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 tailprobabilities, a simple equation determining Pareto exponents, and comparative statics. We present two applications: we show that (i) the tails of the wealth distribution in a heterogeneous-agent dynamic general equilibrium model with idiosyncratic investment risk are Paretian, and (ii) a random growth model for the population dynamics of Japanese municipalities is consistent with the observed Pareto exponent but only after allowing for Markovian dynamics .
This article contains new tools for studying the shape of the stationary distribution of sizes in a dynamic economic system in which units experience random multiplicative shocks and are occasionally reset. Each unit has a Markov-switching type which influences their growth rate and reset probability. We show that the size distribution has a Pareto upper tail, with exponent equal to the unique positive solution to an equation involving the spectral radius of a certain matrix-valued function. We illustrate the use of our results by applying them to the wealth distribution in a heterogeneous-agent general equilibrium model , in which agents engage in private enterprise and trade risk-free bonds while subject to Markov-switching productivity and mortality risk. A plausible numerical calibration yields a Pareto exponent of 1.39 for the upper tail of the wealth distribution, similar to estimates obtained from cross-sectional data .
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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 tailprobabilities, a simple equation determining Pareto exponents, and comparative statics. We present two applications: we show that (i) the tails of
This article contains new tools for studying the shape of the stationary distribution of sizes in a dynamic economic system in which units experience random multiplicative shocks and are occasionally reset. Each unit has a Markov-switching type which influences their growth rate and reset probability. We show that the size distribution has a Pareto upper tail, with exponent equal to the unique positive solution to an equation involving the spectral radius of a certain matrix-valued function. We illustrate the use of our results by applying them to
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with idiosyncratic investment risk are Paretian, and (ii) a random growth model for the population dynamics of Japanese municipalities is consistent with the observed Pareto exponent but only after allowing for Markovian dynamics
, in which agents engage in private enterprise and trade risk-free bonds while subject to Markov-switching productivity and mortality risk. A plausible numerical calibration yields a Pareto exponent of 1.39 for the upper tail of the wealth distribution, similar to estimates obtained from cross-sectional data