Wasserstein-Barycentric Interaction Fields for Spatial Factor Models: Evidence from Language-Model Representations

Wasserstein-Barycentric Interaction Fields for Spatial Factor Models. Evidence from Language-Model Representations. By Marcus Gawronsky and one other, from the University of Cape Town. Published on the thirtieth of August. No code repository is linked to it.

Spatial return models describe how the returns of firms affect one another through an interaction matrix. Two things are left unexamined in that setup. The matrix is taken as given, and the feedback it produces is left uninterpreted.

This work builds the interaction structure instead of assuming it. The starting material is language-model embeddings of news articles about each firm, treated not as a single point per firm but as a distribution. From those distributions the authors construct a field using target-anchored Wasserstein barycentric reconstruction. The field is bandwidth-free.

The second step addresses interpretation. A quadratic exposure-adjustment problem maps the feedback into a single number, a peer-misalignment penalty ratio, which can be estimated and tested.

The test uses fifty-two firms. The field is frozen from news covering two thousand eighteen to two thousand twenty-two, then applied to the period from two thousand twenty-three to two thousand twenty-six. Over that later window the penalty ratio is three point four six, with a ninety-five percent interval from two point eight nine to four point one seven. The field also gives higher conditional quasi-likelihood than two alternatives built on the same distances: equal-weighted peer support, and RBF weighting.

A joint model includes both the barycentric field and a field built from news co-mentions. Their penalty ratios are two point three three and zero point eight six. Boundary calibrated tests reject excluding either one.

The evidence comes from one panel of fifty-two firms and one construction. Within that, both fields carry information the other does not, and the interaction matrix stops being an assumption and becomes something read out of text.