Nonlinear econometric models with cointegrated and deterministically trending regressors
Citations
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Cited by:
- Christian Gourieroux & Joann Jasiak, 2011.
"Nonlinear Persistence and Copersistence,"
Palgrave Macmillan Books, in: Greg N. Gregoriou & Razvan Pascalau (ed.), Nonlinear Financial Econometrics: Markov Switching Models, Persistence and Nonlinear Cointegration, chapter 4, pages 77-103,
Palgrave Macmillan.
- Gourieroux, Christian & Josiak, Joann, 1999. "Nonlinear persistence and copersistence," CEPREMAP Working Papers (Couverture Orange) 9920, CEPREMAP.
- Christian Gourieroux & Joann Jasiak, 1999. "Nonlinear Persistence and Copersistence," Working Papers 2000_1, York University, Department of Economics.
- Christian Gourieroux & Joanna Jasiak, 1999. "Nonlinear Persistence and Copersistence," Working Papers 99-63, Center for Research in Economics and Statistics.
- Dong, Chaohua & Linton, Oliver, 2018.
"Additive nonparametric models with time variable and both stationary and nonstationary regressors,"
Journal of Econometrics, Elsevier, vol. 207(1), pages 212-236.
- Chaohua Dong & Oliver Linton, 2017. "Additive nonparametric models with time variable and both stationary and nonstationary regressions," CeMMAP working papers CWP59/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Chaohua Dong & Oliver Linton, 2017. "Additive nonparametric models with time variable and both stationary and nonstationary regressions," CeMMAP working papers 59/17, Institute for Fiscal Studies.
- Herwartz, Helmut & Reimers, Hans-Eggert, 2006. "Modelling the Fisher hypothesis: World wide evidence," Economics Working Papers 2006-04, Christian-Albrechts-University of Kiel, Department of Economics.
- Park, Joon, 2003. "Nonstationary Nonlinearity: An Outlook for New Opportunities," Working Papers 2003-05, Rice University, Department of Economics.
- Park, Joon, 2003. "Strong Approximations for Nonlinear Transformations of Integrated Time Series," Working Papers 2003-18, Rice University, Department of Economics.
- Tarek Atalla & Simona Bigerna & Carlo Andrea Bollino, 2018. "Energy demand elasticities and weather worldwide," Economia Politica: Journal of Analytical and Institutional Economics, Springer;Fondazione Edison, vol. 35(1), pages 207-237, April.
- Andrew P. Blake & George Kapetanios, 2007.
"Testing for Neglected Nonlinearity in Cointegrating Relationships,"
Journal of Time Series Analysis, Wiley Blackwell, vol. 28(6), pages 807-826, November.
- Andrew P. Blake & George Kapetanios, 2004. "Testing for Neglected Nonlinearity in Cointegrating Relationships," Working Papers 508, Queen Mary University of London, School of Economics and Finance.
- Yicong Lin & Hanno Reuvers, 2019. "Efficient Estimation by Fully Modified GLS with an Application to the Environmental Kuznets Curve," Papers 1908.02552, arXiv.org, revised Aug 2020.
- Wang, Qiying & Wu, Dongsheng & Zhu, Ke, 2018. "Model checks for nonlinear cointegrating regression," Journal of Econometrics, Elsevier, vol. 207(2), pages 261-284.
- Li, Dao & He, Changli, 2012. "Testing for Linear Cointegration Against Smooth-Transition Cointegration," Working Papers 2012:6, Örebro University, School of Business.
- Hong, Seung Hyun & Phillips, Peter C. B., 2010.
"Testing Linearity in Cointegrating Relations With an Application to Purchasing Power Parity,"
Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 96-114.
- Seung Hyun Hong & Peter C. B. Phillips, 2005. "Testing Linearity in Cointegrating Relations with an Application to Purchasing Power Parity," Cowles Foundation Discussion Papers 1541, Cowles Foundation for Research in Economics, Yale University.
- doğru, bülent, 2013. "Dynamic Analysis of Money Demand Function: Case of Turkey," MPRA Paper 48402, University Library of Munich, Germany.
- Chang, Yoosoon, 2002.
