Spreadsheeting r>g

01/05/2014 § 3 Comments

Thomas Piketty’s book, Capital in the 21st Century, has been getting press, some favourable, some lukewarm, some critical. There’s even a bluffer’s guide (bonjour paresse!).

I haven’t read it, but that won’t stop me commenting. Specifically, the little shorthand ‘r>g’ making the rounds had me thinking. Unfortunately, my thought is also the first entry in the bluffer’s guide: the thesis isn’t new. This is the tendency for the rate of profit to fall, by some 19th century economist, dressed up a different way. It’s also something my actuary/economist dad pointed out to me years ago — that stock market returns couldn’t keep outpacing economic growth forever. And something that can’t go on forever, won’t.

But it isn’t real until you can put it in a spreadsheet. So, I tried. My first attempt failed because ‘r>g’ isn’t enough by itself.

So, I tried again, this time including a marginal propensity to save, which you need in order to determine how much income gets converted into wealth. It turns out to make for interesting calculations.

Here’s one example. Start with GDP = 100, divided 60/40 into wages and rents. Assume g = 0.02 and r = 0.08. With the amount and rate of rent, you can calculate initial capital (K), which is here 40/0.08 = 500.

GDP Wealth
g= r= MPS_L= MPS_K=
0.02 0.08 0.1 0.8
Year total wages rent savings, L savings, K Final K
1 100 60 40 6 32 532
2 102 59 43 6 34 566
3 104 59 45 6 36 602
4 106 58 48 6 39 641
5 108 57 51 6 41 682

What happens in the second period depends on what happens to rents. If they are entirely consumed by dissolute third-generation scions, then they don’t add to the stock of capital. So period 2 depends on the marginal propensity to save, which here I’ve assumed is 0.8 (80%). Final K is higher than the initial K, and the amount of rents increases. The result over many periods is the following:


The picture, though, is sensitive to the assumptions. Assume g = 0.03, r = 0.08, and MPS_K = 0.4, and here is the 100-year picture:


It turns out that the results depend on initial allocations, relative rates of returns, and savings rates. Crucially, too, I haven’t actually created a stock of K wealth that is owned by the initial L. I created the category in the spreadsheet, but then didn’t use it. If labour starts owning bits of capital, well, either that’s employee-owned companies or control of the means of production by the proletariat — I’ll let you make the call.

It seems that the problem is prying rents out of the hands of capital-owners, rather than the rate of rent itself. One way, of course, is taxes. A 50% estate tax looks like a useful way to get MPS_K from 0.8 to 0.4, for example. And dissolute grandchildren should also be encouraged.

Happy May Day!


Socially constructed profits

20/06/2013 § 2 Comments

Paul Krugman made a point on his blog yesterday that really struck me:

profits are no longer anything remotely resembling a “natural” aspect of the economy; they’re very much an artifact of antitrust policy or the lack thereof, intellectual property policy, etc.

This is something I’ve seen suggested or hinted at or mentioned in a round-about way, but Krugman made a bold, succinct statement of the issue. Profits — returns to capital — are whatever we decide they are through the legislative choices we make. Profits are socially and politically determined.

Some background: I still think the Cambridge capital controversy is an unsolved conundrum. It isn’t the simplification that bothers me — the aggregation of unlike things into the single lump of Capital. It’s a model of the economy; models simplify. No, I worry about the circularity, that the value of capital is determined by its rate of return, which is a function of the value of capital. Try programming that in Excel.

Also, JK Galbraith described an interesting dynamic in, um, The New Industrial State? Managerial capitalism was administered by managers in large corporations who were managing demand for end products and managing returns to factors of production — labour, management, and shareholders. The point was that the industrial state at the time was a partially-managed economy. Returns to the factors of production were not ‘natural’, but decided in C-suites and boardrooms.

I guess I’m putting Krugman’s observation in an historical context: some economists have been arguing for a while that profit is (at least somewhat) socially determined, rather than a function of scarcity and markets. It’s become really obvious in a case like Disney or Apple, which then explains some amount of rent-seeking in the form of political activity, rather than producing stuff consumers want.

Minor point: If I search the New Palgrave Dictionary of Economics for ‘cambridge capital controversy’, I get:

Your search for ““cambridge capital controversy”” over the entire article content within the 2008, 2009, 2010, 2011, 2012 and 2013 editions returned no results.

And yet, Wikipedia knows exactly what I’m talking about.

