Economic and Political Freedom Go Hand In Hand
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- BJohnson
- BJohnson
- JS_Mill
- JS_Mill
- JS_Mill
- BJohnson
- JS_Mill
- JS_Mill
- JS_Mill
- inlink
This archived discussion is "read only".
» BJohnson - Alex said:
Alex said: Yes, yes, yes. But I still don't see why data for Chad on the tax rate for the average income is any more reliable than taxes % of GDP.Because I can get the tax rate for income and caporate profits, as well as the tax brackets and the income levels they apply to, for the 1998 taxable year for most countries. While for most non-OECD countries, tax revenues as a percentage of GDP are only available for 1995 (most) and 1996 (rest). I don't understand why it is so hard to understand which is better.
-- posted by BJohnson
» BJohnson - Alex said:
Alex said: But why is, say,government spending on education not inconsistent?Again Alex, please consider this for a minute. How are you going to seperate out education spending from total spending figures for 161 countries? Do you have information I don't?
Not only that, I personally don't find such spending inconsistent. To me, it's not necessarily what the government spends, its how much. Sure, some spending programs are probably philosophically more an infringement on economic freedom than others: police versus Official Government Christmas Cards.
But let's say the government only "consumes" five percent of GDP. And that spending is all on education, social welfare, unemployment, subsidies for research, home mortgages, etc., etc. Do you think I care about this?
Moreover, I don't honestly see how you can seperate out spending like you want to anyway. You would need to have the federal budget for every country you grade, and then go in and line item out what you find "wasteful" or "inconsistent" with how you see econonomic freedom. I don't think it can be done.
My way is practicle and generally consistent with how I define economic freedom. Sorry it does not live up to your utopian dreams.
-- posted by BJohnson
» JS_Mill - The weighting issue
First of all, ignore what I said about 11 years of data. I’d clearly been at the cooking sherry or something, although I must confess to not quite seeing the significance of 7 in this context.But I’ve now become interested in this matter of weighting schemes, and had chance to think about it a bit. There follow a few thoughts; comments welcome.
The weighting problem for indices of an unmeasurable quantity
This is the problem of constructing an index such as the Heritage Foundation’s Index of Economic Freedom. Such indices suffer from all the known problems of index construction, plus the problem that they are meant to be closely correlated with an unmeasurable quantity. Thus they differ from indices such as divisia money, or various "shareholder value indices", where the quantity which the index is meant to track is either directly measurable or has available proxies.
There are two main problems in constructing an index of an unknown quantity -- factor selection and weighting. For the purposes of these notes, I am assuming that the factor selection problem has been solved.
Because the index cannot be "checked" against any external source, there will necessarily be an element of arbitrariness entering into its construction. This suggests the simplest possible weighting schema.
Equal Weights. This schema has much to recommend it. It is in many ways the natural response to the absence of information. It avoids the introduction of conscious bias. Furthermore, of course, it is the only defensible weighting scheme when there is not enough data for any other kind of estimation.
Are there better weighting schemata than the equal, however? In order to answer this question, I propose two desiderata from any weighting schema:
1) It should increase the cross-sectional variance of scores. This would mean that the index had a higher degree of discrimination -- that it would give more of a spread of scores (I believe that clustering is a problem in the IEF as currently constructed). There is a clear analogy here with the linear discriminant model of binary choice or "z-score". This model gives a statistic (the z-score) which is monotonically ordered in likelihood for a binary choice problem, but which cannot be easily interpreted on its own. I regard the IEF problem as analagous; the best that can be hoped for, surely, is a cardinal ordering of countries by economic freedom.
However, a criterion which maximised variance of the overall indicator would have perverse results — one would maximise this by putting all the weight on the single component with the highest cross-sectional variance. In order to avoid this (presumed undesirable) result, we add a second desideratum:
2) The weighting schema should not put excessive weight on any one category. Alternatively, one might say it should minimise the variance of the weights.
How do we trade off between these two criteria? One idea is that suggested by Barro:
Barro Weights. Barro has suggested that the components be regressed on the final scores (using some sort of pooled regression or fixed effects model), and that the weights be proportioned to the regression coefficients. We can see from consideration of the properties of the standard multivariate OLS model that this model will give greater weight to those components which have the highest covariances with the other components. Consideration of the formula for variance of a sum shows that this will have the effect of increasing the variance of the index compared to the equal weighting schema. At the same time, the use of the regression model will help to rule out the perverse case outlined above.
