Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure

Angrist, Joshua D.; Chernozhukov, Victor; Fernández‐Val, Iván

doi:10.2139/ssrn.544222

Cited by 92 publications

(155 citation statements)

References 47 publications

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“…Section 2 introduces the GIC and DLC. The results of this paper are also related to those on inference on the quantile process; see, for example, Belloni et al (2011) and Qu and Yoon (2015) for the nonparametric case; Gutenbrunner and Jureckova (1992), Koenker and Machado (1999), Koenker and Xiao (2002), Chernozhukov and Fernandez-Val (2005), and Angrist et al (2006) for the parametric case. The empirical application to the USA and Brazil is presented in Section 4.…”

Section: Introductionmentioning

confidence: 76%

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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Section: Introductionmentioning

confidence: 76%

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

Ferreira

Firpo

Galvao

2018

J of Applied Econometrics

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“…Assuming that the conditional density f Y ( y | x ) exists, we can follow the same procedure as given in Theorem 2 of Angrist et al (2006) and obtain the coefficient

b_{j τ}^{0}

that is the minimizer of the weighted least squares:

b_{j τ}^{0} = arg min_{b_{j τ} \in R} E false[{\tilde{w}}_{τ} false(boldX false) \cdot {false(Q_{τ} false(Y false| boldX false) - b_{j τ} X_{j} false)}^{2} false],

where

{\tilde{w}}_{τ} false(boldX false) = \frac{1}{2} \int_{0}^{1} f_{ε} false(u \cdot Δ_{τ} false(X_{j}, b_{j τ}^{0} false) false| boldX false) d u

, and

Δ_{τ} false(X_{j}, b_{j τ}^{0} false) = b_{0 τ}^{0} + b_{j τ}^{0} X_{j} - Q_{τ} false(Y false| boldX false)

for j = 1, ⋯, p . As a result,

b_{j τ}^{0} = {false{E false({\tilde{w}}_{τ} false(boldX false) X_{j}^{2} false) false}}^{- 1} E false({\tilde{w}}_{τ} false(boldX false) X_{j} Q_{τ} false(Y false| boldX false) false) = β_{j τ}^{0} + d_{j τ},

where

d_{j τ} = \sum_{k \neq j} β_{k τ}^{0} {false{E false({\tilde{w}}_{τ} false(boldX false) X_{j}^{2} false) false}}^{- 1} E false({\tilde{w}}_{τ} false(boldX false) X_{j} X_{k} false) .

…”

Section: Quantile Partial Correlation (Qpcor)mentioning

confidence: 99%

Variable Screening via Quantile Partial Correlation

Tsai

2017

Journal of the American Statistical Association

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In quantile linear regression with ultra-high dimensional data, we propose an algorithm for screening all candidate variables and subsequently selecting relevant predictors. Specifically, we first employ quantile partial correlation for screening, and then we apply the extended Bayesian information criterion (EBIC) for best subset selection. Our proposed method can successfully select predictors when the variables are highly correlated, and it can also identify variables that make a contribution to the conditional quantiles but are marginally uncorrelated or weakly correlated with the response. Theoretical results show that the proposed algorithm can yield the sure screening set. By controlling the false selection rate, model selection consistency can be achieved theoretically. In practice, we proposed using EBIC for best subset selection so that the resulting model is screening consistent. Simulation studies demonstrate that the proposed algorithm performs well, and an empirical example is presented.

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“…However, these models are not appropriate in this application due to substantial conditional heteroskedasticity in log wages (Lemieux (2006) and Angrist, Chernozhukov, and Fernández-Val (2006)). We consider the use of quantile regression, distribution regression, classical regression, and duration/transformation regression.…”

Section: Labor Market Institutions and The Distribution Of Wagesmentioning

confidence: 99%

“…For applications, including to counterfactual analysis, see, for example,Buchinsky (1994),Chamberlain (1994),Abadie (1997),Gosling, Machin, and Meghir (2000),Machado and Mata (2005),Angrist, Chernozhukov, and Fernández-Val (2006), andAutor, Katz, and Kearney (2006b). For applications, including to counterfactual analysis, see, for example,Buchinsky (1994),Chamberlain (1994),Abadie (1997),Gosling, Machin, and Meghir (2000),Machado and Mata (2005),Angrist, Chernozhukov, and Fernández-Val (2006), andAutor, Katz, and Kearney (2006b).…”

mentioning

confidence: 99%

Inference on Counterfactual Distributions

2013

Econometrica

405

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Counterfactual distributions are important ingredients for policy analysis and decomposition analysis in empirical economics. In this article we develop modeling and inference tools for counterfactual distributions based on regression methods. The counterfactual scenarios that we consider consist of ceteris paribus changes in either the distribution of covariates related to the outcome of interest or the conditional distribution of the outcome given covariates. For either of these scenarios we derive joint functional central limit theorems and bootstrap validity results for regression-based estimators of the status quo and counterfactual outcome distributions. These results allow us to construct simultaneous confidence sets for function-valued effects of the counterfactual changes, including the effects on the entire distribution and quantile functions of the outcome as well as on related functionals. These confidence sets can be used to test functional hypotheses such as no-effect, positive effect, or stochastic dominance. Our theory applies to general counterfactual changes and covers the main regression methods including classical , quantile, duration, and distribution regressions. We illustrate the results with an empirical application to wage decompositions using data for the United States. As a part of developing the main results, we introduce distribution regression as a comprehensive and flexible tool for modeling and estimating the entire conditional distribution. We show that distribution regression encompasses the Cox duration regression and represents a useful alternative to quantile regression. We establish functional central limit theorems and bootstrap validity results for the empirical distribution regression process and various related functionals. of the counterfactual operator, exchangeable bootstrap, unconditional quantile and distribution effects

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Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure

Cited by 92 publications

References 47 publications

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

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

Variable Screening via Quantile Partial Correlation

Inference on Counterfactual Distributions

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