King–Plosser–Rebelo preferences: Difference between revisions

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KPR preferences (short for King-Plosser-Rebelo preferences ) are a certain type of preferences that are used in many macroeconomic models and DSGE models in particular. 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 intertemporal elasticity of substitution in consumption with . Strict concavity of the utility function implies . For or the momentarily 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 DSGE 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 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 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[3]

Where 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

  1. ^ King, Robert G.; Plosser, Charles I.; Rebelo, Sergio T. (1998). "Production, Growth and Business Cycles I. The Basic Neoclassical Model" (PDF). Journal of Monetary Economics. 21: 195–232. doi:10.1023/A:1020529028761. {{cite journal}}: Cite has empty unknown parameter: |month= (help)
  2. ^ King, Robert G.; Plosser, Charles I.; Rebelo, Sergio T. (2002). "Production, Growth and Business Cycles: Technical Appendix" (PDF). Computational Economics. 20 (1–2): 87–116. doi:10.1023/A:1020529028761. {{cite journal}}: Cite has empty unknown parameter: |month= (help)
  3. ^ Mertens, Karel; Ravn, Morten O. (2011). "Understanding the aggregate effects of anticipated and unanticipated tax policy shocks". Review of Economic Dynamics. 14: 24–57. doi:10.1016/j.red.2010.07.004. {{cite journal}}: Cite has empty unknown parameter: |month= (help); line feed character in |title= at position 73 (help)
  4. ^ Jaimovich, Nir; Rebelo, Sergio (2009). "Can news about the future drive the business cycle?". American Economic Review. 99 (4): 1097–1118. {{cite journal}}: Cite has empty unknown parameter: |month= (help)