Tackling potential endogeneity bias in panel data model with binary outcome

[Geoffroy Dolphin]

Dear Stata Users,

I am trying to estimate a model which relates the presence (1) or absence (0) of a policy in a given jurisdiction (i) and year (t) to a set of covariates describing the structure of the economy (e.g. VA of industry as a % of total GDP, electricity production mix, GDP,...). I am currently working with -xtlogit, re- and -xtprobit- on a dataset that has N=118 (national jurisdictions) and T=26 (years).

However, I am worried that in doing so, a reverse causality problem may arise in the sense that such policies (at least the most stringent) may also affect some of the covariates, if not contemporaneously, at least with a lag.

I am currently unsure of the following:

1. Does this type of endogeneity plague coefficient estimates with bias the same way it does for standard linear models?
2. If yes, what would be the appropriate way to handle it given that I don't have access to (external) instrumental variables? [My current model relates lagged values of the covariates to the current value of the binary outcome variable, which I believe breaks the contemporaneous correlation between the covariate and the error term but not the dynamic one.]

I would very much appreciate any help on this problem.

Many thanks,
Geoffroy

[Phil Bromiley]

You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

1. Yes, endogeneity is just as much a problem with binary outcomes.
2. You might look at Roodman's cmp estimator. Also, could be done in GSEM.
see also
https://www.stata.com/meeting/german...ukker_gsem.pdf
https://www.stata.com/statalist/arch.../msg00517.html

http://conference.iza.org/conference..._endog_iza.pdf

[Marcos Almeida]

You may wish to take a look at the ERMs, i.e., extended regression models, available in Stata 15.

[Joro Kolev]

For a proper solution to the endogeneity problem, you would need instruments just as in linear models.

What you are doing now, regressing on lagged values, is sort of reasonable approach. You can also think through what is affecting what, and with what lags, and then estimate a regression of the policy on comtemporaneous regressors, however the contemporaneous regressors that you think are endogenous being instrumented by past lagged "structure of the economy" variables.

We did something similar in linear context in Hogarth, Robin M., Mariona Portell, Anna Cuxart, and Gueorgui I. Kolev. "Emotion and reason in everyday risk perception." Journal of Behavioral Decision Making 24, no. 2 (2011): 202-222. Look at the approach there p.212 to p. 215.

[Geoffroy Dolphin]

Hi all,
Thanks very much for your answers and the suggestions given.
Best,
Geoffroy