"Nonlinear IV unit root tests in panels with cross-sectional dependency,"
Journal of Econometrics, Elsevier, vol. 110(2), pages 261-292, October.
- Yoosoon Chang, 2000. "Nonlinear IV Unit Root Tests in Panels with Cross-Sectional Dependency," CIRJE F-Series CIRJE-F-85, CIRJE, Faculty of Economics, University of Tokyo.
- Chang, Yoosoon, 2002. "Nonlinear IV Unit Root Tests in Panels with Cross-Sectional Dependency," Working Papers 2000-08, Rice University, Department of Economics.
- Wagner, Martin, 2008.
"The carbon Kuznets curve: A cloudy picture emitted by bad econometrics?,"
Resource and Energy Economics, Elsevier, vol. 30(3), pages 388-408, August.
- Martin Wagner & Georg M ller-F rstenberger, 2004. "The Carbon Kuznets Curve: A Cloudy Picture Emitted by Bad Econometrics?," Diskussionsschriften dp0418, Universitaet Bern, Departement Volkswirtschaft.
- Wagner, Martin, 2006. "The Carbon Kuznets Curve. A Cloudy Picture Emitted by Bad Econometrics?," Economics Series 197, Institute for Advanced Studies.
- Marmer, Vadim, 2008.
"Nonlinearity, nonstationarity, and spurious forecasts,"
Journal of Econometrics, Elsevier, vol. 142(1), pages 1-27, January.
- Vadim Marmer, 2005. "Nonlinearity, Nonstationarity and Spurious Forecasts," Econometrics 0503002, University Library of Munich, Germany, revised 15 Dec 2005.
- Marmer, Vadim, 2009. "Nonlinearity, Nonstationarity, and Spurious Forecasts," Microeconomics.ca working papers vadim_marmer-2009-60, Vancouver School of Economics, revised 03 Nov 2009.
- Berthold Herrendorf & Christopher Herrington & Ákos Valentinyi, 2015.
"Sectoral Technology and Structural Transformation,"
American Economic Journal: Macroeconomics, American Economic Association, vol. 7(4), pages 104-133, October.
- Berthold Herrendorf & Christopher Herrington & Akos Valentinyi, 2012. "Sectoral Technology and Structural Transformation," CERS-IE WORKING PAPERS 1232, Institute of Economics, Centre for Economic and Regional Studies.
- Berthold Herrendorf & Akos Valentinyi, 2013. "Sectoral Technology and Structural Transformation," 2013 Meeting Papers 349, Society for Economic Dynamics.
- Herrendorf, Berthold & Valentinyi, Akos & Herrington, Christopher, 2013. "Sectoral Technology and Structural Transformation," CEPR Discussion Papers 9386, C.E.P.R. Discussion Papers.
- Jiti Gao & Dag Tjøstheim & Jiying Yin, 2012. "Model Specification between Parametric and Nonparametric Cointegration," Monash Econometrics and Business Statistics Working Papers 18/12, Monash University, Department of Econometrics and Business Statistics.
- Youngsoo Bae & Robert M. de Jong, 2007. "Money demand function estimation by nonlinear cointegration," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(4), pages 767-793.
- Donggyu Sul & Peter C. B. Phillips & Chi‐Young Choi, 2005.
"Prewhitening Bias in HAC Estimation,"
Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(4), pages 517-546, August.
- Donggyu Sul & Peter C.B. Phillips & Choi, Chi-Young, 2003. "Prewhitening Bias in HAC Estimation," Cowles Foundation Discussion Papers 1436, Cowles Foundation for Research in Economics, Yale University.
- Peter C.B. Phillips & Chi-Young Choi & Donggyu Sul, 2004. "Prewhitening Bias in HAC Estimation," Yale School of Management Working Papers ysm426, Yale School of Management.
- Sul, Donggyu & Phillips, Peter & Choi, Chi-Young, 2003. "Prewhitening Bias in HAC Estimation," Working Papers 141, Department of Economics, The University of Auckland.
- Dong, Chaohua & Gao, Jiti & Tjøstheim, Dag & Yin, Jiying, 2017.
