My Econometric Model - Devil's Advocates Wanted

Economics Economics Questions
1

I’ve been building an econometric model for debating with socialists. They’ll say stuff like “in 2005, scandinavia had 67% taxes and record growth rates. So socialism can bring more prosperity than free markets”.

These kind of anecdotes are annoying because you have to remind them that correlation =/= causation, GDP is not a criterion for economic health, etc. Or you can tell them counter anecdotes that are just as inconsequential.

You can ask these people to elucidate theory all you want, but they just reverse engineer theory from “success”. Actually they cherry pick theory, since those governments are basically rich white boy clubs and are structured mainly around narrow service industries like banking. We can’t all be bankers, but they’re not having any of it.

So the only thing they’ll trust is data. Right? Wrong. Because if you showed them data that confirmed free markets, they’d ignore it. Their cognitive dissonance aside, I’m hoping their ideologueness would become painfully obvious to observers.

So I’m building an econometric model. I model per capita GDP by looking at tax rates. It’s a spin off of SED (sum of exponential decline) models used in unconvential gas reserve estimation.

Most countries don’t have data going very far back, especially on taxation. If you know of any sources, then gimmie.

Because I have to start the model in medias res, the GDP in year 1 is taken as given. Its contribution decays over subsequent years. It is given an exponential decline of the following form:

Tau is just a time constant to remove the dimension of “years” on the exponent.

All other years are assumed to have a certain amount of growth associated with them. This growth is delayed by a timeshift. So the growth starting in year 2 might not peak untill year 6, and become negligible in year 10.

Why do I choose to model investment as a delayed peak? Because capital doesn’t pay itself off instantly. I’m theorizing that the benefits of investment take time to yield their full benefits. So if you have one year of free markets, you won’t see much of a dent till later.

Anyway, here’s the equation.

C is just a growth coefficient. dt is the time shift. The exponential is squared to give it a bell shape centered dt after year n. This equation is used after year 1.

So this gives us each year’s contribution to GDP as a function of time. For example, in year 1, model GDP depends only on the first equation. In year 2, the contribution of year 1 will decline, and the contribution of year 2 will begin. In year 12, years 1-12 will contribute to GDP, though years 1,2,3 will probably contribute very little. Year 12 will also contribute very litle. Year 8 may contribute a lot if dt=4, since that is when the growth from year 8 will peak.

Each year’s gdp estimator looks like this:

My optimizer chooses coefficients for Tau, dt, and C that give the best fit of the data. It takes 5 hours to run if I want decimal places… (my optimizer is very robust, which really just means inefficient. Idk anything about optimization optimization.)

So I’ve run this on ireland’s economy. I chose ireland because they have data going back further than most countries, and USED to be free market-y, but are now socialist-y. So how do you explain their modern prosperity in terms of free markets? With SCED!

Here are my program’s charts:

And here’s the QQ plot. If you don’t know what that is, the closer to the 45 degree line (line of equality), the better.

And finally, if you were confused about the “delayed peaks”, here is an example

The correlation coefficient I got was .988… that is almost .99, which is almost 100%.

That’s pretty much perfect. It’s funny because I basically assume that taxes get sucked into a black hole and are never used to grow the economy. My excellent curve fit would seem to support the Austriann notion that government can only destroy wealth :slight_smile:

I want to know what’s wrong with this model, and how you think lefties could try to argue against it.

I’m afraid they’ll argue that the growth coefficient, C, is influenced by government spending on education and such. I can always say “prove it”, but… who knows.

Anyway, thanks for your time, and sorry for such a long post

tl;dr → socialists, u jelly?

2

[edit 9001: nm]

And I’m sorry about any spelling mistakes. I’m traveling and this laptop is so tiny. Its a combination of the keyboard/not being able to see text properly.

3

It takes 5 hours to run if I want decimal places… (my optimizer is very robust, which really just means inefficient. Idk anything about >>optimization optimization.)

hmm. what software do you use? and how many bytes is your source dataset?

sum of exponential decline
This is a 4 word ‘googlewhack’, is it more commonly known by another name?

4

Its a verrry robust (unintelligent) optimizer I built in matlab.

The source dataset is quite small… just gdp and tax rates since 1995.

I don’t know. I saw it in a recent paper for reserve estimation in unconventional gas reservoirs. I’m not actually using SED though, I’m using my own SCED (Sum of Centered Exponential Declines)…

5

This might be an uninformed comment, but isn’t GDP a bad measure of economic performance if you are going to be that precise about it? I mean, GDP measures how much money we spend in an economy. But isn’t the strength of free markets that it brings down prices, i.e. less money is spent in the economy? If commodities are produced in abundance and therefore cheap, then GDP will be small. But if everything is expensive then the GDP will be high.

