Cases of moderate deprivation

A few words from me via You Tube

I intend to continue my research with three strands of ideas. The first is the idea of innovation as collective experimentation and learning, rather than linear progress in terms of productivity. In that context, I would like return to the issue, which I had been developing for a few months, this spring, namely to the role of cryptocurrencies in technological change.  The second direction is that of the production function, as it was formulated, back in the day, by Prof Charles W. Cobb and Prof Paul H. Douglas, in their common work from 1928[1]. I keep reading and rereading their article, together with their source documents, and I can’t help being fascinated by the logical structure those two scientists came up with. The third path is that of innovation being done in two different environments: people wealthy enough not to have any food deficit, on the one hand, and those who starve, with various acuity, on the other hand.

As you might already know from the reading of my earlier posts, I like inverting orders. Thus, taking on the last item – the issue of food deficit in the context of innovation – and making it the first step in all the rest of my research is just fine. Still, continuing with those three strands of ideas means that I want to find connections between them, so as sort of make those three paths converge into one, big theory of whatever it will turn out to be. All this elaborate introduction means, at the bottom line, that I am continuing with the topic, which I already developed in my update from the 10th of August (see or ).

I am returning to a model I built and published this spring, namely that of technological change manifesting itself at the level of monetary systems. First, a few words of explanation and reminder. With the World Bank, you can fish out a statistic called ‘Supply of broad money as % of the GDP’. It is supply of broad money, or ‘M’, divided by the value of real output ‘Q’. Now, this ratio, namely M/Q, happens to be the reciprocal of what the godfather of monetarism, Milton Friedman, used to define as the velocity of money: Q/M. Milton Friedman claimed that the velocity of money is a deeply structural variable, it determines the demand for money in the given economy, and we can assume it to be basically constant. As we invert the statistic provided by the World Bank, and convert it into the velocity of money, it becomes embarrassing: at the scale of the whole global economy, it keeps falling since the 1960ies. That’s life: you invert the way of thinking about something, you convert people into something else, and it becomes embarrassing. Anyway, deeper exploration of data shows a consistent decrease in the velocity of money in emerging markets and developing economies, whilst it stays more or less stable (well, oscillating around a more or less horizontal trend) in the developed economies.

I had that idea that the increasing monetization of the global economy could result from increasingly fast a technological change: we are entrepreneurs, and the faster we have to amortize our productive assets, the thicker cushion of highly liquid, financial assets we tend to maintain in our balance sheets. I formalized that idea in an article, the full version of which you can find by clicking this link . I decided to get back to my quantitative model from that article and to insert food deficit as control variable, just to see what happens. That seeing what happens is basically consistent with my latest findings, namely that the functioning of the monetary system is important for alleviating the deficit of food.

That basic model I decided to get back to unfolds according to the following principles. The variable I am explaining is the velocity of money ‘V’, or output divided by the supply of money. I am testing the hypothesis that ‘V’ is being shaped by the pace of technological change, expressed as the ratio of aggregate depreciation in fixed assets, per million inhabitants, or ‘DeprPop’. Additionally, there is that variable of resident patent applications per million people, or ‘PatappPop’. To that, I add one factor of scale, namely the Gross Domestic Product (GDP), and one structural factor in the form of density in population (DensPop). In my scientific clemency, I allow the explained variable V to have some residual play, independent from explanatory variables. Anyway, I squeeze all that company down to their natural logarithms, and I get this model:

ln(V) = a1*ln(GDP) + a2*ln(DeprPop) + a3*ln(PatappPop) + a4*ln(DensPop) + Residual

Now, I take my compound database, essentially standing on Penn Tables 9.0 (Feenstra et al. 2015[2]), with additional variables stuck to it, and I test the model. In the whole sample of all valid observations, food deficit or not, I get n = 2 238 of those ‘country – year’ records, and a coefficient of determination is R2 = 0,409. The individual coefficients look like that:

variable coefficient std. error t-statistic p-value
ln(GDP) -0,077 0,008 -9,989 0,000
ln(DeprPop) -0,269 0,016 -16,917 0,000
ln(PatappPop) 0,015 0,007 2,044 0,041
ln(DensPop) -0,102 0,006 -16,299 0,000
Constant residual 3,939 0,122 32,202 0,000

