IDEAS home Printed from https://ideas.repec.org/p/cte/wsrepe/24585.html
   My bibliography  Save this paper

Estimating non-stationary common factors : Implications for risk sharing

Author

Listed:
  • Corona, Francisco
  • Poncela, Pilar

Abstract

In this paper, we analyze and compare the finite sample properties of alternative factor extraction procedures in the context of non-stationary Dynamic Factor Models (DFMs). On top of considering procedures already available in the literature, we extend the hybrid method based on the combination of principal components and Kalman filter and smoothing algorithms to non-stationary models. We show that, unless the idiosyncratic noise is non-stationary, procedures based on extracting the factors using the nonstationary original series work better than those based on differenced variables. The results are illustrated in an empirical application fitting non-stationary DFM to aggregate GDP and consumption of the set of 21 OECD industrialized countries. The goal is to check international risk sharing is a short or long-run issue.

Suggested Citation

  • Corona, Francisco & Poncela, Pilar, 2017. "Estimating non-stationary common factors : Implications for risk sharing," DES - Working Papers. Statistics and Econometrics. WS 24585, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:24585
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/rest/api/core/bitstreams/6498c29e-046e-4c6a-a1ea-1905730e7092/content
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Peter Fuleky & Luigi Ventura & Qianxue Zhao, 2015. "International Risk Sharing in the Short and in the long run under Country Heterogeneity," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 20(4), pages 374-384, October.
    2. Banerjee, Anindya & Marcellino, Massimiliano & Masten, Igor, 2014. "Forecasting with factor-augmented error correction models," International Journal of Forecasting, Elsevier, vol. 30(3), pages 589-612.
    3. Beyer, Andreas & Doornik, Jurgen A & Hendry, David F, 2001. "Constructing Historical Euro-Zone Data," Economic Journal, Royal Economic Society, vol. 111(469), pages 102-121, February.
    4. In Choi & Seong Jin Hwang, 2012. "Forecasting Korean inflation," Working Papers 1202, Nam Duck-Woo Economic Research Institute, Sogang University (Former Research Institute for Market Economy).
    5. Bai, Jushan & Wang, Peng, 2014. "Identification theory for high dimensional static and dynamic factor models," Journal of Econometrics, Elsevier, vol. 178(2), pages 794-804.
    6. Zhang, Rongmao & Robinson, Peter & Yao, Qiwei, 2019. "Identifying cointegration by eigenanalysis," LSE Research Online Documents on Economics 87431, London School of Economics and Political Science, LSE Library.
    7. Vahid, F & Engle, Robert F, 1993. "Common Trends and Common Cycles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 341-360, Oct.-Dec..
    8. Charles Engel & Nelson C. Mark & Kenneth D. West, 2015. "Factor Model Forecasts of Exchange Rates," Econometric Reviews, Taylor & Francis Journals, vol. 34(1-2), pages 32-55, February.
    9. Bai, Jushan & Ng, Serena, 2013. "Principal components estimation and identification of static factors," Journal of Econometrics, Elsevier, vol. 176(1), pages 18-29.
    10. Danny Quah & Thomas J. Sargent, 1993. "A Dynamic Index Model for Large Cross Sections," NBER Chapters, in: Business Cycles, Indicators, and Forecasting, pages 285-310, National Bureau of Economic Research, Inc.
    11. Mario Forni & Luca Gambetti & Luca Sala, 2014. "No News in Business Cycles," Economic Journal, Royal Economic Society, vol. 124(581), pages 1168-1191, December.
    12. Matteo Barigozzi & Marco Lippi & Matteo Luciani, 2016. "Non-Stationary Dynamic Factor Models for Large Datasets," Finance and Economics Discussion Series 2016-024, Board of Governors of the Federal Reserve System (U.S.).
    13. Jiazhu Pan & Qiwei Yao, 2008. "Modelling multiple time series via common factors," Biometrika, Biometrika Trust, vol. 95(2), pages 365-379.
    14. Domenico Giannone & Lucrezia Reichlin, 2006. "Does information help recovering structural shocks from past observations?," Journal of the European Economic Association, MIT Press, vol. 4(2-3), pages 455-465, 04-05.
