Tuesday, May 31, 2011

It's a Wonderful Life

Personally, I'd have gone for a big cake with candles, but last week, to celebrate its 50th anniversary, the OECD released a new "Better Life Index" (BLI) for each of its 34 member-countries. More correctly, 11 different measures were released for each country. These covered the areas of Housing, Income, Jobs, Community, Education, Environment, Governance, Health, Life Satisfaction, Safety and Work-Life Balance.  I've downloaded the data into an Excel workbook that's available on the Data page that goes with this blog.

These measures were aggregated into a single, equally-weighted BLI, which you can see here. In addition to this the OECD has provided a nice interactive tool that allows users to select their own weights across the 11 measures, and then compare the rankings of the countries they're interested in on the basis of this personalized measure. Of course, you could just do this in a spreadsheet, but I guess it's more fun to do it in real-time on their site.

So, as the OECD web site says, you can "decide for yourself what contributes most to well-being." If I wanted to, I could tinker with the weights to see what it would take for me to feel that I'd have a better life by leaving Canada (ranked essentially first equal with Australia using the equal-weight index), and going back to New Zealand (ranked fourth). I'll return to this point below.

Indices of this type are useful indicators of societal "well being", but none of them are perfect. Indeed, they don't pretend to be. When a new index comes along, you have to wonder "what's the value added?" In the case of the BLI, where "quality of life" is being measured, in some loose sense, I thought it would be interesting to compare this index with the well-known "Human Development Index" (HDI). This, too, has its limitations and its critics. The question I want to address, though, is "do the two indices tell different stories, or not?" The HDI data for 2010 are also in the workbook on this blog's Data page.

The econometric analysis that follows has been performed using EViews; and as usual, the workfile for this is available on the Code page that goes with this blog.

Figure 1 provides a direct comparison between the BLI and the HDI for the 34 countries in the OECD. The BLI is constructed on a scale of 0 (worst) to 10 (best); and the HDI is on a scale of 0 (worst) to 1 (best).
That's Turkey, sitting by itself in the bottom left corner, with Australia at the top right. The adjusted R2 is 0.738. The estimated intercept and slope coefficients (with heteroskedasticity-consistent std. errors in parentheses) are 0.659 (0.028) and 0.031 (0.004). Do the two indices rank the OECD countries differently? Well, Spearman's rank correlation coefficient is 0.8064, and the t-statistic to test if this correlation is zero is 7.71 (p = 0.00). So, there's a fair degree of concordance in the rankings by each measure.

If I regress the HDI against the eleven components of the BLI, with an intercept (using OLS and het.-consistent std. errors) I find that only the Housing, Education, and Health components are statistically significant, at the 10% level. These components each have positive coefficients, and the adjusted R2 is 0.813. Deleting the insignificant regressors, the adjusted R2 rises to 0.848. How well does this simplified "model" perform in terms of predicting the countries' rankings? Here are the results, based on the OLS equation:

HDI =0.6690 + 0.0087 HOUSING + 0.0112 EDUCATION + 0.0084 HEALTH + residual
         (0.017)   (0.003)                    (0.002)                        (0.002)

Table 1

Country
HDI
Rank
Predicted
HDI
Rank





NOR
0.938
1
0.894
7
AUS
0.937
2
0.906
3
NZL
0.907
3
0.909
2
USA
0.902
4
0.901
4
IRL
0.895
5
0.884
11
NLD
0.890
6
0.891
9
CAN
0.888
7
0.927
1
DEU
0.885
8 =
0.874
12
SWE
0.885
8 =
0.893
8
JAP
0.884
10
0.864
17
KOR
0.877
11
0.846
23
SWI
0.874
12
0.900
5
FRA
0.872
13 =
0.872
14
ISR
0.872
13 =
0.850
21=
FIN
0.871
15
0.895
6
ICE
0.869
16
0.873
13
BEL
0.867
17
0.886
10
DNK
0.866
18
0.871
15
ESP
0.863
19
0.851
20
GRC
0.855
20
0.838
26
ITA
0.854
21
0.839
25
LUX
0.852
22
0.860
18=
AUT
0.851
23
0.860
18=
GBR
0.849
24
0.869
16
CZE
0.841
25
0.850
21=
SVN
0.828
26
0.841
24
SVK
0.818
27
0.805
28
EST
0.812
28
0.804
29
HUN
0.805
29
0.799
30
POL
0.795
30 =
0.824
27
POR
0.795
30 =
0.796
31
CHE
0.783
32
0.787
32
MEX
0.750
33
0.736
33
TUR
0.679
34
0.715
34

(The rankings are only slightly affected if all eleven BLI components are included in the model, in spite of their statistical insignificance.) Spearman's rank correlation coefficient for the actual and predicted HDI rankings in Table 1 is 0.885 (t = 10.73; p = 0.00). Norway and Canada swap rankings; and the group of countries with the lowest HDI values are fairly well predicted (as a group).

