Thursday, 19 January 2017

Book review: Economics of the Undead

I just finished reading "Economics of the Undead", edited by Glen Whitman and James Dow. The premise of the book is a collection of chapters applying economics (and some other social sciences) to better understanding the economics of vampires and zombies. It sounded like a really interesting book (though I admit it has been on my bookshelf for a couple of years), but it took me a while to get through it. Mainly, that was because I found the book to be quite uneven. Some chapters were excellent (such as the chapter What happens next? Endgames of a zombie apocalypse, by Kyle William Bishop, David Tufte, and Mary Jo Tufte), but some were quite weak (I won't single any particular chapter out for this). To be fair, this is a problem with many edited volumes where many different authors contribute chapters on related topics. In this case, often it felt like the examples were forced (maybe they were glamoured?) when they didn't quite fit, while several opportunities were missed.

However, there were several highlights, including this from James Dow in the chapter Packing for the zombie apocalypse:
If you wanted the country to plan for a zombie apocalypse, you might think the most important thing would be to set up installations to preserve modern technology. However, existing books do that pretty well (although less well each year as the Internet - which would not survive the apocalypse - increasingly takes over). What is really needed is a setting that preserves the older technologies today; knowledge that might have been lost otherwise but will be needed after the zombies come.
Indeed, I've often pondered what skills would be in demand if there were a zombie apocalypse. For instance, who is going to make the shoes you need to outrun the zombie hordes? If you think specialisation and trade is bad, in a zombie apocalypse it would become very clear very quickly why doing everything yourself is not a good idea. What do you mean there isn't enough time to fight zombies and grow food?

I also liked this bit, from the aforementioned Bishop et al. chapter:
...economics and biology are complementary, and both suggest the existence of another endgame. What might that look like? In economic terms, zombies face a tragedy of the commons: each individual zombie wants to eat more humans, but if they all do this, then no zombie will have any humans left to eat.
The solution is obvious, isn't it: private property rights for zombies over humans - let each zombie farm their own humans to eat. Ok, Bishop et al. didn't say that, but I thought it needed to be said.

Michael O'Hara's chapter on Zombies as an invasive species gives us this:
The fact that zombies fit standard definitions of invasive species cannot be disputed. The Global Invasive Species Program (GISP) states that "biological invasion occurs when a species enters a new environment, establishes itself there and begins to change the populations of species that existed there before, as well as disturbing the balance of plant and animal communities." In the case of a zombie invasion, this change of the existing population of species is quite literal.
The chapter essentially concludes that control is probably more cost effective than prevention, when it comes to the zombie apocalypse (but try telling that to the first people turned into zombies!).

Dan Farhat (University of Otago) contributed a chapter on using agent-based modelling to model a vampire population within a (human) town, which builds on a similar paper that I blogged about three years ago.

Overall, the book will be of most interest to those who like both economics and undead in pop culture, although even then (like me) not all chapters will appeal.

Tuesday, 17 January 2017

Tax cuts, and misinterpreted average and marginal tax rates

Many, many people don't understand the difference between average and marginal tax rates. Articles like this one by Leicester Gouwland don't help:
The bulk of the default tax collected is from people who have moved from the 17.5 per cent bracket to the 30 per cent bracket, that is a 71 per cent increase in tax.
The people who have moved from the 10.5 per cent bracket to the 17.5 per cent have suffered a 66 per cent increase in tax, however, if they now earn more than $24,000, they qualify for the independent earner rebate.
Neither of those two statements is correct. To see why, let's take a step back first. The average (income) tax rate for a taxpayer is the tax that they pay divided by their income. So, if a taxpayer have income of $50,000 and pay $8,020 in tax, their average tax rate is 16.04% (8,020 / 50,000). The marginal tax rate is the proportion of the next dollar they earn that would be paid in tax.

Most income tax systems are described in terms of marginal tax rates, as Gouwland does early in his article for New Zealand:
The current tax brackets on personal income are; 10.5 per cent for income up to $14,000; 17.5 per cent for income up to $48,000; 30 per cent for income up to $70,000; and then 33 per cent for any income more than $70,000.
So, for our taxpayer that has income of $50,000, their marginal tax rate (the tax rate they would pay on the next dollar they earn) is 30%, even though their average tax rate is only 16.04%.

Now, this is where most people go wrong. A person who moves tax brackets doesn't face a huge increase in their average tax rate, only their marginal tax rate. It's not correct to say that, for someone who moves "from the 17.5 per cent bracket to the 30 per cent, that is a 71 per cent increase in tax". To illustrate, let's take a taxpayer who was previously earning $45,000 (in the 17.5 per cent tax bracket) and give them a pay rise to $50,000 (in the 30 per cent tax bracket). Does their tax payment go up by 71% (as Gouwland suggests)? Hell no. It only goes up by 16.3%, from $6,895 to $8,020. [*] That's still a big increase, but it's certainly not 71%! And remember that their before-tax income has gone up by 11.1% as well.

