Yearly Archives: 2009

Crime Around The Corner

Observant visitors to this blog may have noticed the recent appearance of a “wiki” button at the top of the page. This links to the recently established Stubborn Mule wiki, which I plan to use as a repository of information relevant in some way to the blog. Since so many of the posts here focus on data analysis, I have started with a collection of links to useful sources of data online, particularly economics and finance data.

The latest link I have added is to the New South Wales Bureau of Crime Statistics & Research (while I did not include it in the economics and finance section, maybe it does belong there). This site includes a research data set which provides monthly crime data going back to 1995 broken down by local government (council) area and offence type. Needless to say, the first thing I was interested to learn was the level of criminality in my own local area, particularly as I moved here only very recently.

The chart below shows the total number of crimes in the various offence categories for 2008 in my local government area of Marrickville. While I was not surprised to see theft coming in at the top of the list, there were a few oddities further down. I was initially surprised to see driving offences at the bottom of the list. My driving is, of course, impeccable but I do not know if the same is true of all of my neighbours, not to mention visitors to the area. Digging further, I discovered that from 2003 onwards*, the figures for driving offences have been zero for all areas and transport regulatory offences have leapt up. So, presumably there has been a classification change. One mystery solved.

Marrickville Crime Count (2008)

More intriguing is blackmail and extortion. Until 2008, the highest rate this crime had reached in Marrickville was four cases per year and in three years, the figure was zero. Yet, in 2008, there were nine cases of blackmail and extortion. What lies behind this wave of blackmail around the corner? Mystery not solved.

This led me to examine other trends through time. Starting with theft, I was gratified to learn that 2008 was the lowest year for theft since these records began. I am hoping 2009 will be lower still.

Occurrences of Theft in Marrickille

A look at prostitution also suggests the area has become more law-abiding after a significant spike in offences in 2001.

Occurrences of Prostitution Offences in Marrickville

As for serious crime, Marrickville experienced three homicides in 2008. The total number of homicides in the area since 1995 is 66, putting Marrickville in a somewhat disturbing 14th place out of 155 local government areas, although these two have been reducing over recent years. For those interested in the most murderous areas in New South Wales, here is a list of the top five areas in terms of total homicides since 1995. Any country readers will note that all of these local government areas are in Sydney (the area in the table labelled “Sydney” encompasses only the central business district and some inner-city suburbs).

Area	Homicides
Fairfield	242
Sydney	327
Blacktown	136
Liverpool	102
Parramatta	82

* The historical data for Marrickville is in the “Files” section of the blog.

Is There a Baby Bounce?

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In this first ever guest post on The Stubborn Mule, Mark Lauer takes a careful look at the relationship between national development and fertility rates.

Recently The Economist and the Washington Post reported a research paper in Nature on the relationship between development and fertility across a large number of countries. The main conclusion of the paper is that, once countries get beyond a certain level of development, their fertility rates cease to fall and begin to rise again dramatically. In this post I’ll show an animated view of the data that casts serious doubt on this conclusion, and explain where I believe the researchers went wrong.

But first, let’s review the data. The World Bank publishes the World Development Indicators Online, which includes time series by country of the Total Fertility Rate (TFR). This statistic is an estimate of the number of children each woman would be expected to have if she bore them according to current national age-specific fertility rates throughout her lifetime. In 2005, Australia’s TFR was 1.77, while Niger’s was 7.67 and the Ukraine’s only 1.2.

The Human Development Index (HDI) is defined by the UN as a measure of development, and combines life expectancy, literacy, school enrolments and GDP. Using these statistics, again from the World Bank database, the paper’s authors construct annual time series of HDI by country from 1975 until 2005. For example, in 2005, Australia’s HDI was 0.966, the highest amongst all 143 countries in the data set. Ukraine’s HDI was 0.786, while poor old Niger’s was just 0.3.

A figure from the paper was reproduced by The Economist; it shows two snapshots of the relationship between HDI and TFR, one from 1975 and one from 2005. Both show the well-known fact that as development increases, fertility generally falls. However, the 2005 picture appears to show that countries with an HDI above a certain threshold become more fertile again as they develop further. A fitted curve on the chart suggests that TFR rises from 1.5 to 2.0 as HDI goes from 0.92 to 0.98.

