A Model on Gender Pay Gap

Last week I have finished teaching a short course on "Introduction to Agent-Based Modelling", offered under the label Topics in Economics I, to Master and PhD students at the Department of Economics, University of Insubria in Varese.

The plan is usually that of presenting this type of advanced modelling technique through theory and by developing an agent-based model together, using the software NetLogo. This was my third time in the program in Varese. Over the first two years and, over past years, we developed a model of innovation diffusion among an ecology of firms (I will discuss that in another post). This time I asked if someone wanted to develop a different model.

After a first few uncertainties and at the very last minute, someone proposed to model gender pay gap in an organisation. I thought that was a good idea and, once we voted on it, we decided to pursue this model. The ABM took shape as we were modelling it, with inputs from the students and adjustments to the coding so that it was not too complex — this is still an introductory course, after all!

Although simple and intuitive, I believe that the model serves its purpose very well. Of course, when one is up to modelling a social phenomenon, there should be a purpose, to put it with Edmonds (Different modelling purposes, 2017). The idea was to first illustrate the pay gap in an organisation. However, that soon seemed a bit too narrow for an ABM. By proposing dynamic as a central feature, the model was shaped into a way to explore the conditions through which the gap could expand, reduce itself, or disappear. And, on top of this, one has the opportunity to estimate how long it would take for such a gap to disappear.

The Gender Pay Gap (GPG) Model is built on simple features. I have slightly modified — hopefully enhanced — the one developed in class to reach to a more realistic one. Here is a quick summary of the features:

• number_workers — this could be set from 0 to 1000 from the slider;
• women_proportion — the percentage of women in the organisation;
• manag_proportion —how much management the organisation has, 10%, 20%, or 30%; teams are built around managers and some employees are also connected outside of their team;
• hierarchy — how many layers of management are there (0, 1, or 2 levels);
• years — for how long would the simulation run; this goes by 10 years intervals and up to 50; if the slider is set to 0 then it runs potentially forever but, if the income for women at year 100 is the same that there is at year 150, the simulation will stop (...because it makes no sense to keep going!)
• pay_gap — you can set how large the pay gap is, both positive and negative (just to explore alternative realities), where the slider expresses percentages. So, you can go from Italy's 5% to Germany's 20% (yes, for once, Italians are ahead!);
• mean_bias — it is the extent to which a manager discriminates against the other gender when making decisions about salary increase or promotions;
• the three sliders at the bottom right are for visualisation purposes (try to use them... carefully).

Figure 1. A Model of the Gender Pay Gap in an Organisation

You can click on Figure 1 above or here to get to the online version of the model: [https://netlogoweb.org/web?https://raw.githubusercontent.com/dsecchi/ABMOsimulations/master/gender-balance.nlogo]

The simulation stops if the distance between men and women's salary is below or at 10% of the original gap, so that we can say there is equality, more or less (I mean, a 5% gap would be a 0.5% gap). What comes out of the model is that the gap is extremely resilient and won't go away very easily. Not even a small gap of 5% would go away easily. And this should make us reflect more on how difficult it really is to make things right.

Now it is time you try the model yourself. Let me know if you think there is something important missing. Thank you.

The Context of Inquiry – A Re-Contextualization

I have been reading Emanuele's post 'the context of inquiry' with great interest. I read Emanuele's blog very often and I am intrigued by what he is up to every time I open it. In particular, I feel compelled to comment on this post because (a) we are working together on some model of inquiry/inquisitiveness and (b) I find the assumptions of this particular post to be somehow challenging.

This reply is in invitation to Emanuele and myself to continue to think deeply about science and help our recent reasoning on inquiry and inquisitiveness.

The point of the post is to show that science is mostly about generating ideas instead of providing proofs that something is true or false, right or wrong. If science is about generating ideas then the role of inquiry is particularly relevant and, in fact, it is critical for the scientific enterprise to develop. Whether and how much I agree with this is probably materials for another post but I like the idea that science "glorifies" the inquisitive mind.

Instead, what I would like to reflect on here is the lax picture of science Emanuele describes as typical of some journalists.  There we go:

Very often science – be it natural science or social science – is reduced to a kind of device whose main function is to provide proofs. That is, it is as if the whole enterprise of science is ultimately a game whose main goal is to prove that something is in fact the case or just a myth.

