Distributional vs. Quantile Regression

Koenker, Roger; Leorato, Samantha; Peracchi, Franco

doi:10.2139/ssrn.2368737

Cited by 26 publications

(24 citation statements)

References 20 publications

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“…Given our focus on the bottom of the wage distribution, this aspect is rather critical. Although the two approaches are theoretically equivalent (Koenker et al, 2013), empirical evidence suggests that DR generally provides a better fit to wage distribution data than quantile regression (Rothe and Wied, 2013;Van Kerm et al, 2016).…”

Section: Distributional Analysesmentioning

confidence: 99%

Minimum Wages and the Gender GAP in Pay: New Evidence from the United Kingdom and Ireland

Bargain

Doorley

Kerm

2018

Review of Income and Wealth

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Women are disproportionately in low‐paid work compared to men so, in the absence of rationing effects on their employment, they should benefit the most from minimum wage policies. This study examines the change in the gender wage gap around the introduction of minimum wages in Ireland and the United Kingdom (U.K.). Using survey data for the two countries, we develop a decomposition of the change in the gender differences in wage distributions around the date of introduction of minimum wages. We separate out “price” effects attributed to minimum wages from “employment composition” effects. A significant reduction of the gender gap at low wages is observed after the introduction of the minimum wage in Ireland, while there is hardly any change in the U.K. Counterfactual simulations show that the difference between countries may be attributed to gender differences in non‐compliance with the minimum wage legislation in the U.K.

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Section: Distributional Analysesmentioning

confidence: 99%

Minimum Wages and the Gender GAP in Pay: New Evidence from the United Kingdom and Ireland

Bargain

Doorley

Kerm

2018

Review of Income and Wealth

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“…The formal differentiability condition and details are collected in the Appendix (see Lemma 1). As 6 See Koenker et al (2013) for a discussion and comparison on the statistical properties of the distribution regression and the QR approaches. 7 An alternative estimator for q s,u ( ), where sand u ∈ {t, t − 1}, emerges from the fact that it solves for qthe equation:…”

Section: Asymptotic Propertiesmentioning

confidence: 99%

Actual and counterfactual growth incidence and delta Lorenz curves: Estimation and inference

Ferreira

Firpo

Galvao

2018

J of Applied Econometrics

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Summary Different economic growth episodes display very different distributional characteristics, both across countries and over time. Growth is sometimes accompanied by rising and sometimes by falling inequality. Applied economists have come to rely on the growth incidence curve, which gives the quantile‐specific rate of income growth over a certain period, to describe these differences. This paper introduces a mean‐independent analogue, the delta Lorenz curve, which gives the cumulative change in income share up to each quantile. We also develop estimation and inference procedures for both functions of quantiles. We establish the limiting null distribution of the test statistics of interest for those functions, and propose resampling methods to implement inference in practice. The proposed methods are used to compare the growth processes in the USA and Brazil during 1995–2007. Although growth in the average real wages was disappointing in both countries, the distribution of that growth was markedly different. In the USA, wage growth was mediocre for the bottom 80% of the sample, but much more rapid for the top 20%. In Brazil, conversely, wage growth was rapid below the median, and negative at the top. Wage shares fell in the USA up to the 83rd percentile, and rose in Brazil up to the 65th percentile.

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“…A response-varying coefficient model, also called distribution regression (Foresi and Peracchi 1995;Chernozhukov, Fernández-Val, and Melly 2013;Koenker, Leorato, and Peracchi 2013), for the Boston Housing data is Figure 12 compares the fitted densities for the linear transformation model with constant regression coefficients mlt_BH and the two distribution regression models mlt_BHi and mlt_BHi2.…”

Section: Non-normal Linear Regression: Boston Housing Data (Cont'd)mentioning

confidence: 99%

Most Likely Transformations: The mlt Package

Hothorn¹

2020

J. Stat. Soft.

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The mlt package implements maximum likelihood estimation in the class of conditional transformation models. Based on a suitable explicit parameterization of the unconditional or conditional transformation function using infrastructure from package basefun, we show how one can define, estimate, and compare a cascade of increasingly complex transformation models in the maximum likelihood framework. Models for the unconditional or conditional distribution function of any univariate response variable are set-up and estimated in the same computational framework simply by choosing an appropriate transformation function and parameterization thereof. As it is computationally cheap to evaluate the distribution function, models can be estimated by maximization of the exact likelihood, especially in the presence of random censoring or truncation. The relatively dense high-level implementation in the R system for statistical computing allows generalization of many established implementations of linear transformation models, such as the Cox model or other parametric models for the analysis of survival or ordered categorical data, to the more complex situations illustrated in this paper. Journal of Statistical Software5 transformation model P(Y ≤ y) = Φ(h(y)) = Φ(a(y) ϑ) by maximization of the exact likelihood as follows. After loading package mlt we specify the duration variable we are interested in R> library("mlt") R> var_d <-numeric_var("duration", support = c(1.0, 5.0), + add = c(-1, 1), bounds = c(0, Inf)) This abstract representation refers to a positive and conceptually continuous variable duration. We then set-up a basis function a for this variable in the interval [1, 5] (which can be evaluated in the interval [0, 6] as defined by the add argument), in our case a monotone increasing Bernstein polynomial of order eight (details can be found in Section 2.1) R> B_d <-Bernstein_basis(var = var_d, order = 8, ui = "increasing") The (in our case unconditional) transformation model is now fully defined by the parameterization h(y) = a(y) ϑ and F Z = Φ which is specified using the ctm() function as R> ctm_d <-ctm(response = B_d, todistr = "Normal") Because, in this simple case, the transformation function transforms Y ∼ F Y to Z ∼ F Z = Φ, the latter distribution is specified using the todistr argument. An equidistant grid of 200 duration times in the interval support + add = [0, 6] is generated by R> str(nd_d <-mkgrid(ctm_d, 200)) List of 1 $ duration: num [1:200] 0 0.0302 0.0603 0.0905 0.1206 ...

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Distributional vs. Quantile Regression

Cited by 26 publications

References 20 publications

Minimum Wages and the Gender GAP in Pay: New Evidence from the United Kingdom and Ireland

Minimum Wages and the Gender GAP in Pay: New Evidence from the United Kingdom and Ireland

Actual and counterfactual growth incidence and delta Lorenz curves: Estimation and inference

Most Likely Transformations: The mlt Package

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