My Econometric Model - Devil's Advocates Wanted

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 :)

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?

[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.

 

>> 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?

 

nirgrahamUK:

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

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

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

nirgrahamUK:

This is a 4 word 'googlewhack', is it more commonly known by another name?

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)...

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.

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.

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

^If inflation is symmetric (all prices rising equally)

Inflation is not symmetric.

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.

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

how many other countries have you looked at besides Ireland?

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.

 

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.

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.

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 would`ve had huge deficits if we couldn`t 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.

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?

Sieben:

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?

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.

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

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

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?

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.

Cool shit!   I've only got some basic statistics under my belt so I not very able to comment on the equations themselves but as to your descriptions;

GDP in year 1 is taken as given. Its contribution decays over subsequent years. It is given an exponential decline

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.

While I agree that the effects of  investment can be delayed, these effects, as with many (most/all?) economic phenomena, do not contribute to GDP in a linear fashion through time because human beings do not collectively make decisions that produce outcomes that can be represented by mathematical formulas.  This, in my view, is why market movements don't typically oscillate like gentle sine waves but snap from extreme to extreme.  One dollar of investment does not necessarily produce the same output value through time, too many other variables influence the end results per given unit of input. Technological changes are another example.  If you were to try and add a coefficient for future technological advancement you would not be able to model its contribution to GDP at all because the contribution to GDP of future innovations is absolutely unrelated in significance to the previous ones.  It's just unpredictable no matter how much logic you apply to the question.

Unfortunately these models don't really "prove" anything about the economy because they don't actually describe the economy.  Your model is merely a linear formula crunched out by your optimizer that goalseeked your coefficients for the line of best fit.  If I had to wager, I'd say your R^2 would shrink significantly over time as the causal factors in the economy that the coefficients attempt to model change as the capital structure evolves.

ThreeTrees:

While I agree that the effects of  investment can be delayed, these effects, as with many (most/all?) economic phenomena, do not contribute to GDP in a linear fashion through time because human beings do not collectively make decisions that produce outcomes that can be represented by mathematical formulas.

Its not modeled linearly. Its kind of like a bell shaped curve (last figure of OP).

I just thought that even though I can't know the behaviour of individual investments, the central limit theorem justifies my bell shaped curves. The only suspect part is where I center it at a certain shift - dt - but the optimizer is picking pretty consistent dt values.

ThreeTrees:

If you were to try and add a coefficient for future technological advancement you would not be able to model its contribution to GDP at all because the contribution to GDP of future innovations is absolutely unrelated in significance to the previous ones.  It's just unpredictable no matter how much logic you apply to the question.

And I don't try to. It's actually cool that I get a good fit *without* any changing coefficients. It models economic growth parameters are intrinsic to the economy. For example, Cg most heavily depends upon the existing capital stock when the fit starts. Tau and dt are probably functions of industry type and/or interest rate. 

But you're right. This model actually cannot predict recessions. It has no

ThreeTrees:

If I had to wager, I'd say your R^2 would shrink significantly over time as the causal factors in the economy that the coefficients attempt to model change as the capital structure evolves.

Will post the USA  when I run it.

It wouldn't be too dishonest to just run the program at 10 year increments to model it would it? I feel like econometric models would HAVE to, because you can't predict war, and you can't predict fed policy. I'd actually feel better about it if there were a way to include the federal reserve in my (1-taxes) term. Maybe in terms of pct growth of the monetary base. Hard to find the data though. I'm limited!

Anyway, thanks for your response. I'm not trying to build theomega model here. This is just a "look what the data can also show trololololol". It will be a valuable resource against socialists who argue in happenstance anecdotes, because at least my worldview provides a consistent explanation over time.

Will be using in online debates. Idk if the mises community would benefit from having this kind of thing around. Again, not as proof of theory, but as illustration that numbers can be used to prove anything, even though my model is probably a lot more reasonable than most. I mean the time delay, bell shape, and growth coefficient are all closely mirrored by simply economic and statistical concepts.

To prove the point further, I might construct an econometric model with 50 parameters and get a really good fit for the pro-taxation side... That all growth is due entirely to government and yada yada. And then just re-run random numbers through the optimizer and get the same good curve fit.

Statistics = trolling.

Hey Sieben, I'm actually interested in the data you're putting out.

Question: Have you considered using a linux platform to use econometric software? 

I've been brushing up on some stuff from my undergrad studies--including econometrics--becuase I'm starting a grad program in January.  I was able to download open source econometric software called gretl.

