 # Finite Sample Econometrics

## Synopsis

This book provides a comprehensive and unified treatment of finite sample statistics and econometrics, a field that has evolved in the last five decades. Within this framework, this is the first book which discusses the basic analytical tools of finite sample econometrics, and explores their applications to models covered in a first year graduate course in econometrics, including repression functions, dynamic models, forecasting, simultaneous equations models, panel data models, and censored models. Both linear and nonlinear models, as well as models with normal and non-normal errors, are studied.

## Excerpt

Over the last five decades, significant advances in the estimation and inference of various econometric models have taken place. This includes the classical linear model where the explanatory variables are nonstochastic (fixed) and the error is normally distributed, and the non-classical models, where these classical assumptions are violated. These models are frequently used in applied work, such as the simultaneous equation models, models with heteroskedasticity and/or serial correlation, limited dependent variable models, panel data models, and a large class of time series models. Many of these models may also be nonlinear, explanatory variables can be stochastic and errors follow nonnormal distributions. While the classical linear model is often estimated by the ordinary least squares (LS) or generalized least squares (GLS) estimators, the non-classical models have largely used the maximum likelihood (ML), the method of moments, the instrumental variable, and the extremum estimation techniques. Within this setup, establishing the properties of estimators in the classical linear model are straightforward for samples of any size and they are well presented in econometrics textbooks. For the non-classical models, however, textbooks have mostly presented large sample theory results despite the existing finite sample analytical results. One explanation of this may be the technical difficulties in developing the existing finite sample results and the complexities of their expressions.

It is well known that the large sample theory properties may not imply the finite sample behavior of econometrics estimators and test statistics. in fact, the use of asymptotic theory results for small or even moderately large samples may give misleading results. the field of finite sample theory has been developing rapidly since the seminal contributions of Sir R. A. Fisher. Its applications in improving the inference for finite samples, the issues of bias-adjusted estimation, analyzing weak instruments, determining optimal instruments and bootstrapping have further enhanced the importance of the large existing literature on the finite sample.

This book is intended to provide a somewhat first comprehensive and unified treatment of finite sample theory and to apply the basic tools of this to various estimators and test statistics used in various econometric models. Both time series and cross section data models as well as panel data models are considered.

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