Jaimovich–Rebelo preferences

Jaimovich-Rebelo preferences refer to a utility function that allows to parameterize the strength of short-run wealth effects on the labor supply, originally developed by Nir Jaimovich and Sergio Rebelo in their 2009 article Can News about the Future Drive the Business Cycle?[1]

Let denote consumption and let denote hours worked at period . The instantaneous utility has the form

where

It is assumed that , , and .

The agents in the model economy maximize their lifetime utility, , defined over sequences of consumption and hours worked,

where denotes the expectation conditional on the information available at time zero, and the agents internalize the dynamics of in their maximization problem.

Relationship to other common macroeconomic preference types

Jaimovich-Rebelo preferences nest the KPR preferences and the GHH preferences.

KPR preferences

When , the scaling variable reduces to and the instantaneous utility simplifies to

corresponding to the KPR preferences.

GHH preferences and balanced growth path

When , and if the economy does not present exogenous growth, then the scaling variable reduces to a constant and the instantaneous utility simplifies to

corresponding to the original GHH preferences, in which the wealth effect on the labor supply is completely shut off.

Note however that the original GHH preferences are not compatible with a balanced growth path, while the Jaimovich-Rebelo preferences are compatible with a balanced growth path for . To reconcile these facts, first note that the Jaimovich-Rebelo preferences are compatible with a balanced growth path for because the scaling variable, , grows at the same rate as the labor augmenting technology.

Let denote the level of labor augmenting technology. Then, in a balanced growth path, consumption and the scaling variable grow at the same rate as . When , the stationary variable satisfies the relation

which implies that

for some constant .

Then, the instantaneous utility simplifies to

consistent with the shortcut of introducing a scaling factor containing the level of labor augmenting technology before the hours worked term.

References

  1. Jaimovich, Nir; Rebelo, Sergio (2009). "Can news about the future drive the business cycle?". American Economic Review. 99 (4): 1097–1118. doi:10.1257/aer.99.4.1097.
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