‘Mathiness’ in economics
from Lars Syll
In practice, what math does is let macro-economists locate the FWUTVs [facts with unknown truth values] farther away from the discussion of identification … Relying on a micro-foundation lets an author say, “Assume A, assume B, … blah blah blah … And so we have proven that P is true. Then the model is identified.” …
Distributional assumptions about error terms are a good place to bury things because hardly anyone pays attention to them. Moreover, if a critic does see that this is the identifying assumption, how can she win an argument about the true expected value the level of aether? If the author can make up an imaginary variable, “because I say so” seems like a pretty convincing answer to any question about its properties.
Yes, indeed, modern mainstream economics — and especially its mathematical-statistical operationalization in the form of econometrics — fails miserably over and over again. ‘Modern’ mainstream economics is based on the belief that deductive-axiomatic modelling is a sufficient guide to truth. That belief is, however, totally unfounded as long as no proofs are supplied for us to believe in the assumptions on which the model-based deductions and conclusions build. ‘Mathiness’ masquerading as science is often used by mainstream economists to hide the problematic character of the assumptions used in their theories and models. But — without showing the model assumptions to be realistic and relevant, that kind of economics indeed, as Romer puts it, produces nothing but “blah blah blah.”
The belief that mathematical reasoning is more rigorous and precise than verbal reasoning, which is thought to be susceptible to vagueness and ambiguity, is pervasive in economics. In a celebrated attack on … Paul Krugman, the Chicago economist John Cochrane wrote, ‘Math in economics serves to keep the logic straight, to make sure that the “then” really does follow the “if,” which it so frequently does not if you just write prose.’ But there is a difficulty here which appears to be much more serious in economics than it is in natural sciences: that of relating variables which are written down and manipulated in mathematical models to things that can be identified and measured in the real world … Concepts such as ‘investment specific technology shocks’ and ‘wage markup’ which are no more observable, or well defined, than toves or borogoves. They exist only within the model, which is rigorous only in the same sense as ‘Jabberwocky’ is rigorous; the meaning of each term is defined by the author, and the logic of the argument follows tautologically from these definitions.
Without strong evidence, all kinds of absurd claims and nonsense may pretend to be science. Using math can never be a substitute for thinking. Or as Romer has it in his showdown with ‘post-real’ economics:
Math cannot establish the truth value of a fact. Never has. Never will.
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Real-World Economics Review Blog 
Let’s say I agree with all of the above. Now let’s address an economic problem. Currently there is a lot of concern, possibly justified, possibly not, about the scale of government debt. So how do you value government debt? People tell me it now amounts to nearly 100 per cent of annual GDP in the UK and that obviously worries them. They are afraid such big numbers mean the government may find it hard to borrow in future except at very high interest rates and will be forced to cut spending to prevent inflation. (Yes it can always tax but bond-buyers know there are usually political limits to tax rates). You can point out that inflation is not an immediate concern and that Japan has had no problem placing its bonds despite much higher debt ratios but the newspapers are not reassured and the government is freezing public sector wages.
So let’s try a forward-looking view. The debt has a duration of at least 15 years in the UK and so the roll-over will take place way in the future. If inflation runs at 2 per cent on average the real value of the debt will be nearly a third lower when it has to be refinanced. Not 100 per cent of GDP then but 75 per cent… Ah, but who can predict the inflation rate?
Not me, so try another tack. Over a quarter of the debt is held by the central bank. Why should we count that? Ah, say the economists, because the counterpart of the debt at the central bank is the increase in base money – commercial bank reserves – created when the central bank bought government bonds. And the central bank has to pay interest on those reserves if it is to control commercial bank lending and manage the growth of credit. The government debt has not been abolished but its term structure has been altered – bank reserves instead of bonds. Of course if inflation and credit demand are both low the central bank does not need to pay interest on those bank reserves (they currently pay 0.1 per cent in the UK). The present value of future central bank interest payments could be a lot lower than the nominal value of the bonds they hold. But how can we know what money-market interest rates will be over the next 15 years? Well we can’t. It follows we cannot value government debt properly because the future is uncertain.
