The kind of study and data manipulation you are talking about is huge. Surely, there has been a book or two written on the subject. It would be quite and involved process that is going to take a lot more sorting through than just saying that shorter term impacts "cancel out".
Let me explain what I mean. It's really not that complicated. Take a look at the first graph in this link.
Wealth And Inequality In America
The chart shows very high income inequality in the period before and during the Great Depression, then compressed income inequality (or to put it another way, a closer approach to equality) in the period from World War II until 1980, then a widening of the income gap again after 1981. Narrow income gaps during the war and postwar decades until 1980, wide income gaps before and after.
We also see, on the average, much higher (by more than two to one) rate of growth in per capita GDP during the decades when income gaps were narrow than in either the earlier or later period when they were wide. Per capita GDP growth was at just above 2% per year on the average when income inequality was high, then 4.25% on average when it was low, then back down to just above 2% when it became high again.
In order to posit any other cause, there would need to be some other variable that
held steady throughout the first period, then changed in the second, and then changed back in the third, and there is not. For example, high government spending by itself can't be the reason, because we still have that; government spending did not drop in the 1980s or thereafter, but GDP growth did. America's superpower status, ditto; we still have that, too. Same with demographics, war and peace, increasing globalization, the computer revolution, or any other observable factor.
That's what I meant by saying these other variables "cancel out," and perhaps that was a poorly-chosen phrase. Hopefully the above will clarify what I mean.
The international comparison works the same way. Almost all advanced, high-wealth nations are also low-inequality; almost all third-world, dirt-poor countries are high-inequality. There are very few exceptions, and the exceptions are easily explained; for example, Cuba is a low-inequality nation but is also pre-industrial; the U.S. is a high-inequality nation but our economy is on the decline. Other than the U.S., ALL of the advanced nations (Western Europe, Canada, Japan, Australia, etc.) have low GINI coefficients. Again, there is no other common variable that can explain this.
This is of course exactly what should be expected based on a demand-side theoretical approach such as I described in an earlier post. The empirical data support that theory, and strongly refute the competing supply-side theory.
Here is a link to a study that goes into more detail than I've done and reaches the same conclusion.
Finance & Development, September 2011 - Equality and Efficiency