Of course, this is only a snapshot. If there really is a consistent positive influence of advanced development on fertility, then we ought to see it in the trajectories through time for individual countries. So to explore this, I’ve used a Mathematica notebook to generate an animated bubble chart. The full source code is on GitHub, including a PDF version for anyone without Mathematica but still curious. After downloading the data directly from Nature’s website, the program plots one bubble per country, with area proportional to the country’s current population.

Unlike with the figure in The Economist, here it is difficult to see any turn upwards in fertility rates at high development levels. In fact, the entire shape of the figure looks different. This is because the figure in The Economist uses axes that over-emphasise changes in the lower right corner. It uses a logarithmic scale for TFR and a reflected logarithmic scale for HDI (actually the negative of the logarithm of 1.0 minus the HDI). These rather strange choices aren’t mentioned in the paper, so you’ll have to look closely at their tick labels to notice this.

To help focus on the critical region, I’ve also zoomed in on the bottom right hand corner in the following version of the bubble chart.

One interesting feature of these charts is that one large Asian country, namely Russia, and a collection of smaller European countries, dart leftwards during the period 1989 to 1997. The smaller countries are all eastern European ones, like Romania, Bulgaria and the Ukraine (within Mathematica you can hover over the bubbles to find this out, and even pause, forward or rewind the animation). In the former Soviet Union and its satellites, the transition from communism to capitalism brought a crushing combination of higher mortality and lower fertility. In Russia, this continues today. One side effect of this is to create a cluster of low fertility countries near the threshold HDI of 0.86 in the 2005 snapshot. This enhances the impression in the snapshot that fertility switches direction beyond this development level.

But the paper’s conclusion isn’t just based on these snapshots. The authors fit a sophisticated econometric model to the time series of all 37 countries that reached an HDI of 0.85, a model that is even supposed to account for time fixed-effects (changes in TFR due only to the passage of time). They find that the threshold at which fertility reverses is 0.86, and that beyond this

an HDI increase of 0.05 results in an increase of the TFR by 0.204.

This means that countries which develop from an HDI of 0.92 to 0.98 should see an increase in TFR of about 0.25. This is only about half as steep as the curve in their snapshot figure, but is still a significant rate of increase.

However, even this rate is rather surprising. Amongst all 37 countries, only two exhibit such a steep rise in fertility relative to development between the year they first reach an HDI of 0.86 and 2005, and one of these only barely. The latter country is the United States, which manages to raise TFR by 0.211 per 0.05 increase in HDI. The other is the Czech Republic, which only reaches an HDI of 0.86 in 2001, and so only covers four years. Here is a plot of the trajectories of all countries that reached an HDI of 0.86, beginning in the first year they did this. Most of them actually show decreases in TFR.

So how do the authors of the paper manage a statistically significant result (at the 0.1% level) that is so widely different from the data? The answer could well lie in their choice of the reference year, the year in which they consider each country to have passed the threshold. Rather than using a fixed threshold as I’ve done above, they express TFR

relative to the lowest TFR that was observed while a country’s HDI was within the window of 0.85–0.9. The reference year is the first year in which this lowest TFR is observed.

In other words, their definition of when a country reaches the threshold depends on its path of TFR values. In particular, they choose the year when TFR is at its lowest.

Does this choice statistically bias the subsequent trajectories of TFR upwards? I leave this question as a simple statistical exercise for the reader, but I will mention that the window of 0.85–0.9 is wider than it looks. Amongst countries that reached an HDI of 0.9, the average time taken to pass through that window is almost 15 years, while the entire data set only covers 30 years.

Finally I’d like to thank Sean for offering this space for my meandering thoughts. I hope you enjoy the charts. And remember, don’t believe everything you see in The Economist.

UPDATE:

To show that the statistical bias identified above is substantial, I’ve programmed a quick simulation to measure it. The simulation makes some assumptions about distributions, and estimates parameters from the original data. As such it gives only a rough indication of the size of the bias – there are many alternative possibilities, which would lead to larger or smaller biases, especially within a more complex econometric estimation.

In the simulation, each of the advanced countries begins exactly where it was in the year that it first reached an HDI of 0.85. Thereafter, a trajectory is randomly generated for each country, with zero mean for changes in fertility. That is, in the simulation, fertility does not increase on average at all¹. As in the paper, a threshold is found for each country based on the year with lowest TFR within the HDI window. All shifts in TFR thereafter are used to measure the impact of HDI on TFR (which is actually non-existent).

