Stochastic Ordering of Stationary Distributions of Linear Recurrences: Further Results and Economic Applications

We investigate pairwise stochastic comparisons of stationary solutions to the linear recurrence <inline-formula><math display="inline"><semantics><mrow><msub><mi>X</mi><mrow><mi>t</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><msub><mi>A</mi><mi>t</mi></msub><msub><mi>X</mi><mi>t</mi></msub><mo>+</mo><msub><mi>B</mi><mi>t</mi></msub></mrow></semantics></math></inline-formula>, where <inline-formula><math display="inline"><semantics><msub><mi>A</mi><mi>t</mi></msub></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><msub><mi>B</mi><mi>t</mi></msub></semantics></math></inline-formula> are non-negative random variables. We establish novel order-preserving properties, which enable us to obtain comparison theorems about well-known measures of conditional size, tail variability and skewness across probability distributions. While useful in studies of ergodic wealth accumulation processes and the persistence of inequality, our results can fruitfully be exploited to conduct comparative statics exercises in structural models entailing Kesten-type reduced-form representations. An application of our analysis to a dynamic asset accumulation model uncovers the qualitatively similar effects of capital income and earnings taxation on expected wealth concentration over higher quantiles as well as on conditional upper tail dispersion of wealth holdings, qualifying previous results that solely rely on the determination of Pareto exponents.