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There is no careful analysis. The graphs have basically 3 features: high inequality until the great depression, then low inequality, then inequality rises again

There is no careful analysis. The graphs have basically 3 features: high inequality until the great depression, then low inequality, then inequality rises again. He doesn't have much in the way of graphs of r-g. Rather than explaining why you need more than just a correlation, I'll link to the Lucas Critique: http://en.wikipedia.org/wiki/Lucas_critique http://en.wikipedia.org/wiki/Lucas_critique Finally, could you just explain this a bit more Not sure I can explain better than the comment I linked to. If your capital and mine grow at the same rate, we'll have the same ratio of capital forever. I.e., my wealth will be X exp(rt), yours will be Y exp(rt). This seems to be Piketty's implicit model in most of the book, though once or twice he calls it unrealistic. But he never actually states explicitly what his model is, so it's a bit hard for me to be sure.

mrow84 13y ago
I hadn't heard of the Lucas Critique before, but it seems to be constrained to policy advice that operates on economic variables over which market actors have control, and I'm not sure that applies here - I'll have to think some more. > Not sure I can explain better than the comment I linked to. ... Thanks for the clarification, I'm not feeling very switched on at the moment. I would question your analysis though. It is certainly correct on its own terms, however it conflates wealth with capital (which is something I've seen people saying Piketty does - does he?). To me it seems to be vital to include both major sources of income, capital and labour. If you do that, then you can calculate the quantity (Xl exp(gt) + Xc exp(rt)) / ((Xl + Yl) exp(gt) + (Xc + Yc) exp(rt)) Where Xl and Yl are the labour "holding" for X and Y, and Xc and Yc are the capital holding. Here I'm taking r as the return on capital, and g as the return on labour, which seems abusive but I think it captures the point. This quantity tends to the capital ratio where r > g, and the labour ratio where r < g. Whilst it ends up at the same limit as your model (for r > g), it shows that there is a shift of wealth from labour to capital over time, so the inequality between capital holders and labour "holders" increases over time, as the returns on labour are dominated by the returns on capital. edit: Just thinking about it a bit more, this implies that we definitely do want g > r, because then in the limit wealth is proportional to labour, i.e. productivity, not to capital bequeathment. One can still make returns on capital, but in the limit your wealth will be proportional to your effort. Surely that is the goal of a meritocratic society? edit edit: To clarify, I have broader views on the value of pure meritocracy, in my first edit I was just trying to relate the implications of the wealth ratio given above to meritocratic goals.
- yummyfajitas 13y ago
  The Lucas Critique basically just says that if you want to use broad correlations, you should make sure that the microfoundations which drive those correlations still apply. Unfortunately the relation of r to g tells us very little about meritocratic goals. Suppose that the growth rate r is driven entirely by startup founders building gigantic companies (or lotteries, which would be mathematically equivalent), which cease growing after the founder dies. Then you could have r be huge, inequality would be huge, and everything would be entirely meritocratic.
  - mrow84 13y ago
    I think that the quantity I offered suggests why there might be a correlation between inequality growth and (r - g), independent of the mechanisms that underlie the returns on capital and labour, and inequality. In words, when r > g, the income distribution tends towards the capital distribution, and when r < g the income distribution tends towards the labour distribution. The relationship between this point and meritocracy is that average returns on capital are approximately "unearned" - you can get close to the market rate of return with minimal effort, whereas returns on labour are positively earned, by your labour. So when r < g the limiting case is for income to match labour, i.e. effort. Note that this by no means inhibits the possibility of greater returns to intelligent capital investment (something that you definitely want to keep) - the point is that you control average returns to stop capital domination fostering inequality.

mrow84 13y ago

I hadn't heard of the Lucas Critique before, but it seems to be constrained to policy advice that operates on economic variables over which market actors have control, and I'm not sure that applies here - I'll have to think some more. > Not sure I can explain better than the comment I linked to. ... Thanks for the clarification, I'm not feeling very switched on at the moment. I would question your analysis though. It is certainly correct on its own terms, however it conflates wealth with capital (which is something I've seen people saying Piketty does - does he?). To me it seems to be vital to include both major sources of income, capital and labour. If you do that, then you can calculate the quantity (Xl exp(gt) + Xc exp(rt)) / ((Xl + Yl) exp(gt) + (Xc + Yc) exp(rt)) Where Xl and Yl are the labour "holding" for X and Y, and Xc and Yc are the capital holding. Here I'm taking r as the return on capital, and g as the return on labour, which seems abusive but I think it captures the point. This quantity tends to the capital ratio where r > g, and the labour ratio where r < g. Whilst it ends up at the same limit as your model (for r > g), it shows that there is a shift of wealth from labour to capital over time, so the inequality between capital holders and labour "holders" increases over time, as the returns on labour are dominated by the returns on capital. edit: Just thinking about it a bit more, this implies that we definitely do want g > r, because then in the limit wealth is proportional to labour, i.e. productivity, not to capital bequeathment. One can still make returns on capital, but in the limit your wealth will be proportional to your effort. Surely that is the goal of a meritocratic society? edit edit: To clarify, I have broader views on the value of pure meritocracy, in my first edit I was just trying to relate the implications of the wealth ratio given above to meritocratic goals.

yummyfajitas 13y ago
The Lucas Critique basically just says that if you want to use broad correlations, you should make sure that the microfoundations which drive those correlations still apply. Unfortunately the relation of r to g tells us very little about meritocratic goals. Suppose that the growth rate r is driven entirely by startup founders building gigantic companies (or lotteries, which would be mathematically equivalent), which cease growing after the founder dies. Then you could have r be huge, inequality would be huge, and everything would be entirely meritocratic.
- mrow84 13y ago
  I think that the quantity I offered suggests why there might be a correlation between inequality growth and (r - g), independent of the mechanisms that underlie the returns on capital and labour, and inequality. In words, when r > g, the income distribution tends towards the capital distribution, and when r < g the income distribution tends towards the labour distribution. The relationship between this point and meritocracy is that average returns on capital are approximately "unearned" - you can get close to the market rate of return with minimal effort, whereas returns on labour are positively earned, by your labour. So when r < g the limiting case is for income to match labour, i.e. effort. Note that this by no means inhibits the possibility of greater returns to intelligent capital investment (something that you definitely want to keep) - the point is that you control average returns to stop capital domination fostering inequality.