  I propose a quantile-based nonadditive fixed effects panel model to study
heterogeneous causal effects. Similar to standard fixed effects (FE) model, my
model allows arbitrary dependence between regressors and unobserved
heterogeneity, but it generalizes the additive separability of standard FE to
allow the unobserved heterogeneity to enter nonseparably. Similar to structural
quantile models, my model's random coefficient vector depends on an unobserved,
scalar ''rank'' variable, in which outcomes (excluding an additive noise term)
are monotonic at a particular value of the regressor vector, which is much
weaker than the conventional monotonicity assumption that must hold at all
possible values. This rank is assumed to be stable over time, which is often
more economically plausible than the panel quantile studies that assume
individual rank is iid over time. It uncovers the heterogeneous causal effects
as functions of the rank variable. I provide identification and estimation
results, establishing uniform consistency and uniform asymptotic normality of
the heterogeneous causal effect function estimator. Simulations show reasonable
finite-sample performance and show my model complements fixed effects quantile
regression. Finally, I illustrate the proposed methods by examining the causal
effect of a country's oil wealth on its military defense spending.
