# A Becker–Tomes model with investment risk

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## Abstract

Recent studies find that sufficiently volatile idiosyncratic investment risk plays an important role in generating wealth inequality. I introduce idiosyncratic investment risk into the Becker and Tomes (J Polit Econ 87:1153–1189, 1979) model and find an explicit expression of the stationary wealth distribution in this simple model. This explicit expression brings us new insights of how bequest motives and estate taxes influence wealth distributions. I find that inheritance increases wealth inequality in models with idiosyncratic investment risk through exaggerating labor earnings uncertainty, while inheritance decreases wealth inequality in the Becker and Tomes (1979) model through mitigating labor earnings uncertainty. This causes estate taxes to have different impacts on wealth inequality in my model and the Becker and Tomes (1979) model.

## Keywords

Investment risk Estate taxes Bequest motives Wealth inequality The Becker–Tomes model## JEL Classification

D31 H20## Supplementary material

## References

- Achdou, Y., Han, J., Lasry, J., Lions, P., Moll, B.: Heterogeneous Agent Models in Continuous Time. Princeton University, Mimeo (2015)Google Scholar
- Algan, Y., Challe, E., Ragot, X.: Incomplete markets and the output–inflation tradeoff. Econ. Theory
**46**, 55–84 (2011)CrossRefGoogle Scholar - Angeletos, G.: Uninsured idiosyncratic investment risk and aggregate saving. Rev. Econ. Dyn.
**10**, 1–30 (2007)CrossRefGoogle Scholar - Antunes, A., Cavalcanti, T., Villamil, A.: The effects of credit subsidies on development. Econ. Theory
**58**, 1–30 (2015)CrossRefGoogle Scholar - Aoki, S., Nirei, M.: Zipf’s law, Pareto law, and the evolution of top incomes in the United States. Am. Econ. J. Macroecon.
**9**, 36–71 (2017)CrossRefGoogle Scholar - Becker, G., Tomes, N.: An equilibrium theory of the distribution of income and intergenerational mobility. J. Polit. Econ.
**87**, 1153–1189 (1979)CrossRefGoogle Scholar - Benhabib, J., Zhu, S.: Age, luck, and inheritance. NBER working paper no. 14128 (2008)Google Scholar
- Benhabib, J., Bisin, A., Zhu, S.: The distribution of wealth and fiscal policy in economies with finitely lived agents. Econometrica
**79**, 123–157 (2011)CrossRefGoogle Scholar - Benhabib, J., Bisin, A., Luo, M.: Wealth distribution and social mobility in the US: a quantitative approach. NBER working paper no. 21721 (2015a)Google Scholar
- Benhabib, J., Bisin, A., Zhu, S.: The wealth distribution in Bewley economies with capital income risk. J. Econ. Theory
**159**, 489–515 (2015b)CrossRefGoogle Scholar - Bossmann, M., Kleiber, C., Wälde, K.: Bequests, taxation and the distribution of wealth in a general equilibrium model. J. Public Econ.
**91**, 1247–1271 (2007)CrossRefGoogle Scholar - Brandt, A.: The stochastic equation \(Y_{n+1}=A_{n}Y_{n}+B_{n}\) with stationary coefficients. Adv. Appl. Probab.
**18**, 211–220 (1986)CrossRefGoogle Scholar - Cagetti, M., De Nardi, M.: Entrepreneurship, frictions, and wealth. J. Polit. Econ.
**114**, 835–870 (2006)CrossRefGoogle Scholar - Cagetti, M., De Nardi, M.: Estate taxation, entrepreneurship, and wealth. Am. Econ. Rev.
**99**, 85–111 (2009)CrossRefGoogle Scholar - Cao, D., Luo, W.: Persistent heterogeneous returns and top end wealth inequality. Rev. Econ. Dyn.
**26**, 301–326 (2017)CrossRefGoogle Scholar - Davies, J.: Does redistribution reduce inequality? J. Labor Econ.
**4**, 538–559 (1986)CrossRefGoogle Scholar - Farhi, E., Werning, I.: Progressive estate taxation. Q. J. Econ.
**125**, 635–673 (2010)CrossRefGoogle Scholar - Gabaix, X.: Zipf’s law for cities: an explanation. Q. J. Econ.
