Models for Analyzing Nonlinearities in Price Transmission Dissertation zur Erlangung des Doktorgrades der Fakultät für Agrarwissenschaften der Georg-August-Universität Göttingen vorgelegt von Rico Ihle geboren in Zschopau Göttingen, Dezember 2009 D 7 1. Referent: Prof. Dr. Stephan von Cramon-Taubadel 2. Korreferent: Prof. Dr. José Maria Gil Roig Tag der mündlichen Prüfung: 4. Februar 2010 You always return from a journey as a different man to the one who set off. (Graham Greene) àBñm.Ì'@ð ékA JË@ I. m ' ¼@P @ ... éË IÊ ®¯ X CJ.Ë@ ú¯ ½Ë X I. k @ ú G@ ѪK ( ) éÊgP , é£ñ¢. áK .@ “...I see that you are fond of traveling through foreign lands.” I replied, “Yes, I am.” (Ibn Battuta, Voyage) Danksagung - Acknowledgments Hisde, nuu is suuweid. Nuu werdor Gung emohl ferdsch! Nuu kimmor de Dugdurarb abor nich schreim, uhne duß doo e bill, wingsdns e bill Arzgibargsch drinne schdied. Joa, ze erschdemohl rachd schien Doank an de Luid dehemm, an mei Illorn, mei Schwasdor und un ulle gudn Bekanndn, ze die dar Foodn nuch gehalln hood, ah wen- niech inde ledsdn Goahr rachd viel in dor Waldgischichd rimhargirääsd bie un nichesu viel dehemm giwasn bie, wiemor villeichd dehemm sei hädd kinne. Nuijoa, su is dus Lahm ahm. Schien Doank difier, dussor mier’n Riggn freighalln hubd, dussiech ah emohl ewus annorsch ze du hadd uls wie näär de Arb. E bill Oabwachslung dud nischd schoodn! Un ullis, wus mor dehemm gilernd hood, dudor nidsn, ah wenn de idse mid’n Rachnkasdl un nich middor Goobl dei Gald vordiene dusd. Asso: rachd schien Doank! Nuu muß’ abor uff Englisch weddor gieje, duß die annorn miech ah vorschdieje: The two quotes above illustrate what I consider the last half a decade–but not only that time–to be: a journey. Not only because I traveled, physically, to (or through) 20 countries in this time, but also in the broader and more figurative sense of “journey.” Therefore, I would like to take the opportunity now to thank some of the people who guided me on this journey and have thus played a part in making it turn out the way it did. Those who bear the most guilt for my interest in statistics and econometrics are Professor Stephan von Cramon-Taubadel and Professor Walter Zucchini, who inspired me with their excellent lectures to pursue quantitative methods in my M.Sc. studies. When I was abroad after graduation, I learned about the recently founded Centre for Statistics at Göttingen University, and thus applied from Sana’a, Yemen, for the Ph.D. program “Applied Statistics and Empirical Methods.” I am grateful for the support of Professor von Cramon-Taubadel and Professor Zucchini in my application for this program. I would like to explicitly thank the Centre for Statistics for giving me the chance to study in the program; it has shaped me in a lasting way. Particularly, I would like to thank Professor Manfred Denker for his help in making the start in the program as easy as possible for new students, and for his small bits of wisdom he gave the new Ph.D. students along their way. The courses of Professor Walter Zucchini and Professor Stefan Sperlich familiarized me with the vast and very interesting world of quantitative methods; a warm thank you for this. Because of Professor Edgar Brunner, I became convinced of the usefulness of matrix algebra. Thank you. Special thanks go to the supervisors of my thesis. Professor Stephan von Cramon- Taubadel provided much motivation, many helpful comments and a pleasant interna- tional working atmosphere at the Lehrstuhl. Many thanks to Professor José-Maria Gil and Professor Bernhard Brümmer for their support and helpful advice which made me look at several aspects from new perspectives, and thus enriched the thesis con- siderably (Muchas gracias und vielen Dank!). Thanks also to the friends and good colleagues whom I got to know during these last five years in Göttingen. Some of them I would like to name here. First, I shared the office with Rodrigo and Oleg on the 10th floor of the Blauer Turm during this time which was enjoyable to say the least. Moreover, thanks to Arne, Johannes, Paola, Jei, Yesilda, and Rauf, with whom I spent so much time during my first two years in the Ph.D. program. Thank you to my immediate colleagues of the Agrarpolitiklehrstuhl, Dr. Jochen Meyer, Sebastian, Joseph, Karla, and Linde; and my indirect colleagues of the Marktlehrelehrstuhl on the 10th floor, Stefan, Tinoush, and Martin, for the nice time and interesting discussions we had. I would like to also thank the people who co-founded the Arbeitskreis Ökonometrie with me, Julia, Asif, and Yanjie, for their engagement, and the “new” generation of interested and regular participants who have kept it alive since spring 2006. Thanks for the great meetings and critical discussions we had! Also, I have good memories