Propensity Score Matching (PSM) Reference

2 Assumptions for treatment to be strongly ignorable (Rosenbaum Rubin 1983) thereby making PSM appropirate:
CIA (Conditional Independence Assump.): Conditional on observables (Xs) outcomes (Ys) are independent of treatment status (T=0 or 1).
 Common Support: For each value of observables (Xs) there is a positive probability of being treated and untreated. In other words observe all levels of X in both groups (treated and untreated).  

Pitfall--Curse of Dimensionality
The more observables the more difficult to find close matches across all Xs-hence need PS to gauge 'closeness'.

Matching Algorithms
Nearest Neighbor Matching
Radius Matching (calipers)
Kernel/local-linear matching (non-par that compares treated with w.avg. all all no treated; weighted by PS proximity.
Suggested test for robustness (Heinrich below)is to try all of them.(?)


Assumption and Spec Tests
For specification of the selection equations follow same rules as one would any other regression.
No great way of testing validity of CIA but can use to institutional knowledge to argue basis.
For common support one can test do an F-test (Hotelling test) on the joint X differences between treated and untreated.


Unobserved Heterogeneity and relaxing CIA
CIA can be somewhat relaxed if use DD on outcome comparisons.  Of course this requires the assumption that if there was selection on non-observables the non-observables be *time invariant*.  If that could strongly be argued then there is a strong case.  (requires panel data too).



PSM References: 
Heinrich, Maffioli, Vazquez, "A Primer for Applying Propensity-Score Matching", IDB Working paper 2010.
Angrist and Pirschke, "Mostly Harmless Econometrics", (Book) 2009.
Rosenbaum's "Observational Studies" (Book), 2002.

King, Gakidou, et al.-LANCET-2009

Title-"Public Policy for the poor? A randomized assessment of the Mexican Universal Health Insurance Programme"

Notes: Assesses Seguro Popular in Mexico.  Applies wedged experimental design (politically robust exp. design). This constituted a paired cluster rand. experiment where clusters pairs were selected from number of eligible clusters selected in accord to institutional constraints (needy clusters essentially).  Narrowed clusters based on closeness and likelihood of compliance (at hh level)-observables matched on did not include outcomes of interested. Used  baseline/endline survey data and main outcome of interest was effect of health expenditures on treated (where treatment were ads and increased public funding). In total 100 selected clusters (50 pairs). They estimate ITT as well as CACE (complier average causal effect:exclude always and never takers). CACE methodology is explained in Angrist, Imbs and Rubin 1996 (ref#18 in paper). ITT was estimated non-parametrically (reference to King 2009; (13)). CACE required assumption "only compliers benefited from [program]". Found no increase in participation but did find decreases in 'catastrophic expenditures (over 30% of hh capacity.  For most part other effects negligible-discuss it may be due to short assement period ~1 year.