Rate-agnostic inference for nonlinear dyadic estimators

Develop rate-agnostic Wald inference for nonlinear dyadic estimators, specifically the Poisson pseudo-maximum-likelihood estimator for dyadic trade models, by extending the score-based argument underlying the linear least-squares result and replacing the exact leave-unit-out algebra with an appropriate asymptotic expansion.

Background

The paper establishes rate-agnostic Wald inference for least-squares estimators with dyadic dependence, including settings in which different linear combinations of the coefficient estimator converge at heterogeneous rates. It identifies nonlinear estimation as a further unresolved direction. In particular, the Poisson pseudo-maximum-likelihood estimator used in gravity applications has a score that is also a sum of dyad-indexed terms, suggesting that the central limit and variance-estimation arguments may extend to this setting. However, the exact leave-unit-out identity used for the linear least-squares jackknife is unavailable for a nonlinear estimator and would need to be replaced by an asymptotic expansion.