Research

Working Papers

This paper studies necessary and sufficient conditions to perform valid inference with network dependent data, while allowing for general forms of network denseness and strengths of dependence. The main questions addressed here are (i) what are the necessary and sufficient conditions to consistently discriminate the mean; and (ii) what are the necessary conditions to consistently estimate the variance. It is shown that graph conductance plays a key role for consistent mean discrimination, while the requirements for consistent variance estimation are reminiscent of the many-networks asymptotics. The conditions for valid inference are characterized in terms of objects that are straightforward to compute, making easy their verification in practice. The results are specialized to study causal inference under network interference, providing a new and more general way of verifying the possibility of valid inference in that context.


Prior hyperparameters for Bayesian vector autoregressions (VARs) are often determined by maximization of a marginal data density (MDD). However, if a VAR is misspecified, it is not clear that a MDD based hyperparameter determination is desirable. In this paper we use an asymptotically unbiased estimate of the prediction risk to determine the hyperparameter of a shrinkage estimator in an environment in which the VAR forecasting model is locally misspecified. For multi-step-ahead forecasting applications, we consider (quasi) likelihood-based and loss function based shrinkage estimators. The hyperparameter selection approach is illustrated in a Monte Carlo study and an empirical application. We also discuss the relationship to impulse response function estimation with local projections versus VARs.

Work In Progress