Effect Of Stochastic Drift On Stability And Development Of A Country Is Inversely Proportional To Its Population

This is something I researched upon a few years ago. I then got busy with other things and it gathered dust for a while. But now that I have started my blog, I have published here. It concerns a phenomenon called stochastic drift and how it affects the economic and social development of a country depending on its population. Hopefully you will find it interesting. If you are aware of any similar research do let me know in the comments.

Stochasticity

In probability theory, stochasticity is the quality of randomness and unpredictability in a system. And a process that appears random and unpredictable by current scientific methods is called a stochastic process. A classic example of a stochastic process is coin toss, whose outcome is unpredictable and randomly determined. There are numerous, more complex examples of stochastic processes around us.

These include the behavior of stock market, weather, and evolution of biological species. A central premise of this article is that performance of a country in economic and social spheres, over a period of time, can also be stochastic. This might seem counter intuitive, as government policies are framed after thorough research and with clear time plans in mind. But history shows numerous examples of government policies leading to unexpected outcomes.

Stochastic Drift

A related concept to stochasticity is stochastic drift. Stochastic drift is defined as the random change in the average value of a quantity over time. Once again, the coin toss succinctly explains this concept. The probability of getting either a head or a tail is 50:50. This will be evident if the coin is tossed a thousand times and heads will turn up roughly as frequently as tails. But if the coin is tossed just three times, there is a high chance that you will get a head all three times, giving the impression that the probability of getting a head is 100% and tail is 0%.

This is stochastic drift. It happens because when the number of tosses is small, the effect of stochasticity on the process is high. As the number of tosses increases, the effect of stochasticity decreases. The probability of getting a thousand heads and no tails is negligibly small. But if you perform just three coin tosses every day and calculate the probability of getting a head each day, you might get a 100% probability on first day, 0% probability on second day, 75 % probability on third day and so on.

In other words, the apparent probability of getting a head would keep “drifting” on both sides of the actual probability, which is 50%. So, stochastic drift is random change in probability of getting a head when the number of tosses is small. If you perform a thousand tosses instead of three tosses a day, the probability of getting a head will be close to 50% every single day. This shows that the effect of stochastic drift on a process decreases as the number of events (tosses in this case) in that processes increases.

Examples of Stochastic Drift in Daily Life

As mentioned above, there are several examples of stochastic processes, like stock market, weather and evolution of biological species. And stochastic drift affects all of them depending on the number of events. In stock market for example, blue chip stocks are stocks of large, well-established companies that are highly unlikely to fail.

These stocks are considered very reliable and are expected to give assured and consistent returns over time. Market capitalization is the total number of shares of a company multiplied by the price of one share. Since the market capitalization of blue-chip stocks is typically very high, it’s very difficult for any trader to manipulate their price by buying or selling a huge quantity.

On the other extreme are penny stocks. These are stocks of very small companies. With a very low market capitalization, a manipulative investor can buy huge quantities of this stock, thereby jacking up its price. This increase in price might give unexperienced investors the impression that the stock is worth investing in. Once the stock’s price goes further up due to these investors buying it up, the manipulating investor can sell it, gaining profits. But penny stocks also have a chance of giving much higher returns than stocks of large companies.

So, penny stocks are high risk high reward investments. In other words, amount of market capitalization here is the equivalent of number of coin tosses. As the amount of market capitalization increases, the effect of stochastic drift decreases, making blue chip stocks far more predictable than penny stocks.

Similarly, investing in a startup carries higher risk than investing in an established company, as startups are more likely to fail due to less resources at their disposal. But it also carries higher chances of a huge profit if the startup takes off, as startups have much higher growth potential than an established company, which has already grown to the extent that its further growth potential is rather limited. In this case, the equivalent of number of coin toss is the size of the business. And consequently, stochastic drift makes a startup a high-risk high reward investment compared to a large, established company.

Stochastic drift is also observed in weather prediction. Predicting over a period of few weeks when it will rain or snow, how temperature will vary and how hurricanes will form is difficult. But you can still rest assured that winters will always be cooler than summers and they both will arrive at fixed times every year, as will monsoon. Here, the equivalent of number of coin tosses is the number of days over which you want to predict weather.

Stochastic drift has also played a role in the evolution of species. For example, if in a population of ravens, the gene causing ravens to be black mutates in one raven and causes that raven to be white, this mutated gene will gradually spread to the rest of the population through breeding. The original and mutated versions of the gene will compete with each other to produce either black or white ravens. Here, the likelihood of this white color version of the gene eventually making the rest of the raven population white depends on the size of the population.

If the mutated gene influences 75 ravens in a population of 100, then 75% of the total raven population will eventually be white. But if the mutated gene influences 75 ravens in a population of 10,000, then less than 1% of the raven population will be white. Here the equivalent of the number of tosses is the number of ravens in the population. Hence, a small raven population will evolve faster than a large raven population due to higher influence of stochastic drift on it. This is the reason why small isolated populations of a species on remote islands evolve faster than large populations of the same species on the mainland.

Stochastic Drift in Stability and Development of a Country

Here I attempt to examine weather stochastic drift has a similar effect on the progress of a country. The quantity equivalent to the number of tosses here is the population of the country. To examine the correlation between population of a country and effect of stochastic drift on its performance, I chose three different indices that give a good indication of a country’s overall performance. These are Corruption Perceptions Index (CPI) as measured in 2015, Human Development Index (HDI) as measured in 2015 and Political Instability Index (PII) as measured in 2010.

Global

For each of these three indices, I took various groups of countries and calculated the mean index of the group. Then I subtracted the individual index of every country in the group from the mean index of the group. The result is the figures you will encounter below. Figures 1, 3 and 4 show the distribution of CPI, HDI and PII of various countries with respect to their population.

For the sake of clarity, I have refrained from labeling every individual dot with the country it represents in these figures. But you can find out the country represented by each dot from the raw data file I have attached at the end of this post. The estimates of populations of all the countries were taken from Wikipedia in 2015, and are based on the latest censuses conducted in them by 2015. Therefore, the populations of the countries today, might slightly differ from the estimates in this article.

The X axis represents the difference between the CPI, HDI or PII of an individual country, and the mean CPI, HDI or PII of all countries included in the figure. The Y axis shows population. As can be seen, the low population countries are more widely distributed with varying deviation from mean, and as we go to higher population countries, their CPI, HDI and PII come ever closer to the mean CPI, HDI and PII, giving the distribution a roughly pyramidal shape.

This trend will become more apparent in the coming sections. One anomaly I observed is the Developed countries assuming a separate category in the CPI distribution, as is clear in figure 2 where India and China are not included to make the distribution clearer. However, even the CPI distribution of developed countries assumes a pyramidal form, showing that the interaction between stochastic drift and population stays intact in their case as well. In coming sections, to analyze this interaction in more detail, I have divided countries into smaller groups based on geopolitical regions, developed/undeveloped status, and whether they are former soviet republics.

South Asia

The countries included in South Asia region are India, Pakistan, Afghanistan, Bangladesh, Nepal, Bhutan and Sri Lanka. The usual pyramidal distribution is apparent, with India, the highest population country in the region being very close to the mean of CPI and HDI, though not of PII. At this point a comparison of effect of stochastic drift on probability of a country performing well and its effect on probability of getting head in coin toss is warranted.

It appears that just as the increase in number tosses reduces stochastic drift in the probability of getting a head, the increase in population of a country reduces stochastic drift in its economic and social performance. This will become even more apparent as we analyze other groups of countries in coming sections. But how does stochastic drift happen in a less populated country and how is it subdued in highly populated countries?

It appears that in countries with low populations, especially those with homogenous societies, resistance to new policies and decisions is less. This makes it easier for the whole country to move in a particular direction. Highly populated countries on the other hand, face more resistance against every policy and decision. This is because the higher the population, the higher is the probability that some sections of the population will be opposed to a particular step by government.

The probability of the entire population agreeing to a step decreases with increase in size of population just as probability of getting a head every single time decreases with increase in number of tosses. This is especially true if the country has a heterogeneous society. And highly populated countries tend to have heterogeneous societies comprised of several different religious, social and ethnic groups.

In a low population country, the decision agreed upon by much of the population can either be correct or incorrect. Hence, low population increases the probability of the country either progressing or declining. On the other hand, the resistance offered by sections of population in highly populated countries works against both right and wrong decisions, decreasing the country’s probability of either progressing or declining and helping maintain the status quo. It is this effect of population on stochastic drift that gives rise to the pyramidal shape of CPI, HDI and PII distributions in most figures shown here.  

Another interesting observation is India’s good PII ranking compared to all other countries in the region. This is a deviation from the usual pyramidal distribution that can be seen in most other cases and I propose a possible reason for it. India’s population, along with its diversity, has been cited by many as contributing to its instability. But the data here shows that most of India’s neighbors including Pakistan, Bangladesh and Nepal have fared worse, despite having much smaller populations and societies that are much more homogenous than that of India.

