teffects psmatch做PSM（转载）

http://www.ssc.wisc.edu/sscc/pubs/stata_psmatch.htm

Propensity Score Matching in Stata using teffects

For many years, the standard tool for propensity score matching in Stata has been the psmatch2 command, written by Edwin Leuven and Barbara Sianesi. However, Stata 13 introduced a new teffects command for estimating treatments effects in a variety of ways, including propensity score matching. The teffects psmatch command has one very important advantage over psmatch2: it takes into account the fact that propensity scores are estimated rather than known when calculating standard errors. This often turns out to make a significant difference, and sometimes in surprising ways. We thus strongly recommend switching from psmatch2 to teffects psmatch, and this article will help you make the transition.

An Example of Propensity Score Matching

Run the following command in Stata to load an example data set:

use http://ssc.wisc.edu/sscc/pubs/files/psm

It consists of four variables: a treatment indicator t, covariates x1 and x2, and an outcome y. This is constructed data, and the effect of the treatment is in fact a one unit increase in y. However, the probability of treatment is positively correlated with x1 and x2, and both x1 and x2 are positively correlated with y. Thus simply comparing the mean value of y for the treated and untreated groups badly overestimates the effect of treatment:

ttest y, by(t)

(Regressing y on t, x1, and x2 will give you a pretty good picture of the situation.)

The psmatch2 command will give you a much better estimate of the treatment effect:

psmatch2 t x1 x2, out(y)

You can carry out the same estimation with teffects. The basic syntax of the teffects command when used for propensity score matching is:

teffects psmatch (outcome) (treatmentcovariates)

In this case the basic command would be:

teffects psmatch (y) (t x1 x2)

However, the default behavior of teffects is not the same as psmatch2 so we’ll need to use some options to get the same results. First, psmatch2 by default reports the average treatment effect on the treated (which it refers to as ATT). The teffects command by default reports the average treatment effect (ATE) but will calculate the average treatment effect on the treated (which it refers to as ATET) if given the atet option. Second, psmatch2 by default uses a probit model for the probability of treatment. The teffects command uses a logit model by default, but will use probit if the probit option is applied to the treatment equation. So to run the same model using teffects type:

teffects psmatch (y) (t x1 x2, probit), atet

The average treatment effect on the treated is identical, other than being rounded at a different place. But note that teffects reports a very different standard error (we’ll discuss why that is shortly), plus a Z-statistic, p-value, and 95% confidence interval rather than just a T-statistic.

Running teffects with the default options gives the following:

teffects psmatch (y) (t x1 x2)

This is equivalent to:

psmatch2 t x1 x2, out(y) logit ate

---

Variable     Sample |    Treated     Controls   Difference         S.E.   T-stat

----------------------------±----------------------------------------------------------

y  Unmatched |  1.8910736  -.423243358   2.31431696   .109094342    21.21

ATT |  1.8910736   .930722886   .960350715   .168252917     5.71

ATU |-.423243358   .625587554   1.04883091            .        .

ATE |                           1.01936701            .        .

----------------------------±----------------------------------------------------------

The ATE from this model is very similar to the ATT/ATET from the previous model. But note that psmatch2 is reporting a somewhat different ATT in this model. The teffects command reports the same ATET if asked:

teffects psmatch (y) (t x1 x2), atet

Matching With Multiple Neighbors

By default teffects psmatch matches each observation with one other observation. You can change this with the nneighbor() (or just nn()) option. For example, you could match each observation with its three nearest neighbors with:

teffects psmatch (y) (t x1 x2), nn(3)

Start with a clean slate by typing:

use http://ssc.wisc.edu/sscc/pubs/files/psm, replace

The gen() option tells teffects psmatch to create a new variable (or variables). For each observation, this new variable will contain the number of the observation that observation was matched with. If there are ties or you told teffects psmatch to use multiple neighbors, then gen() will need to create multiple variables. Thus you supply the stem of the variable name, and teffects psmatch will add suffixes as needed.

teffects psmatch (y) (t x1 x2), gen(match)

In this case each observation is only matched with one other, so gen(match) only creates match1. Referring to the example output, the match of observation 1 is observation 467 (which is why those two are listed).

Note that these observation numbers are only valid in the current sort order, so make sure you can recreate that order if needed. If necessary, run:

gen ob=_n

and then:

sort ob

to restore the current sort order.

The predict command with the ps option creates two variables containing the propensity scores, or that observation’s predicted probability of being in either the control group or the treated group:

predict ps0 ps1, ps

Here ps0 is the predicted probability of being in the control group (t=0) and ps1 is the predicted probability of being in the treated group (t=1). Observations 1 and 467 were matched because their propensity scores are very similar.