"Specification testing for nonlinear multivariate cointegrating regressions,"
Journal of Econometrics, Elsevier, vol. 200(1), pages 104-117.
- Chaohua Dong & Jiti Gao & Dag Tjostheim & Jiying Yin, 2014. "Specification Testing for Nonlinear Multivariate Cointegrating Regressions," Monash Econometrics and Business Statistics Working Papers 8/14, Monash University, Department of Econometrics and Business Statistics.
- Chaohua Dong & Jiti Gao & Dag Tjostheim & Jiying Yin, 2016. "Specification Testing for Nonlinear Multivariate Cointegrating Regressions," Monash Econometrics and Business Statistics Working Papers 14/16, Monash University, Department of Econometrics and Business Statistics.
- Arai, Yoichi, 2016.
"Testing For Linearity In Regressions With I(1) Processes,"
Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 57(1), pages 111-138, June.
- Yoichi Arai, 2004. "Testing for Linearity in Regressions with I(1) processes," CIRJE F-Series CIRJE-F-303, CIRJE, Faculty of Economics, University of Tokyo.
- Yoichi Arai, 2015. "Testing for Linearity in Regressions with I(1) Processes," GRIPS Discussion Papers 15-11, National Graduate Institute for Policy Studies.
- Yoichi Arai, 2004. "Testing for Linearity in Regressions with I (1) processes," CARF F-Series CARF-F-014, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
- de Mello Luiz & Moccero Diego & Mogliani Matteo, 2013.
"Do Latin American Central Bankers Behave Non-Linearly? The Experiences of Brazil, Chile, Colombia and Mexico,"
Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(2), pages 141-165, April.
- Luiz de Mello & Diego Moccero & Matteo Mogliani, 2009. "Do Latin American Central Bankers Behave Non-Linearly?: The Experiences of Brazil, Chile, Colombia and Mexico," OECD Economics Department Working Papers 679, OECD Publishing.
- Reed, Albert J. & Levedahl, J. William & Hallahan, Charles B., 2004. "The Generalized Composite Commodity Theorem And Food Demand Estimation," 2004 Annual meeting, August 1-4, Denver, CO 20107, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
- Chang, Yoosoon & Park, Joon Y., 2003. "Index models with integrated time series," Journal of Econometrics, Elsevier, vol. 114(1), pages 73-106, May.
- David E. Allen & Michael McAleer, 2020. "A Nonlinear Autoregressive Distributed Lag (NARDL) Analysis of West Texas Intermediate Oil Prices and the DOW JONES Index," Energies, MDPI, vol. 13(15), pages 1-11, August.
- Rickard Sandberg, 2017. "Sample Moments and Weak Convergence to Multivariate Stochastic Power Integrals," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 1000-1009, November.
- Jungbin Hwang & Yixiao Sun, 2025. "Asymptotic F and t Tests in Cointegrating Regressions with Asymptotically Homogeneous Functions," Working papers 2025-01, University of Connecticut, Department of Economics.
- J. Isaac Miller, 2014.
"Mixed-frequency Cointegrating Regressions with Parsimonious Distributed Lag Structures,"
Journal of Financial Econometrics, Oxford University Press, vol. 12(3), pages 584-614.
- J. Isaac Miller, 2012. "Mixed-frequency Cointegrating Regressions with Parsimonious Distributed Lag Structures," Working Papers 1211, Department of Economics, University of Missouri.
- K. Hassanain, 2004. "Purchasing Power Parity And Cross‐Sectional Dependency," South African Journal of Economics, Economic Society of South Africa, vol. 72(2), pages 238-257, June.
- Yicong Lin & Hanno Reuvers, 2020.
"Cointegrating Polynomial Regressions with Power Law Trends: Environmental Kuznets Curve or Omitted Time Effects?,"
Papers
2009.02262, arXiv.org, revised Dec 2021.
- Yicong Lin & Hanno Reuvers, 2022. "Cointegrating Polynomial Regressions With Power Law Trends: Environmental Kuznets Curve or Omitted Time Effects?," Tinbergen Institute Discussion Papers 22-092/III, Tinbergen Institute.
