causal inference | Chen Xing

Balancing Weights for Causal Inference

TL;DR Cohn et al. (2023) introduces the balancing approach to weighting for causal inference in observational studies. Unlike traditional methods that model the propensity score directly, balancing weights are estimated by solving an optimization problem that directly targets covariate balance between treatment groups.

Oct 22, 2025 5 min read causal inference

🛡️ Triply Robust Panel Estimators: When You Don't Know Which Assumptions Hold

TL;DR Athey, Imbens, Qu, and Viviano introduce the Triply RObust Panel (TROP) estimator, which combines unit weights, time weights, and a flexible low-rank factor model to estimate causal effects in panel data.

Oct 20, 2025 6 min read econometrics, causal inference

The Experimental Selection Correction Estimator

TL;DR Athey, Chetty, and Imbens develop a new method to estimate treatment effects on primary outcomes (like graduation rates) by combining experimental data where treatment is randomized but only secondary outcomes are observed (like test scores) with observational data where both primary and secondary outcomes are measured but treatment is not randomized.

Oct 6, 2025 6 min read causal inference, econometrics

Same Root Different Leaves: Time Series and Cross-Sectional Methods in Panel Data

TL;DR This paper proves that horizontal regression (time series methods like unconfoundedness) and vertical regression (cross-sectional methods like synthetic controls) can produce algebraically identical point estimates for several common estimators including OLS, PCR, and ridge regression.

Oct 5, 2025 4 min read causal inference, econometrics

When Good Controls Aren't Good Enough: The Augmented Synthetic Control Method

Ben-Michael, Eli, Avi Feller, and Jesse Rothstein (2021), “The Augmented Synthetic Control Method,” Journal of the American Statistical Association, 116 (536), 1789–1803. Key insight: Synthetic control method (SCM) can be regarded as a form of inverse propensity score weighting.

Sep 30, 2025 5 min read causal inference, econometrics

Notes on Interactive Fixed Effects

Summary of the Paper The paper by Jushan Bai, published in Econometrica (2009), addresses panel data models with interactive fixed effects, focusing on large

N

(cross-sectional units) and large

T

(time periods) settings.

Jul 10, 2025 8 min read econometrics, causal inference

Notes on Matrix Completion Methods for Causal Panel Data Models

Here are my study notes on the matrix completion method for causal panel data models proposed by Athey et al. (2021). 1. Setup and Notation

Y (0), Y (1)

are potential outcome matrices

Jul 8, 2025 11 min read causal inference

AIPW vs. Residual-on-Residual regression: Non-Parametric Flexibility or Efficiency?

Introduction Two powerful tools in causal inference are the Augmented Inverse Propensity Weighting (AIPW) estimator and the Residual-on-Residual regression estimator for partially linear models. Drawing from Wager’s notes (2024), this post breaks down how these estimators work, compares their strengths and weaknesses, and offers tips for when to use each.

Jun 11, 2025 3 min read causal inference, econometrics

What is the Critical Radius in Riesz Regression?

TL;DR In the paper Automatic Debiased Machine Learning via Riesz Regression by Chernozhukov et al. (2024), the critical radius is a key concept for understanding how accurately machine learning (ML) can estimate the Riesz representer—a function used to debias ML estimates of economic parameters like treatment effects.

Jun 7, 2025 6 min read causal inference, econometrics

Notes on Propensity Score Methods

Introduction Here are my notes on propensity scores, mainly from Prof. Ding’s textbook (2024). The traditional propensity score analysis workflow is shown in the image below, which I will not cover in detail.

Jun 3, 2025 6 min read causal inference, econometrics

Notes on DML for DiD: A Unified Approach

Introduction This blog post explores how Double Machine Learning (DML) extends to conditional Difference-in-Differences (DiD), focusing on doubly robust estimators. The key insight is that conditional DiD can be understood through the lens of cross-sectional ATT estimation.

Jun 2, 2025 3 min read causal inference, econometrics

Notes on causal inference with No Overlap – Regression Discontinuity

Here is my notes on regression discontinuity from Prof. Ding’s textbook (2024) and Prof. Imai’s lecture notes. Motivation We often cannot run a randomized experiment and have to use/design observational studies to find a setting where credible causal inference is possible.

May 31, 2025 2 min read causal inference, econometrics, quantitive-marketing

Notes on Control Function Method

Motivation Endogeneity: When an explanatory variable (treatment) is correlated with the unobserved error term (e.g., due to omitted variables, measurement error, or simultaneity). Consequence: Standard regression (e.g., OLS) yields biased estimates.

May 31, 2025 4 min read causal inference, econometrics, quantitive-marketing

Notes on IV Free Methods

Here’s a overview of instrument-free methods: Latent Instrumental Variable (LIV) Gaussian Copula (GC) The goal is for dealing with endogeneity when no external instruments are available. Motivation Finding good instruments is hard.

May 30, 2025 3 min read causal inference, quantitive-marketing, econometrics

Notes on Instrumental Variables

Here are my notes on instrumental variables from Stefan’s lecture materials. Motivation How can we identify causal eﬀects

W \to Y

when we are in the presence of unobserved confounding

U

?

May 29, 2025 6 min read causal inference, econometrics

Notes on Callaway & Sant’Anna (2021) – Staggered Adoption DiD

0. Motivation Staggered‐adoption policies break the canonical two-period / two-group DiD model. It has been shown that the traditional two-way fixed-effects (TWFE) regression can assign negative weights to treatment effects, thereby obscuring their dynamic and heterogeneous patterns.

May 27, 2025 7 min read causal inference, econometrics

Notes on Synthetic Control

Motivation Abadie et al. (2010) motivate the synthetic control method with a model that generalizes the difference-in-differences (ﬁxed-eﬀects) model commonly applied in the empirical social science literature by allowing the effect of unobserved confounding characteristics to vary over time.

May 22, 2025 5 min read causal inference, econometrics

Intuition for Doubly Robust Estimator

Introduction To estimate ATE, we can either use outcome regression or inverse propensity weighting (IPW). While each approach has merits, combining them offers significant advantage – double robustness. In this post, I summarize the intuition for doubly robust estimator from Professor Ding’s awesome textbook (Ding, 2024), and connects this framework to debiased machine learning (DML) through Riesz representation theory.

May 18, 2025 4 min read causal inference, econometrics

Big Picture of Debiased Machine Learning

Debiased machine learning (DML) is a generic recipe. The idea behind it is adding a correction term to the plug-in estimator of the functional, which leads to properties such as semi-parametric efﬁciency, double robustness, and Neyman orthogonality.

Mar 25, 2025 2 min read causal inference, econometrics

Orthogonal vs Non-orthogonal Learning

The following exercise is from CausalAIBook Notebook. The goal is to illustrate the difference between Neyman orthogonal vs non-orthogonal approach. Setting We compare the performance of the naive and orthogonal methods in a computational experiment where

p = n = 100

,

β_{j} = 1 / j^{2}

,

(γ_{D W})_{j} = 1 / j^{2}

and

Y = 1 \cdot D + β^{'} W + ϵ_{Y}

Feb 22, 2025 3 min read causal inference, econometrics