Angola plays its dominant strategy in defecting against OPEC

The Financial Times reported last week (paywalled):

Angola, Africa’s second biggest oil producer, has said it is leaving Opec after disagreements over its production targets, delivering a blow to the oil cartel chaired by Saudi Arabia.

The decision comes after the producer group lowered Angola’s oil output target last month as part of a series of cuts led by Saudi Arabia to help prop up prices.

OPEC is an example of a cartel. Cartels can arise when a market is an oligopoly - a market where there are many buyers, but few sellers. A cartel essentially acts like a monopoly seller - it is able to use market power to extract greater economic rent from the market (in the form of higher profits, arising from higher prices), than the countries would be able to extract if they were competing with each other. The cartel can be maintained because there are few sellers, so it is relatively easy for them to coordinate their actions. In this case, OPEC coordinates to raise prices by restricting production.

However, there is always an incentive for each cartel member to cheat on the cartel agreement, or to leave the cartel entirely (as Angola has done). To see why, we can apply some game theory. Let's say that there are two players - Angola and 'the rest of OPEC'. Each player has two strategies - high production (which leads to lower prices and lower profits for oil producers), or low production (which leads to higher prices and higher profits). If one player has high production and the other low production, the high production player benefits more. However, if both players have high production, both are worse off. These outcomes and payoffs are illustrated in the diagram below (the payoff numbers represent profits, but are just made up to illustrate this example).

To find the Nash equilibrium in this game, we use the 'best response method'. To do this, we track: for each player, for each strategy, what is the best response of the other player. Where both players are selecting a best response, they are doing the best they can, given the choice of the other player (this is the definition of Nash equilibrium). In this game, the best responses are:

1. If the rest of OPEC chooses high production, Angola's best response is to choose high production (since 2 is a better payoff than 0) [we track the best responses with ticks, and not-best-responses with crosses; Note: I'm also tracking which payoffs I am comparing with numbers corresponding to the numbers in this list];
2. If the rest of OPEC chooses low production, Angola's best response is to choose high production (since 4 is a better payoff than 3);
3. If Angola chooses high production, the rest of OPEC's best response is to choose high production (since 10 is a better payoff than 9); and
4. If Angola chooses low production, the rest of OPEC's best response is to choose high production (since 15 is a better payoff than 12).

Note that Angola's best response is always to choose high production. This is their dominant strategy. Likewise, the rest of OPEC's best response is always to choose high production, which makes it their dominant strategy as well. The single Nash equilibrium occurs where both players are playing a best response (where there are two ticks), which is where all of OPEC (including Angola) chooses high production.

Notice that both players would be unambiguously better off if they chose low production. However, both will choose high production, which makes them both worse off. This is a prisoners' dilemma game (it's a dilemma because, when both players act in their own best interests, both are made worse off).

That's not the end of this story though, because the simple example above assumes that this is a non-repeated game. A non-repeated game is played once only, after which the two players go their separate ways, never to interact again. Most games in the real world are not like that - they are repeated games. In a repeated game, the outcome may differ from the equilibrium of the non-repeated game, because the players can learn to work together to obtain the best outcome.

And that is what happens when a cartel forms. If all of OPEC (including Angola) works together and agrees to choose low production, both players benefit. That is what they were doing, up until Angola chose to leave OPEC. The problem here is that both players choosing low production is not an equilibrium. If Angola knows that the rest of OPEC is choosing low production, it is better off defecting from the agreement and choosing high production. Angola profits more that way (at least, in the short term).

So essentially, by leaving OPEC (and thereby choosing high production), Angola is simply playing its dominant strategy.

Read more:

• The oil price war is actually just a return to equilibrium

This week in research #5

It's been a busy week. Here's what caught my eye in research:

• Anderson builds up a non-parametric gravity model (quite technical, but likely of interest to trade and migration researchers)
• Samahita and Devereaux look at gender inequality in conference acceptance using data from the Irish Economic Association annual conference from 2016 to 2022, and find no gender gap in acceptances; however, male reviewers give female authors lower review scores (open access)
• Ramalingam and Stoddard experimentally test whether experiencing inequality increases cooperation (in terms of contributions to public goods), and find that it doesn't (ungated earlier version here)
• Mills discusses the economics of time travel (open access)
• Ezcurra shows that exposure to ultraviolet radiation is a predictor of national-level state capacity (open access) - related to this post, where I was sceptical of some similar earlier research

The Journal of Economic Behavior and Organization released a special issue on the economics of beauty, which included the following:

• Gründler, Potrafke, and Wochner find that attractive MPs are more likely to be absent from the German parliament and less active in labour-intensive background work than others (ungated earlier version here)
• Adamopoulou and Kaya use Add Health data on US high school students to show that, somewhat surprisingly, for boys both physical and personality attractiveness positively affect performance and peer characteristics also matter (more attractive peers lowers performance), but for girls only personality attractiveness matters (open access)
• Babin, Chauhan, and Kistler show that professional e-sports competitors rated as more attractive are more likely to receive a contract in the following year, but there is no lifetime earnings premium
• Baert, Herregods, and Sterkens use an experiment to show that job candidates with body art are perceived as less pleasant to work with, less honest, less emotionally stable, less agreeable, less conscientious and less manageable (open access) - this would have been more convincing as a field experiment (see here or here, for example)

Book review: The Next Fifty Things that Made the Modern Economy

What do bricks, mail-order catalogues, pensions, vulcanised rubber, the gyroscope, and slot machines have in common? They all feature in Tim Harford's book The Next Fifty Things that Made the Modern Economy. As you might expect, the book is a sequel to Fifty Inventions that Shaped the Modern Economy (which I reviewed here), and is written in the same engaging style as the first book.

