The Hamilton vs. Wellington population showdown

Some of my research was profiled on the front page of the Waikato Times today (paywalled):

Forget Wellington — Hamilton is on track to overtake the capital within 14 years.

New University of Waikato projections show the city’s population could climb to 242,716 by 2040, cementing its status as New Zealand’s fastest-growing city.

Hamilton’s population projection is under the “high variant” forecasts — the growth estimates council staff are recommending, and which the Government requires councils to use when planning their Long Term Plans.

If that is compared to Stats NZ's and the Wellington Regional Growth Framework estimates for Wellington for the same year, Hamilton's population will be larger by 2716 people.

Now, this Hamilton versus Wellington head-to-head population battle seems to be attractive to the media (see this post from 2019, talking about this 2019 Waikato Times article). However, they've got things wrong this time, for a couple of reasons.

First, they are comparing Hamilton City with Wellington City, which is a valid comparison of city council areas, but may not be the comparison many people have in mind. I'll come back to that point at the end of the post.

Second, and more importantly, you shouldn't compare a projection from one source, based on one set of assumptions, with a projection from a totally different source, based on a different set of assumptions. Especially when projections from the same source are available, using consistent assumptions. Otherwise, you are not comparing apples with apples.

So, let's make some consistent comparisons. Stats NZ's projections are available on Aotearoa Data Explorer, Stats NZ’s online data tool. Search for "subnational population projections", and then scroll down to "Subnational population projections, by age and sex, 2023(base)-2053". Stats NZ offers three variants (low, medium, and high) of 2023-base population projections. The difference between the variants is that low variant projections assume low fertility, high mortality, and low international migration, while high variant projections assume high fertility, low mortality, and high international migration (and the medium variant projection is, obviously, in-between the low and high). Here are the three variant Stats NZ projections for Wellington City and Hamilton City:

The bold lines are for Hamilton City. The dotted lines are for Wellington City. The low, medium, and high variants are coloured blue, green, and brown respectively. The key thing to notice is that the lines cross over. Where the lines of the same colour cross, that is the point in time when Hamilton catches up with Wellington under that projection variant. So, with Stats NZ's projections, Hamilton is projected to be larger than Wellington by 2038 under all three projections. If we do a linear interpolation (because Stats NZ only reports their projections for five-year intervals), then Hamilton is projected to be larger than Wellington by 2034 in the low and medium variant projections, and by 2035 in the high variant projections.

Turning to the University of Waikato (UoW) projections (which I produced), there are also three variants (low, medium, and high) that can be interpreted similarly to Stats NZ's projections. The methods and assumptions differ from those used by Stats NZ. These are the projections that Hamilton City Council uses in its planning (as do several other local councils). Here are the three variant UoW projections for Wellington City and Hamilton City:

In my projections, Hamilton is projected to be larger than Wellington by 2040 in the low variant projection, by 2048 in the medium variant projection, and by 2066 in the high variant projection (which is beyond the projection horizon for Stats NZ projections as they only project for 30 years).

Why the difference? The difference between the timing using Stats NZ projections and the timing using my projections is due to differences in assumptions and the underlying models. It would take a long post to unpack all the differences in detail. The differences between the low, medium, and high variants are easier to explain. Wellington has a head start - it was much larger in 2023 than Hamilton. However, Hamilton has both higher fertility and greater net migration than Wellington. That head start makes a bigger difference in the high variant projections than in the low variant projections, because the higher fertility and international migration in the high variant projections allow Wellington to maintain that lead for longer. In the low variant projections, Hamilton's higher fertility and net migration allow it to catch up much faster. In other words, because Wellington starts from a larger population base, assumptions that lift population growth across the whole country add more people to Wellington in absolute terms, delaying Hamilton's catchup, even though Hamilton’s underlying growth rate is higher.

What is interesting is that the differential effect between low-variant and high-variant projections doesn't seem to be anywhere near as prominent in the Stats NZ projections as it is in my (UoW) projections. In part that is because the uncertainty expressed in my projections (proxied by the difference between the low and high variant projections) is much higher than the projections by Stats NZ. I'm comfortable with that, given that international migration in particular is highly uncertain. So, we should expect a fairly high degree of uncertainty when we project future population.

One final thing to note is a point I made in my 2019 post on this topic. Wellington City is only one part of a larger urban area ('Greater Wellington') that also includes Porirua City, Upper Hutt City, and Lower Hutt City. There is no projection that has the Hamilton urban zone catching up in population to the broader Wellington urban zone any time soon. I suspect that many people would be flabbergasted by the suggestion that Hamilton might become larger than Wellington. Many of those people would be thinking about Greater Wellington, and they would be right.

