Capacity utilization drives state-dependent labor tax effects on hours

The paper introduces a business cycle model where production requires a minimum labor input, leading to endogenous capacity utilization.

This creates a kinked aggregate production function: constant returns to scale below capacity (recessions) and decreasing returns at capacity (expansions).

New empirical evidence shows labor tax shocks have significantly larger effects on hours and output when capacity utilization is below trend.

The model, calibrated to U.S. data, confirms that the aggregate hours elasticity is higher in recessions, diverging from the micro elasticity implied by preferences.

This state dependence arises from two adjustment margins: the number of active plants (extensive margin) in recessions, making hours highly responsive, and hours per plant (intensive margin) in expansions, which dampens the response due to decreasing returns.

This mechanism explains why proportional tax changes generate nonlinear, state-dependent effects.

The study addresses the challenge of modeling distortionary taxes in a dynamic general equilibrium with occasionally binding capacity constraints, which renders standard local approximation methods unsuitable.

It adapts the monotone-map (Coleman–Reffett) method to kinked production environments, ensuring a unique, ergodic, and constructive competitive equilibrium.

This approach is crucial because distortionary taxation in such a setting requires solving directly for the competitive equilibrium and prices, unlike models relying on social planner solutions.

The paper also relates to literature on fiscal policy's business cycle variation, showing state dependence can arise in frictionless economies from minimum labor requirements.