City size, Monopolies and Modelling

I need to begin with stating I’m not trained neither in urban nor in environmental studies, yet as a true economist, I will use the liberty of talking about things I’m not educated about. In this case, I believe my attempt is legitimized for two reasons, first, main argument I want to make has to do with the ways in which we use models, not necessarily on the environmental catastrophes and self-organization of cities. Second, this is just a simple blog post where I will intentionally avoid necessary steps to show the validity of the model for the example I will discuss. Thus, I do not claim the proposed model has any explanatory power anyway.

You may have come across to the nasty photos of the Sea of Marmara, an inner sea between the Black Sea and the Aegean Sea. What is believed to be a natural phenomenon, sea snot, seem to have built up uncontrollably both on the shores and on the bottom part of the sea, seriously threatening the sea life. According to a BBC article¹, it was first observed in the Aegean in 2007, yet never at this scale.

It does, of course, have to do with the climate change, yet by the looks of it pretty much all the cities around the Sea of Marmara have been pumping their sewage into the sea, mostly untreated. Some of these cities are important industrial centers, meaning even more pollution. None of these may sound unfamiliar to anyone from a highly populated city of course.

But then, there is the obvious question that needs to be asked: is the root cause of pollution Istanbul? Is Istanbul completely out of control even for its own good?

Is it really the case that Istanbul simply is “too populated”? This is where one starts to think of criterions.  How much of a population would have been acceptable then? Based on what kind of criterions one can state a city like Istanbul is over-crowded or not? In case relatively well-off residents of Istanbul obtain their deepest desire -which they do not even shy away from demanding it out loud in most instances- and relatively poor residents of Istanbul simply leave the city, are they really ready to live in a city without an overabundance of desperate working people ready to do whatever job for whichever price? If something needs to be done, who decides on who stays and who leaves and who decides on what is the criterion for these decisions?

When the question in hand is how cities are shaped and people’s mobility, the obvious complexities mentioned above turn from some inconveniences for modelling purposes to the center of the whole discussion. Most social systems are composed of many actors that are interacting with each other in many ways and together with these interactions there exists strong feedback effects, sometimes negative and sometimes positive feedbacks.

The Self-Organizing Economy, by Krugman, offers a short and insightful introduction to the complex systems. He identifies three definitions for the complex systems, 1) Systems with complicated feedback mechanisms (which, economists should feel maybe too confident but definitely confident to talk about), 2) Systems that emerge, which is different than simply scaling up one individual’s behavior and again resembles notions like, you know, the invisible hand, so should be familiar to the economists, 3) Self-organizing systems: systems that even when they start from an almost homogenous or almost random state, spontaneously form large-scale patterns. What is striking about this third definition is, studying the properties of a self-organizing system may bring many valuable insights, while a self-organizing system itself will not necessarily bring desirable outcomes (very much at odds with the FFTWE). Krugman gives the example of two economies, one in which a strong business-cycle exhibits more temporal self-organization while in the other economy there is just smooth growth, where many would prefer to live in the latter.

Now, back to Istanbul. Is there a way to make sense out of the highly populated life of Istanbul? One may want to check the city populations in Turkey to see if there are any common trends there:

Above, I present the 70 highest populated cities in Turkey on a rank-size plot with a linear fit. As mentioned at the beginning I will not discuss the relevance of the linear model fit and if it is appropriate or not but rather point out to the rich literature studying city sizes and finding the linear relationship between the size of the cities and their ranks on a log-log scale. Such patterns are disregarded and often the studies on such patterns are looked down on by economists, while they may indicate some “hidden principle at work”. I simply tried to present the rank-size rule, and a simple application of it to Turkey and wanted to point out to the spooky fact that Istanbul was consistent with the so called Zipf-law. It’s spooky because, Istanbul was way too consistent with this “rule”.

As arbitrary as it is, I wondered if pre-2007, right before first time sea snot was seen in the Aegean according to BBC, presented similar patterns:

Above is the stacked rank-size log-log plot for the highest populated 70 cities in Turkey between 2001-2007, with Istanbul persistently showing up at the very right bottom. In the light of these findings one wonders, what happened lately?

With a very small deviation, Istanbul still fits into the rank-size rule pretty well. It is worth pointing out for the data before 2007 it is stated that the numbers are estimates and post 2007 are based on address information, so there could be other reasons to expect certain systematic differences before and after. In addition to that, even a not-very-careful-eye could see the impact of the arbitrariness of “70” as the number of cities. Largest 8-10 cities could’ve brought a much better fit and could even find Istanbul as an unexpectedly large city.

The rank-size rule seems to be strong regardless and needs some explanation. A common trick when one encounters with Zipf-laws on a log-log scale is to suppose a hierarchy, which will generate an exponential shape on a linear-linear scale and use that as an explanation. Krugman, however, goes against the hierarchical explanation and states the rule assumes a constant number of parameters while there is no need to make such assumption and maybe more importantly the empirical figures show not only a power-law but a very specific one with parameter estimate almost always equal to 1. He finds Herbert Simon’s explanation as a much better candidate (one may want to check out “On a Class of Skew Distribution Functions”).

What do these say about the sea snot? As an unlikely event that is now threatening the entire sea life and the life around the sea, was it caused by unlikely large populations around it? Clearly, I have nothing to say about the causal mechanism but wanted to point out to the other unlikely events probably tied to this one and located around this one, such as very large populations. This small exercise, however, made me think about models in general which is the main issue I wanted to bring up. Models come with a lot of normative judgements, such as ‘an undisrupted random process will generate the most desirable outcome’, while the outcome could be far from being desirable. In case the outcome turns out to be undesirable, while being consistent with an unfettered process, then the researcher starts to think about how the process was actually not an undisrupted one. So it is either “people would’ve realized the environmental catastrophe around themselves and leave Istanbul if it was that bad, which is what my model says” or “since people did not leave Istanbul already, as opposed to the predictions of a model of unregulated mobility, there should be imperfections or interventions”, meaning, while models are claimed to be simplifications of reality but not reality itself, the researchers tend to have very little room in their mind to distinguish between reality and their model.

Is Amazon anything like the sea snot?

What is it about the city sizes that is related to the monopolies and modelling? Is it awful monopolies destroying our lives and only if we were to live in a more competitive capitalism things would’ve been just fine and monopolies are the sea snot that is now destroying the sea? Am I trying to invite you to some sort of a higher state of consciousness by using some analogies?

Well, not really. I wanted to share some views on how it seems we end up coming to these conclusions. One may define a random process, say a hierarchical one, with that rule of interaction generate patterns consistent with rank-size rule, then observe Istanbul laying above the suggested Zipf-law and then conclude some people need to leave and start studying who needs to leave. Following the same process, one may see Istanbul laying below where it needs to be at and conclude they need to get more people there, maybe start studying ways to do that. This is a very common way of doing theory based empirical work, yet still very much dependent on researchers' views on interactions and feedbacks and how they matter and to what extent they matter.

In a similar way, what is an ok size for a firm? What is an acceptable amount of profit/rate of profit? What legitimizes and delegitimizes a very large firm? One needs to recognize these questions should not have dogmatic answers (treating any deviation from the average rate of profit as failure or monopoly rents). Competition is a complex process just like the formation of cities; it entails a lot of interaction, negative and positive feedbacks while most economics models will put emphasis on only one aspect of these three, and only very partially. A very large firm could be consistent with a self-organizing system, while its’ existence may still not be desirable.

So, models… They tend to carry a lot of normative judgement underneath and I wish these judgements were always very explicit.

1: Turkey president Erdogan vows to solve 'sea snot' outbreak - BBC News