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]

Try this: Crash course economics

There is a new video series on YouTube called Crash Course Economics. The videos star Adriene Hill and Jacob Clifford, and are well worth looking at. Here's the first installment:

Enjoy!

[HT: Mark Johnston at Econfix]

Cost-benefit analysis of averting catastrophes just got a whole lot harder

I'm a bit late to this, given it has already been covered by Tyler Cowen and then by Eric Crampton. However, now that I've read the paper in the American Economic Review (ungated earlier version here) by Ian Martin (London School of Economics) and Robert Pindyck (MIT), I feel I can comment on it.

In the paper, the authors develop a mathematical theory of the costs and benefits of averting (or reducing the impact of) catastrophes (like viral epidemics, Nuclear or bioterrorism, climate change catastrophes, etc.). The core (and somewhat worrying) takeaway from the paper overall is that, in the presence of multiple potential catastrophes, a simple cost-benefit rule doesn't work:

Conventional cost-benefit analysis can be applied directly to “marginal” projects, i.e., projects whose costs and benefits have no significant impact on the overall economy. But policies or projects to avert major catastrophes are not marginal; their costs and benefits can alter society’s aggregate consumption, and that is why they cannot be studied in isolation...

When the projects are very small relative to the economy, and if there are not too many of them, the conventional cost-benefit intuition prevails: if the projects are not mutually exclusive, we should implement any project whose benefit wi exceeds its cost τi. This intuition might apply, for example, for the construction of a dam to avert flooding in some area. Things are more interesting when projects are large relative to the economy, as might be the case for the global catastrophes mentioned above, or if they are small but large in number (so their aggregate influence is large). Large projects change total consumption and marginal utility, causing the usual intuition to break down: there is an essential interdependence among the projects that must be taken into account when formulating policy.

The implications of this are pretty broad, including:

• The value (to society) of averting a catastrophe depends on what other catastrophes are being averted;
• It may be optimal not to avert some catastophes, even when averting those catastrophes might seem justified based on a naive cost-benefit evaluation;
• Deciding which catastrophe is the most serious and prioritising averting that one is not the optimal approach; and
• These results hold if there are many small catastrophes, as well as when there are fewer (but more serious) ones.

The authors conclude:

We have shown that if society faces more than just one catastrophe (which it surely does), conventional cost-benefit analysis breaks down; if applied to each catastrophe in isolation, it can lead to policies that are far from optimal. The reason is that the costs and benefits of averting a catastrophe are not marginal, in that they have significant impacts on total consumption. This creates an interdependence among the projects that must be taken into account when formulating policy.

All of which means that, because of the interdependence between these catastrophes (even if they are many and small), cost-benefit analyses of things like mitigating earthquake or tsunami risk just got a whole lot harder to do in a robust way.

A sugar tax wouldn't just be paid by the manufacturers

There is a very common misperception in the public about who pays the cost of excise taxes (taxes on the sale of goods or services). In most respects, it actually does not matter whether a tax is levied on the sellers (producers) or buyers of the product or service - the tax will be shared between both the sellers and the buyers.

As one recent example of this misconception, see this comment by Gwen in the NZ Herald Rants and Raves yesterday:

After reading the item in the Herald about introducing a sugar tax, I think surely the manufacturers are to blame, and therefore they should be paying a sugar tax, not the taxpayers who already have plenty of tax costs. Come on manufacturers, take a sugar pill and reduce sugar in all your products. Life is so sweet.

Unfortunately, if a sugar tax was introduced there is no way to ensure that it would only affect manufacturers. To see why consider the diagram below, which represents the market for some sugary food product (for simplicity, we'll assume that the sellers in this market are the manufacturers). With no tax, the market operates in equilibrium with the price P0 and the quantity of sugary food products traded is Q0.

Now say that the government introduces a tax - we'll assume it is what we call a 'specific tax', which is a constant per-unit amount (e.g. $1 per sugary food product). Let's say the government levies this tax on the manufacturer - the manufacturer must pay this tax to the government. The effect of this is like increasing the costs of supplying the market (because in addition to their usual costs of production, the manufacturer must now pay a tax for every unit of sugary food product they produce). To represent this on our market diagram, we create a new curve (S+tax), which represents the costs of supply (S) plus the cost to the manufacturer of the tax. In effect the S+tax curve is vertically above the supply (S) curve by exactly the per-unit dollar value of the tax.

With this new tax in place, the manufacturer will increase the price that they charge customers for the sugary food product, to PC. This is the new (higher) price that consumers pay for the product. The manufacturers receive that price, but then must pay the tax to the government, and the quantity of the good that is traded falls to Qt (note that this is likely to be the point of the sugar tax - to reduce consumption). The effective price that the manufacturer receives (after deducting the tax) is the lower price PP. The difference between PC and PP is the per-unit value of the tax. However, the important point here is that, even though the manufacturer is the one paying the tax to the government, the consumers pay part of the tax (the difference between PC and P0), and the manufacturers pay part of the tax (the difference between P0 and PP). It isn't possible to mandate that the manufacturers face the burden of the tax alone. In the diagram above, the manufacturers and the consumers have roughly equal shares of the tax burden.

In fact, it might be worse. There are some that argue that sugary products are addictive. If this were the case, we would expect demand to be relatively inelastic (demand would not respond much to price, because addicts will continue to buy roughly the same amount even if prices rise a lot), which leads to a demand curve that is relatively steep, as in the diagram below. Now think about the share of the tax burdens in this case. Notice that the price for consumers (PC) has increased significantly over P0, while the price for manufacturers (PP) has barely changed. The burden of the tax falls mostly on the consumers! And to make matters worse, the quantity of the sugary food product traded barely changes at all (falling from Q0 to Qt).

So while a sugar tax might be effective in reducing consumption, if sugary products are indeed addictive it would take a large sugar tax to have an effect on obesity and health (unless people switch from sugary food products to fatty food products instead!). Note that large excise taxes are what we currently apply to tobacco.

Finally, what happens if the tax is levied on consumers instead of manufacturers? To do this you would have to find some way of making the consumer pay the tax directly (rather than having it collected by the seller). One way is to require consumers to buy a time-limited licence (or some other document) allowing them to purchase a stated number of units of sugary food products. They buy this licence from the government (which is their tax payment), then take the licence to a seller to buy the product. Sellers would only be legally allowed to sell to licence-holders, and only the quantity that the licence permits. In diagrammatic form, it looks like the market below.

As before, with no tax the market operates in equilibrium with the price P0 and the quantity of sugary food products traded is Q0. With the tax, the net benefit of purchasing is lower for the consumer - this is similar to a decrease in demand. We represent this with a new curve (D-tax), which represents the benefits to consumer of the sugary food product (D) minus the cost of the tax (or licence to purchase). In effect the D-tax curve is vertically below the demand (D) curve by exactly the per-unit dollar value of the tax.

Note that the effects of the tax look identical to those in the first diagram in this post. The consumers pay a higher effective price (PC, which is made up of the PP they pay to the manufacturer, plus the amount paid to the government), the manufacturers receive a lower price (PP), and the government pockets the difference in prices. Quantity traded falls from Q0 to Qt.

However, we don't typically see taxes on consumers (rather than producers) because they are more difficult and costly to collect. It is relatively easy and cost-effective to collect taxes from sellers, because there are fewer of them (than buyers), and because they have to advertise where they are (otherwise buyers couldn't find them) it is easy for the tax collectors to find them.

Having said that, if you wanted to really increase the cost of sugary food products to consumers, making them buy a licence to purchase at a local government office before they can go to the store and buy a Snickers bar is certainly going to make many of them reconsider!