Boy racers can't do statistics

Matthew Hansen wrote in the New Zealand Herald today:

Let's get this out of the way early - "boy racer" is a ridiculous and outdated term. Much of the country's modified car culture is propped up by the middle-aged, and by women. We're a world leader for female involvement in motorsport.

The "boy" aspect isn't exactly prevalent in the New Zealand Transport Agency's numbers for road deaths either. In the past 12 months, 379 drivers have been killed, and the three biggest age groups represented are those from 25-39 (103), 60-plus (91), and 40-59 (91). By contrast, deaths for those aged 15-19 number 25, and 52 for 20- to 24-year-olds.

I'm no rocket scientist, but those numbers are smaller. So why empower an outdated, incorrect term like "boy racer"?

Yes, those numbers are smaller, but that's often what happens when you compare the numbers of events happening to people in a five-year age group (15-19 or 20-24 years) with the comparable numbers for a 15-year age group (25-39), a 20-year age group (40-59), or a 40+-year age group (60 years and over). Before comparing the number of road deaths between age groups, you need to adjust for the relative number of people in each age group, to work out the incidence of road deaths. [*]

The number of road deaths this year so far are available from the NZTA road toll website. There are some small differences with the numbers that Hansen uses (probably because the statistics reported there are for the 12 months that end on the day you access the website), so for comparability I will use Hansen's numbers. The numbers of people in each age group are available from Statistics New Zealand (NZ.Stat) for 30 June 2017 (which is close enough to the mid-point for the year ended on some day in January).

While there have been 103 road deaths among people aged 25-39, there are 962,550 people in that age group. That works out to 1.07 road deaths per 10,000 people. Compare that with 52 road deaths and 355,830 people aged in the 20-24 age group, which works out at 1.46 road deaths per 10,000 people. For completeness, the other values are in the table below.

Clearly, the highest risk group is the 20-24 year age group when it comes to road deaths. I'm no rocket scientist either, but the numbers for other groups are smaller. In some cases close to half of the incidence for the 20-24 year age group. Maybe boy racers should stick to cars, not statistics? And the Herald should send its reporters to a course on some basic statistical literacy.

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[*] Even better would be to adjust for the number of vehicle road miles travelled by members of that age group, which would be a 'more correct' measure of risk exposure (for vehicle travellers, so probably pedestrian and cyclist road deaths should be excluded first too).

That January tradition... rent increases, Wellington edition

It's January, so that means house rental increases are in the news (if you doubt me, here's my 2017 post on the topic, and 2016, and 2015). It starts with Dan Rowe's piece in the Spinoff a couple of weeks ago, in which the details are not at all surprising:

The nightmare that is renting in this country continues to bring new horrors, with reports from Wellington that landlords are explicitly operating tender processes on their rentals in a bid to drive up prices...

Because what tenants aren’t free to do is escape the market altogether – already flat viewings across the city are attracting hordes of applicants, thronging in the streets and clamouring for a place to sleep as much as a full month before university begins for the year.

“I was at one the other day and there were people everywhere streaming up and down the street. Someone came out and asked us what was going on on their street because apparently there’d been like a hundred people walking up and down. It’s been pretty hectic.”

When you have "hordes of applicants" that suggests to me that there is excess demand (a shortage), and when there is excess demand you would expect prices (in this case, rents) to increase (a point that I have made before). However, Eric Crampton has a slightly different take, explaining why we wouldn't necessarily expect the rent to rise so far that it would eliminate the excess demand:

Suppose it's hard to evict a bad tenant. It'll take a long time, it'll be a hassle, and the tenants might destroy the place while you're going through the tenancy tribunal. If you set a high price and if it's hard to monitor and police what's going on in the flat, you might have problems. The high bidder might be the one expecting this to be a short-term game.

Landlords would want to evaluate a potential tenant's bid across a pile of hard-to-specify and possibly illegal-to-specify (but impossible to police unless you're dumb enough to write it in the ad) non-price margins. If you want that, you want to have excess demand at the posted money price so that you can clear on the other margins.

This idea of landlords offering 'below-market' rents in order to have the pick of tenants could be termed an efficiency rent (the rental equivalent of an efficiency wage - see here for more on efficiency wages), which I wrote about back in 2016:

As noted above, there is a moral hazard problem for landlords - tenants' incentives (to look after the property) are not aligned with the landlord's incentive (to keep the property in top condition). If the landlord instead offered an efficiency rent (a rent below the equilibrium market rent), then they would have many potential tenants applying for the property, allowing the landlord to pick the best (the least likely to damage the property). It also gives the tenants an incentive to look after the property after signing the tenancy agreement, because if they don't they get evicted and have to find another place to live at a much higher cost.

Maybe landlords offer efficiency rents already and we just don't realise it? There is certainly plenty of evidence for excess demand for rental properties (see here or here for example), so maybe rents are below equilibrium (though they are rising quickly so it's possible that the observed below-equilibrium rents are simply in transition to a higher equilibrium level). Excess demand by itself is pretty weak evidence for efficiency rents. I'd want to hear landlords telling us they offer lower rents to attract good tenants before I found it believable. There's not a lot of evidence in the academic literature on efficiency rent either (see this paper by Basu and Emerson as one example, ungated here).

I'm still waiting for some clear evidence that efficiency rents are a good characterisation of what drives excess demand in rental housing markets. In the meantime, we are left to ponder the situation. What is clear though, is that by now no one should be surprised that house rents increase in January.

Read more:

• This is what happens when you have shortages of rental property
• Students, rental shortages, and renting over the summer
• January tradition continued... Rent increases again
• A January tradition - complaints about rising rents
• Out-of-control rent increases in Auckland - why?

Will population ageing lower economic growth?

