RUHR ECONOMIC PAPERS Timo Mitze Alfredo R. Paloyo Björn Alecke Quasi-experimental Methods in Empirical Regional Science and Policy Analysis – Is there a Scope for Application? #367 Imprint Ruhr Economic Papers Published by Ruhr-Universität Bochum (RUB), Department of Economics Universitätsstr. 150, 44801 Bochum, Germany Technische Universität Dortmund, Department of Economic and Social Sciences Vogelpothsweg 87, 44227 Dortmund, Germany Universität Duisburg-Essen, Department of Economics Universitätsstr. 12, 45117 Essen, Germany Rheinisch-Westfälisches Institut für Wirtschaftsforschung (RWI) Hohenzollernstr. 1-3, 45128 Essen, Germany Editors Prof. Dr. Thomas K. Bauer RUB, Department of Economics, Empirical Economics Phone: +49 (0) 234/3 22 83 41, e-mail: [email protected] Prof. Dr. Wolfgang Leininger Technische Universität Dortmund, Department of Economic and Social Sciences Economics – Microeconomics Phone: +49 (0) 231/7 55-3297, email: [email protected] Prof. Dr. Volker Clausen University of Duisburg-Essen, Department of Economics International Economics Phone: +49 (0) 201/1 83-3655, e-mail: [email protected] Prof. Dr. Christoph M. Schmidt RWI, Phone: +49 (0) 201/81 49 -227, e-mail: [email protected] Editorial Office Joachim Schmidt RWI, Phone: +49 (0) 201/81 49 -292, e-mail: [email protected] Ruhr Economic Papers #367 Responsible Editor: Thomas K. Bauer