Heckman Model for Selection Bias with Panel Data

[Luisa Michel]

Hello everyone,

I am examining the relation between tax planning and firm value. My data is an unbalanced panel data and I estimated the regression with fixed effects. As I suspect a selection bias, I want to perform a heckman selection model.
However, I am not sure about the control variables and whether to exclude any in the model.

My regression looked like this:

reghdfe tobin btd  TA sales ppe vol nolassets foreigninc std ltd rd, absorb(Year sic) vce(cluster isin Year)

I tried the Heckman approach and the code looks like this:

heckman tobin btd TA sales ppe vol nolassets foreigninc std ltd rd i.Year, select(taxavoid = TA sales vol ppe nolassets foreigninc std ltd rd i.Year) vce(robust)

Heckman selection model                         Number of obs     =      2,829
(regression model with sample selection)        Censored obs      =      1,435
                                                Uncensored obs    =      1,394

                                                Wald chi2(19)     =     237.86
Log pseudolikelihood = -4144.806                Prob > chi2       =     0.0000

------------------------------------------------------------------------------
             |               Robust
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
tobin        |
       w_btd |   6.904373   1.240759     5.56   0.000     4.472531    9.336215
        w_TA |  -4.898546   .6854721    -7.15   0.000    -6.242046   -3.555045
       sales |  -.0730264   .0401021    -1.82   0.069    -.1516251    .0055723
        ppe2 |  -1.255607   .1520859    -8.26   0.000     -1.55369   -.9575241
         vol |   .0260516   .0290061     0.90   0.369    -.0307993    .0829026
   nolassets |   121.1902   113.3512     1.07   0.285     -100.974    343.3544
  foreigninc |    .014931   .0835962     0.18   0.858    -.1489145    .1787765
         std |   .3343805   .8761062     0.38   0.703    -1.382756    2.051517
         ltd |   .4227263   .1981058     2.13   0.033     .0344461    .8110065
    changerd |   23.37676   4.954492     4.72   0.000     13.66613    33.08739
             |
             |
       _cons |    1.31306   .1498813     8.76   0.000     1.019298    1.606822
-------------+----------------------------------------------------------------
taxavoid     |
        w_TA |   .6723251   .3413934     1.97   0.049     .0032062    1.341444
       sales |  -.2075946   .0338522    -6.13   0.000    -.2739438   -.1412455
         vol |   .0559122   .0211032     2.65   0.008     .0145507    .0972737
        ppe2 |   .5709638   .1226611     4.65   0.000     .3305524    .8113752
   nolassets |   419.0152   123.7301     3.39   0.001     176.5086    661.5217
  foreigninc |   .1127357   .0660463     1.71   0.088    -.0167126     .242184
         std |   1.129645   .5186263     2.18   0.029     .1131565    2.146134
         ltd |   .1060875   .0973646     1.09   0.276    -.0847435    .2969186
    changerd |  -.0004607   1.700443    -0.00   1.000    -3.333269    3.332347
             |
             |
       _cons |   .0981113   .0917423     1.07   0.285    -.0817003    .2779229
-------------+----------------------------------------------------------------
     /athrho |   -.009978   .0570314    -0.17   0.861    -.1217576    .1018015
    /lnsigma |   .2156416   .0404441     5.33   0.000     .1363726    .2949106
-------------+----------------------------------------------------------------
         rho |  -.0099777   .0570258                     -.1211595    .1014513
       sigma |   1.240658   .0501773                      1.146109    1.343006
      lambda |  -.0123789   .0707588                     -.1510635    .1263057
------------------------------------------------------------------------------
Wald test of indep. eqns. (rho = 0): chi2(1) =     0.03   Prob > chi2 = 0.8611

I also tried using the code xtheckmanfe but it does keep calculating and calculating and does not deliver any results.
1.) My question is now, is the code for the model conducted right?
2.) My fixed effects model before also showed a positive relation between tax avoidance (btd) and firm value (Tobin). Am I interpreting the Heckman model right that the coefficient of 6.9 also shows a positive relation or do I have to interpret it in another way?
3.) Is it possible that I do not have a selection problem because I cannot reject the H0 of the pictured Wald test?
I am using Stata 14.

Thank you in advance!

[Jeff Wooldridge]

I see some potential problems here. First, the Heckman approach is really only suited to cases where data are missing on y. Do you have missing x variables, too?

Second, you really need a variable that affects selection — tax avoidance — but not y. You seem to have assumed the opposite.

Third, this way of implementing Heckman does not make it more robust. In fact, it makes the very strong assumption that the explanatory variables are independent of the heterogeneity in both equations. This is a very strong assumption.

Fourth, this command rules out serial correlation in the outcome and selection equations. Again, this is way too strong.

If data are only missing on y and you find an exclusion restriction, it’s much easier and more robust to use the pooled correlated random effects approach in my 1995 Journal of Econometrics paper.

[Luisa Michel]

Hello Jeff,

thank you very much for your answer!

First, yes I potentially have missing variables as I have missing ones on y (firm value) and on x (tax avoidance).

Second, thank you I see what you mean. I misunderstood it and just implemented all control variables in the select command but as you stated I just have to implement those that directly affect tax avoidance. I correct the code to this:

heckman tobin btd TA sales ppe vol nolassets foreigninc std ltd rd i.Year, select(taxavoid = TA nolassets foreigninc std ltd i.Year) vce(robust)

About the third and fourth command, are those statistical problems removed if the variables included in "select" only include this affected with tax avoidance or is this "heckman" code generally a problem here?

Sorry for my further questions but I've never worked with heckman and I'm just trying to figure it out.

[Doris Rivera]

Dear Jeff Wooldridge, with regard to the paper you suggest in #2, I am wondering about the differences of using a FE estimation in the second stage instead of a RE (with Mundlak) or a pooled OLS (also with Mundlak). Without bodering you too much, can you clarify a little bit about it?
Thanks a lot in advance.

[Nitin Jain]

I see some potential problems here. First, the Heckman approach is really only suited to cases where data are missing on y. Do you have missing x variables, too?

Second, you really need a variable that affects selection — tax avoidance — but not y. You seem to have assumed the opposite.

Third, this way of implementing Heckman does not make it more robust. In fact, it makes the very strong assumption that the explanatory variables are independent of the heterogeneity in both equations. This is a very strong assumption.

Fourth, this command rules out serial correlation in the outcome and selection equations. Again, this is way too strong.

If data are only missing on y and you find an exclusion restriction, it’s much easier and more robust to use the pooled correlated random effects approach in my 1995 Journal of Econometrics paper.

Dear Prof. Wooldridge,

I have a data with missing y but no missing values for x's. Could you please suggest how to do heckman sample selection for a linear panel model with random effect manually [without using stata package as that works only for versions 16 onwards].

Thanks,
Nitin