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.

アブストラクト：
独立な高次元確率ベクトルの和の成分の最大値として与えられる統計量の分布の近似は、高次元パラメータに対する仮説検定や一様信頼区間の構成を行う上で重要な役割を果たす。V. Chernozhukov, D. ChetverikovおよびK. Katoらによる近年の研究によって、そのような最大値統計量の分布に対する正規型の近似やブートストラップ近似は、次元がサンプル数よりもはるかに大きいような超高次元の設定においても適当なモーメント条件下で正当化できることが明らかにされた。一方で、データの歪度がある程度大きい場合、スチューデント化を行わない場合であっても、高次元の設定では3次モーメントまでマッチさせるようなブートストラップ近似の方が正規型の近似よりも有限標本でのパフォーマンスが優れていることが数値実験によって観察されているが、既存の理論的結果はこのことを説明できない。本報告では、漸近展開を用いることでこの現象が理論的に説明できることを示す。特に、母集団の共分散行列が一定の条件を満たす場合、次元がサンプル数よりも大きい状況では3次モーメントまでマッチさせるようなブートストラップ近似がスチューデント化せずとも2次の精度を持つというblessing of dimensionality phenomenonが現れる。

Abstract: The exclusion restriction plays a key role in the identification of LATE (Imbens & Angrist (1994), Angrist, Imbens & Rubin (1996)). We discuss a particularly ubiquitous way in which the exclusion restriction would seem to be generically violated. We argue that this form of violation is not addressed in the many applications that rely on this influential framework. We characterize the bias that this particular violation gives rise to and, more constructively, discuss how to use the particular structure of the violation along with milder assumptions and additional data to restore identification. We provide sharper bounds by exploiting the specific structure of the exclusion restriction violation we uncover. Further, with an additional assumption which is plausible in many empirical settings, we restore point identification of LATE. We illustrate with examples and discuss why this violation is likely present in most existing empirical applications. We discuss how our arguments naturally extend to other IV settings where the LATE parameter is commonly invoked, such as randomized controlled trials with imperfect compliance and fuzzy regression discontinuity designs. Moving beyond LATE, we also consider how the same problems and solution ideas apply to identification of the MTE profile and more structural “Roy” models of treatment effects.