All rights reserved. Bochum, Dortmund, Duisburg, Essen, Germany, 2012 ISSN 1864-4872 (online) – ISBN 978-3-86788-422-8 The working papers published in the Series constitute work in progress circulated to stimulate discussion and critical comments. Views expressed represent exclusively the authors’ own opinions and do not necessarily reflect those of the editors. Ruhr Economic Papers #367 Timo Mitze, Alfredo R. Paloyo, and Björn Alecke Quasi-experimental Methods in Empirical Regional Science and Policy Analysis – Is there a Scope for Application? Bibliografische Informationen der Deutschen Nationalbibliothek Die Deutsche Bibliothek verzeichnet diese Publikation in der deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über: http://dnb.d-nb.de abrufbar. http://dx.doi.org/10.4419/86788422 ISSN 1864-4872 (online) ISBN 978-3-86788-422-8 Timo Mitze, Alfredo R. Paloyo, and Björn Alecke1 Quasi-experimental Methods in Empirical Regional Science and Policy Analysis – Is there a Scope for Application? Abstract Applied econometrics has recently emphasized the identification of causal parameters for policy analysis. This revolution has yet to fully propagate to the field of regional science. We examine the scope for application of the matching approach – part of the modern applied econometrics toolkit – in regional science and highlight special features of regional