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acceleration = free acceleration + thrift acceleration. (4.5b) Rates are flows divided by capital expressing them. Then define the two flows as free growth = capital * free acceleration, and (4.8) thrift = capital * thriftacceleration, giving (4.9) growth = free growth + thrift. (4.10) These equations apply equally in continuous or discrete-period time. In the latter, they leave the periods of acceleration and growth unspecified. Marginal or current free growth, as with the speed ofa car, is the sum of free accelerations since some past origin when growth was zero. So it is with current thrift. That need not place the origin with Ancestral Eve. Surprising as it might seem in the growth age, zero points appear to recur every few minutes at the longest. Online stock index numbers reverse direction at least that often. They pass through zero each time. Debt claims on the corporate sector figure to be less volatile, but equity (stock) ones outweigh them. Then marginal free growth means accumulated free acceleration, or rise in rate of return, since the last zero growth point no more than a few minutes ago when return and cash flow were equal. Growth is free whenever cash flow rate rises or holds steady. The Charts and Tables Mill lacked data to test whether growth tends to lead with output when it changes, or to lag with consumption, or something else. So did all economists until national accounts began reporting market-valued capital in 1990 or so, and reconstructing it backward over a few decades before. The equations through (4.7) show how to test from data in the Piketty-Zucman and Global Financial Data websites. First | downloaded the Piketty-Zucman data for market-valued capital and consumption for all countries and periods. | chose their “private wealth” data for the Chapter 4 Mill’s Idea 1/11/16 16 HOUSE_OVERSIGHT_011007