Scatter Diagrams And Linear Regressions

The first step is to plot the energy proxy variable EP against the GDP fraction. Figure 9.1 shows the plot for all (131) countries for which we have data. The time frame covers the period from 1960 to 2001 for OECD countries and from 1971 to 2001 for other countries. On the vertical axis is the GDP fraction, and on the horizontal axis is the EP fraction (proxy) as defined above. The US (by definition) is always at the point (1, 1). There is an obvious trend, on average, but with a significant number of outliers, especially countries with high GDP per capita and low EP. To reduce the scatter we can implicitly incorporate some of the other relevant variables discussed above by grouping the countries.

There are three obvious sub-groups based on the EP itself. The main sub-group includes most countries that are neither petroleum exporters nor major hydro-electric producers. The second sub-group consists of petroleum-exporting countries, including OPEC members and a few others

Figure 9.1 Plot of GDP gap against energy policy gap, all countries, all years

like Russia. In general, such countries significantly underprice motor fuel and heating oil, thus distorting the usual patterns of energy use. Moreover, petroleum exporters with very few exceptions, notably Norway, rely too much on export income, spend much of it on arms or consumer luxuries, and fail to develop other sources of revenue or employment. (This phenomenon has been called 'the curse of oil'.)

The third (small) sub-group consists of countries with significant hydroelectric power development, resulting in a very high level of electrification and encouraging inefficient uses such as electric heating. These countries are Norway, Sweden, Iceland, Canada, Austria and Switzerland. Norway is in both groups, and both Russia and China could be. Brazil and Paraguay potentially belong in the high hydro group also. Afghanistan, Nepal, Bhutan, Bolivia and Ecuador are high altitude countries with undeveloped hydro-electric potential.

By separating oil-exporters and countries with a high fraction of hydro-electricity, we obtain a much more concentrated scatter chart. However, without color the two scatter charts are difficult to distinguish, so we have

Table 9.1 Dummy variables

Dummy variable Petroleum export (Hi-Oilexp)

Hydro-electric potential (Hi-Hydro)

Low GDP/cap (Lo-GDP) Medium GDP/cap (Mid-GDP)

High GDP/cap (Hi-GDP) Low latitude (Lo-Lat)

High latitude or altitude (Hi-Lat)

Value, Case

1 if exports > 1.5 X domestic supply;

0 otherwise 1 if hydroelectric power > 0.6 (60%) of total; 0 otherwise 1 if GDP fraction < 0.5; 0 otherwise 1 if 0.5 < GDP fraction < 1;

0 otherwise 1 if GDP fraction > 1; 0 otherwise 1 for tropical countries roughly between the Tropic of Capricorn and the Tropic of Cancer; 0 otherwise 1 for northern countries or high altitude countries (identified in text)

omitted them. Since big countries could be subdivided - in principle - into a number of smaller units (for example, states, provinces), it makes sense to weight each country by its GDP. We have done this.

Clearly, variables such as hydro-electric fraction and fractional oil export are potentially important determinants of the relationship between economic growth and energy consumption. Also, a country's geographic location - whether in the tropics, with lower heating requirements or at high altitudes or high latitudes with high heating requirements but plentiful hydro-electric power, affects its per capita energy consumption. To reflect these, and other differences, we have incorporated several dummy variables in the regressions to indicate whether a country is low-latitude (tropical), temperate or northern/mountainous. To allow for this we introduce dummy variables in Table 9.1, shown above:

Four linear regressions are summarized in Table 9.2. They are all of the general form

The first regression assumes that all the countries follow the same linear development relationship, which doesn't change over time. The coefficients a and b are the same for all countries. Even so, all the independent variables are very significant. The coefficient b of the energy proxy EP is 0.738. This means that, if the world average EP fraction increases by 1 percent the world average GDP fraction would increase by 0.738 percent ceteris

Table 9.2 Results of linear regressions

Regressions Coefficients of R2 Significance of other factors

Energy Proxy

Table 9.2 Results of linear regressions

Regressions Coefficients of R2 Significance of other factors

Energy Proxy

(1)

