Tuesday, August 28, 2012

M.C. Escher revisited

In Gödel, Escher, Bach: An Eternal Golden Braid mathematician and physicist Douglas Hofstadter delves deeply into the idea of recursion and self-referencing, with respect to number theory, language, music, and imagery. The goal of his exploration is to--ultimately--understand the foundations of intelligence, of thinking, with regard to the possibility of arriving at true artificial intelligence. Hofstadter weaves the works of the three masters in the book's title into his narrative, though admittedly it is Gödel's ideas and theories that are most critical to the end game.

It's one of my all time favorite books; I've read it at least ten times, from cover to cover. Thus, the ancillary parts--of which there are many--are very much ingrained in my mind. With all of the talk over the role of government, as regards the economy, now being front and center in the public discourse it occurred to me that there was a lesson here, that some of the things Hofstadter investigates provide a great framework for understanding why the narrative from the Obama Administration and it's neo-Keynesian supporters is just so wrong.

The fundamental belief informing their views is that government activity or spending is, by definition, a catalyst for economic growth, that the government can stimulate the economy via such spending. The more the government spends, the greater the resulting stimulus. This theory is backed by (faulty) analysis, wherein there is a multiplier effect on the overall economy: the government spends x dollars, overall economic output goes up (magically) not by x, but by x times some number greater than 1. The Administration's economic team seems to think the latter is something like 1.5 (once upon a time they said it was 4.0, I kid you not). Robert J. Barro explained all of this several years ago:
If the multiplier is greater than 1.0, as is apparently assumed by Team Obama, the process is even more wonderful. In this case, real GDP rises by more than the increase in government purchases. Thus, in addition to the free airplane or bridge, we also have more goods and services left over to raise private consumption or investment. In this scenario, the added government spending is a good idea even if the bridge goes to nowhere, or if public employees are just filling useless holes. Of course, if this mechanism is genuine, one might ask why the government should stop with only $1 trillion of added purchases.  
What's the flaw? The theory (a simple Keynesian macroeconomic model) implicitly assumes that the government is better than the private market at marshaling idle resources to produce useful stuff. Unemployed labor and capital can be utilized at essentially zero social cost, but the private market is somehow unable to figure any of this out. In other words, there is something wrong with the price system.
Thus, the theory assumes perfect knowledge and "frictionless" results, with regard to government spending. No waste, no corruption, no mistakes. Barro's analysis was before all the evidence was in from Obama's Stimulus spending. But he's been proven correct by the results. Arthur Laffer (of Laffer Curve fame) summed  up the evidence earlier this month, noting the following (my boldface):
Often as not, the qualification for receiving stimulus funds is the absence of work or income—such as banks and companies that fail, solar energy companies that can't make it on their own, unemployment benefits and the like. Quite simply, government taxing people more who work and then giving more money to people who don't work is a surefire recipe for less work, less output and more unemployment.

Yet the notion that additional spending is a "stimulus" and less spending is "austerity" is the norm just about everywhere. Without ever thinking where the money comes from, politicians and many economists believe additional government spending adds to aggregate demand. You'd think that single-entry accounting were the God's truth and that, for the government at least, every check written has no offsetting debit.

Well, the truth is that government spending does come with debits. For every additional government dollar spent there is an additional private dollar taken. All the stimulus to the spending recipients is matched on a dollar-for-dollar basis every minute of every day by a depressant placed on the people who pay for these transfers. Or as a student of the dismal science might say, the total income effects of additional government spending always sum to zero.
There is mathematical certainty in Laffer's two claims that I highlighted, yet these are truths that many people--who are otherwise intelligent--seem unable to process. It is here that I think Hofstader's analysis can be introduced.

When we talk about government spending leading to economic growth, we are talking about a self-referencing idea: as Laffer notes, government revenues--needed to "stimulate"--are dependent on taxes, increasing as a matter of course when there is economic growth. But self-referencing systems are not describable--provable--within the limited framework of rules governing our reality, by and large. In number theory--as Gödel demonstrated with his Incompleteness Theorem--there are true theorems what cannot be demonstrated, theorems which are actually self-referencing. However, when such a theorem is true, this can inferred via trial and error substitution. Sound too complicated? The idea is simple: the self-referencing (or self recursive) system is not logically sustainable, not provable, and therefore not true, except when evidence says it is despite the lack of a mathematical proof.

