# Aaron Hedlund on Piketty

He writes me in an email:

I feel comfortable saying that his extensive documentation of inequality– it’s trends, composition, etc.– is a big contribution that should drive future research.

…the thesis that r > g is the explanation for inequality or an ominous predictor of future inequality is, to be blunt, ridiculous.

1) Consider the most basic economic growth model: the Solow model where households arbitrarily follow a constant savings rate rule. In that model, the long-run growth rate equals the rate of technological progress, and the rate of return to capital is constant and completely independent of that growth rate. Therefore, you could have r > g, r = g, or r < g, simply because there is NO relationship. In that model, the capital/output ratio is stable in the long-run, again regardless of what r is relative to g.

We could beef the model up a bit by allowing households to actively choose how much to save (rather than impose a constant savings rate rule on them). In that model, the economy will also get to a point with stable long-term growth where the growth rate is determined purely by technological progress. In that model under log utility, 1 + r = (1 + g)*(1 + rate of time preference). As long as people are at all impatient, the implication is r > g. Therefore, the economy will have r > g, stable growth, and a stable K/Y ratio.

The flaw with both of these models, of course, is that they are representative household models where there is no inequality. Therefore, we can go a step further and add uninsurable risk to the model (whether that be health risk, earnings risk, or any other important source of economic risk). In *these* models, households also engage in precautionary savings, so in equilibrium r is lower than it is in the rep agent models. In fact, the greater amount of risk, the more wealth inequality and the SMALLER the gap between r and g.

2) Another huge fallacy is to translate “r > g” as “the return to capital is greater than the rate of return to labor.” The notion “rate of return” indicates an intertemporal dimension: for example, if I invest \$1, how much do I get back in return a year later? The growth rate of the economy is not the return to labor. In fact, the “return” to labor is static: I give up x units of time in exchange for y dollars.

The RELEVANT comparison would be to compare the rate of return on capital to the rate of return on investing in human capital (ie you go to college and then reap labor market rewards in the future). The rate of return on human capital is most definitely not just “g.” In fact, the college premium is at an all-time high, which suggests that the rate of return on human capital is quite high and very possibly higher than the rate of return on physical capital.

3) The r > g –> inequality thesis is also based on ignoring the fact that r and g are both determined in equilibrium. Here’s what I mean: it is bad economics to say “Look, r > g, therefore IF people behave in such and such manner, their wealth will grow at a higher rate than g indefinitely.” The reason it is bad economics is because you can’t take the “r > g” as given and THEN impose whatever behavioral assumptions you want. The fact is, people’s behavior affects r and g. In the heterogeneous models I mentioned above, r > g, inequality is STABLE, and the behavior of households is determined by their desire to maximize utility. If I were to go to the model and arbitrarily force the households to behave differently, then the equilibrium r would change.