I have the panel data regression model for which have to test the endogeneity.
i read one research paper which was using Vector Autoregression (VAR) to test the endogeneity.
in that paper, it was mentioned that if the lagged values of the dependent variable of the original regression model are not having significant impact on the independent variables, it indicates that the original model is free from endogeneity.
can anybody suggest whether it is an appropriate way to test the endogeneity of the model.
thanks in advance
In a VAR model, you may have both endogenous and exogenous variables.
There is one equation per endogenous variable, and the exogenous variable(s) enter in the righthand side of the equations.
A way to test whether any of the exogenous variables is actually endogenous, is to estimate a new VAR model, where the variable in question is treated as endogenous. Then do Granger non-causality tests.
Example: You have a bivariate VAR model with x and y as the endogenous variables and z as the exogenous variable. If you want to test whether z is actually endogenous, then you should estimate a trivariate VAR, with x, y, z as endogenous variables. Then perform Granger tests on z. These tests say that if z is exogenous then the coefficients of the lagged values of x and y should appear statistically insignificant in the equation of z.
In panel data models and simple linear regressions there are not really standardized endogeneity tests. This is decided usually based on information available regarding the variables in question. However, making inverse regressions or attempting instrumental variable methods may provide some feedback.
The VAR model basically treat each variable in the model as endogenous and so uses their lags to correct the possible endogeneity problem.
Since you are working with panel data, I will recommend the use of system GMM.
In a dynamic panel model, the inclusion of a lagged dependent model does always cause endogeneity and you need some special estimation techniques (e,g, Arrelano-Bond estimator). You can then use the appropriate technique to estimate the coefficient and significance of the lagged dependent variable. If you then find that the lagged dependent variable is not significant then you can assume that there is no need for a lagged dependent variable in the model.
You may then be able to use more standard techniques if the requirements for panel data are met. (endogeneity can arise from other sources).
Dynamic panel data is an advanced topic. Have a look at the relevant sections in Cameron and Trivedi (2005), Microeconometrics, Cambridge. This is an advanced level technique and the material will be covered in most other advanced level texts on panel data.
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