nopomatch

This repository contains the command nopomatch for Stata, which estimates the decomposition of a binary treatment using non-parametric matching as described in Nopo (2008). This methodology has often been used to decompose wage gaps and other gaps in outcomes for a binary treatment. In other words, this algorithm is useful to decompose the difference in means between two groups (treated v. control) controlling for covariates, restricting comparisions to the common support. This is what the original paper refers to as the unexplained gap, $\Delta_0$.

The program also decomposes the gap in the explanied component ( $\Delta_X$ ), and the components attributable to differences outside of the common support for treatment and control groups ( $\Delta_F$ and $\Delta_M$).

I worked with this methodology many years ago and made an extension of the offical do-file to allow the user decomposing the difference in means for binary outcomes as well, which the official do-file couldn't do properly. Useful information about this kind of decomposition methods can be found in Fortin et al. (2011), Kline (2011) and Sloczynski (2014).

To install the package and update it the following command can be used in Stata:

net install nopomatch, from (https://raw.githubusercontent.com/cfbalcazar/nopomatch/main/nopomatch/) replace force all

A relevant byproduct of nopomatch is the variable _match, which is produced after running the program on a dataset. This variable containes the non-parametric reweighting of the observations in the common support; i.e., a new set of weights. These weights can be used to perform doubly-robust estimation using the standard regression commants (reg, xtreg, reghdfe, ivreg2, etc.), specifying the matching weights as the weights for the regressions (e.g., including [aw=_match] in the regression command).

Since this is a non-parametric technique, keep in mind that it is subject to the curse of dimensionality; i.e., the size of the common support falls with the number of controls included. It may also be sensitive to the identity of the treatment/control group: if observations in A (B) are designated as the treatment (control) group, the decomposition may give different results in comparison to the results obtained if the observations in B (A) are designated as the treatment (control) group; this occurs as a result of the reweighting.