The really textbook-textbook exponential growth

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Here I go again, travelling. Not much of an expedition, just a trip to France, for a family visit of 5 days. As it is usually the case when I go for this type of trip, I am leaving sort of a tiny mess at home. This time, it is a leaking roof, and my son is supposed to handle (hopefully) the professionals, who are supposed (hopefully) to come and fix it.

This is supposed to be a scientific blog, and so I pass to scientific things. I am thinking about two, partly connected topics: my research and teaching about political systems, and a piece of research I am doing on Corporate Social Responsibility, or CSR, in the insurance industry. The connection that I see consists in defining the basic observables in large institutional structures, such as political systems or strongly regulated markets. I mean, how can I sort of know empirically what people do in such structures, with all the foam of propaganda, political and corporate, and with all those metaphysics, based on strong emotions, in the lines of “Corporations always cheat and politicians always cheat!”.

What can I sort of observe empirically, as directly, and as free of bias as possible, in political systems? Two things come to my mind in the first place: legal rules, starting with constitutions, and policies. The latter are partly wrapped in the former, mind you. Then, I am thinking about parties, or coalitions, at power. They are observable through their numerical, electoral scores and the parliamentary seats allotted. In the case of ruling coalitions, the proportions of executive offices, like ministers, deputy ministers, and secretaries of state, held by respective parties in the coalition, can be informative. Now, a little remark: anywhere outside the United States of America, a secretary of state is written in small letters, without capital initials, and means sort of a minister being at the disposition of the prime minister or of the president, inside the structure of respective offices adjacent to those two head jobs. In the United States, the Secretary of State writes himself or herself in with capital initials and is in charge of foreign policy.

As it comes to CSR in the insurance industry, I have three basic observables. One consists of business models, as I can deconstruct them through objective insight into the financials of insurance companies. The other is made of the officially declared policies of social responsibility. Finally, the third observable are the typical contractual patterns applied by insurance companies.

And so I observe those observables. I am strongly quantitative in my approach to anything, and so I am trying to nail down differences across space, as well as changes over time. There is one more thing. Whatever exact avenue I follow, ethics matter. There are certain outcomes of human actions, which can be deemed as social, in the sense of being general and widespread. We are ethical beings, as we want things and strive to achieve goals we see as valuable. If there are any general values, possible to distillate from various goals we are going for, and if these values are essentially constructive and positive, they are ethical values.

Good, that’s theory, and now I am taking on a topic of current importance. The President of my country, Andrzej Duda, has just met President Donald Trump. Apparently, he urged Donald Trump to move American troops from Germany to Poland, and to establish permanent bases of the U.S. military in Poland. That’s what the media say he apparently said he means. This is the foam that I have been just talking about. Now, I am reaching to less foamy a source, namely to the John S. McCain National Defense Authorization Act for Fiscal Year 2019. National Defense Authorisation Acts, voted each year for the next year, are federal peri-budgetary regulations. In the properly spoken Federal Budget of the United States of America, expenditures on defense are essentially presented as discretionary spending, i.e. remaining in the discretion of the executive. Still, the National Defense Authorisation act of each consecutive year gives some detail and some structure to that discretion.

So, in that John S. McCain National Defense Authorization Act for Fiscal Year 2019 three components refer to Poland. Firstly, there is Section 1280, entitled ‘Report On Permanent Stationing of United States Forces in The Republic of Poland. Then, sections 2901 and 4602 give a glimpse of actual expenditures of the U.S. military in Poland, scheduled for 2019. This report is supposed to lay out the feasibility and advisability of permanently stationing United States forces in the Republic of Poland. The type of forces taken into account are both the combat units properly spoken, and the so-called « combat enabler units », i.e. combat engineering, logistics and sustainment, warfighting headquarters elements, long-range fires, air and missile defense, intelligence, surveillance, reconnaissance, electronic warfare.

My experience with studying those things governments do and call ‘policies’ is that governments declare a policy sort of publicly, such as in this case, in an official act, when they have actually already done much in the given direction. In other words, efficient governments do something and then they announce they are going to do it. Inefficient governments declare the willingness to do something, and then they start thinking how the hell they can do it.

