# Tag: markets

# Educational: microeconomics and management, the market and the business model

### My editorial

This time, in the educational stream of my blog, I am addressing the students of 1^{st} year undergraduate. This update is about microeconomic and management. Regarding your overall educational curriculum, these two courses are very much complementary. I am introducing you now into the theory of markets, and, in the same time, into the managerial concept of business model. We are going to consider a business of vital importance for our everyday life, although very much unnoticed: **energy, and, more specifically, electricity**. We are going to have a look at the energy business from two points of view: that of the consumer, and that of the supplier. If you have a look at your energy bill, you can basically see two lines: a fixed amount you pay to your supplier of energy, just for being connected to the grid, and a variable amount, which is, roughly speaking, the mathematical product: **[Price of 1 kWh * Quantity of kWh consumed]**. Of course, ‘kWh’ stands for kilowatt-hour. On the whole, your expenditure on electricity is computed as:

**E = Fixed price for connection to grid + [Price of 1 kWh * Quantity of kWh consumed]**

** P _{1} P_{2} Q **

From the point of view of the supplier of energy, their market is made of N consumers of energy. We can represent this market as a set made of N elements, for example as **N = {k _{1}, k_{2}, …, k_{n}}**, where each

*i-th*consumer

**k**pays the same fixed price

_{i}**P**for the connection to the grid, the same price

_{1}**P**for each kWh consumed, and consumes an individually specific amount

_{2}**Q(k**of energy measured in kWh. In that set of

_{i})**N = {k**consumers, the

_{1}, k_{2}, …, k_{n}}**total volume Q of the market**is computed as:

**Q = Q(k _{1}) + Q(k_{2}) + …+ Q(k_{n}) [kWh]**

…whilst the total value of the market is more complex a construct, and you compute it as:

**Value of the market = N*P _{1} + Q*P_{2}**

Most consumers have a more or less fixed budget to spend on electricity. If you take 1000 people and you check their housing expenses every month, you will see that their expenditures on electric power are pretty constant, unless some of them are building spaceships in their basements. So we introduce in our model of the market a budget on electricity, or **B _{e}**, specific to each individual customer

**k**. Hence, that budget can be noted as

_{i}**B**. Actually, that budget is the same as what we have introduced earlier as expenditure E, so:

_{e}(k_{i})**B _{e}(k_{i}) = E = P_{1} + P_{2}*Q(k_{i})**

This mathematical construct allows reverse engineering of individual power consumption. Each consumer uses the amount **Q(k _{i})** of kilowatt-hours, which satisfies the

**condition**:

**Q(k _{i}) = [B_{e}(k_{i}) – P_{1}] / P_{2}**

In other words, each of us has a budget to spend on electricity bills, from this budget we subtract the fixed amount of money **P _{1}**, to pay for being connected to the power grid, and we use the remaining sum so as to buy as many kilowatt-hours as possible, given the price

**P**. This condition is a first approach to what is called the

_{2}**demand function**, on the part of the consumers. Although this function is still pretty sketchy, we can notice one pattern. The total amount of electricity

**Q(k**that I consume depends on three parameters: my budget

_{i})**B**, and the two prices

_{e}(k_{i})**P**and

_{1}**P**. In economics, we call this an

_{2}**elasticity**. We say that the quantity

**Q(k**

_{i})**is elastic on**:

**B**,

_{e}(k_{i})**P**. How elastic is it? We can calculate it, if we now the magnitudes of change in particular factors. If I know that my consumption of electricity has changed from like 40 000 kWh a year to 42 000 kWh, and I know that in the meantime the price P

_{1}, P_{2}_{2}of one kilowatt-hour has moved from 0,1 euro to 0,12 euro, I can calculate something called deltas:

**delta [Q(k _{i})] = ∆ Q(k_{i}) = 42 000 **

**–**

**40 000 = 2 000 kWh**

**delta (P _{2}) = ∆P_{2} = €0,12 **

**–**

**€0,1 = €0,02**

The local (i.e. specific to this precise situation) **elasticity of my consumption** **Q(k _{i})** to the price

**P**can be estimated, in a first approximation, as

_{2}**e = ∆ Q(k _{i}) / ∆P_{2} = 100 000 kWh per €1**

The first thing to notice about this elasticity is that it is exactly contrary to what you see in my lectures, and what you can read in textbooks, about the demand function. The basic **law of demand **says something like: the greater the price, the lower the consumers’ willingness to buy. Here, we have something contrary to that law: greater consumption of energy is associated with a higher price, through a positive elasticity. I am behaving contrarily to the law of demand. In science, we call such a situation a **paradox**. Yet, notice that it is a local paradox: I cannot keep on increasing my personal consumption of electricity ad infinitum, even in the presence of a constant price. At some point, I have to start saving energy and increase my consumption just as much, as the prices possibly fall. **So, generally, as opposed to locally, I am likely to behave in conformity with the law of demand. **Still, keep in mind that in real life, paradoxes abound. It is not obvious at all to peg down a market equilibrium exactly as shown in textbooks. Most real-life markets are **imperfect markets**.

