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?
denote consumption and let
denote hours worked at period
The instantaneous utility has the form
θ > 1
The agents in the model economy maximize their lifetime utility,
, defined over sequences of consumption and hours worked,
denotes the expectation conditional on the information available at time zero, and the agents internalize the dynamics of
in their maximization problem.
Jaimovich-Rebelo preferences nest the KPR preferences and the GHH preferences.
, the scaling variable
reduces to
and the instantaneous utility simplifies to
corresponding to the KPR preferences.
, 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.
denote the level of labor augmenting technology.
Then, in a balanced growth path, consumption
and the scaling variable
grow at the same rate as
, the stationary variable
satisfies the relation
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.