King plosser rebelo kpr preferences: Meaning, Criticisms & Real-World Uses

King Plosser Rebelo Preferences

What Is King Plosser Rebelo Preferences?

King Plosser Rebelo (KPR) preferences refer to a specific functional form of a utility function used extensively in macroeconomic models to describe how individuals make intertemporal choice decisions regarding consumption and leisure. These preferences are a key component within utility theory, allowing economists to model how people balance their desire for present satisfaction with their plans for future well-being. KPR preferences are particularly valued for their compatibility with models that exhibit a balanced growth path, where key economic variables grow at constant rates over time³⁷,. This feature makes them highly suitable for analyzing long-term economic growth and cyclical fluctuations within dynamic economic frameworks.

History and Origin

King Plosser Rebelo preferences were formally introduced by economists Robert G. King, Charles I. Plosser, and Sergio T. Rebelo. Their seminal work, "Production, Growth and Business Cycles I: The Basic Neoclassical Model," published in the Journal of Monetary Economics in 1988, laid the groundwork for integrating these preferences into the then-developing real business cycle (RBC) models.³⁶ The original paper highlighted the importance of a preference specification that could explain persistent deviations in economic activity from a deterministic trend and offer an integrated approach to understanding economic growth and business cycles.³⁵ The functional form of KPR preferences was specifically designed to ensure that dynamic general equilibrium models could feature a constant interest rate and constant labor supply along a steady-state growth path, reflecting observed macroeconomic regularities,³⁴.

Key Takeaways

King Plosser Rebelo (KPR) preferences are a type of utility function fundamental to modern macroeconomic modeling.
They allow for consistent, balanced growth paths in economic models, reflecting long-term economic trends.
KPR preferences capture individuals' decisions regarding consumption and leisure across different time periods.
They are widely used in Dynamic Stochastic General Equilibrium (DSGE) models and Real Business Cycle (RBC) models to study economic fluctuations and policy impacts.
A key feature is their ability to model intertemporal substitution of consumption and labor supply in response to changes in interest rates and wages³³.

Formula and Calculation

The specific formulation of King Plosser Rebelo preferences allows for a balanced growth path in models where both consumption and leisure contribute to utility. A common representation of the KPR utility function for a representative agent at time (t) is often given as:

U(C_t, L_t) = \frac{1}{1-\sigma} \left( C_t \cdot V(L_t) \right)^{1-\sigma}

Where:

(U(C_t, L_t)) represents the utility derived from consumption (C_t) and leisure (L_t) at time (t).
(C_t) is the level of consumption at time (t).
(L_t) is the amount of leisure at time (t).
(\sigma) (sigma) is a parameter representing the inverse of the intertemporal elasticity of substitution in consumption. It captures the individual's willingness to substitute consumption across different periods,³². A higher (\sigma) implies a lower willingness to substitute.
(V(L_t)) is a strictly increasing and concave function of leisure, reflecting that individuals derive positive but diminishing marginal utility from more leisure.

In the special case where (\sigma = 1), the utility function takes a logarithmic form:

U(C_t, L_t) = \ln(C_t) + \ln(V(L_t))

This multiplicative separability between consumption and leisure is a defining characteristic that differentiates KPR preferences and enables consistent modeling of steady-state economic growth,³¹,³⁰.

Interpreting the King Plosser Rebelo Preferences

King Plosser Rebelo preferences are interpreted within macroeconomic models as a representation of how individuals optimize their lifetime well-being by choosing between current and future consumption, and between work and leisure. The structure of KPR preferences ensures that, as productivity and wages increase over time due to technological progress, agents' optimal choices maintain a stable proportion of time allocated to work, even if their income grows significantly. This property is crucial for aligning theoretical models with empirical observations of "balanced growth" in many economies,²⁹.

The specific form of the utility function means that the relative importance of consumption and leisure for an individual's utility is scaled by the overall level of economic activity. This scaling prevents the "wealth effect" from dominating the "substitution effect" on labor supply decisions as an economy grows, a common challenge with simpler utility function specifications. By doing so, KPR preferences enable models to generate stable patterns of labor supply and investment that are consistent with long-run growth trends.

Hypothetical Example

Consider a hypothetical economy modeled with King Plosser Rebelo preferences. Suppose policymakers are analyzing the long-term impact of a sustained increase in productivity, perhaps due to a new technological innovation. With KPR preferences embedded in the model, economists can project that as the economy's output and wages grow, households will optimally increase their consumption, while their allocation of time between work and leisure remains relatively stable.

For instance, if productivity doubles over several decades, leading to a significant rise in real wages, KPR preferences suggest that individuals will not necessarily reduce their working hours dramatically. Instead, the utility gained from increased consumption, enabled by higher wages, balances out the desire for more leisure. This contrasts with some other utility function forms, where rising wealth might lead to a sharp reduction in labor supply, diverging from observed patterns of sustained economic growth. The model allows for the study of the trade-offs involved in saving, investment, and future consumption in an environment of continuous technological advancement.

Practical Applications

King Plosser Rebelo preferences are widely applied in modern macroeconomics, primarily within the framework of Dynamic Stochastic General Equilibrium (DSGE) models and Real Business Cycle (RBC) models. These models are used by central banks and academic researchers to understand business cycles and evaluate the effects of economic policies.