So, Hamilton will eventually be New Zealand's number three city council area in terms of population. However, the celebrations could easily be put on hold by a council amalgamation process that the government has started, which could conceivably merge some Wellington councils together, putting their combined population out of reach of Hamilton for the foreseeable future.

[HT: The incomparable Emeritus Professor Jacques Poot]

Read more:

• Hamilton won't be our second largest city any time soon

Decision-makers don't dislike uncertain advice, but they do dislike advisors who are uncertain

One aspect of my research and consulting involves producing population projections, which local councils use for planning purposes. Population projections involve a lot of demographic changes, each of which are not perfectly known beforehand, so projections inherently have a lot of uncertainty (for more on that point, see here). [*] Understandably, while planners are trying to make plans for an uncertain future, reducing the uncertainty of that future makes their jobs easier. In my experience, planners are usually looking for projections that give them one single number for the total population (for each year) to focus their planning on. [**] So, it seems natural to me that decision-makers would be averse to uncertainty, and prefer to receive predictions or projections that convey a greater degree of certainty.

It turns out that might not be the case. This 2018 article by Celia Gaertig and Joseph Simmons (both University of Pennsylvania), published in the journal Psychological Science (ungated version here) demonstrates that decision-makers don't have an aversion to uncertain advice at all. Gaertig and Simmons conducted a number of experimental studies where they presented research participants with advice and asked them to make a decision. In the first six studies, using research participants recruited from Amazon Mechanical Turk:

...participants were asked to predict the outcomes of a series of sporting events on the day on which the games were played. Participants in Studies 1 and 2 predicted NBA games, and participants in Studies 3–6 predicted MLB games...

For each of the games that participants were asked to forecast, we told them that, “You will receive advice to help you make your predictions. For each question, the advice that you receive comes from a different person.” Importantly, participants always received objectively good advice, which was based on data from well-calibrated betting markets. For each game, we independently manipulated the certainty of the advice, and, in all but one study, we also manipulated the confidence of the advisor.

Gaertig and Simmons presented research participants with advice, some of which was certain, and some of which was uncertain, with uncertainty expressed in a variety of way, including probabilistically. Research participants were then asked about the quality of the advice they received, and they made an incentivised choice, where they were paid more if they correctly predicted the outcome of the sporting event (the specific outcomes to be predicted varied across the studies). They found that:

As predicted, and consistent with past research, these analyses revealed a large and significant main effect of advisor confidence... Advisors who said “I am not sure but . . .” were evaluated more negatively than advisors who expressed themselves confidently.

More importantly, participants did not evaluate uncertain advice more negatively than certain advice...

Thus, these studies provide no evidence that people inherently dislike uncertain advice in the form of ranges.

Moving on to probabilistic statements of uncertainty, Gaertig and Simmons found that:

As in the previous analysis, there was a large and significant main effect of advisor confidence in all regressions... Advisors who said “I am not sure but . . .” were evaluated more negatively than advisors who expressed themselves confidently. We also found, in Study 6, that advisors who preceded their advice by saying, “I am very confident that . . .” were evaluated more positively than advisors who did not express themselves with such high confidence...

Participants evaluated exact-chance advice (e.g., “There is a 57% chance that the Chicago Cubs will win the game”) more positively than certain advice (e.g., “The Chicago Cubs will win the game”)...

Participants also evaluated approximate-chance advice (e.g., “There is about a 57% chance that Chicago Cubs will win the game”) more positively than certain advice...

In Study 5, we introduced a percent-confident condition, in which participants received confident advice in the form of “I am X% confident that . . . ” We found that participants evaluated this advice the same as certain advice...

The results of the “probably” condition were different, as participants did evaluate advice of the form “The [predicted team] will probably win the game” more negatively than they evaluated certain advice...

Gaertig and Simmons then go on to show that the research participants were no less likely to follow the uncertain advice in their predictions than the certain advice. They also found similar results in a laboratory setting (in Study 7), which also showed that:

...people’s preference for uncertain versus certain advice was greater when the uncertain advice was associated with a larger probability.

In other words, people prefer for advice that demonstrates uncertainty, when the probability is very high (or very low), but not so much when the uncertainty says that the chances of an event are 50-50. That makes some sense. However, it doesn't really accord with the finding of a preference for uncertain advice over certain advice - do decision-makers really prefer advice that says something is 95% certain than saying something is 100% certain? Perhaps they feel that predictions expressed with 100% certainty lack credibility?

