In theoretical macro and finance models, it is important to have time-varying relative risk aversion (TVRRA) to generate observed moments in the macro/financial data.
A popular way to generate TVRRA is to impose habit formation preferences. Macro and finance models with habit formation preferences have successfully generated observed moments in the data.
Even though the theoretical predictions of these models are in line with macro/financial data. Little is known about whether habit formation preferences are in line with micro (households-level) data. One question to check is with micro data is how risky shares will respond to the fluctuations of (financial) wealth. Mathematically, the question focuses on the sign of ρ, where ρ=∂∆a/∂∆w, w denotes the logarithm of (financial) wealth, a denotes risky shares, ∆ denotes the first-order difference, and ∂ denotes the partial derivative.
Brunnermeier and Nagel (2008) tested habit formation preferences with the Panel Study of Income Dynamics (PSID) data:
On the one hand, they set up a portfolio choice model with habit formation preferences. Their analytical solution shows that, with habit formation preferences, households will increase their risky shares when their financial wealth increases.
On the other hand, they showed that, in the PSID data from 1984 to 2003, households' risky shares are negatively correlated with (financial) wealth.
The conflict between the theoretical predictions and empirical evidence casts doubt on the use of habit formation preferences in those models.
A strong implication was rejected in Brunnermeier and Nagel (2008).
A natural question to ask is that can we find weaker implications that are in line with the PSID data?
We introduce labor income to the portfolio choice model in Brunnermeier and Nagel (2008) and show two biases that are related to two mis-specifications:
Internal mis-specification for each agent if ignore income channel. Should control for labor income
External mis-specification if ignore heterogeneity of labor income across households. Compare across groups
We test semi-strong form and weak form implications with the PSID data from 1989 to 2011. Our results indicate that, after controlling both mis-specifications (especially the external one), we find evidence of the weak-form implication. In other words, to be line with the data, it is important to have heterogeneous agents with habit formation preferences.
M. Brunnermeier and S. Nagel, (2008). Do Wealth Fluctuations Generate Time-varying Risk Aversion? Micro-evidence from Individuals' Asset Allocation. American Economic Review, 98 (3), 713–736.