Asymptotic distribution theory is the primary method used to examine the properties of econometric estimators and tests. We present conditions for obtaining cosistency and asymptotic normality of a very general class of estimators (extremum estimators). Consistent asymptotic variance estimators...

A semiparametric model for observational data combines a parametric form for some component of the data generating process (usually the behavioral relation between the dependent and explanatory variables) with weak nonparametric restrictions on the remainder of the model (usually the...

A brief account is given of the methodology and theory for the bootstrap. Methodology is developed in the context of the "equation" approach, which allows attention to be focussed on specific criteria for excellence, such as coverage error of a confidence interval or expected value of a...

This paper provides an introduction to the use of empirical process methods in econometrics. These methods can be used to establish the large sample properties of econometric estimators and test statistics. In the first part of the paper, key terminology and results are introduced and discussed...

This chapter evaluates the most important theoretical developments in ARCH type modeling of time-varying conditional variances. The coverage include the specification of univariate parametric ARCH models, general inference procedures, conditions for stationarity and ergodicity, continuous time...

This chapter reviews inference about large autoregressive or moving average roots in univariate time series, and structural change in multivariate time series regression. The "problem" of unit roots is cast more broadly as determining the order of integration of a series; estimation, inference,...

This chapter describes several nonparametric estimation and testing methods for econometric models. Instead of using parametric assumptions on the functions and distributions in an economic model, the methods use the restrictions that can be derived from the model. Examples of such restrictions...