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Nonparametric IV estimation of shape-invariant Engel curves

  • Richard Blundell

    ()

    (Institute for Fiscal Studies and University College London)

  • Xiaohong Chen
  • Dennis Kristensen

This paper concerns the identification and estimation of a shape-invariant Engel curve system with endogenous total expenditure. The shape-invariant specification involves a common shift parameter for each demographic group in a pooled system of Engel curves. Our focus is on the identification and estimation of both the nonparametric shape of the Engel curve and the parametric specification of the demographic scaling parameters. We present a new identification condition, closely related to the concept of bounded completeness in statistics. The estimation procedure applies the sieve minimum distance estimation of conditional moment restrictions allowing for endogeneity. We establish a new root mean squared convergence rate for the nonparametric IV regression when the endogenous regressor has unbounded support. Root-n asymptotic normality and semiparametric efficiency of the parametric components are also given under a set of Ѭow-level' sufficient conditions. Monte Carlo simulations shed lights on the choice of smoothing parameters and demonstrate that the sieve IV estimator performs well. An application is made to the estimation of Engel curves using the UK Family Expenditure Survey and shows the importance of adjusting for endogeneity in terms of both the curvature and demographic parameters of systems of Engel curves.

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File URL: http://cemmap.ifs.org.uk/wps/cwp0315.pdf
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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP15/03.

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Length: 68 pp.
Date of creation: Oct 2003
Date of revision:
Handle: RePEc:ifs:cemmap:15/03
Contact details of provider: Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE
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Web page: http://cemmap.ifs.org.uk
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  1. Robin, Jean-Marc & Smith, Richard J., 2000. "Tests Of Rank," Econometric Theory, Cambridge University Press, vol. 16(02), pages 151-175, April.
  2. Richard Blundell & Martin Browning & Ian Crawford, 1998. "Nonparametric Engel Curves and Revealed Preference," Discussion Papers 99-07, University of Copenhagen. Department of Economics.
  3. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
  4. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May.
  5. Haerdle,Wolfgang Jerison,Michael, 1988. "Cross section Engel curves over time," Discussion Paper Serie A 160, University of Bonn, Germany.
  6. Serge Darolles & Jean-Pierre Florens & Yanqin Fan & Eric Renault, 2011. "Nonparametric Instrumental Regression," Working Papers 245432, Institut National de la Recherche Agronomique, France.
  7. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-29, October.
  8. Chen, Xiaoheng & Conley, Timothy G., 2001. "A new semiparametric spatial model for panel time series," Journal of Econometrics, Elsevier, vol. 105(1), pages 59-83, November.
  9. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July.
  10. Florens, Jean-Pierre & Heckman, James & Meghir, Costas & Vytlacil, Edward, 2003. "Instrumental Variables, Local Instrumental Variables and Control Functions," IDEI Working Papers 249, Institut d'Économie Industrielle (IDEI), Toulouse.
  11. Xiaohong Chen & Xiaotong Shen, 1998. "Sieve Extremum Estimates for Weakly Dependent Data," Econometrica, Econometric Society, vol. 66(2), pages 289-314, March.
  12. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-26, June.
  13. Whitney K. Newey & James L. Powell & Francis Vella, 1999. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Econometrica, Econometric Society, vol. 67(3), pages 565-604, May.
  14. James H. Stock & Motohiro Yogo, 2002. "Testing for Weak Instruments in Linear IV Regression," NBER Technical Working Papers 0284, National Bureau of Economic Research, Inc.
  15. Peter Hall & Joel L. Horowitz, 2003. "Nonparametric methods for inference in the presence of instrumental variables," CeMMAP working papers CWP02/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  16. Blundell, Richard, 1988. "Consumer Behaviour: Theory and Empirical Evidence--a Survey," Economic Journal, Royal Economic Society, vol. 98(389), pages 16-65, March.
  17. Richard Blundell & James Powell, 2001. "Endogeneity in nonparametric and semiparametric regression models," CeMMAP working papers CWP09/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  18. Pendakur, Krishna, 1998. "Semiparametric estimates and tests of base-independent equivalence scales," Journal of Econometrics, Elsevier, vol. 88(1), pages 1-40, November.
  19. Hausman, Jerry A. & Newey, Whitney K. & Ichimura, Hidehiko & Powell, James L., 1991. "Identification and estimation of polynomial errors-in-variables models," Journal of Econometrics, Elsevier, vol. 50(3), pages 273-295, December.
  20. Richard Blundell & Alan Duncan & Krishna Pendakur, 1998. "Semiparametric estimation and consumer demand," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(5), pages 435-461.
  21. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
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