IV with interaction gone wrong

[Nicole Kashani]

Hi,

I have the following specification:

ivreg2 grades (treatment treatment#exchange = lottery lottery#exchange) exchange, r

grades is my outcome. Variable treatment is the endogenous variable and I use variable lottery as an IV for treatment. I want to see the full interaction effects for "exchange" students, so I decided to interact treatment with exchange and instrument it with lottery*exchange.

I get no results for 1.treatment#1.exchange, it is missing. I get a ranktest error that may be caused by collinearity.
I don't understand this. Have I done something wrong?

[Jeff Wooldridge]

I've always had trouble with this. To force Stata to give the effect you want:

gen treat_exch = treatment*exchange
gen lott_exch = lottery*exchange
ivreg2 grades (treatment treat_exch = lottery lott_exch) exchange, r

[Nicole Kashani]

I've always had trouble with this. To force Stata to give the effect you want:

gen treat_exch = treatment*exchange
gen lott_exch = lottery*exchange
ivreg2 grades (treatment treat_exch = lottery lott_exch) exchange, r

Thank you so much, Professor!

[Andrew Musau]

I've always had trouble with this. To force Stata to give the effect you want:

gen treat_exch = treatment*exchange
gen lott_exch = lottery*exchange
ivreg2 grades (treatment treat_exch = lottery lott_exch) exchange, r

This is the same as assuming the variables are continuous. By default, Stata assumes variables without prefixes constituting an interaction are categorical.

ivreg2 grades (treatment c.treat#c.exch = lottery c.lott#c.exch) exchange, r

[Jeff Wooldridge]

Andrew: Do you know why Stata can't figure out that three of the four terms are irrelevant even if it treats the variables as categorical? It just seems messy to me.

[Andrew Musau]

I find that this happens if you specify the main effects and interactions separately. I assume this is a feature of factor variables. However, if you specify the full set, the redundant interactions are dropped. Consider:

sysuse auto, clear
qui sum length, d
gen longcar= length > r(p50)

* SEPARATE MAIN EFFECTS AND INTERACTIONS
regress mpg foreign foreign#longcar longcar, robust

*SPECIFY MAIN EFFECTS AND INTERACTIONS TOGETHER
regress mpg foreign##longcar, robust

Res.:

. 
. * SEPARATE MAIN EFFECTS AND INTERACTIONS

. 
. regress mpg foreign foreign#longcar longcar, robust
note: 1.foreign#0b.longcar omitted because of collinearity.
note: 1.foreign#1.longcar omitted because of collinearity.

Linear regression                               Number of obs     =         74
                                                F(2, 70)          =          .
                                                Prob > F          =          .
                                                R-squared         =     0.4462
                                                Root MSE          =     4.3969

---------------------------------------------------------------------------------
                |               Robust
            mpg | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
----------------+----------------------------------------------------------------
        foreign |   .0178571   1.757307     0.01   0.992    -3.486981    3.522695
                |
foreign#longcar |
    Domestic#1  |   .4900794   1.813721     0.27   0.788    -3.127272    4.107431
     Foreign#0  |          0  (omitted)
     Foreign#1  |          0  (omitted)
                |
        longcar |  -8.142857   1.431271    -5.69   0.000    -10.99744   -5.288278
          _cons |     25.125   1.019604    24.64   0.000     23.09146    27.15854
---------------------------------------------------------------------------------

. 
. 
. 
. *SPECIFY MAIN EFFECTS AND INTERACTIONS TOGETHER

. 
. regress mpg foreign##longcar, robust

Linear regression                               Number of obs     =         74
                                                F(2, 70)          =          .
                                                Prob > F          =          .
                                                R-squared         =     0.4462
                                                Root MSE          =     4.3969

---------------------------------------------------------------------------------
                |               Robust
            mpg | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
----------------+----------------------------------------------------------------
        foreign |
       Foreign  |   .0178571   1.757307     0.01   0.992    -3.486981    3.522695
      1.longcar |  -7.652778   1.114023    -6.87   0.000    -9.874626   -5.430929
                |
foreign#longcar |
     Foreign#1  |  -.4900794   1.813721    -0.27   0.788    -4.107431    3.127272
                |
          _cons |     25.125   1.019604    24.64   0.000     23.09146    27.15854
---------------------------------------------------------------------------------

.

[Nicole Kashani]

This is the same as assuming the variables are continuous. By default, Stata assumes variables without prefixes constituting an interaction are categorical.

ivreg2 grades (treatment c.treat#c.exch = lottery c.lott#c.exch) exchange, r

My variables are not continuous though. How should I deal with that? If I put i. prefix, I get the error that I don't have enough instruments for identification.

[Andrew Musau]

Can you show the results of

tab treat
tab exchange
tab lottery

?

For 0/1 indicators, treating them as binary or continuous does not change the results.

If I put i. prefix, I get the error that I don't have enough instruments for identification

Note that my suggestion was to prefix the variables with "c." to replicate Jeff's suggestion, not "i.".