We introduce methods for estimating nonparametric, nonadditive models with simultaneity. The methods are developed by directly connecting the elements of the structural system to be estimated with features of the density of the observable variables, such as ratios of derivatives or averages of products of derivatives of this density. The estimators are therefore easily computed functionals of a nonparametric estimator of the density of the observable variables. We consider in detail a model where to each structural equation there corresponds an exclusive regressor and a model with one equation of interest and one instrument that is included in a second equation. For both models, we provide new characterizations of observational equivalence on a set, in terms of the density of the observable variables and derivatives of the structural functions. Based on those characterizations, we develop two estimation methods. In the first method, the estimators of the structural derivatives are calculated by a simple matrix inversion and matrix multiplication, analogous to a standard least squares estimator, but with the elements of the matrices being averages of products of derivatives of nonparametric density estimators. In the second method, the estimators of the structural derivatives are calculated in two steps. In a first step, values of the instrument are found at which the density of the observable variables satisfies some properties. In the second step, the estimators are calculated directly from the values of derivatives of the density of the observable variables evaluated at the found values of the instrument. We show that both pointwise estimators are consistent and asymptotically normal.

We develop a parsimonious model to study the equilibrium and socially optimal decisions of banks to enter, trade in, and possibly exit, an OTC market. Although we endow all banks with the same trading technology, banks' optimal entry and trading decisions endogenously lead to a realistic market structure composed of dealers and customers with distinct trading patterns. We decompose banks' entry incentives into incentives to hedge risk and incentives to make intermediation profits. We show that dealer banks enter more than is socially optimal. In the face of large negative shocks, they may also exit more than is socially optimal when markets are not perfectly resilient.