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.

/pdf/econometric-analysis-of-panel-data-46ld72a5p1.pdf

Econometric Analysis of Panel Data

Statistics for Spatial Data.

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

Anarchy, state, and utopia

A central limit theorem is established for time series regression estimates which include generalized least squares, in the presence of long-range dependence in both errors and stochastic regressors. The setting and results differ significantly from earlier work on regression withlong-range-dependent errors. Spectral singularities are permitted at any frequency. When sufficiently strong spectral singularities in the error and a regressor coincide at the same frequency, least squares need no longer be $n^{1/2}$-consistent, where n is the sample size. However, we show that our class of estimates is $n^{1/2}$-consistent and asymptotically normal. In the generalized least squares case, we show that efficient estimation is still possible when the error autocorrelation is known only up to finitely many parameters. We include a Monte Carlo study of finite-sample performance and provide an extension to nonlinear least squares.

/pdf/time-series-regression-with-long-range-dependence-3az58tv05r.pdf

Time series regression with long-range dependence

https://rmgsc.cr.usgs.gov/outgoing/threshold_articles/Hidalgo_Robinson1996.pdf

Testing for structural change in a long-memory environment☆

We consider a parametric spectral density with power-law behaviour about a fractional pole at the unknown frequency w. The case of unknown w, especially w = 0, is standard in the long memory literature. When w is unknown, asymptotic distribution theory for estimates of parameters, including the (long) memory parameter, is significantly harder. We study a form of Gaussian estimate. We establsih n-consistency of the estimate of w, and discuss its (non-standard) limiting distributional behaviour. For the remaining parameter estimates, we establish Vn-consistency and asymptotic normality.

https://papers.ssrn.com/sol3/Delivery.cfm/em424.pdf?abstractid=1162605&mirid=5&type=2

Gaussian Estimation of Parametric Spectral Density with Unknown Pole

We consider a parametric spectral density with power-law behavior about a fractional pole at the unknown frequency $\omega$. The case of known $\omega$, especially $\omega =0$, is standard in the long memory literature. When $omega$ is unknown, asymptotic distribution theory for estimates of parameters, including the (long) memory parameter, is significantly harder. We study a form of Gaussian estimate. We establish $n$-consistency of the estimate of $\omega$, and discuss its (non-standard) limiting distributional behavior. For the remaining parameter estimates,we establish $\sqrt{n}$-consistency and asymptotic normality.

/pdf/gaussian-estimation-of-parametric-spectral-density-with-3tgcr2n3hq.pdf

Javier Hidalgo

Papers

Time series regression with long-range dependence

Testing for structural change in a long-memory environment☆

Gaussian Estimation of Parametric Spectral Density with Unknown Pole

Gaussian estimation of parametric spectral density with unknown pole

Nonparametric inference on structural breaks