Life-cycle risk-taking with personal disaster risk

Working Paper Series

No 132 / December 2021

Life-cyclerisk-taking with personal disaster risk

by

Fabio C. Bagliano Carolina Fugazza Giovanna Nicodano

Abstract

This paper examines households' self-insurance in financial markets when a rare personal disaster, such as disability or long-term unemployment, may occur during working years. Personal disaster risk alters lifetime ex-ante investment choices, even if most workers will not experience a disaster. Uncertainty about the size of human capital losses, which characterizes rare disasters, results in lower risk-taking at the beginning of working life, and is crucial in order to match the observed age profiles of US investors from 1992 to 2016.

Keywords: disaster risk, portfolio choice, non-linear income process, unemployment risk, disability risk, beta distribution

JEL classification: D15, E21, G11

E-mails: [e-mail]; [e-mail]; [e-mail]

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• Introduction

What happens if a person's future ability to work is permanently reduced? Insurance against permanent shocks, such as disability and long-term unemployment, is well known to be incomplete (Guvenen and Smith, 2014; Low, Meghir and Pistaferri, 2010; Low and Pistaferri, 2015). Therefore, young households make provisions to cushion against a personal disaster, even if the possibility of its occurrence is quite rare. Against this background, the current paper examines the pattern of self-insurance in financial markets over the life-cycle when there is the possibility of a rare personal disaster during working years. The findings show that personal disaster risk can alter lifetime ex-ante investment choices for all workers, even if ex-post most of them will not experience a disaster. Ad- ditionally, this paper reveals that uncertainty about the size of uninsured human capital losses, which characterizes rare disasters, enhances the precautionary behavior of young workers. This behavior will result in lower risk-taking at the beginning of working life, with respect to a comparable deterministic human capital loss. Uncertainty about the extent of losses is crucial in order to closely match the observed age profiles o f U S investors from 1992 to 2016, based on the methods of Ameriks and Zeldes (2004), when the calibrations are conservative.

We contribute to the household finance literature by linking risk-taking in financial markets with the ex-ante uncertain, but potentially extreme, permanent impact of income shocks. In contrast to the household finance l iterature, h owever, we g o b eyond t he positive probability of zero labor income implied by the linear income process proposed by Cocco, Gomes and Maenhout (2005) and later adopted within this strand of literature. Inspired by a growing body of empirical work showing that earnings dynamics display non-linearities (Arellano, Blundell and Bonhomme, 2017; De Nardi, Fella and Paz-Pardo,

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2020; Guvenen, Karahan, Ozkan and Song, 2021), we model the occurrence of a disaster that brings about a permanent income reduction of uncertain proportion. Specifically,

the fraction of human capital lost follows a beta distribution.1 The flexibility of such distribution allows us to concentrate a large probability mass on small values of proportional human capital reduction while leaving open the possibility of extremely unlikely but devastating realizations. This feature of the model is intended to capture the substantial heterogeneity of permanent effects following the occurrence of adverse occupational and/or health shocks documented by Guvenen, Karahan, Ozkan and Song (2017) and Gregory, Menzio and Wiczer (2021). Importantly, when careers are calibrated to broadly match observed US labor market features, optimal investment in the risky asset remains flat over the whole working life, in line with early evidence on US portfolios (Ameriks and Zeldes, 2004), which we update to 2016. This situation occurs even when we account for the large insurance coverage of permanent income shocks, as in Guvenen, Karahan, Ozkan and Song (2017) and Guvenen and Smith (2014), which may ultimately reduce the expected human capital losses due to long-term unemployment. Without disaster risk, the implied optimal stock holding still counter-factually decreases with age before retirement, unless the long-term unemployment rate is as high as that observed in the post-Great Recession and protracted inactivity causes a deterministic human capital drop by at least 25% (Bagliano, Fugazza and Nicodano, 2019).

A closely related paper by Galvez (2017) performs a structural estimation on PSID data, when the income process displays non-linearities `a la Arellano, Blundell and Bonhomme (2017). Galvez (2017) also observes large differences in risk-taking with respect to the optimal portfolios implied by normally distributed permanent income shocks to earnings

• This distribution may also characterize the damage caused by natural disasters (see Bhattacharjee, 2004; Lallemant and Kiremidjian, 2015).

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growth. Another related paper by Inkmann (2020) investigates the value of portfolio choice through the certainty equivalent consumption across US industries. This is explained by both changes in the covariance structure of earnings growth and stock returns and kurtosis of earnings growth.

Our results highlight the role of non-linear income shocks in flattening the age profile of risk taking. With a linear income process, prior models resort to using additional features to explain reduced risk-taking in financial markets (Cocco, 2004; Munk and Sorensen, 2010; Kraft and Munk, 2011; Bagliano, Fugazza and Nicodano, 2014; Hubener, Maurer and Mitchell, 2016; Chang, Hong and Karabarbounis, 2018; Branger, Larsen and Munk, 2019). For instance, in Bagliano, Fugazza and Nicodano (2014), a positive correlation between (highly volatile) permanent income shocks and stock returns leads to lower optimal risk-taking when young. Branger, Larsen and Munk (2019) obtain reduced early-life holdings by introducing unemployment risk correlated with business cycle fluctuations. Since the probability of losing a job and experiencing a subsequent human capital loss is decreasing in the worker's age and in the state of the economy, the optimal investment in risky assets is significantly diminished at young ages. Finally, in Chang, Hong and Karabarbounis (2018) the driver of low risk-taking when young is related to uncertainty which resolves over time thanks to agents' learning about their income volatility. The resolution of uncertainty due to this learning process explains why the young bear more labor income risk, an intuition pioneered by Viceira (2001) and Benzoni, Colling-Dufresne and Goldstein (2007). In our paper, uncertainty resolves because time passes without the occurrence of disasters. More precisely, we model working life careers as a three-state Markov chain driving the transitions between employment, short-term unemployment and personal disaster states. Uncertain permanent earning losses that occur in the dis-

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