IDEAS home Printed from https://ideas.repec.org/p/nwu/cmsems/1470.html
   My bibliography  Save this paper

Topologies on Types: Connections

Author

Listed:
  • Yi-Chun Chen
  • Siyang Xiong

Abstract

For different purposes, economists may use different topologies on types. We char- acterize the relationship among these various topologies. First, we show that for any general types, convergence in the uniform-weak topology implies convergence in both the strategic topology and the uniform strategic topology. Second, we explicitly con- struct a type which is not the limit of any finite types under the uniform strategic topology, showing that the uniform strategic topology is strictly fi ner than the strategic topology. With these results, we can linearly rank various topologies on the universal type space, which gives a clear picture of the relationship between the implication of types for beliefs and their implication for behaviors.

Suggested Citation

  • Yi-Chun Chen & Siyang Xiong, 2008. "Topologies on Types: Connections," Discussion Papers 1470, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1470
    as

    Download full text from publisher

    File URL: http://www.kellogg.northwestern.edu/research/math/papers/1470.pdf
    File Function: main text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. James Heckman & Flavio Cunha, 2007. "The Technology of Skill Formation," American Economic Review, American Economic Association, vol. 97(2), pages 31-47, May.
    2. Angrist, Joshua D. & Guryan, Jonathan, 2008. "Does teacher testing raise teacher quality? Evidence from state certification requirements," Economics of Education Review, Elsevier, vol. 27(5), pages 483-503, October.
    3. Betts, Julian R, 1998. "The Impact of Educational Standards on the Level and Distribution of Earnings," American Economic Review, American Economic Association, vol. 88(1), pages 266-275, March.
    4. Richard C. Edwards, 1976. "Individual Traits and Organizational Incentives: What Makes a "Good" Worker?," Journal of Human Resources, University of Wisconsin Press, vol. 11(1), pages 51-68.
    5. Flavio Cunha & James J. Heckman & Susanne M. Schennach, 2010. "Estimating the Technology of Cognitive and Noncognitive Skill Formation," Econometrica, Econometric Society, vol. 78(3), pages 883-931, May.
    6. Kane, Thomas J. & Rockoff, Jonah E. & Staiger, Douglas O., 2008. "What does certification tell us about teacher effectiveness? Evidence from New York City," Economics of Education Review, Elsevier, vol. 27(6), pages 615-631, December.
    7. Erik Hanushek & F. Welch (ed.), 2006. "Handbook of the Economics of Education," Handbook of the Economics of Education, Elsevier, edition 1, volume 1, number 1, June.
    8. Aloisio Araujo & Daniel Gottlieb & Humberto Moreira, 2007. "A model of mixed signals with applications to countersignalling," RAND Journal of Economics, RAND Corporation, vol. 38(4), pages 1020-1043, December.
    9. Julian R. Betts & Robert M. Costrell, 2000. "Incentives and Equity Under Standards-Based Reform," UMASS Amherst Economics Working Papers 2000-08, University of Massachusetts Amherst, Department of Economics.
    10. Carl Shapiro, 1986. "Investment, Moral Hazard, and Occupational Licensing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(5), pages 843-862.
    11. Costrell, Robert M, 1994. "A Simple Model of Educational Standards," American Economic Review, American Economic Association, vol. 84(4), pages 956-971, September.
    12. Morris M. Kleiner, 2000. "Occupational Licensing," Journal of Economic Perspectives, American Economic Association, vol. 14(4), pages 189-202, Fall.
    13. James J. Heckman & John Eric Humphries & Paul A. LaFontaine & Pedro L. Rodríguez, 2012. "Taking the Easy Way Out: How the GED Testing Program Induces Students to Drop Out," Journal of Labor Economics, University of Chicago Press, vol. 30(3), pages 495-520.
    14. Roger Klein & Richard Spady & Andrew Weiss, 1991. "Factors Affecting the Output and Quit Propensities of Production Workers," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(5), pages 929-953.
    15. Derek Neal, 2002. "How Vouchers Could Change the Market for Education," Journal of Economic Perspectives, American Economic Association, vol. 16(4), pages 25-44, Fall.
    16. Hanushek, Eric A. & Rivkin, Steven G., 2006. "Teacher Quality," Handbook of the Economics of Education, in: Erik Hanushek & F. Welch (ed.), Handbook of the Economics of Education, edition 1, volume 2, chapter 18, pages 1051-1078, Elsevier.
    17. Erik Hanushek & F. Welch (ed.), 2006. "Handbook of the Economics of Education," Handbook of the Economics of Education, Elsevier, edition 1, volume 2, number 2, June.
    18. Gottlieb, Daniel & Moreira, Humberto Ataíde & Araújo, Aloísio Pessoa de, 2004. "A model of mixed signals with applications to countersignaling an the GED," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 553, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    19. Thomas S. Dee & Brian A. Jacob, 2006. "Do High School Exit Exams Influence Educational Attainment or Labor Market Performance?," NBER Working Papers 12199, National Bureau of Economic Research, Inc.
    20. Yona Rubinstein & James J. Heckman, 2001. "The Importance of Noncognitive Skills: Lessons from the GED Testing Program," American Economic Review, American Economic Association, vol. 91(2), pages 145-149, May.
    Full references (including those not matched with items on IDEAS)

