Wednesday, 30 April 2008

Disproportionately useful theories #6: Generalised Method of Moments

It's been a while since my last "disproportionately useful theories" entry (and that was wrongly called number four when it was five, but that's all sorted now). The series returns with one for the econometricians, focussing on the Generalized Method of Moments or GMM as it is known.

The predecessor to GMM was the method of moments, which works by saying that if you have a random numerical outcome which depends on something else, and can work out the expected value of some feature of the outcome in terms of that something else, then you can equate the expected value with the observed value to get an estimate of that something else. The "moment" is another name for the expected value in terms of the something else, roughly speaking.

An example might clear up the statement. If a dice is biased - say its six side is bigger than the others - then the chance of getting a six (this is the random numerical outcome) depends on the size of the area divided by the area of all sides in total (this is the something else), perhaps the chance is equal to the ratio, so we can calculate the expected average score from ten rolls. Then if the dice has been rolled ten times and we have the average score (this is the observed value), we can calculate the ratio of the areas by equating the expected and observed values (this is a moment equation). OK, we could just have measured the dice's sides, but often in economic measurements we won't have the "something else" to measure directly, just the outcomes.

The outcomes might also have some other information which could depend on the size of the six side, perhaps the number of ones compared to the number of sixes in ten rolls. Then if an expected average value can be compared with the observed value, a new estimate of the size of the six side can be made. The two estimates of the size might not agree, and that's where GMM comes in. Under GMM, you choose a value for the estimated size which minimises
(expected - observed value for the first estimation)^2
+ b*(expected - observed value for the second estimation)^2
where b is a constant reflecting the relative importance of the two methods for getting a final estimate.

This is a really rough description, and to stop the post feeling too much like a lecture, here's the point. GMM estimates were shown to be very good estimates, and many of their important statistical properties were worked out by a single author in 1982. It was demonstrated that if you choose the moment equations and the weighting correctly, you get exactly the same estimates and statistical properties as many other methods of estimation, such as the least squares estimates. So the theories about GMM are widely useful.

Tuesday, 29 April 2008 - the next generation

I've entirely revamped my website It provides news and analysis about African business, investment, and economics. It updates automatically whenever you visit, so the information remains up-to-date. There are some useful tools and large studies for the businessperson already in Africa or thinking of investing there.

I'd be delighted if you visit the site when you get a moment.

Friday, 25 April 2008

Who gives the most overseas aid?

I hadn't looked at rich countries' overseas aid budgets recently, but had thought that the UK and US were both moving towards the top of the list for the most generous countries. Their governments had been talking about supporting Africa and promoting their healthcare initiatives there.

But shock. When I looked at the actual figures (at - an Adobe Acrobat file), the UK is in the bottom half of most generous countries, and the US is least generous of the thirty rich countries surveyed. If you look at who they are giving to (at,3349,en_2649_34447_1783495_1_1_1_1,00.html), it is mainly to strategically important countries which at the moment is Iraq and Afghanistan. Other rich countries also give lots of their money to these two states. So overseas development aid has foreign policy goals as a leading consideration, and isn't that big to begin with.

The most generous countries (and their money generally goes to the poorest people) are the Scandinavian countries, the Netherlands, and Luxembourg. Luxembourg? They kept quiet about it. They have a reputation as the bankers of Europe, so hardly who you would think of as generous governmental donors.

I don't have the figures for total country donations after making allowance for private donations, but I don't think it changes things massively. Somewhere on the web there was a really good analysis of total national giving after considering many different forms of transfer (such as allowing in immigrants and sending money to families overseas). Definitively proving that so-and-so country is least generous seems pointless, however.

The figures are often used by critics of the West. However, the generosity of a country does not seem solely to be a function of geography or political system; Japan gives nearly as little as the US, and East European former communist countries do not give much either despite being fairly rich. To give credit where due, the Czech Republic gives most. I would like to see the donations given by the former communist countries when they were communist, or nouveau-oil-riche countries in Africa.

Eagles and dragons circle over Africa

The war in Western Sudan and the crisis in Zimbabwe have attracted a huge amount of political and media attention in the West. The loose affiliation of China with the Sudanese and Zimbabwean governments may increase the attention given to the crises, which are not unique despite their severity. Western countries and companies have enjoyed close ties with their African counterparts, but they have recently been challenged by China (and India, although its presence is currently less visible).

The possibility of Africa becoming a new frontier for an East-West struggle should alarm governments in the continent. Close affiliation with either side during the Cold War often brought violence and corruption. African governments may opt for non-alignment in a new rush as the safest course of action, and some countries are cleverly getting what they can from both sides. Zambia for example has been a major recipient of Chinese investment and Western aid; the DR Congo seems to be gearing its policy to follow suit.

Tuesday, 22 April 2008

Exploitative deals

One of the advantages of Marxist analysis is that it contains precise definitions of terms like middle class and exploitation. In Britain today, Marxist terms and preoccupations live on - perhaps born and sustained independently of Marx - but without the precision found in Marxist tracts. So there are often shows on television and news reports asking people whether they consider themselves middle class, and they reply yes or no depending on where they were born, what accent they have, what their education is, what their job is, and so on. A stricter economic analysis might only ask, do you have enough capital to live on the profits forever?

