Help regarding Max Score Estimator

[Melissa Aliovski]

Hello,
First, I am a student and would really appreciate any help. I am trying to implement a maximum score estimator for a two sided matching model, in the spirit of Fox and applied in Chen et al. 2021. They use CEO-firm interactions. The goal is to model CEO-firm matching and seeing which CEO firm level interactions are significant drivers of the match.
In this setting, the unit of observation is a realized CEO appointment. Markets are defined as CEO appointments occurring in the same industry and year.
I would like to ask whether there is any existing Stata code for a maximum score estimator for this type of two sided matching? Is it possible to do this on Stata?
I think that this slightly different from propensity score matching, as the goal does not seem to be recreating random assignment but to see how they are matched.
Any pointers, code or suggested workflow in Stata would be appreciated .
Thank you!

[Mike Lacy]

You have described your problem in a way that requires idiomatic knowledge within a particular area of economics/business, and that will reduce your chance of getting help quickly. Among other things, your literature citations are not easy to find without insider knowledge (I failed). In this regard, note that advice in the StataList FAQ for new members recommends full citations. If you haven't read that FAQ, that could help you in various ways. That aside: If you post again and describe your data and the matches you want in a more discipline-free way, I think you'll have better luck. I say this because your description sounds to me to have features in common with matching for case-control designs in epidemiology, about which there have been quite a few threads on this list in the past.

[Melissa Aliovski]

Hello,
Thank you very much for your reply. To answer your question: My data consist of observed one to one matches between two types of agents, call them A (CEO) and B (firm). Each agent has observable characteristics. The unit of observation is a realized match between A and B (CEO appointment)..
The data are organized into markets, where a market is defined as all matches occurring within the same group and time period (CEOs appointed within the same industry and same year).
Within each market, matches are assumed to be pairwise stable, in the sense that swapping partners across two observed matches would not increase the joint value created. The estimator is based on inequalities of the form value of observed matches ≥ value of counterfactual swapped matches. The goal is to understand which CEO and firm attributes matter jointly for their matching. Methodologically, this is done using a maximum score estimator that chooses parameters to maximize the number of pairwise stability inequalities satisfied within each market. The match value is modeled using interaction terms between characteristics of agent A and agent B.
My sample size is about 1000 observed matches, and markets vary in size (usually about 4 observations in a market)
I would like to ask: Is there any existing Stata command that implements a maximum score estimator for this type of two sided matching problem?

Full reference of paper:
Chen, G., Huang, S., Meyer‐Doyle, P., & Mindruta, D. (2021). Generalist versus specialist CEOs and acquisitions: Two‐sided matching and the impact of CEO characteristics on firm outcomes. Strategic Management Journal, 42(6), 1184-1214.
Fox, J. T. (2010). Identification in matching games. Quantitative Economics, 1(2), 203–254