handoutcia08 - Cash-In-Advance Models of Money Christiano...

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Cash-In-Advance Models of Money Christiano and Eichenbaum (1992) “Liquidity E f ects and the Monetary Transmission Mechanism", AER, p. 346-353. 1 Environment Prefs: E 0 X t =0 β t [ u ( c t ) v ( n s t )] where n s t [0 , 1] is labor supply, c t 0 is consumption, β (0 , 1) ,u is strictly increasing, concave, and di f erentiable, v is strictly increasing, convex, and di f erentiable with v 0 (0) = 0 and v 0 (1) = . Techn: y t = θn d t . Govt. Budget Constraint is given by P t τ t = M s t +1 M s t (1) where M s t is the nominal money supply, P t is the price level, and τ t are real lump-sum taxes or transfers. The money supply evolves according to M s t +1 =(1+ μ ) M s t + ε t where μ is the growth rate of the money supply and unanticipated money shocks ε t are mean zero and i.i.d. Hhs can also buy or sell private nominal discount (non-contingent) bonds. Timing: (i) hh enters with M t units of money and B t units of money from its prior bond activity; (ii) Shock realized and lump sum taxes/transfers are paid; (iii) the bond market opens, past bond holdings redeemed, hh pur- chases/sells B t +1 at money price Q t ; (iv) the hh separates: worker supplies labor to the f rm (receiving W t n s t units of money for her services) and the shopper purchases consumption goods at price P t ; (v) the worker and shopper meet to consume and count their nominal
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handoutcia08 - Cash-In-Advance Models of Money Christiano...

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