Download economic freedom leads

Is economic freedom related to economic growth?
It is an article of faith among supporters of capitalism: economic freedom leads to
economic growth. The publication Economic Freedom of the World: 2003 Annual Report (James Gwartney and Robert Lawson with Neil Emerick, Economic Freedom of the
World: 2003 Annual Report, Vancouver: The Fraser Institute, 2003; data retrieved from
www.freetheworld.com) is devoted to the examination of economic freedom across the
world (economic freedom being defined as freedom to trade (an open trade policy, with
minimal barriers to imports and minimal subsidies to domestic industries), freedom to invest (few restrictions on foreign investment), freedom to operate a business without overly
burdensome regulation, and secure property rights. The following quote from page xi of
that publication summarizes the beliefs of the authors: “The trend toward [economic] liberalization, that is, continued undisturbed. This suggests it is anything but a passing fad,
the artifact of some economic ‘bubble.’ Rather, it represents a deep worldwide consensus
that the path to prosperity lies in the verities of open trade, sound money, international
flows of goods and capital (and labor), market-determined prices, sensible regulation, and
the protection of property rights.” Do the data support the existence of these benefits of
economic freedom?
This is obviously a complex issue, but regression methods can be useful in looking at
the evidence. Consider the following plot of the 2000 per capita Gross Domestic Product
(GDP, in 1995 U.S. dollars) versus the 2000 Economic Freedom score. Note, by the way,
that by using data from 2000, we are avoiding the effects of the worldwide economic
downturn that started in 2001. The data comprise a near-census of all of the countries of
the world, so when we talk about predicting per capita GDP (for example), we are actually
treating these data as a sample from a reasonably stable ongoing process.
c 2008, Jeffrey S. Simonoff
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The freedom score is on a scale from 1 to 5, with lower values corresponding to more
economic freedom. Presumably we would expect an inverse relationship here, and that is
what we see. On the other hand, it is distinctly nonlinear, as the following fitted line plot
shows:
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It is very apparent from this plot that a straight-line model is not appropriate for
these data. We’ll address that point in a little while, but for now I’m going to ignore the
obvious evidence, and fit a least squares linear regression model anyway.
Here is regression output for this model.
Regression Analysis: Per capita GDP versus 2000 freedom score
The regression equation is
Per capita GDP = 40114 - 10831 2000 freedom score
150 cases used 6 cases contain missing values
Predictor
Constant
2000 fre
S = 8428
Coef
40114
-10831.3
SE Coef
3020
972.8
R-Sq = 45.6%
c 2008, Jeffrey S. Simonoff
T
13.28
-11.13
P
0.000
0.000
R-Sq(adj) = 45.2%
3
Analysis of Variance
Source
Regression
Residual Error
Total
DF
SS
1 8806128436
148 10513603863
149 19319732299
MS
8806128436
71037864
F
123.96
P
0.000
The t-test for the slope and the F -test are of course equivalent here, and they imply
that there is a strongly statistically significant relationship between freedom score and per
capita GDP, as the p-value is quite small. We see that the estimated slope is −10831. This
says that the estimated decrease in per capita GDP for a one point increase in the freedom
score is $10,831. What does this mean? A one point increase in the freedom score is a
large one, as it corresponds to a full category difference in a five-point scale. The following
output can help in interpreting the coefficient:
Descriptive Statistics: 2000 freedom score
Variable
2000 fre
Variable
2000 fre
N
153
SE Mean
0.0605
N*
3
Mean
3.0588
Minimum
1.3000
Median
3.0000
Maximum
5.0000
TrMean
3.0478
Q1
2.5000
StDev
0.7482
Q3
3.6000
As you can see, the mean and median score are right in the middle, at (about) 3. Roughly
one-quarter of the countries fall .5 below this, and roughly one-quarter fall .5 above it, so a
one-unit change in the freedom index corresponds, for example, to the difference between a
country at the 25th percentile and one at the 75th percentile. A per capita GDP difference
of over $10,000 certainly seems to be meaningful from a practical point of view. The
intercept of 40114 is the estimated expected per capita GDP when the freedom score is 0;
since this is impossible, this coefficient has no physical meaning.
Does this model provide useful predictive power? The standard error of the estimate
is $8428, implying (by the standard assumptions) that this model can predict per capita
GDP to within ±(2)(8428) = ±$16856 roughly 95% of the time. Is this a noteworthy
accomplishment? Consider the following output:
c 2008, Jeffrey S. Simonoff
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Descriptive Statistics: Per capita GDP
Variable
Per capi
Variable
Per capi
N
153
SE Mean
914
N*
3
Mean
7250
Minimum
116
Median
1649
Maximum
55744
TrMean
5749
Q1
577
StDev
11309
Q3
7324
The range of per capita GDP values is more than $55,000, so this improvement in predictive
power might be considered moderate. This is consistent with the R2 , which tells us that
a bit less than half of the variability in per capita GDP is accounted for by economic
freedom.