Finally, in the last two studies Gaertig and Simmons asked research participants to choose between two advisors, one of whom provided certain advice while the other provided uncertain advice. They found:

...a large and significantly positive effect of the uncertain-advice condition, indicating that more participants preferred Advisor 2 when Advisor 2 provided uncertain advice than when Advisor 2 provided certain advice. This was true both when the uncertain advice came in the form of approximate-chance advice and in the form of “more-likely” advice. When one advisor provided certain advice and the other approximate-chance advice, 82.4% of participants chose Advisor 2 when Advisor 2 provided approximate-chance advice, but only 16.2% of participants chose Advisor 2 when Advisor 2 provided certain advice...

Gaertig and Simmons conclude that:

Taken together, our results challenge the belief that advisors need to provide false certainty for their advice to be heeded. Advisors do not have a realistic incentive to be overconfident, as people do not judge them more negatively when they provide realistically uncertain advice.

It seems that I may have misjudged decision-makers' preferences for certainty. They don't prefer certain advice; they prefer advisors who are certain about their uncertainty. 

*****

[*] Here I'm using uncertainty in its everyday broad sense. Financial economists distinguish between uncertainty that can be quantified (which they refer to as risk), and uncertainty that cannot be easily quantified.

[**] This is an exaggeration of course, in two ways. First, planners recognise that there is uncertainty. However, explaining that uncertainty to elected decision-makers is difficult, so having a single number makes their job easier in that way as well. Second, planners don't only want a single number for the total population. They usually want to know a bit more detail about the age distribution, etc.

Hamilton won't be our second largest city any time soon

I was interviewed for the Waikato Times last week, and the story appeared on the Stuff website yesterday:

Hamilton city might be growing, but not as explosively as some people might dream. 

Commentators have recently said Waikato is 'ready to go pop' with development, citing the hundreds of millions of dollars spent on community facilities and transport infrastructure. 

Labour list MP Jamie Strange said he believes Hamilton's growth is so significant it could become New Zealand's second biggest city in the next 30 years. 

But a Waikato University professor said it would take drastic change for Hamilton to surpass Wellington and Christchurch in three decades...

"If you are talking about is Hamilton going to be a city of 200,000 - sure it's going to be that.

"But Wellington is certainly going to be big and bigger and Christchurch is also going to be big and bigger."

Read the full story for more from me. The overall point is that the population of Hamilton is growing. But the populations of Wellington and Christchurch are growing as well, and they have a large head start. How long will it take Hamilton to catch up? I gave the reporter (Ellen O'Dwyer) some quick back-of-the envelope calculations.

Based on Census Usually Resident Population counts (available here), Hamilton City grew from 129,588 in 2006 to 141,612 in 2013 and 160,911 in 2018. Wellington City grew from 179,466 in 2006 to 190,956 in 2013 and 202,737 in 2018. Christchurch City declined from 348,456 in 2006 to 341,469 in 2013, then grew to 369,006 in 2013. Hamilton grew faster than Wellington and Christchurch (in both absolute and relative terms) between each of the last two Censuses.

If the absolute rates of growth of both Hamilton and Wellington (from the previous paragraph) between 2013 and 2018 continued, Hamilton would catch up to Wellington in the early 2040s. Based on the absolute rates of growth between 2006 and 2018, this wouldn't happen until the 2080s. As for Christchurch, forget it - the comparable catch-up time is measured in centuries.

None of those calculations take into account the fact that Wellington City is only one part of a larger urban conglomeration that includes Porirua City, Lower Hutt City, and Upper Hutt City. Once you factor those areas in as well, the Wellington urban area is far larger than Hamilton and it would take something spectacular for the Hamilton urban area (even if you include fast-growing Te Awamutu, Cambridge, and Ngaruawahia) to catch up.

Sorry Jamie. Hamilton isn't going to catch Wellington (and definitely not Christchurch) any time soon.

Extrapolating linear time trends... Male teacher edition

I recently read this article from The Conversation, by Kevin McGrath and Penny Van Bergen (both Macquarie University). In the article, the first two sentences read:

Male teachers may face extinction in Australian primary schools by the year 2067 unless urgent policy action is taken. In government schools, the year is 2054.

This finding comes from our analysis of more than 50 years of national annual workplace data – the first of its kind in any country.

