Problem with a partialled out constant, after absorbing year and industry

[Lisa Tara Smith]

Hello,

for my thesis I'm doing an IV regression of the effect of executive compensation on company innovation, with panel data.
My instrument for compensation is "predfirst" which is an dummy variable that is 1 if that year is predicted to be a first year of a new compensation cycle and 0 if it is not predicted to be a first year of the cycle and the dependent variable innovation is "xrd_w" which are the R&D costs.
I cluster for gvkey, but my supervisor told me I should also absorb year fixed effects and industry fixed effects.

However, this comes with the problem that my constant drops out. Which resulted in this:

. ivreghdfe xrd_w predfirst if hitech==1, cluster(gvkey) absorb(fyear sic)
(MWFE estimator converged in 4 iterations)

OLS estimation
--------------

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and clustering on gvkey

Number of clusters (gvkey) = 343 Number of obs = 17246
F( 1, 342) = 0.27
Prob > F = 0.6059
Total (centered) SS = 5.40071e+10 Centered R2 = 0.0001
Total (uncentered) SS = 5.40071e+10 Uncentered R2 = 0.0001
Residual SS = 5.40021e+10 Root MSE = 1771

------------------------------------------------------------------------------
| Robust
xrd_w | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
predfirst | 87.91036 170.2476 0.52 0.606 -246.9538 422.7745
------------------------------------------------------------------------------
Included instruments: predfirst
Partialled-out: _cons
nb: total SS, model F and R2s are after partialling-out;
any small-sample adjustments include partialled-out
variables in regressor count K
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
Absorbed FE | Categories - Redundant = Num. Coefs |
-------------+---------------------------------------|
fyear | 15 0 15 |
sic | 15 1 14 |
-----------------------------------------------------+


I really don't understand what is happening. Anyone who could help me out?
Would really appreciate it.

[Joro Kolev]

1. What you are showing does not look like IV syntax. It looks like a standard fixed effects regression.
2. In fixed effect models the constant is wiped out by the fixed effects. The constant that some fixed effects software reports is a fabrication, and one needs to read the manual carefully to figure out how exactly the fabrication is done.

[Lisa Tara Smith]

I'm sorry, I don't think I understand.
What do you mean by the first point?
Since, before I did a regression of the instrument on option compensation to make sure it was significant with:
reghdfe option_value predfirst, cl(gvkey) a(fyear)

and then using this instrument in the IV regression, wouldn't that then make it a IV regression? And not a standard fixed effect regression?

[Joro Kolev]

The syntax for IV regression from the help file of the command you are using looks like this:

     sysuse auto
        ivreghdfe price weight (length=gear), absorb(rep78, tol(1e-6))
        ivreghdfe price weight (length=gear), absorb(rep78, accel(none))

Your command should look like something like this:

ivreghdfe xrd_w (CEOcompensation = predfirst) if hitech==1, cluster(gvkey) absorb(fyear sic)

or

ivreghdfe xrd_w (option_value = predfirst) if hitech==1, cluster(gvkey) absorb(fyear sic)

I'm sorry, I don't think I understand.
What do you mean by the first point?
Since, before I did a regression of the instrument on option compensation to make sure it was significant with:
reghdfe option_value predfirst, cl(gvkey) a(fyear)

and then using this instrument in the IV regression, wouldn't that then make it a IV regression? And not a standard fixed effect regression?

[Lisa Tara Smith]

Thank you so much! I understand now.
However, I still have the same problem with the partialled out constant.

. ivreghdfe xrd_w (option_value=predfirst) revt if hitech==1, a(fyear sic) cluster(gvkey)
(MWFE estimator converged in 4 iterations)

IV (2SLS) estimation
--------------------

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and clustering on gvkey

Number of clusters (gvkey) = 343 Number of obs = 17037
F( 2, 342) = 16.74
Prob > F = 0.0000
Total (centered) SS = 5.37069e+10 Centered R2 = 0.5626
Total (uncentered) SS = 5.37069e+10 Uncentered R2 = 0.5626
Residual SS = 2.34896e+10 Root MSE = 1175

------------------------------------------------------------------------------
| Robust
xrd_w | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
option_value | .0792776 .0535965 1.48 0.140 -.0261427 .184698
revt | .0736379 .0177 4.16 0.000 .0388234 .1084524
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 2.119
Chi-sq(1) P-val = 0.1455
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 144.426
(Kleibergen-Paap rk Wald F statistic): 2.285
Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38
15% maximal IV size 8.96
20% maximal IV size 6.66
25% maximal IV size 5.53
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 0.000
(equation exactly identified)
------------------------------------------------------------------------------
Instrumented: option_value
Included instruments: revt
Excluded instruments: predfirst
Partialled-out: _cons
nb: total SS, model F and R2s are after partialling-out;
any small-sample adjustments include partialled-out
variables in regressor count K
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
Absorbed FE | Categories - Redundant = Num. Coefs |
-------------+---------------------------------------|
fyear | 15 0 15 |
sic | 15 1 14 |
-----------------------------------------------------+

.
end of do-file

Is it because I am not allowed to absorb the sic and fyear, because if I cluster it then it's fine.

[Joro Kolev]

Constants are rarely interesting so I do not see why you pay so much attention to your constant.

But like I told you already in fixed effects models the constant is wiped out by the fixed effects.

1. If you are including the fixed effects through a Least Squares Dummy Variable regression, the constant is perfectly collinear with the full set of dummies for the groups. So you need to drop either the constant or one of the dummies.

2. If you are doing the within transformation, the transformation wipes out anything that is constant within the group, and the constant is constant within the group, so the constant gets wiped out.

[Jeff Wooldridge]

I suspect part of the confusion about the constant using FE methods -- whether based on OLS or IV -- is that the built-in Stata commands for panel data, xtreg and xtivreg, actually report a "constant." As Joro points out, technically this shouldn't be possible because the within transformation removes all time-constant variables -- with the constant being the most obvious. I often forget to mention this in my teaching because I read right past it when I'm looking at FE output.

But the question is: What is Stata reporting? It's actually reporting the average of the estimated "fixed effects" across the cross-sectional units. If you call the unit-specific effects alpha(i), it is averaging the alphahat(i) across i. If you want to see that constant -- and if you want to be convinced that nothing interesting changes -- you can try this:

xtset sic
xtivreg xrd_w (option_value = predfirst) revt i.fyear if hitech==1, fe vce(cluster gvkey)

You will see a "constant" reported along with the other coefficients. But, again, I want to emphasize that it has no real use. And I recommend against reporting it in any output that goes into a dissertation or research paper.