Dear Statlisters,
I am sorry in advance for the length of this question, I found that a little context would help in understanding what I am looking for.

THE CONTEXT: I am currently dealing with a paper in which my colleagues and I wish to study whether sectoral identification in the Chinese Five Year Plans as prioritized sectors affects the number of M&A in those sectors.
Our dependent variable (number of M&A in sector i in year t) is count non-negative with a large concentration on the zero, while our variable of interest (identification of the sector as strategic) is a dummy (hereinafter EM). I therefore use negative binomial regression with clustered standard errors. We also use a set of variables to control for the structure of the sector (i.e. labour productivity, firm size, sector size and so on).

In the first round of reviews, both the reviewers pointed out a list of technical concerns, in particular related to the endogeneity of EM. In the revised version of the paper, I came out with a three-step IV procedure (Adams et al., 2009; Wooldridge, 2010) to overcome “forbidden regression” issues due to the specific types of variables and to the nonlinearity of the main model. This seemed to work fine for the reviewers.

MY CURRENT ISSUE: However, in this second round one of the reviewer raised another concern related to the endogeneity of the controls. In particular, he claims that there might be serious simultaneity issues which might result in estimation bias of the EM coefficient and that, in addition, these variable might be influenced by our dependent variable.

I am now looking for a sensitive way to deal with this issue. A preliminary question is: is this a real concern one has to look at, even once endogeneity of the variable of interest is already taken into account? If not, do you have any references about?

Coming to how to solve this: Finding instruments for all the controls that I might suspect of being endogenous does not seem a feasible alternative: since they are all related to the economic structure they are all potentially endogenous, and I do not see a way in which I can find external instruments for all of them – letting alone that my sample is not enormous.
Therefore I was thinking whether there are ways to test the sensitivity of EM to the endogeneity of the controls – similarly to Rosenbaum bounds
Code:
rbounds
in propensity score matching methods. I found
Code:
psacalc
- that follows Oster (2016) - might do the trick, but it seems to me this is only for linear models. Do you know any technique that would fit a nonlinear setting?
Any other idea on how to solve this?
Best and thank you all!