Now, if you look at this demand function, you can find it a bit distant from how you consume electricity. I mean, personally I don’t purposefully maximize the quantity of kilowatt-hours consumed. I just buy stuff powered by electricity, like a computer or a refrigerator, I plug it in, I turn it on, and I use it. Sometimes, I vaguely practice energy saving, like turning off the light in rooms where I am not currently staying. Anyway, my consumption of electricity **Q(k _{i})** is determined by the

**technology T**I have at my disposal, which, in turn, consists of a set

**M = {g**of goods powered by electricity: fridge, computer, TV set etc. We say that each

_{1}, g_{2}, …, g_{m}}*j-th*good

**g**, in the set M, is a

_{j}**complementary good**to electricity. I can more or less accurately assume that an average refrigerator consumes

*x*kWh, whilst an average set of house lighting burns

_{1}(fridge)*x*kWh. We can slice subsets out of the set N of consumers:

_{2}(lighting)**N**people with fridges,

_{1}**N**people with air conditioners etc. With

_{2}**Q(g**standing for the consumption of electricity in a given item powered with it, I can write:

_{j}) **Q(k _{i}) = N_{1}*Q(g_{1}) + N_{2}*Q(g_{2}) + …+ N_{m}*Q(g_{m}) = [B_{e}(k_{i}) – P_{1}] / P_{2}**

It means that, besides being elastic on my budget and the prices of electricity, my individual demand for a given amount of kilowatt-hours is **elastic on the range of electricity-powered items I possess**, and this, in turn, means that it is **elastic on the budget I spend on those pieces of equipment, as well as on the prices of those goods** (with a given budget to spend on houseware, I am more likely to buy a cheaper fridge rather than a more expensive one).

Now, business planning and management. Imagine that you are an entrepreneur, and you want to build a solar farm, and sell electricity to the people living around it. Your market works as shown above. You know that whatever you want to do, your organisation will have to satisfy the needs of those N customers, with their individual budgets and their individual elasticities in expenditures. **The size of your organization, and its structure, will be significantly determined by the necessity to maintain profitable relations with N customers**. Two questions emerge: what such organizational structure (i.e. the one serving to build and maintain those customer relations) would look like, and how could it be connected to other functional structures in the business, like building the solar farm, maintaining it in good technical state, purchasing components for construction and maintenance, hiring and firing people etc. You certainly know one thing: you have a given **value of the market = N*P _{1} + Q*P_{2} **and you have to adapt your costs (e.g. the sum total of salaries paid to your people) to this value of the market. Thus, you know that:

**Average salary in my business = [(N*P _{1} + Q*P_{2}) – The profit I want – Other costs] / the number of employees**

In other words, the size of my business, e.g. in terms of the number of people employed, as well as my profit and the wages I can pay, will be determined by the value of my market. Now, let’s go along a path at the frontier of economics and management. I want to know how much capital I should invest in my business. I posit a condition: that capital should return to me, in the form of profits from business, in 7 years. Thus, I know that:

**My initial investment = 7* My annual profit = 7*(N*P _{1} + Q*P_{2} – Current costs) = N*B_{e}(k_{i}) **

**–**

**current costs = N*E**

**–**

**current costs = N*[P**

_{1}+ P_{2}*Q(k_{i})]**–**

**current costs**

This is how the size of my business, both in terms of capital invested, and in terms of the number of people employed, is determined by, or is elastic on, the prices I can practice with my customers, the sheer number of those customers, as well as on their individual budgets.