And so I go to numbers. Those in the National Defense Authorization Act 2019 come first. Section 2901 specifies the expenditures on Authorized Army Construction and Land Acquisition Projects. As for Poland, it makes a total of $144 400 000, and it is more than whatever the U.S. Army, the U.S. Navy, or the U.S. Air Force plan to spend in most other countries in Europe. The United Kingdom tops it with $185 130 000, and Germany closes by, mind you, with $119 000 000 to be spend by the U.S. Air Force in 2901. Section 4602 contains expenditures grouped under the heading of ‘Military Construction for Overseas Contingency Operations’, and it essentially mirrors the same amount as in Section 2901, i.e. $144 400 000.

Now, I compare these numbers with their counterparts specified in, respectively, the National Defense Authorization Act for Fiscal Year 2017  – $8 200 000 to be spent in Poland – and the National Defense Authorization Act for Fiscal Year 2018   >> $22 400 000 in the same category.

US Military Spending in Poland


This is an almost textbook case of exponential growth. How do I know it? I take those values for three consecutive years, thus Money(2017) = $8 200 000, Money(2018) = $22 400 000, and Money(2019) = $144 400 000, and I take natural logarithms out of those numbers. Reminder: a natural logarithm is the power, to which the Euler’s constant e = 2,7182 has to be taken in order to obtain the given number. In this case, Money(2017) = e15,91964471, Money(2018) = e16,92457152, and Money(2019) = e18,78532386.

The really textbook-textbook exponential growth is like y = eb*t, where ‘t’ is the number of the consecutive period on a timeline, and ‘b’ is a parameter. Constant exponential growth occurs when the ‘b’ coefficient is constant over time. When ‘b’ dares to grow with each consecutive period, we have an accelerating exponential growth, whose opposite is the decelerating growth with ‘b’ decreasing over time. What I do now is to assume that my three consecutive years are three periods on a timeline, which is basically what they are, but I need to do it sort of by the book, and so I have 2017 = t1, 2018 = t2, and 2019 = t3. Consequently, I divide the natural logarithms from the preceding paragraph by their respective abscissae on the timeline. That gives Money(2017) = e1*15,91964471, Money(2018) = e2*8,462285758, and Money(2019) = e3*6,261774619.

See? The ‘b’ coefficients of this particular exponential chain decrease over time. Here comes the deep logic of exponential growth: it is a type of process over time, where each consecutive step sort of stands and builds up on the shoulders of the preceding steps. Military spending addressed by U. S. Department of Defense, in Poland grows over time but the exponential pace of this growth decreases. The building up over time is impressive in absolute numbers, but it seems to decelerate.

Now, I come back from maths to politics. Those calculations indicate two things. Firstly, whatever is being said in official meetings between my domestic President, and President Trump, regarding the U.S. military presence in Poland, is already happening. The United States are increasing their military footing in Europe in general, and in Poland in particular, and it happens as President Trump loudly declares being sick of it. Secondly, this policy took its strongest kick-start a few years ago, and now it is progressively coming to maturity.

I am consistently delivering good, almost new science to my readers, and love doing it, and I am working on crowdfunding this activity of mine. As we talk business plans, I remind you that you can download, from the library of my blog, the business plan I prepared for my semi-scientific project Befund  (and you can access the French version as well). You can also get a free e-copy of my book ‘Capitalism and Political Power’ You can support my research by donating directly, any amount you consider appropriate, to my PayPal account. You can also consider going to my Patreon page and become my patron. If you decide so, I will be grateful for suggesting me two things that Patreon suggests me to suggest you. Firstly, what kind of reward would you expect in exchange of supporting me? Secondly, what kind of phases would you like to see in the development of my research, and of the corresponding educational tools?

