Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T18:50:42.216Z Has data issue: false hasContentIssue false
  • English
  • Français

GLOBAL IDENTIFICATION IN NONLINEAR MODELS WITH MOMENT RESTRICTIONS

Published online by Cambridge University Press:  21 May 2012

Ivana Komunjer
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper derives sufficient conditions for global identification in nonlinear models characterized by a finite number of unconditional moment restrictions. The main contribution of this paper is to provide a set of assumptions that are alternative to those of Gale-Nikaidô-Fisher-Rothenberg, and which when satisfied guarantee that the moment conditions globally identify the parameters of interest.

Type
Research Article
Information
Econometric Theory , Volume 28 , Issue 4 , August 2012 , pp. 719 - 729
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

I would like to thank the co-editor, Jin Hahn, as well as anonymous referees for their comments and suggestions. This paper was presented at econometric seminars at Boston College, Brown, Columbia, Concordia, CREATES, Stanford, Toulouse, UC Berkeley, UCL, UCLA, University of Pennsylvania, and Yale, whose participants provided valuable feedback. All errors are my own.

References

REFERENCES

Basye, R.E. (1935) Simply connected sets. Transactions of the American Mathematical Society 38, 341–356.CrossRefGoogle Scholar
Benkard, C.L. & Berry, S. (2006) On the nonparametric identification of nonlinear simultaneous equations models: Comment on Brown (1983) and Rhoerig (1988). Econometrica 74, 1429–1440.CrossRefGoogle Scholar
Bowden, R. (1973) The theory of parametric identification. Econometrica 41, 1069–1074.CrossRefGoogle Scholar
Brown, B.W. (1983) The identification problem in systems nonlinear in the variables. Econometrica 51, 175–196.10.2307/1912253CrossRefGoogle Scholar
Chernozhukov, V. & Hansen, C. (2005) An IV model of quantile treatment effects. Econometrica 73, 245–261.10.1111/j.1468-0262.2005.00570.xCrossRefGoogle Scholar
Chernozhukov, V., Imbens, G.W., & Newey, W.K. (2007) Instrumental variable estimation of nonseparable models. Journal of Econometrics 139, 4–14.CrossRefGoogle Scholar
Chesher, A. (2003) Identification in nonseparable models. Econometrica 71, 1405–1441.CrossRefGoogle Scholar
Choi, I. & Phillips, P.C. (1992) Asymptotic and finite sample distribution theory for IV estimators and tests in partially identified structural equations. Journal of Econometrics 51, 113–150.CrossRefGoogle Scholar
Chua, L.O. & Lam, Y.-F. (1972) Global homeomorphism of vector-valued functions. Journal of Mathematical Analysis and Applications 39, 600–624.CrossRefGoogle Scholar
Church, P.T. (1963) Differentiable open maps on manifolds. Transactions of the American Mathematical Society 109, 87–100.10.1090/S0002-9947-1963-0154296-6CrossRefGoogle Scholar
Church, P.T. & Hemmingsen, E. (1960) Light open maps on n-manifolds. Duke Mathematical Journal 27, 527–536.10.1215/S0012-7094-60-02750-2CrossRefGoogle Scholar
Debreu, G. (1970) Economies with a finite set of equilibria. Econometrica 38, 387–392.10.2307/1909545CrossRefGoogle Scholar
Dominguez, M.A. & Lobato, I.N. (2004) Consistent estimation of models defined by conditional moment restrictions. Econometrica 72, 1601–1615.CrossRefGoogle Scholar
Dufour, J.-M. & Hsiao, C. (2008) Identification. In Blume, L. & Durlauf, S. (eds.), The New Palgrave Dictionary of Economics, 2 nded. Palgrave Macmillan.Google Scholar
Fisher, F.M. (1961) Identifiability criteria in nonlinear systems. Econometrica 29, 574–590.10.2307/1911805CrossRefGoogle Scholar
Fisher, F.M. (1965) Identifiability criteria in nonlinear systems: A further note. Econometrica 33, 197–205.CrossRefGoogle Scholar
Fisher, F.M. (1966) The Identification Problem in Economics. McGraw-Hill.Google Scholar
Gale, D. & Nikaidô, H. (1965) The Jacobian matrix and global univalence of mappings. Mathematische Annalen 159, 81–93.CrossRefGoogle Scholar
Hurewicz, W. & Wallman, H. (1948) Dimension Theory. Princeton University Press.Google Scholar
Koopmans, T.C. (ed.) (1950) Statistical Inference in Dynamic Economic Models, vol. 10 of Cowles Commission Monograph. Wiley.Google Scholar
Koopmans, T.C. & Reiersøl, O. (1950) The identification of structural characteristics. The Annals of Mathematical Statistics 21, 165–181.10.1214/aoms/1177729837CrossRefGoogle Scholar
Matzkin, R.L. (1994) Restrictions of economic theory in nonparametric methods. In Engle, R.F. & McFadden, D.L. (eds.), Handbook of Econometrics, vol. IV, pp. 2524–2559. North-Holland.Google Scholar
Matzkin, R.L. (2007) Nonparametric identification. In Heckman, J.J. & Leamer, E. (eds.), Handbook of Econometrics, vol. 6B, pp. 5307–5368. Elsevier.CrossRefGoogle Scholar
Matzkin, R.L. (2008) Identification in nonparametric simultaneous equations. Econometrica 76, 945–978.Google Scholar
Newey, W.K. & McFadden, D.L. (1994) Large sample estimation and hypothesis testing. In Engle, R.F. & McFadden, D.L. (eds.), Handbook of Econometrics, pp. 2113–2247. Elsevier Science.Google Scholar
Newey, W.K. & Powell, J.L. (2003) Instrumental variable estimation of nonparametric models. Econometrica 71, 1565–1578.CrossRefGoogle Scholar
Palais, R.S. (1959) Natural operations on differential forms. Transactions of the American Mathematical Society 92, 125–141.CrossRefGoogle Scholar
Palais, R.S. (1970) When proper maps are closed. Proceedings of the American Mathematical Society 24, 835–836.Google Scholar
Phillips, P.C. (1989) Partially identified econometric models. Econometric Theory 5, 181–240.CrossRefGoogle Scholar
Phillips, P.C. (2012) Folklore theorems, implicit maps, and indirect inference. Econometrica, forthcoming.Google Scholar
Plastock, R.A. (1978) Nonlinear Fredholm maps of index zero and their singularities. Proceedings of the American Mathematical Society 68, 317–322.10.1090/S0002-9939-1978-0464283-2CrossRefGoogle Scholar
Roehrig, C.S. (1988) Conditions for identification in nonparametric and parametric models. Econometrica 56, 433–447.CrossRefGoogle Scholar
Rothenberg, T.J. (1971) Identification in parametric models. Econometrica 39, 577–591.CrossRefGoogle Scholar
Sard, A. (1965) Hausdorff measure of critical images on Banach manifolds. American Journal of Mathematics 87, 158–174.CrossRefGoogle Scholar
Severini, T.A. & Tripathi, G. (2006) Some identification issues in nonparametric linear models with endogenous regressors. Econometric Theory 22, 258–278.CrossRefGoogle Scholar
Titus, C.J. & Young, G.S. (1952) A Jacobian condition for interiority. Michigan Mathematical Journal 1, 69–72.CrossRefGoogle Scholar