And he continues with the following:

A quite compelling example pointing to that is the number of articles in magazines and newspapers, in which rather trivial beliefs and stereotypes are scientifically proven as true (or false). [...] In other cases, science provides the solid basis for making (alleged) "rational" decisions regarding an almost endless list of things, like the kind of food to eat, the amount of hours to devote to physical exercise or the best economical policy to implement. In all those cases science provides proofs telling us – beyond any reasonable doubt – what we should hold true, believe in or make happen for our own good.

My take is that this kind of "attitude" towards science is rooted in the assumption, which is never quite discussed, that science is superior to other epistemic practices (that is, practices chiefly devoted to knowing) because of the scientific method that is used. So, the superiority of science would rest in the application of a specific procedure whose main role is to test ideas and that type of procedure would then guarantee us that we have achieved certified or beyond-any-reasonable-doubt results. 

First of all, a trivial question: do we (as scientists) care about popularized versions of science appearing in magazines and newspapers? It is clear that those journalists or so-called "experts" who portray these views sometimes are as ignorant about science as one could possibly be. To some extent, I agree we should care about what gets popularized, because the views Emanuele refers to contribute to the belief that science is some kind of religion, something you believe in or not. To some extent, you do "believe" in what you are doing. However, believing in oneself or in the doing is arguably more rational than believing in some god (or goddess). And it is different because of the tools, resources, environment, mindset, instruments available to make up your mind. Science is open. No question is forbidden, no faith is mandatory. It is one of the most powerful resources we have to understand, analyze, process, synthesize, re-process, etc., or, in short, to know ourselves and what is around and beyond us.

Anyway, the point here is that we should probably care about the image of science that some portray. However, there is probably no point in debunking something that is clearly inaccurate or done with careless attention. This is why I would not take time to debunk what I do  not think one should be too serious about. A portrait of science of the kind provided by Emanuele is too weak. Everything is questionable about it. Hence, building a good and interesting point off something that is not so serious, casts doubts on the consistency of this point Emanuele (and I) are making.

The second element is not on the scientific method (that comes only third here). It is on the "beyond any reasonable doubt" sentence that Emanuele uses in the post. I do not think that this sentence is consistent with scientific phrasing. In fact, I am not too sure a scientist would use those words. In fact, we know that is a famous phrase coming from (American fashioned) tribunals. The purpose of science is to have doubts even when you have that a given cause determines an effect, with a given explained variance, an "impact" coefficient, and under a significance level. Due to the many errors possible (e.g., measurement, coding, instrument-based, interpretative), fallacious hypotheses, methodological uncertainties, or ill-intentioned researchers, any scientific result is always subject to further scrutiny. It is neither "right" or "wrong"; it is neither "true" or "false". What scientific results give you — I am referring to quantitative studies in the social sciences in particular (...because that is what I know!) —is some circumstantiated information on a relation, a mechanism, a difference, or else concerning a given phenomenon. In short, you assert that A positively affects B with "intensity" (or "impact") X, and explaining B's variance of a quantity Y, within a certain significance level low enough to make results probable (under the conditions specified). Note that every words mentioned (even the words in parentheses) are crucial to understand the meaning of scientific results. This is probably far away from "beyond reasonable doubts". In fact, the phrase used to describe results is actually a statement that we never know for sure. Doubts are here, there, and everywhere. Doubts are extremely welcome.

The scientific method (there we go!) is my third point, as anticipated. The way science produces its results has to do with the methods it uses but, of course, that is not it. Can we reduce science to its methods? Is that what science is all about? What is in it more than method that makes it different from other ways of knowing? Most importantly, can we use scientific methods to produce bogus results? If we can, then science is not just about methods. And this is the strongest point Emanuele is making. It is not just about methods, also the questions science asks and how we ask them are very relevant to the scientific enterprise.

There is much more to write but I stop here. Thanks to Emanuele for his challenging views expressed on this post and, well, let's see where we go with this!

Notes on the Greek Crisis: Framework

I am on my way to Greece and tomorrow I will be in Athens. This made me think of what is going on and I decided to come back to this blog and write something. The Greek crisis is a drama that could end (or start) in tragedy. There are many aspects of the process that will culminate with the referendum taking place July 5th, 2015. Before getting to an analysis of the rationality of decision making (please wait for my next post), let me try to outline a tentative framework (this post). I will try to state some facts and spread comments around them.

Greece is currently facing dramatic economic and social distress, probably one of the worst of its modern era. This is the result of a mix of wrong policy recommendations and superficial implementation of change mixed with political uncertainty and instability. It makes little sense to recriminate on the cause of the current situation, and consequently blame this or that institutional agent. The only important aspect is that there is a serious problem that needs to be taken care of. The problem is not just important for Greece, it lies at the heart of the European Union. This is for at least two reasons, the first is rooted in history, the second in democracy.