- Kim, Chang Sik & Kim, In-Moo, 2012. "Partial parametric estimation for nonstationary nonlinear regressions," Journal of Econometrics, Elsevier, vol. 167(2), pages 448-457.
- Liang, Hanying & Phillips, Peter C.B. & Wang, Hanchao & Wang, Qiying, 2016.
"Weak Convergence To Stochastic Integrals For Econometric Applications,"
Econometric Theory, Cambridge University Press, vol. 32(6), pages 1349-1375, December.
- Hanying Liang & Peter C.B. Phillips & Hanchao Wang & Qiying Wang, 2014. "Weak Convergence to Stochastic Integrals for Econometric Applications," Cowles Foundation Discussion Papers 1971, Cowles Foundation for Research in Economics, Yale University.
- Matei Demetrescu & Christoph Hanck & Adina I. Tarcolea, 2014.
"Iv-Based Cointegration Testing In Dependent Panels With Time-Varying Variance,"
Journal of Time Series Analysis, Wiley Blackwell, vol. 35(5), pages 393-406, August.
- Hanck, Christoph & Demetrescu, Matei & Tarcolea, Adina, 2012. "IV-Based Cointegration Testing in Dependent Panels with Time-Varying Variance," VfS Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 62072, Verein für Socialpolitik / German Economic Association.
- Suphi Sen & Bertrand Melenberg & Herman R. J. Vollebergh, 2016. "Identification and Estimation of the Environmental Kuznets Curve: Pairwise Differencing to Deal with Nonlinearity and Nonstationarity," CESifo Working Paper Series 5837, CESifo.
- Stypka, Oliver & Wagner, Martin & Grabarczyk, Peter & Kawka, Rafael, 2017. "The Asymptotic Validity of "Standard" Fully Modified OLS Estimation and Inference in Cointegrating Polynomial Regressions," Economics Series 333, Institute for Advanced Studies.
- Andrew P. Blake & George Kapetanios, 2007.
"Testing for Neglected Nonlinearity in Cointegrating Relationships,"
Journal of Time Series Analysis, Wiley Blackwell, vol. 28(6), pages 807-826, November.
- Andrew P. Blake & George Kapetanios, 2004. "Testing for Neglected Nonlinearity in Cointegrating Relationships," Working Papers 508, Queen Mary University of London, School of Economics and Finance.
- Andrew P. Blake & George Kapetanios, 2004. "Testing for Neglected Nonlinearity in Cointegrating Relationships," Working Papers 508, Queen Mary University of London, School of Economics and Finance.
- Jesús Gonzalo & Jean‐Yves Pitarakis, 2006.
"Threshold Effects in Cointegrating Relationships,"
Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 813-833, December.
- Gonzalo, Jesús & Pitarakis, Jean-Yves, 2006. "Threshold effects in cointegrating relationships," UC3M Working papers. Economics we20060621, Universidad Carlos III de Madrid. Departamento de EconomÃa.
- Martin Wagner, 2023.
"Residual-based cointegration and non-cointegration tests for cointegrating polynomial regressions,"
Empirical Economics, Springer, vol. 65(1), pages 1-31, July.
- Martin Wagner, 2023. "Correction to: Residual-based cointegration and non-cointegration tests for cointegrating polynomial regressions," Empirical Economics, Springer, vol. 65(3), pages 1511-1511, September.
- Chang, Yoosoon, 2003. "Nonlinear IV Panel Unit Root Tests," Working Papers 2003-06, Rice University, Department of Economics.
- Hu, Zhishui & Phillips, Peter C.B. & Wang, Qiying, 2021.
"Nonlinear Cointegrating Power Function Regression With Endogeneity,"
Econometric Theory, Cambridge University Press, vol. 37(6), pages 1173-1213, December.
- Zhishui Hu & Peter C.B. Phillips & Qiying Wang, 2019. "Nonlinear Cointegrating Power Function Regression with Endogeneity," Cowles Foundation Discussion Papers 2211, Cowles Foundation for Research in Economics, Yale University.
- Divino, Jose Angelo & Maciel, Daniel T.G.N. & Sosa, Wilfredo, 2020. "Government size, composition of public spending and economic growth in Brazil," Economic Modelling, Elsevier, vol. 91(C), pages 155-166.
