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# The government is always our enemy watch

1. (Original post by Captain Crash)
R squared = 0.42 ..... lol
Hang on, why is that so bad?

Why assume that small government = small proportion of GDP? A minimalist government in an impoverished country may very well spend more as a percentage of GDP than a reasonably 'big' government in a rich western country.
Not correcting for the amount of wealth available leads to absurdities. Suppose, for instance, there is a country with a GDPPC of £1,000,000 and it has a million inhabitants. The government has an absolute income of £1,000,000, or 0.0001% of GDP, and employs 1 person.

In a second country, the GDPPC is £1. It also has a million inhabitants. The government has an absolute income of £900,000, or 90% of all income. It employs almost everyone in the country.

According to your proposed method, the government in the first country should be considered larger than that in the second. Which is exploiting a rhetorical distinction to cook the numbers as far as I am concerned...
2. (Original post by Collingwood)
Hang on, why is that so bad?
Because a value of 0.42 means at best weak correlation. When you take into account causation=/= correlation and the fact the two axes aren't independent means the graph is pretty meaningless.
(Original post by Collingwood)
Not correcting for the amount of wealth available leads to absurdities. Suppose, for instance, there is a country with a GDPPC of £1,000,000 and it has a million inhabitants. The government has an absolute income of £1,000,000, or 0.0001% of GDP, and employs 1 person.

In a second country, the GDPPC is £1. It also has a million inhabitants. The government has an absolute income of £900,000, or 90% of all income. It employs everyone in the country.

According to your proposed method, the government in the first country should be considered larger than that in the second. Which is exploiting a rhetorical distinction to cook the numbers as far as I am concerned...
Or....
Suppose, for instance, there is a country with a GDPPC of £1,000,000 and it has a million inhabitants. The government has an absolute income of £1,000,000, or 0.0001% of GDP, and employs 50,000 people.

In a second country, the GDPPC is £1. It also has a million inhabitants. The government has an absolute income of £900,000, or 90% of all income. It employs 1 person.

My point was that percentage of GDP means very little in deciding how big a government is. For instance, countries experiencing huge growth may not have increases in spending to match it, despite increasing the absolute size of government.
3. (Original post by Captain Crash)
Because a value of 0.42 means at best weak correlation. When you take into account causation=/= correlation and the fact the two axes aren't independent means the graph is pretty meaningless.
0.42 is a weak correlation according to whom? Given the vast number of variables that affect GDP that aren't controlled for here, it would be absolutely remarkable to get such a value if there was no correlation at all. If there were actually a correlation in the other direction as Oswy claims then something very weird indeed must be going on.

Or....
Suppose, for instance, there is a country with a GDPPC of £1,000,000 and it has a million inhabitants. The government has an absolute income of £1,000,000, or 0.0001% of GDP, and employs 50,000 people.

In a second country, the GDPPC is £1. It also has a million inhabitants. The government has an absolute income of £900,000, or 90% of all income. It employs 1 person.

My point was that percentage of GDP means very little in deciding how big a government is. For instance, countries experiencing huge growth may not have increases in spending to match it, despite increasing the absolute size of government.
Hang on, what? You think that a country that funnels 90% of the entire income of the populace to a single person would have a small government compared to one that taxes 0.0001% of GDP to employ 50,000 civil servants? That sounds like some sort of insane personality cult dictatorship to me.

You're quite, of course, that measuring the size of government in absolute terms is the only way to determine the "absolute size of government". But like I say, no one really cares about the absolute size of government, or they would agree that a the first country in my example had a bigger government than the latter country.
4. (Original post by Collingwood)
0.42 is a weak correlation according to whom? Given the vast number of variables that affect GDP that aren't controlled for here, it would be absolutely remarkable to get such a value if there was no correlation at all. If there were actually a correlation in the other direction as Oswy claims then something very weird indeed must be going on.
General laws of statistics.

