Research

We propose a generative network autoregressive model in which the network coefficient is a random matrix following a joint distribution specified by a Bayesian belief network. Rather than treating the coefficient as fixed and observed, we model it as the output of a latent generative process that simultaneously governs the network structure and the resulting panel data. A central feature is that units may exhibit mixed membership across latent groups rather than belonging to a single group. We develop an estimator that recovers the latent membership structure from panel observations, establish identification and consistency as both panel dimensions grow, and assess finite-sample performance through simulations. An application to the U.S. financial system documents substantial mixed exposure across latent groups, showing that mixed membership materially shapes the dependence structure among financial firms.

Latent group structure is a standard device for modeling cross-sectional dependence in large panels, yet existing partial-correlation community methods typically assign each unit to a single group and do not distinguish the formation of conditional-dependence links from their strength. We propose a two-path mixed-membership partial-correlation network (2PMM-PCN). Mixed membership governs link formation along an extensive margin, while node-specific sociability governs link strength along an intensive margin. Although the two paths have distinct economic interpretations, their node-specific components enter the population signal only through a common scale, allowing the mixed memberships to be recovered by a single spectral procedure. We develop PartialCorr-Mixed-SCORE and establish a convergence rate for the average membership estimation error under weak dependence. In an application to U.S. state employment growth, the estimated memberships reproduce the broad group structure found in earlier studies while revealing economically meaningful overlaps that a single-group assignment cannot represent.

This paper develops a framework for measuring and conducting inference on horizon-specific contagion networks in high-dimensional restricted predictive systems. We propose a contagion measure that combines statistical evidence of directional predictive transmission with a scale-free measure of its magnitude. For a given source, receiver, and horizon, contagion strength is defined as the log ratio of forecast-error variances with and without the source’s predictive contribution, conditional on the remaining system; edge weights retain this strength only when the corresponding horizon-specific Granger-noncausality hypothesis is rejected. We develop estimation and inference for a broad class of restricted predictive regressions, including heterogeneous autoregressive and grouped-index specifications. Since aggregation and multi-horizon propagation may fail to preserve sparsity, we impose regularity conditions on the grouped predictive state and construct regularized estimators for the high-dimensional regression and covariance objects underlying the relevant forecast-error variances. Applications to large U.S. equity systems document substantial heterogeneity in the frequency and magnitude of predictive transmission across horizons, revealing features of financial connectedness obscured by horizon-agnostic measures.

In this work, we introduce a novel cluster affiliation vector autoregressive model, termed the mixed membership stochastic block vector autoregression (MMSB-VAR(p)). This model assumes that the VAR coefficients at all lags are random matrices following a joint distribution defined by a probabilistic generative framework. The panel data generated by this model can exhibit either single or multiple membership structures with the estimated VAR coefficients recovering the corresponding non-overlapping or overlapping block structures. To uncover the latent group structure, we propose a two-step algorithm leveraging the key insight that spillover effects within groups are significantly stronger than those between groups. We establish the consistency of the proposed algorithm and the simulation study demonstrates its effectiveness. Finally, we apply our methodology to analyze public opinions about the Ukraine-Russia war on Reddit.

We estimate group-specific heterogeneity in two-way effects models for matched data represented by a bipartite network. When the network is sparse or connected across groups, ordinary least squares (OLS) estimates individual effects imprecisely. We propose a machine-learning-assisted empirical Bayes (EB) estimator that uses the network to estimate group memberships and then shrinks effects toward their group-specific prior distributions. We represent the model’s conditional dependence structure as a Bayesian network, providing a unified framework for the two-step estimation procedure. Under stated conditions, we establish identification and consistency, and show that the feasible EB estimator approaches the oracle posterior mean asymptotically, even when a vanishing fraction of nodes is misclassified. Monte Carlo simulations show that the proposed estimator outperforms OLS and pooled EB when effect distributions differ across groups and the network provides information about group membership. When the true distributions coincide across groups, the estimated group-specific priors converge to the common prior under our consistency conditions. Finally, in an application to Amazon user–product ratings, we estimate and characterize heterogeneity in users’ rating tendencies and product-specific rating components.