IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

Convergency and Divergency of Functional Coefficient Weak Instrumental Variables Models

Listed author(s):
  • Zongwu Cai
  • Henong Li

In this paper, we consider a simultaneous equations model under a functional coefficient representation for the structural equation of interest and adopt the local-to-zero assumptions as in Staiger and Stock (1997) and Hahn and Kuersteiner (2002) on the coefficients of the instruments in the reduced form equation. Under this functional coefficient representation, models are linear in endogenous components with coefficients governed by unknown functions of the predetermined exogenous variables. We propose a two-step estimation procedure to estimate the coefficient functions. The first step is to estimate a matrix of unknown parameters of the reduced form equation based on the least squares method, and the second step is to use the local linear fitting technique to estimate coefficient functions by using the estimated reduced forms as regressors. We investigate how the limiting distribution of the proposed nonparametric estimator changes as the parameterization is allowed for different degrees of weakness. As a result, our new theoretical findings are that the possible convergency of the proposed nonparametric estimators can be attained only for the nearly weak case and the rate of convergence for the nonparametric estimator for coefficient functions of endogenous variables is slower than the conventional rate. But the nonparametric estimator for coefficient functions of endogenous variables is divergent for both the weak and nearly non-identified cases. A Monte Carlo simulation is conducted to illustrate the finite sample performance of the resulting estimator and results support these theoretical findings.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://121.192.176.75/repec/upload/20075211419307055475115776.pdf
Download Restriction: no

Paper provided by Wang Yanan Institute for Studies in Economics (WISE), Xiamen University in its series WISE Working Papers with number 2013-10-14.

as
in new window

Length:
Date of creation: 14 Oct 2013
Publication status: published
Handle: RePEc:wyi:wpaper:001972
Contact details of provider: Web page: http://www.wise.xmu.edu.cn/english/

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as
in new window


  1. Motohiro Yogo, 2004. "Estimating the Elasticity of Intertemporal Substitution When Instruments Are Weak," The Review of Economics and Statistics, MIT Press, vol. 86(3), pages 797-810, August.
  2. Caner, Mehmet & Hansen, Bruce E., 2004. "Instrumental Variable Estimation Of A Threshold Model," Econometric Theory, Cambridge University Press, vol. 20(05), pages 813-843, October.
  3. Nelson, Charles R & Startz, Richard, 1990. "Some Further Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 58(4), pages 967-976, July.
  4. 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 518-529, October.
  5. Hausman, Jerry & Stock, James H. & Yogo, Motohiro, 2005. "Asymptotic properties of the Hahn-Hausman test for weak-instruments," Economics Letters, Elsevier, vol. 89(3), pages 333-342, December.
  6. Jinyong Hahn & Jerry Hausman & Guido Kuersteiner, 2004. "Estimation with weak instruments: Accuracy of higher-order bias and MSE approximations," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 272-306, 06.
  7. Hahn, Jinyong & Kuersteiner, Guido, 2002. "Discontinuities of weak instrument limiting distributions," Economics Letters, Elsevier, vol. 75(3), pages 325-331, May.
  8. Ted Juhl, 2005. "Functional-coefficient models under unit root behaviour," Econometrics Journal, Royal Economic Society, vol. 8(2), pages 197-213, 07.
  9. 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.
  10. Zongwu Cai & Jianqing Fan & Qiwei Yao, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
  11. Cai, Zongwu, 2002. "Two-Step Likelihood Estimation Procedure for Varying-Coefficient Models," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 189-209, July.
  12. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  13. Cai, Zongwu & Das, Mitali & Xiong, Huaiyu & Wu, Xizhi, 2006. "Functional coefficient instrumental variables models," Journal of Econometrics, Elsevier, vol. 133(1), pages 207-241, July.
  14. 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.
  15. Maddala, G S & Jeong, Jinook, 1992. "On the Exact Small Sample Distribution of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 60(1), pages 181-183, January.
  16. Li, Qi, et al, 2002. "Semiparametric Smooth Coefficient Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 412-422, July.
  17. Joshua D. Angrist & Alan B. Keueger, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, Oxford University Press, vol. 106(4), pages 979-1014.
  18. Neely, Christopher J & Roy, Amlan & Whiteman, Charles H, 2001. "Risk Aversion versus Intertemporal Substitution: A Case Study of Identification Failure in the Intertemporal Consumption Capital Asset Pricing Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 395-403, October.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:wyi:wpaper:001972. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (WISE Technical Team)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.