Of course, in actual fact, all of this is useless, since the linear model is inappropriate
here. The scatter plot made this obvious, but there are other clues also. The target
variable is very long right-tailed:
c 2008, Jeffrey S. Simonoff
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This was obvious from the descriptive statistics (the mean is more than four times the
median), and also could have been seen in the original scatter plot. Residual plots reinforce
the problems: increasing variability of the residuals with the fitted values, and a long right
tail:
c 2008, Jeffrey S. Simonoff
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All of this evidence is pointing us in one direction — to analyze these data in a logged
scale. Here is a scatter plot of logged per capita GDP (logs base 10) versus economic
freedom:
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Now, that’s more like it! Here is a fitted line plot, followed by regression output:
c 2008, Jeffrey S. Simonoff
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Regression Analysis: Logged GDPpc versus 2000 freedom score
The regression equation is
Logged GDPpc = 5.66 - 0.764 2000 freedom score
150 cases used 6 cases contain missing values
Predictor
Constant
2000 fre
Coef
5.6608
-0.76425
S = 0.4532
SE Coef
0.1624
0.05231
R-Sq = 59.1%
T
34.86
-14.61
P
0.000
0.000
R-Sq(adj) = 58.8%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
148
149
c 2008, Jeffrey S. Simonoff
SS
43.842
30.394
74.237
MS
43.842
0.205
F
213.48
P
0.000
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How do we interpret these results? The R2 tells us that the index accounts for almost
60% of the variability in logged per capita GDP, a reasonably large amount. Once again
the intercept is meaningless, but what about the slope? The slope coefficient is −.764; this
says that a one-unit increase in the economic freedom index is associated with an expected
.764 unit decrease in the logged per capita GDP. We’ve already talked about what a oneunit increase in the index means, but what does a .764 unit decrease in logged per capita
GDP mean? The key is to remember what logarithms mean. Recall, for example, that
log10 10 = 1, and log10 100 = 2. The logs of these two numbers differs by 1, which is telling
us that the numbers themselves differ by a multiplicative factor of 101 , or 10 (that is 100
is ten times 10). Two numbers whose logs differ by .764 differ by a multiplicative factor of
10.764 = 5.8; that is, one is 5.8 times the other. Equivalently, if one number has log .764
lower than another, it is a multiplicative factor of 10−.764 = .172 smaller. Of course, we
see that the regression itself is highly statistically significant.
So, what does our −.764 coefficient mean? It says that a one-unit increase in the
economic freedom index is associated with multiplying the expected per capita GDP by
10−.764 , or .172; that is, a one-unit increase in the index is associated with an expected
82.8% decrease in per capita GDP. This is quite a lot!
[What if our predictor had also been a logged variable? First, we can just recognize
that the coefficients continue to mean what they always mean. Say the fitted model was
log Y = 2.3 + .6 × log X (that is, a regression was fit the logarithm (base 10) of Y as the
target, and the logarithm of X as the predictor, for some variables X and Y ). The intercept
is the estimated expected value of the target (log Y ) when the predictor (log X) equals 0;
that is, when X = 1 (since log 1 = 0). So, in this hypothetical case, the estimated Y when
X = 1 is 102.3 = 199.5. Whether this means anything or not depends on whether X = 1
is a meaningful condition. The slope tells us the estimated change in log Y when log X
increases by 1, but that just corresponds to X being multiplied by 10. Therefore, in this
hypothetical case, multiplying X by 10 is associated with multiplying Y by 10.6 = 3.98.
Of course, this is also an elasticity, which means that a 1% change in X is estimated to be
associated with a .6% change in Y .]
We need to adjust our thinking regarding the standard error of the estimate in the
same way. It is .453, which we know means that we should be able to predict logged per
capita GDP to within ±(2)(.4532) = ±.9064 roughly 95% of the time, but what does that
c 2008, Jeffrey S. Simonoff
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mean? We just use the same argument as before; since 10−.906 = .124 and 10.906 = 8.06,
this standard error of the estimate says that knowing the economic freedom index allows
us to predict per capita GDP to within a multiplicative factor of (roughly) 8, roughly
95% of the time. So, for example, a country with economic freedom index equaling 3 has
predicted logged per capita GDP of 5.6608 − .76425 × 3 = 3.36805, or predicted per capita
GDP of 103.36805 = $2334. The standard error of the estimate tells us that we wouldn’t be
surprised if the actual per capita GDP was as much as 8 times less that ($289) to as much
as 8 times more that ($18,810). This wide a range might surprise you, but it’s inherent to
the fact that per capita GDP is very long right-tailed; remember, the range of per capita
GDP values is ($116, $55744), so the largest value is more than 480 times the smallest!
Residual plots look okay for this model:
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This is a situation where it is natural to consider the use of confidence and prediction
intervals. Consider the case of Libya. Its 200 freedom score was 4.85, but its per capita
GDP is not given in the data. What does the regression model imply for that value? Here
are confidence and prediction interval results:
Predicted Values for New Observations
New
Obs
Fit
SE Fit
95% CI
95% PI
1
1.9542
0.1025
(1.7517, 2.1567)
(1.0361, 2.8724)X
X denotes a point that is an outlier in the predictors.