# 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: https://data.worldbank.org/indicator/EG.ELC.RNEW.ZS ). 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 (https://data.worldbank.org/indicator/EG.USE.PCAP.KG.OE ), 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 (https://data.worldbank.org/indicator/EG.FEC.RNEW.ZS ). 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 ‘

**’. 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 ‘**

*ln(%RenEl) = a1*ln(RenQ) + ?***X/Q**’. Good, so now, I can proudly state that ‘

**’. Smells interestingly. I drop another size factor, namely population (**

*ln(%RenEl) = a1*ln(RenQ) + a2*ln(X/Q) + ?***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 **R ^{2} = 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 **R ^{2} = 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 **R ^{2} = 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 km ^{2}**. Here, it becomes lax, somehow:

**n = 362**observations yield just

**R**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.

^{2}= 0,410**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 **R ^{2} = 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 R^{2}, as my R^{2} makes **R ^{2} = 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 R

^{2}. 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 km ^{2}**. I have

**n = 299**valid observations in this category, and they allow to determine 56%, or

**R**, 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.

^{2}= 0,560**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):

**1 ^{st} sextile**: Canada (3,909 people per km

^{2})

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

**3 ^{rd} sextile**: USA (34,863), Estonia (31,011),

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

**6 ^{th} 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 http://www.ggdc.net/pwt

# The difference jumps to my eye, but what does it mean?

### My editorial

I hope I am on the right track with that idea that the maturing of markets can be represented as incremental change in the density of population. This is what I came up with yesterday, in my research update in French (see ‘Le mûrissement progressif du marché, ça promet’). I am still trying to sort it out, intellectually. This is one of those things, which just seem to work but you don’t exactly know how they do it. I think I need some time and some writing in order to develop a nice, well-rounded, intellectual crystallization of that concept. It all started, I think, as I multiplied tests on different quantitative models to explain incremental changes in the value of those two variables I am currently interested in: the percentage of renewable energy in the primary production of electricity (https://data.worldbank.org/indicator/EG.ELC.RNEW.ZS ), and the percentage of renewables in the final consumption of energy (https://data.worldbank.org/indicator/EG.FEC.RNEW.ZS ).

With the software I have, that Wizard for MacOS – and this is really not heavy artillery as statistical software comes – testing models sums up to quick clicking. Setting up and testing a model – or an equation – with that tool is much faster than my writing about it. This is both the blessing and the curse of modern technology: it does things much faster than we can wrap our mind around things. In order to understand fully this idea that I came up with yesterday, I need to reconstruct, more or less, the train of my clicking. That should help me in reconstructing the train of my thinking. So, yesterday, I was trying to develop, once again, on that idea of the Wasun, or virtual currency connected to the market of renewable energies. I assumed that empirical exploration of the question would consist in taking the same equations I have been serving you on my blog for the last few weeks, and inserting the supply of money as one more explanatory variable on the right side in those equations. It kind of worked, but just kind of: adding the supply of money, as a percentage of the GDP, to a model explaining the percentage of renewables in the final consumption of energy, for instance, added some explanatory power to that model, i.e. it pumped the R^{2} coefficient of determination up. Still, the correlation attached to the supply of money, in that model, did not seem very robust. With a p-value like 0,3 or 0,4 – depending on the exact version of the equation I was testing – it turned out that I have like 30 or 40% of probability that I can have any percentage of renewable energies with a given velocity of money. That p-value is the probability of the null hypothesis, i.e. of no correlation whatsoever between variables.

Interestingly, I had the same problem with a structural variable I was using as well: the density of population. I routinely use the density of population as a quantitative estimator of difference between social structures. I have that deeply rooted intuition that societies displaying noticeable differences in their densities of population are very different in other respects as well. Being around in a certain number in a given territory, and thus having, on average, a given surface of that territory per person, is, for me, a fundamental trait of any society. Fundamental or not, it behaved in those equations of mine in the same way the supply of money did: it added to the coefficient of determination R^{2}, but it refused to establish robust correlations. Just for you, my readers, to understand the position I was in, as a researcher: imagine that you discover some kind of super cool spice, which can radically improve the taste of a sauce. You know it does, but you have one tiny little problem: you don’t know how much of that spice, exactly, you should add to the sauce, and you know that if you add too much or too little, the sauce will taste much worse. Imagined that? Good. Now, imagine you have two such spices, in the same recipe. Bit of a cooking challenge, isn’t it?

