  We develop a new, spectral approach for identifying and estimating average
counterfactual outcomes under a low-rank factor model with short panel data and
general outcome missingness patterns. Applications include event studies and
studies of outcomes of "matches" between agents of two types, e.g. workers and
firms, typically conducted under less-flexible Two-Way-Fixed-Effects (TWFE)
models of outcomes. Given an infinite population of units and a finite number
of outcomes, we show our approach identifies all counterfactual outcome means,
including those not estimable by existing methods, if a particular graph
constructed based on overlaps in observed outcomes between subpopulations is
connected. Our analogous, computationally efficient estimation procedure yields
consistent, asymptotically normal estimates of counterfactual outcome means
under fixed-$T$ (number of outcomes), large-$N$ (sample size) asymptotics. In a
semi-synthetic simulation study based on matched employer-employee data, our
estimator has lower bias and only slightly higher variance than a
TWFE-model-based estimator when estimating average log-wages.