Here is a sample of the trajectories so generated, along with the fitted response from the paper.

The resulting simulations find, on average, that a 0.06 increase in HDI leads to an increase of about 0.075 in TFR, despite that fact that there is no connection whatsoever. The range of results is quite broad, with an increase of 0.12 in TFR also being a likely outcome. This is half of the value found in the paper; in other words, simulations of a simplified case where HDI does not influence TFR at all, can easily generate half of the paper’s result.

Of course, if the result is not due to statistical bias, then the authors can easily prove this. They need only rerun their analysis using a fixed HDI threshold, rather than one that depends on the path of TFR. Until they do, their conclusion will remain dubious.

¹ For the technically minded, the HDI follows a random walk with drift and volatility matching those of advanced countries, and the TFR follows an uncorrelated random walk with volatility matching the advanced countries, but with zero drift. The full source code and results have been uploaded to the Github repository.

FURTHER UPDATE:

More details can be found in the follow-up post to this one, Fertility Declines Don’t Reverse with Development.

The Muddle of Macroeconomics

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I never formally studied any economics at school or university, but in the years since I have become increasingly interested in the subject. I am sure that is evident from many of the posts here on the Stubborn Mule. What I did study was mathematics and, although there can be internal debates within the subject of mathematics, in the end it is usually clear what is right and what is wrong. No such luck in economics, particularly when economists attempt to understand the working of the world from the broadest perspective: macroeconomics. The level of controversy, debate and antagonism in the field of macroeconomics is quite extraordinary.

In July, The Economist’s cover story asked what was wrong with the field of economics. The leader was accompanied by an article entitled The other-worldly philosophers, which narrowed in on macroeconomics. It quotes Willem Buiter of the London School of Economics describing macroeconomics as a “costly waste of time”, while prominent economist Paul Krugman described most macroeconomics of the past 30 years as “spectacularly useless at best, and positively harmful at worst”. The article goes on to explore the tensions between free-market supporting “freshwater economists” and the more interventionist “saltwater economists”. Following a detente of sorts over recent years, the global financial and economic crisis has inflamed the antagonism once more.

In the May issue of The Monthly Magazine, former banker and author of “The Two Trillion Dollar Meltdown”, Charles R Morris wrote of macroeconomics:

macroeconomics is not a science. Its methods are gross and error-prone, and its models of economic reactions bear only a distant relationship to those in the real world. The theoretical apparatus of economics – its ‘laws’ – are mostly imaginative constructs that can rarely be confirmed with any precision, and stem more often from ideologies than from careful observation.

The issue of ideology is a crucial one. Any macroeconomic theory has implications for government policy, particularly monetary and fiscal policy. Further, almost all monetary and fiscal policy, even “doing nothing” has implications for wealth transfer from one segment of society to another. All things being equal, high interest rates are bad for borrowers and good for depositors. Inflation is good for borrowers and bad for lenders (update: this is really an over-simplification: see comments below). Some policies may benefit wage earners, but create costs for businesses, others may help importers but hinder exporters. With so much real money at stake, it is no wonder that ideological biases are so significant.

Once much of this debate would have been carried to the halls of academia, only reaching the rest of us in the form of those ideas which filtered through to influence the government of the day. These days it is all readily accessible online to anyone who is interested and many of the participants engage directly with the public on their blogs. I do not pretend to have all the answers (or even very many answers), so for now I will simply list just a few of the blogs and websites I have come across in my own quest to better understand this contentious field of study.

Billy Blog

Bill Mitchell is a professor in economics at the University of Newcastle (Australia). He describes himself as a “modern monetary theorist” and focuses on the mechanics of money. On his blog, he argues forcefully that much of the thinking of mainstream macroeconomics, particular that of a neo-classical bent, has not come to terms with the implications of “fiat money” and are steeped in gold standard thinking. This position leads him to advocate strongly for the importance of government spending, particularly to support full employment, and dismiss concerns about budget deficits threatening government solvency. While this may sound Keynesian, Mitchell dislikes the The General Theory of Employment, Interest, and Money and distances himself from aspects of Keynesian thinking which can itself be caught up in misunderstandings of the mechanics of money. While Mitchell does not shy away from expressing his ideological views, he would also argue that his thinking does indeed begin with careful observation.

