[ Search |  Up Level |  Project home |  Index |  Class hierarchy ]

 AiyagariQJE1994.ox

Households face uninsurable idiosyncratic shock; markets are incomplete.

Household Dynamic Program

1. CCP Smoothing: none
2. Clock: Ergodic
3. $\alpha = (a),$ assets to hold at the end of today to earn interest tomorrow (original: $a_{t+1}$)
4. $\theta = (h,A),$
   $l$: Tauchen() shock to earnings/labor supply
   $A$: Assets held, a LaggedAction or, more generally, LiquidAsset
5. Consumption: $C = A(1+r) + we^l - a$
6. $A(\theta) = \{ a: C \ge -\overline{a} \},$ where $\overline{a}=0$ for all reported values.
7. $U(\alpha;\theta) = { C^{1-\mu} -1 \over 1-\mu }.$

Equilibrium Conditions

1. Aggregate production: $f(K,L) = K^\alpha L^{1-\alpha}$
   $K =$ stationary per capita capital $= \sum_\theta P_\infty(\theta)A.$
   $L =$ per capita labour supply $=\sum_\theta P_\infty(\theta)e = \exp{\sigma}$
   $MP =$ vector of marginal products $= \pmatrix{ f_K \cr f_L }$
2. Equilibrium price vector $p^\star = \pmatrix{r^\star \cr w^\star}.$
3. Depreciation of capital $\gamma$
4. Equilibrium System: $$MP - p^\star - \pmatrix{\gamma \cr 0} = \pmatrix{0\cr 0}$$
5. Closed form solution for equilibrium $w$ in terms of $r$: $$w^\star = ?? r^\star$$
6. Equilibrium reduces to a OneDimSystem solved using bracket-and-bisect requiring nested solution of the agent's model and computed value of stationary capital stock $K$.

Author:

© 2020 Nam Pham and Christopher Ferrall

 Aiyagari