PhD Seminar: Determination of Pareto exponents in asymptotically multiplicative model.

Determination of Pareto exponents in asymptotically multiplicative model

Beare and Toda (2022, ECMA) determine Pareto exponents from a spectral-radius equation for exactly multiplicative Markov dynamics with reset. This equation provides a tractable way to study how growth and survival affect Pareto exponent, without computing the stationary distribution. Yet their assumptions of exact multiplicativity and reset limit direct application to economically important models with nonlinear saving, additive inputs, or no reset mechanism. We extend their characterization to asymptotically multiplicative models with nonlinear accumulation and additive inputs, including models without reset. We establish existence and uniqueness of a stationary distribution. The Pareto exponent still follows from one spectral-radius equation, without computing the stationary distribution. We also obtain a positive finite Pareto constant and characterize the limiting distribution of types in the upper tail.