Business Cycle Analysis: KPR preferences are instrumental in explaining aggregate fluctuations in key macroeconomic variables such as output, consumption, and investment. They help illustrate how these fluctuations can be efficient responses to real shocks, particularly those related to technology, within Real Business Cycle models ²⁸,²⁷.
Policy Evaluation: Economists utilize models with King Plosser Rebelo preferences to assess the potential impacts of fiscal policy and monetary policy on economic activity, labor supply, and consumption patterns²⁶. For example, the Federal Reserve Bank of Chicago's DSGE model, which incorporates household preferences, is used for policy analysis and forecasting of the U.S. economy²⁵,²⁴.
Long-Term Growth Studies: The compatibility of KPR preferences with balanced growth makes them suitable for analyzing factors driving long-run economic growth and the determinants of steady-state behavior in an economy,²³.
Quantitative Macroeconomics: They form a foundational element in the calibration and estimation of complex macroeconomic models, allowing researchers to generate artificial data that mimic observed economic time series characteristics²²,²¹.

Limitations and Criticisms

Despite their widespread use, King Plosser Rebelo preferences, like any theoretical construct, have limitations and have faced criticisms. One primary critique stems from their underlying assumptions about how individuals value consumption and leisure and how these valuations interact with wealth effects.

Invariance of Labor Supply to Wealth Effects: A key feature of KPR preferences is their ability to maintain a constant labor supply along a balanced growth path. However, this implies that the income and substitution effects of increasing real wages, resulting from productivity growth, exactly cancel each other out for labor supply decisions. Critics argue that this is a strong assumption, and empirical evidence on long-term labor supply trends can be nuanced, with some studies suggesting a slow decline in hours worked over long periods in developed economies²⁰.
Additive Separability Debate: While the general form of KPR preferences is multiplicatively separable, some discussions around "additively separable preferences along with balanced growth" imply specific shortcuts or conditions (e.g., when the intertemporal elasticity of substitution is 1, leading to a logarithmic utility),¹⁹. This can sometimes lead to confusion regarding the precise conditions under which certain properties hold.
Behavioral Realism: Like many standard rational expectations models, KPR preferences assume perfect foresight or rational expectations about the future. This abstraction from real-world behavioral biases or bounded rationality can be a point of criticism, particularly from behavioral finance perspectives. More complex preference structures, such as habit formation preferences or those accounting for risk aversion beyond constant relative risk aversion, have been proposed to address certain macroeconomic puzzles like the equity premium puzzle¹⁸,¹⁷. A 1995 paper from the Federal Reserve Bank of Minneapolis notes that this puzzle persists despite various attempts to explain it by relaxing assumptions about preferences, among other factors¹⁶.
Empirical Fit: While KPR preferences allow models to match certain stylized facts of business cycles, some studies indicate that single-shock models, even with KPR preferences, may not fully capture the observed correlations between macroeconomic variables like consumption, investment, and hours worked with output¹⁵.

King Plosser Rebelo Preferences vs. Habit Formation Preferences

King Plosser Rebelo (KPR) preferences and Habit Formation preferences are both advanced forms of utility function used in macroeconomic models, but they differ significantly in how they model consumer behavior and the implications for economic dynamics.

Feature	King Plosser Rebelo (KPR) Preferences	Habit Formation Preferences
Primary Focus	Ensuring compatibility with balanced growth paths, particularly concerning labor supply and productivity growth.	Explaining the slow adjustment of consumption to shocks and financial market anomalies like the equity premium puzzle.
Utility Dependence	Current utility depends on current consumption and leisure, often with a multiplicative relationship.	Current utility depends on current consumption relative to some past level of consumption (the "habit stock"). Utility is not time-separable¹⁴,¹³.
Behavioral Implication	Individuals optimally maintain a stable proportion of time working as income grows, facilitating analysis of long-run economic trends¹².	Consumers resist large and sudden changes in consumption, leading to a "smoothing" of consumption paths and persistence in consumption responses to shocks¹¹,¹⁰,⁹.
Common Application	Predominantly in Real Business Cycle (RBC) models and Dynamic Stochastic General Equilibrium (DSGE) models for growth and business cycle analysis.	Used in models attempting to reconcile macroeconomic data with asset pricing puzzles, particularly where consumption smoothing is a key mechanism⁸,⁷.
Response to Shocks	Allows for a consistent response to technology shocks that generates stable long-term growth.	Generates hump-shaped and persistent responses of consumption to various macroeconomic shocks, including monetary policy shocks⁶,⁵.

The choice between using KPR preferences or Habit Formation preferences in a model depends on the specific economic phenomena the researcher aims to explain. KPR preferences excel in modeling long-term aggregate behavior consistent with balanced growth, while habit formation offers a richer dynamic response of consumption, particularly useful for understanding asset pricing and short-run consumption dynamics.

FAQs

What is the main purpose of King Plosser Rebelo preferences in economics?
The main purpose of King Plosser Rebelo preferences is to provide a specific utility function that allows macroeconomic models, especially Dynamic Stochastic General Equilibrium (DSGE) models, to exhibit a balanced growth path. This means that key economic variables can grow at a constant rate over time, which aligns with observed long-run economic trends⁴,.

How do King Plosser Rebelo preferences handle the trade-off between consumption and leisure?
King Plosser Rebelo preferences model the trade-off between consumption and leisure in a way that allows individuals to maintain a stable balance between work and leisure over time, even as their income and productivity increase. This is achieved by incorporating a specific interaction between consumption and leisure in the utility function that offsets the wealth effect on labor supply,³.

Are King Plosser Rebelo preferences compatible with real business cycle models?
Yes, King Plosser Rebelo preferences are highly compatible with Real Business Cycle (RBC) models. They provide the necessary framework for RBC models to explain aggregate economic fluctuations as efficient responses to real shocks, such as changes in technology, while maintaining consistency with observed patterns of economic growth ²,¹.