Instrument-free inference under confined regressor endogeneity; derivations and applications

A fully-fledged alternative to Two-Stage Least-Squares (TSLS) inference is developed for general linear models with endogenous regressors. This alternative approach does not require the adoption of external instrumental variables. It generalizes earlier results which basically assumed all variables in the model to be normally distributed and their observational units to be stochastically independent. Now the chosen underlying framework corresponds completely to that of most empirical cross-section or time-series studies using TSLS. This enables revealing empirically relevant replication studies, also because the new technique allows testing the earlier untestable exclusion restrictions adopted when applying TSLS. For three illustrative case studies a new perspective on their empirical findings results. The new technique is computationally not very demanding. It involves scanning least-squares-based results over all compatible values of the nuisance parameters established by the correlations between regressors and disturbances.