The New Piketty Book and Social Security Privatization

I have not read it, but Tyler is touting it. Apparently, Piketty argues that it is normal for the return on capital to exceed the growth rate of the economy.

I always thought that this was impossible. Ten years ago, I wrote,

If stock prices grow at 7 percent per year while the economy grows at 2 percent per year, then the ratio of stock prices to GDP (P/Y) fifty years from now will be more than ten times what it is today. How could that happen?

If the price-earnings ratio of the stock market (P/E) stays constant, then in order for P/Y to increase tenfold, the ratio of earnings to GDP (E/Y) has to increase tenfold. However, corporate profits are over 10 percent of national output today, so that if the ratio increases by tenfold, then corporate profits will be more than 100 percent of national output. That is impossible.

Alternatively, suppose that the ratio of corporate profits to national output stays constant. Then we need the P/E ratio to increase by tenfold in order to get a tenfold increase in P/Y. So, if the P/E ratio today is about 25, then in fifty years it will be 250. That would require investors to almost ignore risk and the time value of money in valuing stocks. No one believes that this is possible.

Perhaps Piketty has a better grasp on this than I do. But if the return on capital is going to exceed the growth rate of the economy, then this strikes me as powerful argument in favor of privatizing Social Security, so that people don’t get cheated out of these wonderful returns. Again, I have not read the book (it will be released in about 6 weeks). Does he come out in favor of privatizing Social Security? If not, then why not?

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32 Responses to The New Piketty Book and Social Security Privatization

  1. Mathew Halpern says:

    A few potential problems with your reasoning.

    1. The stock market does not represent the entire economy. It is possible the portion of the economy the market represents is particularly profitable. Very few public companies file for bankruptcy every year. Many private companies do.
    2. Inflation. Prices grow 7%, inflation runs 3%, growth runs 2%, then we only need to explain 2% a year. See example 1.

    • Hags says:

      > Prices grow 7%, inflation runs 3%, growth runs 2%

      Your equation is wrong, have to convert nominal growth to real. Using your numbers real growth is -1% and therefor 5% price growth must be explained.

  2. Brent Buckner says:

    You wrote: ” Apparently, Piketty argues that it is normal for the return on capital to exceed the growth rate of the economy.I always thought that this was impossible”

    I think a declining ratio of capital stock to GDP would allow that.

  3. Lupis42 says:

    Is it implausible for stock prices to reflect international earnings not reflect in national GDP?

  4. Yancey Ward says:

    I wonder if this based on indices of stocks like the S&P500. If so, how is the effect of Enron, for example, accounted for? In that case, rather than the S&P counting Enron at zero when it went belly up, it simply replaced Enron with another company not at zero.

    • ed says:

      This type of thing is correctly accounted for in the index.

      When they replace a firm in the index, it is as if an investor sold the stock at the price it was selling at at the time it was replaced. If the price is zero, then the index will reflect the loss.

      If you are really interested, the details of constructing the index are explained in documents available on Standard and Poor’s website.

  5. kebko says:

    If part of the returns are consumed instead of reinvested, it is possible. This has always been estimated with the dividend payout rate. But with the rise of stock buybacks, some of that return of capital now shows up as a capital gain, because of how we account for it.
    To think that returns can’t exceed growth, you’d have to believe there is no equity or risk premium at all. You’d have to believe that stocks with the lowest risk levels would tend to return less than the risk free rate. You’d have to disavow pretty much all of academic finance.

    • ed says:

      Yes, this.

      I tried to explain this to Kling at length in comments to a couple of posts at his old blog, but it seems he never gets it. Kling seems to live in some world where dividends are not part of the return on stocks, or they are always reinvested. It’s very strange.

      (And your point about buybacks is correct as well, of course. On the other side, you have to account for dilution when new firms come into the market. And net buybacks can often be negative, although that hasn’t been the case in most recent years.)

