Essays on RBC, Long-Run Risk, and Portfolio Selection

My dissertation contains three chapters. In Chapter 1 I study the optimal consumption and portfolio choice of a retiree. Chapter 2 is an empirical study of the long-run risk model in explaining asset returns in the cross section. In Chapter 3, I study the implications of RBC models with CES production on the dynamics of labor income share and other macroeconomic variables. In Chapter 1, I solve the optimal consumption and portfolio choice problem of a retiree with recursive preferences and bequest motive. The retiree is endowed with both liquid assets and pre-annuitized wealth in Social Security and/or defined benefit pension plans. He chooses from an investment menu including an equity index, a risk-free asset, a private variable life annuity, and term life insurance with borrowing and short-sales constraints. Due to adverse selection, annuitization is irreversible, and the retiree’s fraction of preannuitized wealth is an important endowment characteristic that determines his optimal consumption profile, equity-bond mix, and annuitization schedule. In the model the retiree can annuitize his liquid wealth anytime during his retirement life, and the option to defer annuitization can be valuable. Unlike fixed annuity, variable annuity allows the retiree to hedge longevity risk and earn an equity premium at the same time, and the gain is substantial for a retiree with relatively low risk aversion. Given the existing Social Security benefits, the irreversibility of future life annuity purchase incurs little utility loss. However, the utility loss due to the irreversibility of existing Social Security benefits can be big. I show that a transition from the current pay-as-you-go Social Security system to a personal investment-based system benefits retirees with high fraction of pre-annuitized wealth the most because the flexibility of choosing the optimal equity-bond mix for one’s annuity portfolio reduces the cost of over-annuitization. Purchasing life insurance can also reduce the adverse effect of over-annuitization. However, it is effective only for impatient retirees with low Elasticity of Intergenerational Substitution. In Chapter 2, I show that the pure-exchange economy with Epstein-Zin recursive utility as in Bansal and Yaron (2004) implies that the cross-section of expected returns depends on three factors: consumption growth, change in expected consumption growth, and change in conditional volatility of consumption growth. I test the model using both quarterly and annual data. At annual frequency the model explains up to 80% of the variation in average returns across the 25 Fama-French size and book-to-market sorted portfolios. The performance is comparable to that of the Fama-French 3-factor model. Unlike the Fama-French 3-factor model, the model performs equally well across the two annual subsamples, and the parameter estimates are more stable. Among the three factors, the change in expected consumption growth, which captures the risk of long-run growth prospect, is the most important for explaining the difference in the measured risk premia across assets. In Chapter 3, I show that a CES production function with elasticity of factor substitution less than one generates a cyclical pattern of labor share of output consistent with what is observed in the data. Output not only correlates negatively with contemporaneous labor share, but also negatively with lagged labor share and positively with leading labor share. However, a change in the elasticity also affects the volatility of other variables. In particular, the volatility of hours is greatly dampened when capital and labor input are complements, even when the representative agent has log-linear utility function over consumption and leisure as implied by the indivisible labor model of Hansen (1985) and Rogerson (1988). The model fit is much better if one takes into account problems measuring hours as identified by Kydland (1984) and Kydland and Prescott (1993). On the other hand, the results call for more research on the source of technology shocks and on mechanisms that generate both volatile labor input and a labor share whose cyclical patterns match those in the data.