Bookies 1 Opinion Polls 0

The referendum campaign lasted more than 2 years. Over that time, more than 100 opinion polls addressed the question “should Scotland be an independent country”. Many thousands of pounds have been spent on collecting the data and analysing the results. Yet in the month of September, at the business end of the campaign, the average poll gave Yes  48 per cent support and No 52 per cent support, if don’t knows are excluded. The narrowness of the margin panicked politicians into making promises about further devolution that may be very difficult to keep. Yet the outcome was Yes 45 per cent, No 55 per cent.

Something clearly went wrong with the polls: this may have lain in their sampling, their weighting of the results or their ability to elicit truthful responses about voting intentions. Justin Wolfers has already noted the poor performance of the opinion polls in the Scottish referendum and suggested that pollsters might switch their attention to asking people who they think will win the election rather than asking how they intend to vote. This may result in both more honest and more thoughtful answers.

In May 27th 2014, building on the research of Wolfers among others, I published a paper, which referenced the strong performance of prediction markets relative to opinion polls. Based on this, using the results from 23 bookmakers, I calculated the implied probability of a No vote in the forthcoming referendum from April 2013 to May 2014. It was clear that the calculated probability suggested that the No camp would prevail but there was a clear, though delayed increase in support for Yes following Mr Osborne’s currency intervention. Subsequently support for No recovered and was unaffected by the first televised debate between Mr Salmond and Mr Darling in early August. However there was a substantial increase in support for Yes following the seconde debate in late August, which Mr Salmond was generally have thought to have won. By comparison, and partly due to different biases between the polling companies and their irregular timing, no clear response to these events was evident in the opinion polls.

Nevertheless, throughout these events, the market estimate of the probability of a No outcome only once fell below 60 per cent and that was following the currency announcement rather than in the run-up to the referendum itself. From the 1st to the 17th September, the probability of No hovered around 75 per cent and started to increase as the window of opportunity for new information to significantly shift the polls disappeared.

I commented on these trends here, here, here, here and here. And as the referendum approached, using data from the betting market on the outcome of the referendum, I predicted that the outcome would be a No vote of 46.5 per cent (and implicitly a Yes vote of 53.5 per cent) (see below).  The outcome, as stated above, was a Yes vote of 45 per cent and a No vote of 55 per cent.

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Given that the empirical evidence in general, and this case in particular, shows the prediction markets perform at least as well, if not better than the opinion polls (and cost much less), perhaps they will be taken more seriously during future British electoral contests.

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Final polling and betting data

The implied probability of a No vote based on bookmakers odds up to 7pm on the 17th of September and the opinion poll probabilities of a No outcome (eliminating the don’t knows) are shown in Figure 1 below. The odds on a No outcome shortened throughout the 17th. The final observation was taken at 7pm.

A number of opinion polls were  also published on the 17th. They tended to show the No campaign having a tiny lead over the Yes campaign. Once the standard errors and the possible impact of the undecided voters are taken into account, there would seem to be little to choose between the likelihood of a Yes or No outcome. Yet this contradicts the bookmakers assessment of the odds, with the implied probability of a No vote now creeping up to 80 per cent.

Figure 1: Opinion Poll and Betting Market Implied Probability of a No vote

both_combined_17-09-14

Sources: What Scotland Thinks, Oddschecker.com, own calculations

A betting market on the share of Yes votes in the referendum is also open. The distribution of these is shown in Figure 2. The most likely range of Yes votes is 45-49 per cent. The chance of an outcome above 50 per cent (a Yes win) is 0.15, which is consistent with the overall odds of a Yes outcome, which can be deduced from Figure 1. However, the implied probability of Yes outcomes in the 35 to 44 per cent range is over 0.4, higher than the probability of a Yes win.

Figure 2: Likely Yes Vote Percentage

Majority

Sources: Oddschecker.com, own calculations (omitting overlapping intervals)

Nevertheless, taken together, the evidence from the betting odds is suggestive is of a No victory with a majority of between between 2 per cent and 10 per cent.

Finally, a market has developed in the local authorities most likely to vote No. These are mainly dominated by the more affluent areas, those close to the Scottish-English border and interestingly, Orkney and Shetland, which are located close to Scotland’s main oil fields.   These are closely followed by Edinburgh, Scotland’s capital city. Clearly a Yes outcome where Edinburgh votes No would also pose significant political challenges.

Those areas least likely to vote No include Scotland’s more depressed former industrial cities – Dundee and Glasgow. These are joined by a group of authorities in central Scotland and the Western Isles (Na h-Eileanan Siar), which has always had close ties with Scottish nationalism.

