Catchup Elasticity

We now introduce a new variable, the 'economic catch-up elasticity of energy', or 'catch-up elasticity' from here on. Although we call it elasticity, it is different from the normal definition of elasticity in that the changes in percentage are with respect to the corresponding values of the US instead of the country itself.

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

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

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

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

For the natural log (ln) model, we define

where Y is the dependent variable (GDP fraction), and x is the independent variable (EP), also expressed as a fraction. The catch-up elasticity is defined:

Similarly, for the square root model (SQRT), we have

The catch-up elasticity in this case is:

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