Optimal treatment assignment of a threshold-based policy: empirical protocol and related issues

ABSTRACT

In the footsteps of the recent literature on empirical welfare maximization, this article wants to contribute by stressing the policy-maker empirical perspective and related issues arising when carrying out optimal policy assignment in practice. By focusing on the class of threshold-based policies, we first set out the theoretical underpinnings of the policy-maker selection problem, to then offer a solution to this via an implementation protocol applied to the popular LaLonde training programme database. This article traces a general application procedure and discusses, in particular, problems of angle solution typically arising in real applications of optimal policy assignment.

KEYWORDS:

• Policy learning
• optimal treatment
• programme evaluation
• threshold-based assignment rule

JEL CLASSIFICATION:

• C53
• C63
• C61

Acknowledgments

I would like to thank prof. Charles Manski for the careful reading of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Notes

¹ For brevity, we directly consider the sample counterparts of the population parameters.

² The authors have programmed a Stata 17 routine for for this purpose. All codes are available upon request.

³ This is an estimate of the so-called Bayesian decision boundary as defined by supervised learning classification models (Gareth et al. 2013). In our case, this boundary should be closer to the boundary of the upper-right quadrant. Yet, it is smoother and imprecise due to the high sparseness (few observations) located in this quadrant, with the largest part of individuals placed in the lower-left quadrant.

⁴ The choice of varying the threshold of education by letting age fixed to its optimal threshold is dictated by education monotonicity as discussed above. It goes without saying that one might do the opposite as well.