Figure 3: Area Most Likely to Vote No

Area Most Likely NoSources: Oddschecker.com, own calculations

The probabilities implicit in the betting odds provide an interesting set of predictions for the outcomes of the referendum. But they are just predictions: nothing more, nothing less. What will be fascinating in the post-referendum analysis is how they perform compared with the opinion polls. This referendum has produced a wealth of data and a unique challenge to both methods of foretelling the outcome.

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Last labour market data for Scotland before the referendum

Today (Wednesday), the Office for National Statistics posted the final set of labour market data for Scotland that will be released before the referendum. So how is Scotland faring?

Scotland’s unemployment rate for the period May-Jul 2014 was 6 per cent. This was a good performance in both an historical and a comparative sense. Figure 1 shows the unemployment rate for Scotland from 1992 to 2014. The unemployment rate peaked at 8.9 per cent in June 2010. Since then unemployment in Scotland has fallen by 33 per cent.

Over this period, which straddles the establishment of the Scottish Parliament, the main event impacting on unemployment was the financial crisis of 2008, which led to a rapid rise in unemployment.  Since then, as the economy has recovered from recession, the Scottish unemployment rate has dropped sharply.

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Eyes on Thursday night’s results

Normally when watching election results come in, there are a few well known “bell-weather” results from which the overall result can be gauged. For the Independence Referendum though, what do we look for as the early results are announced (council by council) to forecast the overall Yes or No result?

Based on the General Election 2010 results, the Arc of Prosperity blog makes some reasonable assumptions to calculate a propensity to vote Yes or No for each local authority. The assumptions made are not so important, they just need to be reasonably correlated with the propensity to vote Yes or No, and be consistent across council areas. I’ve reweighted the propensities to show the percentages required in each council area for a 50:50 result , assuming relative populations from wikipedia and, obviously, the same percentage turnout in each council area.

This is just a quick and dirty calculation – just a bit of fun for Thursday night (as if we needed any more excitement!) The percentages for Yes in each council area consistent with a 50:50 result are in the table below. At 50.3% for a 50:50 result, the results from Glasgow and Fife look like being indicative of the overall result.

Council Population % Yes % req. for 50:50
Aberdeen 4.2% 48.4%
Aberdeenshire 4.7% 52.3%
Angus 2.1% 56.3%
Argyll and Bute 1.7% 52.3%
Clackmannanshire 1.0% 54.3%
Dumfries and Galloway 2.8% 42.4%
Dundee 2.8% 55.3%
East Ayrshire 2.3% 54.3%
East Dunbartonshire 2.0% 43.4%
East Lothian 1.9% 48.4%
East Renfrewshire 1.7% 39.5%
Edinburgh 9.3% 42.4%
Falkirk 2.9% 53.3%
Fife 7.0% 50.3%
Glasgow 11.4% 50.3%
Highland 4.2% 53.3%
Inverclyde 1.5% 48.4%
Midlothian 1.6% 52.3%
Moray 1.7% 59.2%
Na h-Eileanan an lar 0.5% 57.3%
North Ayrshire 2.6% 52.3%
North Lanarkshire 6.3% 52.3%
Orkney Islands 0.4% 55.3%
Perth and Kinross 2.8% 50.3%
Renfrewshire 3.3% 51.3%
Scottish Borders 2.2% 46.4%
Shetland Islands 0.4% 55.3%
South Ayrshire 2.1% 42.4%
South Lanarkshire 6.0% 50.3%
Stirling 1.7% 46.4%
West Dunbartonshire 1.7% 55.3%
West Lothian 3.3% 54.3%
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A conversation, between economists, on the economics of independence

Surely there are solid arguments for negative effects from being a small country relative to being a large country? Economies of scale, the existence of border effects, liquidity premia, and so on?

Yes. Economic theory has proposed many plausible mechanisms that mean that large size should be associated with greater productivity and greater wealth. Further, when attempts are made to estimate the size of these effects, they turn out to be not insignificant. For example, see my own work which suggests that if the only change on Scottish independence were that it traded with the rest of the UK in the way that Ireland seems to trade with the UK, then this should be associated with a 5.5% fall in Scottish GDP.

However, these effects apply to all countries, not just Scotland, and if this were all that was going on then we should expect to see larger countries richer than smaller countries. As shown by Rose (2006), the economic literature on this generally finds no effect of size on growth or level of income (some papers even find a negative correlation e.g. Alouini & Hubert (2010)). This null result can be explained by supposing that there are non-GDP benefits of independence and richer and more productive regions, which can afford the trade-off, choose independence. This selection effect would mask the true relationship between size and GDP.

