Countries never behave as they should

My editorial

After having started, yesterday, an overview of articles concerning renewable energies (see ‘Deux théories, deux environnements’), I continue on this path and I am reading through a paper by Peter D. Lund, entitled ‘Effects of energy policies on industry expansion in renewable energy’ (Lund 2009[1]). Peter D. Lund comes to the conclusion that policies of pure growth, like pumping money in R&D or favouring the development of exports, bring substantial results regarding the development of renewable energies. Moreover, substantial technological change in industries upstream of renewable energies can have a pushing effect on the latter, and the role of public policies, in this case, is to make or facilitate the connection between them. As for details, Peter D. Lund covers the following cases: Denmark, Germany, Finland, Austria, USA, Brazil, Japan, Estonia, Sweden, China, and Canada. The really strong claim of that article is that the size of exports from a given country, in renewable energy properly spoken or in technologies upstream of energy production, is more important for the development of renewable energies in the given country than its domestic market. In general, the capacity to expand into the global market, either with energy as such or with technologies serving to generate it, seems to be crucial for the transition to green energies inside the country.

As usually, I want to confront the claim with my own empirical data. First of all, I took a handful of countries, and I compared the size of their respective, domestic markets in renewable energy, to the share of renewable energies in their primary output of electricity, in 2014. The percentage of variables in electricity output comes straight from the World Bank (see: ). As for the size of domestic markets in renewable, this is my own calculation, mostly on the grounds of World Bank data. First, I took the indicator of final energy consumption per capita, in kilograms of oil equivalent ( ), and I multiplied it by the population of each country reported. That gave me the total size of domestic markets in energy, which I put against another indicator, namely the percentage of renewables in the final consumption of energy ( ). Anyway, you can see the results of that little rummaging in Table 1, below. As I am looking at this form of data, the coin starts dropping: it does not look like a strong correlation between market size in renewables and their share in the output of electricity. I am minting that coin (the one which has just dropped in my mind, I mean) with the royal stamp of Pearson correlation of moments, and it looks respectable: r = -0,075205406. I mean, this is a lousy correlation, it just has the name of correlation, but not the guts it takes to correlate significantly, and still it shows a part of a point: there is no correlation between market size and the share of renewables in the output of electricity. Peter D. Lund, you were at least partly right.

   Table 1

country Renewable electricity output as % of total electricity output, 2014  Renewable energies consumption, in tons of oil equivalent, 2014
Australia 14,9%  12 305 298,40
Austria 81,1%  11 441 257,56
Belgium 17,0%  4 880 723,09
Canada 62,8%  58 225 979,12
Chile 41,2%  10 259 815,33
Czech Republic 10,8%  5 304 306,22
Denmark 55,9%  4 955 203,30
Estonia 11,2%  1 528 618,08
Finland 38,6%  14 145 185,02
France 16,4%  31 607 372,84
Germany 26,1%  40 451 222,42
Greece 24,2%  3 647 766,79
Hungary 10,7%  2 348 769,99
Iceland 100,0%  4 398 469,36
Ireland 24,5%  1 095 777,67
Israel 1,5%  2 113 663,77
Italy 43,4%  24 579 456,45
Japan 14,0%  24 318 733,45
Luxembourg 20,9%  264 125,74
Mexico 17,5%  18 553 983,66
Netherlands 11,3%  4 101 339,30
New Zealand 79,1%  6 181 040,15
Norway 97,7%  17 204 238,06
Poland 12,5%  11 130 427,59
Portugal 60,7%  6 434 268,18
Republic of Korea 1,6%  7 478 135,80
Slovakia 22,9%  1 874 348,18
Slovenia 38,5%  1 533 076,92
Spain 40,1%  19 664 012,75
Sweden 55,8%  23 125 017,52
Switzerland 58,0%  5 921 322,49
Turkey 20,9%  13 827 194,22
United Kingdom 19,4%  12 912 006,53
United States 13,0%  196 963 466,86

Source: World Bank, Penn Tables 9.0

Now, my internal happy bulldog, that cute beast who has just enough brains to rummage in raw empirical data, has gathered momentum. We made a table, so why couldn’t we make an equation? And when we will have made that equation, why not running just some linear regression and test it? Good, let’s waltz. Science can be fun, after all, and so I am unfolding an equation. I take my percentage of renewables in the production of electricity, or ‘%RenEl’, and I put it on the left side of my equation, as explained variable. That gives me ‘ln(%RenEl) = ?’. I follow up with a makeshift right side. There has to be that market size in renewables, which I endow with the symbol ‘RenQ’, and this leads me to saying ‘ln(%RenEl) = a1*ln(RenQ) + ?’. Now, I need something connected to exports. The closest match I can find with the intuitions by Peter G. Lund is the share of exports in the GDP, or ‘X/Q’. Good, so now, I can proudly state that ‘ln(%RenEl) = a1*ln(RenQ) + a2*ln(X/Q) + ?’. Smells interestingly. I drop another size factor, namely population (Pop), into the kettle, and as I keep stirring with my right hand, I use the left one, temporarily left free by having pegged the left side of the equation, to add other logarithm-ized things of life: GDP per capita (Q/Pop), and my dear supply of money as % of GDP (M/Q). The recipe seems to be ready, and it looks like:

ln(%RenEl) = a1*ln(RenQ) + a2*ln(X/Q) + a3*ln(Pop) + a4*ln(Q/Pop) + a5*ln(M/Q) + residual constant

Testing time. I take my database, namely Penn Tables 9.0 (Feenstra et al. 2015[2]), now embroidered with loads of other data from the World Bank, and I am about to test my equation, and this is the moment when my internal curious ape becomes vocal and says: ‘Oooogh’, which means ‘Look, Krzysztof, why not to repeat that trick with density of population as control variable. It worked once, it might work more times, as well. So?’ (meaningful frown). Fine. If could have indulged to the wants of a bulldog, I can cooperate with the ape. Will not kill me, after all. So I slice my database into sextiles of density in population, and I am going to perform, and to delight you, my readers, with the results of seven tests: one general and six specific. I start with the general one: n = 1 913 valid observations yield R2 = 0,427 in terms of explanatory power. The table of coefficients shows an interesting landscape, which, for the moment, contradicts the findings by Peter G. Lund. Everything on the right side of the equation, with the exception of market size in renewable energies, has a negative sign, and the share of exports in GDP does not make exception.

Table 2

variable coefficient std. error t-statistic p-value
ln(Pop) -0,764 0,036 -20,968 0,000
ln(M/Q) -0,251 0,059 -4,286 0,000
ln(Q/Pop) -0,311 0,033 -9,348 0,000
ln(RenQ) 0,756 0,029 25,871 0,000
ln(X/Q) -0,277 0,03 -9,143 0,000
constant -8,316 0,62 -13,41 0,000

Right, now I am ploughing through sextiles (regarding the density of population). First sextile, between 0,632 and 11,713 people per square kilometre: n = 111 observations, coefficient of determination R2 = 0,493. Coefficients in Table 3, below. Small and quite robust, I could say, save for the share of exports in the GDP, which, with a p-value of 0,527 is basically on vacation. Money starts counting, by the way, as I am controlling for that density of population.

Table 3

variable coefficient std. error t-statistic p-value
ln(Pop) -0,332 0,166 -1,998 0,048
ln(M/Q) 1,281 0,491 2,61 0,010
ln(Q/Pop) -1,075 0,238 -4,508 0,000
ln(RenQ) 0,835 0,113 7,416 0,000
ln(X/Q) -0,274 0,431 -0,635 0,527
constant -10,2 3,542 -2,88 0,005

Second sextile, from 11,713 to 29,352 people per square kilometre. It has n = 366 valid observations to present, and they yield quite a crunch into explanatory power, with R2 = 0,720. Table 4, below, shows that all coefficients get back to discipline, in their p-values, and still money becomes negative again. The domestic market size in renewable energies seems rock-solid in this model: it keeps the same sign, same magnitude, and a robust p – value, across all those sampling tricks I have made so far.

 Table 4

variable coefficient std. error t-statistic p-value
ln(Pop) -0,852 0,073 -11,693 0,000
ln(M/Q) -0,102 0,043 -2,39 0,017
ln(Q/Pop) -0,317 0,05 -6,37 0,000
ln(RenQ) 0,895 0,075 11,886 0,000
ln(X/Q) -0,434 0,091 -4,751 0,000
constant -11,513 1,561 -7,376 0,000

Good. Third class of density in population, between 29,352 and 56,922 people per km2. Here, it becomes lax, somehow: n = 362 observations yield just R2 = 0,410 in terms of explanatory power. The coefficients of regression (Table 5) suggest that the story changes as people cluster on that square kilometre. Money is even more deeply negative, and the size of domestic market in renewables becomes negative, as well. I noticed it already with another model, a few updates ago, which I controlled for the density of population. There are some classes of density, which look just like kind of transitory states between more solid equilibriums. That could be the case here.

