2014年-IMF国际货币组织全球_Aggregate_Stability_and_Balanced_26页_335kb

Summary of "Aggregate Stability and Balanced-Budget Rules"

Core Content

This paper investigates the stabilizing and destabilizing effects of balanced-budget rules (BBR) in a real business cycle (RBC) model. It extends the traditional RBC framework by incorporating a constant elasticity of substitution (CES) production function, which allows for a more general analysis of factor substitutability compared to the Cobb-Douglas (CD) specification. The study aims to understand how fiscal policy and tax rules affect equilibrium determinacy and business cycle dynamics.

Main Viewpoints

• Balanced-budget rules can lead to indeterminacy and sunspot fluctuations in an RBC model under certain conditions.
• The degree of substitutability between production factors (captured by the CES elasticity of substitution, σ) is a critical determinant of the stabilizing or destabilizing nature of BBRs.
• Empirical evidence suggests that in the US, EU, and UK, labour and capital are gross complements, i.e., σ is below unity. This has important implications for the likelihood of indeterminacy under BBRs.
• The stabilizing effect of BBRs is more pronounced when σ is below unity, reducing the risk of self-fulfilling expectations and endogenous fluctuations.

Key Information

Model Structure

• The model includes households, firms, and a government that follows a balanced-budget rule.
• The government’s revenue is derived from labour income taxes, and its budget constraint is defined as:
  $ G = \tau_t^h H_t w_t $
• Firms operate under perfect competition and use a CES production function:
  $$
  Y_t = B \left[ \alpha \left(K_t\right)^{\frac{\sigma - 1}{\sigma}} + (1 - \alpha) \left(H_t\right)^{\frac{\sigma - 1}{\sigma}} \right]^{\frac{\sigma}{\sigma - 1}}
  $$
• The CD case is a special case of CES when σ = 1.
• The Laffer curve is central to understanding the non-linear relationship between tax rates and government revenues.

Determinacy and Indeterminacy

• Equilibrium determinacy depends on the signs of the eigenvalues of the linearized system.
• The system is determinate if the determinant of the Jacobian matrix (J) is negative.
• It is indeterminate if the determinant is positive and the trace is negative, implying both eigenvalues are negative.
• The system is unstable if both the determinant and trace are positive, meaning both eigenvalues are positive.

Propositions

• Proposition 1 defines the necessary and sufficient conditions for equilibrium determinacy based on σ and τ^h.
• Proposition 2 classifies the equilibrium outcomes into four cases depending on σ and the threshold tax rate (τ^h)*:
  • If σ ∈ [0, 1 + δ(1 - α)/ρ] and τ^h < τ^h*, the model is indeterminate.
  • If σ ∈ [0, 1 + δ(1 - α)/ρ] and τ^h > τ^h*, the model is unstable.
  • If σ ∈ (1 + δ(1 - α)/ρ, +∞) and ε > τ^h*, the model is indeterminate.
  • If σ ∈ (1 + δ(1 - α)/ρ, +∞) and ε < τ^h*, the model is unstable if τ^h ∈ (ε, τ^h*), and determinate otherwise.

Empirical Relevance

• The elasticity of substitution (σ) is below unity in the US, EU, and UK, indicating that labour and capital are gross complements.
• This reduces the likelihood of indeterminacy compared to the CD case.
• However, for high σ values, sunspot equilibria and instability can still occur, particularly when the economy is on the increasing part of the Laffer curve.

Policy Analysis

• A balanced-budget rule can lead to self-fulfilling expectations and indeterminacy when the Laffer curve slopes upward and the elasticity of substitution is low.
• Capital taxes are introduced to analyze the impact of BBRs on equilibrium determinacy.
• The empirical range of σ is considered, and it is found that lower σ values reduce the possibility of indeterminacy and endogenous fluctuations.

Conclusion

• The elasticity of substitution (σ) plays a central role in determining the stabilizing or destabilizing properties of BBRs.
• The paper provides analytical conditions for determinacy and numerical examples to illustrate the effects of σ on the determinacy of the model.
• It shows that in the US, EU, and UK, the stabilizing effect of BBRs is enhanced when σ is below unity, but instability can still occur under certain parameter conditions.
• The results suggest that CES production functions are more data-consistent and useful for analyzing fiscal policy and business cycle dynamics.