OK, that was the reminder. Now, let’s drop the depth of food deficit into this sauce. First, I go to cases of the most severe food deficit, between 744 and 251 kilocalories a day per person. First remark that jumps to the eye immediately: those people do not have any patentable inventions on record. I have to remove the variable ‘PatappPop’ from the game and I land with n = 265 observations and virtually no determination: my R2 = 0,040. This is hardly worth to study coefficients in this context, but just for the sake of completeness I am giving it here, below:

variable coefficient std. error t-statistic p-value
ln(GDP) -0,099 0,035 -2,851 0,005
ln(DeprPop) -0,058 0,037 -1,567 0,118
ln(DensPop) 0,011 0,022 0,513 0,608
Constant residual 2,68 0,304 8,821 0,000

First provisional conclusion: the really poor people do not have enough scientific input to spin that wheel into motion. I climb one step up in the ladder of alimentary deprivation, to the category between 250 and 169 kilocalories a day per person. This one is quite cosy in terms of size: just n = 36 observations. Basically, it is at the limit between quantitative and qualitative, and still it yields a nice coefficient of determination: R2 = 0,489. The coefficients of regression come as shown in the table below:

variable coefficient std. error t-statistic p-value
ln(GDP) -0,225 0,072 -3,131 0,004
ln(DeprPop) -0,282 0,091 -3,094 0,004
ln(PatappPop) -0,045 0,069 -0,649 0,521
ln(DensPop) -0,088 0,11 -0,801 0,429
Constant residual 5,686 1,018 5,583 0,000

I keep scaling up that ladder of poverty, and I pass to the interval between 168 and 110 kcal a day missing in the food intake of an average person. I get n = 120 observations, and R2 = 0,767 terms of determination in the model. Remarkable jumps as for explanatory power. Interesting. I feel I will need some time to wrap my mind around it. Anyway, as I pass to the coefficients of regression, I get this:

variable coefficient std. error t-statistic p-value
ln(GDP) -0,283 0,021 -13,495 0,000
ln(DeprPop) -0,268 0,057 -4,722 0,000
ln(PatappPop) -0,038 0,019 -1,998 0,048
ln(DensPop) -0,018 0,037 -0,474 0,637
Constant residual 6,234 0,525 11,867 0,000

Second provisional conclusion: as I am scaling up the poverty ladder, the variable of patent applications per million people slowly gains in importance. For the moment, it manifests as increasing significance of its correlation with the explained variable (velocity of money). I keep climbing, and I pass to the category of food deficit between 109 and 61 kcal a day per person. My sample is made of n = 92 observations, and I hit quite a nice coefficient of determination: R2 = 0,786. The table of coefficients looks like that:

variable coefficient std. error t-statistic p-value
ln(GDP) -0,197 0,034 -5,789 0,000
ln(DeprPop) -0,302 0,073 -4,156 0,000
ln(PatappPop) -0,035 0,024 -1,439 0,154
ln(DensPop) -0,264 0,032 -8,302 0,000
Constant residual 6,538 0,547 11,963 0,000

The coefficients are basically similar, in this category, to those computed before. Nothing to write home about. One thing is really interesting, nonetheless: the importance of density of population. In the overall sample, density of population showed high significance in its correlation with the velocity of money. Yet, with those really food-deprived people in the previously studied classes of food deficit, that correlation remained hardly significant at all. Here, as we pass the threshold of 110 kcal a day per person in terms of food deficit, density of population starts to matter. It becomes truly a structural metric, as if the functioning of the social structure changed somewhere around this level of deprivation in food.

