A TIMING PROBLEM IN THE LIMITED PARTICIPATION MODEL

[zhanshuo]

HI, EVERYONE,
I AM WOKRING ON THE LIMITIED PARTCIPATION MODEL.
THE ESSENTIAL MEANING OF THIS KIND OF MODEL IS THAT HOUSEHOLD MAKE THEIR SAVING-CONSUMPTION DECISION BEFORE THE REALIZATION OF MONEY SHOCK, SO MONEY MATTERS FOR LOAN SUPPLY.
THE FIRST ORDER CONDITION IS A KIND OF THAT the basic eular equation has a subscript {T-1}on both sides of the equation, which means that household has to decide C_t at the end of t-1.
SO, THE PROBLEM IS, HOW TO WRITE THIS KIND OF EULAR EQUATION IN DYNARE, ESPECIALLY FOR THE TIMING?
THANK YOU.

[jpfeifer]

Without knowing the exact model, this is hard to tell. But generally, the first order conditions in Dynare pin down variables at time t when the decisions are made. In the type of model you describe, the consumption decision at time t is made before the realization of the money supply shock is known. This suggests giving consumption a t-timing and the money shock a (t+1)-timing in the Euler equation. In other equations, consumption will most probably be showing up with at t-1 timing timing, because from the perspective of other decisions, the consumption decision will be predetermined.
But of course, the exact timing structure depends on the rest of the model.

[zhanshuo]

thanks a lot.
in fact the limited participation model I have referred to is CEE(1997):Sticky price and limited participation models of
money: A comparison, Chiristiano(1992), Furst(1992) and so on, which model the liquidity effect of monetary policy.
I have attached one typical this kind of modeling paper.
the key equation is equation(11) in page 5.
you could have a look at it.

[jpfeifer]

See the manual, Section 4.3.2 Operators. There you have the

Code: Select all

EXPECTATION

operator that should allow you to code such an equation without having to deal with auxiliary variables yourself.

[zhanshuo]

THAT REALLY HELPS.
THANKS!