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?

Russia, Cuba and North Korea had socialist education systems, how come they don't have high standards of living? Russia even was the worlds leading oil producer. And primary education in the US is government run, and a nightmare. The argument that socialist education leads to high standards of living clearly doesn't hold true.

And actually people in Scandinavian "socialist" countries have lower standards of living than Americans. Their GDP figure is just so high because everything is so expensive. They spend more money but they are getting less for it.

And what would the standard of living be in those places if they wouldn't be supplied with free technological advances by countries that do have free markets? They are not producing their own standard of living. Cars were invented in America, planes were invented in America, microwave ovens and washing machines were invented in America... you get the idea. Even the use of petroleum was invented in the US. If one country makes an invention then all industrialized countries can enjoy it. In the statistics they have similar standards of living, but that does not account for who produced it.

If they're smart, they'll claim its a necessary but insufficient condition.

Ricarp:

Hey Sieben, I'm actually interested in the data you're putting out.

Question: Have you considered using a linux platform to use econometric software? 

I've been brushing up on some stuff from my undergrad studies--including econometrics--becuase I'm starting a grad program in January.  I was able to download open source econometric software called gretl.

I'm not looking to build anything too ornate. I'm really not *that* tech savvy with linux and all that. I'm just an engineer, and I know how to make matlab do the math I wanna do. This model should be more than enough to blow any non-math/non-economist lefty out of the water... I just want to know what actual econometricians would say about it.

If they're smart, they'll claim its a necessary but insufficient condition.

I suppose I just made you the devils advocate. Well, how is state education a necessary condition for economic well-being? What can it do that free market education can't? If you think this is off-topic, and you want to keep this thread about your econometric model, then just ignore my question.

It isn't off topic. Education is one of those intangible benefits of socialism.

The market can't provide for education because poor people won't be able to afford as good an education as rich people. Even though education is always getting cheaper, there is still inequality and the rich will always get richer.

The point with getting an education is, hopefully, to get a well-paying job. And if you get a job then you have to pay a lot of income taxes. (The model in northern European "socialist" countries is to pay for social programs trough high personal income taxes and leave corporate taxes relatively low, because corporations flee taxation.) So getting an education directly leads to having to pay a lot of taxes. The very taxes that are used to pay for education. In other words, poor people receive no free lunch, the state merely redistributes their future income to them at the point of a gun. The free market can do that more efficiently. Those who can't pay for their education out-of-pocket would simply sell percentage-shares of their future income. Investors would buy these shares for a few percentages in profit, it would be cheaper than taxes. These shares would be valued depending on what your future income is likely to be, i.e. what you study and how well you do. Buying these shares would be like investing in a car company.
So the poor can pay for an education just fine. And the rich will not be getting richer just because they have money. On the contrary, those who feel they are spending their own money to get educated will be more motivated to learn than those who get their education paid for by their parents.

Moderator can remove this post.

Sieben:

It isn't off topic. Education is one of those intangible benefits of socialism.

The market can't provide for education because poor people won't be able to afford as good an education as rich people.

They can`t afford "good" education/schools, what`s good about them(I`m not refering to todays system, i.e. public vs private)?

Sieben:

Even though education is always getting cheaper, there is still inequality and the rich will always get richer.

Why will the rich always get richer(relatively I assume)?

Is inequality a bad/unnatural thing, in Norway equality in the education system is being upheld to some extent by making everyone follow a rather unambitious standard curriculum, i.e. no one who are above average academically are allowed to follow there own potential, i.e. it`s against the law to divide pupils born in the same year in different groups based on ability(pupils who are below average are exempted).

Its not modeled linearly. Its kind of like a bell shaped curve (last figure of OP).

I just thought that even though I can't know the behaviour of individual investments, the central limit theorem justifies my bell shaped curves. The only suspect part is where I center it at a certain shift - dt - but the optimizer is picking pretty consistent dt values.

Sorry, this is my tenuous grasp of statistics terminology coming into play.  I called it linear not based on the shape of the curve but because it appears as a "line" lol. [self_facepalm]

Anyway!  Regarding the good ol' central limit theorem;  Market outcomes tend not to follow normal distribution.  I would refer you to Nassim Taleb's work:

One problem, labeled the ludic fallacy by Taleb, is the belief that the unstructured randomness found in life resembles the structured randomness found in games. This stems from the assumption that the unexpected may be predicted by extrapolating from variations in statistics based on past observations, especially when these statistics are presumed to represent samples from a bell-shaped curve. These concerns often are highly relevant in financial markets, where major players use value at risk models, which imply normal distributions, although market returns typically have fat tail distributions.

http://en.wikipedia.org/wiki/Black_swan_theory

 

Also, could you elaborate further on this part?  