But can we do a bit better than just wring our hands? Interest time-series are non-ergodic but they don’t have infinite variance. Interest rates are currently effectively zero, five per cent is more common historically, 20 per cent is not unknown but 100 per cent is vanishingly unusual. So I can model that time series as a near-random walk using its historic variance and run 10,000 stochastic simulations. I can’t forecast but I can provide scenarios – high, middle and low. I can use them to put bounds on the how we ought to value the debt. Come to think of it I could do the same for inflation. Now, let’s face it, the exercise might turn out to be wholly uninformative. But what if the bulk of the scenarios indicate that people taking the debt at face value are over-estimating it? Then we have injected some knowledge of a probabilistic kind into the discussion. Note that the exercise is not rocket science but it requires a basic knowledge of monetary institutions and accounting and a some fairly basic statistics.
We are doing little more than any business investor does when she estimates sales of a product and invests to meet the hypothesized demand. She cannot know the future but we she knows her sales will be less than the GDP of China and, with luck, more than zero. Using available information she can probably narrow it more than that. Her alternative is not to invest.
What does Lars think about all this? Should we not bother? Should we rest on methodological purity? Should we fear the hubris of the modellers more than we appreciate any insight they can offer? Yes it’s all terrible but what should we DO?
“Yes it’s all terrible but what should we DO?”
Stop believing that government debt other than its under-performed duties exists, and calculate environmentally affordable credit rations and prices using Fullbrook’s metric rather than the totally illogical GDP. Get our heads round “math” being about methods of learning, not content, and go back to the old method of “geometry”, measuring the real earth. As Herbert Simon advised us, be satisfied with enough.
Economics may be ripe for its own Galileo and others, to move beyond the Aristotelian deductivist approach. Expanding views seemed to work for the rest of the world several hundred years ago.
This is worthy of comment. Can I suggest that the problem is not in deduction as a logic? (What is true of a set is true also of subsets and members of the sets, though it may be less than we are accustomed to think). Aristotle’s problem was that he had to choose his axioms from what he could see, whereas since Francis Bacon, science (taking things to bits and using instruments like telescopes and microscopes, x-rays, information processing and retroductive logic) has become able to see what it previously couldn’t. Axioms can therefore become more fundamental, though in an economics seeking cook-book recipes they haven’t.
Tell your pension fund that government debt doesn’t exist Dave. I bet they’re holding a stack of it. I didn’t dream that the UK chancellor froze public sector wages. He thinks the debt exists too. But I see the effort to get people to think about real issues might not succeed.
A stack of nothing is nothing. The fact that believe that money is valuable doesn’t make it so. What is valuable is the extent to which the world can renew its own life support system and we can trust each other to share and care for it.
Correction. The fact that we have been taught to believe that money is valuable doesn’t make it so.
Are we mixing up prescriptive analysis and descriptive analysis here? The world isn’t a conscious organism so far as we know. In the actual economy people’s claim on the output of the system depends on their holdings of money and other marketable assets. One such asset is government debt. We might well wish the world was different but meanwhile the pensioners’ income is being determined by those debt holdings and the government’s policy is being shaped (wrongly in my view) by their perception of that debt. A more accurate estimate of the transfer obligation the debt represents may improve policy. It won’t solve the ecological crisis or a host of other things. Not all problems can be tackled at once.
“Are we mixing up prescriptive analysis and descriptive analysis here?”
You may be, but I’m not. I am asserting what Werner’s evidence (among other things) shows, you are accepting a dishonest and anachronistic prescription because most people still do. Ontology vs epistemology. You are still pre-Copernican, seeing debt as an asset: the mirror image of the reality. Rather sad how you wordy academics cannot see the reality.
I am accepting an institutional reality. There is not much point in denying reality even if we disapprove of it. I am not accepting any prescription. My aim is to contest the prescription by showing it is inappropriate even on its own terms. People respond better when you speak a language they understand.
in relation to government i think we have to return to Bretton woods use3 of nations having sovereign money where they can stimulate their economy without becoming under of foreign currency ted
the above should read in relation to government debt
“People respond better when you speak a language they understand”.
This is a bit belated, but thanks, Ted, for stirring it up again. I’m sorry, Gerald, but what is sauce for the goose is sauce for the gander. I don’t understand how you can say what you do: how you can contest a prescription – what is written beforehand, an interpretation of reality – while continuing to treat it as if it were the reality. There is a lot of point in denying and refusing to act on lies (or even innocent misrepresentations). Despite what most people think, their fear-inducing money debts are not real, and real gifts (credits) are repaid with gratitude, on-going care and mutual happiness: the way to achieve J S Mill’s utilitarianism and the solvency of Dickens’ Mr McCawber. Even if things are going that way, have trees already ceased to exist because the reality now includes too many ungrateful humans?