I am interpreting my empirical findings about that evolutionary model of technological change. So far, it seems to make a logical structure, all those econometric tests. Yesterday, as I was presenting a research update in French ( see “L’invention mâle de modèles”), I wanted to test the hypothesis that different social structures yield different selection functions, with different equilibriums between the number of patent applications and the capital invested in fixed assets. I added to my initial model two more variables, which I consider as informative about social structure: the density of population, and the depth of food deficit. In turned out quite interesting, although with no surprises. Higher density of population favours greater a number of patent applications, whilst the food deficit works in the opposite way. In the first case, the corresponding correlation seems to be rock-solid, regarding the significance of the null hypothesis ( p < 0,001). The second structural variable, the depth of food deficit, seems a bit wobbly in its correlation, though. With a significance level p = 0.124, the null hypothesis is dangerously close.
You probably already know that I have three inside of me: the curious ape, the austere monk, and the happy bulldog. Those last days, the bulldog could really have had some fun, with all that quantitative data to rummage through and test. The ape and the monk are sitting now, observing the bulldog running after sparse pieces of data, and they are having a conversation. ‘You know what, ape?’ the monk opens up, ‘I am thinking about how far is the obvious from the truth. Catching my drift, somehow, are you?’. ‘Ooookh’, answers the ape. ‘Sure, you are absolutely right’, continues the monk, ‘When I have cut off the bullshit, with that Ockham’s razor, there is still plenty of knowable things left. Take this case: the model looks nice, on the whole, and still I have some doubts. Aren’t we leaving some truth behind?’. ‘Ooookh, oookh!’, the ape is definitely developing a theoretical stance here, which inspires the monk. ‘Right you are, once again, ape. That significant role of labour compensation, in our evolutionary model, suggests that we could consider labour, not capital, as the set of female organisms, which recombine the genetic code of technologies, transmitted in male patent applications. Good! So we take away capital, put the supply of labour instead, in the model, and we see what happens’.
The monk gets on his feet, eager to start. The ape smiles, taps him gently on the shoulder, and forces him to fold his razor (the Ockham’s razor) back into his pocket. Safety first. The ape points at the bulldog. The monk nods. This is going to be bulldog’s task, too. A bit of play with the data, again. So I start, me with those three in me. I reformulate my basic hypothesis: evolutionary selection of new technologies works as an interaction between a set of female organizations of labour force, and a set of male organisms generating intelligible blueprints of new technologies. First, just as I studied the velocity of capital across patentable inventions, I study now the velocity of labour. I take my database made of Penn Tables 9.0 (Feenstra et al. 2015) and additional data from the World Bank. In the database, I select two variables: ‘emp’ and ‘avh’. The first one stands for the number of jobs in the economy, the second for the number of hours worked, on average, by one employee in one year. As I multiply those two, so as I compute ‘emp’*’avh’, I get the total supply of labour in one year.
Now, I make a ratio: supply of labour per one resident patent application. This is my velocity of labour across the units of patentable invention. I compute the mean and the variance of this variable, for each year separately. I put it back to back with the mean and the variance of capital ‘ck’ per one patent application. Right here you can download the corresponding Excel spreadsheet from my Google Disc. Interesting things appear. The mean values of those two ratios are significantly correlated: their mutual coefficient of Pearson correlation in moments is r = 0,557779846. Their respective variabilities, or the thing that happens when I divide the square root of variance by the mean, are even more significantly correlated: r = 0,748282791. Those two ratios seem to represent two, inter-correlated equilibriums, which share a common structure in space (variability for each year is variability between countries). Thus, it would be interesting to follow the logic of the production function, in that evolutionary modelling of mine.
The next thing I do is to play the surgeon. I remove carefully the natural logarithm of physical capital, or ln(ck), from my model, and I put the natural logarithm of labour supply, or ln(emp*avh) instead. I do ceteris paribus, meaning that I leave everything else intact. Like a transplantation. Well, almost ceteris paribus. I have to remove one redundancy, too. The share of labour compensation, in the model I had so far, is clearly correlated with the supply of labour. Stands to reason: the compensation of labour is made of total hours worked multiplied by the average wage per hour. Cool! Organ transplanted, redundancy removed, and the patient seems to be still alive, which is a good thing in the surgery profession. It kicks nicely, with n = 317 valid observations (food deficit sifts away a lot of observations from my database; this is quite a sparse variable), and it yields a nice determination, with R2 = 0,806. Well, well, well, with that new variable instead of the old one, the patient seems even more alive than before. Somehow leaner, though. It happens. Let’s have a look at the parameters:
|ln(Energy use (kg of oil equivalent per capita))||2,133||0,108||19,79||0,000|
|ln(Density of population (people per sq km))||0,481||0,077||6,243||0,000|
|ln(Depth of the food deficit (kilocalories per person per day))||-0,42||0,055||-7,646||0,000|
|ln(emp × avh)||1,01||0,069||14,649||0,000|
Interestingly, the supply of labour seems to have jumped in the seat previously occupied by physical capital with almost the same coefficient of regression. Structural variables (i.e. those describing the social structure) keep their bearings, and even seem to gain some gravitas. The depth of food deficit has lost its previous wobbliness in correlation, and displays a proud p < 0,001 in terms of significance. Oh, I forgot to remove this one: energy intensity. It had its place in the previous model, with capital as peg variable, because at one moment in time, the residual constant from an early version of the model displayed a significant correlation with energy intensity. I just sort of left it, as it did not seem to be aggressive towards the new peg value, labour. Still, it was basically an omission, from my part, not to have removed it. Still, mistakes bring interesting results. When left in the model, energy intensity keeps its importance and its sign, whatever the peg variable, capital or labour.
