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Statistical Test Results

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Tax Progression in OECD Countries

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Abstract

This chapter adds some statistical checks on top of the numerical comparisons reported in Chap. 6. Since LIS provides representative sample data, we can statistically test whether our qualitative statements with respect to uniformly greater tax progression, bifurcate tax progression, and indeterminacy are statistically significant. After elucidating the methodology, we carry out the respective statistical tests for six countries. We find the number of statistically significant dominance relations to increase to 84 percent, and statistically significant bifurcate relations and indeterminate cases to drop to 10 percent and 6 percent, respectively. These results demonstrate that the dominance results which are already striking for our qualitative analyses, are still reinforced for the statistical tests. We also perform statistical tests for intertemporal comparisons for the United States, the United Kingdom, and Germany, which confirm the results gained from our qualitative analyses.

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Notes

  1. 1.

    Note that there is an error in the original formula for the computation of \(\hat{{\Phi }}_{j}\) by Beach and Kaliski (1986, p. 40). The expression on the right hand side of their formula has to be multiplied by the quantile rank j.

  2. 2.

    Note that Definitions 5 and 5 deal with pairs of independent vectors of q-curve ordinate differences (e.g. the first-moment distribution function for gross income minus the one for tax) instead of single curves. Establishing the joint distribution of ordinate differences would require enormous computational effort and is infeasible given the fact that the LIS micro data cannot be accessed directly. Hence, in the tests involving Definitions 5 and 5, we assumed stochastic independence of the two underlying curves, where the joint variance is simply given by the sum of the variances of the two underlying curves. Obviously, the gross income distribution and the tax distribution for the same country at the same point of time are not independent, but—as pointed out above—there is no better alternative available.

  3. 3.

    For 20 vigintiles, we only estimate 19 ordinates as \(\hat{{\Phi }}_{20} = 1\) in any sample and for all curves we analyze.

  4. 4.

    All 30 tables of the statistical tests of progression comparisons are available at http://www.wiwi.uni-bremen.de/traub/index-Dateien/StefanTraub.htm

  5. 5.

    We use boldface characters for statistically significant relationships to distinguish them from the relationships applied for the qualitative analyses.

  6. 6.

    Recall from Sect. 7.1 that statistical tests for equivalized data cannot be carried out.

  7. 7.

    All \(12 \times 3 = 36\) tables with the statistical tests are available on http://www.wiwi.uni-bremen.de/traub/index-Dateien/StefanTraub.htm

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Authors and Affiliations

  1. Faculty of Economics and Social Sciences, University of Kiel, Kiel, Germany

    Christian Seidl

  2. Division of the Humanities and Social Sciences, California Institute of Technology, Pasadena, California, USA

    Kirill Pogorelskiy

  3. Zentrum für Sozialpolitik, University of Bremen, Bremen, Germany

    Stefan Traub

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Seidl, C., Pogorelskiy, K., Traub, S. (2013). Statistical Test Results. In: Tax Progression in OECD Countries. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28317-8_7

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