Semiparametric estimation under shape constraints

Substantial structure and restrictions, such as monotonicity and curvature constraints, necessary to give economic interpretation to empirical findings are often furnished by economic theories. Although such restrictions may be imposed in certain parametric empirical settings in a relatively straightforward fashion, incorporating such restrictions in semiparametric models is often problematic. A solution to this problem is provided via penalized splines, where monotonicity and curvature constraints are maintained through integral transformations of spline basis expansions. Large sample properties, implementation and inferential procedures are presented. Extension to multiple regressions under the framework of additive models is also discussed. A series of Monte Carlo simulations illustrate the finite sample properties of the estimator. The proposed method is employed to estimate a Lorenz curve of income and a production function with multiple inputs.