ABSTRACT
This chapter provides a brief review of some popular parametric and nonparametric estimation methods as well as some approaches to statistical inference. While these methods are now well known and are the subject of comprehensive treatment in various textbooks and monographs, they provide a natural starting point for the material that is introduced and discussed later in the book. Since most of the topics covered in this book are extensions and generalizations of the more conventional econometric methodology, it proves useful to develop the proper context for the subsequent analysis. We start the chapter with a discussion of methods for estimating unknown
parameters or functions that describe the behavior of a particular economic phenomenon or process. The choice of an estimation method is determined to a large degree by information about the underlying data generation process provided by economic theory. Another important criterion in selecting an appropriate estimation method is its asymptotic properties, which are the main subject of discussion for each estimation method considered in this book. As a result, the econometrician is often faced with a trade-o¤ between optimality and robustness of the candidate estimation method. In the …rst part of the chapter, we provide an overview of extremum esti-
mators that comprise a general class which includes the maximum likelihood estimator, generalized method of moments, minimum distance estimators, etc. These methods are based on information that allows us to fully parameterize the model of interest (maximum likelihood) or on limited information obtained only from a set of conditional or unconditional moment restrictions (method of moments). Furthermore, if economic theory does not provide su¢ cient information about the shape of the conditional mean function, researchers often resort to nonparametric methods for estimation. In addition, we brie‡y discuss robust estimation such as quantile regressions. In the second part of the chapter, we review the fundamentals for testing
parametric restrictions, speci…cation testing in overidenti…ed models and con-…dence interval construction by test inversion. The practical implementation
of these inference procedures requires knowledge of the exact or approximate distribution of the statistic of interest. Most of this book is concerned with …rst-or higher-order asymptotic inference. This approach is based on the large sample theory and gives approximate distributional results that are easy to implement for hypothesis testing and construction of con…dence intervals. There are cases, however, when these large sample approximations can deviate substantially from the actual distribution that is the object of interest. There are other approaches to statistical inference that may be better suited when the sample size is relatively small. The exact distribution theory, for example, is designed to handle small-sample problems but its validity depends crucially on some strong assumptions that are rarely satis…ed by non-experimental economic data. One relatively new and easy-to-implement inference method is the bootstrap, which, in many situations, tends to deliver a smaller approximation error than the …rst-order asymptotics. This chapter introduces the theoretical underpinnings and computational aspects of the bootstrap, while later in the book we discuss its higher-order asymptotic properties.