**114**, 739–767 (1999)CrossRefGoogle Scholar - Kaymak, B., Poschke, M.: The evolution of wealth inequality over half a century: the role of taxes, transfers and technology. J. Monet. Econ.
**77**, 1–25 (2016)CrossRefGoogle Scholar - Klass, O., Biham, O., Levy, M., Malcai, O., Solomon, S.: The Forbes 400 and the Pareto wealth distribution. Econ. Lett.
**90**, 290–295 (2006)CrossRefGoogle Scholar - Kopczuk, W.: Taxation of intergenerational transfers and wealth. In: Auerbach, A., Chetty, R., Feldstein, M., Saez, E. (eds.) Handbook of Public Economics, pp. 329–390. Elsevier, Amsterdam (2013)CrossRefGoogle Scholar
- Loève, M.: Probability Theory I, 4th edn. Springer, Berlin (1977)Google Scholar
- Meyn, S., Tweedie, R.: Markov Chains and Stochastic Stability, 2nd edn. Cambridge University Press, Cambridge (2009)CrossRefGoogle Scholar
- Mierau, J., Turnovsky, S.: Demography, growth, and inequality. Econ. Theory
**55**, 29–68 (2014)CrossRefGoogle Scholar - Mino, K., Nakamoto, Y.: Heterogeneous conformism and wealth distribution in a neoclassical growth model. Econ. Theory
**62**, 689–717 (2016)CrossRefGoogle Scholar - Mirek, M.: Heavy tail phenomenon and convergence to stable laws for iterated Lipschitz maps. Probab. Theory Relat. Fields
**151**, 705–734 (2011)CrossRefGoogle Scholar - Müller, A., Stoyan, D.: Comparison Methods for Stochastic Models and Risks. Wiley, Hoboken (2002)Google Scholar
- Ok, E.: Probability Theory with Economic Applications. New York University, Mimeo (2016)Google Scholar
- Panousi, V.: Capital Taxation with Entrepreneurial Risk. Federal Reserve Board, Mimeo (2012)Google Scholar
- Panousi, V., Reis, C.: Optimal Capital Taxation with Idiosyncratic Investment Risk. Federal Reserve Board, Mimeo (2015)Google Scholar
- Pestieau, P., Possen, U.: A model of wealth distribution. Econometrica
**47**, 761–772 (1979)CrossRefGoogle Scholar - Pestieau, P., Thibault, E.: Love thy children or money: reflections on debt neutrality and estate taxation. Econ. Theory
**50**, 31–57 (2012)CrossRefGoogle Scholar - Piketty, T.: Capital in the Twenty-First Century. The Belknap Press of Harvard University Press, Cambridge (2014)CrossRefGoogle Scholar
- Piketty, T., Saez, E.: Income inequality in the United States, 1913–1998. Q. J. Econ.
**118**, 1–39 (2003)CrossRefGoogle Scholar - Piketty, T., Saez, E.: A theory of optimal capital taxation. NBER working paper no. 17989 (2012)Google Scholar
- Piketty, T., Saez, E.: A theory of optimal inheritance taxation. Econometrica
**81**, 1851–1886 (2013)CrossRefGoogle Scholar - Quadrini, V.: Entrepreneurship, saving, and social mobility. Rev. Econ. Dyn.
**3**, 1–40 (2000)CrossRefGoogle Scholar - Rointershtein, A.: One-dimensional linear recursions with Markov-dependent coefficients. Ann. Appl. Probab.
**17**, 572–608 (2007)CrossRefGoogle Scholar - Royden, H.L.: Real Analysis, 3rd edn. Prentice-Hall Inc., Upper Saddle River (1988)Google Scholar
- Saez, E., Zucman, G.: Wealth inequality in the United States since 1913: evidence from capitalized income tax data. Q. J. Econ.
**131**, 519–578 (2016)CrossRefGoogle Scholar - Shaked, M., Shanthikumar, G.: Stochastic Orders. Springer, Berlin (2010)Google Scholar
- Shourideh, A.: Optimal Taxation of Wealthy Individuals. University of Pennsylvnia, Mimeo (2014)Google Scholar
- Wan, J., Zhu, S.: Bequests, estate taxes, and wealth distributions. Econ. Theory (2017). https://doi.org/10.1007/s00199-017-1091-7
- Zhu, S.: Technical appendix of unobservable \(\tilde{R}_{t+1}\): Appendix A.9 of “A Becker–Tomes model with investment risk.” University of International Business and Economics, Online Appendix (2018)Google Scholar