I don't believe that Oswy is claiming a correlation that right here right now countries with relative small governments correlate with economic power. Rather he is claiming that in every case where a country has economic power, there is substantial government of some kind - even the 'smallest' governments aren't actually that small and most are larger.
(Original post by Collingwood)
Hang on, what? You think that a country that funnels 90% of the entire income of the populace to a single person would have a small government compared to one that taxes 0.0001% of GDP to employ 50,000 civil servants? That sounds like some sort of insane personality cult dictatorship to me.
ok, I should have thought that one through. But if we increase the number to say 50/100 people rather than one I hope the point is carried through.
(Original post by Collingwood)
You're quite, of course, that measuring the size of government in absolute terms is the only way to determine the "absolute size of government". But like I say, no one really cares about the absolute size of government, or they would agree that a the first country in my example had a bigger government than the latter country.
But isn't the fact that every successful country has an substantial absolute size of government exactly what Oswy is arguing?
5. (Original post by Captain Crash)
Because a value of 0.42 means at best weak correlation. When you take into account causation=/= correlation and the fact the two axes aren't independent means the graph is pretty meaningless.
This is a pretty weak response. Firstly, an r^2 of .42 is actually pretty good for social science, particularly when no-one is claiming that the size of government is the only variable or tells the whole story about economic growth. Secondly, what the hell are you talking about regarding the axes not being independent? Third, of course, correlation =/= causation. But when you have a vast quantity of economic theory and both quantitive and qualitative data all of which points pretty unequivocally to the conclusion that bigger governments mean less growth it is slightly asinine to try and defend your position that way. If we argue from economic theory, you'll say "but where is the data!" If we show you the data, you'll say "But correlation =/= causation!"

Or....
Suppose, for instance, there is a country with a GDPPC of £1,000,000 and it has a million inhabitants. The government has an absolute income of £1,000,000, or 0.0001% of GDP, and employs 50,000 people.

In a second country, the GDPPC is £1. It also has a million inhabitants. The government has an absolute income of £900,000, or 90% of all income. It employs 1 person.

My point was that percentage of GDP means very little in deciding how big a government is. For instance, countries experiencing huge growth may not have increases in spending to match it, despite increasing the absolute size of government.
Again, this is a ridiculous point to try and nitpick; most people actually define the size of government as the proportion of GDP it spends. If you want to be constructive, feel free to propose an alternative definition; I have a sneaking suspicion both that you are not in fact trying to be constructive, and that any alternative definition you could come up with would be extremely well correlated to the proportion of GDP spent.
6. (Original post by Captain Crash)
My point was that percentage of GDP means very little in deciding how big a government is. For instance, countries experiencing huge growth may not have increases in spending to match it, despite increasing the absolute size of government.
Maybe not, but it matters very much when deciding the effect that the government has on the economy. When Libertarians object to "Big Government" what we're actually objecting to is "costly government" -- we don't really mind how many people the State employs, so long as it's taxation level is low and it's regulatory burden light.
(Original post by Oswy)
the fact remains that societies which have so advanced, or are advancing (i.e. China) are not libertarian societies of minimum or zero government or anything close.
Forgetting of course that the current rate of growth in China was achieved through a lightening of the regulatory burden across the country, and the creation of Special Economic Zones with minimal governments.
7. (Original post by DrunkHamster)
Secondly, what the hell are you talking about regarding the axes not being independent?
As i said, it is entirely concievable for a country to have economic growth outstriping the growth of spending, thus reducing the percentage of GDP spent on government despite spending increase. Therefore the two variables of GDP and GDP % spent by government are not independent.
(Original post by DrunkHamster)
Third, of course, correlation =/= causation. But when you have a vast quantity of economic theory and both quantitive and qualitative data all of which points pretty unequivocally to the conclusion that bigger governments mean less growth it is slightly asinine to try and defend your position that way. If we argue from economic theory, you'll say "but where is the data!" If we show you the data, you'll say "But correlation =/= causation!"
Within the context of a single graph with an r value of 0.42, you adjust your threshold accordingly. The higher the r value, the more likely correlation does equal causation.
(Original post by DrunkHamster)
Again, this is a ridiculous point to try and nitpick; most people actually define the size of government as the proportion of GDP it spends. If you want to be constructive, feel free to propose an alternative definition; I have a sneaking suspicion both that you are not in fact trying to be constructive, and that any alternative definition you could come up with would be extremely well correlated to the proportion of GDP spent.
Absolute size of government in terms of inflation-adjusted pound sterling/dollar? That would do for me, although no doubt you'd need to factor in the non-cost measures of government e.g. regulation.
8. (Original post by sconzey)
[...] and it's regulatory burden light.
And how exactly is that expressed in the % GDP spent by government?
9. (Original post by Oswy)
Yeah, when the actual historical development of human societies doesn't fit your ideals, retreat into the much safer theory, lol
You are assuming that history explains things. It explains nothing. History is a bunch of stuff that happened. Economics, psychology, etc, explain why things happen.
10. (Original post by Captain Crash)
And how exactly is that expressed in the % GDP spent by government?
Oh, no it's not of course. :P But when estimating how detrimental a given govenment will be to an economy, the % GDP is a good approximator -- it doesn't measure all the factors Libertarians care about, but it measures one of them.
(Original post by Captain Crash)
Within the context of a single graph with an r value of 0.42, you adjust your threshold accordingly. The higher the r value, the more likely correlation does equal causation.
What? R is a measurement of correlation... A higher r-value means more-neatly correlated results. It's darn hard to prove causation statistically.
11. (Original post by Captain Crash)
As i said, it is entirely concievable for a country to have economic growth outstriping the growth of spending, thus reducing the percentage of GDP spent on government despite spending increase. Therefore the two variables of GDP and GDP % spent by government are not independent.
If economic growth outstrips the growth of spending then the government has 'really' shrunk. It's not like the government had no choice but to raise spending slower than growth...

