Jaimovich–rebelo preferences

Jaimovich–Rebelo preferences

Jaimovich–Rebelo preferences are a specialized form of utility function commonly employed in macroeconomic modeling. They were developed to provide a more flexible and empirically consistent way to model how individuals make choices between consumption and leisure, particularly in the context of how changes in wealth affect their labor supply decisions. This preference structure is crucial for understanding and replicating the dynamics of modern business cycles in economic models.

History and Origin

Jaimovich–Rebelo preferences were introduced by economists Nir Jaimovich and Sergio Rebelo in their 2009 article "Can News About the Future Drive the Business Cycle?". The underlying research was initially disseminated as a working paper by the National Bureau of Economic Research (NBER) in 2006, and later published in the American Economic Review.

Thei³⁸, ³⁹r work aimed to address a significant challenge in Real Business Cycle Models and Dynamic Stochastic General Equilibrium Models: how to generate realistic economic expansions and contractions in response to "news shocks"—that is, anticipated changes in future economic fundamentals like total factor productivity (TFP). Traditi³⁵, ³⁶, ³⁷onal models often struggled to produce the observed comovement of output, consumption, investment, and hours worked in response to such forward-looking information. Jaimovich and Rebelo identified that the strength of the short-run wealth effect on labor supply was a key factor in resolving this issue, leading to the development of their novel preference specification.

Key³⁴ Takeaways

• Flexible Wealth Effect: Jaimovich–Rebelo preferences allow modelers to precisely parameterize the strength of the short-run wealth effect on labor supply decisions, making them highly adaptable for various macroeconomic analyses.
• Rea³³listic Business Cycle Dynamics: This preference structure is instrumental in building models that can successfully replicate the observed dynamics of business cycles, especially in response to anticipated future economic changes, known as "news shocks."
• Nes³¹, ³²ting Other Preferences: Jaimovich–Rebelo preferences are a general form that encompasses two other widely used preference types as special cases: King-Plosser-Rebelo (KPR) preferences and Greenwood-Hercowitz-Huffman (GHH) preferences.
• Balan³⁰ced Economic Growth Compatibility: Unlike some other preference specifications, Jaimovich–Rebelo preferences are compatible with models that exhibit a balanced economic growth path, a desirable feature for long-run macroeconomic analysis.
• Consump²⁹tion-Leisure Complementarity: The preferences highlight a complementary relationship between consumption and leisure, implying that the enjoyment derived from leisure may increase with the level of consumption.

Formula a²⁸nd Calculation

The instantaneous utility function for Jaimovich–Rebelo preferences is typically expressed as:

Where:

• (C_t): Represents consumption at time (t).
• (N_t): Denotes hours worked or labor supply at time (t).
• (X_t): Is a scaling variable, often reflecting the level of labor-augmenting technology. In models with exogenous growth, (X_t) typically grows at the same rate as technology.
• (\sigma): Is related to the inverse of the intertemporal elasticity of substitution in consumption.
• (\psi): A positive parameter that scales the disutility from labor.
• (\theta): A positive parameter representing the inverse of the Frisch elasticity of labor supply, determining the convexity of labor disutility.
• (\gamma): The crucial parameter that governs the strength of the short-run wealth effect on labor supply. It ranges between 0 and 1.

This formulati²⁷on allows for the modeling of preferences where the disutility of work is scaled by a factor that depends on the state of technology or economic activity.

Interpreting Jaimovich–Rebelo preferences

The interpretation of Jaimovich–Rebelo preferences hinges primarily on the parameter (\gamma). This parameter directly controls how strongly a change in wealth influences an individual's decision to work or enjoy leisure.

• When (\gamma = 1): The preferences simplify to the King-Plosser-Rebelo (KPR) preferences. In this case, the wealth effect on labor supply is strong and can lead to counterintuitive results in some macroeconomic models, such as a decrease in labor supply in response to anticipated future productivity gains.
• When (\gamma²⁶ = 0): The preferences reduce to the Greenwood-Hercowitz-Huffman (GHH) preferences. Here, the wealth effect on labor supply is completely shut off, meaning that changes in wealth do not directly influence labor decisions.
• For values be²⁵tween (0 < \gamma < 1): Jaimovich–Rebelo preferences allow for a continuum of possibilities. This flexibility enables economists to calibrate models where the wealth effect on labor supply is neither completely absent nor excessively strong, thereby better matching empirical observations of how labor responds to economic shocks and news about the future. This nuance is partic²⁴ularly important for models that seek to explain how agents react to information about future economic prospects.

Hypothetical Example

Consider an economy modeled with Jaimovich–Rebelo preferences, where a major technological breakthrough is announced but will only be implemented in five years. This "good news shock" implies a future increase in total factor productivity.

In a traditional model with strong wealth effects (like KPR preferences), households might immediately anticipate greater future wealth and, consequently, choose to work less and enjoy more leisure in the present. This could lead to an immediate recession, which might not align with observed real-world business cycles.

However, with Jaimovic²³h–Rebelo preferences, calibrated with an intermediate (\gamma) parameter, the model can generate a more realistic response. Households, anticipating future prosperity, might actually increase their current investment and labor supply. They work harder and invest more today to take full advantage of the future technological gains, leading to an immediate economic expansion rather than a contraction. This pre-emptive boom is a key feature that Jaimovich–Rebelo preferences help models achieve, better reflecting the forward-looking nature of economic agents.