data that make such an application difficult. In particular, our analysis of the effect of regional subsidies on labor-productivity growth in Germany indicates that such policies are effective, but only up to a certain maximum treatment intensity. Although the matching approach is very appealing due to its methodological rigor and didactical clarity, we faced difficulties in balancing the set of covariates for our regional data given that the regions differ strongly with respect to the underlying structural characteristics. Thus, results have to be interpreted with some caution. The matching approach nevertheless can be of great value for regional policy analysis and should be the subject of future research efforts in the field of empirical regional science. JEL Classification: C21, R11, R58 Keywords: Generalized propensity score; nearest neighbor matching; labor productivity growth; regional policy September 2012 1 Timo Mitze, University of Southern Denmark; Alfredo R. Paloyo, RWI; Björn Alecke, Gesellschaft für Finanz- und Regionalanalysen (GEFRA). – Earlier versions of this paper have been presented at the 50th ERSA Congress in Jönköping and the 51st ERSA Congress in Barcelona. The authors thank conference participants for helpful suggestions. – All correspondence to Timo Mitze, Department of Border Region Studies, University of Southern Denmark, Alsion 2, 6400 Sønderborg, Denmark, E-Mail: [email protected]. ͳ Ǧ ሺǤǤǡ ሻǤ ሺʹͲͳͲሻ Dz dz Ǥͳ Ǧ ǡ Dzdz ǡ Ǧ ǡ ǤʹǦ͵ ǡ DzǦ dz ሺ ʹͲͳͲሻ ǤͶ Ǧ Ǧ ǡ Ǥ ǡ Ǧ Ǧ Ǧ Dz dzሺ ሻ Ǥ Ǥ ǡ̀Ͳ Ǥ ሺሻǤ ǡ Ǧ ǤǡǦ Ǧ Ǧ Ǧ Ǧ Ǥ Ǥ ǡ Ȅ Ȅ ͳሺǤǤǡǦ ǡ Ǥ Ǥ ሺ ʹͲͲ͵ሻǡ ሻ Ǥ Dz dzǦ Ǥ ǡሺʹͲͲͻሻǤ ʹ Dz dzǡ Ǥ Ǥ ͵ǣ ǣȀȀǤǤȀͶͳͲǤ ͶሺʹͲͳͲሻ ǡǡǦǦ Ǥ ǡ ǡ Ǥ Ͷ Ǧ ሺʹͲͲͶሻ ሺǤǤǡሻǤ Ǥ Ǧ Ǧ Ǧǡ ǤǦ Ǧ Ȅ ͳͲͷ ሺ̀ሻ Ȅ Ǥ ǡ Ǥ ǡ Ǥ ሺʹͲͳʹሻǡ Ǥ ǡ Ǥ ǡ Ǧ Dz dzǤ ǡ ǡ Ǥ ǡ Dz Ǧ dz ሺǤǤǡ ǦǦሻ Ǧ Ǥ ǡ Ǥ ʹ Ȅǡ Ǥͷ ǡǦǦǦ ǡ Ǧ Ǧ Ǥ Ǧ ǡ ǡ Ǥ ǡǦ Ǧ ǡ Ǥ Ǥ ሺʹͲͳͲሻ Ǧ ͷ ǡ ǣ ሺʹͲͳͲሻǡ ሺʹͲͳͲሻǡ ïሺʹͲͳͲሻǡሺʹͲͳͲሻǡሺʹͲͳͲሻǤ ͷ ǣ ǡǡ Ǥ Ǧ ǡ Ǧ ǡ Ǧ ǡ Ǥǡ Ǥ Ǥ Ǧ Ǥ ǡ Ǧ Ǥ ǡǦ ሺ ǡ Ȅ Ǧ ሻǤሺሻ Ǥ ǡ Ǥ ǡǤሺʹͲͳͲሻ Ǧ ሺǡሻ Ǥ Ǧ ǡǡǦ Ǣǡ Ǥ ǡǡ ǯǦ ǤሺʹͲͳͲሻ Ǧ ǯ Ǧ Ǥǡ ǤሺʹͲͳͲሻǦ Ǧ Ǥ ͳ ǡ ͷ Ǥ ǡ ͳ Ǥ ǡ ǤሺʹͲͳʹሻ ሺʹͲͲͺሻ Ǥ Ǧ ǡ Ǥ ǡ Ǥǡǡ Ǧ Ǥ ǡ Ǧ Ǥ ǡDz ǫdzǤ Ǧሺ Ǧ ሻ Ǥ ǡ Dz ǫdzǤǡ ǡǡǦ Ǥ ͵ ǡ Ǧ Ǧ Ǥ Ǧ Ǧ ͳͻʹ͵Ǥͺ ܰሺǡሻ݅ ሺǦǦሻǤݕ ሺǡ Ǧ ሻ ǡ ݀ ǡ ͳ ݅ ሺǤǤǡሻͲǤǡ ǡ ݕ ሺͲሻ ݕ ሺͳሻǡ ݅ ǡ Ǥ ǡ ݕ ൌ ݕ ሺ݀ ሻ ൌ ݕ ሺͲሻሺͳ െ ݀ ሻ ݕ ሺͳሻሺ݀ ሻǤ 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ǯ ሺሻǤ Ǧ Ǧ Ǥͳʹ ǡ̀ͳ ǡǦ Ǥ Ǧ Ǧ ሺ̀͵ͻሻǤ ͳͻͻ͵ԟʹͲͲͺ Ͷͳ͵ Ǧ͵ Ǧ Ǥ Ǥ Ǧ Ǥǡ ͳ ͳͻͻ͵ԟʹͲͲͺͲǦ Ǥ ͳʹ ǡǡ ǡ ǤሺʹͲͳʹሻǤ ͳͲ ሺǤǤǡ ሻ ǡ ǣሺͳሻ ͳͻͻʹ ሺǦ ሻǡሺʹሻ ǡ ሺ͵ሻ Ǧ Ǧ ǡ ሺͶሻ ǯǦ ǡሺͷሻ ǡ ሺͺሻ Ǧ ሺሻͳͲͲǡͲͲͲǦ ሺሻሺͻሻ ǡ ͳሺ ሻͻሺሻǤͳ͵ Ǥ ǡ Ǧ ͳͻͻʹ ǡ Dz dz ሺ Ǧ ǡ ǡ ǡ ǤሻǤͳͶ ǡ Ǥ ǡ Ǧ ǡ ǤǡǦ Ǧ ǡ ǡ Ǥǡ ǡ Ǥ Ǧ Ǧ ሺͳͻͻͶԟͳͻͻͺǡͳͻͻͺԟʹͲͲʹǡʹͲͲͲԟʹͲͲͶሻǡ ǡ Ǧͳͻͻ͵ԟ ʹͲͲͺǤͳͷǤǡ ͳ͵ ǡ ሺʹͲͳͳሻǤ ͳͶ Ǧ ǣȀȀǤǤǤȀ ̴Ͳ͵ʹȀ̴ͶͻͷͲͺʹȀȀȀ ȀǦ ȀȀȀȀǦ ǤǤ ͳͷ ͳʹǤ Dz ʹdz ሺ ʹͲͲ͵ሻǢ Ǧ Dzdz ሺ ʹͲͲͺሻǤ Dzdzሺ ʹͲͲሻǤ ͳͳ Ǥ ǡ Ǧ Ǧ Ǧ ǯ Ǥ Ǧ ܠ Ǥ ͳǤ Ǧ ǡሺሻ Ǧ Ǥ Ǥ ǡ Ǧ Ǧ Ǥ Ǥǡ Ǥ ǡ ǤDz dzǡ Ǧ Ǧ ǡǡ Ǥǡ ǡ Ǧ Ǧ Ǥ ͳǣǦ ሺሻ ሺ ሻ ሺͲȀͳሻǣ ሺͲȀͳሻǣ ሺ ሻ ǦǦ ͳͻͻͶԟͳͻͻͺ ԟͳͻͻͺ ͳͻͻͶ ԟͳͻͻͺ ͳǤͶͷʹȗȗȗ ሺǤǤሻ ሺሻ ሺͲǤʹͶʹͺሻ ሺͲǤʹͷͳͺሻ ሺͲǤ͵ͲʹͶሻ ሺͲǤͳʹ͵ͷሻ ͳǤ͵ʹͷȗȗȗ ͳǤʹͶͶȗȗȗ ͲǤͷͷͻȗ ͲǤ͵͵ȗȗȗ ሺͲǤʹͻͺͳሻ ሺͲǤ͵ͳͳͲሻ ሺͲǤͳ͵͵ͷሻ െͳǤͶͺʹȗȗȗ െͳǤͲͻ͵ȗȗȗ െͳǤʹͶͷȗȗȗ ሺͲǤʹͷͺሻ ሺͲǤʹͶሻ ሺͲǤʹͺͲͻሻ ሺͲǤͳʹͳʹሻ െͲǤͶͻͳȗȗȗ ሺͲǤʹͺͻሻ ሺǤǤሻ ሺ ሻ െͳǤͺͶȗȗȗ ሺǤǤሻ ሺ ሻ Ǧ Ǧ ͳͻͻͺԟʹͲͲʹ ԟʹͲͲʹ ͳͻͻͺ ԟʹͲͲʹ ͳǤͺʹ͵ȗȗȗ Ǧ Ǧ ʹͲͲͲԟʹͲͲͶ ԟʹͲͲͶ ʹͲͲͲ ԟʹͲͲͶ ʹǤͶʹͷȗȗȗ ͳͻͻ͵ԟʹͲͲͺ ԟʹͲͲͺ ͳͻͻ͵ ԟʹͲͲͺ ʹǤͲͺͷȗȗȗ െͲǤͺͻʹȗȗȗ െͲǤͳȗȗȗ െͲǤ͵ͻͺ ሺǤǤሻ ሺሻ ሺͲǤʹͷͺͷሻ ሺͲǤʹ͵ሻ ሺͲǤʹͺͳʹሻ ሺͲǤͳʹͲሻ െͲǤͳͻʹ െͲǤͳͳͺ െͲǤͳ െͲǤͲͺͺȗ ሺǤǤሻ ሺͲǤͳʹʹʹሻ ሺͲǤͳͳሻ ሺͲǤͳʹͺሻ ሺͲǤͲͶʹሻ െͲǤʹ͵ʹ െͲǤʹͺͲ െͲǤͷͻȗ െͲǤʹͺȗȗ ሺǤǤሻ ሺͲǤʹͺͶሻ ሺͲǤʹʹሻ ሺͲǤ͵ͲͲͷሻ ሺͲǤͳʹͶሻ ͲǤͲ͵Ͷ ͲǤͲͶͳ ͲǤͲͲͲ ͲǤͲʹͳ ሺǤǤሻ ሺͲǤͲ͵ͻͳሻ ሺͲǤͲ͵ͻͶሻ ሺͲǤͲͶͳͷሻ ሺͲǤͲͳͷሻ ͶͲͺ ͶͲͺ ʹͲʹͲ ʹ ͵ͻͺ ͲǤʹͻ ͲǤ͵Ͳ ͲǤ͵ͷ ͲǤ͵ʹ ǣǦǤǤǤǤȗ൏ͲǤͳͲǡȗȗ൏ͲǤͲͷǡȗȗȗ൏ͲǤͲͳǤ ͳʹ ሺ ǡ ǡ ሻ Ǥ Ǧ ǡ Ȅ Ȅ Ǧ Ǥ ǡ Ǥ Ǧǡ ሺൌͷሻ ͳǤ Ǧ ͷǦ Ǥ ʹǤ Ǧ Ǧ Ǥ ǡ Ǧ ǡǦ Ǧ Ǥ ǡ Ǧ ͳͻͻͻԟʹͲͲͶ ͳͻͻͶԟͳͻͻͺ Ǥ Ǧ ǡ Ǧ Ǥ ǡ ሺ߬ሻ ͳͻͻͻԟʹͲͲͶǤ ǡ ǡ ʹ Ǧ Ǧ Ǥ ͲǤͷ ǡ ʹͲ Ǥ Dz dz Ǧ ǡ Ǧʹ ሺʹͲͲͶሻǤ Ǧ ǦʹǦ Ǥ ǡ Ǧʹ Ǥʹሺ ͳሻǡ ǦǦʹǦDzdzሺͺԟͳʹ ʹͻԟ͵ͷ ǦሻǤ ǡ ǦǦ Ǧʹ ǡǦ Ǥ Ǥ Ǧ ͳ͵ Ǥ ǡ Ǥ ǡሺ ൌͶͳ͵ሻǡ Ǧ Ǥ ʹǣǦሺൌͷሻ ǣ ǣ Ǧ Ǧ Ǧ Ǧ Ǧ Ǧ ͳͻͻͻԟʹͲͲͶ ͳͻͻͻԟʹͲͲͶ ԟʹͲͲͶ ͲǤͲͳͻ ʹͲͲ͵ԟʹͲͲ ʹͲͲ͵ԟʹͲͲ ԟʹͲͲ ͲǤͲʹ͵ ʹͲͲͷԟʹͲͲͺ ʹͲͲͷԟʹͲͲͺ ԟʹͲͲͺ ͲǤͲʹͶ ͲǤͲʹ͵ ሺ ǤǤሻ ʹͳͶሺͳͻͳሻ ͲǤͲͳͺ ʹͳͲሺͳͺͻሻ ͲǤͲͳͻ ͳͺ͵ሺͳ͵ʹሻ ͳͲʹሺͳͻሻ ͲǤͲͳͻ ͲǤͲͳͺ ሺ ǤǤሻ ͳͺͶሺͳͺͶሻ ͳͻͺሺͳͻͺሻ ʹʹͷሺʹʹͷሻ ͻͻ͵ሺͻͻ͵ሻ τ ͲǤͲͲͳ ͲǤͲͲͶȗȗ ͲǤͲͲȗȗ ͲǤͲͲͷȗȗȗ ሺǤǤሻ ǦǦʹ ሺͲǤͲͲʹͳሻ ͲǤͲͺ ሺͲǤͲͲͳͻሻ ͲǤͳͳͻ ሺͲǤͲͲʹͶሻ ሺͲǤͲͲͳሻ ͲǤͲͺ ͲǤͳʹͲ Ȟ ͳ ͶǤͳȗȗȗ ʹǤʹȗȗȗ ͲǤͲͲͶȗȗȗ ͵ͳǤ͵ȗȗȗ ʹͺ͵Ǥʹȗȗȗ ͲǤͲͲͳ ͲǤͲͲͷȗȗȗ ͲǤͲͲͶȗȗȗ ሺǦሻ ȞͳǤͷ ሺͲǤͳͷሻ െͲǤͲͲͳ ሺͲǤͲͲሻ ͲǤͲͲʹȗȗ ሺͲǤͲͲሻ ሺͲǤͲͲሻ ͲǤͲͲ͵ȗȗ ͲǤͲͲͲ ሺǦሻ Ȟ ʹ ሺͲǤͻʹሻ ሺͲǤͲͷሻ ሺͲǤͲ͵ሻ ሺͲǤ͵ͳሻ െͲǤͲͲ͵ ͲǤͲͲͲ ͲǤͲͲͳ െͲǤͲͲʹ ሺǦሻ ሺͲǤͻͻሻ ሺͲǤͶͻሻ ሺͲǤʹͺሻ ሺͲǤͻͻሻ ͵Ǧ ǣǤǤǤȗ൏ͲǤͳͲǡȗȗ൏ͲǤͲͷǡȗȗȗ൏ͲǤͲͳǤ ǡ Ǧ ǡ ǡ Ǥ ǡ ȞǤ Ȟ ʹ Ǧ Ǧ ͳͳǤͷ Ǧ Ǥ ǡ Ǥ ǡ Ǧ Ȟ ൌ ͳǤͷ Ǧ ͵Ǥͷ ሺ ሻǤǡ Ǥ ͳͶ ǡ Ǧ Ǥ ǡ Ȅ Ȅ ͲǤͷ ǦǤǦ ǡ Ǧ Ǥ ǡǡ Ǥ Ǧ ሺ ሻ Ȃ Ǥ ͵ǡ ǡǦ ሺͳͲͲͲ ̀ሻ Ǧ͵Ǥͳ Ǧ ǡ ǣͳ ሺͳሻ Ǧ ͳͻͻ͵ԟʹͲͲͺ ሺʹሻǤ ǡǡǦ ǡ ǡ ǡ ǡ ǡ Ǥ ǡ Ȃ ͵Ǥ Ǧ Ȃ ǡ ǡ ȂǤ Ǧ ǡ Ȃ ͳͺ ሾݕ ȁܹܴܩ ǡ ܵܲܩ ሿ ൌ ߙ ߙଵ ܹܴܩ ߙଶ ܹܴܩଶ ߙଷ ܵܲܩ ߙସ ሺܹܴܩ ൈ ܵܲܩ ሻ ɒǣ ே ଶ ప ǡ ܵܲܩప ሿ ൌ ͳ ൣߙ ෞ ߙ ෞ߬ ෞ߬ ߙ ෞܵܲܩሺ߬ǡ ܺ ሻ ߙ ෞሺ߬ ൈ ܵܲܩሺ߬ǡ ܺ ሻ߬൧Ǥ ሾݕప ȁܹܴܩ ଵ ߙ ଶ ଷ ସ ܰ ୀଵ ǡ Ǧ Ǧ Ǧ Ǥ ͳ ሺሻ Ǧ͵ Ǧ ଵ ழଵ଼ வହ ሻሿǡ ܨܮൌ ሾሺܲ௧ െ ܲ௧ழଵ଼ െ ܲ௧வହ ሻሺܲ௧ିଵ െ ܲ௧ିଵ െ ܲ௧ିଵ ே ͳͺͷǡ Ǥ ȂͳǤ ͳ ሺʹͲͳʹሻǤ ͳͺሺʹͲͲͶሻǡǦ Ǥ Ǥ ͳͷ ǤሺʹͲͳʹሻǡ Ǧ Ǥ ǡ Ȃ ͻͲǦ Ǥ ͵ǣ Ǧ ሺ ሻ ǣ ǣ ሺ ሻ Ǧ Ǧ ͳͻͻ͵ԟʹͲͲͺ ͳͻͻ͵ԟʹͲͲͺ ԟʹͲͲͺ െͲǤͳͷͻȗȗȗ ͳͻͻ͵ԟʹͲͲͺ ͳͻͻ͵ԟʹͲͲͺ ԟʹͲͲͺ െͲǤͳʹȗȗȗ ሺǤǤሻ ሺ ሻ ሺͲǤͲͳͻሻ ͻǤͳͷͺȗȗȗ ሺͲǤͲͳͶሻ ͻǤͶʹͷȗȗȗ ሺǤǤሻ ሺሻ ሺʹǤͺሻ െͲǤͲͺ ሺͳǤͷʹሻ ͲǤͲͶͻ ሺǤǤሻ ሺሻ ሺͲǤͳͲͷሻ ͲǤͷͶ ሺͲǤͳʹͳሻ ͵ǤͶͷͳ ሺǤǤሻ ሺሻ ሺͲǤͳͺͻͳሻ ͲǤͷͷȗȗȗ ሺ͵ǤʹʹͶሻ ͲǤͶȗȗȗ ሺǤǤሻ ሺሻ ሺͲǤͳͺͻͳሻ െͲǤͷͲʹ ሺͲǤͳʹͷͷሻ െͲǤͺͳͳȗȗ ሺǤǤሻ ሺሻ ሺͲǤ͵Ͷ͵ሻ െͲǤͳ͵ͷ ሺͲǤʹͷ͵ሻ െͲǤ͵ͷͺȗȗȗ ሺǤǤሻ ሺ ሻ ሺͲǤͳͶͷሻ ͲǤʹͳͻ ሺͲǤͳͲ͵ሻ ͲǤͷͳͶȗȗ ሺǤǤሻ ሺ ሻ ሺͲǤʹͻሻ ͵Ǥͳ͵͵ȗȗȗ ሺͲǤʹͲ͵ͷሻ ͵ǤͶͷȗȗȗ ሺǤǤሻ ሺሻ ሺͲǤ͵ͳͻͳሻ െͲǤͳʹͳ ሺͲǤʹʹͺͳሻ െͲǤͲͻͷ ሺǤǤሻ ሺͲǤͳͳʹሻ െͳǤͲͷȗȗȗ ሺͲǤͲͶͳሻ െͲǤͺȗȗȗ ሺǤǤሻ ሺͲǤʹͳͺሻ ͲǤʹͲͻȗȗȗ ሺͲǤͳ͵ʹͷሻ ͳǤͳͲʹȗȗȗ ሺǤǤሻ ሺͲǤͲͶʹͻሻ ͲǤͲȗȗȗ ሺͲǤʹʹ͵ͳሻ ͲǤʹ͵ͻȗȗȗ ሺǤǤሻ ሺͲǤͲͳሻ ͺʹͲ ሺͲǤͲ͵ͳͻሻ ͳͺ͵ʹ Ȃ ሺǦሻ ͲǤͲ͵ʹ ͲǤͲͳͶ ሺͲǤ͵ሻ ሺͲǤͺͶሻ ǣǤǤǤȗ൏ͲǤͳͲǡȗȗ൏ͲǤͲͷǡȗȗȗ൏ͲǤͲͳǤ ͳ ͶǣȂ ǣ ǣ ǦǦ ͳͻͻ͵ԟʹͲͲͺ ͳͻͻ͵ԟʹͲͲͺ ԟʹͲͲͺ െͲǤͲͲ͵ȗȗȗ ͳͻͻ͵ԟʹͲͲͺ ͳͻͻ͵ԟʹͲͲͺ ԟʹͲͲͺ െͲǤͲͲʹ ሺǤǤሻ ʹ ሺͲǤͲͲͲሻ ͲǤͲͲͲʹȗȗȗ ሺͲǤͲͲͻሻ ͲǤͲͲͲͳ ሺǤǤሻ ሺͲǤͲͲͲͲሻ െͲǤͲͷ͵ȗ ሺͲǤͲͲͲሻ െͲǤͲͳȗ ሺǤǤሻ ൈ ሺͲǤͲ͵Ͳʹሻ ͲǤͲͳͷȗȗȗ ሺͲǤͲ͵ͺ͵ሻ ͲǤͲͳȗȗȗ ሺͲǤͲͲ͵ሻ ͺʹͲ ሺͲǤͲͲሻ ሺͲǤͲͲͶͺሻ ͳͺ͵ʹ ሺͲǤͲͲሻ ሺǤǤሻ ሺǦሻ ሺǦሻ ǣ ȂǤ ǤǤǤ Ǥȗ൏ͲǤͳͲǡȗȗ൏ͲǤͲͷǡȗȗȗ൏ͲǤͲͳǤ Ȃ Ǧ Ǥ Ȃ Ͷǡ Ȃ Ǧ ͳǤ Ǧ Ȃ Ǥ Ǧ Ǧͳǡ Ǥ ǡ ͺሺȂǦ ሻǡ ̀ͳͲͷ Ǧሺ ሻǤͳͻ ǡ Ǥ ǡ ǡ ǡ Ǧ Ǥ ሺʹͲ ǡ Ǧ ̀ͳͲ ሻǤǡ ǦǦ ͳǤ ͳͻǡͻͷǦ Ǥǡ ̀ ͲǤͷ̀ͶʹͲǤ ͳ ͳǣȂǦ Treatment Effect Function .01 0 -.004 -.002 E[dlye(t+1)]-E[dlye(t)] .02 .015 E[dlye(t)] .025 .002 .03 Dose Response Function 0 2 4 6 Treatment level Dose Response 8 10 0 Low bound 2 4 6 Treatment level Treatment Effect Upper bound 8 10 Low bound Upper bound Confidence Bounds at .95 % level Dose response function = Linear prediction Confidence Bounds at .95 % level Dose response function = Linear prediction ǣȂǦ ͳͻͻ͵ȂʹͲͲͺǤ Ǥ Ǥ ሺʹͲͳʹሻǡ ͳͺ Ǧ ǡሺʹͲͲͺሻǡ Ǥ ǡ ǡ ǡ ሺ ǦǦ ͶሻǤ ǡǡ ሺሻ ǡ Ǧ Ǥ ǫǡ Ǥ ǡ Ǧ ሺ ǡ ሺʹͲͳͲሻሻǤ ǡǦ ͳͺ Ǥ Ǥ Ǧ ሺ ሻǤ ǦǦ Ǧ Ǥ ǡ Ǥ ǡ Ǧ Ǧ Ǧ Ǥ ǡ ǤǦ Ǥ Dz dzሺ ሻ ǡ Ǧ Ǧ Ǧ Ǧ ǦǦ ͳͻͻ͵ԟʹͲͲͺǤ Ǧ ǤǦ ǡǡǦ Ǧ ǡ Ǥǡ ǡ Ǥ ǡ Ǥ Ǧ ǡ Ǧ Dz dzǤ Ǧ Ǧ ǡ Ǥ ǦǦ Ǧ Ǥ ǡ Ǥ ǡ Dz Ǧ dz ሺሻ ǡ ǡ Ǥ ǡ Ǥǡ ͳͻ Ǥ ǡ ǤሺʹͲͳʹሻ Ǧ Ǥ ሺሻǦ Ǧ Ǧ Ǥ ǡ Ǧ Ǥ ʹͲ ǡÚǡǡ ሺʹͲͳʹሻǤDz ǣ dzǡ ǡǤ ǡǤÚǦ ሺʹͲͳͲሻǤDz ǣ dzǡ ʹͶ ʹͶሺʹሻǣ͵Ȃ͵ͲǤ ʹͶ ሺʹͲͳͳሻǤ Dz ò Ǧǡ Ǧ dzǡ Ǥ ò ǣ Ǥ ǡ ሺʹͲͲሻǤDzȂ dzǡ ǤʹͷͶʹǤ ǡ ሺʹͲͲͺሻǤ Dz Ȃ dzǡ ͺ ͺሺ͵ሻǣ͵ͷͶȂ͵͵Ǥ ǡ ሺʹͲͲͺሻǤDz Ǧ dzǡ ʹʹ ʹʹሺͳሻǣ͵ͳȂʹǤ ʹʹ ǡ±ǡǡሺʹͲͳʹሻǤDz dzǡ ͵ͷ ͵ͷሺͳሻǣͶͺԟͻǤ ͵ͷ ǡ ሺʹͲͳͲሻǤ Dzǡ ǡ dzǡ Ͷͺ ͶͺሺʹሻǣͶʹͶԟͶͷͷǤ Ͷͺ ǡ Ǥ ሺͳͻͻͻሻǤ Dz ǣ dzǡ Ǧ ͻͶ ͻͶሺͶͶͺሻǣͳͲͷ͵ȂͳͲʹǤ ͻͶ ǡǤሺʹͲͲʹሻǤDz Ǧ Ǧ dzǡ ͺͶ ͺͶሺͳሻǣͳͷͳȂͳͳǤ ͺͶ ǡ ሺʹͲͳͲሻǤ Dz ǯ dzǡ ͺሺሻǣͳͺ͵ȂͳͻͲ͵Ǥ ͺ ǡ ሺʹͲͲͶሻǤ Dz ǣ Ǧ dzǡ ͵Ͷ ͵Ͷሺͳሻǣʹͳԟ͵ͳͲǤ ͵Ͷ ǡ ǡ Ǥ ǡ ሺʹͲͳͲሻǤ Dz ǣ dzǡ Ǧ ͻʹ ͻʹሺͶሻǣͻͶͷȂͻͶǤ ͻʹ ǡ Ǥ ሺʹͲͲͺሻǤ Dz dzǡ ሺͳሻǣͳȂʹǤ ǡǤሺʹͲͳͲሻǤDz dzǡ Ͷͺ Ͷͺሺʹሻǣ͵ͷԟ͵ͻͺǤ Ͷͺ ǡǤǡ ǡሺͳͻͻሻǤDz Ǧ ǣ dzǡ Ͷ ͶሺͶሻǣͲͷȂͷͶǤ Ͷ ʹͳ ǡǤǡ ǡሺͳͻͻͺሻǤDz Ǧ dzǡ ͷ ͷሺʹሻǣʹͳȂʹͻͶǤ ͷ ǡǤïሺʹͲͳͲሻǤDz ǣ dzǡ ͳͷ ͳͷሺͳሻǣʹԟ͵Ǥ ͳͷ ǡ Ǥ ሺʹͲͲͶሻǤ Dz dzǤ Ǧ ǡ ǦǡǤǡǡǣ ƬǤ ǡǤሺͳͻͺሻǤDz dzǡ Ǧ ͺͳ ͺͳሺ͵ͻሻǣͻͶͷȂͻͲǤ ͺͳ ǡ Ǥ ሺʹͲͳͲሻǤ Dz ǡ ǡ dzǡ ͷͲ ͷͲሺͳሻǣͷȂʹʹǤ ͷͲ ǡ ǤǤሺʹͲͲͻሻǤDz Ǧ dzǡ Ͷ ͶሺͳሻǣͷȂͺǤ Ͷ ǡ ǤሺʹͲͳͲሻǤDz Ǥ dzǡ ͳͷ ͳͷሺͳሻǣ͵ȂʹͲǤ ͳͷ ǡ ሺʹͲͲ͵ሻǤ Dzʹǣ ǡ ǡ Ǧ dzǡ Ͷ͵ʹͲͲͳǡ Ǥ ǡሺʹͲͲͺሻǤDz ǫdzǡ ǤͲͺǦͳͲͶǤ ǡ ǤǢ ǡ Ǥ ሺʹͲͲሻǣ Dz Ǧ dzǡ Ǧ ǡʹͳ ʹͳሺʹሻǣͳͶͻǦͳǤ ʹͳ ǡሺͳͻʹ͵ሺͳͻͻͲሻሻǤDz Ǧ Ǥ Ǥ ͻdzǡ ͷ ͷሺͶሻǣͶͷȂͶʹǤ ǡ ǤሺͳͻʹሻǤDz dzǡ ሺ͵͵ͺሻǣ͵ͲȂ͵ͳͲǤ ǡǤሺʹͲͲʹሻǤǤʹǤǣǤ ǡǤǤሺͳͻͺ͵ሻǤDz dzǡͲ ͲሺͳሻǣͶͳȂͷͷǤ Ͳ ǡ ǤǤ ሺͳͻͷͳሻǤ Dz dzǡ Ǧ ͵ ͵ሺʹሻǣͳ͵ͷȂͳͶǤ ǡǤሺͳͻͺሻǤDzǣ ǫdzǡǦ ͺͳ ͺͳሺ͵ͻሻǣͻͳԟͻʹǤ ͺͳ ǡሺʹͲͲͶሻǤDz Ǧ ͳͻͻͲdzǡ ͺ ͺሺͳሻǣͳ͵͵ȂͳͷͷǤ ͺ ǡ Ǥ ሺʹͲͲ͵ሻǤ Dz Ǧ ǫdzǡ ͳ ͳሺ͵ሻǣͳȂͳͻͶǤ ͳ ǡǤሺʹͲͳͲሻǤ Ǥʹ ǤǡǣǤ ʹʹ ǣ ǣ ሺͳͲͲͲ ሻ ͷͲǤͳ ሺͳͲͲͲሻ ͻ͵ǤͶͳ ͳʹͳǤͳ ͳͺǤ͵ͺ ͳ͵ͺǤͲʹ ሺ ሻ ሺΨሻ Ǧ ሺΨሻ Ǧ Ǧ ͶǤͻʹ ǤǤ ǤǤ Ǥ Ǥ Ǥ Ǥ ͻǤͶͶ ʹʹǤͲ ͳͳͻǤͷʹ ͶǤͲʹ ͲǤͶ ǤͷͲ ͳ͵ͶǤͻʹ ͳͳͳǤͷͲ ͵ͷǤͷ ͳͺͷǤ͵͵ ʹͻǤʹͷ ͳͶǤͶ ͲǤͲͲ ͶʹͲǤ͵ͳ ʹͶǤͶͺ ͳͳǤͲ ͳǤͻͶ ͻǤͲͲ ͳǤͻ͵ ʹͷǤʹ ሺΨሻ ǤͳͶ ͵Ǥ͵ ͳͶǤ͵͵ ͻͶǤͻ͵ ͲǤ͵ ͲǤͶͺ Ͳ ͳ ͲǤ͵ ͲǤͶͶ Ͳ ͳ ͷǤ͵ͻ ʹǤͷʹ ͳ ͻ ͲǤͶͷ ͲǤͷͲ Ͳ ͳ Ǧ Ǧ ሺ ሻǡͲ ǡͲ ሺ ͳൌͻൌ ሻ Ǧ ǡͲ ሺͳͲͲͲǡ̀ሻǡ ଵ ܨܮൌ ሾሺܲ௧ െ ܲ௧ழଵ଼ െ ே ழଵ଼ வହ ሻሿǡ െ ܲ௧ିଵ ܲ௧வହ ሻሺܲ௧ିଵ െ ܲ௧ିଵ Ǧ ͳͺͷ ǡ Ǥ ȂͳǤ ͺǤͳ ͳͺͲǤ͵ͻ ͲǤ͵ͺ ʹ͵ǤͲͳ ͲǤͲͲ ͵ͲͳǤʹͻ ǣ ͳͻͻ͵ȂʹͲͲͺǤ Ǥ ʹ͵
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