- Chang, Yoosoon & Nguyen, Chi Mai, 2012. "Residual based tests for cointegration in dependent panels," Journal of Econometrics, Elsevier, vol. 167(2), pages 504-520.
- Cai, Zongwu, 2003. "Trending Time-Varying Coefficient Models With Serially Correlated Errors," SFB 373 Discussion Papers 2003,7, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Im, K.S. & Pesaran, M.H., 2003. "On The Panel Unit Root Tests Using Nonlinear Instrumental Variables," Cambridge Working Papers in Economics 0347, Faculty of Economics, University of Cambridge.
- Nakashima, Kiyotaka, 2008. "An Extremely Low Interest Rate Policy and the Shape of the Japanese Money Demand Function: A Nonlinear Cointegration Approach," MPRA Paper 70689, University Library of Munich, Germany.
- Breitung, Jörg & Pesaran, Mohammad Hashem, 2005.
"Unit roots and cointegration in panels,"
Discussion Paper Series 1: Economic Studies
2005,42, Deutsche Bundesbank.
- Joerg Breitung & M. Hashem Pesaran, 2005. "Unit Roots and Cointegration in Panels," CESifo Working Paper Series 1565, CESifo.
- Jörg Breitung & M. Hashem Pesaran, 2005. "Unit Roots and Cointegration in Panels," IEPR Working Papers 05.32, Institute of Economic Policy Research (IEPR).
- Breitung, J. & Pesaran, M.H., 2005. "Unit Roots and Cointegration in Panels," Cambridge Working Papers in Economics 0535, Faculty of Economics, University of Cambridge.
- Miller J. Isaac, 2010.
"A Nonlinear IV Likelihood-Based Rank Test for Multivariate Time Series and Long Panels,"
Journal of Time Series Econometrics, De Gruyter, vol. 2(1), pages 1-38, September.
- J. Isaac Miller, 2010. "A Nonlinear IV Likelihood-Based Rank Test for Multivariate Time Series and Long Panels," Working Papers 1001, Department of Economics, University of Missouri.
- Demetrescu Matei, 2009. "Panel Unit Root Testing with Nonlinear Instruments for Infinite-Order Autoregressive Processes," Journal of Time Series Econometrics, De Gruyter, vol. 1(2), pages 1-30, December.
- Cai, Zongwu, 2007. "Trending time-varying coefficient time series models with serially correlated errors," Journal of Econometrics, Elsevier, vol. 136(1), pages 163-188, January.
- Matei Demetrescu & Christoph Hanck, 2013. "Nonlinear IV panel unit root testing under structural breaks in the error variance," Statistical Papers, Springer, vol. 54(4), pages 1043-1066, November.
- Muller-Furstenberger, Georg & Wagner, Martin, 2007.
"Exploring the environmental Kuznets hypothesis: Theoretical and econometric problems,"
Ecological Economics, Elsevier, vol. 62(3-4), pages 648-660, May.
- Müller-Fürstenberger, Georg & Wagner, Martin, 2006. "Exploring the Environmental Kuznets Hypothesis. Theoretical and Econometric Problems," Economics Series 183, Institute for Advanced Studies.
- Choi, Yongok & Jacewitz, Stefan & Park, Joon Y., 2016. "A reexamination of stock return predictability," Journal of Econometrics, Elsevier, vol. 192(1), pages 168-189.
- Donggyu Sul, 2005. "New Panel Unit Root Tests under Cross Section Dependence for Practitioners," Econometrics 0506010, University Library of Munich, Germany.
- Kasparis, Ioannis, 2010. "The Bierens test for certain nonstationary models," Journal of Econometrics, Elsevier, vol. 158(2), pages 221-230, October.
- Burak Alparslan Eroğlu & J. Isaac Miller & Taner Yiğit, 2022.
"Time-varying cointegration and the Kalman filter,"
Econometric Reviews, Taylor & Francis Journals, vol. 41(1), pages 1-21, January.
