## DX b

Using weighted regression results (from Table 9.7b) for oil coefficients of 0.10 and 0.15 as examples, Figures 9.9a and 9.9b show the calculated

EP fraction (x) with respect to GDP fraction (Y)

Figure 9.9b Changes of catch-up elasticity of EP with respect to GDP for two models using weighted regression results

EP fraction (x) with respect to GDP fraction (Y)

Figure 9.9b Changes of catch-up elasticity of EP with respect to GDP for two models using weighted regression results catch-up elasticity curves for the square root (SQRT) and natural log (ln) models. In both models, the catch-up elasticity diminishes both with the increase in x and with the increase in Y. There is no obvious difference between the two values of oil coefficients (0.10 or 0.15) for either model. In fact, the curves are essentially indistinguishable.

However, the difference in catch-up elasticity between the two models is relatively large for countries at early stages of development, for example, EP fraction x < 0.1, or GDP fraction Y < 0.35. Catch-up elasticity decreases faster with the increase in x than with the increase in Y at an early development stage and more slowly at a late development stage. A country's catchup elasticity decreases to about 2 when its EP reaches about 10 percent of the US level, or when its per-capita GDP reaches about 30 percent of that of the US. A country's catch-up elasticity decreases sharply to about 1.0 and then decreases slowly after its EP reaches about 30 percent of that of the US, or after its per-capita GDP reaches about 50 percent of that of the US level. Catch-up elasticity seems to stabilize at around 0.5 as either x or Y approaches unity (we suppose that x and Y are always less than unity).

Until now, we have been looking at countries' development relative to the US. However, in order to have an idea of countries' absolute development we need to know the development trajectory of the US. Figure 9.10 shows the per-capita GDP expressed as a multiple of the 1960 value versus the EP for the US from 1960 to 2001. The overall trend lags below

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EP index USA

Figure 9.10 Development trajectory (GDP versus EP) of the USA from 1960-2001

EP index USA

Figure 9.10 Development trajectory (GDP versus EP) of the USA from 1960-2001

the diagonal (the 45 degree slope line) until 1980 and then returns to the diagonal after that, except for a small reversal in 2001. The same information is presented in a different way in Figure 9.11, where US GDP and the EP are plotted versus time, from 1960 to 2001. The overall diagonal trajectory implies that the per-capita US GDP since 1960 has increased almost in proportion to the EP, except for a lag and a brief reversal in the 1970s (when there was a global oil crisis).

Evidently, the baseline we have been using for the catch-up model is growing more or less in proportion to its energy consumption proxy. This makes it easy to interpret the results of our model where relative values are used. For example, when a country's catch-up elasticity is bigger than unity, it is growing more energy-efficient than the US. Also, its absolute catch-up elasticity (percentage changes with respect to its own original values) is bigger than 1.

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