Skewness, Tax Progression, and Demand for Redistribution: Evidence from the UK

Abstract

We introduce a skewness-based approach to measure tax progression and demand for redistribution. Adapting a novel, quantilebased statistical measure of skewness to right-skewed income distributions, we uncover its political economy foundation, by simultaneously relating the same measure to the classical model of income redistribution due to Meltzer and Richard (1981), to the Prospect Of Upward Mobility (POUM) mechanism due to Bènabou and Ok (2001), and to the progressivity of a tax schedule. In an empirical analysis of UK income distributions in 1979 -2013, we find that skewness has increased over time, with the rich moving further away from the median. While the magnitude of the increase has remained small enough so that observed redistribution (or lack thereof ) could be consistent with POUM hypothesis, more recent periods show an increase in tax progression. JEL: D31, D63, H20, P16

Redistribution under general decision rules

“…, it is immediate from right-skewness*, that for every p > 1 2 , the income at quantile p is farther from the median than the income at quantile p 1 − . This relationship, in ratio form, is very similar to measures of skewness advocated by Pogorelskiy and Traub (2017) and Groeneveld and Meeden (2009). 26 Naturally, right-skewness* implies that the mean income lies above the median.…”

“…Since Meltzer and Richard's seminal analysis, many papers have attempted to confirm their finding that redistribution increases with increased inequality. Positive results in the cross‐country context are documented in Meltzer and Richard (1983), Kristov et al (1992), and Persson and Tabellini (1994), Pogorelskiy and Traub (2017), amongst many others. On the other hand, there has been an abundance of work that questions these findings, beginning with Tullock (1983).…”

“…If so, by Proposition A1, the equilibrium policy is simply the reversion policy. 26 Pogorelskiy and Traub (2017) measure right-skewness by the ratio:…”

“…, for some exogenously chosen p. A distribution is right-skewed if the measure is larger than 0. Groeneveld and Meeden ( 2009) measure skewness by taking the sup of the Pogorelskiy and Traub (2017) measure, over all ∈ p (0.5, 1). 27 If τ = 0 0 , then it is ideal for every voter with income ≥ y y.…”

A new family of skewed distributions with application to some daily closing prices

“…Let Y be a random variable with pdf f (x), V = |Y | and S V a random variable such that, conditionally to {V = v}, we have P(S V = 1|V = v) = 1 − P(S V = −1|V = v) = F( v). Then, the random variable X = S V V has the pdf given by Equation (2). Naturally, other constructive representations of univariate skewed distributions exist in the literature.…”