Within the context of a single graph with an r value of 0.42, you adjust your threshold accordingly. The higher the r value, the more likely correlation does equal causation.
It only means the correlation is better. If the data does not control for a whole host of other variables you know are also affecting the results, getting a perfect correlation here would be sheer chance, and would say little or nothing about the chances of causation. R^2 of 0.42 may be pretty bad for a simple physics experiment, but in this instance it is very compelling. Whether the correlation equals a causation is not demonstrated by this graph, but I hardly think you can accuse us of shying away from presenting theory to back it up on this board...

Absolute size of government in terms of inflation-adjusted pound sterling/dollar? That would do for me, although no doubt you'd need to factor in the non-cost measures of government e.g. regulation.
In this case you do have to defend the notion that the first government in my example is 'bigger' than the second (I assume that your eagerness to posit counter-examples means you don't believe this?). Or indeed than one that takes 90% of all income and distributes it to 50 plutocrats... though I'm not sure why this is more reasonable, but even if it was, you'd still have to defend the other example too.

You are correct about regulation, though.
12. (Original post by sconzey)
What? R is a measurement of correlation... A higher r-value means more-neatly correlated results. It's darn hard to prove causation statistically.
I wasn't saying statisticially causation is proven, but the closer r gets to 1, the more likely it is that the two things are related and therefore more likely that one caused the other.
13. (Original post by Collingwood)
If economic growth outstrips the growth of spending then the government has 'really' shrunk. It's not like the government had no choice but to raise spending slower than growth...
So a government that increases spending, but not at the rate of economic growth is actually rolling back?
(Original post by Collingwood)
It only means the correlation is better. If the data does not control for a whole host of other variables you know are also affecting the results, getting a perfect correlation here would be sheer chance, and would say little or nothing about the chances of causation. R^2 of 0.42 may be pretty bad for a simple physics experiment, but in this instance it is very compelling. Whether the correlation equals a causation is not demonstrated by this graph, but I hardly think you can accuse us of shying away from presenting theory to back it up on this board...
Quite. All you can say at most is that percentage of GDP spent by government represents contributes ~42% of the correlation with GDP assuming independent conditions.
(Original post by Collingwood)
In this case you do have to defend the notion that the first government in my example is 'bigger' than the second (I assume that your eagerness to posit counter-examples means you don't believe this?). Or indeed than one that takes 90% of all income and distributes it to 50 plutocrats... though I'm not sure why this is more reasonable, but even if it was, you'd still have to defend the other example too.
Ok, maybe an absolute amount isn't the only factor. Evidently population of government employees, extent of government activities and regulation play part as well.
14. (Original post by Captain Crash)
As i said, it is entirely concievable for a country to have economic growth outstriping the growth of spending, thus reducing the percentage of GDP spent on government despite spending increase. Therefore the two variables of GDP and GDP % spent by government are not independent. [1]

Within the context of a single graph with an r value of 0.42, you adjust your threshold accordingly. The higher the r value, the more likely correlation does equal causation. [2]

Absolute size of government in terms of inflation-adjusted pound sterling/dollar? That would do for me, although no doubt you'd need to factor in the non-cost measures of government e.g. regulation. [3]
Virtually any credibility you had on statistical matters has now gone after this post, as far as I am concerned. It's hard to put into words how wrong you are here.

