Inquiry Regarding Econometric Issues in Export Survival Analysis

[Mariska Aucamp]

Good day

I am reaching out for any assistance on the xtprobit command in stata, specifically with regards to how to test for and address endogeneity.

My research examines the relationship between export survival and trade potential at a detailed product-country level. For my econometric analysis, I am employing the xtprobit command in Stata, following the research findings of Hess & Persson (2012). Their study suggests that a probit model with random effects is the most suitable for export survival analysis, as it accounts for unobserved heterogeneity while effectively handling tied duration times and non-proportionality. In line with their argument, I am clustering the random effects at the product-country level.
However, I have encountered some uncertainty regarding how best to test for and address endogeneity in this context:

1. I initially followed the approach suggested by Professor Wooldridge from the Stata forum (Engogeneity test after xtlogit - Statalist), testing for endogeneity using lead values alongside time averages in my regression. The results suggested that I can accept the null hypothesis of strict exogeneity with respect to the idiosyncratic errors.
2. I then applied the Mundlak approach by including time averages of covariates to check for correlation with u(i). The results indicated that some covariates may be correlated with u(i), leading me to the following questions:
   • Should I simply retain the time averages in my regression to account for this form of endogeneity? Or is it unnecessary to use this approach to test for correlation between the covariates and u(i), given that Hess & Persson argue that the probit model with random effects already accounts for unobserved heterogeneity?
   • Since xtprobit does not allow a fixed-effects specification in Stata, many studies instead introduce fixed-effect dummy variables (e.g., for duration, sector, destination, and year). Would this be a valid approach to mitigate endogeneity, or should I include these dummies and re-run the Mundlak approach?
   • If the Mundlak approach is used and correlation is present, should the final regression include the time averages permanently? Additionally, I have noticed that the signs of the time-average variables often differ from the original covariates (e.g., the mean of GDP per capita is negative, while the original variable is positive). How should this be interpreted?

Thank you for your time and consideration. I look forward to your response.

[Mariska Aucamp]

It should also be noted, I have lagged the trade potential variable to address simultaneity issues.