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Educational: power and money, or short introduction to fiscal policy

My editorial

This is another piece of educational content on my blog. Whilst I am preparing the manuscript of my book on technological change and renewable energies, my classes are going at their ordinary pace, and so I came to the moment of discussing fiscal policy with my 3rd year Undergraduate students. Thus, here are a few introductory notes to that general topic. As most of you can easily notice, governments have capital. I deliberately use the term ‘capital’ and not ‘money’, as my students have already worked through the fundamentals of monetary policy and they know (I hope) the distinction between money and capital. The scientific way of investigating the phenomenon of a government being able to afford an army consists in asking ‘How do governments have capital?’. The first and most inductive answer to that is: governments have capital in very idiosyncratic, strongly local ways. You can see that your government has capital, when said government spends money, i.e. when it pays wages to its employees and when it buys things. When a road is being built in your neighbourhood, this is your government buying construction output from companies specialized in that sort of heavy stuff. When you pay that delightful visit to your local tax authority, and you explain why you didn’t declare the income from that oil field in Turkmenistan into your annual Personal Income Tax (PIT for friends) statement, it is your government buying the qualified labour of the tax inspector sitting on the other side of the desk, and his or her labour is being purchased in order to extract taxes from your pocket, and those taxes will serve to pay their salary etc. Logical? What? Not quite logical? Well, here you have one of those apparently closed loops in the economic system. There are lots of them, don’t worry.

Anyway, you can know a government by its expenditures, and this is the nominator I used in that Excel file. I put this nominator (the expenditures of the central government) over two distinct denominators in order to understand its relative magnitude. I have prepared, on the grounds of my own, compound database, made of Penn Tables 9.0 (Feenstra et al. 2015[1]), enriched with data from the World Bank, a selective comparison of countries, regarding the share of expenditures, made annually by their central governments, in the stock of fixed capital available in the national economy (machines, buildings etc.), as well as in the stock of money being supplied to said economy, and all that in 2014. Click this link to access the corresponding Excel file. As you do so (cmon, click!), you can see, for example, the central government of Switzerland (the Swiss are a federation, keep that in mind, this is just the central government, not the cantons), with its expenditures making 1,9% of the local stock of fixed capital and just 4% of the money supply. You move up in the ranking, like to France, and you have the French government with its annual expenditures that make 4,9% of the available fixed capital and 16,5% of the national money supply. You move really up the scale, and you get to Armenia, and here, brothers and sisters, you have a nice piece of a government. Its expenditures make 13,2% of the national stock of fixed capital, and 64,8% in the supply of money. You can also use another denominator to measure the relative importance of public expenditures: the Gross Domestic Product. You can find this proportion in different countries by clicking here. Once again, you can see strong differentiation across countries. The first piece of science we have, thus, about the topic of fiscal policy, is that national governments form local, strongly idiosyncratic, institutional environments for the appropriation of capital.

As we have quickly overviewed differences across space, let’s do the same over time. By clicking this particular link you will open an Excel file, which shows the share of the expenditures, made annually by the central, federal government of the United States of America, denominated over three different aggregates: GDP, supply of money, and the stock of fixed capital. You can observe that the latter, namely the share of government spending in the capital stock, changes very little over time. The one in the middle – the proportion between annual expenditures of the central government and the supply of money – varies a little bit more. It is the first column, the share of government spending in the Gross Domestic Product, which displays the greater variance over time. Yet, as I repeat the same analytical procedure in the case of Uganda (you know, click), we can see that, obviously, all countries are not like United States. In Uganda, the share of government spending in the GDP looks quite steady over time, whilst the proportions between said spending and both fixed capital, and money supply, tend to swing wildly. Here, we have the second piece of science: the local, national mechanisms of appropriating capital, on the part of the government, can take the form of participating rather in the current output of the economy (case United States), or, on the other hand, the form of tapping directly into the assets of the economic system (case Uganda). A government can behave like a steady rentier, just sipping the cream from over the milk of current output in the economy, or like an aggressive investor, who comes and goes in the balance sheet of the productive sector.

Now, as we know the possible changes over time and differences between countries, let’s focus on the process of appropriating capital in the government. You can go to the website of the International Monetary Fund and there you can look for the title ‘World Economic Outlook’ . After you have localised it, you can download the latest version of the database, which accompanies that report. As you open the database, you can see each country described with truly broad a range of metrics, and, among them, you can see those:

