ordered-logit Difference in Difference

[Ke Ju]

Hi,

I am using a data similar to Card & Krueger (1994), so allow me to use this as an example.
treated is a dummy variable (treatment group = 1 and control group= 0) ; t is a dummy variable (baseline = 0 and follow-up= 0) ; fte_gt is an ordered multicategorical variable that is assigned the values 0, 1, 2. The higher the better.

. use http://fmwww.bc.edu/repec/bocode/c/CardKrueger1994.dta, clear
. gen fte_gt = 0
. replace fte_gt = 1 if fte >= 15 & fte <= 20
. replace fte_gt = 2 if fte > 20

My question is, in this case, how do I evaluate the effect of the policy (or treatment)?

Kind regards,
Ke Ju

[Jared Greathouse]

I should know how to interpret ordered logit since irk likely be on my comps next fall, but the standard DD interpretation doesn't change. It's still the average difference in the log odds, compared to the reference group, holding constant the predictor covariates.

I'm certain that I messed part of this up, but the story remains the same.

[Ke Ju]

Thanks for your reply Mr. Greathouse.

Do you think the following code is a kind of solution

Dear Mr. Masterov and Mr. Kumar,

Thank you very much for the discussion, one question I have is if my dependent variable is an ordered categorical variable, is there a good solution?
For example, take the following code as an example:

code:

. use http://fmwww.bc.edu/repec/bocode/c/CardKrueger1994.dta, clear
. gen fte_gt = 0
. replace fte_gt = 1 if fte >= 15 & fte <= 20
. replace fte_gt = 2 if fte > 20

. ologit fte_gt i.treated##i.t

Iteration 0: log likelihood = -891.35925
Iteration 1: log likelihood = -888.60219
Iteration 2: log likelihood = -888.60179
Iteration 3: log likelihood = -888.60179

Ordered logistic regression Number of obs = 820
LR chi2(3) = 5.51
Prob > chi2 = 0.1377
Log likelihood = -888.60179 Pseudo R2 = 0.0031

------------------------------------------------------------------------------
fte_gt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
treated |
NJ | -.3304535 .229076 -1.44 0.149 -.7794343 .1185273
1.t | -.0275562 .2911727 -0.09 0.925 -.5982442 .5431318
|
treated#t |
NJ#1 | .3312446 .3249211 1.02 0.308 -.305589 .9680782
-------------+----------------------------------------------------------------
/cut1 | -.5515638 .2081406 -.9595118 -.1436158
/cut2 | .6056132 .2083374 .1972795 1.013947
------------------------------------------------------------------------------


. margins treated#t

Adjusted predictions Number of obs = 820
Model VCE : OIM

1._predict : Pr(fte_gt==0), predict(pr outcome(0))
2._predict : Pr(fte_gt==1), predict(pr outcome(1))
3._predict : Pr(fte_gt==2), predict(pr outcome(2))

------------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------------+----------------------------------------------------------------
_predict#treated#t |
1#PA#0 | .3655017 .0482699 7.57 0.000 .2708944 .460109
1#PA#1 | .3719156 .048834 7.62 0.000 .2762027 .4676285
1#NJ#0 | .4449465 .0258516 17.21 0.000 .3942784 .4956147
1#NJ#1 | .3717308 .0251531 14.78 0.000 .3224316 .4210301
2#PA#0 | .2814378 .0158507 17.76 0.000 .250371 .3125046
2#PA#1 | .2812922 .0158883 17.70 0.000 .2501517 .3124326
2#NJ#0 | .2733579 .0157735 17.33 0.000 .2424425 .3042734
2#NJ#1 | .2812977 .0158378 17.76 0.000 .2502563 .3123392
3#PA#0 | .3530605 .0475861 7.42 0.000 .2597935 .4463275
3#PA#1 | .3467922 .0474462 7.31 0.000 .2537993 .4397851
3#NJ#0 | .2816955 .0221846 12.70 0.000 .2382146 .3251765
3#NJ#1 | .3469714 .024574 14.12 0.000 .2988073 .3951356
------------------------------------------------------------------------------------


. margins r.treated#r.t


Contrasts of adjusted predictions
Model VCE : OIM

1._predict : Pr(fte_gt==0), predict(pr outcome(0))
2._predict : Pr(fte_gt==1), predict(pr outcome(1))
3._predict : Pr(fte_gt==2), predict(pr outcome(2))

----------------------------------------------------------
| df chi2 P>chi2
-----------------------+----------------------------------
treated#t@_predict |
(NJ vs PA) (1 vs 0) 1 | 1 1.09 0.2954
(NJ vs PA) (1 vs 0) 2 | 1 2.72 0.0994
(NJ vs PA) (1 vs 0) 3 | 1 0.96 0.3278
Joint | 2 2.72 0.2573
----------------------------------------------------------

------------------------------------------------------------------------
| Delta-method
| Contrast Std. Err. [95% Conf. Interval]
-----------------------+------------------------------------------------
treated#t@_predict |
(NJ vs PA) (1 vs 0) 1 | -.0796296 .0761059 -.2287944 .0695351
(NJ vs PA) (1 vs 0) 2 | .0080854 .004907 -.0015321 .017703
(NJ vs PA) (1 vs 0) 3 | .0715442 .0731111 -.0717509 .2148394
------------------------------------------------------------------------


. gen tg = treated*t
. ologit fte_gt i.(treated t tg) bk kfc roys

Iteration 0: log likelihood = -891.35925
Iteration 1: log likelihood = -783.15648
Iteration 2: log likelihood = -782.16628
Iteration 3: log likelihood = -782.16161
Iteration 4: log likelihood = -782.1616

Ordered logistic regression Number of obs = 820
LR chi2(6) = 218.40
Prob > chi2 = 0.0000
Log likelihood = -782.1616 Pseudo R2 = 0.1225

------------------------------------------------------------------------------
fte_gt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
treated |
NJ | -.2485957 .2416733 -1.03 0.304 -.7222667 .2250753
1.t | -.0341401 .3056148 -0.11 0.911 -.6331341 .5648538
1.tg | .4041914 .342902 1.18 0.239 -.2678842 1.076267
bk | .221209 .1965724 1.13 0.260 -.1640658 .6064838
kfc | -2.91014 .3010229 -9.67 0.000 -3.500134 -2.320146
roys | -.2896749 .214392 -1.35 0.177 -.7098755 .1305257
-------------+----------------------------------------------------------------
/cut1 | -.9599848 .2655394 -1.480432 -.4395372
/cut2 | .4281474 .2631292 -.0875763 .9438711
------------------------------------------------------------------------------