Habits and Heterogeneity

Question 1

Describe the three choices of habit formation?

Answer 1

1) Functional form (C-X vs C/x); 2) Internal vs external habit; 3) Speed of adjustment (X vs C)?

Question 2

What is the RRA of habit formation? what is S_t

Answer 2

RRA = \gamma / S_t
S_t = (C_t - X_t )/ C_t

Question 3

What is necessary for the surplus risk exposure lambda to generate counter cyclical risk premium?

Answer 3

Decreasing lambda as a function of s_t

Question 4

How is lambda calibrated in habit formation?

Answer 4

constant risk free

Question 5

Four interpretations of habit formation:

Answer 5

1) RA with habit formation; 2) Investors with house money effect; 3) Heterogeneous risk aversion and shifting wealth; 4) Participation constraints for investors

Question 6

Grossman-Shiller style heterogenous trick:

Answer 6

1) Habit SDF; 2) Taylor Expansion first order for SDF; 3) 1-A_t * \Delta C_t+1^i; 4) Aggregate as harmonic mean of risk aversion.

Question 7

Constantinides Duffie SDF Trick; Difference in RA?

Answer 7

Take household average distribution of SDF. Valid since projections–assume infinite households. Cross sectional variance term due to aggregation of individual SDFs.