I perfomed 2SLS ,
In the robust version i found the endogeneity , but did not found in non robust version.
The results in robust version is validy? need your help.
Non Robust options
Tests of endogeneity
H0: Variables are exogenous
Durbin (score) chi2(1) = .242302 (p = 0.6225)
Wu-Hausman F(1,613) = .227544 (p = 0.6335)
. estat overid
Tests of overidentifying restrictions:
Sargan (score) chi2(1) = .035671 (p = 0.8502)
Basmann chi2(1) = .033487 (p = 0.8548)
. estat firststage, all
First-stage regression summary statistics
--------------------------------------------------------------------------
| Adjusted Partial
Variable | R-sq. R-sq. R-sq. F(2,613) Prob > F
-------------+------------------------------------------------------------
TURN_1 | 0.1681 0.1152 0.0632 20.6714 0.0000
--------------------------------------------------------------------------
Shea's partial R-squared
--------------------------------------------------
| Shea's Shea's
Variable | partial R-sq. adj. partial R-sq.
-------------+------------------------------------
TURN_1 | 0.0632 0.0036
--------------------------------------------------
Minimum eigenvalue statistic = 20.6714
Critical Values # of endogenous regressors: 1
H0: Instruments are weak # of excluded instruments: 2
---------------------------------------------------------------------
| 5% 10% 20% 30%
2SLS relative bias | (not available)
-----------------------------------+---------------------------------
| 10% 15% 20% 25%
2SLS size of nominal 5% Wald test | 19.93 11.59 8.75 7.25
LIML size of nominal 5% Wald test | 8.68 5.33 4.42 3.92
---------------------------------------------------------------------
Robust options
- Tests of endogeneity
- H0: Variables are exogenous
- Robust score chi2(1) = 2.99494 (p = 0.0835)
- Robust regression F(1,613) = 2.77036 (p = 0.0965)
- . estat overid, forcenonrobust
- Tests of overidentifying restrictions:
- Sargan chi2(1) = .035671 (p = 0.8502)
- Basmann chi2(1) = .033487 (p = 0.8548)
- Score chi2(1) = .514465 (p = 0.4732)
- . estat overid
- Test of overidentifying restrictions:
- Score chi2(1) = .514465 (p = 0.4732)
- . estat firststage, all
- First-stage regression summary statistics
- --------------------------------------------------------------------------
- | Adjusted Partial Robust
- Variable | R-sq. R-sq. R-sq. F(2,613) Prob > F
- -------------+------------------------------------------------------------
- TURN_1 | 0.1681 0.1152 0.0632 13.7239 0.0000
- --------------------------------------------------------------------------
- Shea's partial R-squared
- --------------------------------------------------
- | Shea's Shea's
- Variable | partial R-sq. adj. partial R-sq.
- -------------+------------------------------------
- TURN_1 | 0.0632 0.0036
- --------------------------------------------------
The difference between robust and non-robust versions in regression analysis typically refers to the handling of heteroskedasticity in the error terms.
Robust Version: Adjusts for heteroskedasticity in the error terms. If you find evidence of endogeneity using a robust version, it means that after accounting for non-constant variance in the residuals (heteroskedasticity), there's still a correlation between the independent variable and the error term.
Non-Robust Version: Assumes constant variance in the error terms (homoskedasticity). If you don't find evidence of endogeneity in the non-robust version, it means the initial test did not detect correlation between the independent variable and the error term under the assumption of homoskedasticity.
In your 2SLS regression, the robust test indicating endogeneity suggests that after accounting for potential heteroskedasticity, the instrument may not be as valid as assumed. The non-robust result can be misleading if there's heteroskedasticity in the model. It's generally safer to trust the robust version, especially if there's a reason to suspect non-constant variance in the residuals.
The estat endogenous command in Stata can be used to test for the endogeneity of regressors in an instrumental variables (IV) model. The robust version of the test is designed to be more reliable in the presence of heteroskedasticity and autocorrelation in the errors.
The non-robust version of the test is based on the assumption that the errors are i.i.d. (independently and identically distributed). This assumption may not be valid in many real-world applications. If the errors are heteroskedastic or autocorrelated, the non-robust test may be unreliable and may produce false positives.
The robust version of the test is based on a different set of assumptions that are more likely to be valid in real-world applications. The robust test is therefore more reliable than the non-robust test, especially in the presence of heteroskedasticity and autocorrelation in the errors.
Which version of the test should you use?
It is generally recommended to use the robust version of the estat endogenous test, unless you are confident that the errors in your model are i.i.d. The robust test is more reliable and is less likely to produce false positives.
How do you interpret the results of the test?
The estat endogenous test produces a chi-squared statistic and a p-value. If the p-value is less than your chosen significance level (e.g., 0.05), then you can reject the null hypothesis of exogeneity. This means that there is evidence of endogeneity in the regressor(s) being tested.
Example
The following Stata code shows how to use the estat endogenous command to test for the endogeneity of the regressor x1:
ivregress y x1 x2 (z1 = z2), vce(robust) estat endogenous x1
The output of the estat endogenous command will include a chi-squared statistic and a p-value. If the p-value is less than your chosen significance level, then you can reject the null hypothesis of exogeneity for x1.
Conclusion
The robust version of the estat endogenous test is more reliable than the non-robust version, especially in the presence of heteroskedasticity and autocorrelation in the errors. It is generally recommended to use the robust version of the test.
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