# Bootstrap Methods in Econometrics: Theory and Numerical Performance

## Abstract

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 first-order 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 income-effect 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 first-order asymptotic approximations but does not entail the algebraic complexity of higher-order expansions. Thus, it can provide a practical method for improving upon first-order approximations. First-order 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 well-known 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.## Download Info

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## Bibliographic Info

Paper provided by EconWPA in its series Econometrics with number 9602009.

**Length:**45 pages

**Date of creation:**29 Feb 1996

**Date of revision:**05 Mar 1996

**Handle:**RePEc:wpa:wuwpem:9602009

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## Related research

**Keywords:**

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**C1**- Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General**C2**- Mathematical and Quantitative Methods - - Single Equation Models; Single Variables**C3**- Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables**C4**- Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics**C5**- Mathematical and Quantitative Methods - - Econometric Modeling**C8**- Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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