    • F.F. Wiley says:

      Another way to explain this is to imagine a world where the P/E is always 10, the payout ratio is always 1, margins never change and both sales growth and inflation are always 0. (think constant population, no productivity growth and distributions applied to consumption.) The return on equity capital in this world is 10% without any growth. If you add on some productivity growth accruing to capital, you get more than 10%. Long-term returns are based on market pricing (investor preferences), not economic growth.

  6. Lord says:

    In a stationary state, the return on stocks will be twice the growth of the economy with half consumed as dividends (or capital gains liquidation equivalently). His argument is not a stationary one though, but a dynamic one, and the easiest way for the return on capital to exceed the growth of the economy is through the suppression of growth, with both tending towards zero. Good for capital relatively, but bad for both absolutely.

  7. gaspard says:

    This is not a theoretical argument he is making but a very long term historical and empirical one.

    He says something like this in the French version:

    The return greater than growth r > g argument should be regarded as a historical reality (during the hundreds of years when growth was very low, return on capital was always around 4-5%). Things break down somewhat in the 20th century, as so much of the growth is catch up due to wars and demographics, but he thinks the conditions of the 19th century could return as capital concentrates. Remember r here includes all returns on property, land and so on, and so stock dividends rather than prices represent r in this model. Think in terms of the income on Mr Darcy’s estate vs growth in Regency England.

    His stuff on inheritance is very striking too.

    I can’t wait for the anglophone blogosphere to really start discussing this.

    • Alex says:

      In the long run, total returns to all factors of production can’t exceed the total value of production–that’s an identity. So if it’s a “historical fact” that the return to “capital” exceeds the growth rate of “the economy,” then at least one thing is being mismeasured by the historian. My guess is someone is forgetting to account for human capital. And I suspect that the overall pool of human capital is more easily redeployable in seeking high returns than is physical capital. If so, investments in human capital, broadly conceived, are less risky than physical capital investments, hence the latter tends to command higher returns.

      • ed says:

        This is incorrect. “Returns to capital” and “growth rate” are both percentages, not totals. There is no reason the return to capital can’t exceed the growth rate. (I suppose it’s true that “total returns” can’t exceed “total production” in the long run, but that’s a different statement altogether.)

        For example, imagine a static economy with piece of farmland that produced a constant crop every year. The rate of return on the land is the value of the crop (minus the labor and other inputs) divided by the price of the land, while the growth rate could just be zero.

      • TangoMan says:

        total returns to all factors of production can’t exceed the total value of production–that’s an identity.

        Total returns to factors of production is split between Labor Share and Capital Share. The return to capital can grow faster than the economy if the capital share grows at the expense of labor, that is, growing income inequality. Of course there is a limit to how much of an imbalance between labor and capital can arise but who has quantified that limit?

        Piketty’s oddball era is the period from the 1920s to 1970s when he claims that inequality was falling. I wonder if he accounted for the demographic shocks of war casualties and reduced birthrates during the war periods and their immediate aftermath and their immediate and delayed effects on the labor market? Those WWI casualties were horrendously large and I would imagine that there had to have been some measurable scarcity effect in the labor market, thus improving the bargaining power of labor vis a vis capital.

  8. Matt Young says:

    I have no idea what capital is, but I do know this. If some guy makes a product with this thing called capital, and I use that product; then Piketty is saying that the total gain (his gain plus my gain) is less than his gain. That that is impossible. I am still here, I would not be here if I was losing by buying.

    • R Richard Schweitzer says:

      Capital as defined by Piketty is more akin to what is often called wealth. He uses the two terms (“capital” and
      “patrimoine”=wealth) interchangeably (see Chapter 1, p. 84). Regarding land, he rejects the distinction between
      the “original and indestructible productive powers of the soil” and land improvements which alone for some
      should be “capital”. Similarly, he rejects the distinction between wealth used in “unproductive” and “productive” activities (where only the latter would be called capital). Any asset that enables its owner to receive a return,
      including the implicit return on housing, is capital.

