Banging My Head Against Linear Economics

As I’ve written elsewhere recently, banging your head against a wall is a hobby which has probably got a bad rep as a sort of shorthand for the acme of pointlessness. After all, you strengthen your head and neck by doing so, and a well-placed headbutt can be a fearsome weapon (for the interested, here’s a guide). And sometimes the wall breaks, which is cool … However, repeatedly smacking your head against a brick wall is not a recommended method of conditioning for any school of martial arts of which I am aware, and, although I will stand up for the intellectual equivalent, anything which makes you want to physically beat yourself unconscious is most likely to be avoided.

All of which pointless rambling is meant to a) demonstrate that this weblog jumped the shark weeks ago, and b) introduce a few comments on an idea of Jason McCullough’s that I’ve been meaning to put down for a while.

Jason runs the perfectly fine weblog “Hronkomatic”, which would be in my link list if I could be bothered maintaining one. It’s in the MaxSpeak list, so you’re only two clicks away from it (by the way, here’s the new linking policy; if Sawicky links to you, I don’t need to, and if he doesn’t, I probably don’t want to. I’m sure this is massively unfair; special cases can make their plea in the comments section or something). In order to save you the pain of trying to get to grips with his archives, I’ve reproduced the post below:

Thursday, September 26, 2002

I’ve been seriously considering the half-assed suggestion I made a while back to completely eliminate taxes and fund the government entirely through bonds. The obvious problems with this are issues of cost distribution (would the poor necessarily end up paying more than the rich under an all-bond system, though?), effects on the net level of investment, and the tendency of this system to east the constraints on government spending (which is a good thing or a bad thing, depending on your bent). So, here’s an estimate of how it’d change investment.

According to this, the MPC for the U.S. is about .85. The change in consumption by entirely eliminating taxes should, therefore, be MPC * G while the change in investment is (1-MPC) * G – G = -MPC * G. Investment would drop by 177 billion, or 20%. Unfortunately, I’m using the APC here to estimate the MPC, because I can’t find an estimate of the MPC for the life of me. You’d assume it should be lower than the APC, though.

Is there someway for the government to incentivize investment to make up this shortfall, without taxes? Another interesting possibility: rational expectations implies consumption and investment should, over the long run (the level of investment should be determined by the desired future level of income), be completely unchanged; would total consumption (government spending included) and investment return to their previous levels?

I’m toying with this theory because it completely eliminates the tactic of conservatives limiting the size of government with deficits; they’d have to actually argue against spending on the merits.

It’s quite a jolly idea in its own way. The obvious objection being, who’s going to buy these bloody bonds if you’ve abolished the taxes that are meant to pay them back, but apparently according to Jason, he’s aware of that. The idea is to give us a temporary holiday from taxes, which is something I’m in favour of; let future generations pick up some of their share since they’re the ones who will get most of the benefit from the current technological revolution. But I don’t want to get into the specifics of this scheme, mainly because I don’t want to steal Jason’s thunder. I’m interested in the calculation in the middle.

Jason clearly knows his Keynesian multiplier maths, but this extreme case shows up some serious deficiencies in the model. We actually get an apology for having used the Average Propensity to Consume instead of the “theoretically correct” Marginal Propensity. Now riddle me this:

Is the removal of the entire system of taxation a “marginal” change?

Is it hell. It’s a massive, huge, earth-shattering change. The MPC is the amount which you would consume out of a marginal extra dollar. If someone gives you a sum of money equal to 40% of your income, would your behaviour be proportionately the same as if they gave you a dollar? Of course not. So where did Jason go wrong?

The ugly and tragic secret is that he didn’t go wrong at all. Of all the operationally usable models of neoclassical eocnomics, there’s not a one of them in which it is not assumed that marginal rates of preference are constant. The possibility of diminishing MPC with respect to wealth or income is certainly acknolwedged in theoretical discussion, but these models aren’t used in any “live” applications because they aren’t tractable given the mathematical toolkit of most economists. In fact, as Steve Keen points out in the book I reviewed here a while ago (hmmm, must do some more book reviews), you can’t even derive anything so simple as a conventional downward-sloping demand curve without assuming conditions which imply a constant MPC.

This is a really, really nasty flaw in economics as she is done. Most economic things are of a nature to be best modelled in a non-linear fashion. Linear modelling works as a local approximation at best. But most things that you might be interested in modelling in economics aren’t small incremental changes; they’re big changes in important things. Linear approximations are, very probably, very wrong indeed.

But when you point this out to the general mass of academic economists, as Paul Davidson has been doing for years, you get treated as a harmless loony. If you try to teach economists the sort of mathematics they might need to correct these massive holes in the models, as Barkley Rosser has been trying to do for a while, your general reward is exclusion from the mainstream of academia, plus snotty articles from the likes of Paul Krugman accusing you of having “Santa Fe syndrome” and of using sophisticated mathematics “precisely because they seem to absolve intellectuals from the need to understand the models that underpin orthodox views”1.

It’s like banging your head against a brick wall ….

1This is quite a long article, but worth reading all the way through for the mixture of good sense and overpowering blinkered arrogance which is Krugman’s signature. Particularly funny is the bit where he accuses John K Galbraith of not understanding mathematics, because it led on to this piece where he accused James K Galbraith of also not being able to hack the math, and as a result got his head handed to him in this debate. The point being that Galbraith pere was an old-school institutionalist, but Galbraith fils is a scary linear algebra whizz. It is not impossible that Krugman confused the two.


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