6

Its real per capita gdp in 2005 dollars. So its only ‘volume’.

But you’re right. There are many improvements that would reduce economic volume, such as the durability of goods etc.

I guess you’re right that socialists could complain more about inequality than raw GDP. It would be haaaaaarrrrd to find that as a function of time though.

I’m also doing some work with global indicators. I’m using Sen’s Social Welfare Function as my target to predict. It turns out that SSWF depends really really heavily on just raw GDP, which can vary drastically between countries. But you’re right, it’s a weak spot.

7

@EmperorNero If GDP is adjusted for inflation, then GDP will not be affected by prices.

8

^If inflation is symmetric (all prices rising equally)

Inflation is not symmetric.

9

Oh, and incase you feel unqualified to critique this model, think again.

  1. I am not that smart or sophisticated. Idk anything about econometrics. This is just blind curve fitting.

  2. Even if you are unqualified, if you are more qualified than a generic leftist, I want your input. Even if you’re wrong, I want people will try to argue.

10

are you going to share the data and the matlab code?

how many other countries have you looked at besides Ireland?

11

I can share my matlab code if you promise not to laugh.

I haven’t run the code on any other countries. I have the data for a lot though. I also might run it for regions. I developed the code on a dummy country with taxes = [10 20 30 40 50 60 70 80 95] and pcgdp = [3000 4000 5000 7000 10000 15000 20000]. The fit was still pretty good despite it being made up data. IIRC I got an R2=.97.

I need to go back and add a squared decline for the initial timestep, since the model currently discounts any economic growth from year 1. Derp.

12

you need to do this on countries that go down after having been up and countries that are up go down and up again, and countries that go down then up then down again etc.

13

The problem is that most developed countries just get richer over time. I’ll make something up… will post new results in a few hours. Gonna make that change above, run it on a couple more euro countries, and make up a few fake countries that do wierd stuff.

14

I`m norwegian and most of the technology/innovation etc which gives us a high standard of living is imported and to a certain extent paid for with petrodollars and from exporting other natural resources.

Sweden/Denmark have large debts. The Scandinavian countries are very small. We have close ties to other European countries/North-America, which enable us to benfit from the innovation that takes place in those countries.

Here are Norways import/export numbers in NOK(norwegian kroner), which shows that we wouldve had huge deficits if we couldnt sell natural resources at a high price, i.e. way above cost(thanks to the absence of competition, i.e. OPEC etc). NB! If the USA were to export as much oil pr capita as Norway does, they would have to export about 120 million barrels of oil pr day, but problem is mankind only consumes about 86 million barrels pr day, so that would make it difficult.

So you could ask social democrats etc how mankind(in a social democratic society) would cope in a world where there were no countries who were different than the Scandinavian countries, and who mankind could sell natural resources to at a high price, i.e. way above cost.

15

Thanks for your post Johnny. I brought this up in a discussion, and the opponent simply pointed out that denmark has far less oil and yet maintains a high standard of living because of their strong socialist education system. Thoughts?

16

Denmark have oil, but very little compared to Norway, so for Denmark/Sweden it`s the other factors, i.e. they are small(few inhabitants), are indebted, have close ties to other developed countries.

17

Denmark - r2=.9571, correlation = .9783

Sweden - r2 = .9839, correlation = .9919

up-down model. The optimizer set dt=0. I.e. this means that the capital formed in that year begins decaying instantly.

up-down-up and down-up-down - the optimizer has a harder time fitting.

The data for the up/down ones is made up. I’m sure I could have made up data that was easier to fit. They all have the same tax trend (high initial taxes, lower finishing taxes). Which probably throw the model off.

Basically, these models are built to only show growth. Any decrease in models is due to a lack of growth, not any negative variable…

Hmm

18

It basically looks like it can’t turn tight corners, especially when taxes are doing their own thing.

19

can you explain why the model predicts in the direction of the actual that you invented regardless of the tax regime (given you say that taxes are always going from high to low?)

or perhaps I misunderstood your comments?

20

Probably because it either stretches or compresses the curves to avoid/land on high/low regions of growth.

[edit] Like I said, I built this to be a delayed model. The “peak growth” from year X doesn’t happen untill X+dt. The optimizer chooses a dt. For all the real life cases, it’s chosen a dt between 7 and 11. So you can see low growth during free market periods and high growth during socialist periods, because the peak growth from free markets is delayed a while.