Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-26T11:48:47.853Z Has data issue: true hasContentIssue false
  • English
  • Français

WELFARE ANALYSIS VIA MARGINAL TREATMENT EFFECTS

Published online by Cambridge University Press:  16 September 2024

Yuya Sasaki  and
Takuya Ura
Yuya Sasaki
Affiliation:
Vanderbilt University
Takuya Ura*
Affiliation:
University of California, Davis
*
Address correspondence to Takuya Ura, Department of Economics, University of California, Davis, One Shields Avenue, Davis, CA 95616, USA; e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider a causal structure with endogeneity, i.e., unobserved confoundedness, where an instrumental variable is available. In this setting, we show that the mean social welfare function can be identified and represented via the marginal treatment effect as the operator kernel. This representation result can be applied to a variety of statistical decision rules for treatment choice, including plug-in rules, Bayes rules, and empirical welfare maximization rules. Focusing on the application of the empirical welfare maximization framework, we provide convergence rates of the worst-case average welfare loss (regret).

Type
ARTICLES
Information
Econometric Theory , First View , pp. 1 - 24
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Footnotes

We thank Toru Kitagawa, Simon Lee, two anonymous referees, and the seminar participants at LMU Munich for their very useful comments. The usual disclaimers apply. Sasaki thanks Brian and Charlotte Grove Chair for research support.

