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
Dynamic stochastic general equilibrium modeling (abbreviated as DSGE, or DGE, or sometimes SDGE) is a macroeconomics, macroeconomic method which is often employed by monetary and fiscal authorities for policy analysis, explaining historical time-se ...
models. Having originally been proposed in an article that appeared in the ''
Journal of Monetary Economics'' in 1988,
[
] the corresponding technical appendix detailing their derivation has only been published in 2002.
[
]
Denote consumption with C, leisure with L and the absolute value of the inverse of the
intertemporal elasticity of substitution Elasticity of intertemporal substitution (or intertemporal elasticity of substitution, EIS, IES) is a measure of responsiveness of the growth rate of consumption to the real interest rate. If the real interest rate rises, current consumption may ...
in consumption with
. Strict
concavity
In calculus, the second derivative, or the second order derivative, of a function is the derivative of the derivative of . Roughly speaking, the second derivative measures how the rate of change of a quantity is itself changing; for example, ...
of the utility function implies
.
For
or
the utility function has the multiplicatively separable form
where
is increasing and concave if
or decreasing and convex if
. Further restrictions are required to assure overall concavity of the momentarily utility function.
In the limit case of
the resulting preferences specification is additively separable and given by
where
is increasing and concave.
The reason for the prevalence of this preference specification in macroeconomics is that they are compatible with
balanced growth along the optimal
steady state. Hence, they are used in many
dynamic stochastic general equilibrium
Dynamic stochastic general equilibrium modeling (abbreviated as DSGE, or DGE, or sometimes SDGE) is a macroeconomics, macroeconomic method which is often employed by monetary and fiscal authorities for policy analysis, explaining historical time-se ...
models, which are typically derived from the
neoclassical growth model. The reason for their compatibility with
balanced growth is twofold. First, having a constant
interest rate in
steady state, the growth rate of
marginal utility
In economics, utility is the satisfaction or benefit derived by consuming a product. The marginal utility of a Goods (economics), good or Service (economics), service describes how much pleasure or satisfaction is gained by consumers as a result o ...
must be constant, which is the case here. Second, having a finite time endowment, balanced growth together with an optimal choice of labor by the agents implies that
income and
substitution effect of the increase in
real wages due to
productivity
Productivity is the efficiency of production of goods or services expressed by some measure. Measurements of productivity are often expressed as a ratio of an aggregate output to a single input or an aggregate input used in a production proces ...
increases must cancel each other.
Shortcut to achieve balanced growth compatibility
To have additively separable preferences along with
balanced growth, some studies use the shortcut of introducing a scaling factor containing the level of labor augmenting technology before the leisure term. An example of such a utility function would be
[
]
Where
denotes the inverse of the
Frisch elasticity The Frisch elasticity of labor supply captures the elasticity (economics), elasticity of hours worked to the wage rate, given a constant marginal utility of wealth. Marginal utility is constant for Risk neutral preferences, risk-neutral individuals ...
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 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 Fut ...
. The latter allow to freely scale the
wealth effect on the labor supply. The other polar case is the
Greenwood–Hercowitz–Huffman preferences Greenwood–Hercowitz–Huffman preferences are a particular functional form of utility developed by Jeremy Greenwood, Zvi Hercowitz, and Gregory Huffman, in their 1988 paper ''Investment, Capacity Utilization, and the Real Business Cycle''.An arch ...
, 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.
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]
References
{{DEFAULTSORT:King-Plosser-Rebelo preferences
Neoclassical economics
Utility function types