Related papers: The Yule-Frisch-Waugh-Lovell Theorem for Linear In…
This paper traces the historical and analytical development of what is known in the econometrics literature as the Frisch-Waugh-Lovell theorem. This theorem demonstrates that the coefficients on any subset of covariates in a multiple…
The Frisch--Waugh--Lovell Theorem states the equivalence of the coefficients from the full and partial regressions. I further show the equivalence between various standard errors. Applying the new result to stratified experiments reveals…
The residualization procedure has been applied in many different fields to estimate models with multicollinearity. However, there exists a lack of understanding of this methodology and some authors discourage its use. This paper aims to…
In this note we introduce a generalized formula for Cohen's $d$ under the presence of additional independent variables, providing a measure for the size of a possible effect concerning the location difference of a variable in two groups.…
We offer straightforward theoretical results that justify incorporating machine learning in the standard linear instrumental variable setting. The key idea is to use machine learning, combined with sample-splitting, to predict the treatment…
We provide a Copula-based approach to test the exogeneity of instrumental variables in linear regression models. We show that the exogeneity of instrumental variables is equivalent to the exogeneity of their standard normal transformations…
A basic principle in the design of observational studies is to approximate the randomized experiment that would have been conducted under controlled circumstances. Now, linear regression models are commonly used to analyze observational…
We provide a justification for why, and when, endogeneity will not cause bias in the interpretation of the coefficients in a regression model. This technique can be a viable alternative to, or even used alongside, the instrumental variable…
Instrumental variables regression is a tool that is commonly used in the analysis of observational data. The instrumental variables are used to make causal inference about the effect of a certain exposure in the presence of unmeasured…
This paper develops a first-stage linear regression representation for the instrumental variables (IV) quantile regression (QR) model. The quantile first-stage is analogous to the least squares case, i.e., a linear projection of the…
The linear regression model is widely used in the biomedical and social sciences as well as in policy and business research to adjust for covariates and estimate the average effects of treatments. Behind every causal inference endeavor…
The quantile residual lifetime (QRL) regression is an attractive tool for assessing covariate effects on the distribution of residual life expectancy, which is often of interest in clinical studies. When the study subjects are exposed to…
We demonstrate that regression models can be estimated by working independently in a row-wise fashion. We document a simple procedure which allows for a wide class of econometric estimators to be implemented cumulatively, where, in the…
This paper considers a multi-environment linear regression model in which data from multiple experimental settings are collected. The joint distribution of the response variable and covariates may vary across different environments, yet the…
In a causal graphical model, an instrument for a variable X and its effect Y is a random variable that is a cause of X and independent of all the causes of Y except X. (Pearl (1995), Spirtes et al (2000)). Instrumental variables can be used…
We present a fast and memory efficient algorithm for the estimation of generalized linear models with an additive separable k-way error component. The brute force approach uses dummy variables to account for the unobserved heterogeneity,…
From a variational perspective, many statistical learning criteria involve seeking a distribution that balances empirical risk and regularization. In this paper, we broaden this perspective by introducing a new general class of variational…
The endogeneity issue is fundamentally important as many empirical applications may suffer from the omission of explanatory variables, measurement error, or simultaneous causality. Recently, \cite{hllt17} propose a "Deep Instrumental…
In this paper, we propose deep partial least squares for the estimation of high-dimensional nonlinear instrumental variable regression. As a precursor to a flexible deep neural network architecture, our methodology uses partial least…
In this paper, we study statistical inference in functional quantile regression for scalar response and a functional covariate. Specifically, we consider a functional linear quantile regression model where the effect of the covariate on the…