Take a look at The Conversation article. It's hilarious. The authors take time series data on the proportion of teachers in Australia who are male, and essentially fit a linear time trend to the data (and in some cases a quadratic time trend also), then extrapolate. I took a look at the paper, which was just published in the journal Economics of Education Review. Any half-decent second-year quantitative methods student would be able to do the analysis from that paper, but most would not then extrapolate and conclude:

Looking forward, it is not possible to determine whether the decreasing representation of male teachers in Australia will continue unabated. If so, however, the situation is dire. In primary schools Australia-wide, for example, male teachers were 28.49% of the teaching staff in 1977. Taking the negative linear trend observed in male primary teaching staff and extrapolating forward, it is possible to determine that Australian male primary teachers will reach an ‘extinction point’ in the year 2067. In Government primary schools, where this decline is sharpest, this ‘extinction point’ comes much sooner – in the year 2054.

There is nothing to suggest a linear time trend is going to continue into the future. Certainly, it seems unlikely when you have a variable (like the proportion of teachers who are male) that is bounded by 0% and 100% that it will behave in any way linearly when you get close to the extremes, even if it is behaving linearly for past data. Here's the key data from their paper (there's also a more interactive version at The Conversation):

If you're set on trying out polynomials of time trends, why stop at a quadratic? The primary school data (the lower line in the diagram above) looks like it might be a cubic since it starts off upward sloping then starts going downwards, but at a decreasing rate. I manually scraped their data from the article in The Conversation for male primary teachers, then ran different polynomial time trends through it. The linear time trend had an R-squared of 0.939 (close to the 0.95 they report in the paper), a quadratic had an R-squared of 0.939, a cubic increased this to 0.982. In the cubic, all three variables (time, time-squared, and time-cubed) are highly statistically significant. Moreover, this model has a much higher R-squared than their quadratic, so is more predictive of the actual data. In the cubic model (shown below), the forecast shows an increase in male teacher proportions from about now!

Now, I'm not about to use my model to suggest that the proportion of male primary school teachers would accelerate to 100% (if you extrapolate the cubic model, this happens by 2049, which is sooner than the proportion reaches zero under McGrath and Van Bergen's model extrapolation!), but I could. And then I would be just as wrong as McGrath and Van Bergen. The British mathematician George Box once said: "All models are wrong, but some are useful". In this case, both the linear time trend model of McGrath and Van Bergen and the cubic model I've shown here are both wrong and not useful. Hopefully people haven't taken McGrath and Van Bergen's results too seriously. The gender gap in teaching is potentially a problem, but trying to show this by extrapolating time trends using a very simple model is not helpful.

The relative (un)certainty of subnational population decline

Over the three years up to March of this year, I was involved in a Marsden Fund project led by Natalie Jackson, looking at subnational depopulation in New Zealand. That is, among other things we were trying to explain why some areas of New Zealand have been declining in population over time, and continue to do so. The outputs of that project have been summarised in a recent issue of the journal Policy Quarterly.

My contribution to that issue of Policy Quarterly (from pages 55-60) is entitled "The relative (un)certainty of subnational population decline", and looks at how certain (or uncertain) population decline is for different territorial authorities in New Zealand. However, the article has a broader purpose, and is worth reading because it outlines some of the key points that decision-makers need to understand about population projections, especially in terms of their uncertainty. If you know nothing about population projections, other than that they are forecasts of the future that can be useful for decision-making, then you should read the article.

The main results categories New Zealand's territorial authorities (TAs) by the probability that they will experience a decline in population over the decades 2023-2033 and 2043-2053. I won't spoil the results by naming particular TAs, but here's a summary:

...the number of TAs appearing in each category increases between the two periods. More TAs are facing population decline in the 2043–2053 decade than in the 2023–2033 decade. This corroborates recent work that has shown similar results... In the 2023–2033 decade 20 TAs face a 90 percent or greater probability of population decline, compared with 26 TAs in the 2043–2053 decade. Granted, these TAs have relatively small population, representing 12.2 percent of the national population in 2023 (for the 2023–2033 group based on median population size) and 17.2 percent of the national population in 2043 (for the 2043–2053 group).

Unsurprisingly, rural and peripheral areas face the highest probability of future population decline. Other papers in that issue of Policy Quarterly posit some reasons why we observe population decline in particular areas. My paper is descriptive and future-focused, and doesn't explore the institutional or other non-demographic factors that might explain why some rural areas, rather than others, are projected to experience population decline. That's something for future research.

Read more:

• The Maxim Institute on dealing with population decline
• Newsflash! Population growth will be highest on the fringes of fast-growing urban areas
• Winners and losers in population growth
• Forget 'zombie towns', there's entire 'zombie districts' coming to a rural area near you

Future life expectancy is good for NZ men, but be cautious

What are the limits of human life expectancy? I don't think any of us really know. Last month, I posted about an article in the journal Nature that claimed we were already at the limit by the mid-1990s. Now, almost at the other extreme, a new article by Vasilis Kontis (Imperial College London) and others, and published in the The Lancet (and appears to be open access), projects larger-than-expected future increases in life expectancy.

