Using post-estimation command test for weak instrument testing in the first stage

[james xu]

Dear colleagues,
I'm conducting a 2SLS regression analysis. Because of the specialness of my data, I cannot directly use the command like ivreg2, ivreghdfe. Instead, I regress the endogenous variable on my instrument and then predict the fitted value. Then regress my dependent variable on my fitted value with other control variables. I am wondering that in estimating the F-statistics of my instrument in the first stage, can I use the command

reg endog_var instrument control_var
test instrument

I understand that in my scenario, I only have one instrumental variable so the F-statistics would simply be the square of my T-statistics. My question is that in my output below, when the joint F-statistics of all my regressors are just 8 but the Wald test on my instrument is well above 10, do I need to worry about the weak instrument?

 reghdfe endog_var instrument control_1 control_2 ,a(state year) cluster(year)
(MWFE estimator converged in 5 iterations)

HDFE Linear regression                            Number of obs   =        996
Absorbing 2 HDFE groups                           F(   3,     20) =       8.62
Statistics robust to heteroskedasticity           Prob > F        =     0.0007
                                                  R-squared       =     0.9440
                                                  Adj R-squared   =     0.9397
                                                  Within R-sq.    =     0.0319
Number of clusters (year)    =         21         Root MSE        =     0.0695

                                  (Std. err. adjusted for 21 clusters in year)
------------------------------------------------------------------------------
             |               Robust
  endog_var | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  instrument |    .050349   .0105729     4.76   0.000     .0282944    .0724037
    control_1 |  -.0013304   .0208834    -0.06   0.950    -.0448923    .0422316
    control_2 |   .0001265   .0000605     2.09   0.050     2.70e-07    .0002527
         _cons |   .5053363    .242177     2.09   0.050      .000164    1.010509
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
        state |        49           1          48     |
        year |        21          21           0    *|
-----------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

. test instrument

 ( 1)  instrument = 0

       F(  1,    20) =   22.68
            Prob > F =    0.0001

Thank you in advance for any help!

[Maxence Morlet]

Out of curiosity, why can you not use ivreghdfe (from the SSC repository) or ivreg2?

[james xu]

Out of curiosity, why can you not use ivreghdfe (from the SSC repository) or ivreg2?

Thanks for your reply Maxence! I don't (or I can't) implement ivreghdfe or ivreg2 is because my instrument is at state-year level whereas my dependent variable in my second stage is at firm-state-year level. Plus, I have some additional controls that are at firm-year level that I don't want them to be in my first stage. When I tried using ivreghdfe , it seems the same set of controls is included in both stages by default.

Please correct me if I could actually get around this issue. Much appreciated!