I climb up. The next class is between 60 and 28 kcal a day per person. I have n = 121 observations and R2 = 0,328. Interesting: in previous classes, the explanatory power of the model grew as the food deficit got shallower. Now, the pattern inverts: the model loses a lot of its power. The coefficients are to find in the table below:

variable coefficient std. error t-statistic p-value
ln(GDP) 0,159 0,046 3,445 0,001
ln(DeprPop) -0,78 0,116 -6,739 0,000
ln(PatappPop) 0,023 0,037 0,619 0,537
ln(DensPop) -0,166 0,064 -2,609 0,010
Constant residual 4,592 0,694 6,612 0,000

Another interesting observation to make: this particular class of food deficit seems to be the only one, where the scale factor, namely Gross Domestic Product, appears with a positive sign, i.e. it contributes to increasing the velocity of money. In all the other tests, it has a negative sign. Another puzzle to solve. Cool! I go up: between 28 and 0 kcal a day missing per person. Size: n = 140. The point of doing regression: questionable. The coefficient of determination is R2 = 0.209, and as for the significance to find in individual correlations, there is hardly any. You will see by yourselves in the table below:

variable coefficient std. error t-statistic p-value
ln(GDP) -0,013 0,087 -0,148 0,883
ln(DeprPop) -0,048 0,069 -0,705 0,482
ln(PatappPop) 0,022 0,043 0,51 0,611
ln(DensPop) -0,203 0,066 -3,079 0,003
Constant residual 1,837 0,998 1,841 0,068

I remember that in this particular class of food deprivation, I intuitively guessed a lot of internal disparity, as I measured the coefficient of variability in the ratio of patent applications per one million people. It seems to be confirmed here. This particular class of countries seems to contain a lot of local idiosyncrasies. Another cool puzzle to solve.

Now, I switch to the wealthy ones, among whom I have the luck to live and write those lines: no food deficit recorded. My sample is n = 1 726 observations, this time, and it lands with an acceptable determination in the model: R2 = 0,445. Correlations are straight as rain. All the explanatory variables hit a significance p < 0,001. Just as if getting rid of poor, undernourished people suddenly made science simpler to practice. See the table of coefficients:

variable coefficient std. error t-statistic p-value
ln(GDP) -0,043 0,008 -5,238 0,000
ln(DeprPop) -0,316 0,018 -17,229 0,000
ln(PatappPop) 0,035 0,01 3,524 0,000
ln(DensPop) -0,092 0,007 -13,776 0,000
Constant residual 3,737 0,134 27,874 0,000

Now, time to get to the general point. What I think I have demonstrated is that the level of food deprivation matters for the way that my model works. In other words: the economic system, and, logically, the whole social structure, work differently according to the relative place of the given population in the ladder of that most abject poverty, measured by hunger. Another general conclusion emerges: there is a certain level of poverty, where people seem to make the most out of technological change. Depending on the kind of test I am using, it is either below 28 kcal per person per day (my previous post on the topic), or between 169 and 61 kcal a day per person (this time). There is some kind of social force, which I will have to put a label on but it still has to wait and crystallize, and which appears in these particular cases of moderate deprivation. This force seems to disappear in wealthy populations, to the benefit of steel-hard coherence in the model.

[1] Charles W. Cobb, Paul H. Douglas, 1928, A Theory of Production, The American Economic Review, Volume 18, Issue 1, Supplement, Papers and Proceedings of the Fortieth Annual Meeting of the American Economic Association (March 1928), pp. 139 – 165

[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

Everything even remotely economic

My editorial

Back to my work on innovation, I am exploring a new, interesting point of view. What if we perceived technological change and innovation as collective experimentation under uncertainty, an experimentation that we, as a species, are becoming more and more proficient at?  Interesting path to follow. It has many branches into various fields of research, like games theory, for example. The curious ape in me likes branches. They allow it to dangle over problems and having an aerial view. The view involves my internal happy bulldog rummaging in the maths of the question at hand, and my internal monk, the one with the Ockham’s razor, fending the bulldog away from the most vulnerable assumptions.

One of the branches that my ape can see almost immediately is that of incentives. Why do people figure out things, at all? First, because they can, and then because they’d better, under the penalty of landing waist deep in shit. I think that both incentives, namely ‘I can’ and ‘I need to’ sum up very much to the same, on the long run. We can do things that we learn how to do it, and we learn things that we’d better learn if we want our DNA to stay in the game, and if such is our desire, we’d better not starve to death. One of the most essential things that we have historically developed the capacity of learning about is how to get our food. There is that quite cruel statistic published by the World Bank, the depth of food deficit. It indicates the amount of calories needed to lift the undernourished from their status, everything else being constant. As the definition of that variable states: ‘The average intensity of food deprivation of the undernourished, estimated as the difference between the average dietary energy requirement and the average dietary energy consumption of the undernourished population (food-deprived), is multiplied by the number of undernourished to provide an estimate of the total food deficit in the country, which is then normalized by the total population’.

