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Identification in Models with Discrete Variables

Author

Listed:
  • Laffers, Lukas

    (Dept. of Economics, Norwegian School of Economics and Business Administration)

Abstract
This paper provides a new simple and computationally tractable method for determining an identified set that can account for a broad set of economic models when economic variables are discrete. Using this method it is shown on a simple example how can imperfect instruments affect the size of the identified set when strict exogeneity is relaxed. It could be of great interest to know to what extent are the results driven by the exogeneity assumption which is often a subject of controversy. Moreover, flexibility gained from the new proposed method suggests that the determination of the identified set need not be application-specific anymore. This paper presents a unifying framework that approaches identification in an algorithmic way.

Suggested Citation

  • Laffers, Lukas, 2013. "Identification in Models with Discrete Variables," Discussion Paper Series in Economics 1/2013, Norwegian School of Economics, Department of Economics.
    • Handle: RePEc:hhs:nhheco:2013_001
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    References listed on IDEAS

    as
    1. Marc Henry & Romuald Méango & Maurice Queyranne, 2015. "Combinatorial approach to inference in partially identified incomplete structural models," Quantitative Economics, Econometric Society, vol. 6(2), pages 499-529, July.
    2. Beresteanu, Arie & Molchanov, Ilya & Molinari, Francesca, 2012. "Partial identification using random set theory," Journal of Econometrics, Elsevier, vol. 166(1), pages 17-32.
    3. Galichon, Alfred & Henry, Marc, 2009. "A test of non-identifying restrictions and confidence regions for partially identified parameters," Journal of Econometrics, Elsevier, vol. 152(2), pages 186-196, October.
    4. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    5. Tamer, Elie, 2010. "Partial Identification in Econometrics," Scholarly Articles 34728615, Harvard University Department of Economics.
    6. Aviv Nevo & Adam M. Rosen, 2012. "Identification With Imperfect Instruments," The Review of Economics and Statistics, MIT Press, vol. 94(3), pages 659-671, August.
    7. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4ao8ocg is not listed on IDEAS
    8. Marc Henry & Romuald Méango & Maurice Queyranne, 2012. "Combinatorial Bootstrap Inference IN in Prtially Identified Incomplete Structural Models," CIRJE F-Series CIRJE-F-837, CIRJE, Faculty of Economics, University of Tokyo.
    9. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    10. Joshua Angrist & Eric Bettinger & Erik Bloom & Elizabeth King & Michael Kremer, 2002. "Vouchers for Private Schooling in Colombia: Evidence from a Randomized Natural Experiment," American Economic Review, American Economic Association, vol. 92(5), pages 1535-1558, December.
    11. Donald W. K. Andrews & Xiaoxia Shi, 2013. "Inference Based on Conditional Moment Inequalities," Econometrica, Econometric Society, vol. 81(2), pages 609-666, March.
    12. David S. Lee, 2009. "Training, Wages, and Sample Selection: Estimating Sharp Bounds on Treatment Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(3), pages 1071-1102.
    13. Lukáš Lafférs, 2019. "Bounding average treatment effects using linear programming," Empirical Economics, Springer, vol. 57(3), pages 727-767, September.
    14. Freyberger, Joachim & Horowitz, Joel L., 2015. "Identification and shape restrictions in nonparametric instrumental variables estimation," Journal of Econometrics, Elsevier, vol. 189(1), pages 41-53.
    15. Andrew Chesher, 2009. "Single equation endogenous binary reponse models," CeMMAP working papers CWP23/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. repec:cwl:cwldpp:1840rr is not listed on IDEAS
    17. Martin Huber & Lukas Laffers & Giovanni Mellace, 2017. "Sharp IV Bounds on Average Treatment Effects on the Treated and Other Populations Under Endogeneity and Noncompliance," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(1), pages 56-79, January.
    18. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4ao8ocg is not listed on IDEAS
    19. Andrew Chesher & Adam M. Rosen & Konrad Smolinski, 2013. "An instrumental variable model of multiple discrete choice," Quantitative Economics, Econometric Society, vol. 4(2), pages 157-196, July.