The Conscience of a Liberal

With the Nobel Prize for Economics in 2008 and a number of popular books under his belt, Paul Krugman is the best known of the economists in this list. Krugman’s approach to macroeconomics is more firmly in the Keynesian tradition than Mitchell’s and he has been a passionate advocate online and on television for extensive economic stimulus packages, as well as an ardent critic of much of the way that bailout of US banks was handled. Like Mitchell, Krugman dismisses concerns about escalating government debt.

Maverecon

Having been a member of theBank of England’s Monetary Policy Committee, Willem Buiter has direct experience of the real world operation of monetary policy. In his blog he criticises the whole enterprise of macroeconomics, attacking both the neo-classical and the neo-Keynsian schools of thought. Buiter has more time for “heterdox” economic thought that attempts to deal with the messier realities of the economy, such as inefficient markets, illiquidity and irrational behaviour.

Von Mises Institute

Many economists, Krugman included, dismiss the Austrian school of economics as an oddball fringe distraction from the real business of economics. However, the Austrian way of thinking has a surprisingly strong hold on the thinking of a number of people outside the economics profession. I suspect that this is due, in part, to the fact that a number of the school’s classic books such as Hazlitt’s “Economics in One Lesson”, are easily accessible to non-economists. Among the recurring themes of the Austrian school are the evils of fiat money, fractional reserve banking and the intervention of central banks in free markets. While many of their arguments that get them to these stark conclusions initially have superficial appeal, I have not found that they stand up to closer scrutiny. Presumably this is why they are not taken very seriously by most professional economists. Either that or all professional economists are either deluded fools, or swayed by vested interested or both, which I am sure would be the Austrian’s counter-argument. Indeed, another thread running through the Von Mises Institute blog and other Austrian school writings is an acrimonious tendency to ad hominem attacks on their opponents, particularly Krugman.

Econbrowser

Written by James D. Hamilton, Professor of Economics at the University of California, San Diego and Menzie Chinn, Professor of Public Affairs and Economics at the University of Wisonsin, this blog has a strong focus on data analysis, which clearly appeals to me. Nevertheless, their attitude towards government debt does show signs of the sort of gold standard thinking that Bill Mitchell criticises.

The Daily Reckoning and Money Morning

I have grouped these two blogs together as they seem to share a number of contributors and have a similar style and outlook. Many of the writers are Austrian school fellow travellers and like nothing more than a rant about the evils of fiat money, except perhaps a rant on why the banking system is a giant Ponzi scheme. I primarily visit these sites if I am looking for a bit of an adrenaline boost or an argument.

Steve Keen’s Debtwatch

Steve Keen is another iconoclastic opponent of neo-classical economics. His book Debunking Economics was an attack on the traditional underpinnings of neo-classical macroeconomics. Most of the writings on the blog focus more on his concerns about the growth in private sector debt in Australia and the US. The concerns lead him to his pessimistic view of the prospects for the Australian housing market, a view he is best known for in the mainstream press and one I have discussed elsewhere.

Photo credit: p22earl on flickr (cc licence).

How Important Is China?

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Today I attended a presentation by TD Securities global strategist Stephen Koukoulas. While exploring the “green shoots” of recovery, Koukoulas made an interesting observation about China. Many observers of the Australian economy, Reserve Bank governor Glenn Stevens included, place great weight on the importance of China for Australia’s economy. But Koukoulas pointed out that, while exports to the US make up over 20% of Canada’s GDP, Australia’s exports to China only contribute 3% of GDP. In fact, the Australian Capital Territory (ACT) contributes more to GDP than China does.

As soon as I got back to my desk, I went straight to the Australian Bureau of Statistics to confirm these figures. Sure enough, merchandise exports to China for the 12 months to March 2009 were 3.1% of seasonally adjusted GDP, while the contribution of the ACT to GDP was 3.2%. So far, so good, but a historical perspective is revealing.

Australian Annual Exports to China

While the contribution of Chinese exports is still relatively small, it has been accelerating over the last few years. Over the 12 months to March 2009, Chinese exports grew by 0.8%, so they were a significant contributor to economic growth, despite the low base. Not surprisingly, China has been taking a growing share of total Australian exports over this period.

China’s Share of Total Australian Exports

As for the nation’s capital (and surrounds), on current trends, it will not exceed China for very much longer.