I have already made reference to this statistic in one of my recent updates (see ). This time, I am coming back with the whole apparatus. I attach this variable, as reported by the World Bank, to my compound database made of Penn Tables 9.0 (Feenstra et al. 2015[1]), as well as of other data from the World Bank. My curious ape swings on a further branch and asks: ‘What does innovation and technological progress look like in countries where people still starve? How different is it from those wealthy enough for not worrying so much about food?’. Right you are, ape. This is a good question to ask, on this Thursday morning. Let’s check.

I made a pivot out of my compound database, summarizing the distribution of key variables pertaining to innovation, across the intervals defined regarding the depth of food deficit. You can grab the Excel file at this link: . A few words of explanation are due as for the contents. The intervals in the depth of food deficit have been defined automatically by my statistical software, namely Wizard for MacOS, version 1.9.9 (222), created by Evan Miller. Those thresholds of food deficit look somehow like sextiles (spelled together!) of the distribution: there is approximately the same number of observations in each interval, namely about 400. The category labelled ‘Missing’ stands for all those country – year observations, where there is no recorded food deficit. In other words, the ‘Missing’ category actually represents those well present in the sample, just eating to their will.

I took three variables, which I consider really pertinent regarding innovation: Total Factor Productivity, the share of the GDP going to the depreciation in fixed assets, and the ratio of resident patent applications per one million people. I start with having a closer look at the latter. In general, people have much more patentable ideas when they starve just slightly, no more than 28 kilocalories per day per person. Those people score over 312 resident patent applications per million inhabitants. Interestingly, those who don’t starve at all score much lower: 168,9 on average. The overall distribution of that variable looks really interesting. Baby, it swings. It swings across the intervals of food deficit, and it swings even more inside those intervals. As the food deficit gets less and less severe, the average number of patent applications per one million people grows, and the distances between those averages tend to grow, too, as well as the variance. In the worst off cases, namely people living in the presence of food deficit above 251 kilocalories a day, on average, that generation of patentable ideas is really low and really predictable. As the situation ameliorates, more ideas get generated and more variability gets into the equation. This kind of input factor to the overall technological change looks really unstable structurally, and, in the same time, highly relevant regarding the possible impact of innovation on food deficit.

I want this blog to have educational value, and so I explain how am I evaluating relevance in this particular case. If you dig into the theory of statistics, and you really mean business, you are likely to dig out something called ‘the law of large numbers’. In short, that law states that the arithmetical difference between averages is highly informative about real differences between populations these averages have been computed in. More arithmetical difference between averages spells more real difference between populations and vice versa. As I am having a look at the distribution in the average number of resident patent applications per capita, distances between different classes of food deficit are really large. The super-high average in the ‘least starving’ category, the one between 28 kilocalories a day and no deficit at all, together with the really wild variance, suggest me that this category could be sliced even finer.

Across all the three factors of innovation, the same interesting pattern sticks out: average values are the highest in the ‘least starving’ category, and not in the not starving at all. Unless I have some bloody malicious imp in my dataset, it gives strong evidence to my general assertion that some light discomfort is next to none in boosting our propensity to figure things out. There is an interesting thing to notice about the intensity of depreciation. I use the ratio of aggregate depreciation as a measure for speed in technological change. It shows, how quickly the established technologies age and what economic effort it requires to provide for their ageing. Interestingly, this variable is maybe the least differentiated of the three, between the classes of food deficit as well as inside those classes. It looks as if the depth of food deficit hardly mattered as for the pace of technological change.

Another interesting remark comes as I look at the distribution of total factor productivity. You remember that on the whole, we have that TFP consistently decreasing, in the global economy, since 1979. You remember, do you? If not, just have a look at this Excel file, here: . Anyway, whilst productivity falls over time, it certainly climbs as more food is around. There is a clear progression of Total Factor Productivity across the different classes of food deficit. Once again, those starving just a little score better than those, who do not starve at all.

