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Strategic Manipulation of Empirical Tests

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  • Wojciech Olszewski
  • Alvaro Sandroni

Abstract

Theories can be produced by individuals seeking a good reputation of knowledge. Hence, a significant question is how to test theories anticipating that they might have been produced by (potentially uninformed) experts who prefer their theories not to be rejected. If a theory that predicts exactly like the data generating process is not rejected with high probability then the test is said to not reject the truth. On the other hand, if a false expert, with no knowledge over the data generating process, can strategically select theories that will not be rejected then the test can be ignorantly passed. These tests have limited use because they cannot feasibly dismiss completely uninformed experts. Many tests proposed in the literature (e.g., calibration tests) can be ignorantly passed. Dekel and Feinberg (2006) introduced a class of tests that seemingly have some power of dismissing uninformed experts. We show that some tests from their class can also be ignorantly passed. One of those tests, however, does not reject the truth and cannot be ignorantly passed. Thus, this empirical test can dismiss false experts.We also show that a false reputation of knowledge can be strategically sustained for an arbitrary, but given, number of periods, no matted which test is used (provided that it does not reject the truth). However, false experts can be discredited, even with bounded data sets, if the domain of permissible theories is mildly restricted.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1425.

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Date of creation: Mar 2006
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Handle: RePEc:nwu:cmsems:1425

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  1. Alvaro Sandroni & Wojciech Olszewski, 2008. "Manipulability of Future-Independent Tests," PIER Working Paper Archive 08-014, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  2. S. Hart & A. Mas-Collel, 2010. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Levine's Working Paper Archive 572, David K. Levine.
  3. Hart, Sergiu & Mas-Colell, Andreu, 2001. "A General Class of Adaptive Strategies," Journal of Economic Theory, Elsevier, vol. 98(1), pages 26-54, May.
  4. Fudenberg, Drew & Levine, David K., 1999. "An Easier Way to Calibrate," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 131-137, October.
  5. Kalai, Ehud & Lehrer, Ehud & Smorodinsky, Rann, 1999. "Calibrated Forecasting and Merging," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 151-169, October.
  6. Eddie Dekel & Yossi Feinberg, 2006. "Non-Bayesian Testing of a Stochastic Prediction," Discussion Papers 1418, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Fudenberg, Drew & Levine, David, 1995. "Consistency and Cautious Fictitious Play," Scholarly Articles 3198694, Harvard University Department of Economics.
  8. Nabil I. Al-Najjar & Jonathan Weinstein, 2008. "Comparative Testing of Experts," Econometrica, Econometric Society, vol. 76(3), pages 541-559, 05.
  9. Anderson Robert M. & Zame William R., 2001. "Genericity with Infinitely Many Parameters," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-64, February.
  10. Drew Fudenberg & David K. Levine, 1997. "Conditional Universal Consistency," Levine's Working Paper Archive 471, David K. Levine.
  11. Vladimir Vovk & Glenn Shafer, 2005. "Good randomized sequential probability forecasting is always possible," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 747-763.
  12. Yossi Feinberg & Colin Stewart, 2008. "Testing Multiple Forecasters," Econometrica, Econometric Society, vol. 76(3), pages 561-582, 05.
  13. Alvaro Sandroni & Wojciech Olszewski, 2008. "Falsifiability," PIER Working Paper Archive 08-016, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  14. Ehud Lehrer & Eilon Solan, 2003. "No-Regret with Bounded Computational Capacity," Discussion Papers 1373, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  15. Rustichini, Aldo, 1999. "Optimal Properties of Stimulus--Response Learning Models," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 244-273, October.
  16. Lehrer, Ehud, 2001. "Any Inspection Is Manipulable," Econometrica, Econometric Society, vol. 69(5), pages 1333-47, September.
  17. Alvaro Sandroni, 2003. "The reproducible properties of correct forecasts," International Journal of Game Theory, Springer, vol. 32(1), pages 151-159, December.
  18. Shmaya, Eran, 2008. "Many inspections are manipulable," Theoretical Economics, Econometric Society, vol. 3(3), September.
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Cited by:
  1. Yossi Feinberg & Colin Stewart, 2008. "Testing Multiple Forecasters," Econometrica, Econometric Society, vol. 76(3), pages 561-582, 05.
  2. Dean Foster & Rakesh Vohra, 2011. "Calibration: Respice, Adspice, Prospice," Discussion Papers 1537, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Al-Najjar, Nabil & Sandroni, Alvaro, 2013. "A difficulty in the testing of strategic experts," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 5-9.
  4. Alvaro Sandroni & Wojciech Olszewski, 2008. "Manipulability of Future-Independent Tests," PIER Working Paper Archive 08-014, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  5. Colin, Stewart, 2011. "Nonmanipulable Bayesian testing," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2029-2041, September.
  6. Hu, Tai Wei & Shmaya, Eran, 2013. "Expressible inspections," Theoretical Economics, Econometric Society, vol. 8(2), May.
  7. Al-Najjar, Nabil I. & Sandroni, Alvaro & Smorodinsky, Rann & Weinstein, Jonathan, 2010. "Testing theories with learnable and predictive representations," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2203-2217, November.
  8. Feinberg, Yossi & Lambert, Nicolas S., 2011. "Mostly Calibrated," Research Papers 2090, Stanford University, Graduate School of Business.

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