And I don't try to. It's actually cool that I get a good fit *without* any changing coefficients. It models economic growth parameters are intrinsic to the economy. For example, Cg most heavily depends upon the existing capital stock when the fit starts. Tau and dt are probably functions of industry type and/or interest rate.

I'm not exactly sure what you mean.  And could you describe your methodology as well?  I'm very curious how you determine the values of your coefficients and am a complete noob at econometrics.

Emperor Nero:

The point with getting an education is, hopefully, to get a well-paying job. And if you get a job then you have to pay a lot of income taxes. (The model in northern European "socialist" countries is to pay for social programs trough high personal income taxes and leave corporate taxes relatively low, because corporations flee taxation.) So getting an education directly leads to having to pay a lot of taxes. The very taxes that are used to pay for education. In other words, poor people receive no free lunch, the state merely redistributes their future income to them at the point of a gun.

I think the idea is that you educate the poor, and then they are no longer poor. They pay taxes with their higher incomes, and you use that to help more poor people still.

So once they're educated and upper-middle class, they don't matter anymore.

Emperor Nero:

The free market can do that more efficiently. Those who can't pay for their education out-of-pocket would simply sell percentage-shares of their future income. Investors would buy these shares for a few percentages in profit, it would be cheaper than taxes. These shares would be valued depending on what your future income is likely to be, i.e. what you study and how well you do. Buying these shares would be like investing in a car company.

The issue is not whether postive NPV projects will be undertaken, the issue is with perpetual inequality.

Emperor Nero:

So the poor can pay for an education just fine. And the rich will not be getting richer just because they have money. On the contrary, those who feel they are spending their own money to get educated will be more motivated to learn than those who get their education paid for by their parents.

The rich can just live off the interest of their fortunes. They can pay poor mathematical geniuses to manage it for them.

The only possible argument we can make is that there will be *more* mobility in free markets vs the status quo.

/lefty-advocate

ThreeTrees:

Anyway!  Regarding the good ol' central limit theorem;  Market outcomes tend not to follow normal distribution.  I would refer you to Nassim Taleb's work:

One problem, labeled the ludic fallacy by Taleb, is the belief that the unstructured randomness found in life resembles the structured randomness found in games. This stems from the assumption that the unexpected may be predicted by extrapolating from variations in statistics based on past observations, especially when these statistics are presumed to represent samples from a bell-shaped curve. These concerns often are highly relevant in financial markets, where major players use value at risk models, which imply normal distributions, although market returns typically have fat tail distributions.

First, almost by definition, I cannot predict a black swan event. No one can. My model doesn't even try to build in any snap changes to the economy.

Second, the central limit theorem does not assume that the underlying structure is normally distributed. Market projects could be any smattering of random functions. But an aggregate sampling of functions tends towards a normal distribution by the central limit theorem. To the extent that the actual aggregate distribution tends *away* from a normal distribution is unknown, but is itself a random variable. Since each year's economic growth is an aggregate of all previous years, I'm aggregating it AGAIN, so there's an even better reason for it to come out normal :P

ThreeTrees:

Also, could you elaborate further on this part?  

And I don't try to. It's actually cool that I get a good fit *without* any changing coefficients. It models economic growth parameters are intrinsic to the economy. For example, Cg most heavily depends upon the existing capital stock when the fit starts. Tau and dt are probably functions of industry type and/or interest rate.

So my base model I've been pitching has 3 coefficients. They are constant for the whole life of the economy. Because they do not change, they are unaffected by any economic changes. So if the government doubles education spending, it will not show up in the coefficients, and therefore not result in growth (insofar as the fit is still good).

The growth coefficient, C, depends mostly on how much PCGDP you have in the starting year.

ThreeTrees:

And could you describe your methodology as well?  I'm very curious how you determine the values of your coefficients and am a complete noob at econometrics.

I just built an optimizer to choose the coefficients. If you have excel, you can use solver. You tell the optimizer to minimize the absolute or squared error between the model and actual PCGDP. My optimizer is a lot more robust than excel (you risk finding a local minimum), but it takes a long time.

 

I just tried to fit the United States from 1929 to 2003. The curve fits well for the first 15 years but then it can't keep up. This is because there is allowed no growth in the coefficient.... I programmed it as a 4th parameter to optimize and its running now. I know I'll get a better fit but idk how much better.

