Brendan K. Beare, Alexis Akira Toda
arXiv 5 Dec 2017 · Econometrics
arXiv:1712.01431 · PDF · Extracted main text
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. Under a non-lattice condition on growth rates, an eigenvector associated with the Pareto exponent provides the distribution of types in the upper tail of the size distribution.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Gouin-Bonenfant, Émilien and Alexis A.\ Toda (2022) Pareto extrapolation: An analytical framework for studying tail inequality self | 0.843 | 3 | 3 | 100% |
| 2 | Beare, Brendan K., Won-Ki Seo, and Alexis A.\ Toda (2022) Tail behavior of stopped Lévy processes with Markov modulation self | 0.754 | 7 | 3 | 43% |
| 3 | Kesten, Harry (1973) Random difference equations and renewal theory for products of random matrices | 0.737 | 3 | 2 | 100% |
| 4 | Reed, William J.\ (2001) The Pareto, Zipf and other power laws | 0.737 | 3 | 2 | 100% |
| 5 | Cao, Dan and Wenlan Luo (2017) Persistent heterogeneous returns and top end wealth inequality | 0.644 | 2 | 2 | 100% |
| 6 | Benhabib, Jess, Alberto Bisin, and Shenghao Zhu (2011) The distribution of wealth and fiscal policy in economies with finitely lived agents | 0.644 | 2 | 2 | 100% |
| 7 | Horn, Roger A.\ and Charles R.\ Johnson (2013) Matrix Analysis | 0.585 | 10 | 4 | 20% |
| 8 | Collamore, Jeffrey F.\ (2009) Random recurrence equations and ruin in a Markov-dependent stochastic economic environment | 0.511 | 2 | 1 | 100% |
| 9 | de Saporta, Benoîte (2005) Tail of the stationary solution of the stochastic equation $Y_n+1=a_nY_n+b_n$ with Markovian coefficients | 0.511 | 2 | 1 | 100% |
| 10 | Roitershtein, Alexander (2007) One-dimensional linear recursions with Markov-dependent coefficients | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 48 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Non-Existent Moments of Earnings Growth | 0.405 | 1 | 1 |