However, I have some concerns with the schema as specified above. First, it is likely to deliver negative weights on some components, and it is not clear how these should be interpreted. Presumably this problem could be cured by running the regression with restriction that the coefficients be non-negative. Second, it seems somewhat ad hoc to use the regression procedure to satisfy the criteria outline above. With this in mind I suggest a third method:
The V-Score. (V standing for variance). I will define the "v-score" for a weighting schema W as follows (pooling the obervations over time)
Where
I is the index (ie the components multiplied by the weights in W)
Wj are the j weights in W
V(W) =[cross-sectional variance of I under W/mean I] - [j*variance of Wj]
Thus, the v-score is a loss function which gives equal weight to the coefficients of variation of the index itself and of the weights. (Note that the mean weight is 1/j, hence the second term). W should be chosen to minimise the v-score (one could probably come up with a linear estimation method for this, but I would use Newton-Raphson, or Excel Solver).
Enough from me now, I think.
jsm
-- posted by JS_Mill
» BJohnson - JSM:
JSM:Thanks for the comments. I can see you have thought about this. Anyway, this will be my last post until January, for I am leaving for Christmas holiday. I will be vacationing for three glorious weeks in a tropical climate, far, far, away from indices and media hounds, Congressional staffers and members, etc., etc., etc.
In any event, here are a few of my comments:
You said: Because the index cannot be "checked" against any external source, there will necessarily be an element of arbitrariness entering into its construction. This suggests the simplest possible weighting schema.
But of course. You are very much correct. Even the identification of factors contains an element of arbitrariness. That is why it is essential to check the findings statistically to begin with. the whole idea of doing an OLS regression is to determine whether the findings of the IEF are consistent with our expectations. If we start with the expectation that the more economically free a country is, the more wealth it is likely to have, or the longer it will have sustainable growth, you want to determine through science whether this expectation is a valid one. We beleive we have done this.
However, I don't want to overstate the possible "arbtrariness" in the scoring. We are careful to make the methodology as transparent as possible. I detail all of the 50 independent criteria I examine on each country. I also detail the specific conditions that must exist in each of the five score levels in order to assign a grade. It is not entirely implausible to assume that a different person than myself, using the exact sources, would also achieve near identicle results. So, I do not beleive that there is a great deal of arbitrariness to the scoring (although it does probably exist to a certain extent).
You said: We can see from consideration of the properties of the standard multivariate OLS model that this model will give greater weight to those components which have the highest covariances with the other components. Consideration of the formula for variance of a sum shows that this will have the effect of increasing the variance of the index
compared to the equal weighting schema. At the same time, the use of the regression model will help to rule out the perverse case outlined above.
I do beleive that this is what Barro told us a few years back. I am not sure how much has changed though. His new book, Determinants of Growth is supposed to have made some significant progress in this area. We will probably be meeting with him again in the future.
All I can say is that for now, this is a new emerging field. We are all just stumbling around at the moment, trying to increase the level of scientific procedures as much as possible. be assured, whatever decision we make in the future, we will include multiple methods of scoring.
Happy Holidays.
-- posted by BJohnson
» inlink - An Expert's Opinion
I'm bedazzled by statics galore, the persuasions therefrom, as well as the qualifications of the participants in this discussion. I'm one of the bottom fish looking up. I'm not blinded by surface reflections.Unfortunately, my voice is never heard where it counts. If it were, the problems of our working poor would vanish like mist in morning sun. Notwithstanding all the figures discussed -- all employed to prove this or that untruth -- let us turn our attentions and concentrate on these pertinent figures: While 20 percent of the U.S. working population is prospering, 80 percent is not, and the bottom 20 percent is doing rather poorly. Do we let them eat cake? How do America's chosen experts account for this nation's poor showing? In the greatest economy on earth, where equal opportunity is our creed, is it simply because the bottom 20 percent is born lazy, stupid, or evil? Is it because the top 20 percent are born resourceful, intelligent -- morally superior humans? Is this a social problem or largely a political problem in the U.S.? The chosen experts have been on a snipe hunt for 50 years. One of the favorite ruses is making statistical comparisons between the U.S. economy and other economies. In my travels I've found that the quality of life is better in countries that rank near the bottom in their economies. A multimillionaire once told me that he would give every cent he had for what I have. I think of myself as being very lucky. I live a very good life, even though my income is near the poverty level.
Talk is cheap. Ask someone who knows. The working poor taxpayer in the U.S. has no more right to freedom than U.S. slaves before they were emancipated. The world has seen many great economies come and go. America's chosen experts are lawlessly violating fundamental laws and intrinsic values, the best way I know of wrecking "the land of the brave and the free" and changing the course of history.
-- posted by inlink
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