Diff in diff with IV for treatment dummy

[Sophia Magis]

Hi all,

For my data analysis, I am estimating a difference-in-difference model of the sort

 Y = a + bPOST + cTREAT + dPOST##TREAT +eCONTROLS + u

Since I am concerned with the endogeneity of my treatment variable TREAT, I would like to employ an IV strategy, in line with the relevant literature.

However, I am not sure how to run the IV regression in Stata, given that TREAT is part of an interaction term. I do not think the following code gives me the correct result:

 ivreg 2sls Y POST (TREAT = Z1)  POST##TREAT CONTROLS

What is the right way of going about this?
Many thanks in advance.

Best,
Sophia

[Sophia Magis]

Please do let me know if you require any more information to be able to answer the question.

[Dimitriy V. Masterov]

Try this:

ivregress 2sls y post (i.treat i.treat#i.post = z) x

I am not sure if this is completely valid econometrically, but it does what you ask.

[Sophia Magis]

Thank you, Dimitriy. Indeed, this code gives me the error

equation not identified; must have at least as many instruments not in
the regression as there are instrumented variables

Do I understand right that you are suggesting it does not make sense econometrically to use an IV for a treatment variable in a diff-in-diff setting? Could you please explain why? Thanks a lot!

[Dimitriy V. Masterov]

You will need additional instruments since you have two endogenous variables. One common approach is this:

. use http://fmwww.bc.edu/repec/bocode/c/CardKrueger1994.dta
(Dataset from Card&Krueger (1994))

. ivregress 2sls fte i.t (i.treated#i.t = bk bk#i.t)
note: 1.bk#1.t omitted because of collinearity

Instrumental variables (2SLS) regression          Number of obs   =        801
                                                  Wald chi2(3)    =       0.60
                                                  Prob > chi2     =     0.8965
                                                  R-squared       =          .
                                                  Root MSE        =     80.642

------------------------------------------------------------------------------
         fte |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   treated#t |
       NJ#0  |  -225.4102    454.179    -0.50   0.620    -1115.585    664.7642
       NJ#1  |  -180.7203   303.9624    -0.59   0.552    -776.4758    415.0351
             |
         1.t |   -36.2768   440.8818    -0.08   0.934    -900.3893    827.8357
       _cons |   199.5123   366.5129     0.54   0.586    -518.8398    917.8644
------------------------------------------------------------------------------
Instrumented:  1.treated#0b.t 1.treated#1.t
Instruments:   1.t bk 1.bk#0b.t

But I am not sure if this is strictly valid since I know nothing about your empirical setting and what kind of endogeneity problem you have.

You should probably think about adjusting your standard errors for clustering as well.

[Sophia Magis]

Thank you so much Dimitriy, and apologies for the delayed reply. I managed to reproduce the code in my data, and it works. However, I would also need 1.treated to be included in the regression output (in my case 1.user) - any suggestions on how to achieve that? Many thanks!

. ivregress 2sls lneducexp i.shock (  i.user#i.shock= c.agdist c.agdist#i.shock), vce(cl
> uster hhid)

Instrumental variables (2SLS) regression          Number of obs   =        595
                                                  Wald chi2(3)    =       4.90
                                                  Prob > chi2     =     0.1794
                                                  R-squared       =          .
                                                  Root MSE        =     1.9605

                                    (Std. Err. adjusted for 427 clusters in hhid)
---------------------------------------------------------------------------------
                |               Robust
      lneducexp |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
user#shock |
           1 0  |   .8662527   .8800556     0.98   0.325    -.8586246     2.59113
           1 1  |   4.418828    9.02754     0.49   0.624    -13.27483    22.11248
                 |
      1.shock  |  -1.907025   3.920626    -0.49   0.627    -9.591311     5.77726
        _cons |   7.902556   .4587876    17.22   0.000     7.003349    8.801763
---------------------------------------------------------------------------------
Instrumented:  1.user#0b.shock 1.user#1.shock
Instruments:   1.shock agdist 1.shock#c.agdist

[Dimitriy V. Masterov]

I don't understand how your model above relates to the equation in your original question. But, presumably, you need to include i.user in your specification if you want to see the coefficient.