This selection effect however does not convince me. Given the persistence of national borders, then the randomising effect of technological change on productivity of different regions over time should mean that a small productive region which made the choice to be independent several hundred years ago is expected to be no more or less productive than another region that was poor several hundred years ago and made the choice to remain as part of a large country. Given random productivities, the benefits of size should be visible. They are not.

This either means that the benefits of size are wrong (I don’t believe this) or that there are countervailing effects. Perhaps small countries are better run or function at a more appropriate scale (convex costs of complexity?). Perhaps there are spillover benefits to running a country rather than being a peripheral region of a larger country like the ability to attract talent (high status government employment, and many international firms want at least a small office presence in your region) which leads to a more diverse business ecology, which involves the provision of the full range of support services that new and growing businesses require.

In any case, if the correlation between size and income is approximately zero, then it suggests that the (GDP-related) costs and benefits of size roughly cancel out. This does not, itself, provide a case for independence or for union. It just suggests that if we value independence for other, non-GDP reasons, then there does not appear be any significant GDP cost/benefit to pay/gain in general. Of course, there may be issues specific to Scotland and the UK could lead to the expectation of GDP costs or benefits of independence.

If there is no relationship between country size and long run growth/wealth then surely this is bad for independence, given transition costs?

Usually, yes. But Scotland already has most of the infrastructure of a state. HMT’s estimates of the transition costs were rubbished by the author whose research they relied upon. In any case, even if HMT’s figures were appropriate, this is a one off cost which should be met by extra government borrowing and amortised over a very long period. If we, extremely pessimistically, assume £3bn cost at 5% borrowing rate, then this is an annual cost of £150m or 0.1% of GDP. This is not a big issue.

Lumping lots of disparate countries together produces this zero correlation between size and income. Would it not be more valid to consider subsets of reasonably similar polities? For example biggest is richest for Spanish-speaking Latin American countries (excluding Puerto Rico which is really part of the United States). And for English-speaking countries, the largest, the USA, stands out as the richest, in spite of the fact that it does not appear to have better institutions or national endowments per capita than Canada, Australia or New Zealand.

Interesting points. I’m glad you thought of making comparisons across countries which, other than size, have some similarities. I contend that a suitable comparison group for looking Scotland and the UK is the EU members of northern Europe which have never been communist. For these 11 countries (Ireland, UK, France, Belgium, Luxembourg, Netherlands, Germany, Austria, Denmark, Sweden, & Finland), there is a significantly negative correlation between size and income. Set against the Spanish speaking Latin American countries, or the worldwide English speaking countries, this isn’t something that nails the argument – but it does show that your other two examples certainly don’t nail the argument either.

More interestingly, looking at these countries may allow us to make a specific point about Scotland and the UK rather than considering only the general size of countries issue. Eurostat has data that divides these countries up into 48 “NUTS1 regions” (*). These are shown in the graph below. I know of no reason to expect that 7 of the 12 UK regions should occupy the bottom 7 places in the ranking, with 11 of the 12 in the bottom half. The UK is not less fertile, it is not landlocked, nor is it lacking in natural resources (indeed it has the largest oil and gas reserves of any of these 11 countries). This may be indicative of institutional problems in how the UK is run: perhaps to the benefit of London which is one of the richest regions in Europe, despite the poverty of the rest of the UK (indeed, the UK has the highest regional inequality in Europe) [though France is also a centralised state and German decentralisation may be more symbolic than real]. If there is only an institutional reason, rather than some structural or fundamental reason, for the low position of all the regions in the UK other than London and its environs in this ranking, then institutional change (such as independence or radical devolution/federalism) may be accompanied by an expectation that Scotland can gain – in GDP terms. This is of course in addition to the non GDP benefits of  this institutional change, like electing political parties more closely aligned with preferences of the Scottish electorate.

(*) All NUTS1 regions of these 11 countries excluding 1 region from France: French overseas territories – not in northern Europe; and 6 regions from Germany: the East German Länder – formerly communist.
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Why are the opinion polls and the bookies odds so different?


The latest odds (Sunday 14th September) show that the implied probability of a No vote, based on the odds offered by 24 bookmakers up to midday on Sep 14th have stabilised at around 0.8. To find out how I calculate these odds, see here.

The market estimates of the probability of a No vote are consistently higher than the opinion polls suggest.  Figure 1 shows the estimated probability of a No vote from the opinion polls and the bookmakers odds for the period from 1st March 2014 to 14th September 2014. The latest data show that the bookmakers odds suggest an 80 per cent chance of a No outcome, while the opinion polls are close to evens – a 50 per cent chance of a No vote.

