XTIVREG / XTIVREG2 Interpretation of coefficients

[Felix Hofmann]

Dear Statalists,

I am using secundary data with a panel data structure (6 years of observation). Basically I am interested in the effect of employee share ownership (NUMBERESO), i.e. number of stocks employees purchase from their employer annualy, on employee individual work behavior (NEWIDEA_C), i.e. number of ideas an employee has issued to a corporate idea suggestion scheme per year.

At first I have been running my model (xtreg) with time fixed effects (i.YEAR), robust and clustered Standard Errors. Then I did run xtivreg 2 to test and account for endogeneity using monthly BASE SALARY (BASEFROMSALARYCAT_COLLAGREEM) as an Instrument. I belief that BASE SALARY serves as a good Instrument as it is correlated with employees decision ot purchase ESO (the higher the salary the more likely is ESO purchase) but not related to the dependent variable (NEWIDEA_C).

The results (see below) indicate that BASE SALARY works as an Instrument and that ESO is endogneous.

My first and main question is how I will have to Interpret my coefficients for NUMBERESO (number of stocks purchased per year) and the two interaction terms (ESOxYEAR_LN and ESOxTEAM) when using BASE SALARY (euro-denominated) as an Instrument variable? Is it still possible to Interpret the coefficients like "one raw unit increase in X results in 0.4 raw unit increases of Y"?


My second question is whether it is possible to include time fixed effects in xtivreg or xtivreg2?

Thanks and best regards

Felix

xtivreg2 NEWIDEA_C GENDER AGE FULLTIME DUMMY_FUNCTION_1 DUMMY_FUNCTION_2 DUMMY_LEVEL_1 DUMMY_LEVEL_2 DUMMY_LEVEL_3 SIZE NUMBEROTHER YEAR_LN ES
      > O_REMAININGTEAM (NUMBERESO   ESOxYEAR_LN  ESOxTEAM= BASEFROMSALARYCAT_COLLAGREEM   BASE_COLLAGREEMxYEAR_LN   BASE_COLLAGREEMxTEAM), fe robust
      > cluster(NEWID) endog(NUMBERESO)
      Warning - singleton groups detected.  8784 observation(s) not used.
      Warning - collinearities detected
      Vars dropped:       GENDER
    
      FIXED EFFECTS ESTIMATION
      ------------------------
      Number of groups =    143680                    Obs per group: min =         2
                                                                     avg =       5.4
                                                                     max =         6
      Warning - collinearities detected
      Vars dropped:  GENDER
    
      IV (2SLS) estimation
      --------------------
    
      Estimates efficient for homoskedasticity only
      Statistics robust to heteroskedasticity and clustering on NEWID
    
      Number of clusters (NEWID) =    143680                Number of obs =   772216
                                                            F( 14,143679) =    29.03
                                                            Prob > F      =   0.0000
      Total (centered) SS     =   6884674.65                Centered R2   =  -0.3002
      Total (uncentered) SS   =   6884674.65                Uncentered R2 =  -0.3002
      Residual SS             =  8951365.278                Root MSE      =    3.774
    
      -----------------------------------------------------------------------------------
                        |               Robust
              NEWIDEA_C |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
      ------------------+----------------------------------------------------------------
              NUMBERESO |   .4050563   .0904055     4.48   0.000     .2278647    .5822479
            ESOxYEAR_LN |   .0754752   .0090132     8.37   0.000     .0578098    .0931407
               ESOxTEAM |  -.1803543   .0477385    -3.78   0.000      -.27392   -.0867887
                 GENDER |          0  (omitted)
                    AGE |   .3938983   .1020707     3.86   0.000     .1938434    .5939531
               FULLTIME |  -.0887728   .0571195    -1.55   0.120     -.200725    .0231793
       DUMMY_FUNCTION_1 |  -.1896942   .0772684    -2.46   0.014    -.3411374    -.038251
       DUMMY_FUNCTION_2 |  -.3134369   .0711406    -4.41   0.000      -.45287   -.1740038
          DUMMY_LEVEL_1 |  -.1029985   .1285364    -0.80   0.423    -.3549253    .1489283
          DUMMY_LEVEL_2 |  -.6442772   .1177418    -5.47   0.000    -.8750469   -.4135075
          DUMMY_LEVEL_3 |  -.8376678    .137887    -6.08   0.000    -1.107921   -.5674141
                   SIZE |  -.0008579    .000448    -1.92   0.055    -.0017359    .0000201
            NUMBEROTHER |  -.0006346   .0002529    -2.51   0.012    -.0011303    -.000139
                YEAR_LN |  -1.304807   .2800987    -4.66   0.000     -1.85379   -.7558232
      ESO_REMAININGTEAM |  -.3713397   .1583561    -2.34   0.019    -.6817121   -.0609674
      -----------------------------------------------------------------------------------
      Underidentification test (Kleibergen-Paap rk LM statistic):            143.468
                                                         Chi-sq(1) P-val =    0.0000
      ------------------------------------------------------------------------------
      Weak identification test (Cragg-Donald Wald F statistic):               53.600
                               (Kleibergen-Paap rk Wald F statistic):         48.047
      Stock-Yogo weak ID test critical values:                       <not available>
      ------------------------------------------------------------------------------
      Hansen J statistic (overidentification test of all instruments):         0.000
                                                       (equation exactly identified)
      -endog- option:
      Endogeneity test of endogenous regressors:                              28.942
                                                         Chi-sq(1) P-val =    0.0000
      Regressors tested:    NUMBERESO
      ------------------------------------------------------------------------------
      Instrumented:         NUMBERESO ESOxYEAR_LN ESOxTEAM
      Included instruments: AGE FULLTIME DUMMY_FUNCTION_1 DUMMY_FUNCTION_2
                            DUMMY_LEVEL_1 DUMMY_LEVEL_2 DUMMY_LEVEL_3 SIZE NUMBEROTHER
                            YEAR_LN ESO_REMAININGTEAM
      Excluded instruments: BASEFROMSALARYCAT_COLLAGREEM BASE_COLLAGREEMxYEAR_LN
                            BASE_COLLAGREEMxTEAM
      Dropped collinear:    GENDER