Pakistan’s and Nepal’s histories have been particularly chequered with military coups, insurgencies and civil wars. This points to a counter intuitive conclusion- that India’s massive population, instead of destabilizing her, might actually have prevented her destabilization in face of immense political, social and economic challenges, challenges that her less populous neighbors found much harder to deal with.

In fact, the high population of India appears to have counteracted even the possible destabilizing effect its immense cultural and ethnic diversity, because an ethnically heterogeneous society can indeed destabilize a country, as was seen from the violent breakup of Yugoslavia and Sudan along ethnic lines.  This shows that while a homogenous society might be stabilizing for a less populous country, the small population might itself cause instability due to its vulnerability to stochastic drift.

But as mentioned above, less population increases the probability not only of a country destabilizing, but also of it going in the opposite direction and achieving very high levels of growth and prosperity, surpassing even highly populous countries like India. In south Asia, an example of this can be seen in Bhutan. In fact, Nepal and Bhutan are quite similar in their geography, climate and populations. Yet, as a testament to the effect of stochastic drift on low population countries, they are found on opposite extremes of the CPI and HDI distributions.

East Asia

East Asia shows the same pyramidal distribution in CPI and PII, with China, the most populous country, having a CPI and PII quite close to mean of the region and the distribution spreading out at the bottom. A dramatic example of how much stochastic drift affects low population countries is found in the two Koreas. Despite belonging to the same geographical region, ethnic group and culture, they are polar opposites in their policies. With China, there is a deviation from the pyramidal distribution in case of HDI. This deviation in HDI is likely because the communist nature of Chinese state inherently limits the choices that people have in life, a key component used in calculating HDI.

Southeast Asia

Southeast Asia again shows Indonesia, the highest population country in the region, having its CPI, HDI and PII values very close to the mean CPI, HDI and PII of the region. Malaysia and Singapore, two countries in the region with very good rankings in these indices, are low population countries, as are those countries that have poor rankings in all three indices.

Middle East and North Africa

The region of Middle East and north Africa has a smoother population gradient among the countries compared to the huge differences produced by the massive populations of China and India in the previous two regions discussed. This, coupled with the higher number of countries included in this region, makes the pyramidal distribution of CPI, HDI and PII even more clear.

A clear example of interaction between stochastic drift and population can be seen in the effect Arab Spring had on countries in this region. An extreme case can be seen in Tunisia, a low population country that by most accounts has benefited from Arab Spring, with its government transformed from a dictatorship into a true democracy and its economy growing. At another extreme is Syria, another low population country. Arab Spring had the most negative effect on Syria, with its devastating civil war already having claimed more than 400,000 lives as I write this.

Egypt, the most populated country in the region, seems to have been least affected by Arab Spring either positively or negatively. In 2011, the Mubarak government was overthrown, leading to election of Mohammad Morsi of Muslim Brotherhood as the president in 2012, only for Morsi to be overthrown in a coup de tat in 2013 and replaced by Abdel Fattah el-Sisi in the 2014 election. El-Sisi government is politically similar to the erstwhile Mubarak government and is secular in outlook, while the Morsi government, composed of Muslim brotherhood members, was Islamist.

Egypt thus appears to have come full circle since Arab Spring swept it with little change in its political situation in the end.  When viewed in context of stochastic drift, it appears that unlike low populations of Tunisia and Syria, Egypt’s high population prevented the country from going towards either of the two extremes as a result of Arab Spring. Also, there has been a significant change of HDIs of North and South Sudan in opposite directions. This can be seen in context of their respective populations decreasing as a result of division and hence making both countries more responsive to stochastic drift.

Sub Saharan Africa

This region, with the large number of countries with varying population sizes, and hence with more data points, shows the pyramidal distribution in CPI, HDI and PII very clearly. Congo, the country with highest population in the region, has its CPI, HDI and PII values closest to the mean CPI, HDI and PII of the region. While the extremes of CPI, HDI and PII are occupied by the countries with lowest populations.

South America

An interesting example of effect of stochastic drift on low population countries can be seen in the way the fortunes of two South American countries have dramatically changed in recent past- Venezuela and Colombia. Colombia has been on a path of recovery from the ravages of its long conflict with communist rebels and drug cartels while Venezuela, after enjoying high financial and political stability under Hugo Chavez, has suddenly plunged into extreme unrest and instability under Muduro.

