The endogeneity problem, to my knowledge, is treated using instrumental variables. The models used in the studies of CG are: 2SLS; GMM; SEM; lagged variables.

Thanks you Fabrizio,

GMM is certainly a powerful methodology but as Hoechle and al JFE(2012) and Wintocki and all JFE (2012) suggest, it doesn't eradicate all possibilities of endogeneity

Thanks you EriK,

The use of external experiment is a good idea to tackle endogeneity problems, but not always available. Sometimes a new regulation,( The Sarbanes-Oxley Law for example) or a new tariff-policy for exportations may be used, but they are not often usable. I am wondering if GMM is a good solution?

I found these recent discussions on endogenity related methodology debates. 

http://www.sciencedirect.com/science/article/pii/S0378426614003902(science direct subscription)

Anh Dang Kim and Shin, April 2015, In search of robust methods for dynamic panel data models in empirical corporate finance, JBF

We examine which methods are appropriate for estimating dynamic panel data models in empirical corporate finance. Our simulations show that the instrumental variable and GMM estimators are unreliable, and sensitive to the presence of unobserved heterogeneity, residual serial correlation, and changes in control parameters. The bias-corrected fixed-effects estimators, based on an analytical, bootstrap, or indirect inference approach, are found to be the most appropriate and robust methods. These estimators perform reasonably well even in models with fractional dependent variables censored at [0, 1]. We verify these results in two empirical applications, on dynamic capital structure and cash holdings. 

http://www.sciencedirect.com/science/article/pii/S092911991200096X(science direct subscription)

Flannery and Hankins, 2013, Estimating dynamic panel models in corporate finance, JCF

Dynamic panel models play a natural role in several important areas of corporate finance, but the combination of fixed effects and lagged dependent variables introduces serious econometric bias. Several methods of counteracting these biases are available and these methodologies have been tested on small datasets with independent, normally-distributed explanatory variables. However, no one has evaluated the methods' performance with corporate finance data, in which the dependent variable may be clustered or censored and independent variables may be missing, correlated with one another, or endogenous. We find that the data's properties substantially affect the estimators' performances. We provide evidence about the impact of various data set characteristics on the estimators, so that researchers can determine the best approach for their datasets.

http://www.sciencedirect.com/science/article/pii/S0378426614003902

http://www.sciencedirect.com/science/article/pii/S092911991200096X

Thanks you Amit for this very comprehensive response. I agree that fixed effects may avoid heterogeneity (it wipes out the individiual effects) but we suffer a large loss of degrees of freedom. By the way, what do you think about the omitted variables' problem?

HI Patrick, Omitted Variables is a more critical problem in the research I am undertaking. A topic such as Corporate Governance may not be fathomed by 100 variables(in a cogent index) and the role of Private information rules out the use of Heckman's estimator in the 2SLS/3SLS form, leaving you with inconsistent propositions that are not reproduced in the data. Try Li and Prabhala(2007) for his explanation of Omitted variables being in the nature of Private information