In this regard, I give you government spending, assuming perfect knowledge and no waste/corruption, via M.C. Escher:

The waterfall is government spending, pouring into the economy and powering it, the churning water-wheel. The water flows on and on--theoretically downhill--yet every bit the government pours in returns to it in full, to be poured down again. The multiplier effect here would be 1.0. A perfect return on money spent. And despite the apparent impossibility of this scenario, the Administration would have us believe the number is even greater than 1.0, that--somehow--more water would flow up then went down to begin with!

Despite the logically implausibility of all this, there remains the possibility that it could be true, that it could be one of those truths that cannot be proven via formulas and numbers. But its not. We know it's not because the evidence is already in. So the next time someone talks about how government spending automatically stimulates the economy, ask that person if they've ever seen this picture...or a perpetual motion machine.

Cheers, all.


  1. back when I was in (engineering) school, I had a favourite professor who had a particular thought which he deemed worth repetition.

    when looking at a problem, if you can turn it into a perpetual motion machine, start over. something is badly wrong and you need to go over the statement of the problem with a fine tooth comb.

  2. Well, yes and no. You are the one who likes to remind people that economy is an open system. The gov doesn't _have_ to tax more to get the money. It can print or borrow. Now, there are consequences, but in many cases they are deferred. Think about the gov as a company and China as a bank. The gov borrows money, produces something, that in turn brings more revenue. At that time, the gov is paying interest, which is less than the borrowed sum. Sure, in the future it would need to return the whole sum, but in the meanwhile the economy will start growing again, the gov will have more revenue and it can return the loan. Same with printing. In that case, inflation is somewhat mitigated by the fact that people outside US use dollars, and the effects are not as large and not as immediate. Anyway, this is the way the thinking goes. Does that mean, stimulus and such are a good idea? The answer is "it depends" on how you spend the money. Do you just add money or do you reallocate your revenues to different things. Sometimes, government intervention can help. There are examples. In Israel I can think of two cases, one was in the 90th. The gov jumpstarted the venture capital scene by creating a program that matched private investments on a one to one basis. This mitigated risk and allowed vc funds to flourish. Of course, the smart thing was that the gov butted out after five years and stopped its meddling. The other case was during this recession. The gov reallocated some of the resources to mitigate job losses by paying for one day out of five for companies who were willing not to fire people. This isn't the most productive thing, but it allowed some companies to retain workers and people to keep their jobs untill the economy started picking up again. The good thing was, the gov did that without raising taxes or borrowing, but by changing priorities within the budget. Can this always work? No.

  3. @Roy--yep, I had a prof say basically the same thing.

    @Dm--all of that's true. But remember, the people claiming there is a multiplier effect seem to think it is a closed system. And they believe additional government spending is not funded by economic growth, but by tax increases. So in that World, the Escher print is, I think, I very spot-on critique. :)

  4. I understand, but I think your critique is incomplete. Who cares what they think. You know better. You know the reality (by the way, this deferred payment can in theory be considered a multiplier effect). The problem is not borrowing per se and not spending per se, but what you spend it on, how you control your spending/borrowing and whether you are realistic about your revenues/expenditures. This is what buggs me the most about people from the left when I talk to them (this was rather apparent on AW as well). You put out the Houser's law (that the revenue remained around 18-19% of GDP irregardless of tax rates) and you point out to the fact that spending now is 24-25% of GDP, and people start shutting down. Or change the subject to the revenue part, arguing that taxes need to be increased to bring them back to historical level. Let's say I agree with this, you still need to reduce your spending by 3-5% of GDP. Then they either ignore you or bring in the defense budget (I still remember a claim recently made on AW that _waste_ in defense budget is higher than all the transfer payments). It is insane.