These two countries also happen to have low populations and are found at the extremes of the CPI, HDI and PII distributions of South American countries. Brazil, the country with the highest population in the region, is also very close to the mean in all three distributions for the region. Interestingly, just like India, Brazil has a better PII ranking than the mean PII for the region, again suggesting that high population might create political stability, especially for democracies.

North America

North America is characterized by the vast difference between the populations of the United States and other countries in the region. United States, with the highest population in the region, has PII ranking very close to the mean for the region. It is, however, far from the regional mean in its HDI and CPI ranking, closely competing with Canada.

This probably reflects the fact that US and Canada are the only developed countries in North America. In PII distribution however, US ranking is very close to the mean PII of North America. If we exclude US and Canada and only look at developing countries in North America, we again see the characteristic pyramidal distribution (Figure 8b), And in the later section on developed countries, we see pyramidal distribution as well.

Former Soviet Republics

While the general distribution of CPI, HDI and PII in case of former soviet republics follows the same path as others discussed so far, a peculiar feature is observed in case of their CPI distribution. In addition to the main pyramidal distribution, a smaller, separate pyramidal distribution is formed on the right of the mean, formed by the CPIs of Poland, Estonia, Latvia and Lithuania.

There is one common feature that unites these four former soviet republics- they all have joined the European Union and have now been classified as developed countries as per Wikipedia. This echoes the observation of a separate pyramidal distribution composed of developed countries in case of global CPI-Population distribution, and the CPI and HDI values of US and Canada being far away from the mean CPI and HDI of North America.

Developed Countries

As mentioned before, developed countries tend to form a group separate from the rest of the world in the global CPI distribution, although this deviation is not as pronounced in the global HDI and global PII distributions. But even the separate cluster formed by developed countries in global CPI-Population distribution shows the typical pyramidal distribution, with most populous developed country, the US, being very close to the mean.

On the right extreme of the distribution is Denmark, with the CPI score of 91 and one of the lowest populations in the group. On the left extreme is Turkey, with CPI score of 42 and population of 79463663. One can see that Turkey causes a slight deviation in the pyramidal distribution, as it is not among the least populous countries in the group and yet has the lowest CPI score in it. However, it must be remembered that turkey was considered a developing country until a while ago and has only recently attained the developed status.

Effect Of Extent Of Democracy On Stochastic Drift

A comparison between India and China shows that the extent to which stochastic drift influences a country depends not just on its population but also on its form of government. Both India and China have comparable populations. But one is a democracy while the other is communist. Democracy seems to subdue the effect of stochastic drift on the country by enhancing the effect of its population on decision making process of the government. On the other hand, a non-democratic country, even with high population, can behave to some extent like a low population country as far as stochastic drift is concerned.

This is because the decision making process of the government of a non-democratic country like China is influenced by the country’s population to a lesser extent then it would have in a democracy. This higher influence of stochastic drift is why China’s progress has been more erratic than India’s in the last seven decades. In the 1950s, Mao Zedong introduced the economic policies to achieve what he called the “great leap forward”. Instead, the attempt resulted in a widespread famine that killed almost 40 million people and even led to instances of cannibalism.

Later in the 1960s, the “cultural revolution” started by Mao led to large scale destruction of Chinese culture and heritage and led to large scale environmental degradation. Today, in contrast, China is among the most prosperous countries in the world, having left India far behind in the size of its economy, technological and scientific expertise and poverty alleviation. This erratic performance of China is in contrast to India’s performance, which has been much more smooth.

During the last seven decades, India has neither suffered the tens of millions of deaths by famine or the destruction of culture and heritage or the environmental degradation suffered by China in the 50s and 60s, nor has India enjoyed the phenomenal economic, social, scientific and technological progress that China is enjoying today. India has progressed slowly but steadily in the last seven decades.

In other words, China, due to its non-democratic nature enhancing the influence of stochastic drift, has experienced both the extremes of progress scale, reminiscent of a low population country. India on the other hand, due to its democratic nature allowing its high population to reduce influence of stochastic drift, has largely stayed somewhere in the middle of the progress scale, reminiscent of a high population country.

Stochasticity and Historical Progress

This correlation between a country’s performance in various spheres and its population might also help explain some puzzling historical questions. Why did the industrial revolution begin in Europe? Why did most African countries lag behind in progress? Why among Asian countries, Japan was quick to embrace industrial revolution and attain developed status while China and India lagged behind, though still ahead of African countries?

