Does Relative Risk Aversion Vary with Wealth? Evidence from Households' Portfolio Choice Data

We analyze whether relative risk aversion varies with wealth. We first derive theoretical predictions on how risky shares respond to wealth fluctuations in a portfolio choice model with both external habits and time-varying labor income. Our analytical results indicate that: (1) for each household, there are two channels through which the risky share responds to wealth fluctuations, the habit channel and the income channel; (2) across households, there are heterogeneous responses through the habit channel: those who experience large negative income shocks reduce their share of risky assets; and (3) two potential mis-identification problems arise when both the heterogeneity in responses through the habit channel and the income channel are ignored. We then test the theoretical predictions with data from the Panel Study of Income Dynamics. Contrary to the existing literature, our empirical results show evidence of relative risk aversion varying with wealth over time after correcting those two mis-identification problems.