Is it possible that we, humans, have a general tendency to favour technologies with high energy intensity? From the engineering point of view, it sounds stupid. Any decent engineer would look for minimizing energy intensity. Still, a species, understood as a biological mass with no official graduation in engineering, could be looking for appropriating as much energy from its environment as possible. So could we. That could mean, in turn, that all the policies aiming at minimizing the consumption of energy go essentially against the basic selection functions, which, in turn, animate our technological change. Systematically trying to minimize energy consumption means carving a completely new selection function.
The coefficient attached to the natural logarithm of ‘delta’, or the rate of depreciation in fixed assets, has undergone an interesting personal transformation in that new model. It has changed its sign: in the model with capital as peg variable, its sign was positive, now it is negative. When I assumed that capital chooses inventions, the selection function seemed to favour technologies with shorter a life (higher depreciation). Now, as I assume that labour chooses technologies, the selection process favours technologies with longer a life, or lower rate of depreciation. We have two opposing forces, though: the push to rotate technologies faster, in the selection function based on capital, and the strive to keep those technologies alive as long as possible, in the selection process based on labour. The respective velocities of the two production factors across the units of patentable invention are closely correlated, so I have some kind of economic equilibrium, here. That would be the equilibrium between investors wanting new technologies to pop all the time, and organizations (groups of workers) desiring technological standstill.
Ok, it had to happen. This is what happens when you let the bulldog play with data, unattended. It sniffed the money. I mean, the supply of money. I explain. In my evolutionary models, capital and labour, so the production factors, play the role of some primal substance of life, which gets shaped by technological innovation. Logically, a sexual model of reproduction needs a device for transmitting DNA from male organisms to the female ones, for further treatment. In biological reality, that device consists in semen for animals, pollen and seeds for plants. I could not figure out exactly, how to represent a spermatozoid in economic terms, and so I assumed that in economic evolution, money is the transmitting device. Each dollar is a marker, attached to a small piece of valuable resources. What if the transmitting mechanism had brains of its own? What if it was a smart transmitting mechanism? Well, for what I know about our transmitting mechanism, it is not very smart. I mean, it takes one billion spermatozoids to make one zygote. It is a bit as if it took one billion humans to make one new technology. We would be still struggling with the wheel. Yet, plants seem to be smarter in that respect. The vegetal pollen, and especially vegetal seeds, display amazing intelligence: they choose other organisms as conveyors, they choose the right place to fall off the conveyor etc.
So, what if money was a smart mechanism of transmission in my evolutionary model? What if there was a selection function from the part of money? The problem with ‘whatifs’ is that there is an indefinite multitude of them for each actual state of nature. Still, nobody forbids me to check at least one, right? So I take that model ln(Patent Applications) = a1*ln(Supply of broad money) + a2*ln(delta) + a3*ln(Energy use) + a4*ln(Density of population) + a5*ln(Depth of food deficit) + residual ln, and I test. Sample size: n = 494 observations. Could have been worse. Explanatory power: R2 = 0,615. Nothing to inform the government about, but respectable. Parameters: in the table below.
|ln(Energy use (kg of oil equivalent per capita))||0,834||0,134||6,222||0,000|
|ln(Density of population (people per sq km))||0,406||0,1||4,041||0,000|
|ln(Depth of the food deficit (kilocalories per person per day))||-0,218||0,063||-3,469||0,001|
|ln(Supply of broad money, % of GDP / 100 × rgdpo)||0,791||0,06||13,102||0,000|
It is getting really interesting. The supply of broad money takes the place of capital, or that of labour, as smoothly as if it had been practicing for years. Same sign, very similar magnitude in the coefficient, rock-solid correlation. Other variables basically stand still, even the structural ones. One thing changes: ‘delta’, or the rate of depreciation, seems to have lost the north. A significance at p = 0,569 is no significance at all. It means that with other variables constant, money could choose any life expectancy in technologies available for development, with a probability of such random choice reaching 56,9%. So, wrapping it up: There are three selection functions (probably, there is very nearly an infinity of them, but those three just look cool, to an economist), which share a common core – dependence on social structure, preference for energy maximization – and differ as for their preference for the duration of life-cycle in technologies. Capital likes short-lived, quick technologies. Labour goes for those more perennial and long-lasting. Money essentially doesn’t give a s*** (pronounce: s-asterisk-asterisk-asterisk). Whatever aggregate I take as the primal living substance of my model, the remaining part of the selection function remains more or less the same.
 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 www.ggdc.net/pwt