Instrumental weighted variables under heteroscedasticity, Part I -- Consistency

Instrumental weighted variables under heteroscedasticity, Part I - Consistency

Consistency of the least weighted squares under heteroscedasticity

A robust version of the Ordinary Least Squares accommodating the idea of weighting the order statistics of the squared residuals (rather than directly the squares of residuals) is recalled and its properties are studied. The existence of solution of the corresponding extremal problem and the consistency under heteroscedasticity is proved. 1. BASIC FRAMEWORK AND WEIGHTING THE ORDER STATISTICS Le...

Consistency without Inference: Instrumental Variables in Practical Application

I use the bootstrap to study a comprehensive sample of 1400 instrumental variables regressions in 32 papers published in the journals of the American Economic Association. IV estimates are more often found to be falsely significant and more sensitive to outliers than OLS, while having a higher mean squared error around the IV population moment. There is little evidence that OLS estimates are su...

Semiparametric Qualitative Response Model Estimation with Unknown Heteroscedasticity or Instrumental Variables

This paper provides estimators of discrete choice models, including binary, ordered, and multinomial response (choice) models. The estimators closely resemble ordinary and two stage least squares. The distribution of the model’s latent variable error is unknown and may be related to the regressors, e.g., the model could have errors that are heteroscedastic or correlated with regressors. The est...

An Introduction to Instrumental Variables Analysis: Part 1

There are several examples in the medical literature where the associations of treatment effects predicted by observational studies have been refuted by evidence from subsequent large-scale randomised trials. This is because of the fact that non-experimental studies are subject to confounding – and confounding cannot be entirely eliminated even if all known confounders have been measured in the...