What you can do, and what great cooks allegedly do, is to prepare a few alternative sauces, each with the same recipe, but with a different, and precisely defined amount of the spice under investigation. As you taste each of those alternative sauces, you can discover the right amount of spice to add. If you are really good at it, you can even discover the gradient of taste, i.e. the incremental change in taste that has been brought by a given incremental change in the quantity of one particular ingredient. In quantitative research, we call it ‘control variable’: instead of putting a variable right in the equation, we keep it out, we select different subsets of empirical data, each characterized by a different class of value in this particular variable, and we test the equation, without the variable in question, in those different subsets. The mathematical idea behind this approach is that we never know for sure whether our way of counting and measuring things is accurate and adequate to the changes and differences we can observe in those things. Take distance, for example: sometimes it is better to use kilometres, but sometimes even a centimetre it too much. Sometimes, small incremental changes in a measurable phenomenon induce too much complexity for us to crystallize any intelligible thought about it. In statistics, it manifests as a relatively high p-value, or the probability of the null hypothesis. Taking that complexity out of the equation and simplify it into a few big chunks of reality can help our understanding.

Anyway, I had two spices: the density of population, and the supply of money. I had to take one of them out of the equation and treat as control variable. As I am investigating the role of monetary systems in all that business of renewable energies, it seemed just stupid to take it out of the equation. Mind you: it seemed, which does not mean it was. There is a huge difference between seeming to be stupid and being really stupid. Anyway, I decided to keep the supply of money in, whilst taking the density of population out and just controlling for it, i.e. testing the equation in different classes of said density. For a reason that I ignore, when I ask my statistical software to define classes in a control variable, it makes sextiles (spelled jointly!), i.e. it divides the whole sample into six subsets of roughly the same size, 1577 or 1578 observations each in the case of the actual database I am using in that research. Why six? Dunno… Why not, after all?

So I had those sextiles in the density of population, and I had my equation, regarding the percentage of renewable energies in the final consumption of energy, and I had that velocity of money in it, and I tested inside each sextile. Interesting things happened. In the least dense populations, the equation barely had any explanatory power at all. As my equation was climbing the ladder of density in population, it gained explanatory power as well. Still, there is an interval of density, where that explanatory power fell again, just to soar in the densest populations. Those changes in the coefficient of determination R^{2} were accompanied by visible changes in the sign and the magnitude of the regression coefficient attached to the velocity of money. The same happened in other explanatory variables as well. My equation, as I was trying to wrap my mind around all that, works differently in different types of populations, regarding their density. It works the most logically, in economic terms, in the densest populations. The percentage of renewable energy in the final basket of consumption depends nicely and positively on the accumulation of production factors and on the supply of money. The more developed the local economic system, the better are the chances of going greener and greener in that energy mix.

In economics, demographic variables tend to be considered as a rich and weird cousin. The cousin is rich, so they cannot be completely ignored, but the cousin is kind of a weirdo as well, not really the kind you would invite risk-free to a wedding, so we don’t really invite them a lot. This nice metaphor sums up to saying that I tried to find a purely economic interpretation for those changes I observed when controlling for the density of population. My roughest guess was that money matters the most when we have really a lot of people around us and a lot of transactions to make (or avoid). With hardly any people around me (around is another simplification here, it can be around via Internet), money tends to have less importance. That’s logical. In other words, the velocity of money depends on the degree of development in the market we consider. The more developed a market is, the more transactions are there to finance, and the more money we need in the system to make that market work. Right, this works for any market, regardless whether we are talking about long-range missiles, refrigerators or spices. Now, how does it matter for this particular market, the market of energy? Please, notice: I used the ‘how?’ question instead of ‘why?’. Final consumption of energy is a lifestyle and a social structure doing its job. If the factors determining the percentage of renewable energies in said final consumption work differently in different classes of density in the population, those classes probably correspond to different lifestyles and different types of local social structures.

I imagined a local community, where people progressively transition towards the idea of renewable energies. In the beginning, there are just a few enthusiasts, who, with time, turn into a few hundred, then a few thousands and so on. From then on, I unhinged my mind a bit. I equalled the local community at the starting point, when nobody gives a s*** about green energy, as a virgin land. As new settlers come, new social relations emerge, and new opportunities to transact and pay turn up. Each person, who starts actively to use renewable energies, is like a pioneering settler coming to that virgin land. The emergence of a new market, like that of renewable energy, in an initially indifferent population, is akin to a growing density in a population of settlers. So, I further speculated, the nascence and development of a new market can be represented as a growing density in the population of customers. I know: at this point, it could be really hard to follow me. I even have trouble following myself. After all, if there are like 150 people per square kilometre in a population, according to my database, there are just them in that square kilometre, and no one else. It is not like they are here, those 150 pioneers, and a few hundred others, who are there, but remain kind of passive. Here, you have an example of the kind of mindfuck a researcher deals all the time. Data exploration is great, but data tends to have sharp edges. There is a difference, regarding the role of money in going green in our energies, between a population of 100 per km^{2} and a population of 5000 per km^{2}. The difference is there, it jumps to my eye, but what does it mean? How does it work? My general intuition is that the density of population, as control variable, controls for the intensity of social interactions (i.e. interactions per unit of time). The degree of maturity in a market is the closest economic meaning I can associate with that intensity of interactions, but there could be something else.