Maybe I'll go back and see if there's a way I can just put growth to be a positive function of time instead. I think I really do need to have a way to change the growth coefficient over time.

Maybe it makes sense to take the average of the previous 3 years' capital...?

[edit] Ahh I know. I can multiply each C by PCGDP(n+1)/PCGDP(n), so that it will grow when the economy grows and shrink when it shrinks.

Sieben:

I think the idea is that you educate the poor, and then they are no longer poor. They pay taxes with their higher incomes, and you use that to help more poor people still.

So once they're educated and upper-middle class, they don't matter anymore.

Equality/inequality = relative poverty, i.e. as long as people are different, politicians will wage a war on "poverty".

I changed my model a bit. Initially, C, the growth coefficient, had been constant throughout. This doesn't allow the model to grow at late time. I eventually got a flat curve when fitting the USA from 1929 to 2003.

Instead, C is updated to grow as the model grows. So if the model predicts 2% growth in year 1, C grows by 2%. This growth is cumulative. The model fits the C in the following equation, and  the model uses Ci for year i.

I fit the US economy from 1929 to 2003, and obtained an r2 = .9811, correl = .9905

 

Here's a chart of the total effects selected years have on the economy. The initiall blue line looks wonky because it is the sum of the initial decline from past years, as well as the SCED from 1929.

 

The optimal time shift was 3 years. I have yet to rerun the other simulations with this model.

I'll probably tweak some things, think about it, and repost results in a week or two when people are back from xmas.

Sieben, 

I think I see mathematically waht you're doing here (though I've never worked with these types of models so I could be wrong). But I am not sure I follow the economics behind it. Would you mind adding a few words about the economics modivating your model?

One thing I would like to hear about specificlaly is the growth coefficient C. It is a parameter estimated by your optimization model, but what does it mean? And what does it mean to multiply that coefficient by (1-taxes)? 

If you are just interested in the marginal impact of a increase in tax rates, then I would think that a straight forward regression analysis would be better suited (and would not take 5 hours to run :P). You could just include lag variables to see the impact tax rates in year t have on GDP 5 years later (t+5). Plus you would be able to explicitly include other factors that influence growth besides taxes. But I might be missing something/ Could you also explain why regression analysis was illsuited for the task? 

The tax rates and growth rates in Scandinavia have nothing to do with socialism.  Take Norway for example.  What is the difference between the state of Norway and any random resource corporation?  One mines resources and distributes earnings to "shareholders", which are a tiny portion of the population of one state.  The other mines resources and distributes earnings to "citizens", which are a tiny portion of the population of the world.  The only difference is that "citizens" didn't buy their share.

The idea of socialism is, "From each according to his abilities, to each according to his needs."  I'm pretty sure that more than 4.8m people have needs.  Try distributing the wealth to 6 billion people and get back to me about growth rates... or should I say shrink rates?

Student:

Would you mind adding a few words about the economics modivating your model?

The philosophy of the model is that GDP today depends on all previous years, and that investment does not necessarily show net returns overnight. So delay each year's growth contribution to GDP, and spread it out over time to approximate when all the investments show returns (central limit theorem).

Student:

It is a parameter estimated by your optimization model, but what does it mean? And what does it mean to multiply that coefficient by (1-taxes)?

Something like the amount of the economy that is growing.

Student:

If you are just interested in the marginal impact of a increase in tax rates, then I would think that a straight forward regression analysis would be better suited (and would not take 5 hours to run :P)

I don't understand... I stayed away from linear type analyses because it compares growth in year X to policy in year X, when growth in year X really depends on all previous policies and growths.

Student:

And what does it mean to multiply that coefficient by (1-taxes)?

It means that each year, the government takes some of the growth. In all fairness, they gov might not take from the growth-economy at the same rate as the rest of the economy, but its an approximation. The end result is that the model assumes government spending goes down a black hole and is never used to grow (or harm) the economy.

Student:

You could just include lag variables to see the impact tax rates in year t have on GDP 5 years later (t+5)

First, I think you can get any result you want if you just set an arbitrary time shift. I *TRY* to avoid that because I don't shift everything by dt, its just centered at dt. So there's still an impact before/after, which I hope constrains my model (haven't gotten any negateve dts yet).

Student:

Could you also explain why regression analysis was illsuited for the task?

Hmm... because regression would only establish correlation... but if I build an econometric model that assumes causation, and then show that model is empirically valid, that's stronger in my dumb engineering mind.