It's a Wonderful Life

Personally, I'd have gone for a big cake with candles, but last week, to celebrate its 50^th 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 4^th to 1^st. 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