IDEAS home Printed from https://ideas.repec.org/p/pen/papers/08-010.html
   My bibliography  Save this paper

Conditional Moments and Independence

Author

Listed:
  • Aureo de Paula

    (Department of Economics, University of Pennsylvania)

Abstract

Consider two random variables X and Y. In initial probability and statistics courses, a discussion of various concepts of dissociation between X and Y is customary. These concepts typically involve independence and uncorrelatedness. An example is shown where E(Y^n|X) = E(Y^n) and E(X^n|Y) = E(X^n) for n = 1, 2,… and yet X and Y are not stochastically independent. The bi-variate distribution is constructed using a well-known example in which the distribution of a random variable is not uniquely determined by its sequence of moments. Other similar families of distributions with identical moments can be used to display such a pair of random variables. It is interesting to note in class that even such a degree of dissociation between the moments of X and Y does not imply stochastic independence. and yet X and Y are not stochastically independent. The bi-variate distribution is constructed using a well-known example in which the distribution of a random variable is not uniquely determined by its sequence of moments. Other similar families of distributions with identical moments can be used to display such a pair of random variables. It is interesting to note in class that even such a degree of dissociation between the moments of X and Y does not imply stochastic independence.

Suggested Citation

  • Aureo de Paula, 2008. "Conditional Moments and Independence," PIER Working Paper Archive 08-010, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    • Handle: RePEc:pen:papers:08-010
    as

    Download full text from publisher

    File URL: https://economics.sas.upenn.edu/sites/default/files/filevault/working-papers/08-010.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Robert S. Pindyck & Julio J. Rotemberg, 1993. "The Comovement of Stock Prices," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(4), pages 1073-1104.
    2. McDonald, Robert L & Siegel, Daniel R, 1985. "Investment and the Valuation of Firms When There Is an Option to Shut Down," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(2), pages 331-349, June.
    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. Ebrahimi, Nader & Jalali, Nima Y. & Soofi, Ehsan S., 2014. "Comparison, utility, and partition of dependence under absolutely continuous and singular distributions," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 32-50.
    2. Ebrahimi, Nader & Hamedani, G.G. & Soofi, Ehsan S. & Volkmer, Hans, 2010. "A class of models for uncorrelated random variables," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1859-1871, September.
    3. Mukhopadhyay, Nitis, 2009. "On px1 dependent random variables having each (p-1)x1 sub-vector made up of IID observations with examples," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1585-1589, July.
    4. Matthew Masten & Alexandre Poirier, 2016. "Partial independence in nonseparable models," CeMMAP working papers 26/16, Institute for Fiscal Studies.

    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. Małgorzata Doman & Ryszard Doman, 2013. "Dynamic linkages between stock markets: the effects of crises and globalization," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 12(2), pages 87-112, August.
    2. Alvarez, Luis H. R., 1998. "Exit strategies and price uncertainty: a Greenian approach," Journal of Mathematical Economics, Elsevier, vol. 29(1), pages 43-56, January.
    3. AltInkIlIç, Oya & Hansen, Robert S., 2009. "On the information role of stock recommendation revisions," Journal of Accounting and Economics, Elsevier, vol. 48(1), pages 17-36, October.
    4. Goodness C. Aye & Rangan Gupta, 2019. "Macroeconomic Uncertainty And The Comovement In Buying Versus Renting In The Usa," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(3), pages 93-121, September.
    5. Manuel Guerra & Cláudia Nunes & Carlos Oliveira, 2021. "The optimal stopping problem revisited," Statistical Papers, Springer, vol. 62(1), pages 137-169, February.
    6. Giovanni Villani, 2008. "R&D Cooperation in Real Option Game Analysis," Quaderni DSEMS 19-2008, Dipartimento di Scienze Economiche, Matematiche e Statistiche, Universita' di Foggia.
    7. Geraci, Marco Valerio & Gnabo, Jean-Yves & Veredas, David, 2023. "Common short selling and excess comovement: Evidence from a sample of LSE stocks," Journal of Financial Markets, Elsevier, vol. 65(C).
    8. Benjamin M. Blau & Todd G. Griffith & Ryan J. Whitby, 2020. "Opacity and the comovement in the stock prices of banks," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 60(4), pages 3557-3580, December.
    9. Nguyen, Duc Binh Benno & Prokopczuk, Marcel, 2019. "Jumps in commodity markets," Journal of Commodity Markets, Elsevier, vol. 13(C), pages 55-70.
    10. Bar-Ilan, Avner & Strange, William C., 1998. "A model of sequential investment," Journal of Economic Dynamics and Control, Elsevier, vol. 22(3), pages 437-463, March.
    11. Tsekrekos, Andrianos E., 2010. "The effect of mean reversion on entry and exit decisions under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 725-742, April.
    12. Tauer, Loren W., 2006. "When to Get In and Out of Dairy Farming: A Real Option Analysis," Agricultural and Resource Economics Review, Cambridge University Press, vol. 35(2), pages 339-347, October.
    13. Greenwood, Robin, 2005. "Short- and long-term demand curves for stocks: theory and evidence on the dynamics of arbitrage," Journal of Financial Economics, Elsevier, vol. 75(3), pages 607-649, March.
    14. Peng, Lin & Xiong, Wei, 2006. "Investor attention, overconfidence and category learning," Journal of Financial Economics, Elsevier, vol. 80(3), pages 563-602, June.
    15. Chi H. Truong, 2014. "A Two Factor Model for Water Prices and Its Implications for Evaluating Real Options and Other Water Price Derivatives," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 62(1), pages 23-45, March.
    16. Quoc V. Luong & Loren W. Tauer, 2006. "A real options analysis of coffee planting in Vietnam," Agricultural Economics, International Association of Agricultural Economists, vol. 35(1), pages 49-57, July.
    17. Alain Bensoussan & Benoit Chevalier-Roignant & Alejandro Rivera, 2022. "A model for wind farm management with option interactions," Post-Print hal-04325553, HAL.
    18. Xi Zhang & Jiawei Shi & Di Wang & Binxing Fang, 2018. "Exploiting Investors Social Network for Stock Prediction in China's Market," Papers 1801.00597, arXiv.org.
    19. Paolo M. Panteghini, 2012. "Corporate Debt, Hybrid Securities, and the Effective Tax Rate," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 14(1), pages 161-186, February.
    20. Chiara D'Alpaos & Cesare Dosi & Michele Moretto, 2005. "Concession lenght and investment timing flexibility," Working Papers ubs0502, University of Brescia, Department of Economics.

    More about this item

    Keywords

    indeterminate distributions; moments; independence;
    All these keywords.

    JEL classification:

    • A2 - General Economics and Teaching - - Economic Education and Teaching of Economics
    • C00 - Mathematical and Quantitative Methods - - General - - - General

    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:pen:papers:08-010. 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: Administrator (email available below). General contact details of provider: https://edirc.repec.org/data/deupaus.html .

    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.