Simple regression without considering fixed effects or time effects

0.738 (t =

39)

0.657

Very significant

(2)

Regression (1) weighted with GDP

0.812 (t =

54)

0.875

Very significant

(3)

Weighted fixed effect regression with each country as an intersection, considering time effects at the same time

0.346 (t =

= 7)

0.978

A lot of the country dummies and all of the year dummies are not significant

(4)

Considering cross-terms so that each group of

Different slopes

0.99

Very significant

countries has not only a different intercept but also a

different slope

Table 9.3 Detailed results of regression 4

Independent variables

Coefficient

t

EP fraction

1.18

44.81

cross_GDP_high

-1.21

-3.8

cross_GDP_mid

-0.65

-24.33

cross_hydro_high

-0.13

-9.16

cross_large_oilex

-0.39

-8.22

GDP_high

1.25

5.81

GDP_mid

0.46

80.05

High_hydroele

0.06

9.56

Large_oil_expter

0.12

5.48

Low_lat

0.05

13.41

High_lat

-0.18

-13.53

Year

0.0001

* 0.32

Number of observations = 3906 cross_GDP_high = EP fraction GDP_high

F(12, 3894) = 55,993.92 cross_GDP_mid = EP fraction GDP_mid

Prob > F = 0.0000 cross_hydro_high= EP fraction High_hydroele

R2 = 0.9900 cross_large_oilex= EP fraction Large_oil_expter Root MSE = 0.06953

Number of observations = 3906 cross_GDP_high = EP fraction GDP_high

F(12, 3894) = 55,993.92 cross_GDP_mid = EP fraction GDP_mid

Prob > F = 0.0000 cross_hydro_high= EP fraction High_hydroele

R2 = 0.9900 cross_large_oilex= EP fraction Large_oil_expter Root MSE = 0.06953

paribus. In this regression the R2 is just 0.6566. In the second regression GDP is used to weight the countries. The coefficient b for the energy proxy is increased to 0.812, and the R2 is much higher at 0.8746.

However, these two regressions are obviously very crude. They ignore two categories of complications. The first is known to statisticians as 'fixed effects'. In simple language, this allows for the fact that the regression equations for different countries may have different values of the constant a (that is, intercepts at the origin, where EP = 0), while having the same slope b. The results are given in Table 9.2 as regression (3). It yields an unreliable energy proxy coefficient b of 0.346. However, this assumption is unrealistic. In reality, different countries or different groups of countries have different slopes or even different growth relationships.

The second complication, known as 'time effects', allows for different values of both the intercepts a and the slopes b. Regression (4) reflects this. Several cross-terms are also included in regression (4). They are products of the energy proxy and some dummy variables which are used to indicate countries' features. The details are given in Table 9.3. Figure 9.2 plots samples and fitted trends given by regression (4). There are several different sets of data points with both different slopes and different intercepts. Evidently, the dummy variables included in our regression affect the

EP fraction USA

Figure 9.2 Fitted results from regression 4 (Table 9.3)

EP fraction USA

Figure 9.2 Fitted results from regression 4 (Table 9.3)

relationship between the GDP fraction and the energy proxy (EP). Among all the factors, GDP-high and GDP-mid are endogenous, appearing on both sides of the equation, as contrasted with the other dummies, which are exogenous. The fact that they are significant suggests that the underlying EP-GDP relationship is likely to be non-linear.

The exogenous dummy variables divide the set of all countries into several sub-groups. We then analyse the relationship for each group. Since we made no adjustments to the raw data, there might be some 'noise' among the samples. Therefore the next thing to do is to examine the development 'trajectory' of each country. By examining the development history for individual countries, we can eliminate the ones that failed to grow or catch up due to reasons that cannot be accounted for by our grouping scheme. Such reasons might include military conflicts, regional boundary changes, the breakup of the former USSR, failures in macroeconomic management and so on.

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