# It warms my heart to know I am not totally insane

### My editorial

This is a rainy morning in Amplepuis, France, where I am staying until tomorrow. I am meditating, which means I am thinking without pretending to think anything particularly clever. Just basic, general flow of thinking, enough not to suck my thumb, sitting in a corner. I am mentally reviewing that report by Sebastiano Rwengabo (Rwengabo 2017[1]), which I commented on in my last two updates, and in some strange way I keep turning in returning in my mind that formula of multiple probability by Thomas Bayes (Bayes, Price 1763[2]), namely that if I want more than one success over n trials, at some uncertain, and therefore interesting action, I have always more than one way to have those *p* successes over *n* trials. Thomas Bayes originally equated that ‘more than one’ to (p^{q})/q!, where *q* is the tolerable number of failures. You can try by yourself: as long as you want more than one success, your (p^{q})/q! is always greater than one. There is always more than one way to have more than one success. Interesting intuition.

I am digging into the topic of local power systems based on renewable energies, possibly connected to a local cryptocurrency. I want to prepare something like a business plan for that idea. I want to know how many ways of being successful in this type of endeavour are reported in the literature. I start with a leaflet I found and archived on my https://discoversocialsciences.com website under this link . It is entitled ‘100% – RES communities’. As usually, I start at the end, and the end is sub-headed ‘*Stay in The Game*’. Good. If it is important to stay in the game, then logically it is important not to drop off, which, in turn, means that dropping off is an observable end to local efforts at going 100% renewable. One of the ways to stay in the game consists in joining other people who want to. There is a network, the Global Covenant of Mayors (http://www.globalcovenantofmayors.org ), which currently unites 7 477 cities with almost 685 million people living in them and which has been created quite recently by the merger of the Covenant of Mayors, mentioned in that ‘100% – RES communities’ leaflet, with the Compact of Mayors, in June, 2016. Having more than one success in going 100% means, thus, staying in the game with others, in networks, and those networks tend to merge and create even bigger networks. I have a nice conditional probability, here: my probability of successfully going 100% green, as a local community, depends on the probability we manage to stick to our commitments, which, in turn, depends on our ability to join a network of other communities with similar goals. There are other networks, besides the Covenant of Mayors, such as the RES League (http://www.res-league.eu ), 100% RES Communities (http://www.100-res-communities.eu ), or the French RURENER (http://fr.rurener.eu ).

The next thing, which apparently helps to stay in the game is a SEAP, or Sustainable Energy Action Plan. As I am writing this paragraph, I am browsing the Internet in the search of details about this approach, and I am simultaneously reading that leaflet. SEAP seems to be a general line of approach, which sums up to assuming that we can induce only as much change as we can really plan, i.e. that we can translate into real action on a given date and in a given place. If I am grasping well the concept, it means that whenever a ‘*we will do it somehow*’ pokes its head out of our action plan, it indicates we have no proper SEAP. I like the approach, I have experienced its soundness in other areas of life: we can usually achieve more than we think we can, but we need to understand very precisely what is the path to cover, step by step. Here, the coin drops: if we need a good SEAP, it is important to tap into other people’s experience, whence the point of forming networks. Being maybe a bit less ambitious, but more realistic and more in touch with what the local community really can do, is apparently helpful in going 100% green.

That was a leaflet, now I take a scientific paper: “Exploring residents’ willingness to pay for renewable energy supply: Evidences from an Italian case study” by Grilli et al.[3] , an unpublished working paper accessible via the Social Sciences Research Network . The paper explored the attitudes of people living in the Gesso and Vermenagna valleys, towards the prospect of paying higher energy bills as long as those bills will be 100% green. The case study suggests an average acceptance for a 5,1€, or 13% increase in the monthly energy bill. Knowledge about renewable energies seems to be a key factor in shaping those attitudes. Good, so I have another nice, conditional probability: having more than one success in going 100% green locally depends on the local acceptance of higher energy bills, which, in turn, depends on the general awareness of the population involved.