* Example generated by -dataex-. To install: ssc install dataex
clear
input double(NEWIDEA_C GENDER TENURE FULLTIME) float(DUMMY_FUNCTION_1 DUMMY_FUNCTION_2 DUMMY_LEVEL_1 DUMMY_LEVEL_2 DUMMY_LEVEL_3) double(SIZE NUMBEROTHER NUMBERESO) float YEAR_LN double ESO_REMAININGTEAM float BASEFROMSALARYCAT_COLLAGREEM
 2 0 14 1 0 0 1 0 0 18 100  0         0  .3333333333333333 4191.4
 1 0 15 1 0 0 1 0 0 18   0 22  .6931472                 .5 4191.4
 0 0 16 1 0 0 1 0 0 19   0 22 1.0986123  .2631578947368421 4191.4
 1 0 17 1 0 0 1 0 0 20   0 22 1.3862944                 .3 4191.4
 0 0 18 1 0 0 1 0 0 19   0  0  1.609438 .10526315789473684 4191.4
 0 0 19 1 0 0 1 0 0 21   0  0 1.7917595 .04761904761904762 4191.4
 0 0 30 1 0 1 0 1 0  5   0  0         0                  0 2428.2
 0 0 31 1 0 1 0 1 0  5   0  0  .6931472                 .4 2428.2
 0 0 32 1 0 1 0 1 0  6   0  0 1.0986123 .16666666666666666 2648.6
 0 0 33 1 0 1 0 1 0  5   0  0 1.3862944                 .2 3089.4
 0 0 34 1 0 1 0 1 0  6   0  0  1.609438  .3333333333333333 3089.4
 0 0 35 1 0 1 0 1 0  6   0  0 1.7917595 .16666666666666666 3309.8
 0 0 13 1 1 0 0 0 1 11   0  0         0 .09090909090909091   5073
 0 0 14 0 1 0 0 0 1  6   0  0  .6931472 .16666666666666666   5073
 1 0 13 1 0 0 0 0 0 46   0  0         0 .08695652173913043 3089.4
 6 0 14 1 0 0 0 0 0 49   0  0  .6931472 .08163265306122448 3089.4
 1 0 15 1 0 0 0 0 0 40   0  0 1.0986123                .05 3089.4
 4 0 16 1 0 0 0 0 0 43   0  0 1.3862944 .09302325581395349 3089.4
 3 0 17 1 0 0 0 0 0 35   0  0  1.609438 .14285714285714285 3089.4
14 0 18 1 0 0 0 0 0 33   0  0 1.7917595 .09090909090909091 3089.4
 0 0 13 1 0 1 0 0 1  1   0  0         0                  0 5293.4
 0 0 14 0 0 1 0 0 1  2   0  0  .6931472                  0 5293.4
 0 0 15 0 0 1 0 0 1  1   0  0 1.0986123                  0 5293.4
 0 0 16 0 0 1 0 0 1  1   0  0 1.3862944                  0 5293.4
 0 0 17 0 0 1 0 0 1  1   0  0  1.609438                  0 5293.4
 0 0 18 0 0 1 0 0 1  1   0  0 1.7917595                  0 5293.4
 0 0 12 1 0 0 0 0 0 29   0  0         0                  0 3309.8
 2 0 13 1 0 0 0 0 0 30   0  0  .6931472 .03333333333333333 3309.8
 0 0 14 1 0 0 0 0 0 29   0  0 1.0986123                  0 3309.8
 4 0 15 1 0 0 0 0 0 29   0  0 1.3862944                  0 3309.8
 2 0 16 0 0 0 0 0 0 30   0  0  1.609438 .03333333333333333 3309.8
 1 0 17 0 0 0 0 0 0 30   0  0 1.7917595 .03333333333333333 3309.8
 0 1 12 1 0 1 0 1 0  4   0  0         0                 .5 3530.2
 0 1 13 1 0 1 0 1 0  4   0  0  .6931472                  0 3530.2
 0 1 14 1 0 1 0 1 0  2   0  0 1.0986123                  0 3750.6
 0 1 15 1 0 1 0 1 0  5   0  0 1.3862944                 .2   3971
 0 1 16 1 0 1 0 1 0  5   0  0  1.609438                 .6   3971
 0 1 17 0 0 1 0 1 0  7   0  0 1.7917595  .2857142857142857 4191.4
 0 1 12 0 0 1 0 1 0  7   0  0  .6931472  .2857142857142857 3750.6
 0 1 13 0 0 1 0 1 0  7   0  0 1.0986123  .2857142857142857 3750.6
 0 1 14 0 0 1 0 1 0  9   0  0 1.3862944  .2222222222222222 3750.6
 0 1 15 0 0 1 0 1 0  8   0  0  1.609438                .25 3750.6
 0 1 16 0 0 1 0 1 0  9   0  0 1.7917595  .2222222222222222 3750.6
 0 0 10 1 0 1 0 0 1 10   0  0         0                 .2 5513.8
 0 0 11 1 0 1 0 0 1  8   0  0  .6931472               .375 5513.8
 0 0 12 1 0 1 0 0 1  6   0  0 1.0986123                 .5 5513.8
 0 0 13 1 0 1 0 0 1  8   0  0 1.3862944               .375 5513.8
 0 0 14 1 0 1 0 0 1  9   0  0  1.609438  .2222222222222222 5513.8
