Help on modelling- endogeneity-panel data

[Simona Battipaglia]

Hello,

I am running a model to find the effect of corurption on GDP in across Italian regions using panel data. I have found endogeneity between corruption and GDP growth,hence I am trying to use either fixed effects with instrumental variables or OLS with dummy variables.

As for the first case, I am having difficulties when specifying the following:

--> specification 1:
GDP growth= population growth + human capital + public investment + Corruption + Corruption ^2 + log of the lagged GDP pro capite

My coding is:
xtivreg Ygrowth I H logYlevel_1 n (Cor Cor2=Cor_1 Cor_12),fe vce (robust)
where Cor2=Cor^2 and Cor_12=(Cor_1)^2
- however, STATA says that Cor^2 is omitted because of collinearity. why is that the case?


--> specification 2:
GDP growth= population growth + human capital + public investment + logCorruption + log of the lagged GDP pro capite

My coding is:
xtivreg Ygrowth I H logYlevel_1 n (logCor= logCor_1 ),fe vce (robust)
- however, this results in everything being insignificant although I had found the following specification to be significant: xtivreg Ygrowth I H logYlevel_1 n (Cor= Cor_1 ),fe vce (robust)

--> model 2:
I wanted to try the following: reg Ygrowth H logYlevel_1 n I i.Region##c.Cor##i.Year, but it gives me an error message saying I have not coded this right. How do I code a dummy interaction variable to know the effect of corruption for each region for each year?

[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.
You should generally specify interactions and squares using factor variable notation. If you use factor variable notation, then the margins statement correctly handles both linear and non-linear effects at once. As for something being colinear, have you looked at the correlation between Cor and Cor2 and between Cor2 and the other variables? Have you tried regressing Cor2 on Cor Cor_1 and Cor_12 and the other variables? It is hard to diagnose a data problem like colinearity without the data.

In spec 2, does Cor have negative values? If so, logging it will reduce your sample size by creating missing values.

If you only have one observation per region per year, you can't include a region/year interaction. I also doubt if "not coded right" is what Stata told you. Knowing the exact error message is essential to helping you.