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either grows while the other declines, the index is zero or less; zero if one grew as much as the other declined, and less if the change in capital growth rate was larger than the opposite one in consumption rate. Interpreting the Charts and Tables Now look again at the charts captioned “free growth index” in the appendix. I will summarize them and all other charts and tables only briefly here, and save most description for there. They cover all eight countries. Each chart covering free growth tracks three separate versions of the free growth index labeled @(K), @(K,,) and ~p(SM). The one I have discussed so far is g(K). @(K,,) is a version including human capital, and @(SM)is taken from stock markets only. @(K,,) will be explained in the next chapter. The powerful spikes both up and down in the free growth charts were described in Chapter 2. Spikes tend to be explained by the fact that acceleration, the denominator in both the free growth and the thrift index, is occasionally close to zero. Near-zero denominators, whether above zero or below, can magnify mismeasurements. Some charts report the free growth index every year, and show all the spikes. Others filter out years where denominators fall below a chosen threshold, and spikes disappear accordingly. Filtration is unbiased in that free growth index is corrected down as often as up. What jumps out from all those charts is that all versions of the free growth index @ fluctuate around one. That means that the unshown thrift index fluctuates around zero. We just saw that the thrift index will show as negative whenever the thrift numerator and acceleration denominator disagree in sign, meaning that thrift gain coincided with deceleration (negative acceleration) or conversely. Charts and tables show that thrift gain, meaning drop in consumption rate, coincides as often witha lower as a higher capital growth rate. Growth by thrift is a theoretical possibility Chapter 4 Mill’s Idea 1/11/16 18 HOUSE_OVERSIGHT_011009