 0 0 15 1 0 1 0 0 1 11   0  0 1.7917595 .36363636363636365 5513.8
 0 0 11 1 0 1 0 1 0  6   0  0         0 .16666666666666666   5073
 0 0 12 1 0 1 0 1 0  5   0  0  .6931472                 .2   5073
 0 0 13 1 0 1 0 1 0  6   0  0 1.0986123 .16666666666666666   5073
 0 0 14 1 0 1 0 1 0  6   0  0 1.3862944 .16666666666666666   5073
 0 0 15 1 0 1 0 1 0  6   0  0  1.609438 .16666666666666666   5073
 0 0 16 1 0 1 0 1 0  6   0  0 1.7917595 .16666666666666666   5073
 0 1 11 1 0 1 0 1 0  8   0  0         0               .125 4852.6
 0 1 13 0 0 1 0 1 0  7   0  0 1.0986123 .14285714285714285 4852.6
 0 1 14 1 0 1 0 1 0  6   0  0 1.3862944 .16666666666666666 4852.6
 0 1 15 1 0 1 0 1 0  6   0 11  1.609438 .33333333333333337 4852.6
 0 1 16 1 0 1 0 1 0  6   0  0 1.7917595                  0 4852.6
 0 1 11 1 1 0 0 1 0 10   0 20         0                  0 5293.4
 0 1 12 1 1 0 0 1 0 10   0 22  .6931472                 .1 5293.4
 0 1 13 1 0 0 0 0 1  1   0 22 1.0986123                  0 5293.4
 0 1 14 1 0 0 0 0 1  1   0 22 1.3862944                  0 5293.4
 0 1 11 1 0 0 0 0 1  8   0  0         0                .25 5513.8
 0 1 12 1 0 0 0 0 1  6   0  0  .6931472  .3333333333333333 5513.8
 0 1 13 1 0 0 0 0 1  6   0  0 1.0986123  .3333333333333333 5513.8
 0 1 14 1 0 0 0 0 1  6   0  0 1.3862944  .3333333333333333 5513.8
 0 0 14 1 0 1 0 1 0  2   0  0 1.0986123                  0 4852.6
 0 0 15 1 0 1 0 1 0  3   0  0 1.3862944                  0 4852.6
 0 0 16 1 0 1 0 1 0  2   0  0  1.609438                  0 4852.6
 0 0 17 1 0 1 0 1 0  6   0  0 1.7917595 .16666666666666666 4852.6
 0 1 13 1 0 1 0 1 0 14   0  0  .6931472  .2857142857142857   5073
 0 1 14 1 0 1 0 1 0 13   0  0 1.0986123  .3076923076923077   5073
 0 1 15 1 0 1 0 1 0  5   0  0 1.3862944                 .4   5073
 0 1 17 0 0 1 0 1 0  6   0  0 1.7917595 .16666666666666666   5073
 0 0  6 1 0 1 0 0 1  5   0  0         0                  0   5073
 0 0  7 1 0 1 0 0 1  5   0 42  .6931472                 .2   5073
 0 0  8 1 0 1 0 0 1  6   0 42 1.0986123 .16666666666666666   5073
 0 0  9 1 0 1 0 0 1  6   0 22 1.3862944                  0   5073
 0 0 10 1 0 1 0 0 1  5   0 22  1.609438                  0   5073
 0 0 11 1 0 1 0 0 1  5   0 11 1.7917595                 .2   5073
 0 0 20 1 0 1 0 0 1  1   0  0 1.7917595                  0 5513.8
 0 0 11 1 0 1 0 1 0  3   0  0         0  .3333333333333333 4852.6
 0 0 12 1 0 1 0 1 0  3   0  0  .6931472  .3333333333333333 4852.6
 0 0 13 1 0 1 0 1 0  2   0  0 1.0986123                  0 4852.6
 0 0 14 1 0 1 0 1 0  4   0  0 1.3862944                  0 4852.6
 0 0 15 1 0 1 0 1 0  2   0  0  1.609438                  0 4852.6
 0 0 16 1 0 1 0 1 0  2   0  0 1.7917595                  0 4852.6
 0 1  9 1 0 0 0 1 0 12   0  0         0                  0 4411.8
 0 1 10 1 0 0 0 1 0 17   0  0  .6931472 .11764705882352941 4411.8
 0 1 11 1 0 0 0 1 0  4   0  0 1.0986123                .25 4632.2
 0 1 12 1 0 0 0 1 0 11   0  0 1.3862944 .09090909090909091 4632.2
 0 1 13 1 0 0 0 1 0 11   0  0  1.609438  .2727272727272727 4852.6
 0 1 14 1 0 0 0 1 0 11   0  0 1.7917595 .18181818181818182 4852.6
 0 0 32 1 0 1 0 1 0 20   0  0  .6931472                  0 4411.8
 0 0 33 1 0 1 0 1 0 20   0  0 1.0986123                  0 4411.8
 0 0 34 1 0 1 0 1 0 21   0  0 1.3862944 .04761904761904762 4411.8
 0 0 35 1 0 1 0 1 0 24   0  0  1.609438 .04166666666666666 4411.8
 0 0 36 1 0 1 0 1 0 11   0  0 1.7917595 .09090909090909091 4411.8
end
label values GENDER GENDER
label def GENDER 0 "Male", modify
label def GENDER 1 "Female", modify