Kontis et al. basically ran every major model type that is used to model age-specific death rates (21 models in all) across 35 industrialised (high-income) countries, and then took a weighted average of those models [*]. The modelling approach also allowed them to make probabilistic forecasts (which is something that Jacques Poot and I have been working on, in terms of population projections, for many years). They looked at life expectancy at birth, and life expectancy (remaining life years) at age 65. I'm just going to focus on the first of those. Here's what they found:

Taking model uncertainty into account, we project that life expectancy will increase in all of these 35 countries with a probability of at least 65% for women and 85% for men, although the increase will vary across countries. There is nonetheless a 35% probability that life expectancy will stagnate or decrease in Japanese women by 2030, followed by a 14% probability in Bulgarian men and 11% in Finnish women...

There is 90% probability that life expectancy at birth among South Korean women in 2030 will be higher than 86·7 years, the same as the highest life expectancy in the world in 2012, and a 57% probability that it will be higher than 90 years... a level that was considered virtually unattainable at the turn of the 21st century by some researchers.

So, they are offering better than even odds that life expectancy for South Korean women will exceed 90 years by 2030, a point that has been picked up in the media (see for example here and here). However, something that wasn't picked up (even by the NZ media) was the somewhat surprising projection for male life expectancy in New Zealand. Here's the relevant part of their Figure 3:

Male life expectancy in New Zealand for 2010 is already one of the highest in those 35 countries (ranking us sixth out of 35), but look at the left panel of the graph, which is their projection for 2030. Notice that, based on the median projection (the red dot), New Zealand pretty much retains its same ranking. However, notice also that the green smudge (the distribution of projected life expectancies) for New Zealand is much wider than for other countries (I guess they are much less certain about their projection for New Zealand). That leads to, on the right panel of the graph, New Zealand having a relatively high probability of holding the top ranking for male life expectancy in 2030. I must say I was a little surprised by this. Maybe good reason for men to stay in New Zealand?

There's a lot to commend in this research, and the BMJ article is not too mathy (but I wouldn't recommend reading the online appendix on that score). However, it isn't without its problems. The authors have done a good job of using multiple models and bringing them together using a weighted average.

However, one of the key problems with models is that they are less good at extrapolating beyond the range of data that are inputs into the model. And essentially, that is unavoidable when it comes to projecting life expectancy. No industrialised country has ever had life expectancy before as high as it is in those countries today, let alone projecting future further gains in life expectancy. One of the big remaining questions in human biology is the limits to human lifespan, and this sort of trend extrapolation doesn't really help us to understand that. There may be biological limits to lifespan that we haven't approached yet and maybe we won't even know we have approached them until we hit them. At which point, extrapolations of past trends will not be a good predictor of future gains in life expectancy.

The authors themselves note:

Early life expectancy gains in South Korea, which has the highest projected life expectancy, and previous to that in Japan, were driven by declines in deaths from infections in children and adults; more recent gains have been largely due to postponement of death from chronic diseases.

That's not just true in South Korea and Japan, but all industrialised countries. For most of these countries, the future gains in life expectancy at birth that could arise from further reductions in infant and child mortality are limited. The low-hanging fruit of life expectancy gains have already been picked. Further increases in life expectancy now are most likely to arise through reductions in the 'stupid-young-male effect' (e.g. reductions in injury deaths). Remember that life expectancy at birth is measured as the age by which half of that birth cohort will have died (half would still be alive). So, life extending medical technologies that work for the very-old (likely to be those already above the median age for those born in their cohort) will have no effect on measured life expectancy.

Overall, it might be wise to be more cautious in interpreting these projected gains in life expectancy. For New Zealand men, it may be premature to be popping champagne in anticipation of our long-livedness.

*****

[*] What they actually did is called Bayesian model averaging, which essentially means that they weighted the models by how good they are at predicting actual data, with models that are better predictors receiving higher weights.

Climate change won't much affect internal migration in NZ

Climate change is likely to be one of the key challenges facing humankind over the coming century (or more). We are likely facing increases in mean temperature, desertification, rising sea levels, and increasing frequency and intensity of extreme weather. But how big is the impact likely to be on a country like New Zealand, anyway?

