How do wealth–income ratios react to slowing growth in the long run? On Piketty’s second fundamental law of capitalism

Thomas Piketty and some of his coauthors have suggested an economic law named the Second Fundamental Law of Capitalism by Piketty, implying that a long-lasting and considerable growth slowdown will cause substantial increases in wealth–income ratios in the long run. Critics have pointed out that the reaction of wealth–income ratios depends on the reaction of saving/investment rates and, in particular, that sufficiently large decreases in these rates in response to a growth slowdown will revert the direction of Piketty’s law. We conduct a theoretical investigation in a framework that endogenizes the reaction of saving rates in a standard way and find support for a version of Piketty’s Second Law based on an exogenous gross saving rate, but not for Piketty’s original version assuming an exogenous net saving rate. Consequently, the reaction of wealth–income ratios to a substantial growth slowdown will be smaller than suggested by Piketty’s version of the law, but in the same direction and still substantial.