I currently have the correlation/covariance matrix for a set of variables and the results of regression analysis but lack access to the raw dataset. Under these constraints, is it feasible to conduct a thorough analysis of endogeneity? I welcome any guidance on methodologies or statistical techniques that could be utilized to examine the presence of endogeneity given these limitations.
As a provisional solution, I have employed Cholesky decomposition to simulate data, which can generate a correlation matrix that closely approximates the original. Nevertheless, this method presents potential issues because it constructs data predicated on the assumption that all features are normally distributed. Please advise whether this is an appropriate course of action.