[Sophia Magis]

Let me try again, sorry if I wasn't really clear so far.

So basically, I estimate the most basic form of my model via:

reg lneducexp i.shock##i.user, vce(cluster hhid)

This is basically a DID setup. That is, I analyse whether mobile money users' education expenditure is more resistant to exogenous illness shocks compared to non-users. I.e. I analyse whether in the event of a shock mobile money users can smooth consumption better than non-users.

However, the decision to become a mobile money user is by no means random, but rather depends on several observable and unobservable factors. I would thus like to use distance to the nearest mobile money agent -c.agdist- as an IV for i.user (which is a common instrument in the literature). The reason I was confused how to implement this in Stata is that i.user is part of an interaction term in my model. In my IV regression output, I would need the coefficients for i.user, i.shock and 1.user#1.shock.
Hope this makes more sense now!

[Jeff Wooldridge]

Sophia: This is where the Stata factor notation can be confusing. I would do the following, essentially what Dimitriy suggested. I prefer using "c." in these situations so I don't get extra (dropped) interactions.

ivregress 2sls lneducexp c.shock (c.user c.shock#c.user = c.agdist c.shock#c.agdist), vce(cluster id)

JW

[Sophia Magis]

Thank you very much, Mr. Wooldridge, this works and is exactly what I was looking for.

[Nicolas Orgeira]

Hi Jeff Wooldridge,

Thank you for providing the code for the Wald-DID. I'm trying to replicate it to estimate the local average treatment effect from my generalized DID:

 
 svy: regress OUTCOMEVAR i.time##i.intervention

using the following code:

 
 svy: ivregress 2sls OUTCOMEVAR i.time (i.intervention i.time#i.intervention = i.instrument i.time#i.instrument)

and heterogeneous effects by gender, using the following:

 
 svy: ivregress 2sls OUTCOMEVAR i.time i.female i.time#i.female (i.intervention i.intervention#i.female i.time#i.intervention i.time#i.intervention#i.female = i.instrument i.instrument#i.female i.time#i.instrument i.time#i.instrument#i.female)

where time (pre/post), intervention (0=Control, 1=Treatment 1, 2=Treatment 2) and instrument (indicating whether the treatment was actually administered for non-attriters, 0 "Control" 1 ="Treatment 1", 2="Treatment 2") are categorical variables.

At first, the basic ivregress code was working perfectly fine until I noticed I made a small error when generating the variable instrument. After correcting it, I keep getting the following message: "instrumental variable equation not identified; must have at least as many instruments not in the regression as there are instrumented variables", despite not having changed the code. I have gone over your very informative books (Introductory Econometrics and Econometric Analysis of Cross Section and Panel data) but I am struggling to implement IV in the DID setting, or understand the issue. I would be very grateful if you could provide me with some guidance.

Please find attached the log file. Apologies for the cross-posting (https://www.statalist.org/forums/for...in-differences).

Thank you

[Nicolas Orgeira]

Hi all,

I've rerun the following code, setting the trace on and comparing the outputs using the "wrong" and "right" instrument".

 
 svy: ivregress 2sls OUTCOMEVAR i.time (i.intervention i.time#i.intervention = i.instrument i.time#i.instrument)

When using the "wrong" instrument, the instrument in the background were:
0b.instrument 1.instrument 3.instrument 0b.time#0b.instrument 0b.time#1o.instrument 0b.time#3o.instrument 1o.time#0b.instrument 1.time#1.instrument 1.time#3.instrument,

as expected. However, when using the "corrected" instrument, only the following were generated:
0b.instrument 1.instrument 0b.time#0b.instrument 0b.time#1o.instrument 0b.time#3o.instrument 1o.time#0b.instrument 1.time#1.instrument,
that is, 3.instrument and 1.time#3.instrument were not included in the background. Would anyone know what the problem could be?


Thank you