margins and marginsplot

[Mohieddine Rahmouni]

For the analysis of the effect of the political connection dummy variable (PoliticConnect) in moderating the negative impact of political instability (PoliticInstab) on innovation outcomes, I used the eprobit and rbiprobit commands to estimate 4 models. Comments on the interpretation of the results (margins and marginsplot) and the estimation strategy are welcome.

Model 1: PoliticInstab and PoliticConnect are exogenous covariates

probit innovation i.PoliticInstab i.PoliticConnect i.PoliticInstab#i.PoliticConnect lnWorkers i.BroadSupervisor i.Overdraft i.PettyCorruption i.Competition i.businessGOV i.BusinessMember i.NationalSales100, vce(robust) nolog
margins i.PoliticInstab i.PoliticConnect i.PoliticInstab#i.PoliticConnect
marginsplot

. margins i.PoliticInstab i.PoliticConnect i.PoliticInstab#i.PoliticConnect

Predictive margins                                         Number of obs = 539
Model VCE: Robust

Expression: Pr(innovation), predict()

----------------------------------------------------------------------------------------------
                             |            Delta-method
                             |     Margin   std. err.      z    P>|z|     [95% conf. interval]
-----------------------------+----------------------------------------------------------------
               PoliticInstab |
                          0  |   .1765938   .0286924     6.15   0.000     .1203578    .2328299
                          1  |   .1155426     .01419     8.14   0.000     .0877306    .1433546
                             |
              PoliticConnect |
                          0  |   .1226924   .0149398     8.21   0.000     .0934109    .1519738
                          1  |   .1476572   .0280579     5.26   0.000     .0926649    .2026496
                             |
PoliticInstab#PoliticConnect |
                        0 0  |   .2235395    .035193     6.35   0.000     .1545625    .2925164
                        0 1  |   .0563568   .0394509     1.43   0.153    -.0209656    .1336792
                        1 0  |   .0920216   .0161732     5.69   0.000     .0603228    .1237204
                        1 1  |   .1756861   .0340182     5.16   0.000     .1090116    .2423607
----------------------------------------------------------------------------------------------

Graph1.gph

Model 2: PoliticInstab is an endogenous variable

eprobit innovation i.PoliticInstab i.PoliticConnect i.PoliticInstab#i.PoliticConnect lnWorkers i.BroadSupervisor i.Overdraft i.PettyCorruption i.Competition i.businessGOV i.BusinessMember i.NationalSales100, endogenous(PoliticInstab = lnWorkers BroadSupervisor BusinessMember Overdraft NationalSales100  highOBSlaborRegul OBSenvironmtRegul TaxTransparency, probit povariance)  vce(robust) nolog
margins i.PoliticInstab i.PoliticConnect i.PoliticInstab#i.PoliticConnect
marginsplot

. margins i.PoliticInstab i.PoliticConnect i.PoliticInstab#i.PoliticConnect

Predictive margins                                         Number of obs = 499
Model VCE: Robust

Expression: Average structural function probability, predict()

----------------------------------------------------------------------------------------------
                             |            Delta-method
                             |     Margin   std. err.      z    P>|z|     [95% conf. interval]
-----------------------------+----------------------------------------------------------------
               PoliticInstab |
                          0  |   .5703818   .0594922     9.59   0.000     .4537793    .6869843
                          1  |   .0936494   .0117728     7.95   0.000     .0705752    .1167237
                             |
              PoliticConnect |
                          0  |   .1283634   .0158149     8.12   0.000     .0973667    .1593601
                          1  |   .1459384   .0258005     5.66   0.000     .0953703    .1965066
                             |
PoliticInstab#PoliticConnect |
                        0 0  |   .6263346    .052183    12.00   0.000     .5240578    .7286115
                        0 1  |   .3868386   .1009799     3.83   0.000     .1889217    .5847555
                        1 0  |   .0748945     .01366     5.48   0.000     .0481214    .1016675
                        1 1  |    .131799   .0246083     5.36   0.000     .0835676    .1800304
----------------------------------------------------------------------------------------------

Graph2.gph

Model 3: PoliticInstab and PoliticConnect are endogenous variables

eprobit innovation i.PoliticInstab i.PoliticConnect i.PoliticInstab#i.PoliticConnect lnWorkers i.BroadSupervisor i.Overdraft i.PettyCorruption i.Competition i.businessGOV i.BusinessMember i.NationalSales100, endogenous(PoliticInstab= lnWorkers BroadSupervisor BusinessMember  Overdraft NationalSales100  highOBSlaborRegul OBSenvironmtRegul TaxTransparency, probit) endogenous(PoliticConnect = highOBSfinance businessGOV TaxTransparency BroadSupervisor , probit) vce(robust) nolog
margins i.PoliticInstab i.PoliticConnect i.PoliticInstab#i.PoliticConnect
marginsplot

. margins i.PoliticInstab i.PoliticConnect i.PoliticInstab#i.PoliticConnect

Predictive margins                                         Number of obs = 495
Model VCE: Robust

Expression: Average structural function probability, predict()

