Complementarity between variables is an important phenomenon in economics. Modern theoretical analysis of complementarity has benefited substantially from the mathematical theory of supermodular functions, which makes explicit the necessary and sufficient conditions for complementarity without imposing auxiliary functional form assumptions. However, empirical analysis of complementarity has remained encumbered by auxiliary assumptions. The aim of Chapter 2 is to move empirical analysis forward by providing a nonparametric framework for estimating and testing supermodularity of regression functions.; Chapter 2 introduces two methods of nonparametric estimation of supermodular mean regression functions for randomly-sampled data. The piecewise-linear supermodular spline method imposes the supermodularity restriction using quadratic programming on a grid and then interpolates linearly to the whole domain. The polynomial flexible form method is based on an extension of the Weierstrass theorem to supermodular functions. The two methods appear different from one another, but can be related through the unifying framework of estimation by sieves.; Chapter 3 examines various ways to extend the theory developed in Chapter 2. Three main extensions are discussed. First, I show that restrictions like monotonicity and supermodularity can be generalized to restrictions on partial derivatives of any order. Moreover, if the regression function is not assumed to be differentiable, these restrictions can be imposed using a difference analogue of the partial derivatives. Second, I show that various function bases can be used to build restricted estimators. The third part of Chapter 3 addresses homogeneity. I discuss the differences between homogeneity and restrictions on partial derivatives and suggest an estimator which is consistent with the homogeneity assumption.; Chapter 4 includes empirical research on telephone companies in the US and implements the estimation methods developed in previous chapters. I use data on Local Exchange Carriers (LECs) to investigate the question of cost complementarities between the production of local and long distance calls. The estimation methods used here are nonparametric. The results support the assumption of cost complementarities. These complementarities are especially strong for small companies. This result suggests that mergers between two small companies can be efficient but mergers of big companies can increase monopoly power.
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