of the engaging talks with and the hospitality of Afsaneh and Arash. And, I will not forget the good time with Ren un de Sochs’n of the Ökonometrielehrstuhl on the 8th floor. I am also thankful for the help of Kristin, Mary, and Stefan for proofreading this thesis. Last but not least, I do not want to forget the many nice people all over the world whose ways met briefly with mine. Many thanks for their reliability, hospitality, and helpfulness which kept me from getting lost, whether it be in Arabia Felix, the Pamirs, the Rub’ al Khali, the Atacama, or the Dasht-e Lut. ^¨ Contents List of FiguresV List of TablesVI List of AbbreviationsIX List of SymbolsXI Executive SummaryXV 1 Introduction1 1.1 Motivation..................................1 1.2 Definitions..................................2 1.3 Vector Error-Correction Model.......................7 1.3.1 Basic Idea..............................7 1.3.2 Model Structure...........................8 1.3.3 Estimation.............................. 12 1.3.4 Interpretation............................ 16 1.3.5 Applications............................. 18 1.4 Nonlinearities in Price Transmission.................... 19 1.4.1 The VECM and Nonlinearities................... 19 1.4.2 Literature Review.......................... 22 2 Models in Detail 25 2.1 Threshold Vector Error-Correction Model................. 25 2.1.1 Basic Idea.............................. 25 2.1.2 Model Structure........................... 28 2.1.3 Estimation.............................. 33 2.1.4 Interpretation............................ 34 2.1.5 Applications............................. 34 2.2 Markov-Switching Vector Error-Correction Model............ 35 2.2.1 Basic Idea.............................. 35 2.2.2 Model Structure........................... 38 2.2.3 Estimation.............................. 41 2.2.4 Interpretation............................ 41 2.2.5 Applications............................. 42 I 2.3 Semiparametric Vector Error-Correction Model............. 45 2.3.1 Basic Idea.............................. 45 2.3.2 Model Structure........................... 46 2.3.3 Estimation.............................. 46 2.3.4 Interpretation............................ 49 2.3.5 Applications............................. 49 2.4 Parity Bounds Model............................ 51 2.4.1 Basic Idea.............................. 51 2.4.2 Model Structure........................... 52 2.4.3 Estimation.............................. 55 2.4.4 Interpretation............................ 55 2.4.5 Applications............................. 57 3 Summary 59 3.1 Cointegration Models............................ 59 3.2 Parity Bounds Models........................... 63 3.3 Parity Bounds vs. Cointegration Models................. 67 4 Conclusion 79 Bibliography 80 Appendices 98 Appendix A: Spatial Market Integration in the EU Beef and Veal Sector: Policy Decoupling and the Outbreak of Blue Tongue Disease...... 101 Appendix B: Markov-Switching Estimation of Spatial Maize Price Transmis- sion Processes between Tanzania and Kenya............... 125 Appendix C: Grenzeffekte in der Marktintegration bei Mais in Ostafrika: Einsichten aus einem semi-parametrischen Regressionsmodell...... 139 Appendix D: A Comparison of Threshold Cointegration and Markov-Switching Vector Error-Correction Models in Price Transmission Analysis..... 161 Appendix DI: Literature Review of Applications of the TVECM.... 197 Appendix DII: Simulation Study...................... 201 II List of Figures 1.1 Nonstationary Process vs. Mean Reversion of a Stationary Process...4 1.2 Stochastic vs. Deterministic Trend....................5 1.3 Example of a VECM............................9 1.4 Characteristic Graphs of the VECM.................... 13 2.1 Example of a Continuous and Symmetric Band-TVECM........ 31 2.2 Example of a Symmetric EQ-TVECM.................. 32 2.3 Characteristic Graphs of a Typical Sym. and Continuous Band-TVECM 33 2.4 Characteristic Graphs of a Typical Symmetric EQ-TVECM....... 33 2.5 Estimated Constants of a MSM-VAR and a MSI-VAR Specification.. 39 2.6 Characteristic Graphs of a Typical MSVECM.............. 40 2.7 Example of a MSVECM.......................... 41 2.8 Characteristic Graphs of a Typical SPVECM............... 47 2.9 Examples of Unweighted Estimated Mixture Distributions....... 54 2.10 Examples of Weighted Estimated Mixture Distributions......... 55 2.11 Characteristic Graphs of a Typical PBM................. 56 3.1 Mean and Variance of a Band-TVECM.................. 63 3.2 Mean and Variance of an EQ-TVECM.................. 64 3.3 Mean and Variance of a MSVECM.................... 65 3.4 Distribution of Band-TVECM Realizations (Weak Adjustment).... 73 3.5 Distribution of Band-TVECM Realizations (Strong Adjustment).... 74 3.6 Distribution of