Title: Geometrically stopped Markovian random growth processes and Pareto tails,
Abstract: Many empirical studies document power law behavior in size distributions of
economic interest such as cities, firms, income, and wealth. One mechanism for
generating such behavior combines independent and identically distributed
Gaussian additive shocks to log-size with a geometric age distribution. We
generalize this mechanism by allowing the shocks to be non-Gaussian (but
light-tailed) and dependent upon a Markov state variable. Our main results
provide sharp bounds on tail probabilities and simple formulas for Pareto
exponents. We present two applications: (i) we show that the tails of the
wealth distribution in a heterogeneous-agent dynamic general equilibrium model
with idiosyncratic endowment risk decay exponentially, unlike models with
investment risk where the tails may be Paretian, and (ii) we show that a random
growth model for the population dynamics of Japanese prefectures is consistent
with the observed Pareto exponent but only after allowing for Markovian
dynamics.