Now, my internal ape has spotted another branch to swing its weight on. How does innovation contribute to alleviate that most abject poverty, measured with the amount of food you don’t get? Let’s model, baby. I am stating my most general hypothesis, namely that innovation helps people out of hunger. Mathematically, it means that innovation acts as the opposite of food deficit, or:

Food deficit = a*Innovation     , a < 0

 I have my three measures of innovation: patent applications per one million people (PattApp), the share of aggregate depreciation in the GDP (DeprGDP), and total factor productivity (TFP). I can fit them under that general category ‘Innovation’ in my equation. The next step consists in reminding that anything that happens, happens in a context, and leaves some amount of doubt as for what exactly happened. The context is made of scale and structure. Scale is essentially made of population (Pop), as well as its production function, or: aggregate output (GDP), aggregate amount of fixed capital available (CK), aggregate input of labour (hours worked, or L). Structure is given by: density of population (DensPop), share of government expenditures in the capital stock (Gov_in_CK), the supply of money as % of GDP (Money_in_GDP, or the opposite of velocity in money), and by energy intensity measured in kilograms of oil equivalent consumed annually per capita (Energy Use). The doubt about things that happen is expressed as residual component in the equation. The whole is driven down to natural logarithms, just in order to make those numbers more docile.

In the quite substantial database I start with, only n = 296 observations match all the criteria. On the one hand, this is not much, and still, it could mean they are really well chosen observations. The coefficient of determination is R2 = 0.908, and this is a really good score. My model, as I am testing it here, in front of your eyes, explains almost 91% of the observable variance in food deficit. Now, one remark before we go further. Intuitively, we tend to interpret positive regression coefficients as kind of morally good, and the negative ones as the bad ones. Here, our explained variable is expressed in positive numbers, and the more positive they are, the more fucked are people living in the given time and place. Thus, we have to flip our thinking: in this model, positive coefficients are the bad guys, sort of a team of Famine riders, and the good guys just don’t leave home without their minuses on.

Anyway, the regressed model looks like that:

variable coefficient std. error t-statistic p-value
ln(GDP) -5,892 0,485 -12,146 0,000
ln(Pop) -2,135 0,186 -11,452 0,000
ln(L) 4,265 0,245 17,434 0,000
ln(CK) 3,504 0,332 10,543 0,000
ln(TFP) 1,766 0,335 5,277 0,000
ln(DeprGDP) -1,775 0,206 -8,618 0,000
ln(Gov_in_CK) 0,367 0,11 3,324 0,001
ln(PatApp) -0,147 0,02 -7,406 0,000
ln(Money_in_GDP) 0,253 0,06 4,212 0,000
ln(Energy use) 0,079 0,1 0,796 0,427
ln(DensPop) -0,045 0,031 -1,441 0,151
Constant residual -6,884 1,364 -5,048 0,000

I start the interpretation of my results with the core factors in the game, namely with innovation. What really helps, is the pace of technological change. The heavier the burden of depreciation on the GDP, the lower food deficit we have. Ideas help, too, although not as much. In fact, they help less than one tenth of what depreciation helps. Total Factor Productivity is a bad guy in the model: it is positively correlated with food deficit. Now, the context of the scale, or does size matter? Yes, it does, and, interestingly, it kind of matters in opposite directions. Being a big nation with a big GDP certainly helps in alleviating the deficit of food, but, strangely, having a lot of production factors – capital and labour – acts in the opposite direction. WTH?

Does structure matter? Well, kind of, not really something to inform the government about. Density of population and energy use are hardly relevant, given their high t-statistic. To me, it means that I can have many different cases of food deficit inside a given class of energy use etc. Those two variables can be useful if I want to map the working of other variables: I can use density of population and energy use as independent variables, to construe finer a slicing of my sample. Velocity of money and the share of government spending in the capital stock certainly matter. The higher the velocity of money, the lower the deficit of food. The more government weighs in relation to the available capital stock, the more malnutrition.

Those results are complex, and a bit puzzling. Partially, they confirm my earlier intuitions, namely that quick technological change and high efficiency in the monetary system generally help in everything even remotely economic. Still, other results, as for example that internal contradiction between scale factors, need elucidation. I need some time to wrap my mind around it.

[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