### 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 10^{th} of August (see https://discoversocialsciences.com/2017/08/10/everything-even-remotely-economic/ or http://researchsocialsci.blogspot.com/2017/08/everything-even-remotely-economic.html ).

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 **R ^{2} = 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 **R ^{2} = 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: **R ^{2} = 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 **R ^{2} = 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: **R ^{2} = 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 **R ^{2} = 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 **R ^{2} = 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: **R ^{2} = 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 http://www.ggdc.net/pwt