Testing nonstationary panels under cross-correlation [Elektronische Ressource] : new methods and empirical evidence / vorgelegt von Adina Ioana Tarcolea

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Testing Nonstationary Panels
under Cross-Correlation:
N ew Methods and Empirical Evidence
Inaugural-Dissertation
zur Erlangung des Doktorgrades
des Fachbereichs Wirtschaftswissenschaften
der Johann Wolfgang Goethe-Universität
Frankfurt am M ain
vorgelegt von
Dipl.-Math. Adina Ioana Tarcolea
aus Bukarest
2006 ii
Erstgutacher: Prof. Dr. Uwe Hassler
Zweitgutachter: Prof. Dr. Michael Binder
Tag der Promotion: 06.11.2006 List of original working papers
This thesis consists of the following original working papers.
1. Testing for Linear Trends in Dependent Heterogeneous Panels
Submitted.
2. Panel Cointegration Testing using Nonlinear Instruments
Co-authored by dr. Matei Demetre,scu, submitted.
3. Combining Significance of Correlated Statistics with Application
to Panel Data
Co-authored by dr. Matei Demetrescu and prof. dr. Uwe Hassler, G.rford
Bulletin of Economics and Statistics 68 (2006), 647-633.
4. Combining Multi-Country Evidence on Unit Roots: The Case of
Long-Term Interest Rates
Co-authored by prof. ell'. Uwc Hassler, Applied Economics Qua·rterly 51
(2005), 181-189. Abstract
This thesis is concerned with the derivation of new methods for the analysis uf
nonstationary, cross-correlated panels. The suggested procedures are carefully
quantified by means of Monte Carlo experiments. Typical applications of the
developed methods consist in multi-country studies, with several countries
observed over a couple of decades. The empirical applications implemented
here are the testing for trends in the investment share in European GDPs and
the examination of OECD interest rates.
In the first chapter, a panel test for the presence of a linear time trend is
proposed. The test is applicable in cross-correlated, heterogeneous panels and
it can also be used when the integration order of innovations is unknown, by
means of subsampling.
In the next chapter a cointegration test having asymptotic standard nor­
mal distributiun and not requiring exogeneity assumptions is derived. In pan­
els exhibiting cross-correlation or cointegration, individual test statistics are
asymptotically independent, which leads to a panel test statistic robust tu
dependence across units.
The third cha.pter examines in an econometric context the simple idea of
combining p-values from a series of statistical tests and improves its applica­
bili ty in the presence of cross-correlation.
The last chapter applies recent panel techniques to OECD long-term inter­
est rates and differentials thereof, finding only rather week evidence in favor
of stationarity when allowing for cross-correlation.
iii Acknowledgements
The following is my heartfelt appreciation to those people, both past and
present, who gave me the spirit, knowledge and insight to begin, conduct and
complete this thesis.
First and foremost, I would like to acknowledge my adviser, Prof. Dr. Uwe
Hassler. Throughout the course of my research he provided me with timely
and valuable advice and excellent facilities. His courtesy, professionalism, and
patience made working with him very rewarding and gratifying. I would like
to thank my committee members for their constructive criticisms and useful
suggestions and in particular, to my second examiner, Prof. Dr. Michael
Binder. My colleagues, Dr. Matei Demetrescu and Vladimir Kuzin, provided
me with useful discussions and a stimulating work environment.
I would also like to express gratitude towards the people who taught me
mathematics: my father, Prof. Dr. Constantin Tarcolea, and my math teacher,
Mr. Armand Martinov. My statistics knowledge is due to Prof. Dr. Virgil
Craiu and Prof. Dr. Vasile Preda from University Bucharest. Two persons
offered me guidance, support and advice in particular at the beginnings of my
academic career: Prof. Dr. Hans-Dieter Heike and Prof. Dr. Mariana Craiu -
I am deeply indebted to them.
My research took place within the project "Integration and Cointegration
Analysis with Panel Data" , financed by the Deutsche Forschungsgemeinschaft
(German Research Foundation), to which I express my thanks.
Finally, I would like to thank my family, for their constant help and en­
couragement. I am also grateful to all my true and dear friends, because I
know this research has profited from their support.
v Table of Contents
List of original working papers
List of figures ix
List of tables xii
Preface 1
1 Testing for Linear Trends 5
1.1 Introduction.... 5
1.2 Model and test .. 6
1.2.1 1(0) panels. 7
1.2.2 1(1) 10
1.2.3 Unknown integration order. 11
1.3 Investment shares of per capita GDP 16
1.4 Conclusions . . . . . . . . . 20
2 Panel Cointegration Testing 21
2.1 Motivation........ 21
2.2 Model and assumptions. 22
2.3 Asymptotic results .. 24
2.3.1 Single unit test 25
2.3.2 Panel test . . . 30
2.4 Small sample behavior 32
2.4.1 Behavior of the single unit test 33
2.4.2 of the panel test 35
2.5 Conclusions 38
Appendix ............... . 39
3 Combining Significance of Correlated Statistics 47
3.1 Introduction........ ........ 47
vii viii TABLE OF CONTENTS
3.2 The modified inverse normal method 49
3.3 Panel tests. . . . . . . . . 53
3.3.1 Standard case ... 54
3.3.2 Non-standard case 56
3.4 Concluding remarks . 60
Appendix ........... . 60
4 Combining Multi-Country Evidence 63
4.1 Introduction.......... 63
4.2 Combining Dickey-Fuller tests 64
4.3 p values . 65
4.4 Empirical results .. 68
4.5 Concluding remarks . 70
Zusammenfassung 71
Bibliography 75
,