*Bounty: 50*

*Bounty: 50*

I am using 2SLS for my research and I want to test for overidentification. I started out with the Hausman test of which I have a reasonable grasp.

The problem I have is that from the Hausman and the Sargan Test I am getting very different results.

The Sargan test is done by `ivmodel`

from `library(ivmodel)`

. I copied the Hausman test from “Using R for Introductory Econometrics” page 226, by Florian Heiss.

```
[1] "############################################################"
[1] "***Hausman Test for Overidentification***"
[1] "############################################################"
[1] "***R2***"
[1] 0.0031
[1] "***Number of observations (nobs)***"
[1] 8937
[1] "***nobs*R2***"
[1] 28
[1] "***p-value***"
[1] 0.00000015
Sargan Test Result:
Sargan Test Statistics=0.31, df=1, p-value is 0.6
```

On top of this I am also using `ivtobit`

from Stata, which provides a Wald test of exogeneity.

Lastly I read about a fourth which is the `Hansen J statistic`

.

What is the difference between all of these tests?