    20. William A. Brock & Steven N. Durlauf, 2001. "Discrete Choice with Social Interactions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(2), pages 235-260.
    21. Joseph P. Romano & Azeem M. Shaikh, 2010. "Inference for the Identified Set in Partially Identified Econometric Models," Econometrica, Econometric Society, vol. 78(1), pages 169-211, January.
    22. Manski, Charles F. & Thompson, T. Scott, 1986. "Operational characteristics of maximum score estimation," Journal of Econometrics, Elsevier, vol. 32(1), pages 85-108, June.
    23. Arie Beresteanu & Ilya Molchanov & Francesca Molinari, 2011. "Sharp Identification Regions in Models With Convex Moment Predictions," Econometrica, Econometric Society, vol. 79(6), pages 1785-1821, November.
    24. Andrew Chesher, 2010. "Instrumental Variable Models for Discrete Outcomes," Econometrica, Econometric Society, vol. 78(2), pages 575-601, March.
    25. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, July.
    26. Chernozhukov, Victor & Hansen, Christian & Jansson, Michael, 2009. "Finite sample inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 152(2), pages 93-103, October.
    27. Ivar Ekeland & Alfred Galichon & Marc Henry, 2010. "Optimal transportation and the falsifiability of incompletely specified economic models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 355-374, February.
    28. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    29. Andrews, Donald W.K. & Shi, Xiaoxia, 2014. "Nonparametric inference based on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 179(1), pages 31-45.
    30. Federico A. Bugni, 2010. "Bootstrap Inference in Partially Identified Models Defined by Moment Inequalities: Coverage of the Identified Set," Econometrica, Econometric Society, vol. 78(2), pages 735-753, March.
    31. Rosen, Adam M., 2008. "Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities," Journal of Econometrics, Elsevier, vol. 146(1), pages 107-117, September.
    32. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    33. Bo E. Honoré & Elie Tamer, 2006. "Bounds on Parameters in Panel Dynamic Discrete Choice Models," Econometrica, Econometric Society, vol. 74(3), pages 611-629, May.
    34. Jinyong Hahn & Jerry Hausman, 2010. "Estimation with Valid and Invalid Instruments," NBER Chapters, in: Contributions in Memory of Zvi Griliches, pages 25-57, National Bureau of Economic Research, Inc.
    35. Azeem M. Shaikh & Edward J. Vytlacil, 2011. "Partial Identification in Triangular Systems of Equations With Binary Dependent Variables," Econometrica, Econometric Society, vol. 79(3), pages 949-955, May.
    36. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, September.
    37. Alfred Galichon & Marc Henry, 2011. "Set Identification in Models with Multiple Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(4), pages 1264-1298.
    38. Charles F. Manski & John V. Pepper, 2000. "Monotone Instrumental Variables, with an Application to the Returns to Schooling," Econometrica, Econometric Society, vol. 68(4), pages 997-1012, July.
    39. Komarova, Tatiana, 2013. "Binary choice models with discrete regressors: Identification and misspecification," Journal of Econometrics, Elsevier, vol. 177(1), pages 14-33.
    40. repec:adr:anecst:y:2005:i:79-80:p:02 is not listed on IDEAS
    41. repec:cwl:cwldpp:1761rr is not listed on IDEAS
    42. Charles F. Manski, 2007. "Partial Identification Of Counterfactual Choice Probabilities," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1393-1410, November.
    43. Lafférs, Lukáš, 2013. "A note on bounding average treatment effects," Economics Letters, Elsevier, vol. 120(3), pages 424-428.
    44. Elie Tamer, 2010. "Partial Identification in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 167-195, September.
    45. Ivar Ekeland & Alfred Galichon & Marc Henry, 2010. "Optimal transportation and the falsifiability of incompletely specified economic models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 355-374, February.
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    Cited by:

    1. Lukáš Lafférs, 2019. "Bounding average treatment effects using linear programming," Empirical Economics, Springer, vol. 57(3), pages 727-767, September.

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    More about this item

    Keywords

    Identification; Models; Discrete Variables.;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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