Practical Applications

²¹, ²²
Jaimovich–Rebelo preferences are predominantly applied in the field of macroeconomic modeling, particularly within Real Business Cycle Models and Dynamic Stochastic General Equilibrium Models. Their primary utility lies in their ability to improve the empirical fit of these models by allowing for a more nuanced representation of household behavior.

Some key practical applications include:

• Analyzing News Shocks: These preferences are crucial for understanding how economies respond to anticipated future events or "news shocks." They allow models to generate realistic co-movements in variables such as consumption, investment, and labor supply in response to such forward-looking information.
• Business Cycle Research¹⁹, ²⁰: Researchers use Jaimovich–Rebelo preferences to better explain the sources and propagation mechanisms of business cycles, including the role of expectations and technological advancements. The preferences contribute to a more accurate depiction of how economic activity fluctuates over time. The Bank of England, for instance, has published research investigating how various "news shocks," including risk-related news, affect business cycles.
• Policy Analysis: Centra¹⁷l banks and other economic institutions may utilize models incorporating Jaimovich–Rebelo preferences to evaluate the potential impacts of monetary policy and fiscal policies on household decisions and overall economic activity, particularly regarding how wealth effects influence outcomes.
• Understanding Labor Market ¹⁶Dynamics: By adjusting the (\gamma) parameter, economists can explore different scenarios regarding the responsiveness of labor supply to economic incentives and disincentives, contributing to a deeper understanding of labor market fluctuations.

Limitations and Criticisms

While Jaimovich–Rebelo preferences offer significant advantages in macroeconomic modeling, they also come with certain limitations and have faced criticisms:

• Calibration Challenges: The introduction of additional parameters, particularly (\gamma), can increase the complexity of model calibration. Accurately determining the optimal value of (\gamma) to match real-world data can be challenging and may require extensive empirical work.
• Reconciliation with Empirical¹⁴, ¹⁵ Estimates: Some studies suggest that reconciling Jaimovich–Rebelo preferences with micro-econometric evidence for the Frisch elasticity of labor supply can be difficult, especially when combined with other preference specifications like habit formation preferences. Research by the [Bank of Canada](http¹¹, ¹², ¹³s://www.bankofcanada.ca/2018/06/staff-working-paper-2018-26/) has specifically explored the constraints and potential solutions for reconciling these different preference types.
• Assumptions on [Capital Utiliza⁹, ¹⁰tion](https://diversification.com/term/capital-utilization) and Investment Adjustment Costs: The ability of models with Jaimovich–Rebelo preferences to generate realistic responses to news shocks often relies on other model features, such as variable capital utilization and adjustment costs to investment. If these complementary assumptions are not carefully chosen or validated, the efficacy of the preferences alone may be limited.
• Theoretical vs. Empirical Fit: ⁷, ⁸While designed to improve empirical fit in specific areas like news shocks, the overall performance of models with Jaimovich–Rebelo preferences across all dimensions of economic reality can still be subject to debate and further refinement.

Jaimovich–Rebelo preferences vs. Habit Formation Preferences

Jaimovich–Rebelo preferences and habit formation preferences are distinct yet sometimes complementary concepts in utility function design within economic models.

Jaimovich–Rebelo preferences primarily focus on how the relative importance of consumption versus leisure changes with wealth, specifically controlling the short-run wealth effect on labor supply. They are particularly useful for models that aim to explain business cycles driven by anticipated future economic conditions or "news shocks." The core innovation is the non-separability between consumption and leisure.

Habit Formation Preferences, on the other ⁵, ⁶hand, propose that an individual's utility function from current consumption is not absolute but is influenced by their past consumption levels (internal habits) or the consumption levels of others (external habits). This concept helps explain the persistence of consumption patterns, asset pricing puzzles, and the low marginal utility from additional consumption if consumption habits are strong.

While both preference types enhance the realis⁴m of macroeconomic models, they address different aspects of individual decision-making. Jaimovich–Rebelo preferences address the responsiveness of labor supply to wealth changes and news, whereas habit formation preferences address the intertemporal dynamics and social aspects of consumption. It is possible, and sometimes done, to incorporate both Jaimovich–Rebelo preferences and habit formation into a single model, though this can introduce additional complexity in calibration and reconciliation with empirical data.

FAQs

What problem do Jaimovich–Rebelo prefer¹, ², ³ences help solve in economic models?
Jaimovich–Rebelo preferences help economic models, especially those used for business cycles, better capture how economies respond to "news shocks"—anticipated future changes in productivity or other fundamentals. Without them, models often struggle to show a boom in response to good news about the future, sometimes predicting the opposite.

Are Jaimovich–Rebelo preferences widely used in macroeconomic research?
Yes, Jaimovich–Rebelo preferences are a standard and widely adopted feature in modern macroeconomic modeling, particularly in Dynamic Stochastic General Equilibrium Models, due to their ability to improve the empirical fit of these models to observed economic dynamics.

How do Jaimovich–Rebelo preferences affect labor decisions?
They allow for a more realistic representation of the wealth effect on labor supply. Depending on the specific parameterization, they can dampen or strengthen the tendency for people to reduce their work effort when they anticipate future increases in wealth, thus better matching how labor markets react to economic news.