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There has been a rise in the number of studies that study long term trends in income inequality. In this paper, I highlight that for time dependent analyses there are many inequality measures that may not be suited, since many measures are estimated relative to the average (income).

To illustrate this problem I put together a new dataset of 18 inequality measures for 34 countries for 100 years using mortality (by age) distributions as a proxy for income distributions. I then model the time series of these inequality measures as a fractionally integrated process and find that there are more countries that have mean-reverting and stationary absolute inequality measures than relative measures. A panel regression application estimating the relationship between inequality and economic growth using GMM panel regression methods shows that regression models that use mean-reverting or stationary inequality measures have a more stable relationship between inequality and growth. To further investigate the time dependent properties of these inequality measures, I estimate impulse response functions to observe the effect of a shock in GDP on the inequality measures. The effect of the shock dissipates about 10 years earlier for absolute measures than for relative measures. Tests for volatility in the temporal distribution of the inequality measures also strikingly reveal that measures with volatility clustering around the mean are also not mean-reverting or stationary, and slow to converge in the impulse response functions.

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