Monday, Aug 3: 10:30 AM - 12:20 PM
1709
Topic-Contributed Paper Session
Thomas M. Menino Convention & Exhibition Center
Room: CC-204A
Applied
No
Main Sponsor
Business and Economic Statistics Section
Co Sponsors
Business Analytics/Statistics Education Interest Group
Section on Statistical Learning and Data Science
Presentations
This paper develops a general causal inference method for treatment effects models with noisily measured confounders. The key feature is that a large set of noisy measurements are linked with the underlying latent confounders through an unknown, possibly nonlinear factor structure. The main building block is a local principal subspace approximation procedure that combines K-nearest neighbors matching and principal component analysis. Estimators of many causal parameters, including average treatment effects and counterfactual distributions, are constructed based on doubly-robust score functions. Large sample properties of these estimators are established, which only require relatively mild conditions on the principal subspace approximation. The results are illustrated with an empirical application studying the effect of political connections on stock returns of financial firms, and a Monte Carlo experiment. The main technical and methodological results regarding the general local principal subspace approximation method may be of independent interest.
We develop a spectral approach for identifying and estimating average counterfactual outcomes under a low-rank factor model with short panel data and general outcome missingness patterns. Applications include event studies and studies of outcomes of "matches" between agents of two types, e.g. people and places, typically conducted using less-flexible Two-Way Fixed Effects (TWFE) models of outcomes. Given finite observed outcomes per unit, we show our approach identifies all counterfactual outcome means, including those not identified by existing methods, if a particular graph algorithm determines that units' sets of observed outcomes have sufficient overlap. Our analogous, computationally efficient estimation procedure yields consistent, asymptotically normal estimates of counterfactual outcome means under fixed-T (number of outcomes), large-N (sample size) asymptotics. When estimating province-level averages of held-out wages from an Italian matched employer-employee dataset, our estimator outperforms a TWFE-model-based estimator.
This paper studies the imputation and inference for large-dimensional non-stationary panel data with general missing observations. Our novel method, Within-Transform-PCA (wi-PCA), transforms the data under endogenous missingness to remove non-stationarities and heterogeneous mean effects before estimating an approximate latent factor structure with PCA. This within-transformation is equivalent to estimating two-way non-stationary fixed effects separately from the latent factor structure. Our approach allows for one of the most general and broadly applicable models for data generation and missing patterns in the factor modeling literature. We provide entry-wise inferential theory for the values imputed with wi PCA. The key application of wi-PCA is the estimation of counterfactuals on causal panels, where we allow for two-way endogenous treatment effects, time trends and general latent confounders. In an empirical study of the liberalization of marijuana, we show that wi-PCA yields more accurate estimates of treatment effects and more credible economic conclusions compared to its two special cases of conventional difference-in-differences and PCA.
Statistical analysis requires that something be random, e.g. random sampling from a population or randomized assignment of treatment. But often, it's unclear what, if anything, is actually random in the panels we're working with, so whatever statistical claims we make are based on a random mechanism we're imagining. This talk is about basing our analysis on imagined randomization of treatment: what assignment mechanisms we might want to imagine, what we can conclude if we buy into what we're imagining, and how we might interpret those conclusions with a little more skepticism. The main example will be an analysis of synthetic control methods having imagined that units select treatment independently with unknown unit-specific probabilities.
Matrix completion concerns the imputation of missing entries in a partially observed matrix. While its rapid development was originally motivated by applications in recommendation systems, it has also opened new possibilities in causal inference, where missing counterfactual outcomes can be imputed to estimate individual treatment effects.
In causal inference problems, the missingness pattern in potential outcomes is induced by the treatment adoption process. Although treatment assignment may satisfy the missing at random (MAR) assumption in randomized experiments and certain quasi-experimental designs, this assumption is often violated in observational studies. For instance, when a program is introduced at a particular time for a subset of units, the potential outcomes under control become unobserved for treated units after treatment adoption, creating a block missingness structure.
I present an inferential framework for matrix completion under missing not at random (MNAR) mechanisms and its application to treatment effect estimation. I also compare our approach with existing methods and discuss several promising extensions.