Similarly, has someone who has moved "from the 10.5 per cent bracket to the 17.5 per cent ...suffered a 66 per cent increase in tax"? Let's take a taxpayer who was previous earning $12,000 (in the 10.5 per cent tax bracket), and increase their income to $16,000 (in the 17.5 per cent tax bracket). Their tax payment goes from $1,260 to $1,820, an increase of 44.4% (but in the context of a 33.3% increase in pre-tax income).

So, more care is needed in interpreting average and marginal tax rates, and articles like Gouwland's certainly don't help.


[*] The tax paid by a taxpayer with an income of $45,000 is calculated as [$14,000 x 0.105] + [($45,000 - $14,000) x 0.175] = $6,895. The tax paid by a taxpayer with an income of $50,000 is calculated as [$14,000 x 0.105] + [($48,000 - $14,000) x 0.175] + [($50,000 - $48,000) x 0.3] = $8,020.

[**] The tax paid by a taxpayer with an income of $12,000 is calculated as [$12,000 x 0.105] = $1,260. The tax paid by a taxpayer with an income of $16,000 is calculated as [$14,000 x 0.105] + [($16,000 - $14,000) x 0.175] = $1,820.

Monday, 16 January 2017

I should have changed my name to Aaron A. Aardvark

Alphabetic discrimination in economics was a topic of casual conversation while I was completing my PhD, mainly as a result of this paper (ungated earlier version here) by Liran Einav (Stanford) and Leeat Yariv (CalTech). I was reminded of this paper when I read the William Olney paper that I blogged about a couple of weeks ago, that had the researchers' surname first initial as a control variable.

Now, Matthias Weber (Bank of Lithuania, and Vilnius University) has a new and very readable paper that reviews the literature on alphabetical discrimination. It is argued that economists with surnames closer to the start of the alphabet (e.g. A, or B) have an advantage in terms of career progression, etc. compared with economists with surnames closer to the end of the alphabet (e.g. Y, or Z). This arises because of the convention in economics to list authors on multi-authored papers in alphabetical order.

How does this lead to an advantage? There are a couple of likely mechanisms. First, only the name of the first author appears in a citation when there are three or more authors. The rest of the authors disappear into the 'et al.' So, if visibility is important for name recognition, then authors who are more-often the first author (those with names closer to the start of the alphabet under an alphabetical ordering convention) would benefit most. Second, disciplines that don't use an alphabetical ordering convention typically order the authors by their relative contribution, so that the first author had the largest or most important contribution to the article. Therefore, readers in these disciplines may assume that the first author under an alphabetical ordering was also the author who made the largest contribution to the article, and give them greater credit (again, advantaging those with names closer to the start of the alphabet).

The alphabetical author ordering convention is peculiar to economics and to a few other disciplines -Weber notes "‘Business & Finance’, ‘Economics’, ‘Mathematics’, and ‘Physics, Particles & Fields’" as the disciplines that use this system, with others using a contributions-based ordering.

There are three main papers that have investigated the effect of alphabetical discrimination in economics, and Weber provides a useful summary of all three (along with other papers of interest). The first paper is the Einav and Yariv article linked above. They use data on faculty from the top 35 economics departments in the U.S., and find that:
Faculty with earlier surname initials are significantly more likely to receive tenure at top ten economics departments, are significantly more likely to become fellows of the Econometric Society, and, to a lesser extent, are more likely to receive the Clark Medal and the Nobel Prize.
The latter results (on the John Bates Clark Medal and the Nobel Prize) are not statistically significant, so are suggestive at best. The size of the effect on tenure is quite large:
In the regression for top five departments, each letter closer to the front of the alphabet increases the probability of being tenured by about 1 percent.
The same result holds for the top ten economics departments, but fades as lower quality departments are included (probably because the best economists with names early in the alphabet are already employed at the top universities).

