Re: how to make Durbin–Wu–Hausman test for the equation?
This post has NOT been accepted by the mailing list yet.
I can answer your first questions about the endogeneity test.
I am assuming that chine_exp is the endogenous variable, and distance is the instrumental variable.
1) run OLS regression where chine_exp is the dep var and distance is the indep var along with the rest of the variables included in your original equation.
2) get the residuals from the regression "vhat".
3) run your equation including the residuals from the first OLS as follow exporter=z*vhat+a*china_exp+b*gdp_capita_exp+c*gdp_exp+d*comlang_off+error
4) if the coefficient on the residuals (z) is significant then you have endogeneity and you should run 2SLS, else there is no endogeneity and hence no need for 2SLS.
keep in mind that your results are as good as your instrumental varibale. Make sure that it is a valid instrument.
Hope this helps.