Abstract
This paper reviews strategies that allow one to identify the effects of policy interventions on the unconditional or conditional distribution of the outcome of interest. This distinction is irrelevant when one focuses on average treatment effects since identifying assumptions typically do not affect the parameter’s interpretation. Conversely, finding the appropriate answer to a research question on the effects over the distribution requires particular attention in the choice of the identification strategy. Indeed, quantiles of the conditional and unconditional distribution of a random variable carry a different meaning even if identification of both these set of parameters may require conditioning on observed covariates.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Capital letters denote random variables and lower case letters denote realizations.
- 2.
The review will not cover strategies that focus on other objects and may deliver QTEs as by-product such as [8], for instance.
- 3.
In the continuous case δ(τ) represents the change in Y induced by a change in D from d to d +ε when ε is small.
$$\displaystyle{ \delta (\tau ) = \frac{\partial Q_{Y }(\tau \vert d)} {\partial d} \qquad 0 <\tau < 1 }$$(1) - 4.
To the best of my knowledge, [17] is the first to distinguish between total and observed proneness.
- 5.
Under comonotonicity of potential outcomes, the structural quantile function describes the link between potential outcomes.
- 6.
- 7.
This approach can be used when the treatment and instrument are binary, discrete as well as continuous.
- 8.
In the second example, only reforms that increased compulsory schooling for 3 years are considered (i.e. only Greece, Italy and Finland) and the original treatment (years of education) and instrument (years of compulsory schooling) were recoded to binary. Estimates of columns (1)–(4) have been computed by the author using the STATA package ivqte by Froelich and Melly [12], except column (3) for the first example (taken from the article). Estimates in column (1) replicate original results in the papers except that standard errors are now robust to heteroskedasticity; estimates of columns (5)–(8) are taken from [18] for the AAI02 example and obtained using the STATA package ivqreg by Do Wan Kwack available from Christian Hansen’s research page.
- 9.
When endogeneity of training is addressed, point estimates of the returns to training are generally lower in the unconditional distribution with respect to the returns observed holding race, age, education and marital status fixed.
- 10.
In this example, we look at the effect of three more additional years of schooling on wages. Assuming linearity and dividing point estimates reported by three, the results in columns (1)–(3) are fairly consistent with the literature: association is lower than causal effects; causal estimate suggests a return between 10 % and 4 % for each additional year of education.
- 11.
A similar point was made by Powell [16] in his discussion of the analysis of the effect of vouchers on student achievements.
References
Abadie, A.: Semiparametric instrumental variable estimation of treatment response models. J. Econ. 113, 231–263 (2003)
Abadie, A., Angrist, J., Imbens, G.: Instrumental variables estimates of the effect of subsidized training on the quantiles of trainee earnings. Econometrica 70, 91–117 (2002)
Barlevy, G., Neal, D.: Pay for percentile. NBER Working Paper No. 17194 (2010)
Betebenner, D.W.: Norm and criterion-referenced student growth. Educ. Meas. Issues Pract. 28(4), 42–51 (2009)
Brunello, G., Fort, M., Weber, G.: Changes in compulsory schooling, education and the distribution of wages in Europe. Econ. J. 119(536), 516–539 (2009)
Chernozhukov, V., Hansen, C.: An IV model of quantile treatment effects. Econometrica 73, 245–261 (2005)
Chernozhukov, V., Hansen, C.: Instrumental variable quantile regression: a Robust Inference Approach. J. Econ. 142(1), 379–398 (2008)
Chesher, A.: Identification in nonseparable models. Econometrica 71, 1405–1441 (2003)
Doksum, K.: Empirical probability plots and statistical inference for nonlinear models in the two-sample case. Ann. Stat. 2, 267–277 (1974)
Firpo, S.: Efficient semiparametric estimation of quantile treatment effect. Econometrica 75, 259–276 (2007)
Froelich, M., Melly, B.: Unconditional quantile treatment effects under endogeneity. IZA Discussion Papers No. 3288 (2010)
Froelich, M., Melly, B.: Estimation of quantile treatment effects with STATA. Stata J. 10(3), 423–457 (2010)
Imbens, G., Rubin, D.: Estimating the outcome distribution for compliers in instrumental variables models. Rev. Econ. Stud. 64, 555–574 (1997)
Koenker, R., Bassett, G.S.: Regression quantiles. Econometrica 46, 33–50 (1978)
Lehmann, E.H.: Nonparametrics: Statistical Models Based on Ranks. Holden Day, San Francisco (1974)
Powell, D.: Unconditional quantile regression for panel data with exogenous or endogenous treatment variables. RAND Working Paper No. WR-710 (2010)
Powell, D.: Unconditional quantile treatment effects in the presence of covariates. RAND Working Paper No. WR-816 (2010 )
Powell, D.: Unconditional quantile regression for exogenous or endogenous treatment variables. RAND Working Paper No. WR-824 (2011)
Acknowledgements
This paper benefited from comments by E. Rettore, B. Pacini and F. Mealli. Financial support of MIUR- FIRB 2008 project RBFR089QQC-003-J31J10000060001 grant is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Fort, M. (2016). Unconditional and Conditional Quantile Treatment Effect: Identification Strategies and Interpretations. In: Alleva, G., Giommi, A. (eds) Topics in Theoretical and Applied Statistics. Studies in Theoretical and Applied Statistics(). Springer, Cham. https://doi.org/10.1007/978-3-319-27274-0_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-27274-0_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-27272-6
Online ISBN: 978-3-319-27274-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)