# Testing for endogeneity in a negative binomial model

I'm trying to fit a negative binomial model to my data because the dependent variable exhibits overdispersion. However, one of my reviewers is insisting that I also test for endogeneity. He or she is worried that two independent variables are potentially endogenous (one of them might potentially be so...). My question is how one goes about testing for endogeneity in a negative binomial model, ideally in R. Can it be done simultaneously for two variables? I already found a potential instrument for the most problematic of these two variables (correlated with the endogenous independent variable but uncorrelated to the dependent variable). I'm just not sure how to go from here... I see papers that implement a two-step Heckman procedure, running the negative binomial regression with the inverse Mills ratio. However, I also read that this might not be appropriate...

My current model looks like this, I'm using R. Basically I'm pooling three years of data from two different countries. I'm primarily interested in the differences between these two countries. I have 2 control variables and 9 independent variables of interest. X1 and X3 are the potential problematic variables. Y is a count of different countries in which firms are present, and independent variables are things like international experience, international education, board independence, etc. Endogeneity arises, for instance, because international firms might hire people with more international experience/education than their local counterparts.

negbin <- glm.nb(Y~ Control1 + Contro2 + Year + Country
+ X1*Country
+ X2*Country
+ X3*Country
+ X4*Country
+ X5*Country
+ X6*Country
+ X7*Country
+ X8*Country
+ X9*Country
+ X10*Country, data = mydata)
summary(negbin)
car::vif(negbin)

Deviance Residuals:
Min        1Q    Median        3Q       Max
-2.04651  -1.16581  -0.56598   0.01105   3.00675

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept)              1.588771   1.742045   0.912 0.361761
Control1                 0.240602   0.086086   2.795 0.005191 **
Control2                -0.013200   0.003732  -3.537 0.000404 ***
YearThree                0.152904   0.277186   0.552 0.581203
YearTwo                  0.085071   0.276648   0.308 0.758459
Country                 -1.899136   2.604823  -0.729 0.465950
X1                       1.609189   0.652992   2.464 0.013727 *
X2                       0.146868   0.111476   1.317 0.187674
X3                      -4.792707   0.748956  -6.399 1.56e-10 ***
X4                       4.352965   0.677561   6.424 1.32e-10 ***
X5                      -0.054561   0.015381  -3.547 0.000389 ***
X6                      -1.497622   0.374987  -3.994 6.50e-05 ***
X7                      -2.689511   0.768235  -3.501 0.000464 ***
X8                      -0.078919   0.069243  -1.140 0.254394
X9                       4.237630   1.544278   2.744 0.006068 **
X10                      3.333337   1.258869   2.648 0.008100 **
Country:X1               0.584704   0.992207   0.589 0.555662
Country:X2              -0.635671   0.332893  -1.910 0.056193 .
Country:X3               4.508881   0.884777   5.096 3.47e-07 ***
Country:X4              -7.823156   1.411851  -5.541 3.01e-08 ***
Country:X5              -0.003909   0.032332  -0.121 0.903779
Country:X6               1.001702   0.570836   1.755 0.079294 .
Country:X7               4.870946   0.991810   4.911 9.05e-07 ***
Country:X8               0.403581   0.100593   4.012 6.02e-05 ***
Country:X9              -2.151496   1.953145  -1.102 0.270655
Country:X10            -21.951529   4.102211  -5.351 8.74e-08 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

• Your bounty is running out without attracting an answer. I wanted to let you know that it attracted my attention (+1), and it made me look into the literature about endogeneity. But I do not know enough about it. It mostly left me confused and I still find it a vague concept. Being more like a physicist I am not used to this type of modelling, I can not share my experience, but I can share that I am confused as well (maybe you should ask the question on some econometrics platform?). Regarding your question... it made me wonder about the background and the specific parameters and instruments. Jun 24, 2020 at 15:08