I am running a triple differences linear probability regression, where I am evaluating the effects of a state-level insurance policy change (i.policy -- ie, the treated group), that could have been implemented anytime after 2010 (i.post -- i.e., TWFE not DID/DDD), that we are theorizing had differential effects on two different age-groups of people (i.age). Our outcome is binary (i.screened -- i.e.,screened for cancer). We have a large national data set.
My objective is to get not only the "DDD" coefficient, but also the predicted screening rates for the each of the two age groups both pre- and post- the policy change in treated vs control states, however I am both confused as to the proper margins command to be using and also confused about margins output I am getting.
The regression I am using is:
Code:
reghdfe screen i.age##i.post#i.policy ib2.RACE i.EDUC, absorb(state year) vce(cluster state) pool(1)
(MWFE estimator converged in 4 iterations)
note: 1.age#1.post omitted because of collinearity
note: 1.post#0b.policy omitted because of collinearity
note: 1.post#1.policy omitted because of collinearity
HDFE Linear regression Number of obs = 9,130,961
Absorbing 2 HDFE groups F( 11, 36) = 214.87
Statistics robust to heteroskedasticity Prob > F = 0.0000
R-squared = 0.0329
Adj R-squared = 0.0329
Within R-sq. = 0.0111
Number of clusters (state_num) = 37 Root MSE = 0.4595
(Std. Err. adjusted for 37 clusters in state_num)
---------------------------------------------------------------------------------------------
| Robust
screen | Coef. Std. Err. t P>|t| [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
age#policy |
younger#1 | -.0208939 .0221751 -0.94 0.352 -.065867 .0240792
older#0 | .0778104 .0140845 5.52 0.000 .0492457 .1063752
older#1 | 0 (omitted)
|
post#policy |
0 1 | .0101914 .00729 1.40 0.171 -.0045934 .0249762
1 0 | 0 (omitted)
1 1 | 0 (omitted)
|
age#post#policy |
older#1#0 | -.0032618 .0067761 -0.48 0.633 -.0170043 .0104808
older#1#1 | .0129391 .007872 1.64 0.109 -.003026 .0289041
|
RACE |
Hispanic | .018485 .0070756 2.61 0.013 .0041351 .032835
Black, NH | .0871647 .007065 12.34 0.000 .0728363 .1014932
Asian, NH | .0334286 .0105761 3.16 0.003 .0119793 .0548778
|
EDUCATION |
HS | -.0457087 .0028512 -16.03 0.000 -.0514911 -.0399263
Some Col | -.0610266 .0045289 -13.47 0.000 -.0702116 -.0518415
Bach/Grad | -.0554348 .0064723 -8.56 0.000 -.0685612 -.0423083
|
_cons | .2794276 .0089781 31.12 0.000 .2612192 .297636
---------------------------------------------------------------------------------------------
Absorbed degrees of freedom:
-----------------------------------------------------+
Absorbed FE | Categories - Redundant = Num. Coefs |
-------------+---------------------------------------|
state_num | 37 37 0 *|
year | 9 1 8 |
-----------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computationCode:
margins i.age##i.post##policy, atmeans noestimcheck
Adjusted predictions Number of obs = 9,130,961
Model VCE : Robust
Expression : Linear prediction, predict()
at : 0.age = .681696 (mean)
1.age = .318304 (mean)
0.policy = .4287486 (mean)
1.policy = .5712514 (mean)
0.post = .4573222 (mean)
1.post = .5426778 (mean)
1.RACE = .393269 (mean)
2.RACE = .4001108 (mean)
3.RACE = .1699526 (mean)
4.RACE = .0366676 (mean)
2.EDUCATION = .3711704 (mean)
3.EDUCATION = .3085791 (mean)
4.EDUCATION = .1976261 (mean)
5.EDUCATION = .0968208 (mean)
---------------------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
age |
younger | .3067197 .0035853 85.55 0.000 .2996927 .3137467
older | .3552687 .0073577 48.29 0.000 .3408478 .3696897
|
post |
0 | .3242972 .0025805 125.67 0.000 .3192396 .3293549
1 | .320383 .0023248 137.81 0.000 .3158265 .3249395
|
age#post |
younger#0 | .3098791 .0040138 77.20 0.000 .3020122 .317746
younger#1 | .3040572 .0042475 71.59 0.000 .2957324 .3123821
older#0 | .3551759 .0100741 35.26 0.000 .335431 .3749208
older#1 | .355347 .0063635 55.84 0.000 .3428747 .3678193
|
policy |
0 | .3401969 .008783 38.73 0.000 .3229825 .3574113
1 | .3086454 .0067858 45.48 0.000 .2953455 .3219453
|
age#policy |
younger#0 | .3159929 .009111 34.68 0.000 .2981357 .3338502
younger#1 | .2997598 .0126543 23.69 0.000 .2749578 .3245617
older#0 | .3920333 .0121487 32.27 0.000 .3682222 .4158443
older#1 | .3276754 .0072428 45.24 0.000 .3134799 .3418709
|
post#policy |
0 0 | .3407603 .0089327 38.15 0.000 .3232524 .3582681
0 1 | .311941 .007286 42.81 0.000 .2976608 .3262213
1 0 | .3397221 .0087769 38.71 0.000 .3225197 .3569244
1 1 | .3058682 .0085404 35.81 0.000 .2891293 .322607
|
age#post#policy |
younger#0#0 | .3159929 .009111 34.68 0.000 .2981357 .3338502
younger#0#1 | .3052904 .0128555 23.75 0.000 .2800941 .3304868
younger#1#0 | .3159929 .009111 34.68 0.000 .2981357 .3338502
younger#1#1 | .295099 .0134205 21.99 0.000 .2687954 .3214026
older#0#0 | .3938034 .0144269 27.30 0.000 .3655271 .4220796
older#0#1 | .3261843 .0121676 26.81 0.000 .3023363 .3500323
older#1#0 | .3905416 .0108428 36.02 0.000 .36929 .4117931
older#1#1 | .328932 .0065028 50.58 0.000 .3161868 .3416772
---------------------------------------------------------------------------------------------(1) Is it ok to be using -noestimcheck in this case?
(2) If it is (or regardless), why am I getting identical predictions for younger#0 (ie, younger age group, in non-treated states) as for the triple interaction predictions of younger#0#0 (ie, younger, pre-policy, in non-treated states) and younger#1#0 (ie, younger, post-policy, non-treated states)? I guess I was expecting that even if my regession coefficients were not statistically significant (which the DDD coefficient is not), these numbers still shouldn't be exactly the same.
(3) Am I using the corrent margins command? It confuses me that Stata puts up all the "at" means of all of the variables, when (I think) I am asking it to evaluate the predicted probabilities at specific values of variables (or at least my 3 interaction variables).
I have read a lot on this listserv and other places, but still couldn't answer these questions -- any insights greatly appreciated!
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