    15. Doz, Catherine & Giannone, Domenico & Reichlin, Lucrezia, 2011. "A two-step estimator for large approximate dynamic factor models based on Kalman filtering," Journal of Econometrics, Elsevier, vol. 164(1), pages 188-205, September.
    16. James H. Stock & Mark W. Watson, 1993. "Business Cycles, Indicators, and Forecasting," NBER Books, National Bureau of Economic Research, Inc, number stoc93-1.
    17. Del Negro, Marco, 2002. "Asymmetric shocks among U.S. states," Journal of International Economics, Elsevier, vol. 56(2), pages 273-297, March.
    18. Jörg Breitung & Sandra Eickmeier, 2006. "Dynamic Factor Models," Springer Books, in: Olaf Hübler & Jachim Frohn (ed.), Modern Econometric Analysis, chapter 3, pages 25-40, Springer.
    19. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    20. Kapetanios, George, 2010. "A Testing Procedure for Determining the Number of Factors in Approximate Factor Models With Large Datasets," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 397-409.
    21. repec:cte:wsrepe:3680 is not listed on IDEAS
    22. Canova, Fabio, 1998. "Detrending and business cycle facts: A user's guide," Journal of Monetary Economics, Elsevier, vol. 41(3), pages 533-540, May.
    23. Pierfederico Asdrubali & Bent E. Sørensen & Oved Yosha, 1996. "Channels of Interstate Risk Sharing: United States 1963–1990," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 111(4), pages 1081-1110.
    24. Matteo Barigozzi & Marco Lippi & Matteo Luciani, 2014. "Dynamic Factor Models, Cointegration and Error Correction Mechanisms," Working Papers ECARES ECARES 2014-14, ULB -- Universite Libre de Bruxelles.
    25. Forni, Mario & Giannone, Domenico & Lippi, Marco & Reichlin, Lucrezia, 2009. "Opening The Black Box: Structural Factor Models With Large Cross Sections," Econometric Theory, Cambridge University Press, vol. 25(5), pages 1319-1347, October.
    26. Moon, H.R.Hyungsik Roger & Perron, Benoit, 2004. "Testing for a unit root in panels with dynamic factors," Journal of Econometrics, Elsevier, vol. 122(1), pages 81-126, September.
    27. Canova, Fabio, 1998. "Detrending and business cycle facts," Journal of Monetary Economics, Elsevier, vol. 41(3), pages 475-512, May.
    28. Catherine Doz & Domenico Giannone & Lucrezia Reichlin, 2012. "A Quasi–Maximum Likelihood Approach for Large, Approximate Dynamic Factor Models," The Review of Economics and Statistics, MIT Press, vol. 94(4), pages 1014-1024, November.
    29. Becker, Sascha O. & Hoffmann, Mathias, 2006. "Intra- and international risk-sharing in the short run and the long run," European Economic Review, Elsevier, vol. 50(3), pages 777-806, April.
    30. Gonzalo, Jesus & Granger, Clive W J, 1995. "Estimation of Common Long-Memory Components in Cointegrated Systems," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 27-35, January.
    31. Byeongchan Seong & Sung K. Ahn & Peter A. Zadrozny, 2013. "Estimation of vector error correction models with mixed-frequency data," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(2), pages 194-205, March.
    32. repec:dgr:rugccs:200605 is not listed on IDEAS
    33. Jushan Bai & Serena Ng, 2004. "A PANIC Attack on Unit Roots and Cointegration," Econometrica, Econometric Society, vol. 72(4), pages 1127-1177, July.
    34. Francisco Corona & Pilar Poncela & Esther Ruiz, 2017. "Determining the number of factors after stationary univariate transformations," Empirical Economics, Springer, vol. 53(1), pages 351-372, August.
    35. Jörg Breitung & In Choi, 2013. "Factor models," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 11, pages 249-265, Edward Elgar Publishing.
      • In Choi & Jorg Breitung, 2011. "Factor models," Working Papers 1121, Nam Duck-Woo Economic Research Institute, Sogang University (Former Research Institute for Market Economy), revised Dec 2011.
    36. Mario Forni & Luca Gambetti & Marco Lippi & Luca Sala, 2017. "Noisy News in Business Cycles," American Economic Journal: Macroeconomics, American Economic Association, vol. 9(4), pages 122-152, October.
    37. Michael J. Artis & Mathias Hoffmann, 2008. "Financial Globalization, International Business Cycles and Consumption Risk Sharing," Scandinavian Journal of Economics, Wiley Blackwell, vol. 110(3), pages 447-471, September.
