I have another new working paper coauthored with Zsuzsanna Csereklyei out titled: "Global Energy Use: Decoupling or Convergence?". This paper follows up on our paper on the the stylized facts of energy and growth using the methods from our paper on modeling the emissions-income relationship using long-run growth rates.

In particular, we focus on the stylized facts that there is a stable relationship between energy use and GDP per capita over time and that there has been convergence in energy intensity over time.

The following graph shows the relationship between the long-run growth rates of energy use and GDP per capita from 1971 to 2010:

As we saw in our previous paper, higher economic growth rates are associated with higher rates of growth in energy use, though there is quite a lot of variation in individual countries. As the intercept of the regression line is zero, on average there is no time effect that is reducing energy use across all countries in the absence of economic growth. On the other hand, many developed countries like the UK, Sweden, or even the United States have seen declines or little increase in energy use per capita in recent decades. So, what can explain that?

Our model adds additional explanatory variables to the regression illustrated above. To test whether there is decoupling, so that growth has less effect or even a negative effect on energy use at higher income levels we include an interaction term between the growth rate and level of income per capita. This is the same idea as the test for the environmental Kuznets curve in the Anjum

Though, as shown by the black dots, the growth rate of energy use per capita is highest in upper middle income countries, the contribution of economic growth is greater in high income countries. But this positive effect of growth is offset by "weak decoupling" and other effects.

The most important of these other effects globally is convergence. Countries that had high energy intensities at the beginning of the period saw declines in energy intensity,

Projections and forecasts of future energy use should not, therefore, assume that economic growth will be associated with decreased energy use in the future. Instead, the scale effect seems to be alive and well. On the other hand, there appear to be improvements in energy efficiency across high income countries irrespective of their growth rates or their initial level of energy intensity. These would tend to moderate the growth in energy use as countries get richer at the upper end of the income continuum. At the lower end of the income continuum the same effects serve to raise energy intensity. But, some of the major reductions in energy intensity in countries, such as in the United States and China, have probably been the result of convergence towards the global mean, and so are unlikely to be reproduced in the future.

On the more technical side there are a couple of innovations in this paper too. We extend the method we used in the growth rates paper to allow for a spatially correlated error term. If there are omitted variables which are spatially correlated and the explanatory variables are also spatially correlated then it is likely that the two are correlated and regression coefficient estimates will be inconsistently estimated. To deal with this problem we use an approach called spatial filtering. This removes the spatial autocorrelation by adding additional variables to the regression which model the spatial process. These are in fact the eigenvectors of a transformation of the spatial weighting matrix. With 93 countries there are 93 eigenvectors, so the tricky part is deciding which of these eigenvectors to include in the regression. Tiefelsdorf and Griffith (2007) developed a procedure to do this, which we use.

Another issue is that if we want to give our model a causal interpretation, then we have to assume that GDP growth causes growth in energy use and not

In particular, we focus on the stylized facts that there is a stable relationship between energy use and GDP per capita over time and that there has been convergence in energy intensity over time.

The following graph shows the relationship between the long-run growth rates of energy use and GDP per capita from 1971 to 2010:

As we saw in our previous paper, higher economic growth rates are associated with higher rates of growth in energy use, though there is quite a lot of variation in individual countries. As the intercept of the regression line is zero, on average there is no time effect that is reducing energy use across all countries in the absence of economic growth. On the other hand, many developed countries like the UK, Sweden, or even the United States have seen declines or little increase in energy use per capita in recent decades. So, what can explain that?

Our model adds additional explanatory variables to the regression illustrated above. To test whether there is decoupling, so that growth has less effect or even a negative effect on energy use at higher income levels we include an interaction term between the growth rate and level of income per capita. This is the same idea as the test for the environmental Kuznets curve in the Anjum

*et al*. paper. We find that the regression coefficient for this interaction term is actually positive! So, actually growth has larger rather than smaller effects on energy use in higher income countries. However, we find that the level of income has a negative effect on the growth rate of energy use. This means that at higher income levels there is an improving energy efficiency effect so that energy use declines over time*ceteris paribus*. We call this "weak decoupling". The following graph shows the contribution of these and other effects to the growth in energy use in different groups of countries:Though, as shown by the black dots, the growth rate of energy use per capita is highest in upper middle income countries, the contribution of economic growth is greater in high income countries. But this positive effect of growth is offset by "weak decoupling" and other effects.

The most important of these other effects globally is convergence. Countries that had high energy intensities at the beginning of the period saw declines in energy intensity,

*ceteris paribus*. But, this effect was most important in the low income countries, some of which were the most energy intensive in our sample in 1971. In the high income countries, convergence raised energy use on average. But in the US and Canada it contributed -1.0% and -0.9% p.a., respectively, to reducing energy use. So, there is a lot of variation across countries.Projections and forecasts of future energy use should not, therefore, assume that economic growth will be associated with decreased energy use in the future. Instead, the scale effect seems to be alive and well. On the other hand, there appear to be improvements in energy efficiency across high income countries irrespective of their growth rates or their initial level of energy intensity. These would tend to moderate the growth in energy use as countries get richer at the upper end of the income continuum. At the lower end of the income continuum the same effects serve to raise energy intensity. But, some of the major reductions in energy intensity in countries, such as in the United States and China, have probably been the result of convergence towards the global mean, and so are unlikely to be reproduced in the future.

On the more technical side there are a couple of innovations in this paper too. We extend the method we used in the growth rates paper to allow for a spatially correlated error term. If there are omitted variables which are spatially correlated and the explanatory variables are also spatially correlated then it is likely that the two are correlated and regression coefficient estimates will be inconsistently estimated. To deal with this problem we use an approach called spatial filtering. This removes the spatial autocorrelation by adding additional variables to the regression which model the spatial process. These are in fact the eigenvectors of a transformation of the spatial weighting matrix. With 93 countries there are 93 eigenvectors, so the tricky part is deciding which of these eigenvectors to include in the regression. Tiefelsdorf and Griffith (2007) developed a procedure to do this, which we use.

Another issue is that if we want to give our model a causal interpretation, then we have to assume that GDP growth causes growth in energy use and not

*vice versa*. Obviously changes in energy use might also cause GDP. We argue though that the latter effect is probably quite small compared to the effect of GDP on energy and so the estimated effect of GDP on energy is only biased upwards by a relatively small amount. The income elasticity of energy is likely to be close to unity whereas the elasticity of GDP w.r.t. to energy might be only 0.05. This is possibly one reason why it has been so hard for researchers to find robust signs of Granger causality from energy use to GDP. On other hand, this is maybe why a simple naive regression of GDP on energy use appears to find a very large effect of energy on GDP. The estimated regression coefficient is biased upwards by the effect of income on energy demand.