A Companion to Econometric Analysis of Panel Data - Softcover

Baltagi, Badi H.

Softcover

ISBN 10: 0470744030 ISBN 13: 9780470744031

Verlag: John Wiley & Sons, 2009

Inhaltsangabe

This book is a companion to Baltagi’s (2008) leading graduate econometrics textbook on panel data entitled Econometric Analysis of Panel Data, 4^th Edition.

The book guides the student of panel data econometrics by solving exercises in a logical and pedagogical manner, helping the reader understand, learn and apply panel data methods. It is also a helpful tool for those who like to learn by solving exercises and running software to replicate empirical studies. It works as a complementary study guide to Baltagi (2008) and also as a stand alone book that builds up the reader’s confidence in working out difficult exercises in panel data econometrics and applying these methods to empirical work.

The exercises start by providing some background information on partitioned regressions and the Frisch-Waugh-Lovell theorem. Then it goes through the basic material on fixed and random effects models in a one-way and two-way error components models: basic estimation, test of hypotheses and prediction. This include maximum likelihood estimation, testing for poolability of the data, testing for the significance of individual and time effects, as well as Hausman's test for correlated effects. It also provides extensions of panel data techniques to serial correlation, spatial correlation, heteroskedasticity, seemingly unrelated regressions, simultaneous equations, dynamic panel models, incomplete panels, measurement error, count panels, rotating panels, limited dependent variables, and non-stationary panels.

Über diesen Titel

Über die Autorin bzw. den Autor

Badi H. Baltagi is Distinguished Professor of Economics, and Senior Research Associate at the Center for Policy Research, Syracuse University. He is a fellow of the Journal of Econometrics, a recipient of the Multa and Plura Scripsit Awards from Econometric Theory, and the Journal of Applied Econometrics Distinguished Authors Award.

The book guides the student of panel data econometrics by solving exercises in a logical and pedagogical manner, helping the reader understand, learn and apply panel data methods. It is also a helpful tool for those who like to learn by solving exercises and running software to replicate empirical studies. It works as a complementary study guide to Baltagi (2008) and also as a stand alone book that builds up the reader’s confidence in working out difficult exercises in panel data econometrics and applying these methods to empirical work.

The exercises start by providing some background information on partitioned regressions and the Frisch-Waugh-Lovell theorem. Then it goes through the basic material on fixed and random effects models in a one-way and two-way error components models: basic estimation, test of hypotheses and prediction. This include maximum likelihood estimation, testing for poolability of the data, testing for the significance of individual and time effects, as well as Hausman's test for correlated effects. It also provides extensions of panel data techniques to serial correlation, spatial correlation, heteroskedasticity, seemingly unrelated regressions, simultaneous equations, dynamic panel models, incomplete panels, measurement error, count panels, rotating panels, limited dependent variables, and non-stationary panels.

The book provides several empirical examples that are useful to applied researchers, illustrating them using Stata and EViews showing the reader how to replicate these studies. The data sets are provided on the Wiley web site: www.wileyeurope.com/college/baltagi.

The book guides the student of panel data econometrics by solving exercises in a logical and pedagogical manner, helping the reader understand, learn and apply panel data methods. It is also a helpful tool for those who like to learn by solving exercises and running software to replicate empirical studies. It works as a complementary study guide to Baltagi (2008) and also as a stand alone book that builds up the reader’s confidence in working out difficult exercises in panel data econometrics and applying these methods to empirical work.

The exercises start by providing some background information on partitioned regressions and the Frisch-Waugh-Lovell theorem. Then it goes through the basic material on fixed and random effects models in a one-way and two-way error components models: basic estimation, test of hypotheses and prediction. This include maximum likelihood estimation, testing for poolability of the data, testing for the significance of individual and time effects, as well as Hausman's test for correlated effects. It also provides extensions of panel data techniques to serial correlation, spatial correlation, heteroskedasticity, seemingly unrelated regressions, simultaneous equations, dynamic panel models, incomplete panels, measurement error, count panels, rotating panels, limited dependent variables, and non-stationary panels.

The book provides several empirical examples that are useful to applied researchers, illustrating them using Stata and EViews showing the reader how to replicate these studies. The data sets are provided on the Wiley web site: www.wileyeurope.com/college/baltagi.

Auszug. © Genehmigter Nachdruck. Alle Rechte vorbehalten.

A Companion to Econometric Analysis of Panel Data

By Badi Baltagi

John Wiley & Sons

Copyright © 2009 Badi Baltagi
All right reserved.
ISBN: 978-0-470-74403-1

Chapter One

Partitioned Regression and the Frisch-Waugh-Lovell Theorem

This chapter introduces the reader to important background material on the partitioned regression model. This should serve as a refresher for some matrix algebra results on the partitioned regression model as well as an introduction to the associated Frisch-Waugh-Lovell (FWL) theorem. The latter is shown to be a useful tool for proving key results for the fixed effects model in Chapter 2 as well as artificial regressions used in testing panel data models such as the Hausman test in Chapter 4.

