Are there any straight lines in economics? Roman and Anglo Saxon roads.

This post is meandering philosophical whimsy that goes nowhere. If you don't get off on that sort of thing, best stop reading now.

Suppose you were looking at a map, or satellite photo. If you saw a straight line, you could be sure it had been drawn by a human hand, not by natural forces. Rivers, coastlines, mountain ranges, all curve and squiggle in irregular ways. But some roads and boundaries are straight lines. They were drawn by human hand. Or alien hand, like Martian canals.

But not all roads and boundaries drawn by human hand are straight lines. In England, if you see a road that's a straight line, you can be fairly sure it's a Roman road (or modern). As for the rest, the Anglo Saxon roads: "the rolling English drunkard" made them. They weren't planned and drawn by one hand at one time. They were drawn by many hands (or feet) at many times, and meander all over the place.

So when I saw David Beckworth's graph of the the Euro monetary base, and how straight the line looked, my reaction was immediate. "That's a Roman road; it's not Anglo Saxon". Somebody must have deliberately made it straight.

There are straight lines in physics. At least in Newtonian physics. Are there any straight lines in economics?

My basic answer is no. Everything in the economy is drawn by human hand. But nearly everything is drawn by many hands at many times. Economics roads are Anglo Saxon roads. If we see a straight line in economics, it means it's a Roman road, deliberately made straight by some single hand. Like an exchange rate that some central bank has decided to fix.

Here are some exceptions: The Long Run Aggregate Supply Curve is vertical; the BP curve in Mundell-Fleming is horizontal; the demand curve facing an individual seller in a perfectly competitive market (like the supply curve facing the individual buyer) is horizontal; the budget line is a straight line.

But all these exceptions seem to be a special case. When we draw the LRAS as vertical, we are saying there is zero relationship between P and Y, in the long run. Likewise with individual sellers' and buyers' demand supply and budget lines in perfectly competitive markets. And the BP curve for a small open economy in a competitive world market for loanable funds. There is zero effect of the individual's purchases or sales and the prices.

There are constants in physics that are not zero. Are there any constants in economics that are anything other than zero, or one?

Plus, no econometrician ever observes any of these straight lines, just by looking at the data. The straight lines (if they are straight) have to be estimated, by holding all other things constant. We would only observe them with the naked eye if all the other things were in fact constant, which they never are.

Economists may draw straight lines, but that usually means nothing except they don't know which way it curves.

I can't think of any processes that would tend to make an Anglo Saxon road in economics -- an unplanned road drawn by many hands -- a straight line. By sheer fluke it might be straight, if all the individual meanderings exactly cancelled out in aggregate. But the chance of that happening would be almost zero. If we see a straight line it is almost certainly a Roman road, that a single hand decided to draw straight.

I sometimes hear it said that economics is a "linear" subject. There are two meanings of the word: straight lines; and a plot that starts at the beginning and goes on to the end, with A causing B causing C....etc. In neither of those senses is economics a linear subject. It's all curves; and there's lots of feedback and simultaneous causality.

Comments

[Frances Woolley]

Nick: "It's all curves; and there's lots of feedback and simultaneous causality." So does this mean we
- throw out the linear models?
- replace them with really fancy complex non-linear models?
- replace them with with words ("follow that there road to where it forks by the old oak tree, then take a right and go up the hill...")

On your exceptions: "the demand curve facing an individual seller in a perfectly competitive market (like the supply curve facing the individual buyer) is horizontal; the budget line is a straight line.

But it's hard to think if a market that's really perfectly competitive. Financial markets are close, but the demand curve facing an individual seller changes from minute to minute - can we agree that continuously oscillating straight lines don't count?

On budget constraints - a typical person will spend a good chunk of their income on housing. That part of the budget constraint is not a straight line at any point of time - it's lumpy and fixed. Income/leisure budget constraints are totally kinked - people have jobs with fixed hours of work and fixed salaries then face complex tax schedules.

[Gregor Bush]

Nick,

I’m terribly sorry for getting off topic here but Brad Delong is blaming one economist in particular for the fact that so many prominent economists today (Kocherlakota) don’t seem to believe that nominal shocks have real effects. The economist he blames: Milton Froedman. That’s right. The man who spent his entire life teaching us about the power of monetary policy and showing us, in his magnum opus, that the greatest macroeconomic catastrophe of all time was entirely a nominal and not a real shock, is somehow responsible for economists holding the belief that monetary policy doesn’t matter and that all recession are caused by real shocks.

Brad never mentions in his slides that Friedman criticized the BoJ in 1998 for being much too tight and pleaded with them to run policy such that inflation would return to the rates that predominated in the 1980s. He also fails to mention that Friedman thought that Fed policy was appropriate in the 2001-2003 period despite the fact that growth of the monetary aggregates was well above trend. There was clearly much more to Friedman’s views on monetary policy that simply the growth of the aggregates, particularly in the last 15 years of his life when he correctly observed that technological change had made the aggregates much less reliable indicators than they used to be.