  9. My guess is that I’ll be intrigued by his diagnosis, but turned off by his prescription.

    The book will probably be several hundred pages of careful empirical analysis that’ll really make you think followed by several chapters that are filled value injected policy prescriptions that are attached to a certain political bias.

  10. genauer says:

    From the postings above it seems Mr. Kling needs some repitition for this:

    of course the return can be higher than the growth rate and can be paid out as dividends (or buy backs)

    Half a century ago, the so called wiki/Dividend_discount_model was used to assess the “real value” of a company : – )

  11. david says:

    No, no, you misconstrue Piketty’s argument. To translate from long term growth to finance, the core of his model assumes that the investment market is highly actually imperfect – only the rich receive the high R, the poor can only access low R; the difference is large but absorbed by financial intermediaries and the costs of collateral ownership. This is what underlies the wealth/income ratio that Piketty uses to outline the model. Appropriately, the rich save and the poor borrow.

    When you see summaries saying that Piketty’s mechanism assumes perfect capital markets, what they really mean is that more perfect capital markets will increase the degree to which the rich save and the poor borrow in this model (and of course they would! It is logical behavior implied by the segmented market). The more perfect market improves access to the market but not the underlying segmented access to investment opportunities. The rich save even more and the poor dissave even more; thus the rich get richer etc.

    Added to standard workhorse K accumulation long-term-growth assumptions, everything else follows in the model, but the imperfect investment assumption is what is “doing the work”. It drives the inequality result, and it is what implies the bundled assumption that non-capital-owners do not and should not own capital investments, because they are intrinsically poorly placed to do so.

  12. daguix says:

    I have wrote the book. Yes, Piketty says that private pension plans will have better returns than public pensions. But, this is riskier for pensioners and that can raise social issues as some pensioners will lose their pensions. Government will force pension plans to hold a large part in less risky assets.
    So Piketty’s answer is yes in theory. But politically it is not feasible.
    You are forgetting dividends and capital depreciation, life and death of companies in your arguments.

    • daguix says:

      I have read the book. Sorry for the typo.

    • david says:

      What, really? That would seem to contradict the powerpoint by Piketty floating about.

      • david says:

        (seriously, the Piketty line of argument relies on wealth preservation via inheritance, plus some choice of accumulative mechanism to concentrate this wealth. My impression is that his previous work has emphasized credit market imperfections.

        If it’s possible for low-wealth private investment to beat g, then the private/public social insurance fund distinction is irrelevant because governments can just force people to maintain individual savings accounts)

  13. R Richard Schweitzer says:

    I have not read the book, but have the World Bank review of last fall.

    It appears (but is not “defined”) that “Growth” is correlated with GPD, which is generally derived from the consumption functions. However, we may assume (as economists do!) that “Growth” results in some percentage of increase in “Wealth” (the unconsumed portions of GDP), particularly some accretions in durable, transferable assets, some of which are “productive” or substitute for consumption (dwellings, e.g.) values on which no expenditures occur.

    [Capital as defined by Piketty is more akin to what is often called wealth. He uses the two terms (“capital” and“ patrimoine”=wealth) interchangeably (see Chapter 1, p. 84). Regarding land, he rejects the distinction between
    the “original and indestructible productive powers of the soil” and land improvements which alone for some should be “capital”. Similarly, he rejects the distinction between wealth used in “unproductive” and “productive” activities (where only the latter would be called capital). Any asset that enables its owner to receive a return, including the implicit return on housing, is capital.] (from a review of the French Ed.)

    So far, I have not seen a reference to a very simple explanation of the cited “phenomenon” of increasing returns on capital as “Growth” slows. Let’s consider one.

    If there is a substance of economic use and value, a certain “price” will be attained for its possession, or “return” for its use. If more of that substance is being accumulated or accretes from economic activities, particularly if the rates of accumulation and accretion correlate to the rate of the economic activity (“Growth”) and most potential users expect (and can observe) some rate of increase in the availability of the substance in succeeding periods, the price and return for that substance will stay within a range (because there will be more of the substance “coming on stream.”). But, if the sources of the additions to the substance slow down in adding to the availability, and the deployments of the substance continue, those possessing and those desiring the substance will adjust the range in accordance with the expectations of decreasing availability from the slowing of the source – in this case the slowing of “Growth”, which indicates lessening accretions to capital, thus, raising the value of access to what does exist or to what is added.

