Quantile structural treatment effects: application to smoking wage penalty and its determinants

Abstract

We propose a new treatment effect parameter called the quantile structural treatment effect (QSTE) to distinguish between observed and unobserved treatment heterogeneity in the semiparametric additive potential outcome framework. The QSTE is defined as the quantile treatment effect if the observed covariates were exogenously set to a fixed value while keeping unobserved heterogeneity unchanged. We show the QSTE is identified under unconfoundedness and propose a semiparametric inverse probability weighted-type estimator that converges weakly to a Gaussian process. A multiplier bootstrap procedure is also carried out to construct uniform confidence bands. Using data from the Panel Study of Income Dynamics and focusing on the female group for the plausibility of the unconfoundedness assumption, we examine observed and unobserved determinants of the adverse effects of smoking on wages known as the smoking wage penalty. Our findings suggest that different levels of observable human capital may partly explain the smoking heterogeneity on wages. However, no evidence is found to support unobservable explanations such as discrimination against smokers, especially in the upper tail of the unobserved heterogeneity distribution.

Keywords:

• Heterogeneous treatment effect
• quantile structural function
• uniform inference
• smoking wage penalty

JEL CLASSIFICATION:

• C14
• C21
• I12
• J31

Acknowledgement

We would like to thank Shakeeb Khan, Chung–Ming Kuan, Tatsushi Oka, the editor Esfandiar Maasoumi, an anonymous referee, and the participants at the 10th International Symposium on Econometric Theory and Applications for helpful comments and suggestions. All errors and omissions are our responsibility.

Notes

1 See Imbens and Wooldridge (2009) for a comprehensive review.

2 As pointed out by Brinch, Mogstad, and Wiswall (2017), the additive separability between observed and unobserved components in (2.1(2.1) $$\begin{array}{ll}{Y}_1=m_1(X,{\beta }_1)+{ϵ}_1,\hfill & E({ϵ}_1|X)=0,\hfill \\ Y_0=m_0(X,{\beta }_0)+{ϵ}_0,\hfill & E({ϵ}_0|X)=0,\hfill \end{array}$$(2.1) ) is implied by the linear regression of Y on D and X where the treatment indicator D and covariates X are additively separable.

3 Alternatively, one can estimate p(x) parametrically by logit or probit regression similar to Wooldridge (2007).

4 Although the WNLS is not the most efficient estimator among the class of estimators under the conditional moment restriction or Assumption 3.2(i), the focus of this paper is the estimation and inference of the QSTE so we use WNLS here for its simplicity.

5 We set the white–collar dummy equal to one if the respondent’s occupation code belongs to management, business, science, and arts occupations as classified by the 2010 Census occupation codes. The blue–collar dummy equals one if the code belongs to natural resources, construction, maintenance, production, transportation, and material moving occupations.

6 Although prices and religiosity were treated as instruments in Auld (2005), Some authors (e.g., French and Popovici, 2011) argue that religiosity might be correlated with unobserved personal characteristics that directly affect labor market outcomes.

7 Van Ours (2004) used whether started smoking before age 16 as an instrument because his sample includes individuals aged 16 to over 65. We use age 25 as a cutoff because we focus on individuals between the ages of 25 and 65.

8 For the early–smokers, we assume that they do not smoke currently had they not smoked before age 25.

9 We also try different fixed values for continuous variables such as the overall means. The results are similar and are available upon request.

Additional information

Funding

Yu-Chin Hsu gratefully acknowledges the research support from Ministry of Science and Technology of Taiwan (103-2628-H-001-001-MY4 and 107-2410-H-001-034-MY3) and Career Development Award of Academia Sinica, Taiwan.