The second paper (ungated version here) is one I hadn't read before, by Georgios Efthyvoulou (Birkbeck College, University of London). Efthyvoulou extends the Einav and Yariv analysis by looking at the top 17 and bottom 51 (of 68) economics departments in the U.S. He finds that, when restricting the sample to full professors only:
...having a last name initial “A” instead of “Z” increases the probability of being employed by a top economic institution, by slightly more than 20%.
The results for economists at all academic ranks are statistically insignificant. Efthyvoulou also finds similar results for the U.K. (but again they are statistically insignificant). More interestingly, he looks at the number of downloads and citations on RePEc, and finds that:
...being an A-author, and not a Z-author, increases (the logarithm of) the total number of file downloads by 13% and (the logarithm of) the total number of abstract views by 11%.
The third paper is this one (ungated earlier version here) by Mirjam van Praag and Bernard van Praag (both University of Amsterdam). The van Praags use data on all articles published in eleven top economics journals from 1997 to 1999, and look at the effect of alphabetical ranking (i.e. the first initial of the author's surname) on productivity. They find:
...a significantly negative effect of 'letter' on scientific performance; this indicates a reputational advantage of A-authors over Z-authors, resulting in an increased scientific output of 3.4 articles... and a 0.16... -article higher annual productivity.
All of this suggests that economists with an "A" surname have a distinct advantage over those with a "Z" surname, and all of the articles linked above have recommended some move towards either a contributions-based ordering or a random ordering of authors (the latter being a point that Debraj Ray and Arthur Robson have also made). However, no such change has yet been made, so clearly I missed an opportunity to change my name to Aaron A. Aardvark.

Saturday, 14 January 2017

The limit to human lifespan, or not?

Back in October, an article was published in the journal Nature by Xiao Dong, Brandon Milholland, and Jan Vijg (all Albert Einstein College of Medicine in New York), entitled "Evidence for a limit to human lifespan". Dong et al. demonstrate what they suggest is evidence that natural human lifespan reached a peak in the mid-1990s, at about 114.9 years. Here is their key graph, which shows the maximum reported age at death for each year in their dataset (from the International Database on Longevity):

You can clearly see that, prior to 1995, the trend-line is upward sloping, and after 1995, the trend-line is downward sloping. This result was widely reported in the media (see for example here, and here, and here).

However, these results were also rubbished (see for example this piece by Hester van Santen). Van Santen makes the obvious point that the authors chose 1995 as their potential break point in the data:
An important bit of information: Vijg assumed this break in the trend in advance, he told NRC on the phone – in Dutch, as the biologist was born in Rotterdam. Vijg then had the computer calculate two underlying ‘trends’, one for the period before 1995 and one for after. These are the lines seen on the graph.
That’s not how these things are supposed to be done.
“No,” confirms statistician Van der Heijden. “You need to have solid theoretical substantiation before you start. When you infer that kind of turnaround using only the data, there’s a good chance that what you’re seeing is mere coincidence.”
The key point is that there wasn't anything special about 1995 in particular that makes it the best theoretical choice. If they had chosen some other year to break their data, the result might disappear (which van Santen suggests, but doesn't actually demonstrate for us).

I have another gripe with the Nature paper however. The data points used to construct their regressions are annual maximum recorded age at death from the dataset. So, there is only one data point for each year. So, the orange regression line (1995 onwards) is based on only twelve data points. No regression line is valid based on only twelve observations, and it's statistically illiterate to think otherwise.

Van Santen concludes (emphasis theirs):
Statistical evidence to support the assertion that the oldest living people haven’t gotten any older since 1995 is weak, according to two professors. We find the idea that the maximum human lifespan is 115 years to be unfounded.
However, it's important not to overstate this conclusion. Just because one of Dong et al.'s results is suspect, that is not enough to suggest that there is no maximum human lifespan, only that Dong et al. haven't provided enough evidence to support it. I really like this post by Matt Ridley from a few years ago, which makes some good points:
For all the continuing improvements in average life expectancy, the maximum age of human beings seems to be stuck. It’s still very difficult even for women to get to 110 and the number of people who reach 115 seems if anything to be falling. According to Professor Stephen Coles, of the Gerontology Research Group at University of California, Los Angeles, your probability of dying each year shoots up to 50 per cent once you reach 110 and 70 per cent at 115...
The lack of any increase in people living past 110 is surprising. Demographers are so used to rising average longevity all that they might expect to see more of us pushing the boundaries of extreme old age as well. Instead there is an enormous increase in 100-year-olds and not much change in 110-year-olds...
Next time you hear some techno-optimist say that the first person to live to 250, or even 1,000, may already have been born, remind them of these numbers. The only way to get a person past the “Calment limit” of (say) 125 will be some sort of genetic engineering.
I'd go a little bit further. The size of the cohorts reaching age 100 is increasing (because of improved health at younger ages, especially at very young ages), then we should also expect to see larger cohorts achieving age 110, age 115, and age 120. However, there isn't any evidence of these hyper-aged cohorts getting much bigger. [*] This suggests to me that the mortality rate for those aged 100 years and over might be increasing over time, thereby offsetting the effect of larger cohorts achieving age 100. If I get some spare time, this is a research question that deserves further attention.


[*] Although an absence of evidence is not evidence of absence. There's probably an opportunity for an honours or Masters project to look at New Zealand longitudinal census data on those aged 100 years and over.