One of the assumptions for the plug-in solution to provide consistent estimators of β₁ and β₂ is that the error u is uncorrelated with all the independent variables.

Question

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This assumption is known as the exogeneity assumption and it requires that the error term u is uncorrelated with all independent variables, including the ones included in the interaction terms. This is necessary in order to obtain consistent estimates for the coefficients of the interaction terms using the plug-in estimator.

One of the Assumptions for the Plug-In Solution to Provide