    38. Eichler, Michael & Motta, Giovanni & von Sachs, Rainer, 2011. "Fitting dynamic factor models to non-stationary time series," Journal of Econometrics, Elsevier, vol. 163(1), pages 51-70, July.
    39. Stock, James H. & Watson, Mark W. (ed.), 1993. "Business Cycles, Indicators, and Forecasting," National Bureau of Economic Research Books, University of Chicago Press, edition 1, number 9780226774886.
    40. Thomas J. Sargent & Christopher A. Sims, 1977. "Business cycle modeling without pretending to have too much a priori economic theory," Working Papers 55, Federal Reserve Bank of Minneapolis.
    41. Eleonora Pierucci & Luigi Ventura, 2010. "Risk Sharing: A Long Run Issue?," Open Economies Review, Springer, vol. 21(5), pages 705-730, November.
    42. Sandra Eickmeier, 2009. "Comovements and heterogeneity in the euro area analyzed in a non-stationary dynamic factor model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(6), pages 933-959.
    43. Alexei Onatski, 2010. "Determining the Number of Factors from Empirical Distribution of Eigenvalues," The Review of Economics and Statistics, MIT Press, vol. 92(4), pages 1004-1016, November.
    44. repec:hal:journl:peer-00844811 is not listed on IDEAS
    45. Byrne, Joseph P. & Fiess, Norbert, 2016. "International capital flows to emerging markets: National and global determinants," Journal of International Money and Finance, Elsevier, vol. 61(C), pages 82-100.
    46. Pilar Poncela & Esther Ruiz, 2016. "Small- Versus Big-Data Factor Extraction in Dynamic Factor Models: An Empirical Assessment," Advances in Econometrics, in: Dynamic Factor Models, volume 35, pages 401-434, Emerald Group Publishing Limited.
    47. Bai, Jushan, 2004. "Estimating cross-section common stochastic trends in nonstationary panel data," Journal of Econometrics, Elsevier, vol. 122(1), pages 137-183, September.
    48. Pan, Jiazhu & Yao, Qiwei, 2008. "Modelling multiple time series via common factors," LSE Research Online Documents on Economics 22876, London School of Economics and Political Science, LSE Library.
    49. Ryan Greenaway‐McGrevy & Nelson C. Mark & Donggyu Sul & Jyh‐Lin Wu, 2018. "Identifying Exchange Rate Common Factors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(4), pages 2193-2218, November.
    50. Engle, Robert F. & Issler, João Victor, 1993. "Common trends and common cycles in Latin America," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 47(2), April.
    51. Ryan Greenaway‐McGrevy & Nelson C. Mark & Donggyu Sul & Jyh‐Lin Wu, 2018. "Identifying Exchange Rate Common Factors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(4), pages 2193-2218, November.
    52. Sebnem Kalemli‐Ozcan & Emiliano Luttini & Bent Sørensen, 2014. "Debt Crises and Risk‐Sharing: The Role of Markets versus Sovereigns," Scandinavian Journal of Economics, Wiley Blackwell, vol. 116(1), pages 253-276, January.
    53. Bai, Jushan & Ng, Serena, 2010. "Panel Unit Root Tests With Cross-Section Dependence: A Further Investigation," Econometric Theory, Cambridge University Press, vol. 26(4), pages 1088-1114, August.
    54. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    55. Onatski, Alexei, 2012. "Asymptotics of the principal components estimator of large factor models with weakly influential factors," Journal of Econometrics, Elsevier, vol. 168(2), pages 244-258.
    56. James H. Stock & Mark W. Watson, 1989. "New Indexes of Coincident and Leading Economic Indicators," NBER Chapters, in: NBER Macroeconomics Annual 1989, Volume 4, pages 351-409, National Bureau of Economic Research, Inc.
    57. Mario Forni & Lucrezia Reichlin, 1998. "Let's Get Real: A Factor Analytical Approach to Disaggregated Business Cycle Dynamics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 453-473.
    58. Bai, Jushan & Ng, Serena, 2008. "Large Dimensional Factor Analysis," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(2), pages 89-163, June.
    59. Alvaro Escribano & Daniel Peña, 1994. "Cointegration And Common Factors," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(6), pages 577-586, November.
    60. Stock, James H. & Watson, Mark, 2011. "Dynamic Factor Models," Scholarly Articles 28469541, Harvard University Department of Economics.
