David A. Armstrong II
University of Wisconsin - Milwaukee
Department of Politics Science
PO Box 413
Milwaukee, WI 53201-0413
e: armstrod@uwm.edu
t: 414-229-4239
w: http://www.quantoid.net

A Revision of The Heritage Foundation Economic Freedom Index: Which Variables to Use

A Revision of The Heritage Foundation Economic Freedom Index: Which Variables to Use

The Heritage Foundation uses the following set of variables to create an additive index.
  1. Business Freedom
  2. Trade Freedom
  3. Fiscal Freedom
  4. Government Spending
  5. Monetary Freedom
  6. Investment Freedom
  7. Financial Freedom
  8. Property Rights
  9. Freedom from Corruption
  10. Labor Market Freedom (2005-2010)
If we refer to the each of the variables as Yij where j refers to the particular variable (e.g., Yi1 refers to each country's score on Business Freedom, Yi2 refers to each country's score on Trade Freedom and so forth), then the index created by the Heritage Foundation is done as follows:

Economic Freedomi =
∑
j 
 Yij
(1)
The underlying model allowing them to use this method is called the `Summated Rating Model' [Jacoby, 1991,McIver and Carmines, 1981,Nunnally, 1978]. This basically takes the form:

Yij = Zi + εij
(2)
The intuition is that each observed indicator is an imperfect (i.e., error-laden) realization of the unobservable latent variable Zi. By aggregating across the variables for each observation, we get a better idea of what the underlying trait looks like.1
This method makes a number of assumptions, but the important one is:
This assumption basically has two important parts. First, it assumes that there is only one underlying dimension. Second, it assumes that each of the indicators is a function of this underlying dimension. We will test both of these in turn below.

1  Dimensionality and Reliability of the Indicators

We can test whether there is a single dimension and if all of the variables are functions of that single dimension with exploratory factor analysis Gorsuch [1983],Lattin, Carroll and Green [2003] on each of the 16 years in the dataset (I do each of these separately). To do this I use the 9 or 10 variables (depending on the year) used by the Heritage Foundation in the following model:

Yij = λj1Zi1 + λj2Zi2 + …+ λjmZim + εij
where, in this implementation, Yij (as it did above) stands the jth observed variable (of 9 or 10, depending on the year) for the ith (of 154) countries.2 This is essentially a series of linear regressions where the independent variables are the (unobserved) underlying common dimensions and the dependent variables are the observed indicators. To the extent that the indicators are well explained by a single dimension, the variance explained by Zi1 will be much greater than the variance explained by the other Zim variables. To the extent that variables Yij are reliable and valid indicators of the underlying dimension, λjm will be closer to 1 than zero.3
First, consider the λ's or factor pattern coefficients (often referred to as "loadings"). If the model in equation 2 (i.e., the one used by the Heritage Foundation) is right, then the black circles (the λ's from the first dimesion) in Figure 1 should all be close about the same value and closer to one than zero and the gray squares (the λ's from the second dimension) should all be pretty close to zero. This is approximately true for all of the variables except 2 - Fiscal Freedom and Government Spending. For these two variables the second dimension coefficients (gray squares) are closer to one and the black circles are closer to zero. This indicates that these two variables are poor indicators of the underlying concept. In fact, government spending is negatively related to the underlying dimension (nominally, Economic Freedom) as the black circles on the left of the zero line in the figure indicate. The suggestion from this model is that these two variables are not indicators of economic freedom and should not be used as such.
Figure 1: Factor Pattern Coefficients
loads.png
NB: The points in the figure represent factor pattern coefficients (loadings) for a two-factor solution. The black circles represent the first factor coefficients and the gray squares represent the second factor coefficients. The expectation is that the black circles will be close to +1 and the gray squares will be close to zero, which is indicated by the dotted vertical line.
This is further confirmed by the "scree plots", which plot eigenvalues (the variance explained in all of the observed indicators by each factor) on the y-axis against factors themselves on the x-axis. Generally, there is an elbow in the plot (a point at which the slope changes drastically) and the dimensionality of the space (the number of unique sources of variation in the observed indicators) is taken to be the number of dimensions before the elbow. While this is a subjective measure, it is one that has withstood the test of time. Figure 2 shows the scree plots for each year both including the two offending variables (solid line) and excluding the two variables mentioned above (dotted line). What we can see is that removing the two variables does not change the amount of common variance explained by the first factor, but it does reduce the variance explained by the second factor.
Figure 2: Eigenvalues
eigen.png
NB: The figure shows the scree plots for each year. The expectation is that the first factor will have a high eigenvalue and the others will have eigenvalues lower than 1, or at least much lower than the first one. The two lines are eigenvalues including the government spending and fiscal freedom (solid line) and excluding the same variables (dotted line)
All of this taken together suggests that the two variables - government spending and fiscal freedom are not valid indicators of economic freedom and thus should be removed from the analysis. I proceed below in accordance with this recommendation.

References

Gorsuch, Richard. 1983. Factor Analysis. Hillsdale, NJ: Lawrence Erlbaum.
Jacoby, William G. 1991. Data Theory and Dimensional Analysis. Thousand Oaks: Sage.
Lattin, James, J. Douglas Carroll  Paul E. Green. 2003. Analyzing Multivariate Data. Brooks/Cole - Thomson Learning.
McIver, John P.  Edward G. Carmines. 1981. Unidimensional Scaling. Thousand Oaks: Sage.
Nunnally, James C. 1978. Psychometric Theory. New York: McGraw-Hill.

Footnotes:

1A good example of where this is used in the public domain is the aggregation of polls done by blogs like Pollster.com. Here, they use information from all sorts of polls to get a better idea of what the aggregate vote will look like. Where any one poll might exhibit bias, by aggregating the polls, they are average bias on the left with bias on the right and they end up with a much cleaner measure than any single poll.
2Some of the smaller countries with less than 10 years worth of data have been dropped from the analysis, though with no noticeable effect on the observations remaining in the model.
3Here all of the variables (both the Y's and Z's are rescaled to have means of zero and variances of one), so the regression coefficients λ's represent the correlation between the Y's and Z's.

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On 8 Apr 2010, 10:36.