Causal inference · Module 3: Getting an answer: study designs

Comparing like with like

What is propensity score matching?

3.2 · 3 min 5 s · published

A propensity score is a unit’s probability of being treated, given everything you measured. In 1983 Paul Rosenbaum and Donald Rubin showed that units with the same score are, on average, balanced on all those characteristics at once. You can match on that one number, or weight by it, so the groups you compare line up on what you measured.

Key points

  • Matching pairs each treated farm with an untreated one that looks the same on what you measured.
  • Always check balance, characteristic by characteristic: if the groups still differ, the estimate can’t be trusted.
  • In India, smallholders using certified seed had paddy yields estimated over 20 per cent higher after matching.
  • Matching balances what you measured, never what you didn’t.

Chapters

  1. 0:00 Recap: clusters
  2. 0:17 Build the comparison
  3. 0:38 One number to match on
  4. 1:20 Check the balance
  5. 1:39 Seed in India

Key terms

Propensity score
A unit’s probability of being treated, given everything measured about it. Paul Rosenbaum and Donald Rubin showed in 1983 that units with the same score are, on average, balanced on all those characteristics at once, so you can match or weight on one number instead of many. It balances only what was measured.
Matching
Building a fair comparison without randomising, by pairing each treated unit with an untreated one that looks the same on everything measured, such as size, soil, rainfall and enterprise. A balance check then confirms the groups line up. Matching balances what you measured, never what you didn’t.
Weighting
An alternative to matching that gives each unit a weight based on its propensity score, so that units which were unlikely to be treated but were count for more. The weighted groups then line up on what was measured. Like matching, weighting can’t balance anything that wasn’t recorded.

Transcript

Last time's quick check: families in a cluster are alike, so each extra cluster adds more information than each extra person. When you can't randomise, you can try to build the comparison randomisation would have given you. Matching pairs each treated farm with an untreated farm that looks the same on everything you measured: size, soil, rainfall, enterprise. Compare the pairs, and the measured differences are taken out of the comparison.

With many characteristics, finding an exact twin is hopeless. In 1983, Paul Rosenbaum and Donald Rubin showed that you don't need one. Work out each farm's propensity score: its probability of being treated, given everything you measured. Farms with the same score are, on average, balanced on all of those characteristics at once.

Match on that one number. Or weight each farm by it instead, so that farms which were unlikely to be treated but were count for more. Either way, the groups you compare line up on what you measured. Then you check. Put the treated and comparison groups side by side, characteristic by characteristic. If they still differ, the matching hasn't worked, and the estimate can't be trusted.

Good studies show this balance check, and it's one of the first things to look for when you read one. In India, a study used the national survey of farm households to compare smallholders using seed from formal sources, such as certified seed, with similar farmers using saved or informal seed.

After propensity-score matching, paddy yields were estimated over 20 per cent higher, arhar, or pigeon pea, nearly 50 per cent higher, and paddy net income 23 per cent higher. But the study's own caution applies to every matched study. Matching balances what you measured. Farmers who seek out certified seed may also be better connected, better informed or better financed. If the survey didn't record that, it's still in the answer.

Whether like-with-like on paper is like-with-like in reality depends on your map, and on what you couldn't measure. That's where Module 2's dashed boxes and the prologue's sensitivity analysis come back in. Next: before and after, with a comparison.

Questions

What can’t matching do?

It can’t balance what you didn’t measure. In the Indian seed study, farmers who seek out certified seed may also be better connected, better informed or better financed. If the survey didn’t record that, it’s still in the answer. That’s where the dashed boxes on a causal map, and sensitivity analysis, come back in.

What is a balance check?

After matching or weighting, you put the treated and comparison groups side by side, characteristic by characteristic. If they still differ, the matching hasn’t worked and the estimate can’t be trusted. Good studies show this check, and it’s one of the first things to look for when you read one.

Sources

  1. Rosenbaum, P.R. and Rubin, D.B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70(1), 41–55. doi:10.1093/biomet/70.1.41
  2. Nandi, S. (2024). Impact of formal seed sources on smallholder farming in India: evidence from NSS survey using propensity score matching. Indian Journal of Agricultural Economics, 79(3), 709–724. doi:10.63040/25827510.2024.03.026

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