Groupings And Nonlinear Regressions

Three criteria (defined by three dummy variables) are used for grouping. They are (1) geographical (high, mid or low latitude), (2) a high or low

Table 9.4 The 12 groups

Group

Latitude

Hydro-

Oil-export

No. of

Percent

electricity

important

samples

fraction

1

Low

Big

Yes

124

4.12

2

Low

Big

No

341

11.34

3

Low

Small

Yes

465

15.46

4

Low

Small

No

728

24.21

5

Mid

Big

Yes

0

0

6

Mid

Big

No

219

7.28

7

Mid

Small

Yes

62

2.06

8

Mid

Small

No

816

27.14

9

High

Big

Yes

0

0

10

High

Big

No

168

5.59

11

High

Small

Yes

0

0

12

High

Small

No

84

2.79

Total

3 007

100

hydro-electricity fraction: and (3) high or low oil exporter. Based on the possible combinations of the three factors, we can divide all the countries into 12 groups, as shown in Table 9.4.

For all of the countries, hydro and oil export factors can and do change over time, mainly due to the building of new dams or the exhaustion of old oil or gas fields or the discovery and exploitation of new ones. To simplify the analysis, each country is assigned to the group where it appears for the longest period. Henceforth, we exclude countries that have experienced significant military conflicts and countries that have shifted from central planning to capitalism during the period for which we have data. After this adjustment, we obtain nine non-empty sub-groups of countries. Most countries belong to sub-groups 2, 3, 4 or 8. Figures 9.3a-d display the development tracks of countries in these four sub-groups respectively. Further analysis of the remaining five small sub-groups is not included here.

From Figures 9.3a and 9.3b it appears that low latitude countries (near the equator) with a lot of hydro-electric power or a lot of oil exports did not show any 'catch-up' progress with respect to the US during the last several decades. These countries exhibited development tracks with flat or even negative slopes. This suggests that there must have been exogenous political or institutional obstacles that have impeded economic growth. However in sub-groups 4 and 8, both of which are non-exporters of oil, most countries have been reducing their GDP gaps with respect to the US, as shown in Figures 9.3c and 9.3d.

EP fraction USA

0.15

Figure 9.3a Development tracks of countries in group 2

EP fraction USA

0.15

Figure 9.3a Development tracks of countries in group 2

CL Q

CL Q

EP fraction USA

Figure 9.3b Development tracks of countries in group 3

By grouping countries according to the criteria noted above, the nonlinear relationship between GDP fraction and energy proxy (EP) becomes clearer. It seems that the non-linear growth path exhibited by 'catch-up' countries was disguised by the noisy information from sub-groups 2 and 3.

EP fraction USA

Figure 9.3c Development tracks of countries in group 4

EP fraction USA

Figure 9.3d Development tracks of countries in group 8

EP fraction USA

Figure 9.3d Development tracks of countries in group 8

For sub-groups 4 and 8, the GDP fraction (with respect to the US) seems to evolve in time either as a natural logarithm or as a square root of the EP.

Assuming that, within each group, countries follow the same catch-up trajectory and that it doesn't change over time, we ran several regressions for each of the two non-linear functional relationships. The results are given in Tables 9.5a and 9.5b and Figures 9.4a and 9.4b and 9.5a and 9.5b. Since the fraction of oil combined with electricity in the energy proxy EP was given roughly in proportion to the efficiency of internal combustion engines, its sensitivity should be tested. The results are also set out in Tables 9.5a and 9.5b. Table 9.5a displays the results of unweighted regressions, and Table 9.5b displays the results of regressions weighted by GDP. Countries in sub-group 4 and sub-group 8 are listed in Appendix C, Table C.2. From the results in Table 9.5, it appears that the regressions are not very sensitive to the oil coefficient. The best values of the oil coefficient seem to be in the range 0.1 to 0.15, although the other choices are not significantly worse. For all the regressions, R2 values are very good, and F-values are large. All the coefficients are very significant. The square root model is slightly better than the natural log model, but the differences between them are quite small and probably not significant.

Going Green For More Cash

Going Green For More Cash

Stop Wasting Resources And Money And Finnally Learn Easy Ideas For Recycling Even If You’ve Tried Everything Before! I Easily Found Easy Solutions For  Recycling Instead Of Buying New And Started Enjoying Savings As Well As Helping The Earth And I'll Show You How YOU Can, Too! Are you sick to death of living with the fact that you feel like you are wasting resources and money?

Get My Free Ebook


Post a comment