Those new SUVs are visibly purchased with some capital rent

My editorial

I am collecting empirical data regarding my idea of local power systems, 100% based on renewable energies. I took a metric published by the World Bank, namely the renewable energy consumption as a percentage of total final energy consumption (see ). I combined it with the database I already have, built on the frame of Penn Tables 9.0 (Feenstra et al. 2015[1]). I did some preliminary rummaging in that data, notably computing the mean, national value of that indicator over years  putting it against the global, weighted average provided directly by the World Bank. Another piece of rummaging consisted in using the already existing content of my database to compute the mean national consumption of renewable energies, as an aggregate, and comparing it, as a fixed-base index, with the average national stock of fixed capital, which you can see under this link. Before I present any more applications of this ‘% of renewable energy’ metric, a little methodological explanation is due. We are talking, in the case of this precise indicator, about the final consumption of energy, not about its primary output. We are talking about the energy we use in everyday life, not about electricity produced in power plants. About 1/3rd in the global consumption of energy corresponds to transportation, which, in turn, represents mostly the fossil fuels burnt in vehicles. As you explore that dataset as provided by the World Bank, you will notice many countries, especially the developing ones and some emerging economies, who display a strongly descending share of renewables in the final consumption of energy. This is not a conspiracy from the part of oil companies: this is simply me, my neighbour, and his son-in-law buying (and driving around) a second car, or replacing a Ford Fiesta with a fancy SUV, in our respective households. This is very much what I could observe in China.

Anyway, now that I have this metric, my internal happy bulldog starts serious sniffing and digging through that data. I hypothesise that the share of renewable energies in the final consumption, or ‘%Ren’, depends essentially on the GDP per capita, in the presence of population size ‘Pop’, as a scale factor, and with a possible residual freedom in the explained variable. I take it all down to natural logarithms (much safer, tends to calm down those moody swings in my variables), and thus, mathematically, it looks like that:

ln(%Ren) = a1*ln(GDP per capita) + a2*ln(Pop) + residual

Good, and so I am waltzing. My internal happy bulldog dug out n = 4 151 valid observations in my database, and still this is not really the height of explanatory power: my coefficient of determination is just R2 = 0,326. Nothing to write home about. Anyway, the table of coefficients looks as presented below (Table 1):

Table 1

variable coefficient std. error t-statistic p-value
ln(Pop) 0,061 0,011 5,551 0,000
ln(GDP per capita) -0,795 0,018 -44,88 0,000
constant -1,399 0,103 -13,591 0,000

So far, it unfolds more or less logically. My share of renewable energy in the final consumption is negatively correlated with GDP per capita. See? What did I tell you? More bucks per head means more cars per village, and more cars per village means more fossil fuels burnt. The scale factor does not really kill: significant, but modest in its impact. Now, it is my internal curious ape who grabs the bulldog by the head and directs its nose on the constant residual: ‘Good dog, search for correlations in that residual’. The bulldog barks just by one variable: the share of labour compensation in the Gross National Income, or ‘Labsh’ in the nomenclature of Penn Tables 9.0. The residual of my first model is correlated with that variable at r = 0,3. Once again, nothing to put on Instagram, and still interesting. That would mean that labour-intensive economies tend to develop a relatively larger share of renewables in their energy consumption. Logical: as they are busy working, they don’t drive to much around. Anyway, I rephrase my model and I hypothesise that:

           ln(%Ren) = a1*ln(GDP per capita) + a2*ln(Pop) + a3*ln(Labsh) + residual

The bulldog, when called, fetches n = 3 111 observations, which, in turn, yield an R2 = 0,359. Weeeeell, maybe not a quantum leap I have here, but some modest advancement is to notice. The table of coefficients (Table 2) shows interesting outcomes of this little experimentation. The inclusion of labour-intensity in my model essentially drove crazy the residual – there is a more than 40% probability that it is different from that (– 0,096) shown – and put the scale factor of population slightly below the level of respectability in its p-value. Less than p = 0,05 is generally bad taste. The labour-intensity in itself seems to be a potent explanatory factor, with the highest coefficient of regression in the model, and rock-solid in its p-value.