Table 5

variable coefficient std. error t-statistic p-value
ln(Pop) 0,146 0,092 1,587 0,113
ln(M/Q) -1,36 0,175 -7,784 0,000
ln(Q/Pop) 0,08 0,118 0,68 0,497
ln(RenQ) -0,181 0,09 -2,02 0,044
ln(X/Q) -0,635 0,113 -5,633 0,000
constant 9,478 1,766 5,366 0,000

And so I swing my intellectual weight towards the fourth class of density in population, 56.922 ÷ 97.881 people per square kilometre. I have n = 336 observations here, and they echo to me with a R2 = 0,510 coefficient of determination. It looks like my house when my wife decides to do what she calls ‘put order in all that’. The result is a strange mix of scalpel-sharp order in some places with bloody mess in other places. Here, as you can see in Table 6, this is something akin. The size of domestic market in renewables comes back to the throne, and good for it. Still, the velocity of money goes completely unhinged, with the probability of null hypothesis towering over 90%. Another transitory state? Maybe.Table 6

variable coefficient std. error t-statistic p-value
ln(Pop) -0,487 0,054 -8,956 0,000
ln(M/Q) 0,008 0,066 0,114 0,909
ln(Q/Pop) -0,362 0,047 -7,673 0,000
ln(RenQ) 0,795 0,054 14,834 0,000
ln(X/Q) -0,04 0,045 -0,889 0,375
constant -10,109 1,335 -7,571 0,000

And so I climb the ladder of density, and I come to the fifth sextile, which hosts between 97,881 and 202,36 people on my average square kilometre. I mean, not just mine, yours as well. I have n = 419 observations, and I have a bit of disappointment in my R2, as my R2 makes R2 = 0,342 this time, and I have the coefficients shown in Table 7. Those coefficients look nice, and robust in their p-values, but on the whole, they are not really blockbusters in terms of R2. What do you want, there are those situations in life, when being nice and predictable does not necessarily give you power.

Table 7

variable coefficient std. error t-statistic p-value
ln(Pop) -1,104 0,12 -9,233 0,000
ln(M/Q) 0,502 0,088 5,703 0,000
ln(Q/Pop) -0,39 0,061 -6,443 0,000
ln(RenQ) 0,817 0,111 7,378 0,000
ln(X/Q) -0,628 0,082 -7,65 0,000
constant -11,583 2,39 -4,846 0,000

And so comes the top dog, namely the sixth and highest sextile of density in population: 202,36 ÷ 21 595,35 people per km2. I have n = 299 valid observations in this category, and they allow to determine 56%, or R2 = 0,560, of the overall variance in the percentage of electricity coming from renewable sources. Table 8 gives details regarding the coefficients of my equation. This highest class of population density seems to be the only one that yields a result fully coherent with the findings by Peter G. Lund: both the size of the domestic market in renewable energies, and the share of exports in the GDP have positive signs, respectable magnitudes, and robust correlations. Interestingly, my pampered factor, namely the velocity of money, goes feral again. There must be something about social structures, as measured by the density of their populations, which sometimes just creates an opening for money to play a significant role. Interesting. Worth going deeper. Bulldog! Come over, please. Here, dig.

Table 8

variable coefficient std. error t-statistic p-value
ln(Pop) -0,214 0,186 -1,149 0,251
ln(M/Q) 0,073 0,125 0,584 0,559
ln(Q/Pop) -0,92 0,102 -9,042 0,000
ln(RenQ) 0,784 0,073 10,73 0,000
ln(X/Q) 0,976 0,213 4,571 0,000
constant -5,162 1,871 -2,758 0,006

Now, some general discussion about those results. In general, my research partly contradicted the findings by Peter G. Lund. Cross-sectional analysis (Table 1) shows no correlation between the size of domestic market in renewable energies, and their share in the output of electricity. More elaborate an investigation, with hypotheses-testing in a time-space sample of observations, shows a major role to be played by domestic markets. Still, in the highest class of population density, the pattern found by Peter G. Lund seems to hold. I can categorize the countries studied by Peter G. Lund into those classes of density in population I have defined. It looks like (numbers in brackets are densities of population in 2014):

1st sextile: Canada (3,909 people per km2)

2nd sextile: Brazil (24,656), Finland (17,972), Sweden (23,805),

3rd sextile: USA (34,863), Estonia (31,011),

5th sextile: Austria (103,505), Denmark (133,535), China (145,317),

6th sextile: Germany (232,108), Japan (348,727),

Unfortunately, I cannot really test my equation at the level of countries. When all the variables have been accounted for, I have like 17 – 24 observations per country, which is just not enough for quantitative tests, and the correlations I get are not robust regarding their p – values. I cannot say, thus, if those countries behave as they should, regarding their density of population. But you know what? Countries never behave as they should.

[1] Lund, P.D., 2009, Effects of energy policies on industry expansion in renewable energy, Renewable Energy 34, pp. 53–64

[2] 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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