  • General government revenue, consisting of taxes, social contributions, grants receivable, and other revenue. It is being assumed that a financial inflow to the government is really revenue, when it increases the government’s net worth, which is the difference between its assets and liabilities.
  • General government total expenditure, which corresponds to the total expense and the net acquisition of nonfinancial assets.
  • General government net lending/borrowing, which is simply revenue minus total expenditure. This metric says that the government can either put financial resources at the disposal of other sectors in the economy and non-residents (net lending), or utilize the financial resources generated by other sectors and non-residents (net borrowing).
  • General government primary net lending/borrowing Primary net lending/borrowing is net lending (+)/borrowing (?) plus net interest payable/paid (interest expense minus interest revenue).
  • General government structural balance, which refers to the general government cyclically adjusted balance. In other words, we can statistically distinguish, in the net lending or borrowing of the government, a slice corresponding to the impact of cyclical phenomena, mostly inflation and real economic growth, although unemployment has two words to say as well.
  • General government gross debt, which covers all liabilities of the public sector, which require payment or payments of interest and/or principal by the debtor to the creditor at a date or dates in the future.
  • General government net debt, calculated as gross debt minus financial assets corresponding to debt instruments.

So far, I have used the metrics pertaining to central governments. At the International Monetary Fund, they use aggregates corresponding to general governments.  Political systems host many distinct pockets of political power, and said pockets can be found in many places outside the central government. You have local governments (like cantons in Switzerland or states in the US), you have peripheral agencies (Finland or Israel have a cartload of these), and you have public funds, like the really big Social Security Fund in Poland. In any country, any government is a heterogeneous structure, which combines four types of fiscal entities, namely: budgetary units, executive agencies, targeted funds, and public-private partnerships. Budgetary units are the building blocks of the strictly spoken administrative structure in the public sector. They are fully financed through the current budget of the government, and fully accountable within one fiscal year. If they have any freedom in spending cash, this freedom is of short range. Public executive agencies follow specific missions ascribed by specific laws distinct from the budget, and from the regulations of fiscal governance. These laws form the legal basis of their existence. The mission of executive agencies usually consists in carrying out long-term tasks connected to large non-wage expenditures, e.g. the distribution of targeted subsidies, or the maintenance of strategic reserves. Executive agencies have more fiscal autonomy than budgetary units: they usually govern some kind of circulating capital untrusted with them by the government. Whilst they receive subsidies from the current budget, they usually do not make the full financial basis of their expenditures. In the same manner, they can retain their current financial surpluses over many fiscal years. The financial link of executive agencies with the current fiscal flows is fluid and changing from one budgetary cycle to another. Targeted public funds are separate public entities in charge of managing specific masses of capital paired with specific public missions to carry out. Just as executive agencies, targeted funds have a separate legal basis of their own. Their specificity consists in quite a strict distinction in their accounts: all the current costs of governance should be covered out of the financial rent of the capital managed, and the possible budgetary subsidies should serve only to back up the financial disbursements directly linked to the mission of the given fund. The distinction between executive agencies and targeted funds may be fluid: some agencies are de facto funds, and some funds are actually agencies. Public-private partnerships are joint ventures, through which private agents are commissioned to carry out specific public missions, in exchange of subsidies, direct payments or specific rights. One of the most obvious examples are contract-based healthcare systems, in which private providers of healthcare services are commissioned to fulfil the constitutional mission of the state to provide for citizens’ health. More subtle schemes are possible, of course. Private agents may provide, with their own financial means, for the creation of some infrastructure commissioned by the government, and their payment is the right to exploit said infrastructure.

The point of all that structural specification is to demonstrate that the broad category of fiscal flows that we use to call “public expenditures” is actually a financial compound. It covers both the expenditures strictly spoken (i.e. current payments for goods and services), and capital outlays that accrue to many different pockets of capital appropriated by public agents in many different ways. Capital accruals have different cycles, ranging from the ultra-short (days or weeks) cycle of consolidated accounting in budgetary units, passing through the mid-range cycle of appropriation in executive agencies and public-private partnerships, up to the frequently many-decade long cycle of capital appropriation in targeted public funds. Each of those pockets of capital makes a unit of economic power, in the hands of some public agents. Each accrual to or from such a capital pocket means a shift up or down in the actual economic power of those agents. Thus, it can be argued that the total stream of financial inflows to public treasury, through current revenues and current borrowing, is congruent with the sum of the strictly spoken public expenditures, and capital accruals in the public sector. Each such accrual corresponds to a pocket of political power in the structure of government.

[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