In a new working paper, I evaluate the impact of climate change on internal migration in New Zealand, and what that means for the future spatial distribution of population. That is, which regions are likely to gain population from climate change, and which will lose population? I make use of a gravity modelling framework (which I have written about before). Essentially, a gravity model suggests that the migration flow between two regions is positively related to the population of the origin and the population of the destination, and negatively related to the distance between the two places. I tried out a bunch of climate variables from NIWA to find those that appeared to have the biggest impact on internal migration, using data on inter-regional migration from the last four Censuses (1991-2013).

Three climate variables are found to have statistically significant associations with internal migration: (1) mean sea level pressure in the destination; (2) surface radiation in the origin; and (3) wind speed at ten metres at the destination. The sign of the effects suggest that migrants attracted to areas with more settled weather (higher mean sea level pressure); migrants are less likely to move away from areas with more sunlight hours (but interestingly, don't move towards those areas); and migrants prefer to avoid moving to areas that are windier.

I then embedded the gravity model within a cohort-component population projection model, which is something that Jacques Poot and I have been working on for a number of years. I used the projections model to evaluate the effect of different climate change scenarios on regional populations out to a horizon of 2100.

Including the three climate variables in the population projection model makes a small difference to the regional population distribution. The inclusion of climate variables increases the projected populations of Northland, Bay of Plenty, Gisborne, Hawke’s Bay, Taranaki, and Nelson. The overall impact is quite small, as you can see from the diagram below for Northland. The orange line tracks the projected population of Northland excluding any impact of climate, while the grey line includes the impact of climate. Bear in mind that Northland shows the biggest effects in relative terms - the effects on other regions are smaller.

I also looked at the effect of different climate change scenarios, and the difference between different climate scenarios is negligible. The diagram below shows the projections under different climate scenarios for the Southland region. As you can see, there is little difference between them (and that result is similar for other regions as well).

Overall, the results suggest that, while statistically significant, climate change will have a negligible effect on the population distribution of New Zealand at the regional level. This is not to say that climate change will not have important and substantial effects at very localised levels, as a result of sea level rise, for instance. However, most if not all of the displacement of people will be within regions. For example, maybe those displaced by sea level rise simply move a little further inland, or we build walls to keep the sea at bay.

Read the full working paper here.

Riccardo Trezzi is immortal

I very much enjoyed reading this new paper by Riccardo Trezzi (US Federal Reserve Board of Governors), forthcoming in Economic Inquiry (sorry I don't see an ungated version anywhere). In the paper, Trezzi creates a time series model of his own ECG, and uses it to estimate his life expectancy:

In this paper, I go well beyond the frontier. I employ time series econometrics techniques to suggest a decomposition of the heart electrical activity using an unobserved components state-space model. My approach is innovative because the model allows not only to study electrical activity at different frequencies with a very limited number of assumptions about the underlying data generating process but also to forecast future cardiac behavior (therefore estimating the date of death), overcoming the “sudden death forecast” issue which typically arises when using standard time-series models.

My results are duo-fold. First, I show how the heart electrical activity can be modeled using a simple state-space approach and that the suggested model has superior out-of-sample properties compared to a set of alternatives. Second, I show that when the Kalman filter is run to forecast future cardiac activity using data of my own ECG I obtain a striking result: the n-step ahead forecast remains positive and well bounded even after one googol period, implying that my life expectancy tends to infinite. Therefore, I am immortal.

And people wonder about the validity of economic forecasts...

[HT: Marginal Revolution]

Corporate prediction markets work well, given time

Prediction markets were all the rage in the 2000s. The Iowa Electronic Markets were at their peak, and James Surowiecki wrote the bestseller The Wisdom of Crowds. The basic idea is that the average forecast of a bunch of people is better than the forecast of most (or sometimes all) experts. I was quite surprised that prediction markets appeared to go away in recent years, or at least they weren't in the news much (probably crowded out by stories about big data). I was especially surprised we didn't see many stories about corporate prediction markets, which suggested they weren't particularly prevalent. It turns out that wasn't the case at all.

This paper in the Review of Economic Studies (ungated earlier version here) by Bo Cowgill (UC Berkeley) and Eric Zitzewitz (Dartmouth College) shows that this wasn't the case at all, as demonstrated by their Table 1:

The paper has much more of interest of course. It looks at three prediction markets, at Google, Ford, and an unnamed basic material and energy conglomerate (Firm X), and tests whether these markets are efficient. They find:

Despite large differences in market design, operation, participation, and incentives, we find that prediction market prices at our three companies are well calibrated to probabilities and improve upon alternative forecasting methods. Ford employs experts to forecast weekly vehicle sales, and we show that contemporaneous prediction market forecasts outperform the expert forecast, achieving a 25% lower mean-squared error... At both Google and Firm X market-based forecasts outperform those used in designing the securities, using market prices from the first 24 hours of trading so that we are again comparing forecasts of roughly similar vintage.

