Propensity Score Matching with xtreg regressions

[Badar Khalid]

Dear Statalist users,

I am applying Propensity Score Matching in my research and I face problem when I apply firm fixed effects models after the matching command:

First, I have run the following matching command and the results appear normally

psmatch2 BOARD_DIV_Dummy BoardSize LogTotalAsset $Y $I $C , out(IO_Total) n(4) ai(4) logit

Then I have run firm fixed effects regressions as follwos:

xtreg BOARD_DIV  L.( IO_Total $X $Y)[aweight=_weight],fe robust cluster (CompanyID)

But I have got the following error:

weight must be constant within CompanyID

Can any body help please on how to solve this problem as I need to run xtreg after the matching command. Thank you.

[Clyde Schechter]

Your -psmatch2- command appears to be unrelated to your -xtreg- command. You have used -psmatch2- to calculate the propensity for an observation to have value 1 for the variable BOARD_DIV_Dummy. But then BOARD_DIV_Dummy does not clearly appear in your -xtreg- command as a predictor (unless it is contained in $X). If the dependent variable of -xtreg-, BOARD_DIV is actually the same variable, then your -psmatch2- command is mis-specified because you need to compute the propensity for assignment to a treatment group, not the propensity towards a given outcome. Indeed, if you match your sample on propensity to a given outcome, an analysis of that outcome is bound to yield pretty much null results!

Turning to your question, the error message means exactly what it says. In -xt- analyses, the weight must be constant within panels (CompanyID) here. But your -psmatch2- command assigns a different weight to every observation, so there is no consistency within panels here. So you need to revise your propensity analysis to run on a single observation per CompanyID (I can't advise you how to select the one observation from among the several in the panel, or whether to synthesize it from mean values, etc.--that's a scientific, not a statistical, issue.) Then you can attach the propensity weights consistently within each Company_ID.

Finally, with nearest neighbor matching, as you have done here, the _weight_ variable is not, as I understand it (I haven't used -psmatch2- in a long time) suitable for use as a weight in a propensity matched analysis. I believe you should use 1/_pscore use as your weight in the -xtreg- analysis, and I believe it is best used as a -pweight-.

[Badar Khalid]

Dear Clyde, Thank you for your valuable comment on my query. As a result, I have fixed the matching command (please see below). can you recommend me how I can modify the matching command to run on a single observation per Company ID, so that I can run the xtreg regression properly. Thank you and looking forward to your valuable comment in this regard.

 psmatch2 IO_Total_Dummy LogTotalAsset $Y $I $C, out(BDI_16) n(4) ai(4) logit
note: Year_2012 omitted because of collinearity
note: Industry_9 omitted because of collinearity
note: UK omitted because of collinearity

Logistic regression                             Number of obs     =      2,586
                                                LR chi2(29)       =    1059.97
                                                Prob > chi2       =     0.0000
Log likelihood = -1253.9593                     Pseudo R2         =     0.2971

--------------------------------------------------------------------------------
IO_Total_Dummy |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
 LogTotalAsset |  -1.192142   .1136383   -10.49   0.000    -1.414869   -.9694153
     Year_2006 |   -.143858    .187519    -0.77   0.443    -.5113885    .2236725
     Year_2007 |   .2801084   .1853113     1.51   0.131    -.0830951    .6433118
     Year_2008 |   .2832782   .1832989     1.55   0.122     -.075981    .6425374
     Year_2009 |   .1296116   .1813213     0.71   0.475    -.2257717    .4849949
     Year_2010 |  -.0091846   .1811794    -0.05   0.960    -.3642897    .3459206
     Year_2011 |  -.1080594   .1806143    -0.60   0.550     -.462057    .2459381
     Year_2012 |          0  (omitted)
    Industry_1 |  -.0386987   .2716604    -0.14   0.887    -.5711432    .4937459
    Industry_2 |  -.1516284   .2818318    -0.54   0.591    -.7040087    .4007519
    Industry_3 |  -.2104899   .2705929    -0.78   0.437    -.7408423    .3198625
    Industry_4 |  -.2455584   .3131994    -0.78   0.433    -.8594179    .3683011
    Industry_5 |    .140914   .2645556     0.53   0.594    -.3776055    .6594336
    Industry_6 |  -.2634441   .2814478    -0.94   0.349    -.8150716    .2881833
    Industry_7 |   .1112017   .3384089     0.33   0.742    -.5520675    .7744709
    Industry_8 |  -.5356857   .3254116    -1.65   0.100    -1.173481    .1021093
    Industry_9 |          0  (omitted)
     Australia |  -2.623011   .2067445   -12.69   0.000    -3.028223   -2.217799
       Belgium |  -3.493948   .3208538   -10.89   0.000     -4.12281   -2.865086
        Canada |  -.5516089   .1915833    -2.88   0.004    -.9271052   -.1761125
       Denmark |  -2.881466   .2896858    -9.95   0.000     -3.44924   -2.313692
       Finland |   -3.26325   .2462681   -13.25   0.000    -3.745926   -2.780573
        France |  -2.448561   .2124253   -11.53   0.000    -2.864907   -2.032215
         India |  -4.416427   .3433739   -12.86   0.000    -5.089428   -3.743427
       Ireland |  -1.672811   .2796542    -5.98   0.000    -2.220923   -1.124699
         Italy |  -4.504373   .3803465   -11.84   0.000    -5.249838   -3.758907
 
         _cons |   10.23794   .9087804    11.27   0.000     8.456767    12.01912
--------------------------------------------------------------------------------
----------------------------------------------------------------------------------------
        Variable     Sample |    Treated     Controls   Difference         S.E.   T-stat
----------------------------+-----------------------------------------------------------
          BDI_16  Unmatched | 10.3122896   9.99284692   .319442638   .087414632     3.65
                        ATT | 10.3122896   10.4541246  -.141835017   .136794248    -1.04
----------------------------+-----------------------------------------------------------
Note: Sample S.E.

           | psmatch2:
 psmatch2: |   Common
 Treatment |  support
assignment | On suppor |     Total
-----------+-----------+----------
 Untreated |     1,398 |     1,398
   Treated |     1,188 |     1,188
-----------+-----------+----------
     Total |     2,586 |     2,586


.
end of do-file

. do "C:\Users\nwd13fta\AppData\Local\Temp\STD00000000.tmp"

. xtreg BDI_16 L.( IO_Total_Dummy $X $Y)[aweight=_weight],fe robust cluster (CompanyID)
weight must be constant within CompanyID

[Clyde Schechter]

Well, as I said, it is precisely on this aspect of things that I cannot advise you as it is a question of substantive economics, not a statistical matter. I have no expertise in the area. In terms of general guidance, you need to decide on those attributes of a Company that are likely to be predictive of whether it is in the treatment or control group. The difficulty you face is that some of these attributes may vary over time, yet you must come up with a single propensity score/weight for each company that is constant across time. There are numerous ways to do this. One can pick the most recent values. Or for some attributes it may make the most sense to average those attributes over time. For others the lowest or highest value might make sense. Or the median, or other ways of selecting a value. Which approach to use for which attributes depends on how these attributes actually work in the real world to affect the company's treatment vs control status. That, as I say, is not a statistical issue but a matter of substantive economics. There are some economists who participate in this forum, and perhaps they will weigh in. If not, you probably should seek advice from a colleague in your field.