    Now what this has to do with the fabled “inequality” (Rousseau anyone?) is probably beyond my pay grade (even when I was working).

  14. Steve Sailer says:

    Mexico during the Porfirio Diaz days of 1875-1910 is a good example of the concentration of wealth via debt peonage, even in a growing economy.

  15. Fonzy Shazam says:

    Consider this: You own a factory that produces a product called GDP. This past year the factory produced 100,000 GDPs. The factory employs one worker who is paid 50,000 GDPs per year and one machine that costs 45,000 GDPs per year. Hence, the return on capital last year was 11% (5,000/45,000). This year an improvement to the machine that cost 2,000 GDPs will enable the factory to produce 103,000 GDPs. The worker will still be paid 50,000 GDPs while the total cost of the machine for the year is now 47,000 GDPs. Output has grown 3% (103,000/100,000-1). Return to capital for this year is 12.8% [(103,000-50,000-47,000)/47,000]. Notice also that while labor’s share of output has declined, labor still enjoys the same standard of living. We now have a return to capital and a growth rate in the return to capital that far exceed the growth in output.

  16. Larry Siegel says:

    Most of the comments have been fairly complex, so let’s simplify this. The total return on an equity is the dividend plus the capital gain. For the whole economy, if the P/E is constant and corporate profits as a share of GDP are also constant, then P (the price of stocks) must grow at the GDP growth rate. The dividend is then the equity risk premium (not over bonds or cash, but over a hypothetical asset, sometimes called a trill, delivering the GDP growth rate). Assume furthermore no leverage so the return on capital is the return on equity.

    In practice every variable varies instead of being a constant, but this kind of simplification is the way you begin to work toward an answer. With positive dividends (payout >0), the total return on capital can be higher than the growth rate of the economy. Please see my article here:

    If there were no risk to equity investing, then a completely privatized social security system might work. However, there is plenty of risk to equity investing. A defined benefit retirement plan (such as U.S. Social Security) smooths returns and makes it possible for people of modest means to plan for the future, as long as there is not too much redistribution in the benefit formula.

  17. Jon says:

    Others have said, let me distill it:

    The return on capital can exceed the growth rate forever, the only assumption you need to make this so is that not all return on capital is reinvested. i.e., the ratio of capital and gdp can ve steady–this is mostly what we observe too.

    It may also be true that the propensity to reinvest capital income could be a key driver of RGDP/capita growth. Thus the ratio of capital to gdp may be quite stable and stable gdp growth rates reflect a stable propensity to reinvest.

  18. jon says:

    There are a couple of issues with making this a non-sequitor. First, “privatization” generally implies more than just investing in stocks; it also means tying ones retirement entirely to ones investing savy and a degree of luck and longevity. Social security is one income stream for retired people that does not bear this risk factor, so privatizing it removes the diversification benefit one gets.

    Also the future income available to retirees is already a function of the return on capital. If the return on capital is going to be so great in years to come, the government has some ability to tax the wealth to pay for social security and other government programs.

  19. Paul says:

    The return on equity is the return on private capital, while GDP growth is the value added for the economy as a whole. If the public sector is highly inefficient, then the returns on equity can easily exceed the growth rate of GDP. The larger the public sector, the greater will this effect be (France, perhaps?)

  20. James Oswald says:

    Even in a world with no growth, the return on that stock can be whatever you like, so long as the capital stock doesn’t change. People don’t have to reinvest dividends, necessarily.

    You could have a situation where time preference was 10% per year, an asset which produced an annual payout of $10 forever would be worth $100. The return would be 10% and the annual change in GDP would be 0. Capital stock wouldn’t change because people would, on the margin, be indifferent to expanding it.

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