----------------------------------------------------------------------------------------------
                             |            Delta-method
                             |     Margin   std. err.      z    P>|z|     [95% conf. interval]
-----------------------------+----------------------------------------------------------------
               PoliticInstab |
                          0  |   .5745013   .0617119     9.31   0.000     .4535483    .6954543
                          1  |   .0945496   .0119545     7.91   0.000     .0711192      .11798
                             |
              PoliticConnect |
                          0  |   .1539277   .0358591     4.29   0.000     .0836451    .2242103
                          1  |   .1023205    .044548     2.30   0.022     .0150081    .1896329
                             |
PoliticInstab#PoliticConnect |
                        0 0  |   .6403577   .0584658    10.95   0.000     .5257669    .7549486
                        0 1  |   .3344634   .1316851     2.54   0.011     .0763654    .5925614
                        1 0  |   .0967497     .02759     3.51   0.000     .0426743    .1508251
                        1 1  |   .0915078   .0391246     2.34   0.019     .0148249    .1681907
----------------------------------------------------------------------------------------------

Graph3.gph

Model 4: PoliticInstab is an endogenous variable that depends on PoliticConnect

eprobit innovation i.PoliticInstab i.PoliticConnect i.PoliticInstab#i.PoliticConnect lnWorkers i.BroadSupervisor i.Overdraft i.PettyCorruption i.Competition i.businessGOV i.BusinessMember i.NationalSales100, endogenous(PoliticInstab= lnWorkers BroadSupervisor BusinessMember  Overdraft NationalSales100  highOBSlaborRegul OBSenvironmtRegul TaxTransparency, probit) endogenous(PoliticConnect = highOBSfinance businessGOV TaxTransparency BroadSupervisor , probit) vce(robust) nolog
margins i.PoliticInstab i.PoliticConnect i.PoliticInstab#i.PoliticConnect
marginsplot

. margins i.PoliticInstab i.PoliticConnect i.PoliticInstab#i.PoliticConnect

Predictive margins                                         Number of obs = 499
Model VCE: Robust

Expression: Average structural function probability, predict()

----------------------------------------------------------------------------------------------
                             |            Delta-method
                             |     Margin   std. err.      z    P>|z|     [95% conf. interval]
-----------------------------+----------------------------------------------------------------
               PoliticInstab |
                          0  |   .5732719   .0652555     8.79   0.000     .4453736    .7011703
                          1  |   .0935673   .0118427     7.90   0.000     .0703561    .1167785
                             |
              PoliticConnect |
                          0  |   .1172716   .0147741     7.94   0.000      .088315    .1462282
                          1  |   .1847767   .0366335     5.04   0.000     .1129764    .2565769
                             |
PoliticInstab#PoliticConnect |
                        0 0  |   .5929149   .0569762    10.41   0.000     .4812435    .7045863
                        0 1  |    .505953   .1289578     3.92   0.000     .2532004    .7587056
                        1 0  |   .0695727   .0126289     5.51   0.000     .0448204    .0943249
                        1 1  |   .1554037   .0307193     5.06   0.000      .095195    .2156124
----------------------------------------------------------------------------------------------

[Mohieddine Rahmouni]

Carlo Lazzaro Clyde Schechter

[Clyde Schechter]

I am not familiar with the -eprobit- command, so I cannot comment on that part of your output. It looks like it is an application of instrumental variables to -probit- regression. But instrumental variables is another area where I cannot comment; it is little used technique in my discipline, epidemiology, and I have very little experience with it. So I'm limited to just commenting on the -probit- results. I suspect what I have to say will not be anything you have not yourself already figured out. Also, the differences among the models seem to be rather large (to the limited extent I understand them), and probably figuring those out, were I able to do so, would be more interesting than just making some fairly obvious comments about the -probit- results. But I can only do what I can do.

The -probit- results are pretty standard. Probably the most important parts of the -margins- output are the four rows corresponding to the levels of the interaction. Adjusting for the distributions of all the other variables in your -probit- regression, the predicted probability of innovation is about 0.22 when PoliticInstab and PoliticConnect are both 0, about 0.6 when PoliticInstab = 0 and PolitConnect = 1, about 0.09 when PoliticInstab = 1 and PoliticConnect = 0, and 0.18 when PoliticInstab = 1 and PoliticConnect = 1. The confidence intervals for PoliticInstab = 1 and PoliticConnect = 0 or vice versa do not overlap that for when both are zero. They do somewhat overlap those where both are one, but not extensively.

The -margins- results for PolitcInstab and PoliticConnect separately can be read in a similar way. Given the apparent size of the interaction effects, however, I don't think these separate results are very meaningful.

As for what to make of the apparent finding that innovation probability is apparently higher when PoliticInstab and PoliticConnect agree than when they disagree, that is a substantive question that is outside my area.

Hopefully, Carlo Lazzaro will respond and have something more helpful to say. This is much more in his wheelhouse than mine.

[Mohieddine Rahmouni]

Thank you very much Clyde! The results show that likelihood of innovation is higher when PoliticInstab and PoliticConnect agree than when they disagree. I think I need to dig deeper into the data!