Research

We introduce a network two-way fixed effect regression with group structure. We propose a group prior for unobserved heterogeneity. While the OLS estimator exists under this model, it can perform poorly when the bipaetite network is sparse and with group structure. We therefore develop a machine-learning-assisted empirical Bayes estimation framework that combines a structural causal model with a Bayesian belief network. This framework yields a class of empirical Bayes estimators designed specifically for the proposed group-network two-way fixed effect regression.

We propose a network autoregression to learn mixed membership in large panel of time series. The data generating process, coefficient matrix and Mixed membership structure are integrated into one unified system using joint distribution specified by probabilistic graph. We also propose a set of algorithm to learn latent mixed membership structure with the model.

We develop a directed, weighted, horizon-specific network framework for measuring contagion across financial markets. An edge from one market to another indicates that past movements in the former predict future movements in the latter, conditional on the remaining markets; the edge weight measures the resulting reduction in forecast uncertainty. The network is estimated from a multi-horizon heterogeneous autoregressive model using debiased machine learning, allowing for high-dimensional dependence among markets. The framework identifies transmitters and receivers of shocks, traces transmission paths over rolling windows, characterizes horizon-specific contagion patterns, and distinguishes direct predictive spillovers from co-movement induced by common factors. The proposed approach provides a unified empirical tool for analyzing contagion, systemic risk, and stress propagation in interconnected financial markets.

We propose a methodology for estimating mixed-membership structure in large panels of time series. Unlike pure-membership models, in which each unit belongs exclusively to one group, mixed-membership models allow each unit to have partial affiliations with multiple latent groups. We develop a two-path partial-correlation network model in which the sparsity pattern and interaction intensity are governed separately by mixed membership and node-specific sociability. These latent structures are integrated into a unified probabilistic system through a Bayesian network and enter the panel model through the innovation process. We then propose a spectral algorithm to estimate the latent mixed-membership structure.

We propose a novel network-based peer effect model with unobserved unit-specific heterogeneity, in which the regression structure is augmented by a probabilistic graph that characterizes the latent dependence mechanism among all components of the model. This probabilistic graph, in turn, provides the foundation for the empirical Bayes estimator developed in the paper. The group structure embedded in the unit heterogeneity arises from a group prior, which we introduce to capture the latent heterogeneity across units. Although a least squares estimator exists for the proposed model, it performs poorly in the presence of sparsity in network. To address these challenges, we develop a machine learning–assisted empirical Bayes estimator. Building on this estimation framework and the proposed group prior, we further introduce a methodology for learning latent group structures in regression models. Simulation results demonstrate that the proposed empirical Bayes estimator substantially outperforms least squares based alternatives. Finally, we apply our framework to an empirical analysis of democratic spillovers across countries.

We propose a mixed membership stochastic block vector autoregression which allows for multiple memberships in large panel of time series. A set of algorithm is proposed to learn the multiple membership structure with the model. We prove the consistency of proposed algorithm.