Wednesday, May 04, 2011

Macro Aggregate Vacuousness

Brad DeLong had a post on Hayek, and at one point he buttresses his argument with this observation:

We start with our quantity theory of money, which tells us what nominal income PY is:

PY = MV(i)

Normally one would stabilize nominal income by boosting M. The problem is that the normal way the central bank boosts M is via open-market operations by which it buys safe savings vehicles for cash. Reduce the supply of safe savings vehicles and you raise their price--and thus lower the safe nominal interest rate i some more. Lowering i further reduces the opportunity cost of holding money and further reduces V. The net effect on PY is:

d(PY) = [V(i) + M(dV/di)(di/dM)]dM

Now, this all seems pretty scientific. Its logic is best exemplified by Don Patinkin’s Money, Interest and Prices (1957), which had page after page of such equations, and has been called the 'height of the IS/LM' theory. It appeared to be a very compelling theory, because it was consistent and logical at every step. All the partial derivatives made sense, but one had to hope that such simple models were sufficient to overcome all the variables and interactions not explicitly addressed, because in a complex economy there's an almost infinite number of relationships and omitted factors.

But what are theses variables and relationships that have such mathematical precision? Consider V, velocity. Velocity is the residual of the measurables nominal income and money. Thus, the derivative of V with respect to i (the interest rate) is really from the derivatives, and their correlations, of nominal income and money. Are either of these stable in any sense (d(PY)/di, dM/di)? No. They have no stable values and suggest they are no better than asserting a mathematical relationship between your body temperature and how much coffee you drank based on thermodynamics: there's a simple effect from the initial impact, but very shortly feedback effects that make the initial physical model worthless.

And so it goes with all these relationships. The economy is a complex, nonlinear, adaptive system where short run effects are often opposite of long run effects. Ultimately, people need to be involved in activities that generate more benefit than they they cost for they to be sustainable, and they must appear attractive to individuals given their other opportunities as they see them. A higher growth rate simply involves having more people near their unknown optimal--unknown because only rudimentary laborers know what the truly best use of their time is at any moment--and stagnation is caused when too many individuals lose their ability or willingness to actively search and make these choices. The more government puts in rules saying we can't drill in the Arctic because of potential effects of exhaust on a nearby village of 100 Eskimos, or that we can't cut hair without a state license, the lower our productivity. Economic freedom results in long term growth and so the key to macro policy is not from some chain rule but rather the wisdom of Smith, Bastiat, von Mises, Hayek, Friedman, Stigler, and the rest who found aggregate prosperity and economic freedom synonymous.

Increasing the money supply to fool employees into thinking they have more money than they do, hoping on a multiplier effect via such derivative compounding logic, is simply absurd. Currently, we are changing M to affect i, so the relationship should be di/dM, not dM/di, highlighting why the empirical relationship between i and M is so spastic. If countries could simply print and spend to increase GDP, the 1970's would have been an era of great growth, instead of the disaster it was, which is why the 1970s--increasing inflation, increased government spending--is such a profound empirical contradiction to the Keynesian model.

Thinking about aggregates this way is pure blather, like the way Marxist intellectuals talked about the laws of motion a century ago when their Oracle bloviated in Das Kapital that just 'as the heavenly bodies, once thrown into a certain definite motion, always repeat this, so it is with social production.' Yeah, just like celestial mechanics. I generally just ignore any argument based on or alluding to such pretentious, hopeful, willfully naive twaddle, but if for some reason someone accosted me at a Town Hall meeting and said such an equation implied we should do X, I would simply ask that they show me the regression results for it on a handful of developed countries in the modern era. The parameters would not be consistent over times or between countries.


Ian Lippert said...

I just finished my MA in Econ and I was getting much the same feeling as I sat through the last 4 months of my macro class. In your opinion is there any benefit to macro economic modeling? There are times when reasonable assumptions are made and results are derived that seem to make some sense with the available data. It seems like if the models were complete garbage they would spit out nonsense derivations. Or are these results simply the result of selection bias, ie models that start off making sense and then give nonsensical results get thrown out. That is a suspicion I've had but have no plans to do a phd so will probably never find out.

brad said...

