How much capital is enough?
People often criticise economists for assuming that if they can’t measure something, it doesn’t exist. Nothing could be further from the truth. In fact, one of the biggest rackets in economics is taking something which doesn’t exist and measuring it anyway. Let me explain …
When we play economics, one of the things we’re often interested in is production, because it’s an important subject. In the simplest possible model of production, you have three inputs:
- Labour (if you’re an American, this is spelt “entrepreneurship”)
So the first thing to do when you’re trying to say something clever about production in an economy is to measure the available inputs of land (in units of one acre), of labour (in units of one person, or if you’re a pinko like Maxspeak’s Tom “Sandwichman” Walker, one person/hour) and of capital (in units of ….. what?)
What is the unit of capital? It doesn’t come in more or less homogeneous chunks; it comes in all different types and there is no obvious way of squaring off a blast furnace against a computer controlled lathe. You can’t sensibly compare capital by its wattage, by the precision of its engineering, or whatever. You could in principle reduce the inputs of capital to labour by assuming that each piece of capital represented “frozen labour time”, but that leads down a path that we don’t want to go down right at this precise second. So what do you do?
My American readers will be asking two questions at this point:
- What the fuck is “Labour”?
- Why can’t you just measure capital in DOLLARS?
The second of these is quite a subtle question, and was the result of spilling a whole lot of ink and beer (perhaps blood, I dunno) in the 1970s in something called the Cambridge Capital Controversy. Basically an academic fight between Keynesian/NeoRicardian lefties at Cambridge UK and neoclassical hardnosed types at MIT. The Yanks won the fight because of their greater derring-do and vigour, but the Brits were actually right, is my summary of the issue (Joel Stiglitz disagrees, as is his right). But it left us with this argument about why you can’t measure the capital stock in dollars.
Basically, how many dollars?
Well, the market price of the machine.
But what determines the price of the machine?
Well, the amount of stuff it can produce over its useful life.
But we don’t want to know the value of the machine “over its useful life”, we want to know today!
So, project how much stuff it can produce, assume the price it will sell at and discount those cash flows back to today (discounting is an application of compound interest, to give less weight to cash flows further in the future).
OK laughing boy, what interest rate do we use to discount the cash flows?
Well, why not choose the current market rate, doofus? (I’m adding a few mild insults to give you the acrimonious flavour of the controversy as it happened)
Well, OK, but what determines the market rate of interest?
Two things; a factor which reflects “impatience”, the reward you have to pay people for delaying their consumption, a factor which reflects risk aversion (because anything could happen in the time the money is out on loan) and another factor which is the reward you have to pay people for having their money tied up in a loan to you, rather than putting it to productive use.
What determines the third factor?
Well, the “productivity of capital”.
And what’s the “productivity of capital”, when it’s at home?
Well, it’s the amount of stuff that the average unit of capital can produce, divided by … the average cost … of a unit of capital
So how, my dear chap, are we going to work out what that is, given that the whole point of the exercise is to find an acceptable unit of capital to use????
“Oh dear, I hadn’t thought of that”
(NB for economic historians: up to a reasonable paraphrase, this is what Paul Samuelson actually said, to his credit).
So there we have it. Obviously, this doesn’t stop people from measuring the capital stock in dollars, nor indeed from measuring “productivity” numbers based on it. But it does give a pretty powerful argument that this aggregate dollar number, constructed by taking historical costs, assuming depreciation rates and adjusting for inflation, does not actually describe a particularly meaningful economic quantity. For example, if we were to say, oh I don’t know, maybe that the risk aversion component of the rate at which people discount future returns might have risen, say as a result of people becoming nervous after a load of corporate scandals, then that would be equivalent to a massive revaluation of the capital stock which would never show up in the estimated numbers. It’s a real problem, and perhaps a minor scandal of academic economics that undergraduates are still taught about aggregated measures of capital as if they were totally unproblematic. Geoff Harcourt describes the state of neoclassical economic theory on this basis as “is an uneasy state of rest, under the foundations of which a time bomb is ticking away, planted by a small, powerless group of economists who are either ageing or dead�
Still, not to worry. It’s not as if anything important turns on such trivial academic curiosa