Optimal selection of the number of control units in kNN algorithm to estimate average treatment effects

TL;DR

This paper introduces a non-parametric method to optimally select the number of control units in kNN for estimating average treatment effects, improving accuracy and confidence interval precision.

Contribution

It proposes a new approach to choose the optimal k in kNN for treatment effect estimation, reducing mean squared error and enhancing confidence interval accuracy.

Findings

The method achieves smaller mean squared errors in simulations.

It produces significantly narrower confidence intervals for ATET.

Application confirms significant effects of 401(k) participation on financial assets.

Abstract

We propose a simple approach to optimally select the number of control units in k nearest neighbors (kNN) algorithm focusing in minimizing the mean squared error for the average treatment effects. Our approach is non-parametric where confidence intervals for the treatment effects were calculated using asymptotic results with bias correction. Simulation exercises show that our approach gets relative small mean squared errors, and a balance between confidence intervals length and type I error. We analyzed the average treatment effects on treated (ATET) of participation in 401(k) plans on accumulated net financial assets confirming significant effects on amount and positive probability of net asset. Our optimal k selection produces significant narrower ATET confidence intervals compared with common practice of using k=1.