# Jaimovich-Rebelo preferences response to TFP shock

I’m running a model using Jaimovich-Rebelo preferences (2009): u(c_t,n_t)=\left(c_t-\psi X_t\frac{n_t^{1+\xi}}{1+\xi}\right)^{1-\sigma}, where X_t=c_t^{\gamma}X_{t-1}^{1-\gamma}, and as mentioned in the article \gamma=0 makes u correspond to GHH preferences, and \gamma=1 to KPR preferences.

My model has Calvo stickiness and transaction costs, including this type of preferences I get as response to TPF shock when I set \gamma=0 (c_t= consumption, n_t=labor, w_t=wages, a_t=TPF):

And when I set \gamma=1:

I expected labor to decline in GHH case (\gamma=0) but it doesn’t. Is that behavior right and I’m misinterpreting something about the differences between KPR-GHH-additively separable preferences?

Thanks!!

Why do you think there is a problem? GHH preferences kill the wealth effect on labor supply. If there is a TFP shock, agents become richer and work less as they consume more leisure. With GHH, that effect is absent and households will only react to the substitution effect, i.e. the increase in wages. Thus, labor should react more strongly.

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Yes, sorry I had a confusion with government spending shock, where labor actually decreases in one case and increase in the other case, but that’s another story than the one in TFP. Thanks!!