What say you Nick? Will you let Delong’s smear stand?

[Nick Rowe]

Frances: I have always interpreted a linear model as a simplification. The modeller doesn't know which way the curve curves, so has assumed it's a straight line. Plus it makes the math easier, and in a stochastic model you can use certainty equivalence. But, like all models, it's only ever an approximation. Doesn't mean we throw them out though.

"But it's hard to think if a market that's really perfectly competitive." Agreed. An approximation.

"Financial markets are close, but the demand curve facing an individual seller changes from minute to minute - can we agree that continuously oscillating straight lines don't count?"

That was something I was trying to get my head around. If a straight line were oscillating up and down, would we ever see it in the data with the naked eye?

Gregor: I've been thinking about that. I really disagree with Brad there. I am not the best person to do the job though. My memory of who said what when is always so crap. Scott Sumner could do it better. So could others. Steve Williamson responded here: http://newmonetarism.blogspot.com/2011/03/ignorance.html Steve is coming at it from a slightly different angle. Despite my disagreements with Steve, over Kocherlakota and other stuff, I tend to lean a bit towards him here.

I am hoping someone else would do a better job of this than me. But I'm still mulling it over.

Personally, I blame Ricardo, for the Ricardian vice. Or James Tobin, for forcing Friedman to write down his macro model!

[Daniel Kuehn]

And the exceptions you list are all theoretical schedules that (while still maintaining their straightness) shift over time. The straight line Beckworth presents is a nexus of equilibrium points observed in the real world, not theoretical schedules of the "if p is X then q is Y" variety, making it even more implausibly "natural".

Economics is a very specialized form of biology - it's the scientific study of a very specific social behavior of a single species of highly evolved primates. If there are any non-zero, non-one constants in it, they're going to be of the same form that we see in biology. Something like Dunbar's number - although even that is just an estimate, and in an impersonal monetary economy that one is irrelevant. I doubt there are any - but if there are some, they are of that form.

Still, even without such universal constants, we still have useful approximations. Certain supply and demand elasticities may not be universal constants, but they appear to be stable enough to be useful.

[Josh]

"So when I saw David Beckworth's graph of the the Euro monetary base, and how straight the line looked, my reaction was immediate...Somebody must have deliberately made it straight."

This was precisely my initial reaction as well.

[Tim Worstall]

"As for the rest, the Anglo Saxon roads: "the rolling English drunkard" made them."

Ahem....

The poem opens:

" Before the Roman came to Rye or out to Severn strode,
The rolling English drunkard made the rolling English road. "

The Anglo Saxons turned up after the Romans left, post 410 AD. The Romans turned up at 55 BC (J Caesar, then they all went away again) or 43 AD (Claudius).

So those rolling English drunkards *before* the Romans turned up were the Celts....the "Britannicae".

/pedantry

[Nick Rowe]

Daniel, Josh: yep.

Tim: Ah well. I got a grade 7 in O-level history! (borderline fail). The Icknield Way and Ridgeway are the only pre-Roman roads I can think of, and they are not very straight. And (according to "Time Team" on TV Ontario last week), the English are only about 10% Anglo Saxon anyway. We have almost as much Neanderthal genes as Anglo Saxon! So people should stop calling us WASPs.
http://en.wikipedia.org/wiki/Icknield_Way says it's not even sure the Icknield Way is pre-Roman!

[Bob Smith]

"So those rolling English drunkards *before* the Romans turned up were the Celts....the "Britannicae""

Since the English ended up with the country, the least they could do is take the blame for the roads.

[Kevin Donoghue]

Nick: “I am hoping someone else would do a better job of this than me. But I'm still mulling it over.”

Go for it. But first look at Krugman’s effort.

[POWinCA]

I'm skeptical of the analogy.

The shortest distance between two points on a plane is a straight line, but with contoured terrain, the shortest path is NOT a straight line. For engineering, the path of least cost across terrain almost certainly isn't a straight line. The engineers are solving an optimization problem.

There are straight lines in economics which cannot have meaning UNLESS they are straight lines: Fixed costs of production, separating hyperplanes, a budget line for two alternative choices.

We do not have a "linear subject." In economics we have lots of curves. We draw rectangular hyperbolas for average fixed cost. We draw curves for log linear relationships, diminishing returns, increasing costs.

When we draw a straight line, in many cases we do so without loss of generality. They serve a didactic purpose in making calculations of the slope easy for the students.

I see lots of stepwise functions in economics, and lots of observations varying about a linear trend.