In other words, the prediction markets perform well. There are some inefficiencies though - for instance, Google's market exhibits an optimism bias, which is driven by traders who are overly optimistic about their own projects (and their friends' projects), as well as new hires being especially optimistic. However, the inefficiencies disappear over time, and:

Improvement over time is driven by two mechanisms: first, more experienced traders trade against the identified inefficiencies and earn higher returns, suggesting that traders become better calibrated with experience. Secondly, traders (of a given experience level) with higher past returns earn higher future returns, trade against identified inefficiencies, and trade more in the future. These results together suggest that traders differ in their skill levels, they learn about their ability over time, and self-selection causes the average skill level in the market to rise over time.

So, prediction markets work well for firms, given enough time for inefficiencies to be driven out of the markets. This is what you would expect - traders who are consistently poor forecasters either drop out of the market or they learn to be better forecasters.

However, as the authors note they were limited to looking at just three prediction markets, and only those who would share data with them. There is likely to be some survival bias here - prediction markets that don't work well won't last in the market long, and are unlikely to be observed. On the other hand, by the time of writing the paper, the markets at Google and Ford had closed down in spite of their good overall predictive performance. On this last point, the authors note that "decisions about the adoption of corporate prediction markets may... depend on factors other than their utility in aggregating information". Other forecasters don't like being shown up.

[HT: Marginal Revolution]

Forget 'zombie towns', there's entire 'zombie districts' coming to a rural area near you

In the NZ Herald last Sunday, Bernard Hickey looks at the possibility of depopulation in New Zealand. He quotes this Royal Society of New Zealand report:

Some territorial local authorities will have increasing difficulty in maintaining service levels for an ageing and possibly dwindling population, not to mention burgeoning numbers of visitors and tourists.

Hickey says:

Councils will have to make difficult decisions to return tarseal roads to gravel, turn off town water and let parks return to bush... Anyone buying property in places such as Wanganui, Gisborne, Whangarei and Greymouth should look at their area's population projections before putting deposits on houses or office buildings.

But forget future 'zombie towns', there's entire districts that are already depopulating, and that trend is only going to increase. Consider this Treasury Guest Lecture (PDF) given by my NIDEA colleague Natalie Jackson. Between 2006 and 2013, the population of the Gisborne Region declined (all other regions increased in population), and the population of 20 of the 66 territorial authorities declined.

And this isn't a new phenomenon either. Consider these examples [*]: between 1964 and 1984, Patea (in Taranaki) declined from a population of 2,040 to 1,928; Raetihi (in the central North Island) declined from 1,390 to 1,247; Taihape (the gumboot capital of the world!) declined from 2,800 to 2,586; and Runanga (on the West Coast) declined from 1,720 to 1,264. By the 2013 Census, the populations were 1,098 for Patea, 1,002 for Raetihi, 1,512 for Taihape, and 1,023 for Runanga (excluding neighbouring Rapahoe). So, those rural towns have been in decline for a long time.

And there's more to come. Bill Cochrane and I have been working on population projections for the Waikato Region. Of the ten component territorial authorities in the region (excluding Rotorua District, of which a little bit is in the Waikato), all but Waikato District and Hamilton City are projected to peak in population and begin to decline sometime between now and 2063. Three of them are projected to experience immediate and sustained decline in population (Otorohanga, South Waikato and Waitomo Districts). Moreover, South Waikato District is projected to decline in population in even the most optimistic high scenario (the other two increase slightly in population in the highest scenario).

We saw something similar when we did projections for the Bay of Plenty region earlier in the year (see here, PDF). Of the six territorial authorities in the Bay of Plenty, only Western Bay of Plenty District and Tauranga City are projected to avoid any population decline, and three of the other four (Kawerau, Whakatane, and Opotiki Districts) are projected to experience sustained decline. See for example Kawerau:

Maybe it's not all bad news though. Population decline could just be a slow-burn version of the collapses that lead to a redistribution of towns and cities to more preferable locations. And there is lots to learn from population decline, which hasn't been investigated nearly as much as population growth. Natalie Jackson is leading a multi-disciplinary team in a Marsden-funded research project to further explore these issues, by identifying, classifying and modelling the mechanisms and thresholds of subnational decline. Bill Cochrane and I are both contributing to this project, through which we hope to be able to better project population decline and when and where it might begin.

