The conclusion of a study by IMF economists is that inaction politically regarding income inequality is “unlikely to be appropriate in many cases”.  On average the things that governments have typically done to redistribute income do not seem to have led to bad growth outcomes, unless they were extreme. They also conclude that “resulting narrowing of inequality helped support faster and more durable growth, apart from ethical, political, or broader social considerations“. They express caution about “over-interpreting” their results because of the difficulty of bridging from correlations to causations. However, the implication is (if not a causation proof) that inequality damages growth.
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