    61. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
    62. EICHLER , Michael & Motta, Giovanni & von Sachs, Rainer, 2011. "Fitting dynamic factor models to non-stationary time series," LIDAM Reprints ISBA 2011013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    63. Clifford Lam & Qiwei Yao & Neil Bathia, 2011. "Estimation of latent factors for high-dimensional time series," Biometrika, Biometrika Trust, vol. 98(4), pages 901-918.
    64. Lam, Clifford & Yao, Qiwei & Bathia, Neil, 2011. "Estimation of latent factors for high-dimensional time series," LSE Research Online Documents on Economics 31549, London School of Economics and Political Science, LSE Library.
    65. Matteo Barigozzi & Matteo Luciani, 2017. "Common Factors, Trends, and Cycles in Large Datasets," Finance and Economics Discussion Series 2017-111, Board of Governors of the Federal Reserve System (U.S.).
    66. Jushan Bai & Peng Wang, 2016. "Econometric Analysis of Large Factor Models," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 53-80, October.
    67. Markus Leibrecht & Johann Scharler, 2008. "Reconsidering Consumption Risk Sharing among OECD Countries: Some Evidence Based on Panel Cointegration," Open Economies Review, Springer, vol. 19(4), pages 493-505, September.
    68. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chiara Casoli & Riccardo (Jack) Lucchetti, 2022. "Permanent-Transitory decomposition of cointegrated time series via dynamic factor models, with an application to commodity prices [Commodity-price comovement and global economic activity]," The Econometrics Journal, Royal Economic Society, vol. 25(2), pages 494-514.
    2. Gonzalo, Jesús & Pitarakis, Jean-Yves, 2021. "Spurious relationships in high-dimensional systems with strong or mild persistence," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1480-1497.
    3. Francisco Corona & Graciela González-Farías & Pedro Orraca, 2017. "A dynamic factor model for the Mexican economy: are common trends useful when predicting economic activity?," Latin American Economic Review, Springer;Centro de Investigaciòn y Docencia Económica (CIDE), vol. 26(1), pages 1-35, December.
    4. Philip Hans Franses & Thomas Wiemann, 2020. "Intertemporal Similarity of Economic Time Series: An Application of Dynamic Time Warping," Computational Economics, Springer;Society for Computational Economics, vol. 56(1), pages 59-75, June.
    5. Casoli, Chiara & Lucchetti, Riccardo (Jack), 2021. "Permanent-Transitory decomposition of cointegrated time series via Dynamic Factor Models, with an application to commodity prices," FEEM Working Papers 312367, Fondazione Eni Enrico Mattei (FEEM).
    6. Poncela, Pilar & Ruiz, Esther & Miranda, Karen, 2021. "Factor extraction using Kalman filter and smoothing: This is not just another survey," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1399-1425.
    7. Miljkovic, Dragan & Vatsa, Puneet, 2023. "On the linkages between energy and agricultural commodity prices: A dynamic time warping analysis," International Review of Financial Analysis, Elsevier, vol. 90(C).
    8. Proietti, Tommaso & Giovannelli, Alessandro & Ricchi, Ottavio & Citton, Ambra & Tegami, Christían & Tinti, Cristina, 2021. "Nowcasting GDP and its components in a data-rich environment: The merits of the indirect approach," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1376-1398.
    9. Francisco Corona & Graciela Gonz'alez-Far'ias & Jes'us L'opez-P'erez, 2021. "A nowcasting approach to generate timely estimates of Mexican economic activity: An application to the period of COVID-19," Papers 2101.10383, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Poncela, Pilar & Ruiz, Esther & Miranda, Karen, 2021. "Factor extraction using Kalman filter and smoothing: This is not just another survey," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1399-1425.
    2. Stock, J.H. & Watson, M.W., 2016. "Dynamic Factor Models, Factor-Augmented Vector Autoregressions, and Structural Vector Autoregressions in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 415-525, Elsevier.
    3. Matteo Barigozzi & Matteo Luciani, 2017. "Common Factors, Trends, and Cycles in Large Datasets," Finance and Economics Discussion Series 2017-111, Board of Governors of the Federal Reserve System (U.S.).