Consider the partitioned regression given by

y = X + u = [X.sub.1][.sub.1] + [X.sub.2][.sub.2] + u (1.1)

where y is a column vector of dimension (n x 1) and X is a matrix of dimension (n x k). Also, X = [[X.sub.1], [X.sub.2]] with [[X.sub.1] and [[X.sub.2] of dimension (n x [k.sub.1]) and (n x [k.sub.2]), respectively. One may be interested in the least squares estimates of [.sub.2] corresponding to [[X.sub.2], but one has to control for the presence of [[X.sub.1] which may include seasonal dummy variables or a time trend; see Frisch and Waugh (1933) and Lovell (1963). For example, in a time-series setting, including the time trend in the multiple regression is equivalent to detrending each variable first, by residualing out the effect of time, and then running the regression on these residuals. Davidson and MacKinnon (1993) denote this result more formally as the FWL theorem.

The ordinary least squares (OLS) normal equations from (1.1) are given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.2)

Exercise 1.1 (Partitioned regression). Show that the solution to (1.2) yields

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.3)

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the projection matrix on [X.sub.1], and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Solution

Write (1.2) as two equations:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Solving for [[??].sub.1,OLS] in terms of [[??].sub.2,OLS] by multiplying the first equation by [([X.sup.'.sub.1][X.sub.1]).sup.-1], we get

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Substituting [[??].sub.1,OLS] in the second equation, we get

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Collecting terms, we get [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Hence, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], y as given in (1.3). [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the orthogonal projection matrix of [X.sub.1] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] generates the least squares residuals of each column of [X.sub.2] regressed on all the variables in [X.sub.1]. In fact, if we write [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], then

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.4)

using the fact that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is idempotent. For a review of idempotent matrices, see Abadir and Magnus (2005, p.231). This implies that [[??].sub.2,OLS] can be obtained from the regression of [??] on [[??].sub.2]. In words, the residuals from regressing y on [X.sub.1] are in turn regressed upon the residuals from each column of [X.sub.2] regressed on all the variables in [X.sub.1]. If we premultiply (1.1) by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and use the fact that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], we get

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.5)

Exercise 1.2 (The Frisch-Waugh-Lovell theorem). Prove that:

(a) the least squares estimates of [.sub.2] from equations (1.1) and (1.5) are numerically identical;

(b) the least squares residuals from equations (1.1) and (1.5) are identical.

Solution

(a) Using the fact that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is idempotent, it immediately follows that OLS on (1.5) yields [[??].sub.2,OLS] as given by (1.3). Alternatively, one can start from (1.1) and use the result that

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.6)

where [P.sub.X] = [X(X' X).sup.-1] X' and [P.sub.X] = [I.sub.n] - [P.sub.X]. Premultiplying (1.6) by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and using the fact that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], one gets

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.7)

But [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Hence, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Using this fact along with [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], the last term of (1.7) drops out yielding the result that [[??].sub.2,OLS] from (1.7) is identical to the expression in (1.3). Note that no partitioned inversion was used in this proof. This proves part (a) of the FWL theorem. To learn more about partitioned and projection matrices, see Chapter 5 of Abadir and Magnus (2005).

(b) Premultiplying (1.6) by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and using the fact that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], one gets

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.8)

Note that [[??].sub.2,OLS] was shown to be numerically identical to the least squares estimate obtained from (1.5). Hence, the first term on the right-hand side of (1.8) must be the fitted values from equation (1.5). Since the dependent variables are the same in equations (1.8) and (1.5), [P.sub.x] y in equation (1.8) must be the least squares residuals from regression (1.5). But [P.sub.x] y is the least squares residuals from regression (1.1). Hence, the least squares residuals from regressions (1.1) and (1.5) are numerically identical. This proves part (b) of the FWL theorem. Several applications of the FWL theorem will be given in this book.

Exercise 1.3 (Residualing the constant). Show that if [X.sub.1] is the vector of ones indicating the presence of a constant in the regression, then regression (1.8) is equivalent to running ([y.sub.i] - [bar.y]) on the set of variables in [X.sub.2] expressed as deviations from their respective sample means.

Solution

In this case, X = [[l.sub.n], [X.sub.2]] where n is a vector of ones of dimension n. [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is a matrix of ones of dimension n. But [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [J.sub.n] y/n = [bar.y]. Hence, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] has...

Details zur Ausgabe

• Verlag: John Wiley & Sons
• Erscheinungsdatum: 2009
• Sprache: Englisch
• ISBN 10: 0470744030
• ISBN 13: 9780470744031
• Einband: Taschenbuch
• Auflage: 1
• Anzahl der Seiten: 308
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: gpsr@libri.de; gpsr@libri.de; ; Friedensallee 273; Hamburg; 22763; Deutschland