Imposing Curvature and Monotonicity on Flexible Functional Forms: An Efficient Regional Approach

Abstract In many areas of economic analysis, economic theory restricts the shape as well as other characteristics of functions used to represent economic constructs. Obvious examples are the monotonicity and curvature conditions that apply to utility, profit, and cost functions. Commonly, these regularity conditions are imposed either locally or globally. Here we extend and improve upon currently available estimation methods for imposing regularity conditions by imposing regularity on a connected subset of the regressor space. This method offers important advantages over the local approach by imposing theoretical consistency not only locally, at a given evaluation point but also within the whole empirically relevant region of the domain associated with the function being estimated. The method also provides benefits relative to the global approach, through higher flexibility, which generally leads to a better model fit to the sample data compared to the global imposition of regularity. Specific contributions of this paper are (a) to increase the computational speed and tractability of imposing regularity conditions in estimation, (b) to provide regularity preserving point estimates, (c) to avoid biases existent in previous applications, and (d) to illustrate the benefits of the regional approach via numerical simulation results