Smooth Minimum Distance Estimation and Testing in Conditional Moment Restrictions Models: Uniform in Bandwidth Theory

We propose a new estimation method for models defined by conditional moment restrictions,that minimizes a distance criterion based on kernel smoothing. Whether the bandwidth parameter is fixed or decreases to zero with the sample size, our approach defines a whole class of estimators. We develop a theory that focuses on uniformity in bandwidth. We establish a pn-asymptotic representation of our estimator as a process depending on the bandwidth within a wide range including fixed bandwidths and that applies to misspecified models. We also study an efficient version of our estimator. We develop inference procedures based on a distance metric statistic for testing restrictions on parameters and we propose a new bootstrap technique. Our new methods apply to non-smooth problems, are simple to implement, and perform well in small samples.