Will that help local councils that are trying to arrest population decline and encourage more people to live in their jurisdictions? Unfortunately it's unlikely to help much - these councils are largely engaged in a zero-sum battle for future population. If one council comes up with a new 'sure-fire' attractor of new migrants, then other councils will quickly copy it. It's a Tiebout competitive race-to-the-bottom at the subnational level, that none of them can 'win'. Absent any sudden shift in economic fortunes (like the shale oil boom that has led to massive increases in population in North Dakota), future subnational population growth in New Zealand will most likely continue to be concentrated in the major cities, particularly in the golden triangle of Auckland, Hamilton and Tauranga.

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[*] These figures are taken from the New Zealand Official Yearbooks for 1965 and 1985. It's pretty cool that these historical treasure troves are all freely available online.

Can music soothe the savage stock market?

I recently read this 2012 paper from the North American Journal of Economics and Finance by Philip Maymin of NYU-Polytechnic Institute (ungated earlier version here). The paper investigates whether the complexity of songs (as measured by the variability in beats) is related to stock market volatility. Specifically:

This paper investigates the question of whether more complexity in music on Top 100 Billboard songs leads to less future complexity in the market through lower subsequent realized market volatility, because the complexity of popular music reflects the mood and the choices made by economic actors in light of their cognitive load with respect to future activity...

When they tend to contemplate more complex possibilities, they will prefer simpler music; further, contemplating more complex possibilities is linked to an increase in future risky activity, thus leading to future market volatility. In this way, popular preference for simple music today predicts turbulent market activity in the future, while popular preference for complex music today predicts relatively calmer market activity in the future. Finally, musical preferences explain more than can be explained simply by mean reverting market volatility: popular music decisions contain additional information.

It's an interesting paper, and it's apparently been around in various forms for a while (see blog posts or articles talking about earlier versions of the paper here, here, and here). The author uses music data analysed by The Echo Nest on the average beat variance (which will be higher when there are lots of changes in speed or tempo), and compares it with the annual volatility of the S&P 500 index.

There are some interesting notes on artists in the results:

Among artists with at least five appearances on the charts, Ray Charles had the highest average beat variance of 0.1298, ranging from a low of 0.0390 to a high of 0.2860 in his eleven hits. Other artists who averaged a high beat variance are Barbra Streisand, Bobby Vinton, Alicia Keys, and Alice Cooper. These artists sang relatively volatile songs. At the other end of the list, Billy Idol had the lowest average beat variance of 0.0034, ranging from a low of 0.0020 to a high of 0.0050. Other artists who averaged a low beat variance are Ace of Base, Genesis, Al Green, and Bobby Brown. These artists sang relatively stable songs.

The lowest beat variance of any song was 0.0010. Sixty-five songs achieved this lowest level, including A-ha's 1985 hit "Take On Me."... A-ha's "Take On Me" occurred in the year with the most such low beat variance songs, two years before the high volatility market crash of 1987.

A-ha may have a lot to answer for in terms of boring repetitive music (if you don't know who A-ha are, this is the best summary), but this is the first time I've seen them linked to the 1987 stock market crash.

What's also great about this paper is that when you search for it online, you come across some really interesting things. Like this infographic that the author produced for the Boston Globe. Or this YouTube video which tracks the data over time (with musical accompaniment, of course).

The paper did make me wonder about what it means in the context of the Efficient Markets Hypothesis (EMH), which even in its weakest form suggests that asset prices (including stocks) incorporate all available public information about the stocks. Do we listen to simpler music when information about future returns is uncertain? Does this imply that future market volatility is also priced into asset prices? And of course, if you know what people are listening to now, can you use that to work out market volatility later? Unfortunately, if you read the paper carefully, you discover this point buried on the tenth page:

The only evidence of Granger-causality in either direction is a weak one (p-value of 8.9%) for a one-year lag that suggests that last year's average beat variance has some small predictive power about the future market volatility.

In other words, the entire paper is constructed around a weak correlation between the average beat variance in a given year and the market volatility in the following year. Moreover, while the paper shows some profit opportunities on the basis of predicting future market volatility, the profits become statistically insignificant when predicting out-of-sample.

So, it appears music may not soothe the savage stock market. The results don't establish cause (of course, and the author never claims they do). Damnit - I so wanted to be able to advocate a policy solution to excess market volatility that involved minimum content standards on radio for Tool, System of a Down, or Mastodon. [*]

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[*] Yes, there are better bands I could have chosen as examples of song complexity, and probably more complex songs by these three. But these ones came immediately to mind.