ACT versus Exports to China

Of course, these figures do not disentangle volume and price effects and whether or not China’s own growth will remain strong enough to keep pushing our exports up is an interesting question. But, based on these charts, I can understand why Glenn Stevens considers China so important for an economic recovery.

Note: the code used to produce these charts is available on github.

Taking It Too Far: Verb and Adjective Clouds

Malcolm Turnbull’s Word Cloud

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My last post looked at the favourite words of Australia’s prime minister, Kevin Rudd. In the interests of balance, I will now turn the word cloud lens onto the opposition leader, Malcolm Turnbull. Turnbull’s speeches are conveniently assembled online and the graphic below illustrates the frequency of his words from speeches made in 2009. Unlike the analysis of Rudd’s speeches, this analysis does include some speeches given in parliament.

Just like Rudd, Turnbull’s favourite word is “Government”, and “Australia” is not far behind. But from there, differences appear. The word “billion” is far more prominent, reflecting the opposition leader’s obsession with growing public debt. The appearance of “Rudd”, “Labor” and “Coalition” clearly reflect the realities of life in opposition where so much time is taken attacking the other side.

Interestingly, the word “emissions” is clearly visible in the cloud, whereas nothing relating to climate change was visible in Rudd’s cloud.

“Now” is as prominent as Rudd’s “also”. Does this reflect a constant sense of urgency from a man of little patience?

What is Kevin Saying?

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Last week, Politico published an analysis of Barack Obama’s language. The words he used most often were “America”, “Health” and “Economy” (Politico included “American” in the count along with “America”). This prompts the obvious question: what are the favourite words of our own Kevin Rudd?

Fortunately, the prime minster’s website publishes transcripts of all Kevin’s public utterances (although this does not include his speeches in parliament). There is a lot there and the Stubborn Mule was lucky enough to have OldFuzz do the hard work, assembling over 400 pages of text constituting Kevin Rudd’s speeches from 2009. If he has the time and inclination, prior years may follow. And here is what it looks like as a word cloud.

It is no surprise that, just as Barrack Obama is fond of saying “America” and “American”, so too Kevin Rudd likes to say “Australia” and “Australian”. He also throws in “Australians” reasonably frequently. It seems in keeping with his public servant mandarin style that Rudd uses the word “Government” more liberally than does Obama. While “global”, “world”, “national”, “economy” and “economic” are all appropriately big-picture words for a prime minister to be using.

There are a few intriguing words looming from the cloud. It seems that Mr Rudd says “also” a lot. Given that this analysis is case sensitive*, we can also glean that Rudd frequently starts his sentences with the word “Building”. It may seem fleeting strange that the word “cent” appears so prominently, but then again it is matched in size by the word “per”, so we are just seeing common use of “per cent” not some homespun wisdom about watching the small denominations of money.

So, peruse the cloud at your leisure and make of it what you will. Of course, please share your thoughts in the comment section below.

UPDATE: an abridged version of this post has appeared on The Punch.

* Here is a case-insensitive version of the word cloud.

Where Have the Fish Come From?

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After reading my posts on the international arms trade, a friend thought I might be interested in some data on the international trade in fish. While I know almost as little about fish as about arms, I always welcome good data. The data in question is published by the Food and Agriculture Organization (FAO) of the United Nations. The FAO also hosts FAOStat, which looks like an interesting data repository. If I can get myself a subscription to this service, it may provide the subject matter for future posts on the Mule.

But back to the fish. The first point my correspondent made was that many fish exporters are also importers. Among the top 50 importers of fish, all but 16 countries also appear in the list of the top 50 exporters. The chart below* gives an indication of the relative scale of fish imports and exports in 2006 of the top 10 importing countries. Of these big importers, only China and Denmark export even more fish than they import.

Fish Trade by the Top 10 Importers (2006)

But the real mystery my fishy correspondent alerted me to is the difference between total worldwide imports and exports of fish. According to the figures, total worldwide imports of fish amounted to US $89.6 billion while exports only amounted to US $85.9 billion. That would appear to mean that US $3.7 billion worth of fish was imported in 2006 from nowhere! While I am sure that statistics of this kind may not be too accurate, the report does report each country’s trade figures to the nearest US $1000, so it seems to be a big difference. I speculated that some countries were not admitting to exporting whale meat to Japan, but my correspondent pointed out that whales are not fish. While the US Supreme court has ruled that tomatoes are vegetables, I do not know their view on whales, and this is probably not the answer anyway. Any theories out there, readers?