How do we teach this?

15/02/2013 § 10 Comments

Reading through the post-mortems of the financial crisis, I’ve been struck by something. The behaviour of the finance sector doesn’t fit the standard economics model, the Samuelson textbook depiction, or the Heckscher–Ohlin model of trade, or the Solow model, or any of the other bog-standard depictions of the economic system that we like to teach.

A key idea is that capital is a factor of production, like labour, land, and maybe entrepreneurship, management, natural resources, human capital, or any of the other factors people like to add. Two things about this capital:

  • capital gets a return for its use, which accrues to the owner of said capital, and
  • owners (capitalists, entrepreneurs, whatever) receive a return commensurate with the risk they take: higher returns are required to entice people to take greater risks (and thereby promote innovation).

But, but, but…that’s not what’s happened.

If you read the accounts of the financial crisis, two things are clear:

1. The people administering the mortgage-backed securities (MBSs) are having a hard time proving they own the mortgaged they say they do. To quote Adam Levitin:

The mortgage foreclosure process is beset by a variety of problems.  These range from procedural defects (including, but not limited to robosigning) to outright counterfeiting of documents to questions about the validity of private-label mortgage securitizations that could mean that these mortgage-backed securities are not actually backed by any mortgages whatsoever.  While the extent of these problems is unknown at present, the evidence is mounting that it is not limited to one-off cases, but that there may be pervasive defects throughout the foreclosure and securitization processes.

That is, these folks aren’t sure of what they own, and yet they are selling derivatives based on what they think they might have. More frighteningly, banks are taking or selling houses they don’t own.

2. Risk and reward are now de-coupled. Companies in the finance sector took gambles on the housing market, and things didn’t go their way. That happens. An evolutionary account of the market economy is that success should be rewarded and failure should lead to extinction. AIG, just to name one company, took massive risk onto its books by insuring the value of MBSs. Their clients claimed against the policies, which was going to drive AIG into bankruptcy. AIG got bailed out, as did a number of other financial firms. So, for finance firms, success is rewarded but so was failure.

Thomas Baxter, Jr., New York Fed:

In the months leading up to early November 2008, AIG had been actively engaged in efforts to negotiate tear-ups of its CDS contracts with its counterparties. AIG was completely unsuccessful. The need for the tear-ups was real; AIG was effectively hemorrhaging cash.

But what happened? Wall Street posted record profits in 2009 and had its fourth-most-profitable year in 2010, after it ‘benefited from a series of federal bailouts as well as low interest rates’.

Why aren’t more economists having a crisis of faith? The story and the models that we use to talk about the economy appear flawed in a fundamental way. It isn’t about innovation and efficiency, the supply side responding to signals from the demand side. Instead, fraud, crime, and collusion seem to be the path to riches.

Thoughts on the rate of return on capital

20/08/2012 § 2 Comments

I’ve found myself wondering what the average rate of return on capital really is. Some of the numbers that get tossed around are an 8% average stock market return over the long term, a 15% to 20% risky rate of return for capital invested in a business, and an 8% to 10% rate of return for business generally (which is the basis for the country’s discount rate).

When I look at specific examples, though, that’s not what I see. Just for starters, the S&P 500 still hasn’t moved past its intraday high in 2000, over 12 years ago. Maybe a dollar-cost-averaging strategy would have helped, but this guy did the maths and found merely that it just reduced the losses. Residential real estate, a common Kiwi investment, depends on capital gains, as it is generally cash negative. When I look at businesses’ financial statements, many small businesses are just paying the equivalent of a wage to their owners. Of course, that calculation doesn’t even include the businesses that go bankrupt and produce a negative return.

And then think about infrastructure spending. Railroads, for example, were built with enormous sums of borrowed money, and then defaulted on a significant percentage of the loans. Proposed roads have low benefit-cost ratios — less than one in some cases. There are questions, too, about the gains from ultra-fast broadband.

This may just be the standard economic problem of making micro and macro pictures consistent. At the micro level, some investments do poorly, some businesses go under, and some time periods show weak returns. At the macro level, though, there is a clear trend.

The other thing it may show — other than my continued obsession with why things go wrong — is that good returns are not ‘normal’ and we shouldn’t expect them to be. Someone has to make 20% or 50% returns along the way, just to keep the averages up. If someone does it year after year, well, that’s pretty special. The rest of us chumps might have to settle for passbook rates.

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