This paper derived new measures of tax progressivity where the forms of initial income distribution and of tax function are given. We considered in particular the case in which initial income is distributed log-normally. Several forms of tax function are considered. Attention was paid to investigating whether the form of tax function is crucial in determining the degree of tax progressivity. We examined empilically not only the difference in the actual degrees of personal income tax progressivity between Japan and the U. S. but also the time-series change in the estimated tax progressivity in Japan. At the same time, a decomposition analysis, which was made feasible under our methodology, was attempted to estimate the contributions by income distribution factor and tax factor to an overall change in tax progressivity.

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