King–Plosser–Rebelo preferences

In economics, King–Plosser–Rebelo preferences are a particular functional form of utility that is used in many macroeconomic models and dynamic stochastic general equilibrium models. Having originally been proposed in an article that appeared in the Journal of Monetary Economics in 1988,^[1] the corresponding technical appendix detailing their derivation has only been published in 2002.^[2]

Denote consumption with C, leisure with L and the absolute value of the inverse of the

${\displaystyle \sigma _{c}}$

${\displaystyle \sigma _{c}>0}$

${\displaystyle 0<\sigma _{c}<1}$

${\displaystyle \sigma _{c}>1}$

${\displaystyle u\left({C,L}\right)={\frac {1}{1-{\sigma _{c}}}}{C^{1-{\sigma _{c}}}}v\left(L\right)}$

where ${\displaystyle v\left(L\right)}$ is increasing and concave if ${\displaystyle 0<\sigma _{c}<1}$ or decreasing and convex if ${\displaystyle \sigma _{c}>1}$. Further restrictions are required to assure overall concavity of the momentarily utility function. In the limit case of ${\displaystyle \sigma _{c}=1}$ the resulting preferences specification is additively separable and given by

${\displaystyle u\left({C,L}\right)=\ln {C_{t}}+v\left(L\right)}$

where ${\displaystyle v\left(L\right)}$ is increasing and concave.

The reason for the prevalence of this preference specification in macroeconomics is that they are compatible with

${\displaystyle u\left(C,L\right)={\frac {1}{1-\sigma _{c}}}C^{1-\sigma _{c}}-z^{1-\sigma _{c}}{\frac {\left(1-L\right)^{1+\kappa }}{1+\kappa }}}$

Where ${\displaystyle \kappa }$ denotes the inverse of the

Frisch elasticity

of labor supply and z is the level of labor augmenting technology.

Relationship to other common macroeconomic preference types

KPR-preferences are one polar case nested in Jaimovich–Rebelo preferences. The latter allow to freely scale the wealth effect on the labor supply. The other polar case is the Greenwood–Hercowitz–Huffman preferences, where the wealth effect on the labor supply is completely shut off. However, this naturally implies that they are incompatible with a balanced growth path.^[4]

References