Globally, the world population is ageing, and it is ageing in some countries (mostly developed countries, but also China) faster than others. That leads to a potential problem. Older people are less likely to work than younger people, and some consider that older workers are less productive (although that point is contested - see here). [*] So, it is reasonable to wonder: will population ageing have a negative impact on economic growth?

If we take GDP per capita as a measure of living standards or wellbeing (and hence, economic growth is represented by an increase in GDP per capita), we can decompose GDP per capita as follows [**]:

[Y/P] = [Y/L] * [L/WA] * [WA/P]

where Y is output, P is population, L is the labour force, and WA is the working age population. This identity simply says that GDP per capita (or output per person, Y/P) is made up of labour productivity (or output per unit labour, Y/L), labour force participation (L/WA), and the share of the working age population in the total population (WA/P).

For an ageing population to decrease the growth in Y/P, then it must decrease either:

1. Labour productivity - contested, but possible, especially if you consider manual-labour-intensive tasks;
2. Labour force participation - seems possible, since older workers are less likely to be in the labour force, especially in countries where they have access to pensions or can draw from retirement savings; and/or
3. The share of the working age population in the total population - almost certain, given that as the population ages overall, then young people (who are not in the working age population) make up a smaller and smaller proportion of the total population.

So we've established that, in theory, the ageing population should reduce economic growth. But what does the empirical evidence tell us?

A recent NBER working paper by Daron Acemoglu (MIT) and Pascual Restrepo (Boston University) looks directly at the available data on population ageing and economic growth (ungated version here), and finds that:

...since the early 1990s or 2000s, the periods commonly viewed as the beginning of the adverse effects of aging in much of the advanced world, there is no negative association between aging and lower GDP per capita... we show that even when we control for initial GDP per capita, initial demographic composition and differential trends by region, there is no evidence of a negative relationship between aging and GDP per capita; on the contrary, the relationship is significantly positive in many specifications.

In other words, countries that are ageing faster actually also have faster (not slower) economic growth. What is going on? Acemoglu and Restrepo argue that it is the rise of labour-saving technology, in the form of robots and artificial intelligence, and they show that:

...countries experiencing more rapid aging are the ones that have been at the forefront of the adoption of one important type of automation technology: industrial robots.

Going back to our identity from earlier in the post, it seems that even if labour force participation (L/WA) and the share of the population that is working age (WA/P) are decreasing, they are being more than offset by an increase in labour productivity (Y/L). It is difficult to say whether this situation can continue indefinitely, but for now, perhaps those that believe that population ageing will have negative effects on economic growth are just as wrong as Malthus about unsustainable population growth, and for the same reason (technological change)?

[HT: Marginal Revolution, this time last year]

Read more:

• People are retiring later in life, and why that might be a good thing

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[*] Also, the secular stagnation hypothesis suggests that, when interest rates are low (and the real interest rate is negative), an ageing population will lead to lower growth (see here). 

[**] As per this earlier post, I note that this decomposition comes from a discussion with Jocelyn Finlay from Harvard School of Public Health, when I was on Study Leave there back in 2016.

Professional tennis players are optimisers

With plenty of action in Melbourne at the Australian Open this week, it seems timely for me to write a post about tennis. I've already noted in an earlier post that tennis players appear to be loss averse. But are they optimising nonetheless? Do they make decisions that maximise their chances of winning (which would also be consistent with loss aversion)?

A recent paper by Jeffrey Ely (Northwestern University), Romain Gauriot (University of Sydney), and Lionel Page (Queensland University of Technology), published in the Journal of Economic Psychology (sorry I don't see an ungated version) provides us with some answer. The authors look specifically at the risk behaviour of servers on first and second serve:

When serving, players can opt for risky serves which are more likely to fail but are harder to return if successful or more conservative serves which are less likely to fail but are also easier to return.

The key is whether players behave differently on first and second serves (more on that in a moment). However, simply comparing first and second serves is not so straightforward. The authors correctly note that there is:

...a potential caveat with raw data on tennis serve: it can be characterised by a selection problem. First serves are always observed while second serves are only observed when the first serve failed. This means that second serves may be more likely to be observed when serving is harder than usual either for natural reasons (e.g wind conditions), fitness (e.g. tiredness late in the match) or strategic reasons (e.g. opponent having learned how to return the player’s serve).

Their solution is quite ingenious:

To cleanly compare first and second serves one ideally wants to observe some random events which determines in a given situation whether a serve is going to be a first or a second serve. We argue that such a situation occurs when the ball hits the tape (top of the net) on the first serve. The impact with the net gives the ball an unpredictable trajectory leading the ball to be either in or out. It introduces the required randomness as a first serve follows a ball let which lands in the court and a second serve follows a ball which lands outside the court.

The serve immediately following a 'let serve' is randomly either a first serve (if the 'let serve' landed in) or a second serve (if the 'let serve' landed out). Ely et al. use a dataset from 3,188 matches, involving over 690,000 serves, of which 7,605 follow a 'let serve' and are the core sample of interest. They test four conditions which would imply that players are correctly maximising their chance of winning:

1. That first serves are more risky than second serves (the probability that a serve lands in is lower for first serves);
2. That first serves are harder to return than second serves (players are more likely to win the point on their first serve);
3. Using two first serves is a suboptimal strategy (it leads to a lower probability of winning the point); and
4. Using two second serves is also a suboptimal strategy.

They find that:

...the serves from professional tennis players meet four conditions which make them consistent with the optimal strategy of risk taking between first and second serves. This result is observed both overall and when splitting the sample by gender and ranking.

So, it appears that professional tennis players are optimisers. Which we should expect - they are trained professionals who have developed skills in strategic play over many years.

Read more:

• Is Roger Federer more loss averse than Serena Williams?