This paper establishes that instruments enable the identification of nonparametric regression models in the presence of measurement error by providing a closed form solution for the regression function in terms of Fourier transforms of conditional expectations of observable variables. For parametrically specified regression functions, we propose a root n consistent and asymptotically normal estimator that takes the familiar form of a generalized method of moments estimator with a plugged-in nonparametric kernel density estimate. Both the identification and the estimation methodologies rely on Fourier analysis and on the theory of generalized functions. The finite-sample properties of the estimator are investigated through Monte Carlo simulations.

We show experimentally that fairness concerns may have a decisive impact on the actual and optimal choice of contracts in a moral hazard context. Bonus contracts that offer a voluntary and unenforceable bonus for satisfactory performance provide powerful incentives and are superior to explicit incentive contracts when there are some fair-minded players, but trust contracts that pay a generous wage up front are less efficient than incentive contracts. The principals understand this and predominantly choose the bonus contracts. These results are consistent with recently developed theories of fairness, which offer important new insights into the interaction of contract choices, fairness, and incentives.