Sunday, August 23, 2015

Gomme, Ravikumar, and Rupert on the Rate of Return to Capital

Paul Gomme, Ravikumar, and Peter Rupert would like to respond to comments on their 2011 RED paper, and St. Louis Fed Economic Synopsis, in blog posts by Noah Smith and Robert Waldmann. Here, I've put in my own words the results of some email conversations with them.

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:
For those calcuations, Gomme et al. work with the measurements the Bureau of Economic Analysis (our national income accountants) provide. In particular, from the flow national income accounts - income side - they take the flow income that can be attributed as factor payments to the owners of the relevant component of the capital stock, then divide by the relevant capital stock, which is also measured by the BEA. So, that is an average rate of return on capital, net of depreciation, measured as a ratio of income (in units of real GDP) to capital (in units of real GDP).

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.

6 comments:

  1. "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."

    Well there must be a measurement problem here. Someone may be able to translate this into economics. But in financial analysis what is happening is this.

    Companies are portfolios of old and new projects. The old ones were made at high yields. Yields on new ones went to near zero post crisis, and the available size sank. Smart managers began maintaining their old ones to extend their lives and reduce other expense. Parsing out the numbers, it appears new projects offer near 6% on average.

    I'm not in position to know, but it seems possible that the pickup is investment spending you cite is more like maintenance on tech investments with short lives.

    If the world had investment returns and volume you cite, we would be having lots of growth.

    So there must be a measurement problem.

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    1. "If the world had investment returns and volume you cite, we would be having lots of growth."

      What would be "lots?" You can see in the charts that investment is indeed growing. It should be growing at a higher rate? Based on what evidence?

      "So there must be a measurement problem."

      So what is it? This is just direct measurement from the BEA, our national income accountants. You're claiming they must not have done it right? What you're offering is casual evidence. You need to worker harder - give me some science.

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  2. Well, your and wiki's ROIs are off base way to the high side. Let's just let it lie there.

    Remember, this marginal vs average problem is just not addressed by nearly everyone. I suggest this is a good place for you to look because if there were the ROIs you claim, nominal GDP growth would be quite significantly higher, and bond yields, too.

    ReplyDelete
    Replies
    1. "off base way to the high side."

      Off what base? To the high side of what?

      "Remember, this marginal vs average problem is just not addressed by nearly everyone."

      No, I addressed that above.

      You haven't told me what your evidence is. Is this based on talking to a ouija board, or what?

      Delete
  3. I'm sorry, the wiki mention was unrelated.

    ReplyDelete
    Replies
    1. Yes, I'm not sure what you meant. I guess if the facts don't fit your view of the world you can try to argue with the facts. In this case, I don't see how you can.

      Delete