So, looking at Figure 1 and Table 1, there's a fair amount of agreement between the country rankings implied by the BLI, and those implied by the HDI - especially when it comes to simply clustering the top and bottom groups of countries.

Now, just for fun, let's see what it would take to make the BLI "line up" exactly with the HDI. I'm going to take the top twelve HDI values and regress this sub-set of data against the eleven components of the BLI (and an intercept), for the corresponding twelve countries. From Table 1, we see that these countries are (starting from the top): Norway, Australia, New Zealand, U.S.A., Ireland, Netherlands, Canada, Germany , Sweden, Japan, Korea and Switzerland.

I'm fitting an OLS regression with n = k = 12, so you can guess what's going to emerge - right? I have zero degrees of freedom, so I've forced the model to give me a set of weights (regression coefficients), estimated from the data, that will exactly determine the twelve HDI values. The standard errors for the coefficients are undefined, and the R2 is exactly unity. This is what I get:

Table 2
Variable
Coefficient




Constant
1.031434
HOUSING
0.023148
INCOME
0.002375
JOBS
0.018082
COMMUNITY
-0.014977
EDUCATION
-0.047587
ENVIRONMENT
0.016513
GOVERNANCE
-0.005138
HEALTH
-0.032127
LIFE SATISFACTION
0.017665
SAFETY
0.013208
WORK-LIFE BALANCE
-0.014303


Of course, I could have chosen any twelve values for the HDI. The answers (weights) would have been different. For instance, I could choose the values for the bottom twelve HDI countries: Austria, Great Britain, Czech Republic, Slovenia, Slovak Republic, Estonia, Hungary, Poland, Portugal, Chile, Mexico and Turkey


To match the BLI to the HDI for these countries I certainly can’t use equal weights for the eleven components. For example, “Housing” has to be given approximately ten times the weight given to “Income”; and “Jobs” and “Community” have to be given roughly equal, but oppositely signed weights. I’ll leave you to draw your own conclusions from Table 2, but keep in mind that the BLI and the HDI are really not attempting to measure the same things.


Notice that I've imposed a pretty rigid requirement in this last little bit of analysis. I wanted to perfectly predict twelve values of the HDI. If' I'd wanted to simply predict a bunch of rankings in the HDI series, using the components of the BLI to do this, possibly I could have fiddled with the weights and predicted more than twelve ranks. But the weights wouldn't have been unique.

Let’s return to my earlier question: “What would it take to make me feel that life in New Zealand is better than life in Canada, based on the BLI?” It’s a matter of fiddling with the weights for the 11 components so as to drive New Zealand’s ranking from 4th to 1st. There’s no unique answer to this, of course, but here is one possible scenario. The weights I’ve used for the 11 components, “Housing” through “Work-Life Balance” are, in order:

0.147058824, 0.014705882, 0.102941176, 0.147058824, 0.073529412, 0.147058824, 0.117647059, 0.073529412, 0.044117647, 0.073529412, and  0.058823529.

Table 3


Country
Equal  Wt.
Non-Equal Wt.

Rank
Rank
Australia
1
1=
Austria
14=
15
Belgium
17
16=
Canada
2
4
Chile
32
33
Czech Republic
23
20=
Denmark
6
5
Estonia
31
31
Finland
9
8
France
18
16=
Germany
16
16=
Greece
27
27
Hungary
29
29
Iceland
12
7
Ireland
14=
11=
Israel
20
23
Italy
24
24
Japan
19
20=
Korea
26
28
Luxembourg
11
14
Mexico
33
32
Netherlands
10
11=
New Zealand
4
1=
Norway
5
6
Poland
25
25
Portugal
30
30
Slovak Republic
28
26
Slovenia
21
20=
Spain
22
19
Sweden
3
3
Switzerland
8
13
Turkey
34
34
Great Britain
13
9=
USA
7
9=


So, if I cared strongly about “Housing” (I’d question the data on this one), “Community”, “Environment” and “Governance”, but didn’t give a hoot about “Income”, “Health”, “Safety”, “Education”, “Life Satisfaction” or “Work-Life Balance”, then I’d be hopping on a ‘plane and flying South. Not likely to happen!

The OECD's new Better Life Index is an interesting addition to the stable of such measures that are available already. It's nice that we can choose out own weights to aggregate the eleven components into a single index. However, the countries that are covered are (of course) just the 34 OECD members, and that's a bit of a limitation.

One interesting question that I haven't addressed here is: "What's really driving the variability in the country rankings?" I'll be dealing with that in an up-coming post.



© 2011, David E. Giles

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