Bootstrap Methods in Econometrics: Theory and Numerical Performance
The bootstrap is a method for estimating the distribution of an estimator or test statistic by resampling one's data. It amounts to treating the data as if they were the population for the purpose of evaluating the distribution of interest. Under mild regularity conditions, the bootstrap yields an approximation to the distribution of an estimator or test statistic that is at least as accurate as the approximation obtained from firstorder asymptotic theory. Thus, the bootstrap provides a way to substitute computation for mathematical analysis if calculating the asymptotic distribution of an estimator or statistic is difficult. The maximum score estimator Manski (1975, 1985), the statistic developed by Ha..rdle et al. (1991) for testing positive definiteness of incomeeffect matrices, and certain functions of time series data (Blanchard and Quah 1989, Runkle 1987, West 1990) are examples in which evaluating the asymptotic distribution is difficult and bootstrapping has been used as an alternative.1 In fact, the bootstrap is often more accurate in finite samples than firstorder asymptotic approximations but does not entail the algebraic complexity of higherorder expansions. Thus, it can provide a practical method for improving upon firstorder approximations. Firstorder asymptotic theory often gives a poor approximation to the distributions of test statistics with the sample sizes available in applications. As a result, the nominal levels of tests based on asymptotic critical values can be very different from the true levels. The information matrix test of White(1982) is a wellknown example of a test in which large finite sample distortions of level can occur when asymptotic critical values are used (Horowitz 1994, Kennan and Neumann 1988, Orme 1990, Taylor 1987). Other illustrations are given later in this chapter. The bootstrap often provides a tractable way to reduce or eliminate finite sample distortions of the levels of statistical tests.
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.
Length:  45 pages 
Date of creation:  29 Feb 1996 
Date of revision:  05 Mar 1996 
Handle:  RePEc:wpa:wuwpem:9602009 
Note:  Zipped using PKZIP v2.04, encoded using UUENCODE v5.15. Zipped file includes 1 files  ui9510.wpa (body in MSWord, 45 pages); 
Contact details of provider:  Web page: http://econwpa.repec.org

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.:
 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 96776, July.
 Nelson, C. & Startz, R., 1988. "Some Furthere Results On The Exact Small Sample Properties Of The Instrumental Variable Estimator," Working Papers 8806, University of Washington, Department of Economics.
 Nelson, C. & Startz, R., 1988. "Some Furthere Results On The Exact Small Sample Properties Of The Instrumental Variable Estimator," Discussion Papers in Economics at the University of Washington 8806, Department of Economics at the University of Washington.
 Charles R. Nelson & Richard Startz, 1988. "Some Further Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," NBER Technical Working Papers 0068, National Bureau of Economic Research, Inc.
 Nelson, Charles R & Startz, Richard, 1990.
"The Distribution of the Instrumental Variables Estimator and Its tRatio When the Instrument Is a Poor One,"
The Journal of Business,
University of Chicago Press, vol. 63(1), pages S12540, January.
 Nelson, C. & Startz, R., 1988. "The Distribution Of The Instrumental Variables Estimator And Its TRatio When The Instrument Is A Poor One," Working Papers 8807, University of Washington, Department of Economics.
 Charles R. Nelson & Richard Startz, 1988. "The Distribution of the Instrumental Variables Estimator and Its tRatioWhen the Instrument is a Poor One," NBER Technical Working Papers 0069, National Bureau of Economic Research, Inc.
 Nelson, C. & Startz, R., 1988. "The Distribution Of The Instrumental Variables Estimator And Its TRatio When The Instrument Is A Poor One," Discussion Papers in Economics at the University of Washington 8807, Department of Economics at the University of Washington.
 Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on GeneralizedMethodofMoments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891916, July.
 Andrews, Donald W K, 1991.
"Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation,"
Econometrica,
Econometric Society, vol. 59(3), pages 81758, May.
 Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
 Hardle, Wolfgang & Hildenbrand, Werner & Jerison, Michael, 1991.
"Empirical Evidence on the Law of Demand,"
Econometrica,
Econometric Society, vol. 59(6), pages 152549, November.
 Haerdle,W. Hildenbrand,W. Jerison,M., 1988. "Empirical evidence on the law of demand," Discussion Paper Serie A 193, University of Bonn, Germany.
 Wolfgang Härdle & Werner Hildenbrand & Michael Jerison, 1989. "Empirical Evidence on the Law of Demand," Discussion Paper Serie A 264a, University of Bonn, Germany.
 HARDLE, Wolfgang & HILDENBRAND, Werner & JERISON, Michael, . "Empirical evidence on the law of demand," CORE Discussion Papers RP 968, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
 Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 102954, July.
 Horowitz, Joel L., 1994. "Bootstrapbased critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395411, April.
 Gregory, Allan W & Veall, Michael R, 1985. "Formulating Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 53(6), pages 146568, November.
 Olivier Jean Blanchard & Danny Quah, 1988.
"The Dynamic Effects of Aggregate Demand and Supply Disturbances,"
NBER Working Papers
2737, National Bureau of Economic Research, Inc.
 Blanchard, Olivier Jean & Quah, Danny, 1989. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," American Economic Review, American Economic Association, vol. 79(4), pages 65573, September.
 Olivier Jean Blanchard & Danny Quah, 1988. "The Dynamic Effects of Aggregate Demand and Supply Disturbance," Working papers 497, Massachusetts Institute of Technology (MIT), Department of Economics.
 Hillier, Grant H., 1985. "On the Joint and Marginal Densities of Instrumental Variable Estimators in a General Structural Equation," Econometric Theory, Cambridge University Press, vol. 1(01), pages 5372, April.
 HÃ„RDLE, Wolfgang & HART, Jeffrey D., .
"A bootstrap test for positive definiteness of income effect matrices,"
CORE Discussion Papers RP
999, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
 Härdle, Wolfgang & Hart, Jeffrey D., 1992. "A Bootstrap Test for Positive Definiteness of Income Effect Matrices," Econometric Theory, Cambridge University Press, vol. 8(02), pages 276292, June.
 Haerdle,W. & Hart,J.D., 1989. "A bootstrap test forpositive definiteness of income effect matrices," Discussion Paper Serie A 199, University of Bonn, Germany.
 Hardle, W. & Hart, J., 1990. "A bootstrap test for positive definiteness of income effect matrices," CORE Discussion Papers 1990053, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
 Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205228, August.
 Chesher, Andrew & Jewitt, Ian, 1987. "The Bias of a Heteroskedasticity Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 55(5), pages 121722, September.
 MacKinnon, James G. & White, Halbert, 1985.
"Some heteroskedasticityconsistent covariance matrix estimators with improved finite sample properties,"
Journal of Econometrics,
Elsevier, vol. 29(3), pages 305325, September.
 James G. MacKinnon & Halbert White, 1983. "Some Heteroskedasticity Consistent Covariance Matrix Estimators with Improved Finite Sample Properties," Working Papers 537, Queen's University, Department of Economics.
 Donald W.K. Andrews & Christopher J. Monahan, 1990.
"An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator,"
Cowles Foundation Discussion Papers
942, Cowles Foundation for Research in Economics, Yale University.
 Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 95366, July.
 repec:cup:etheor:v:8:y:1992:i:2:p:27690 is not listed on IDEAS
 Lancaster, Tony, 1984. "The Covariance Matrix of the Information Matrix Test," Econometrica, Econometric Society, vol. 52(4), pages 105153, July.
 Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313333, March.
 Lafontaine, Francine & White, Kenneth J., 1986. "Obtaining any Wald statistic you want," Economics Letters, Elsevier, vol. 21(1), pages 3540.
 Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 126986, September.
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:wpa:wuwpem:9602009. 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: (EconWPA)
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.