Posts tagged with ceteris paribus

## Nonlinear Superdimensions?

I’m not the first person to say "ceteris paribus is a lie". What this aphorism means is that if you make a c.p. assumption in order to think something through, then the conclusion you reach may be irrelevant to the real world.

Worse, because people don’t understand models, someone might take your careful “A implies B” statement to mean “Both A and B are the case”. For example rather than Edgeworth boxes implying that trade be always mutually beneficial, people might take you to mean that

1. exchange is characterised by Edgeworth boxes
2. private transactions are always Pareto optimal

which is not at all what the theory’s saying. The theory is just connecting assumptions to conclusion: yes, if this were true, then that would surely follow. Which is great because some people don’t actually think such things through.

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Anyway. Ceteris paribus assumptions make thinking easier, but they hamstring whatever you find out—so that it may be useless, or (hopefully not) worse than useless: misleading.

But maybe it’s possible to keep the crutch of c.p. and make it less foolish.

There are some situations where it’s impossible to do what I’m going to suggest—like where space overlaps itself. But in Euclidean spaces it is possible.

Econometricians are already familiar with principal components analysis. You make one “composite dimension” which is composed of a fixed combination of existing dimensions.

`composite = .4 × X₁   +   .2 × X₂   +   1.7 × X₃`

This is what I’m calling a “super-dimension”.

You hold all other things constant so you can think logically about a situation that has the geometry of a single straight line. By creating a composite dimension maybe one could still use the handy ceteris-paribus assumption but roll more of real-life into the model too.

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For example let’s say as wealth ↑, trips to the emergency room ↓. Then you could form a composite dimension with a positive coefficient on wealth, negative on emergency room visits, and talk about both at once with everything else held constant. One step forward relative to talking only about only wealth ↑↓.

But wait — maybe these are only linearly related around a small neighbourhood of some point. Well, we could still create a composite “super-dimension” by varying the coefficients. This could either come in the form of pre-transforming wealth to be log of wealth, or something else — like a threshold effect where we use two or three linear pieces (eg, rich enough with slope=0, way too poor with slope=0, and middle with a linear decrease). In general, whereas linear means `+k+k+k+k+k+k+…`, nonlinear can be interpreted as `+1.2k+k+.9k+.8k+k+1.1k+1.3k+1.2k+1.4k+…`. So instead of constructing a composite dimension with fixed coefficients before ignoring everything else, perhaps one could vary the coefficients along with the space.

That’s all. This may not be a new idea.

320 Plays

In other news, Art Laffer has become a parody of himself.

• Deliberately misrepresenting the flat tax. Making it sound like 12% is a tax cut for most Americans, when in fact the effective tax rate for everyone making under \$100k is already under 12%.

• If what you really want to do is raise taxes on the poor and cut taxes on the rich, why don’t you just come out and say it, Art?
• Conflating simplicity of tax returns with elimination of tax brackets.
• Poverty is caused by high tax rates and welfare. Quick, tell Somalia!

• Brings up sin taxes as a distraction, like a magician’s trick.

• No estimates of how much income is being “accelerated” from 2013 into 2012, only statements that the number is huge.
• Of course when the tax rates rise on the rich, they’re all going to flee the US. Because ceteris paribus it’s in their interest to do so. All other things considered, the first thing I do every morning is ask what tax rates are on various activities I could engage in and various countries I could move to.
• The sign is negative, therefore the magnitude is large.
• Also austerity is equivalent to growth, although later on he contradicts that and says a lot of government spending is necessary. (Wonder whether he wants to cut health benefits, elderly benefits, military protection, or government jobs?)
•  Some government spending is wasteful (again no discussion of magnitude—.00001% or 10%?) therefore austerity.
• Ricardian Equivalence, because I say so.
• Twisted reasoning like “Poor people are poor because of disincentives to work, but rich people would pay all of their tax if only you didn’t ask so much of them.” However not going to prove any of that, it’s just “common sense”.
• This passes for argument: “Come on, you know that.” (I count four.)
• Because, incentives. Because, markets.

If you laugh and squeal while you say it, you’re right.

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I would love to have a less cynical view of the world than that any yahoo who claims taxes can be vastly reduced on the rich with no negative consequences to anyone gets banquets in his honour, funding from “think tanks”, and handed the reins of policy. But this sh*t tests me.

Searching for something positive to say…at least he said the goal of government is to get poor people to be prosperous.

(Source: BBC)