T-Statistic Based Correlation and Heterogeneity Robust Inference

45 Pages Posted: 21 Feb 2007

See all articles by Rustam Ibragimov

Rustam Ibragimov

Harvard University - Department of Economics

Ulrich K. Müller

Princeton University - Department of Economics

Date Written: February 2007

Abstract

We develop a general approach to robust inference about a scalar parameter when the data is potentially heterogeneous and correlated in a largely unknown way. The key ingredient is the following result of Bakirov and Sz´ekely (2005) concerning the small sample properties of the standard t-test: For a significance level of 5% or lower, the t-test remains conservative for underlying observations that are independent and Gaussian with heterogenous variances. One might thus conduct robust large sample inference as follows: partition the data into q ≥ 2 groups, estimate the model for each group and conduct a standard t-test with the resulting q parameter estimators. This results in valid inference as long as the groups are chosen in a way that ensures the parameter estimators to be asymptotically independent, unbiased and Gaussian of possibly different variances. We provide examples of how to apply this approach to time series, panel, clustered and spatially correlated data.

Keywords: t-test, dependence, least favorable distribution, variance estimation, Fama-MacBeth method

JEL Classification: C32

Suggested Citation

Ibragimov, Rustam and Müller, Ulrich K., T-Statistic Based Correlation and Heterogeneity Robust Inference (February 2007). Harvard Institute of Economic Research Discussion Paper No. 2129, Available at SSRN: https://ssrn.com/abstract=964224 or http://dx.doi.org/10.2139/ssrn.964224

Rustam Ibragimov (Contact Author)

Harvard University - Department of Economics ( email )

Littauer Center
1805 Cambridge St.
Cambridge, MA 02138
United States
617-496-4795 (Phone)
617-495-7730 (Fax)

HOME PAGE: http://www.economics.harvard.edu/faculty/ibragimov/ibragimov.html

Ulrich K. Müller

Princeton University - Department of Economics ( email )

Princeton, NJ 08544-1021
United States
609-258-3216 (Phone)
609-258-4026 (Fax)

HOME PAGE: http://www.princeton.edu/~umueller

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