First, the crisis demonstrated that the single currency project needs to be implemented in its different legs. The monetary union makes little sense without a political executive power that controls it. This is nothing new. The European Single Act (from where the project originated) states the political plan clearly. Subsequent steps along the way, especially in the Nineties, also refer to the single currency as a step towards a political union. When the Euro was born, we would still hear many politicians making clear statements on the upcoming political integration. Something happened in the turn of the millennium. Three factors may have caused this lack of memory:

1. The rise of political parties that had been relegated to a 'limbo' for the fifty years following World War II. These parties are either detached from the traditional moderate centre-right PPE-like style because their roots are fascist, xenophobic, racist, and reflect the core of what has always characterized the history of European politics in the last three millennia. This can be summarized as: (a) find a 'good' enemy ('good' in the sense that is a likely enemy, appealing to citizens), (b) radicalize the party's position, and (c) be verbally ruthless and, sometimes, physically aggressive. All in all, these are building a positive attitude towards conflict (or, if it goes bad, towards war). Of course, these politicians have no interest in European integration.

2. The other politicians from the 'regular' European parties have lost contact with the founding values of the European Union. World War II is very far from us now, we do not think of peace very often, nor we reflect on what an amazing achievement it is for Europe. We take it for granted. In the last fifteen years, most politicians are not 'sons of war', meaning that their grandparents took part to the war, not their parents. Most of grandparents are not with us any more. War is unexperienced but it is still conceivable among European states. The first wave of the European integration process is over.

3. The many waves of the process called 'enlargement' brought in the EU many Eastern and Southern European countries. This is certainly an extremely positive factor that witness the inclusive and open nature of the integration process. It also reflects the importance that solidarity and cooperation has for the European Union project. However, EU enlargement, matched with the economic crisis and an insufficient change in the institutional decision mechanisms, contributed to very slow progress. Clearly, most of these new members are not interested in a more advanced integration. Being part of the EU is already a significant step ahead in integration/unification for most of them.

On a different angle, the deep economic depression destabilized the process. Among the many implications of that event, one seems to have been the emphasis on the technical over the value-driven side of problems. Of course there is always a very important technical side, but technique is nothing — maybe even dangerous — if it is not at the service of ideals, principles, or values. The desperate search for a technical solution that could 'save us' (and our economies) brought politicians to completely lose sight of the underlying values of their actions.

Second, the Greek crisis shows something rather obvious. The form democracy takes at the European level is still underdeveloped. There is a need for quick and effective action that cannot be guaranteed by a pseudo-executive that is, for example, the collection of finance (or the prime) ministers of the eurozone. They represent the interests of their nation states, not those of the eurozone as a whole. Moreover, among the many issues, there is a disproportion in that small states are represented the same way as large states (i.e., one minister per state). This is not the place to propose a solution for this (there are, indeed, many), just to point at the fact that the current state of affairs has proven to be ineffective, and repeatedly so.

This underdeveloped democracy at the institutional level (so-called 'democratic deficit') seems to cause confusion, even to the eyes of the most expert. In fact, many blame the European Central Bank (ECB) or the single currency for the inability to deal with the depression and for the crisis in Greece. The ECB and the euro, many say, are designed to preserve the strongest economies, i.e. Germany. This is undoubtedly so. I would add, just like the dollar preserves the economy of California, first and foremost. Just like the British Pound Sterling is very much tailor-made to protect and enhance financial London. The difference? Well, traditionally European countries have been different and Europeans still believe that the other states are 'foreign', their citizens are foreigners, strange, other, different. This is the problem. But there are positive externalities for the other states when the Californian economy goes up. And there are positive externalities for other EU states when the German economy goes up.  The point is that we do not have an executive power that counterbalances that of the ECB. This is the real issue here. Do not look at the ECB (the finger), go deep, look at the lack of democratic representation in European institutions (the moon).


Finally, the Greek crisis bears the risk that Europeans won't be able to find the second wave of integration. However, we all need a stronger and better union. The alternative is the old bloodthirsty Europe that we all hope to leave to history books. Of course, there are economic, social, research, developmental advantages of a deeper union, but they cannot be seen if there is no clear understanding of what Europeans want to be.

What I outlined here constitutes the framework to understand under which conditions rationality works among parties who try to find a solution. As I tried to outline in this post, a solution is much needed by every single player involved in the process.