- Burak Alparslan Eroglu & J. Isaac Miller & Taner Yigit, 2019. "Time-Varying Cointegration and the Kalman Filter," Working Papers 1905, Department of Economics, University of Missouri.
- Chan, Nigel & Wang, Qiying, 2015. "Nonlinear regressions with nonstationary time series," Journal of Econometrics, Elsevier, vol. 185(1), pages 182-195.
- Kasparis, Ioannis & Phillips, Peter C.B., 2012.
"Dynamic misspecification in nonparametric cointegrating regression,"
Journal of Econometrics, Elsevier, vol. 168(2), pages 270-284.
- Ioannis Kasparis & Peter C. B. Phillips, 2009. "Dynamic Misspecification in Nonparametric Cointegrating Regression," University of Cyprus Working Papers in Economics 2-2009, University of Cyprus Department of Economics.
- Ioannis Kasparis & Peter C.B. Phillips, 2009. "Dynamic Misspecification in Nonparametric Cointegrating Regression," Cowles Foundation Discussion Papers 1700, Cowles Foundation for Research in Economics, Yale University.
- Peter C.B.Phillips & Ioannis Kasparis, 2009. "Dynamic Misspecification in Nonparametric Cointegrating Regression," Working Papers CoFie-01-2009, Singapore Management University, Sim Kee Boon Institute for Financial Economics.
- Ho, Tsung-wu, 2015. "Income inequality may not converge after all: Testing panel unit roots in the presence of cross-section cointegration," The Quarterly Review of Economics and Finance, Elsevier, vol. 56(C), pages 68-79.
- J. Isaac Miller, 2007. "Cointegrating Regressions with Messy Regressors: Missingness, Mixed Frequency, and Measurement Error," Working Papers 0722, Department of Economics, University of Missouri, revised 15 Apr 2009.
- Chaohua Dong & Jiti Gao & Bin Peng & Yundong Tu, 2021. "Multiple-index Nonstationary Time Series Models: Robust Estimation Theory and Practice," Papers 2111.02023, arXiv.org.
- Juan Gabriel Brida & Diego Giuliani, 2012. "Empirical assessment of the tourism-led growth hypothesis: the case of the “Tirol-Südtirol-Trentino†Europaregion," DISA Working Papers 2012/02, Department of Computer and Management Sciences, University of Trento, Italy, revised Mar 2012.
- Canning, David & Bennathan, Esra, 2000. "The social rate of return on infrastructure investments," Policy Research Working Paper Series 2390, The World Bank.
- Wang, Shaoping & Wang, Peng & Yang, Jisheng & Li, Zinai, 2010. "A generalized nonlinear IV unit root test for panel data with cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 157(1), pages 101-109, July.
- Yoosoon Chang & Wonho Song, 2002. "Panel Unit Root Tests in the Presence of Cross-Sectional Dependency and Heterogeneity," 10th International Conference on Panel Data, Berlin, July 5-6, 2002 B5-2, International Conferences on Panel Data.
- Dong, Chaohua & Linton, Oliver & Peng, Bin, 2021. "A weighted sieve estimator for nonparametric time series models with nonstationary variables," Journal of Econometrics, Elsevier, vol. 222(2), pages 909-932.
- Tu, Yundong & Liang, Han-Ying & Wang, Qiying, 2022. "Nonparametric inference for quantile cointegrations with stationary covariates," Journal of Econometrics, Elsevier, vol. 230(2), pages 453-482.
- Ioannis Kasparis, 2008. "Functional Form Misspecification in Regressions with a Unit Root," University of Cyprus Working Papers in Economics 2-2008, University of Cyprus Department of Economics.
- David Peel & Michael Peel & Ioannis Venetis, 2004. "Further empirical analysis of the time series properties of financial ratios based on a panel data approach," Applied Financial Economics, Taylor & Francis Journals, vol. 14(3), pages 155-163.
- Chaohua Dong & Jiti Gao & Bin Peng & Yundong Tu, 2021. "Multiple-index Nonstationary Time Series Models: Robust Estimation Theory and Practice," Monash Econometrics and Business Statistics Working Papers 18/21, Monash University, Department of Econometrics and Business Statistics.
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