Every chapter focuses on one 'thing' and explains its effects (positive or negative) on the modern economy. Unlike the first book though, Harford doesn't limit himself to 'inventions', although if defined sufficiently broadly, almost all of the things were invented at some point, except for fire and oil. However, as Harford explains in the introduction:

In selecting the fifty-one subjects of this book, my aim has been to tell stories that will surprise you, about ideas that have had fascinating consequences. There are plenty of other books about inventions that changed the world; this book is about inventions that might change the way you see that world.

It mostly succeeds in that aim. Each chapter also ranges a bit more widely than the chapter title might suggest. For instance, the chapter on tulips is really about asset bubbles more generally, but uses 'tulipmania' as a motivating example. The chapter on Santa Claus is more about the commercialisation of Christmas. Many of the chapters (like the opening chapter on the pencil) covered ground that I already knew relatively well (probably because I follow Harford's blog). Personally, I particularly enjoyed the chapters on canned food, cellophane, and the Langstroth hive.

This was a perfect book to read during a summer holiday. It is not too taxing, and the thought-provoking and surprising factoids can be a family conversation starter. Like most (if not all) of Harford's books, I highly recommend this one.

Family leave and the gender wage gap

The gender wage gap has been decreasing slowly and steadily over time. At least, that's what I thought until I read this 2023 NBER Working Paper by Peter Blair (Harvard University) and Benjamin Posmanick (St. Bonaventure University). They present the following graph of the gender wage gap in the US (for White women, compared with White men, between 1975 and 2015:

Note that the upward trend here represents a decrease in the gender wage gap (the y-axis is negative). What is apparent from the graph is that the gender wage gap in the US decreased relatively quickly from 1975 to 1993, and then the decrease suddenly and dramatically tailed off. What happened?

Blair and Posmanick single out the Family and Medical Leave Act, which was passed in 1993, and "which guarantees 12 weeks of unpaid, job-protected leave to qualified workers for covered family or medical circumstances". The birth of a child is one of the 'family or medical circumstances' that is covered. However, a lot of other changes to welfare and other things happened in 1993, so Blair and Posmanick smartly avoid looking purely at 1993. Instead, they conduct an event study, taking advantage of the fact that twelve states and the District of Columbia had implemented family leave policies prior to 1993. So, in their main analyses, they look at how the gender wage gap changed between the period before, and the period after, implementing family leave, for the states (and D.C.) that had these policies in place prior to 1993. They focus on the impact on White women (compared with White men), but the appendix presents wage gaps (compared with White men) for Black men and Black women as well. It is reassuring (in terms of the validity of their results) that the results look similar (albeit not as great) for Black women, and that there is no change in the trend of a declining wage gap for Black men (consistent with the results being specific for the gender wage gap, rather than picking up some change in welfare that might affect disadvantaged groups more generally).

They find that:

...prior to the leave policy the gender wage gap experienced by white women was falling at a rate of 0.70 percentage points per year (p-value <0.001). In the post period, the rate of gender wage convergence falls by 0.53 percentage points per year to 0.17 percentage points per year. The decline is statistically and economically significant, and the post-leave rate of gender wage convergence is marginally different from zero.

In other words, the rate of decline of the gender wage gap decreased by 75 percent (from 0.70 percentage points per year to 0.17 percentage points per year). An interesting implication of their results, which they don't address, is what it implies about the length of time required for the gender wage gap to be eliminated (based on an assumption of a linear decline). The gender wage gap for White women was 23.8 percent in 1993 (from Appendix Table A2). So, at the rate of decline from 1975 to 1992, the gender wage gap would be eliminated in a further 34 years (that is, in 2025). But, after the family leave policy was enacted, that extends out to 140 years (that is, in 2133).

The results that Blair and Posmanick obtain when looking at the full sample of states (where most states got the family leave policy in 1993) are similar, but paint a worse picture:

We find that the gender wage gap faced by white women declined by a statistically significant 0.70 percentage points per year prior to the policy change, which is identical to the pre-leave rate of gender wage convergence that we estimated using only the state variation... After the policy change, the rate of wage convergence for white women declines by 0.67 percentage points to 0.03 percentage points.

In those results, the rate of decline of the gender wage gap decreased by nearly 96 percent (from 0.70 percentage points per year to 0.03 percentage points per year). Don't even ask how long it would take to eliminate the gender wage gap at that rate. Ok, do ask. It's 793 years.

Blair and Posmanick then go on to show that the family leave policy can explain 94 percent of the unexplained change in the gender wage gap (the 'Gap Effect') between 1993 and 2015 (after accounting for the explained change due to changes in observable factors like age, education, and occupation). On this point they note that:

As articulated in Blau and Kahn (2006): "The Gap Effect measures the effect of changing differences in the relative positions of men and women in the male residual wage distribution, including the effect of an improvement in women’s unmeasured characteristics or a reduction in the extent of discrimination against women.” Given the differences in family-leave taking between men and women, family leave policies may simultaneously decrease the unmeasured characteristics of women in the labor market and increase the extent of discrimination women face.

Overall, it is clear from the results of this paper that family leave policies are a case of unintended consequences. They are designed to make the labour market more flexible for parents, but they result in a stymieing of efforts to reduce or eliminate the gender wage gap. Given that the family leave provisions in the US are far less generous than in other Western countries in Europe and Australasia, it makes me wonder how much of an effect family leave has on maintaining the gender wage gap in those countries.

[HT: Marginal Revolution, early last year]