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Latest Odds: Increased Chance of No Vote

The betting odds have changed once more.  They fell substantially from the 24th of August to the 9th of September. The implied probability of a No vote fell from 0.85 to 0.68. But between the 9th and the 12th of Sptember, there has been a substantial rebound, increasing to 0.79 at midday on the 12th of September.

betp_final_12-9-2014

 

The odds change in the light of new information. The decline in late August and early September perhaps reflects Mr Salmond’s success in the second televised debate which, in turn, led to a considerable narrowing of the margin between Yes and No in the opinion polls.

However, a concerted effort by the Labour Party, including Mr Brown, followed by the visit of all three main party leaders to Scotland may have reversed the upward momentum of the Yes campaign. Further, statements made by the banks and various prominant business leaders may also have pushed up the probability of a No outcome in the eyes of punters.

Clearly, this recent pattern shows that the odds are hugely volatile.  Further reversals are quite possible. I will continue to monitor their progress.

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Poll panic

As the polls tighten, there is some market reaction. The BBC reports that “The value of the pound has fallen … by about 1.3% against the US dollar to a 10-month low of $1.61. Shares in some firms with Scottish links have also fallen.”

Over the weekend, YouGov reported the first independently commissioned poll since the referendum was announced that showed Yes in the lead. So the market reaction can be gauged by comparing the close price on Friday 5th September, with the close price on Monday 8th September. However, headline numbers overstate this reaction, since there was a wider market fall than just relating to the independence referendum.

To quantify the “indyref component” we can perhaps construct an “exposed portfolio” and a “counterfactual portfolio”. This is just some informal, back-of-the-envelope analysis, so the method of constructing these portfolios is not at all scientific. Suppose we buy a $100 portfolio at the Friday close price consisting of 50% currency and 50% equity, and sell at the Monday close price. Our exposed porfolio could be Sterling plus Standard Life, RBS, Lloyds and SSE. A counterfactual portfolio could be the Euro plus Aviva, Barclays, HSBC and Centrica (so that all 4 of the Big 4 banks, and the top 2 of the Big 6 energy companies are represented). The selling price of the exposed portfolio was $97.99 compared with $99.30 for the counterfactual portfolio[1].

Sterling fell 1.0% against the dollar, while the Euro only fell by 0.1%. The “exposed” equities fell 3.1% while the “counterfactual” equities only fell 1.3%. Overall then there does seem to be a market reaction in response to the opinion poll changes – but the changes reported in the media are not wholly due to this. We might have expected the “exposed” equities to fall by 1.3% anyway, and the opinion poll only accounts for the additional 1.7% fall, not the full 3.1% fall.

If we suppose that the markets are now pricing in the impact of a Yes vote at the probabilities implied by the YouGov (or the TNS poll last night), approximately 50:50, then we may expect a similar market fall – to the additional falls over and above the counterfactual falls – if a Yes vote is realised.

[1] All data from http://markets.ft.com/research/Markets

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Latest Odds

The latest odds show that bookmakers are responding to the opinion polls by shortening the odds on a Yes outcome and lengthening the odds on a No vote. Their implied assessment of the probability of a No (Yes) outcome has therefore been plumetting (rising rapidly). The implications for the likelihood of a No vote are shown in Figure 1, which reflects data up to 11am on September 8th.

Figure 1: Implied Probability of a No vote based on odds offered by bookmakers on Yes and No outcomes.

betp_final_all_8-9-2014

 

 

It is interesting that the odds do not yet show that the probability of Yes and No outcomes to be evenly balanced, as is the case with the opinion polls. This would require the probability of a No vote to fall to 0.5, rather than its latest value of 0.67.

Are the opinion polls correctly anticipating the outcome of the referendum, or are the betting public discounting the patest poll results or expecting a late rebound for the No campaign? The current odds suggest that punters are still, on average, putting their money behind a No outcome rather than a Yes outcome.

Whatever else may happen, this referendum will provide an invaluable test of the predictive ability of opinion polls on the one hand and betting markets on the other.

 

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Increased probability of a Yes vote

There has been a substantial increase in the probability of a Yes vote in the referendum. This conclusion is based on bookmakers’ odds over the last week. Over this period the probability of a No vote has dropped from 85% to 75% (and that of a Yes increased from 15% to 25%), the most rapid decline seen since Mr Osborne made his infamous currency announcement in February 2014. The decline is probably associated with the latest televised referendum debate in which Mr Salmond is thought to have won a decisive victory. Figure 1 tracks the probability of a No vote as implied by the odds on both No and Yes being offered by 23 bookmakers on a daily basis.

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