    4. Catherine Doz & Peter Fuleky, 2019. "Dynamic Factor Models," Working Papers 2019-4, University of Hawaii Economic Research Organization, University of Hawaii at Manoa.
    5. Francisco Corona & Pilar Poncela & Esther Ruiz, 2017. "Determining the number of factors after stationary univariate transformations," Empirical Economics, Springer, vol. 53(1), pages 351-372, August.
    6. repec:cte:wsrepe:23974 is not listed on IDEAS
    7. Francisco Corona & Pedro Orraca, 2019. "Remittances in Mexico and their unobserved components," The Journal of International Trade & Economic Development, Taylor & Francis Journals, vol. 28(8), pages 1047-1066, November.
    8. Pilar Poncela & Esther Ruiz, 2016. "Small- Versus Big-Data Factor Extraction in Dynamic Factor Models: An Empirical Assessment," Advances in Econometrics, in: Dynamic Factor Models, volume 35, pages 401-434, Emerald Group Publishing Limited.
    9. Francisco Corona & Graciela González-Farías & Pedro Orraca, 2017. "A dynamic factor model for the Mexican economy: are common trends useful when predicting economic activity?," Latin American Economic Review, Springer;Centro de Investigaciòn y Docencia Económica (CIDE), vol. 26(1), pages 1-35, December.
    10. Matteo Barigozzi & Marc Hallin, 2023. "Dynamic Factor Models: a Genealogy," Papers 2310.17278, arXiv.org, revised Jan 2024.
    11. Kihwan Kim & Norman Swanson, 2013. "Diffusion Index Model Specification and Estimation Using Mixed Frequency Datasets," Departmental Working Papers 201315, Rutgers University, Department of Economics.
    12. Francisco Corona & Graciela Gonz'alez-Far'ias & Jes'us L'opez-P'erez, 2021. "A nowcasting approach to generate timely estimates of Mexican economic activity: An application to the period of COVID-19," Papers 2101.10383, arXiv.org.
    13. Martin Solberger & Erik Spånberg, 2020. "Estimating a Dynamic Factor Model in EViews Using the Kalman Filter and Smoother," Computational Economics, Springer;Society for Computational Economics, vol. 55(3), pages 875-900, March.
    14. Matteo Barigozzi & Antonio M. Conti & Matteo Luciani, 2014. "Do Euro Area Countries Respond Asymmetrically to the Common Monetary Policy?," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(5), pages 693-714, October.
    15. Yuefeng Han & Rong Chen & Cun-Hui Zhang, 2020. "Rank Determination in Tensor Factor Model," Papers 2011.07131, arXiv.org, revised May 2022.
    16. Barigozzi, Matteo & Trapani, Lorenzo, 2020. "Sequential testing for structural stability in approximate factor models," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 5149-5187.
    17. Matteo Barigozzi & Marco Lippi & Matteo Luciani, 2014. "Dynamic Factor Models, Cointegration and Error Correction Mechanisms," Working Papers ECARES ECARES 2014-14, ULB -- Universite Libre de Bruxelles.
    18. repec:cte:wsrepe:27047 is not listed on IDEAS
    19. Jörg Breitung & In Choi, 2013. "Factor models," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 11, pages 249-265, Edward Elgar Publishing.
      • In Choi & Jorg Breitung, 2011. "Factor models," Working Papers 1121, Nam Duck-Woo Economic Research Institute, Sogang University (Former Research Institute for Market Economy), revised Dec 2011.
    20. Rua, António, 2017. "A wavelet-based multivariate multiscale approach for forecasting," International Journal of Forecasting, Elsevier, vol. 33(3), pages 581-590.
    21. Han, Xu, 2018. "Estimation and inference of dynamic structural factor models with over-identifying restrictions," Journal of Econometrics, Elsevier, vol. 202(2), pages 125-147.
    22. Chihwa Kao & Lorenzo Trapani & Giovanni Urga, 2012. "Asymptotics for Panel Models with Common Shocks," Econometric Reviews, Taylor & Francis Journals, vol. 31(4), pages 390-439.

    More about this item

    Keywords

    Consumption smoothing;

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cte:wsrepe:24585. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ana Poveda (email available below). General contact details of provider: http://portal.uc3m.es/portal/page/portal/dpto_estadistica .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.