Essays on Firm, Health, Risk Aversion and Wealth Distribution

Studies show that historically wealth distribution has again become very concentrated in the US since the end of the 1970s (Wolff 1996, 2010). Both the heavy concentration and the rapid increase in top wealth share in the US are well documented by Wolff (2006). In the US, the wealthiest 5 percent of American households held 54 percent of all wealth reported in the 1989 Survey of Consumer Finance; this share has reached 63 percent as of 2013 (Yellen, 2014). In the second chapter I study how firm heterogeneity affects wealth distribution through entrepreneurial income and capital gains. As shown in Hottman, Redding and Weinstein 2016, size distribution of firms is highly skewed. Top 1% of firms in a product group on average have market shares of 50%. I develop a dynamic general equilibrium model with heterogeneous households and multiproduct firms. Each product has its own rate of return and scale, which result in heterogeneity in the rate of return and size of firms. Firms with larger scope of products benefit more from stricter control in product quality and thus grow faster than the others do. Households need to pay a premium to firm owners to invest in their firm, which can be interpreted as capital gain. Wealth of households, especially entrepreneurs, accumulates partly because of entrepreneurial income, which is their claim on their firm\u27s profits, and partly because they receive capital gain. Firms in the model have two dimensions: its rate of return and the firm size. The premium increases in both, which allows households to sort into different firms based on their wealth. The distribution of product space is calibrated with Nielsen barcode dataset. The simulation shows that the firm heterogeneity in its two dimensions results in a severe wealth inequality. The model can explain 90% of the rise in top wealth concentration between 2003 and 2012 in the United States. The result is consistent with findings in Saez and Zucman 2016 that the upswing in the top 1% wealth share is due to the rise in the top 0.1% and that the increase in wealth inequality is not due to rate of return differential on corporate stocks. Counterfactual exercises highlight entrepreneurship as the main driver in wealth equality and show that fluctuations in risk free rate of return and access to new investment opportunities reduce wealth inequality, of which each may offset up to half of the effect of entrepreneurship. The third chapter studies how households\u27 cumulative health shocks affect their health investment, health insurance premium, and wealth. I develop a rich lifecycle model of endogenous health capital, insurance premium and wealth, with a diffusion income process and Poisson health shocks. In this model, health shocks affect a household\u27s wealth through three channels. It increases medical spending, lowers productivity and thus income, and increases the probability of death. Theoretical results show that since health increases life expectancy, it becomes a luxury good relative to consumption. When income rises, health generates larger marginal utility relative to consumption. As a result, rich people invest more in health, live longer, and save more. This implies that vital health shocks may facilitate top concentration in wealth distribution. With the CDC data for the top nine death-causing diseases I estimate vital disease processes and calibrate the model. The counterfactual exercise shows that effects of vital health shocks indeed help explain wealth inequality. The fourth chapter is a complement to the second chapter Firm Heterogeneity and Wealth Distribution where households are risk-neutral due to linear utility. In this chapter I study effects of difference in households\u27 attitudes to risk on wealth distribution by introducing heterogeneity on the risk aversion parameter of the utility function. A two-period model reveals that risk aversion heterogeneity exacerbates wealth inequality. Households with relatively low level of risk aversion or high level of wealth are more exposed to risk. The more risk-averse, the less risky the optimal project and, under some condition, the less the agent may invest. The wealthier, the larger the investment. As risks in investment opportunities are realized, the variance of income among relatively wealthy households are larger than its counterpart among poor households, which leads to a heavier top concentration in wealth distribution. Lucky wealthy risk lovers tend to move to the top while unlucky investors go to the bottom of the wealth distribution