References

REFERENCES

Abadie, A., Angrist, J., & Imbens, G. (2002). Instrumental variables estimates of the effect of subsidized training on the quantiles of trainee earnings. Econometrica , 70, 91–117.Google Scholar
Armstrong, T., & Shen, S. (2015). Inference on optimal treatment assignments [Working paper].Google Scholar
Athey, S., & Wager, S. (2021). Policy learning with observational data. Econometrica , 89, 133–161.Google Scholar
Bhattacharya, D. (2009). Inferring optimal peer assignment from experimental data. Journal of the American Statistical Association , 104, 486–500.Google Scholar
Bhattacharya, D. (2013). Evaluating treatment protocols using data combination. Journal of Econometrics , 173, 160–174.Google Scholar
Bhattacharya, D., & Dupas, P. (2012). Inferring welfare maximizing treatment assignment under budget constraints. Journal of Econometrics , 167, 168–196.Google Scholar
Björklund, A., & Moffitt, R. (1987). The estimation of wage gains and welfare gains in self-selection models. The Review of Economics and Statistics , 69, 42–49.Google Scholar
Bloom, H. S., Orr, L. L., Bell, S. H., Cave, G., Doolittle, F., Lin, W., & Bos, J. M. (1997). The benefits and costs of JTPA Title II-A programs: Key findings from the National Job Training Partnership Act study. Journal of Human Resources , 32, 549–576.Google Scholar
Brinch, C. N., Mogstad, M., & Wiswall, M. (2017). Beyond LATE with a discrete instrument. Journal of Political Economy , 125, 985–1039.Google Scholar
Byambadalai, U. (2021). Identification and inference for welfare gains without unconfoundedness [Working paper].Google Scholar
Carneiro, P., Heckman, J. J., & Vytlacil, E. (2010). Evaluating marginal policy changes and the average effect of treatment for individuals at the margin. Econometrica , 78, 377–394.Google Scholar
Carneiro, P., & Lee, S. (2009). Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality. Journal of Econometrics , 149, 191–208.Google Scholar
Carneiro, P., Lokshin, M., & Umapathi, N. (2017). Average and marginal returns to upper secondary schooling in Indonesia. Journal of Applied Econometrics , 32, 16–36.Google Scholar
Chamberlain, G. (2011). Bayesian aspects of treatment choice. In Geweke, J., Koop, G., & Dijk, V. H. (Eds.), The Oxford handbook of Bayesian econometrics (pp. 11–39). Oxford University Press.Google Scholar
Cornelissen, T., Dustmann, C., Raute, A., & Schönberg, U. (2016). From LATE to MTE: Alternative methods for the evaluation of policy interventions. Labour Economics , 41, 47–60.Google Scholar
Cui, Y., & Tchetgen Tchetgen, E. (2020). A semiparametric instrumental variable approach to optimal treatment regimes under endogeneity. Journal of the American Statistical Association , 116, 162–173.Google Scholar
Dehejia, R. H. (2005). Program evaluation as a decision problem. Journal of Econometrics , 125, 141–173.Google Scholar
French, E., & Song, J. (2014). The effect of disability insurance receipt on labor supply. American Economic Journal: Economic Policy , 6, 291–337.Google Scholar
Han, S. (2023). Optimal dynamic treatment regimes and partial welfare ordering. Journal of the American Statistical Association , (forthcoming).Google Scholar
Han, S. (2020). Comment: Individualized treatment rules under endogeneity. Journal of the American Statistical Association , 116, 192–195.Google Scholar
Heckman, J. J., Ichimura, H., & Todd, P. E. (1997). Matching as an econometric evaluation estimator: Evidence from evaluating a job training programme. Review of Economic Studies , 64, 605–654.Google Scholar
Heckman, J. J., & Vytlacil, E. (1999). Local instrumental variables and latent variable models for identifying and bounding treatment effects. Proceedings of the National Academy of Sciences , 96, 4730–4734.Google Scholar
Heckman, J. J., & Vytlacil, E. (2001). Policy-relevant treatment effects. American Economic Review , 91, 107–111.Google Scholar
Heckman, J. J., & Vytlacil, E. (2005). Structural equations, treatment effects, and econometric policy evaluation. Econometrica , 73, 669–738.Google Scholar
Heckman, J. J., & Vytlacil, E. (2007). Econometric evaluation of social programs, part II: Using the marginal treatment effect to organize alternative econometric estimators to evaluate social programs, and to forecast their effects in new environments. In Heckman, J. J., & Leamer, E. E., Handbook of econometrics (Vol. 6, Chapter 71, pp. 4875–5143). Elsevier.Google Scholar
Hirano, K., & Porter, J. R. (2009). Asymptotics for statistical treatment rules. Econometrica , 77, 1683–1701.Google Scholar
Hirano, K., & Porter, J. R. (2020). Asymptotic analysis of statistical decision rules in econometrics. In Handbook of econometrics (Vol. 7, pp. 283–354). Elsevier.Google Scholar
Kallus, N., & Zhou, A. (2018). Confounding-robust policy improvement. Advances in Neural Information Processing Systems , 31.Google Scholar
Kitagawa, T., & Tetenov, A. (2018). Who should be treated? Empirical welfare maximization methods for treatment choice. Econometrica , 86, 591–616.Google Scholar
Kitagawa, T., & Tetenov, A. (2021). Equality-minded treatment choice. Journal of Business & Economic Statistics , 39, 561–574.Google Scholar
Kock, A. B., & Thyrsgaard, M. (2017). Optimal sequential treatment allocation [Working paper].Google Scholar
Lee, S., & Salanié, B. (2018). Identifying effects of multivalued treatments. Econometrica , 86, 1939–1963.Google Scholar
Liu, Y. (2022). Policy learning under endogeneity using instrumental variables. Preprint. arXiv:2206.09883.Google Scholar
Manski, C. F. (2004). Statistical treatment rules for heterogeneous populations. Econometrica , 72, 1221–1246.Google Scholar
Manski, C. F. (2009). Identification for prediction and decision . Harvard University Press.Google Scholar
Mbakop, E., & Tabord-Meehan, M. (2021). Model selection for treatment choice: Penalized welfare maximization. Econometrica , 89, 825–848.Google Scholar
Moffitt, R. (2008). Estimating marginal treatment effects in heterogeneous populations. Annales d’Economie et de Statistique , 91 /92, 239–261.Google Scholar
Mogstad, M., Santos, A., & Torgovitsky, A. (2018). Using instrumental variables for inference about policy relevant treatment parameters. Econometrica , 86, 1589–1619.Google Scholar
Qiu, H., Carone, M., Sadikova, E., Petukhova, M., Kessler, R. C., & Luedtke, A. (2020). Optimal individualized decision rules using instrumental variable methods. Journal of the American Statistical Association , 116, 174–191.Google Scholar
Rai, Y. (2018). Statistical inference for treatment assignment policies [Working paper].Google Scholar
Sakaguchi, S. (2021). Estimating optimal dynamic treatment assignment rules under intertemporal budget constraints [Working paper].Google Scholar
Sasaki, Y., & Ura, T. (2023). Estimation and inference for policy relevant treatment effects. Journal of Econometrics , 234, 394–450.Google Scholar
Schlag, K. H. (2007). Eleven% designing randomized experiments under minimax regret [Working paper].Google Scholar
Stoye, J. (2009). Minimax regret treatment choice with finite samples. Journal of Econometrics , 151, 70–81.Google Scholar
Stoye, J. (2012). Minimax regret treatment choice with covariates or with limited validity of experiments. Journal of Econometrics , 166, 138–156.Google Scholar
Sun, L. (2020). Empirical welfare maximization with constraints [Working paper].Google Scholar
Tetenov, A. (2012). Statistical treatment choice based on asymmetric minimax regret criteria. Journal of Econometrics , 166, 157–165.Google Scholar
Viviano, D. (2019). Policy targeting under network interference [Working paper].Google Scholar
Viviano, D. (2022). Policy design in experiments with unknown interference [Working paper].Google Scholar