The second edition of this acclaimed graduate text provides a unified treatment of two methods used in contemporary econometric research, cross section and data panel methods. By focusing on assumptions that can be given behavioral content, the book maintains an appropriate level of rigor while emphasizing intuitive thinking. The analysis covers both linear and nonlinear models, including models with dynamics and/or individual heterogeneity. In addition to general estimation frameworks (particular methods of moments and maximum likelihood), specific linear and nonlinear methods are covered in detail, including probit and logit models and their multivariate, Tobit models, models for count data, censored and missing data schemes, causal (or treatment) effects, and duration analysis. Econometric Analysis of Cross Section and Panel Data was the first graduate econometrics text to focus on microeconomic data structures, allowing assumptions to be separated into population and sampling assumptions. This second edition has been substantially updated and revised. Improvements include a broader class of models for missing data problems; more detailed treatment of cluster problems, an important topic for empirical researchers; expanded discussion of "generalized instrumental variables" (GIV) estimation; new coverage (based on the author's own recent research) of inverse probability weighting; a more complete framework for estimating treatment effects with panel data, and a firmly established link between econometric approaches to nonlinear panel data and the "generalized estimating equation" literature popular in statistics and other fields. New attention is given to explaining when particular econometric methods can be applied; the goal is not only to tell readers what does work, but why certain "obvious" procedures do not. The numerous included exercises, both theoretical and computer-based, allow the reader to extend methods covered in the text and discover new insights.

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Econometric Analysis of Cross Section and Panel Data

Traditional econometric models assume a constant one-period forecast variance. To generalize this implausible assumption, a new class of stochastic processes called autoregressive conditional heteroscedastic (ARCH) processes are introduced in this paper. These are mean zero, serially uncorrelated processes with nonconstant variances conditional on the past, but constant unconditional variances. For such processes, the recent past gives information about the one-period forecast variance. A regression model is then introduced with disturbances following an ARCH process. Maximum likelihood estimators are described and a simple scoring iteration formulated. Ordinary least squares maintains its optimality properties in this set-up, but maximum likelihood is more efficient. The relative efficiency is calculated and can be infinite. To test whether the disturbances follow an ARCH process, the Lagrange multiplier procedure is employed. The test is based simply on the autocorrelation of the squared OLS residuals. This model is used to estimate the means and variances of inflation in the U.K. The ARCH effect is found to be significant and the estimated variances increase substantially during the chaotic seventies.

Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation

http://public.econ.duke.edu/~boller/Published_Papers/joe_86.pdf

Generalized autoregressive conditional heteroskedasticity

Preface.1. Introduction.1.1 Panel Data: Some Examples.1.2 Why Should We Use Panel Data? Their Benefits and Limitations.Note.2. The One-way Error Component Regression Model.2.1 Introduction.2.2 The Fixed Effects Model.2.3 The Random Effects Model.2.4 Maximum Likelihood Estimation.2.5 Prediction.2.6 Examples.2.7 Selected Applications.2.8 Computational Note.Notes.Problems.3. The Two-way Error Component Regression Model.3.1 Introduction.3.2 The Fixed Effects Model.3.3 The Random Effects Model.3.4 Maximum Likelihood Estimation.3.5 Prediction.3.6 Examples.3.7 Selected Applications.Notes.Problems.4. Test of Hypotheses with Panel Data.4.1 Tests for Poolability of the Data.4.2 Tests for Individual and Time Effects.4.3 Hausman's Specification Test.4.4 Further Reading.Notes.Problems.5. Heteroskedasticity and Serial Correlation in the Error Component Model.5.1 Heteroskedasticity.5.2 Serial Correlation.Notes.Problems.6. Seemingly Unrelated Regressions with Error Components.6.1 The One-way Model.6.2 The Two-way Model.6.3 Applications and Extensions.Problems.7. Simultaneous Equations with Error Components.7.1 Single Equation Estimation.7.2 Empirical Example: Crime in North Carolina.7.3 System Estimation.7.4 The Hausman and Taylor Estimator.7.5 Empirical Example: Earnings Equation Using PSID Data.7.6 Extensions.Notes.Problems.8. Dynamic Panel Data Models.8.1 Introduction.8.2 The Arellano and Bond Estimator.8.3 The Arellano and Bover Estimator.8.4 The Ahn and Schmidt Moment Conditions.8.5 The Blundell and Bond System GMM Estimator.8.6 The Keane and Runkle Estimator.8.7 Further Developments.8.8 Empirical Example: Dynamic Demand for Cigarettes.8.9 Further Reading.Notes.Problems.9. Unbalanced Panel Data Models.9.1 Introduction.9.2 The Unbalanced One-way Error Component Model.9.3 Empirical Example: Hedonic Housing.9.4 The Unbalanced Two-way Error Component Model.9.5 Testing for Individual and Time Effects Using Unbalanced Panel Data.9.6 The Unbalanced Nested Error Component Model.Notes.Problems.10. Special Topics.10.1 Measurement Error and Panel Data.10.2 Rotating Panels.10.3 Pseudo-panels.10.4 Alternative Methods of Pooling Time Series of Cross-section Data.10.5 Spatial Panels.10.6 Short-run vs Long-run Estimates in Pooled Models.10.7 Heterogeneous Panels.Notes.Problems.11. Limited Dependent Variables and Panel Data.11.1 Fixed and Random Logit and Probit Models.11.2 Simulation Estimation of Limited Dependent Variable Models with Panel Data.11.3 Dynamic Panel Data Limited Dependent Variable Models.11.4 Selection Bias in Panel Data.11.5 Censored and Truncated Panel Data Models.11.6 Empirical Applications.11.7 Empirical Example: Nurses' Labor Supply.11.8 Further Reading.Notes.Problems.12. Nonstationary Panels.12.1 Introduction.12.2 Panel Unit Roots Tests Assuming Cross-sectional Independence.12.3 Panel Unit Roots Tests Allowing for Cross-sectional Dependence.12.4 Spurious Regression in Panel Data.12.5 Panel Cointegration Tests.12.6 Estimation and Inference in Panel Cointegration Models.12.7 Empirical Example: Purchasing Power Parity.12.8 Further Reading.Notes.Problems.References.Index.

