in large firms (socio/gestore di societá).
Contrary to our main results, an increase in income variance over time leads to lower housing wealth. We explain this evidence with the possible correlation between individual income fluctuations and housing wealth variability. Housing value is indeed variable and its prices are correlated with the overall economy. When housing becomes riskier, investment in it declines. In other words, as already mentioned, we believe that housing is not a planned channel for intended bequests, but rather an unintended one. Furthermore, such coefficient of income risk over time becomes statistically indistinguishable from zero once we consider observations with positive gross housing wealth only, while the coefficients of self-employment and income risk within family remain positive and insignificant.
These results are robust to using a more restrictive definition of valuables which includes only jewelry, gold coins, antiques, and works of art, excluding transportation vehicles and household appliances.
As discussed in the previous section, one may argue that income risk may affect the probability of buying a term insurance, but not the probability of holding such insurance. This section provides additional prof against this argument since, if income risk does indeed influence the decision to subscribe to a term insurance, there is no reason to believe that it should not affect the premium paid for such insurance.
SE computed with the Delta-method.
See (Greene 2012) page 856.
As an alternative to the Tobit model, we have followed (Burke 2009) and we have also estimated Cragg’s double hurdle model. This model also allows for different coefficients in the two estimation stages. Indeed, it first estimates a probit model to determine the probability that the dependent variable is positive, and then it fits a truncated normal model on the positive values. The marginal effect of self-employment status is still positive and significant, although the magnitude is smaller than in the Tobit model. Tables available upon request.
The premium amount paid has been set equal to zero for individuals without a pure or mixed term insurance, as we did for the Tobit estimation. We have also tried to estimate the same models by treating as missing such values, like we did for the Heckman model. Although the number of observations drops substantially, the OLS and FE estimates remain qualitatively similar in most of the specifications. Tables available upon request.
We have also tried to estimate a FE and 2SLS model using the same exclusion restriction exploited in the previous sections. However, the estimates are extremely noisy, and it is not possible to reject the null hypothesis of zero impact for self-employment or income risk (with both definitions). Nevertheless, if we use the logarithm of the premium amount as dependent variable, the coefficient of self-employment is also significant, even when we instrument this variable.
Indeed, the average compulsory contribution rate for employees is around 33%, while for self-employed, the average rate is 23% (Italian Government 2001). Furthermore, if the individual dies, the spouse is usually entitled to 60% of his or her pension. For the offspring, if he or she is a minor or a student, he or she is entitled to 70% of the pension when an only child. If there are more than one offspring, each child receives 20% (or 40% if the spouse is not entitled). See (INPS 2015b), (INAS 2013).
See (SSA 2012).
Another reason behind the role of self-employment status could be related to health and life expectancy: if self-employed people believe that their life expectancy is lower than the average, they may apply for death insurance in order to protect their families against their premature death. However, we cannot test if this interpretation is valid, because our dataset does not contain any information about life expectancy.
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We are grateful to Mauro Mastrogiacomo, Stefan Hochguertel, Hans Bloemen, Arthur van Soest, Adriano Rampini, Costanza Torricelli, Givi Melkadze, one anonymous referee, to the participants to the ESPE 2016 Conference, and to the seminars at Georgetown University, Vrije Universiteit (VU), University of Modena, and Reggio Emilia for their helpful comments. Discussions with Elisa Luciano on a companion paper are also gratefully acknowledged (Luciano, Rossi, and Sansone 2015). We also thank Medium NETSPAR grant on self-employment (PI: Mauro Mastrogiacomo) for funding this project.
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Rossi, M., Sansone, D. Precautionary savings and the self-employed. Small Bus Econ 51, 105–127 (2018). https://doi.org/10.1007/s11187-017-9919-x
- Precautionary savings
- Term insurance