I move forward along that financial path, and I am having a look at a published article, entitled “*Is energy efficiency capitalized into home prices? Evidence from three US cities.*“, by Walls et al.[4] . Margaret Walls and the team of associated researchers found a positive impact of ‘green certification’ of residential properties upon their market price, with a premium ranging from 2 to 8%. Still, this premium remains strongly local, thus largely idiosyncratic. Staying in this path of thinking, i.e. thinking about money whilst thinking about grand green initiatives, I am having a look at an article by Patrick Hartmann and Vanessa Apaolaza-Ibáñez as for the consumers’ attitude towards the so-called ‘green energy brands’[5]. In this case, the most interesting thing is the methodology, as the results are quite tentative, based on a total of 726 street interviews in six towns and villages in northern Spain. The methodology is based on a set of assumed benefits that an individual can derive from purchasing energy from suppliers certified as 100% green in their process of generation. There is a nice piece of fine reasoning from the part of Patrick Hartmann and Vanessa Apaolaza-Ibáñez. They hypothesise that altruistic environmental concerns and their satisfaction are just one among the many psychological factors affecting the decision of purchasing renewable energy. There is a bunch of egoistic factors, slightly in the lines of Thorstein Veblen’s theory of the leisure class: consuming green energy can provide something described as ‘warm glow’, or personal satisfaction derived from experiencing a subjectively positive impact on the social and natural environment, as well as from the social recognition of that impact that we experience as a feedback from other people. In other words, if a person can expect interactions like ‘*Oh! You are buying that 100% green energy? Fantastic! You are such a precious member of the community!*’. Let’s face it: each of us would like to be praised like that, from time to time. On the top of that, the purchase may be further affected by the general reputation of the given brand, and by individual attitudes towards experiencing the contact with nature. Whilst tentative, the results of those interviews suggest, quite interestingly that the general attitude towards the suppliers of green energy is strongly influenced by that personal, individual experience of nature in general.

Still following the money, but moving from the small money spent by consumer towards the big money held by banks, I am browsing through an unpublished paper by Karen Wendt, from MODUL University in Vienna[6]. This particular paper is precious, from my point of view, mostly because of the interesting stylized facts it presents. In science, stylized facts are facts that we can express in a graph, but we cannot exactly explain why the graph looks the way it looks. So, Karen Wendt lets me learn, for example, that a large part of the known reserves in fossil fuels, probably between 60 and 80% of them, must stay nicely in the ground if we are to meet the 2°C limit of temperature jump. These reserves are accounted for as assets in the balance sheet of your average Exxon Mobil. If they are to stay where they are, they will have to be kicked the hell out of those balance sheets, and that’s gonna hurt. The same is valid for carbon-intensive infrastructure, like chains of petrol stations or oil-refining plants. If we turn green, all that stuff will have to be written off someone’s equity, and this, once again, is likely to make some people nervous. It shows that if we really want to go green, we really could do with some capitalistic mechanism of transition, which would allow, sadly but realistically, to switch relatively smoothly from a carbon-intensive balance sheet, with the corresponding capital profits financing the corresponding private islands, to a balance sheet based on renewable energies. It warms my heart, those observations from Karen Wendt, as it suggests I am not totally insane when I think about monetary systems specifically oriented on giving market value to green energy.

[1] Rwengabo, S., 2017, Efficiency, Sustainability, and Exit Strategy in the Oil and Gas Sector: Lessons from Ecuador for Uganda, ACODE Policy Research Series No.81, 2017, Kampala, ACODE, ISBN: 978-9970-567-01-0

[2] Mr. Bayes, and Mr Price. “An essay towards solving a problem in the doctrine of chances. by the late rev. mr. bayes, frs communicated by mr. price, in a letter to john canton, amfrs.” Philosophical Transactions (1683-1775) (1763): 370-418

[3] Grilli, G., Balest, J., Garengani, G., Paletto, A., 2015, Exploring residents’ willingness to pay for renewable energy supply: Evidences from an Italian case study, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2669975

[4] Walls, M., Palmer, K., Geranden, T, Xian Bak, 2017, Is energy efficiency capitalized into home prices? Evidence from three US cities, Journal of Environmental Economics and Management vol. 82 (2017), pp. 104-124

[5] Hartmann, P., Apaolaza-Ibáñez, V., 2012, Consumer attitude and purchase intention toward green energy brands: The roles of psychological benefits and environmental concern, Journal of Business Research, vol. 65.9 (2012), pp. 1254-1263

[6] Wendt, K., 2016, Decarbonizing Finance – Recent Developments and the Challenge Ahead, Available at SSRN: https://ssrn.com/abstract=2965677