Abstract: This paper develops semiparametric Bayesian methods for estimating the average treatment effect on the treated (ATT) in difference-in-differences (DiD) designs. We propose two Bayesian procedures with frequentist validity. The first places a Gaussian process prior on the conditional mean function of the control group. The second is a double-robust Bayesian approach that adjusts the prior on the conditional mean function and then corrects the posterior distribution of the ATT. We establish a semiparametric Bernstein¨Von Mises theorem, showing the asymptotic equivalence between our Bayesian procedures and efficient frequentist estimators. For the second approach, the result holds under double-robust smoothness conditions: the lack of smoothness in the conditional mean function can be compensated by high regularity of the propensity score, and vice versa. Monte Carlo simulations and an empirical application demonstrate strong finite-sample performance of our Bayesian DiD methods. We also extend the Bayesian framework to staggered DiD designs.

Distributional Effects with Two-Sided Measurement Error: An Application to Intergenerational Income Mobility∗ (joint with Brantly Callaway, Irina Murtazashvili, Emmanuel S. Tsyawo)

Abstract: This paper considers identification and estimation of distributional effect parameters that depend on the
joint distribution of an outcome and another variable of interest (“treatment”) in a setting with “two-
sided” measurement error — that is, where both variables are possibly measured with error. Examples
of these parameters in the context of intergenerational income mobility include transition matrices, rank-
rank correlations, and the poverty rate of children as a function of their parents’ income, among others.
Building on recent work on quantile regression (QR) with measurement error in the outcome (particu-
larly, Hausman, Liu, Luo, and Palmer (2021)), we show that, given (i) two linear QR models separately
for the outcome and treatment conditional on other observed covariates and (ii) assumptions about the
measurement error for each variable, one can recover the joint distribution of the outcome and the treat-
ment. Besides these conditions, our approach does not require an instrument, repeated measurements,
or distributional assumptions about the measurement error. Using recent data from the 1997 National
Longitudinal Study of Youth, we find that accounting for measurement error notably reduces several
estimates of intergenerational mobility parameters.

Abstract: This talk will survey recent advances in understanding Chatterjee’s graph correlation coefficient. I will introduce, for the first time, a comprehensive theoretical framework for statistical inference based on this coefficient. The framework involves results on asymptotic normality, bias correction, and the (in)consistency of bootstrap methods.

Another title: Necessary and sufficient conditions for convergence in distribution of quantile and P-P processes in L1(0,1), (joint with Tetsuya Kaji, Chicago Booth)
https://arxiv.org/abs/2502.01254

Title: Scalable Estimation of Multinomial Response Models with Random Consideration Sets (with Siddhartha Chib)

Abstract: A common assumption in the fitting of unordered multinomial response models for J mutually exclusive categories is that the responses arise from the same set of J categories across subjects. However, when responses measure a choice made by the subject, it is more appropriate to condition the distribution of multinomial responses on a subject-specific consideration set, drawn from the power set of {1,2,…,J}. This leads to a mixture of multinomial response models governed by a probability distribution over the J* = 2^J -1 consideration sets. We introduce a novel method for estimating such generalized multinomial response models based on the fundamental result that any mass distribution over J* consideration sets can be represented as a mixture of products of J component specific inclusion-exclusion probabilities. Moreover, under time-invariant consideration sets, the conditional posterior distribution of consideration sets is sparse. These features enable a scalable MCMC algorithm for sampling the posterior distribution of parameters, random effects, and consideration sets. Under regularity conditions, the posterior distributions of the marginal response probabilities and the model parameters satisfy consistency. The methodology is demonstrated in a longitudinal data set on weekly cereal purchases that cover J = 101 brands, a dimension substantially beyond the reach of existing methods.

Title: The Estimation of Diffusion Processes with Private Network Information

Abstract: Innovations, either products or ideas, often spread through social networks. This paper introduces an econometric framework for identifying and estimating diffusion processes within these networks. Unlike traditional diffusion models that assume a continuous population with stochastic network structures, our approach examines scenarios where Bayesian agents observe their immediate neighbours within a persistent network. We establish the existence of a symmetric equilibrium and provide its characterization. Building upon these results, we propose a consistent and tractable two-step estimator for the payoff parameters, addressing endogeneity arising from exposure during the diffusion process. We evaluate the finite-sample performance of the estimator through Monte Carlo simulations and apply our method to the network data from Banerjee et al. (2013).

Abstract:
This paper provides novel nonparametric methods for estimation and uniform inference of optimal policy allocation rules and the resulting welfare. The original problem is formulated as a partially identified model, which entails non-standard asymptotics. We show that employing a surrogate risk function ensures point identification of a representing function, thereby enabling tractable asymptotic analysis based on Gaussian approximations. We propose a two-step cross-fitting procedure for estimating the nonparametric optimal policy, which achieves the standard nonparametric convergence rate and admits standard Gaussian approximations for inference. Leveraging these results and coupling principles, we develop a new method for nonparametric inference on both the optimal policy and the associated welfare. We also emphasize that the limiting distribution of the welfare estimator admits a Gaussian approximation, supported by the stochastic equicontinuity of the policy function estimator.

要旨：　Exclusion and shape restrictions are crucial for defining causal effects, understanding individual heterogeneity, and interpreting estimators in potential outcome models. This paper is concerned with characterizing the empirical content of such restrictions. To date, the testable implications of these restrictions have been studied on a case-by-case basis within a limited set of models. Using a novel graph-based representation of the model, we provide a systematic approach to deriving sharp testable implications of general support restrictions. We illustrate the proposed approach in simulations and an empirical application.