The po option creates variables containing the potential outcomes for each observation:

predict y0 y1, po

Because observation 1 is in the control group, y0 contains its observed value of y. y1 is the observed value of y for observation 1’s match, observation 467. The propensity score matching estimator assumes that if observation 1 had been in the treated group its value of y would have been that of the observation in the treated group most similar to it (where “similarity” is measured by the difference in their propensity scores).

Observation 467 is in the treated group, so its value for y1 is its observed value of y while its value for y0 is the observed value of y for its match, observation 781.

Running the predict command with no options gives the treatment effect itself:

predict te

The treatment effect is simply the difference between y1 and y0. You could calculate the ATE yourself (but emphatically not its standard error) with:

sum te

and the ATET with:

sum te if t

Regression on the “Matched Sample”

We will discuss how to run regressions on a matched sample because it remains a popular technique, but we cannot recommend it.

psmatch2 makes it easy by creating a _weight variable automatically. For observations in the treated group, _weight is 1. For observations in the control group it is the number of observations from the treated group for which the observation is a match. If the observation is not a match, _weight is missing. _weight thus acts as a frequency weight (fweight) and can be used with Stata’s standard weighting syntax. For example (starting with a clean slate again):

use http://ssc.wisc.edu/sscc/pubs/files/psm, replace

psmatch2 t x1 x2, out(y) logit

reg y x1 x2 t [fweight=_weight]

Observations with a missing value for _weight are omitted from the regression, so it is automatically limited to the matched sample. Again, keep in mind that the standard errors given by the reg command are incorrect because they do not take into account the matching stage.

teffects psmatch does not create a _weight variable, but it is possible to create one based on the match1 variable. Here is example code, with comments:

gen ob=_n //store the observation numbers for future use

save fulldata,replace // save the complete data set

keep if t // keep just the treated group

keep match1 // keep just the match1 variable (the observation numbers of their matches)

bysort match1: gen weight=_N // count how many times each control observation is a match

by match1: keep if _n==1 // keep just one row per control observation

ren match1 ob //rename for merging purposes

merge 1:m ob using fulldata // merge back into the full data

replace weight=1 if t // set weight to 1 for treated observations

The resulting weight variable will be identical to the _weight variable created by psmatch2, as can be verified with:

assert weight==_weight

It is used in the same way and will give exactly the same results:

reg y x1 x2 t [fweight=weight]

Obviously this is a good bit more work than using psmatch2.

Other Methods of Estimating Treatment Effects

While propensity score matching is the most common method of estimating treatment effects at the SSCC, teffects also implements Regression Adjustment (teffects ra), Inverse Probability Weighting (teffects ipw), Augmented Inverse Probability Weighting (teffects aipw), Inverse Probability Weighted Regression Adjustment (teffects ipwra), and Nearest Neighbor Matching (teffects nnmatch). The syntax is similar, though it varies whether you need to specify variables for the outcome model, the treatment model, or both:

teffects ra (y x1 x2) (t)

teffects ipw (y) (t x1 x2)

teffects aipw (y x1 x2) (t x1 x2)

teffects ipwra (y x1 x2) (t x1 x2)

teffects nnmatch (y x1 x2) (t)

Complete Example Code

clear all

use http://www.ssc.wisc.edu/sscc/pubs/files/psm

ttest y, by(t)

reg y x1 x2 t

psmatch2 t x1 x2, out(y)

teffects psmatch (y) (t x1 x2, probit), atet

teffects psmatch (y) (t x1 x2)

psmatch2 t x1 x2, out(y) logit ate

teffects psmatch (y) (t x1 x2), atet

use http://www.ssc.wisc.edu/sscc/pubs/files/psm, replace

teffects psmatch (y) (t x1 x2), gen(match)

predict ps0 ps1, ps

predict y0 y1, po

predict te

l if _n1 | _n467

use http://www.ssc.wisc.edu/sscc/pubs/files/psm, replace

psmatch2 t x1 x2, out(y) logit

reg y x1 x2 t [fweight=_weight]

gen ob=_n

save fulldata,replace

teffects psmatch (y) (t x1 x2), gen(match)

keep if t

keep match1

bysort match1: gen weight=_N

by match1: keep if _n==1

ren match1 ob

merge 1:m ob using fulldata

replace weight=1 if t

assert weight==_weight

reg y x1 x2 t [fweight=weight]

reg y x1 x2 t

teffects ra (y x1 x2) (t)

teffects ipw (y) (t x1 x2)

teffects aipw (y x1 x2) (t x1 x2)

teffects ipwra (y x1 x2) (t x1 x2)

teffects nnmatch (y x1 x2) (t)