Identification and Welfare Analysis

Hi all,

I am currently doing some work on durable goods models kinked demand curves. In these models, the New Keynesian Phillips Curve is given by:

Pi_hat = BetaPi_hat(+1) + KappaPsi*Marginal Cost

where Kappa is the standard nominal rigidity and Psi represents the real rigidity associated with the smoothed kink in the demand curve. Because they enter together, I assume they cannot be uniquely identified.

What I want to do is estimate the model, find what Kappa*Psi are in combination, then investigate the welfare effects of different combinations of rigidities. (I am not confident enough to derive the model specific loss function by and). Prior to estimating the model, I calibrated it in Dynare and ran a trial with:

Utility = log((c^(1-ALPHA))(d^ALPHA))-((n^(1+PHI))/(1+PHI));
Welfare = Utility + BETA

with order=2, and periods=100,000. For different values of Kappa and Psi, I get no difference in the means of utility and welfare (from oo_mean), but slight differences in their variances. I have to say, I expected that the means would be different and reflect the differences in welfare arising from the two rigidities.

Can anyone help me with the interpretation?

KD_proper.mod (2.65 KB)

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What exactly did you do? And why do you conduct simulations instead of using theoretical moments. When I run

stoch_simul(irf=0, order=2) Welfare; oo_mean=oo_.mean; set_param_value('THETAc',0.1); stoch_simul(irf=0, order=2) Welfare; oo_.mean-oo_mean
at the end of your file, there are significant differences in mean welfare