When investment expenditure takes place, the economic measure of the cost of investment is resources foregone, which we measure in the national income accounts as the real value (units of real GDP) of investment expenditure. Then, for example, if there is one unit of investment expenditure, in units of real GDP today, and that unit of investment expenditure becomes usable capital in the future and yields to the owner of the capital a payoff of r in units of real GDP, net of depreciation, we would say that the capital has a rate of return r and, if we've measured depreciation properly, we know how many units of capital we have left, in units of real GDP.
So, note that in defining the rate of return on capital, we don't have to think about market interest rates, discounting, or how the investment is financed. Those things are relevant for the investment decision, but not for calculating the rate of return on investment, or for determining the economic cost of investment. This is just accounting - not corporate finance.
In the 2011 paper by Gomme et al., the idea is to measure average r at a point in time. In this chart, from their Economic Synopsis, they show us before-tax and after tax rates of return on all capital, and on business capital:
Note that the Gomme et al. measure is net of depreciation. On page 2-9 of the BEA manual the BEA shows us how they calculate gross domestic income. The profits measure is net of depreciation, and then the BEA adds depreciation back in to get gross domestic income (that's what "gross" means - GDP and GDI do not net out depreciation). So the Gomme et al. rate of return is not too high because they fail to net out depreciation.
Another complaint (from Waldmann) relates to the fact that, for investment decisions, what we care about is capital's marginal rate of return, not average. Of course, if the production function is Cobb-Douglass, then the marginal product of capital is proportional to the average product of capital, so in that case it does not make any difference whether we're looking at average or marginal. By continuity, anything close to Cobb-Douglass will work as well. In any case, it's hard to imagine why the average return on existing capital would increase as observed without a commensurate increase in the marginal product of capital, or why investment would have increased as it did post-recession unless the marginal product of capital had increased in line with average product.
The main thrust of the Economic Synopsis related to "secular stagnation." Larry Summers holds the view that investment expenditures are stagnant because the rate of return on capital is low. Gomme et al. say that no, as measured, the rate of return on capital is not low and, by the way, investment does not appear to be stagnating. "Stagnation" seems an odd characterization given the data, as Gomme et al. point out. That's not saying that the behavior of of investment is not somehow puzzling, i.e. that we don't have to work hard to explain how it is behaving. Just to repeat, here are Figures 3 and 4 from Gomme et al., which certainly don't look like stagnation in investment spending:
In his post, Noah Smith does in fact express puzzlement that the rates of return in the first chart above are so high currently, while the corporate bond rate is so low. That is, he thinks that investment should be even higher than it is, given those observations, which leads him to conclude:
I suspect that either 1) Gomme et al. have measured the return on capital incorrectly, or 2) basic corporate finance theory doesn't capture what's going on in our economy, or 3) both.If the recent behavior of investment puzzles Noah, he should also be puzzled as to why there was an investment boom in the 1990s when corporate bonds rates were so high. And if he's worried about the measurement that Gomme et al. report, he should take that up with the Bureau of Economic Analysis.