At the suggestion of singingfish, I will be making available the code used to produce charts here on the Stubborn Mule. Most of the charts are produced using the R statistical package, which is free and open-source. R can be downloaded here. The data and code for the chart above is here. I will gradually add the code for charts from older posts as well.

UPDATE: I forgot to mention that my correspondent also suggested fish rain as an explanation. I, however, am not convinced. Regardless of the original source, I am sure most countries would treat fish rain as a natural bounty rather than an import.

* Tip for reading the chart: there is no label on the right hand side for the USA and no label on the left for Denmark, but following the lines should make it obvious where they would be if there was room.

The Big Arms Traders

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My last post looked at the international arms trade. Taking data from SIPRI, I produced maps showing arms exports for a number of countries, including Australia and the USA. While these maps gave an indication of the spread of arms trading, it did not show which are the biggest overall importers and exporters of arms.

To remedy this, I have created two “word clouds”. The first shows arms importers. The size of the text varies with the total value of arms imported over the period 1980 to 2008 (figures are adjusted for inflation and are expressed in 1990 US dollars). The three biggest arms importers over this period were India ($58 billion), Japan ($37 billion) and Saudi Arabia ($35 billion). Australia’s imports over this period totaled $15 billion.

Arms Importers (1980-2008)

The word cloud for exporters is far more concentrated. Between them the USA and Russia* accounted for almost 65% of total arms exports, with exports of $60 billion and $48 billion respectively. France then comes in at a distant third with exports totaling just under $12 billion.

Arms Exporters (1980-2008)

If you like the look of these word clouds, you can easily create your own. With Wordle you can create word clouds which are based on word frequency. This example is based on words used here on the Stubborn Mule (notice the prominent appearance of the word “debt”). For a bit more flexibility, IBM have a freely available Word-Cloud Generator, which can either work on word frequencies or take columns of words and numbers. It is written in java and is very easy to configure and run. I used it to produce the images in this post.

* As in the previous post, figures for the USSR and Russia have been aggregated.

The Arms Trade

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Yesterday iconoclastic commentator on technology, politics and culture, Stilgherrian, shared an interesting discovery on twitter. He had come across the website of the Stockholm International Peace Research Institute (SIPRI) and their Arms Transfer Database. SIPRI has been monitoring international arms trades since 1968 and in the process have assembled an extraordinary database with details of all international transfers of major conventional weapons since 1950. Since March 2007 this database has been available online.

The business of international arms trading is certainly not within my area of expertise, but a rich data-set like this presents a perfect opportunity for a type of data visualization that has not yet appear on the blog: maps. The SIPRI database provides “Trend Indicator Value (TIV)” tables which aggregate trade values between countries. Values are inflation-adjusted, expressed in 1990 US dollars.

Starting with Australia, the data shows that the total value of arms imported by Australia from 1980 onwards exceed exports by a factor of almost 30 times. Imports are largely sourced from North America and Europe, while exports are spread more broadly and include a range of Asian and Pacific countries. Click on the charts to see larger images.

Arms transfers from Australia (1980-2008)

Arms transfers to Australia (1980-2008)

Needless to say, the distribution of arms transfers in and out of the USA looks very different. Over the last 30 years, the USA has exported arms to well over 100 countries across every continent other than Antarctica.

Arms transfers from the USA (1980-2008)

Arms transfers to the USA (1980-2008)

Another big exporter of arms to a wide range of countries is the United Kingdom.

Arms transfers from the UK (1980-2008)

Arms transfers to the UK (1980-2008)

Russia offers a rather different distribution of arms transfers. Russia has exported arms to almost 100 counties, most notably China, but since 1980 has only imported from Germany, Poland and the Ukraine.

Arms transfers from Russia (1980-2008)

Arms transfers to Russia (1980-2008)

I will not offer any further comment on this data, but will leave the maps to speak for themselves. If you would like to see a map for any other countries, feel free to contact me on twitter, @seancarmody. I will add them to this flickr image set.

UPDATE: As Mark Lauer correctly pointed out, these maps were originally inaccurate when it came to countries which were formerly part of the Soviet Union. This has now been corrected in the maps above.