    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. Eduardo de Carvalho Andrade & Luciano I. de Castro, 2008. "Tougher Educational Exam Leading to Worse Selection," Discussion Papers 1469, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Eduardo Andrade & Luciano De Castro, 2010. "Tougher Educational Exam Leading to Worse Selection," Discussion Papers 1533, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. de Carvalho Andrade, Eduardo & de Castro, Luciano I., 2011. "Tougher educational exam leading to worse selection," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 5, pages 1-24.
    4. Richard J. Murnane, 2013. "U.S. High School Graduation Rates: Patterns and Explanations," Journal of Economic Literature, American Economic Association, vol. 51(2), pages 370-422, June.
    5. Burgess, Simon, 2016. "Human Capital and Education: The State of the Art in the Economics of Education," IZA Discussion Papers 9885, Institute of Labor Economics (IZA).
    6. Bernal, Pedro & Mittag, Nikolas & Qureshi, Javaeria A., 2016. "Estimating effects of school quality using multiple proxies," Labour Economics, Elsevier, vol. 39(C), pages 1-10.
    7. Elke Lüdemann, 2011. "Schooling and the Formation of Cognitive and Non-cognitive Outcomes," ifo Beiträge zur Wirtschaftsforschung, ifo Institute - Leibniz Institute for Economic Research at the University of Munich, number 39.
    8. Hatsor, Limor, 2012. "Occupational choice: Teacher quality versus teacher quantity," Labour Economics, Elsevier, vol. 19(4), pages 608-623.
    9. Lex Borghans & Angela Lee Duckworth & James J. Heckman & Bas ter Weel, 2008. "The Economics and Psychology of Personality Traits," Journal of Human Resources, University of Wisconsin Press, vol. 43(4).
    10. Albarrán, Pedro & Hidalgo-Hidalgo, Marisa & Iturbe-Ormaetxe, Iñigo, 2020. "Education and adult health: Is there a causal effect?," Social Science & Medicine, Elsevier, vol. 249(C).
    11. Gutierrez, Italo A. & Molina, Oswaldo & Nopo, Hugo R., 2018. "Stand Against Bullying: An Experimental School Intervention," IZA Discussion Papers 11623, Institute of Labor Economics (IZA).
    12. Jessica Leight & Elaine M. Liu, 2020. "Maternal Education, Parental Investment, and Noncognitive Characteristics in Rural China," Economic Development and Cultural Change, University of Chicago Press, vol. 69(1), pages 213-251.
    13. Gervas Huxley & Mike Peacey, 2014. "A Simple Model of Learning Styles," The Centre for Market and Public Organisation 14/322, The Centre for Market and Public Organisation, University of Bristol, UK.
    14. Gensowski, Miriam, 2018. "Personality, IQ, and lifetime earnings," Labour Economics, Elsevier, vol. 51(C), pages 170-183.
    15. Kautz, Tim & Heckman, James J. & Diris, Ron & ter Weel, Bas & Borghans, Lex, 2014. "Fostering and Measuring Skills: Improving Cognitive and Non-Cognitive Skills to Promote Lifetime Success," IZA Discussion Papers 8696, Institute of Labor Economics (IZA).
    16. Etienne Dagorn & David Masclet & Thierry Penard, 2022. "The Behavioral Determinants of School Achievement: A Lab in the Field Experiment in Middle School," Economics Working Paper Archive (University of Rennes & University of Caen) 2022-05, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.
    17. Eric A. Hanushek & Marc Piopiunik & Simon Wiederhold, 2019. "The Value of Smarter Teachers: International Evidence on Teacher Cognitive Skills and Student Performance," Journal of Human Resources, University of Wisconsin Press, vol. 54(4), pages 857-899.
    18. Cunha, Flavio & Heckman, James J. & Lochner, Lance, 2006. "Interpreting the Evidence on Life Cycle Skill Formation," Handbook of the Economics of Education, in: Erik Hanushek & F. Welch (ed.), Handbook of the Economics of Education, edition 1, volume 1, chapter 12, pages 697-812, Elsevier.
    19. Hanushek, Eric A., 2011. "The economic value of higher teacher quality," Economics of Education Review, Elsevier, vol. 30(3), pages 466-479, June.
    20. Hofmarcher, Thomas, 2021. "The effect of education on poverty: A European perspective," Economics of Education Review, Elsevier, vol. 83(C).

    More about this item

    Keywords

    the universal type space; the strategic topology; the uniform strategic topology; the uniform-weak topology; interim correlated rationalizable actions;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

    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:nwu:cmsems:1470. 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: Fran Walker (email available below). General contact details of provider: https://edirc.repec.org/data/cmnwuus.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.