Table 2

variable coefficient std. error t-statistic p-value
ln(Pop) 0,024 0,014 1,79 0,074
ln(GDP per capita) -0,773 0,019 -40,417 0,000
ln(Labsh) 1,517 0,129 11,767 0,000
constant -0,096 0,117 -0,821 0,412

My internal curious ape tries to repeat the same trick with the bulldog: ‘Fetch me some correlations in the residual’. It doesn’t work this time, though. This particular residual is small, random and, on the top of that, it is lonely. The ape does not give up, mind you. It sends the bulldog to rummage in the probability of being struck by an asteroid whilst driving around without your seat belts on, and it calls my internal austere monk: that guy who walks around with the Ockham’s razor in his pocket. Woosh! The monk swings that razor and carves two more variables out of the dataset: the stock of fixed capital available per capita, and the depth of food deficit. The more capital is there per person, the more it is likely being invested in the generation of renewable energies, and the more likely it is to make people less in need of new cars. On the other hand, the food deficit has already proven to be an interesting variable in my earlier research, and it is a measure of poverty, potentially correlated with the unfulfilled need for transportation. Still, the monk reminds gently: food deficit is reported as a non-null value only in cases when it is really present. When I include food deficit in my model, I automatically shift towards developing and emerging countries. At this point, it is prudent to split my model into two versions:

Version A, general:

  ln(%Ren) = a1*ln(GDP per capita) + a2*ln(Pop) + a3*ln(Labsh) + a4*ln(Capital stock per capita) + residual

and Version B, with food deficit, oriented on developing countries and emerging markets:

           ln(%Ren) = a1*ln(GDP per capita) + a2*ln(Pop) + a3*ln(Labsh) + a4*ln(Capital stock per capita) + a5*ln(Food deficit) + residual

The results, this time, are ambiguous. The general model brings nearly nothing in terms of general explanatory power. With n = 3 111 observations, the coefficient of determination changes at the third digit after the decimal point, and makes R2 = 0,360 now. Not really an earthquake. The capital stock per capita, or the capital-intensity of the economy, essentially gets in the way of labour intensity and wastes some of that labour. The more capital is there per capita, the lower the share of renewables in the final basket of energy consumption. Those new SUVs are visibly purchased with some capital rent. My internal monk was right to pick up that variable – it is significant – but he was dead wrong as for how it works. What do you want, austere monasticism is not a job devoid of risk. Still, the position of labour intensity in the model seems rock-solid.

Table 3

variable coefficient std. error t-statistic p-value
ln(Pop) 0,025 0,014 1,854 0,064
ln(GDP per capita) -0,618 0,061 -10,206 0,000
ln(Labsh) 1,521 0,129 11,796 0,000
ln(Capital stock per capita) -0,135 0,049 -2,772 0,006
constant 0,133 0,148 0,896 0,370

Now, I switch to the specific model, with food deficit inside, applied to the developing countries and partly to emerging markets (like early South Korea, for example). With n = 1 680 valid observations, I get R2 = 0,424 in terms of determination. Here, that Ockham’s razor has brought some change. Razors tend to, when used properly. Table 4 below shows the coefficients of regression thus obtained. The depth of food deficit works interestingly but predictably: the greater it is, the greater the share of renewables. Poor people burn less fossil fuels and can do just with some wind, water, and sun, harnessed properly. I can notice, as well, that in those relatively poor populations, their size stops mattering. With the p-value at 0.146, its impact tends towards random.

Table 4

variable coefficient std. error t-statistic p-value
ln(Pop) -0,021 0,014 -1,455 0,146
ln(Depth of the food deficit) 0,252 0,036 7,08 0,000
ln(GDP per capita) -0,395 0,068 -5,809 0,000
ln(Labsh) 1,397 0,149 9,364 0,000
ln(Capital stock per capita) -0,257 0,046 -5,539 0,000
constant -0,203 0,215 -0,942 0,346

I can feel my brain sizzling. Enough science for now.

[1] Feenstra, Robert C., Robert Inklaar and Marcel P. Timmer (2015), “The Next Generation of the Penn World Table” American Economic Review, 105(10), 3150-3182, available for download at


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