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Econometric Analysis of Panel Data

This paper introduces an ARCH model (exponential ARCH) that (1) allows correlation between returns and volatility innovations (an important feature of stock market volatility changes), (2) eliminates the need for inequality constraints on parameters, and (3) allows for a straightforward interpretation of the "persistence" of shocks to volatility. In the above respects, it is an improvement over the widely-used GARCH model. The model is applied to study volatility changes and the risk premium on the CRSP Value-Weighted Market Index from 1962 to 1987. Copyright 1991 by The Econometric Society.

Conditional heteroskedasticity in asset returns: a new approach

Many econometric models are susceptible to analysis only by asymptotic techniques and there are three principles, based on asymptotic theory, for the construction of tests of parametric hypotheses. These are: (i) the Wald (W) test which relies on the asymptotic normality of parameter estimators, (ii) the maximum likelihood ratio (LR) procedure and (iii) the Lagrange multiplier (LM) method which tests the effect on the first order conditions for a maximum of the likelihood of imposing the hypothesis. In the econometric literature, most attention seems to have been centred on the first two principles. Familiar " t-tests " usually rely on the W principle for their validity while there have been a number of papers advocating and illustrating the use of the LR procedure. However, all three are equivalent in well-behaved problems in the sense that they give statistics with the same asymptotic distribution when the null hypothesis is true and have the same asymptotic power characteristics. Choice of any one principle must therefore be made by reference to other criteria such as small sample properties or computational convenience. In many situations the W test is attractive for this latter reason because it is constructed from the unrestricted estimates of the parameters and their estimated covariance matrix. The LM test is based on estimation with the hypothesis imposed as parametric restrictions so it seems reasonable that a choice between W or LM be based on the relative ease of estimation under the null and alternative hypotheses. Whenever it is easier to estimate the restricted model, the LM test will generally be more useful. It then provides applied researchers with a simple technique for assessing the adequacy of their particular specification. This paper has two aims. The first is to exposit the various forms of the LM statistic and to collect together some of the relevant research reported in the mathematical statistics literature. The second is to illustrate the construction of LM tests by considering a number of particular econometric specifications as examples. It will be found that in many instances the LM statistic can be computed by a regression using the residuals of the fitted model which, because of its simplicity, is itself estimated by OLS. The paper contains five sections. In Section 2, the LM statistic is outlined and some alternative versions of it are discussed. Section 3 gives the derivation of the statistic for

https://www.jstor.org/stable/pdfplus/2297111.pdf

The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics

A simple test for heteroscedastic disturbances in a linear regression model is developed using the framework of the Lagrangian multiplier test. For a wide range of heteroscedastic and random coefficient specifications, the criterion is given as a readily computed function of the OLS residuals. Some finite sample evidence is presented to supplement the general asymptotic properties of Lagrangian multiplier tests.

A Simple Test for Heteroscedasticity and Random Coefficient Variation.

Econometric Issues in the Analysis of Regressions with Generated Regressors.

Dissecting the cycle: a methodological investigation

The description “nonparametric” seems to be used in two different ways in the statistical and econometric literature. The older use of the word refers to tests (such as Wilcoxon, Mann-Whitney, etc.) which don’t rely on classical normality assumptions, and which are often based on ranks rather than raw data. More recently, the term has been used to refer to smoothing techniques, especially in density estimation and regression. This book takes the more modern definition of “nonparametric” and covers a large range of smoothing methods which can be applied in econometrics.

Adrian Pagan

Papers

The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics

A Simple Test for Heteroscedasticity and Random Coefficient Variation.

Econometric Issues in the Analysis of Regressions with Generated Regressors.

Dissecting the cycle: a methodological investigation

Nonparametric Econometrics