Don't be silly. These equations come, IIRC, from Milton Friedman's "The Quantity Theory of Money: A Restatement."

The point is that when the Federal Reserve buys bonds for cash two things happen:

1. People have more cash in their pockets, and so they tend to spend money at a faster rate.

2. The fact that there are fewer bonds out there pushes up their price and makes them less attractive investments, so people who are holding money not to spend but as a form of savings are less eager to pass their cash along to somebody who will spend it.

The first effect dominates the second, but when short-term safe nominal interest rates are low the second can come close to wiping out the first.

If you don't like this reasoning of Friedman's, it's a free country. But to say that you need to replace reasoning like this with the reasoning of... Milton Friedman is profoundly silly.

Brad DeLong

Anonymous said...

The Fed is essentially buying from the Treasury, not the public. They are subsidizing less productive government consumption and implicitly taxing savers. I've saved $100k for my daughter's college education which I grudgingly have put into a money market fund. (It also serves a reserve in case I lose my job.) I estimate that over the last three years I have foregone $6,000 to $7,000 in income. This foregone income was captured by banks and lowers the cost of debt financing for the government, which like the low rates for teaser mortgages, suckers the government into believing that that it is getting a great deal. In fact, we're pushing our risks into the future. Like those teaser rates, I worry that this leads to great ruin when it turns out we can't afford the recasted rates.

Eric Falkenstein said...

BDL: I agree that Friedman's Consumption Function uses similar logic, which circa 1950 was a reasonable idea. Subsequently, it has proven so empirically impotent, I think it is no longer defensible. Does anyone really care whether it's the Life Cycle or the Permanent Income hypothesis? It seemed important at the time, now, both irrelevant. Like most academics, such models generate bona fides, later then ignored by everyone except academics making footnotes(see Romer, Krugman, Stiglitz, none of whom make daily arguments related in a straightforward way to their 'seminal' models). The Friedman most people find profound is Friedman the historian who argued analytically about liberty, and how it relates to growth, in his many non-technical articles.

Anonymous said...

"1. People have more cash in their pockets, and so they tend to spend money at a faster rate."

No, they don't. This is known as the "money burns holes in pockets" theory and it is extremely naive.

People spend more when they have more income.

brad said...

Re: "BDL: I agree that Friedman's Consumption Function uses similar logic, which circa 1950 was a reasonable idea. Subsequently, it has proven so empirically impotent, I think it is no longer defensible. Does anyone really care whether it's the Life Cycle or the Permanent Income hypothesis? It seemed important at the time, now, both irrelevant."

Friedman's "Quantity Theory of Money: A Restatement" is not his "Theory of the Consumption Function."

You really have no idea what you are talking about, do you?

Anonymous said...

Why does Brad remind me of Comic Book Guy on the Simpsons?

Eric Falkenstein said...

BDL: I understand it well enough to avoid such rhetoric, just as I avoid getting into the weeds on DSGE models. Like Freudianism, post-modern lit crit, Marxism, all are technical paradigms locally logical, but ultimately sterile because their basic concepts reify things not amenable to such simplification. To ‘go there’ is a waste of time, and only impresses outsiders via intellectual intimidation, as they are all empirically sterile.

What I was alluding to was that Milton Friedman’s signature technical work on the consumption function was full of such macro algebra, and it is now irrelevant. His technical work on the Quantity Theory contains the specific points you address, but that is even more irrelevant. His lasting contribution to Monetary Theory is his Monetary History of the US, which is in the mold of Bagehot, Minsky, and Eichengreen, and is not really amenable to simple algebra—as a model of the macro economy the Q-theory fails, but its essence is captured via a narrative and will remain a classic.

Yet I still admire Friedman a lot even though this technical macro work I find irrelevant. That is not a paradox, as I like things written by Newton, Hiedegger, and Chomsky, even though they each wrote and did a lot of bat-shiat crazy stuff.

Ralph Musgrave said...

Anon above claims that increasing households’ stock of money does not induce them to spend, whereas increasing their income does. The evidence is people do spend a significant proportion of windfalls within a year or so. See:

Anonymous said...

Musgrave, an income windfall is income.

"Quantitative easing" is not a money drop (fiscal operation). It's just an asset swap. The Fed doing a rain dance.