Western European countries have much lower populations than India and China, as do Japan and African countries. Their low populations might therefore have played some role in the extreme results in progress that they witnessed, with Japan and European countries ending up most industrialized and African ones least industrialized. India and China, being highly populated ended up somewhere in the middle of the scale of industrialization.

This is not to say that this difference in the level of industrialization will stay for perpetuity. As the level of industrialization increases across the world, the difference is likely to become less and less apparent. A historical example that illustrates this is the US. Most of the scientific and technological breakthroughs of the 19^th and 20^th centuries happened in western Europe, and yet the most scientifically and technologically advanced country in the world today is the US, despite being much more populous than any of the European countries that were the cradle of industrial revolution.

During World War 2, the UK sent the Tizard mission to US, which involved transporting a briefcase containing top secret documents about cutting edge technological breakthroughs of the UK to the US as a part of cooperation between the two allies to fight the war. This briefcase, which included documents about world changing technologies like radar and jet engine, has been called the most important cargo to have ever arrived on US shores.

Of course, stochastic drift is not the only factor behind the vastly different growth trajectories these different countries have experienced so far. There are many other known factors. For example, the alignment of Africa and the Americas along the north-south axis, created major geographical and climatic barriers between different settlements, making exchange of goods and ideas difficult. Asia and Europe on the other hand, are aligned along the east west axis, making exchange of goods and ideas between settlements far easier due to less geographical and climatic barriers.

A detailed discussion of this phenomenon is beyond the scope of this article. But it has been lucidly explained by Jered Diamond in his book “Guns, Germs and Steel”. Its also explained at 10:14 mark onward in the video below. Another factor appears to be the presence of sea routes of transport in Europe. As explained in the Wealth of Nations by Adam Smith, the fact that most European cities are close to the sea and therefore connected to each other through it, vastly aided industrial revolution there.

Then there is simply the fact that once a society achieves a certain level of sophistication, its technological and economic achievements feed further technological and economic progress. This positive feedback continuously accelerates the progress of society and makes it highly non-linear. So, once a country has a head start in the level of progress, the gap between it and other countries gets amplified over time. Nonetheless, to me, stochastic drift also appears to have played a role in determining the pace of progress in regions around the world apart from all these factors.

Role of Stochastic Drift in Predicting the Future

Mathematical models have their own place in attempts to predict impending crises, be they economic, political or environmental. The CIA for example, set up Political Instability Task Force (PITF) in 1994. Formerly known as State Failure Task Force, this is a long running research project that monitors 167 countries on a daily basis and calculates the probability of a crisis happening between 6 months and 2 years into the future.

It focuses on four major types of crisis, namely regime change, state collapse, revolutionary or ethnic civil war and genocide. Jay Ulfelder, former director of PITF, has used his own mathematical model to predict civil wars on his site. Then there is Sean Gourley, a physicist who has come up with a simple mathematical equation to predict the course of a war. The equation that he and his team use is P(x) = Cx^-a. Here, P is the probability of an event that kills people happening, x is the number of people killed, C is a constant and a is the slope of the trend line of the conflict.

Such attempts to use mathematical models to predict future of countries are always works in progress. And since stochastic drift clearly affects the stability and development of a country depending on its population, it might be a significant factor to look into in this context. Moreover, as the populations of countries change, the extent to which they are subjected to stochastic drift could also change measurably. For example, Japan’s population has been declining over time due to its low fertility rate, and many European countries might follow suit in near future, as fertility rates there decline as well.

In 2014, Japan’s population was 127 million. But if the current rate of population decline continues, then by 2050, Japan’s population will have shrunk to 97 million. It might be useful to investigate by what factor the effect of stochastic drift on these countries would increase over time as their populations decrease, and whether stochastic drift would be likely to affect them positively or negatively in context of growth, stability and prosperity.

The estimation of positive or negative effect on these countries through stochastic drift could be difficult. This is because stochastic drift also seems to cause sudden, unpredictable changes in the fate of a country, as can be seen from the sudden reversal in fortunes of Venezuela and Colombia.

Conclusion

Stochastic drift seems to affect the progress of a country. And its effect on a country’s progress depends on the country’s population, and also, to some extent, on its form of government. As the country’s population increases, the effect of stochastic drift on it decreases. And this correlation between population and stochastic drift is more pronounced in democratic countries than non democratic countries. Stochastic drift, therefore, could be one of the reasons behind the birth of industrial revolution in Europe, and it could also be a useful factor to look into when developing mathematical models to predict the future progress of countries.

Raw Data

In case you want to look at the raw data that I have used to create the graphs in this article, you can download it from below.