[Sebastian Kripfganz]

The interpretation of the coefficients does not depend on the instruments used. It is the same as if you were just estimating the model by OLS. You can include time dummies just as any other exogenous regressor.

[Felix Hofmann]

Dear Sebastian, thanks for your quick and clear response. With regards to the tests that are performed when I include the option endog, how would I correctly Interpret the results of the Underidentification test (Kleibergen-Paap rk LM statistic); Hansen J statistic (overidentification test of all instruments); and the Endogeneity test of endogenous regressors?

1. Rejecting the null-hypothesis for Underidentification test (Kleibergen-Paap rk LM statistic) means that my Instrument(s) are rather strong?
2. Rejecting the null-hypothesis for Hansen J statistic (overidentification test of all instruments) tells me that my Instrument(s) are NOT valid meaning that they are correlated with the error term?
3. Rejecting the null-hypothesis for the Endogeneity test tells me that my regressors are endogeneous?

My question is whether I can still trust the endogeneity test when my Hansen J overidentification test is significant, meaning that my Instrument is somehow correlated with my error term - although it should not be from a theoretical point of view ?

Edit: I did run my regression with my instrument variable as additional regressor but the Instrument does not predict variance in my dependent variable (p>0.7) - does this reject the suspicion that my Instrument is correlated with my error term?

Thanks for your help!

Felix

[Felix Hofmann]

I received an answer to my question whether one can trust the endogeneity test when the instruments fail the overidentification test from Kit Baum (coauthor of ivreg2).

"Felix,
By placing all endogenous variables into the endog() option, you are conducting a Durbin-Wu-Hausman test of OLS vs IV, as described in the Baum-Schaffer-Stillman Stata Journal papers. It does appear that there is no rejection of the null that OLS would be adequate. However, that conclusion is based on the appropriateness of the IV specification, and the Hansen J test rejects its null, suggesting that the instruments may not be uncorrelated with the error, or that the specification of the model may be flawed. That in my mind casts doubt on the appropriateness of an OLS specification of this equation (as well as the implemented IV specification).

I would recommend that you remove singleton groups (as they provide no useful information in a fixed effects model) and the collinear dummies, use the IV-GMM form of estimation rather than 2SLS, and further investigate why you might be getting a value of Hansen's J that rejects its null.

Best wishes

Kit Baum"