Values of Predictors for New Observations
c 2008, Jeffrey S. Simonoff
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2000
New
1
freedom Obs
score
4.85
The confidence interval would correspond to an interval for the average response for
all observations in the population with 2000 freedom scores equal to 4.85, but since the
response variable is in the log scale it is not meaningful here. On the other hand, the prediction interval is useful here. The 95% interval for logged per capita GDP of (1.0361, 2.8724)
converts to an interval of (10.87, 745.42). Note that the interval is asymmetric around the
geometric mean of 101.9542 = 89.99, which reflects the much higher natural variability in
per capita GDP at the upper end compared to at the lower end. Note that the ratio of the
high to the low end of the interval is roughly 68.6, which corresponds closely to our earlier
rough prediction interval of being able to predict per capita GDP to within a multiplicative
factor of about 8.
Thus, it would seem that we’re done, except for one thing — this analysis doesn’t
really address that quote at the beginning of this handout. It’s not surprising that wealth
and economic freedom would go together, but that doesn’t necessarily say anything about
whether it is in a country’s economic best interest to become more economically free. As
the quote says, it’s the “path to prosperity” that matters; that is, economic growth, not
current economic status. Is economic freedom related to economic growth? Here is a plot
of 2000 growth in GDP versus 2000 economic freedom index:
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This is not very encouraging, as the fitted line plot shows:
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There is apparently very little relationship between one-year economic growth and
economic freedom. Now, of course, one-year growth might be too variable a measure,
and longer-term growth measure might be more useful. Still, this result is disappointing,
especially since it came at a time of general economic prosperity.
Regression Analysis: GDP growth rate versus 2000 freedom score
The regression equation is
GDP growth rate = 3.10 + 0.372 2000 freedom score
153 cases used 3 cases contain missing values
Predictor
Constant
2000 fre
S = 3.108
Coef
3.100
0.3719
SE Coef
1.061
0.3369
R-Sq = 0.8%
c 2008, Jeffrey S. Simonoff
T
2.92
1.10
P
0.004
0.271
R-Sq(adj) = 0.1%
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Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
151
152
SS
11.767
1458.533
1470.300
MS
11.767
9.659
F
1.22
P
0.271
With an R2 less than 1%, there’s not much need to try to interpret the slope coefficient
(in any event, it’s positive, which would imply that more freedom is associated with less
growth!). The regression is of course not close to statistically significant. Do the regression
assumptions seem reasonable here? Maybe not:
c 2008, Jeffrey S. Simonoff
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There are two clearly unusual points: Equatorial Guinea and Turkmenistan. Each
of these countries had very high growth in 2000 (16.9% and 17.6%, respectively), despite
repressive economic situations (freedom scores 4.05 and 4.3, respectively). Equatorial
Guinea’s GDP growth is unusual in that extensive offshore oil exploitation only began
in 1997, while Turkmenistan’s high growth came from oil and natural gas exports. It is
important to explore whether these two countries have had a strong effect on the overall
model, since they are not at all typical of the general pattern. We can do this by omitting
them and seeing how things are affected, being sure to report that this is what we
have done.
Overall, not much changes; in fact, the relationship becomes even weaker:
c 2008, Jeffrey S. Simonoff
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Regression Analysis: GDP growth rate versus 2000 freedom score
The regression equation is
GDP growth rate = 3.99 + 0.026 2000 freedom score
151 cases used 3 cases contain missing values
Predictor
Constant
2000 fre
S = 2.750
Coef
3.9872
0.0257
SE Coef
0.9482
0.3027
R-Sq = 0.0%
T
4.20
0.09
P
0.000
0.932
R-Sq(adj) = 0.0%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
149
150
c 2008, Jeffrey S. Simonoff
SS
0.055
1126.886
1126.941
MS
0.055
7.563
F
0.01
P
0.932
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The model now seems to fit fine, so we should just accept it as reflecting what is really
going on here:
c 2008, Jeffrey S. Simonoff
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So what have we learned? The results are decidedly mixed. There is a clear relationship between a country’s current level of wealth and economic freedom, although this is
accompanied by a good deal of variability. There is apparently no relationship between
economic freedom and short-term GDP growth. Whether there is a relationship between
economic freedom and long-term growth cannot be addressed with these data.
c 2008, Jeffrey S. Simonoff
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MINITAB commands
Although it is possible to omit observations in a sample by simply highlighting them
in the data worksheet and pressing the delete key, this is generally not advisable, since
then the observation cannot be recovered without reopening the original file (and if you
save the data before doing that, the observation is gone completely). A better approach
is to create a subset of the worksheet that has the observations you want; this will create
a new worksheet that can be analyzed, but the original worksheet will still be there as
well. Click on Data → Subset Worksheet. You can give the new worksheet an identifying
name if you like under Name:. Click the radio button next to Specify which rows to
exclude, click the radio button next to Specify rows:, and enter the row numbers of the
outliers in the associated box. Note that there is a good deal of flexibility in the subsetting;
you can identify rows to include or exclude, identify them by some condition (for example,
observations with values of a predictor greater than 10), or brush them on a scatter plot
and identify them that way, in addition to specifying them by row number(s).
c 2008, Jeffrey S. Simonoff
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