This paper proposes a new discount rate that pension funds can use to discount their future obligations. If the payouts of a pension fund depend on the return of the fund's assets, then neither the risk-free rate nor the expected return is an equitable way to discount future liabilities. Using...

This paper extends Imbens and Manski’s (2004) analysis of confidence intervals for interval identified parameters. For their final result, Imbens and Manski implicitly assume superefficient estimation of a nuisance parameter. This appears to have gone unnoticed before, and it limits the...

This paper studies nonparametric estimation of conditional moment models in which the residual functions could be nonsmooth with respect to the unknown functions of endogenous variables. It is a problem of nonparametric nonlinear instrumental variables (IV) estimation, and a difficult nonlinear...

Suppose that a target function is monotonic, namely weakly increasing, and an original estimate of this target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates. We show that these estimates can always be improved with...

This paper considers the first order large sample properties of the GEL class of estimators for models specified by non-smooth indicators. The GEL class includes a number of estimators recently introduced as alternatives to the efficient GMM estimator which may suffer from substantial biases in...

We present a simple way to estimate the effects of changes in a vector of observable variables X on a limited dependent variable Y when Y is a general nonseparable function of X and unobservables. We treat models in which Y is censored from above or below or potentially from both. The basic idea...

We consider cross-sectional data that exhibit no spatial correlation, but are feared to be spatially dependent. We demonstrate that a spatial version of the stochastic volatility model of financial econometrics, entailing a form of spatial autoregression, can explain such behaviour. The...