Timing pitfall for a simple BGG model

General DSGE Modeling Replication Attempts
1

Dear professor：

I have a timing problem for a simple BGG model.

In my opinion, for the incentive compatibility constraint of entrepreneurs, the two expressions below are the same:

(Rk(+1)/R)*(Gamma_cdf(+1) - mu*G_cdf(+1))=lev/(1+lev);

(Rk/R(-1))*(Gamma_cdf - mu*G_cdf)=lev(-1)/(1+lev(-1));

When I use the first expression, error comes up. It says “Blanchard & Kahn conditions are not satisfied: indeterminacy.”

When I use the second expression, everything seems fine.

I have realized to some extent the importance of “timing” for dynamic programming, but I still cannot understand what is happening at a deeper level.

So why is this happening, and how can I get deep understanding of this problem.

BGGreal.mod (7.0 KB)
BGGreal_steadystate.m (1.8 KB)
main.m (446 Bytes)
myfun_findss.m (745 Bytes)

2

Given Dynare’s timing convention,

(Rk(+1)/R)*(Gamma_cdf(+1) - mu*G_cdf(+1))=lev/(1+lev);

is
E_t[(R^k_{t+1}/R)*(Gamma\_cdf_{t+1} - \mu*G\_cdf_{t+1})]=lev_t/(1+lev_T);
That is, the left part of the equation only needs to hold in expectations. In contrast,

(Rk/R(-1))*(Gamma_cdf - mu*G_cdf)=lev(-1)/(1+lev(-1));

needs to hold in all states of the world.

3

Professor jpfeifer, thank you for your patience in your reply. Your answer has enlightened me.