[1] I don't think you understand that the entire point of exhibiting the graph was to show some kind of relationship between GDP and GDP spent by government. That does not mean that the variables are 'dependent' any more than a graph showing a correlation between calories ingested and weight shows has 'dependent' variables. The point is that they measure two separate things, which we are trying to show are correlated. You are essentially saying that the very fact there is a correlation means the variables are not independent; presumably you think all graphs (no matter what correlation they purport to show) are fundamentally misleading for the same reason. Good job!

[2] Uh, no, it doesn't. This is just wrong. Not like wrong in the sense that I disagree with your opinion, but just plain wrong. If I plot a graph of height in feet against height in metres with linear axes, the r-squared will be 1. Yet there is no causation at play. Given that r-squared is a measure only of correlation, and correlation is not causation, this is about as wrong as it's possible to be on the matter.

[3] How on earth can you define "size of government" in terms of "Absolute size of government in terms of inflation-adjusted pound sterling/dollar?" Do you not see the obvious circularity?
15. damn the libertarians have invaded! calling for backup...
16. (Original post by tomheppy)
damn the libertarians have invaded! calling for backup...
17. (Original post by DrunkHamster)
Virtually any credibility you had on statistical matters has now gone after this post, as far as I am concerned. It's hard to put into words how wrong you are here.

[1] I don't think you understand that the entire point of exhibiting the graph was to show some kind of relationship between GDP and GDP spent by government. That does not mean that the variables are 'dependent' any more than a graph showing a correlation between calories ingested and weight shows has 'dependent' variables. The point is that they measure two separate things, which we are trying to show are correlated. You are essentially saying that the very fact there is a correlation means the variables are not independent; presumably you think all graphs (no matter what correlation they purport to show) are fundamentally misleading for the same reason. Good job!

[2] Uh, no, it doesn't. This is just wrong. Not like wrong in the sense that I disagree with your opinion, but just plain wrong. If I plot a graph of height in feet against height in metres with linear axes, the r-squared will be 1. Yet there is no causation at play. Given that r-squared is a measure only of correlation, and correlation is not causation, this is about as wrong as it's possible to be on the matter.

[3] How on earth can you define "size of government" in terms of "Absolute size of government in terms of inflation-adjusted pound sterling/dollar?" Do you not see the obvious circularity?
1) Government spending as a percentage of GDP may be influenced by the absolute size of GDP. For instance a growing economy may have GDP growth that outstrips spending increases. The two variables aren't neccesarily independent, especially considering one is a function of the other and a third hidden varible (i.e. absolute government spending)

2)This wasn't a statisical argument per se. Let p = probability that correlation=causation in a given graph. Let q = probability that correlation is true. By looking at a set of data, probability that the data represents causation is ~pq. The closer r gets to 1, the closer q gets to 1. Therefore, the closer pq gets to 1 and the more likely the correlation represents causation (with relation to a data set with a smaller r). As for your example with height in feet vs height in metres, that would be a defunct linear regression as both factors are 100% dependent on each other - independence is needed for linear regression.

3) I defined government size in terms of absolute inflation adjusted sterling pounds/dollars spent. Admittedly I didn't word it so well, but there's no circularity there. Moreover, I retracted it in the above post.
18. (Original post by Captain Crash)
So a government that increases spending, but not at the rate of economic growth is actually rolling back?
Since size of government is defined here as percentage of GDP spent by the government, yes. I don't see what this has to do with the two values not being independent, though. At most it is just an argument for your other proposed definition of gov't size which we have already discussed...

Quite. All you can say at most is that percentage of GDP spent by government represents contributes ~42% of the correlation with GDP assuming independent conditions.
Err, no, you can justifiably say that "government spending contributes 42% of the correlation", though I think that sort of statement is still dubious. It doesn't at all imply that this is an absolute maximum. Suppose next year we run the new values through the same graph. If all the non-GDP influences are just random noise, it may well drop below, but would you expect it to never be able to rise above 42%? Clearly not. But that aside, surely you've now conceded that there is a significant correlation...?

Ok, maybe an absolute amount isn't the only factor. Evidently population of government employees, extent of government activities and regulation play part as well.
In other words, all factors that take into account proportionate impact of government (...unless you're seriously going to suggest we use absolute values for govt employees as well, making the US government larger under that measure than, say, the HK government, which 'employs' almost the whole population). I really don't see any justification for adopting this absolute measure for spending, then adding a whole bunch of ad hoc patches rather than changing it when it repeatedly fails to output sensible results.

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