Exploitation in Marxist terms is neat too. Any money earned from capital can be called exploitation, as all income is considered to be derived from human labour. Today, exploitation is a more amorphous term, being a value judgement given by campaigners to wages which are not high enough for example. It is a moral call, and doesn't get a place in modern mainstream economics. It often doesn't seem to get a place in business deals with the developing world either, with Western companies striking the best financial arrangement possible even if they would be considered unacceptable in their home country.

I formerly had no substantial intellectual opinion on such deals and the amoral economic approach which underpins it. The amorality of the whole affair is beguiling. The market operation is mechanical and predicts long-run benefits for many people involved, both in the West and developing countries. There is apparently no reason to introduce morality in the arrangement at all.

I still agree, but the insertion of the impressively mechanical arrangements of capitalism in wider society and its values seem clearer to me today. So I would now say that it would be considered immoral for the West in its entirety - not just companies, but including them - to permit very high corporate profits because a developing country is in a poor bargaining position due to temporary market movements, corruption, or ignorance. By immoral is meant that it will be considered eventually in a similar way to the theft of land or forced labour during colonial rule, although perhaps not equivalent to the worst excesses of colonial rule.

Probably something similar could be said about restriction of workplace unionisation, child labour, and the use of prison labour, but I haven't been smart enough to include them in the picture yet.

Stagflationary pressures in Burundi

I mentioned last week that stagflation is a real possibility in the US and UK. Developing countries feel the same pressures - Burundi for example is experiencing imported inflation, as reported on the Burundi Quotidien site ( - it's in French). The stagflationary effects are modified versions of the Western ones, since petrol prices are reportedly controlled in Burundi, so market shortages accompany price increases.

It is not clear whether the domestic financial system is simultaneously facing a debt crisis. The prominent Burundian bank Interbank in February reported a good annual performance (at, also in French), which is a little evidence that the Burundian financial sector has escaped some of the problems afflicting the Western sector. However, the African banking sector is increasingly heavily tied to Western banks through international ownership, so there may be an imported debt crisis. The financing or refinancing of government debt is likely to be made more expensive by the Western debt crisis, as states try to access Western finance.

Saturday, 19 April 2008

The Doing Business database

There's an interesting database on doing business administered by the World Bank at It grades countries according to an index of how easy it is for businesses to operate in them.

Some of the index components may be viewed as double-edged; the ease of firing workers is one of the determinants of how high a country is ranked, for example. Other components are more unambiguously related to efficiency, such as the number of days to register a company, and information on them could be useful to a government looking to streamline its dealings with companies.

Thursday, 17 April 2008

Meat and African food

There's an interesting article on IRIN today entitled "People compete with chickens for food" ( It tells how people in Nigeria are finding it more difficult to buy grain because farmers are buying it to feed their chickens for sale. It describes the perverse situation where real incomes of both farmers and non-farmers may go down as consequently rising food prices mean that people switch from expensive chicken to grain. The origin of the problem is the expansion of the inefficient food-production vehicle that is animal flesh. For any amount of animal flesh produced, a far greater weight is required of grain and food inputs.

Animal rearing is also one of the major causes of global warming. Some people do not accept this, or think that it is vegetarian propaganda. The UN Food and Agricultural Organization publication, Livestock's Long Shadow (available from its website, has extensive information on the damage rearing causes and also has statistics on the input/output efficiency of production.

People in developing countries usually eat far less meat than in developed countries, but the amount rises quickly once agricultural intensification occurs. At very low incomes, animals can have uses and status other than as sources of meat, which may influence some to suggest that vegetarianism is not known or relevant in Africa. It is de facto practised there much of the time (if not generally because of ethical concerns), and I have found it just as easy to get vegetarian food in any part of the continent as in London. With global warming, a worldwide expansion of vegetarianism - or just everyone adopting a similar food consumption pattern to the Africa average - would be great news for the continent.

Stagflation and debt

In the UK and US there is the non-negligible possibility of stagflation - an economic contraction combined with inflation. A plausible mechanism is simple; a cyclical economic decline in these countries is combined with high and rising global oil prices, so they import inflation faster than they deflate their economies by recession.

The reported current economic recession in the US (accurate figures are still pending) was foreshadowed by widespread defaults on debt. The UK, although it does not seem to be presently in recession, is likely to see its growth rates fall and also has had a local debt crisis. The possibility of debt default leading to economic decline is clear - banks lose money, stop lending, so people and companies can't fund their plans for future business projects or their consumption.

The debt crisis was so spectacular, with bankruptcies and liquidity problems among leading US and UK banks, that the question arises whether the debt-recession-imported inflation nexus is more fundamental than the simple analysis just given would have it. Stagflation has received attention in the post-Keynesian literature, but I usually treat it as a curiosity arising from exceptional circumstances, like the OPEC price hikes of the 1970s and the rise of China and India today, leading to high imported inflation. It can be analysed in terms of its separate components, as is done above.

Even if one accepts that the nexus is tightly bound, then it can still be explained in an augmented neo-classical framework, for example if capitalism is viewed as always pushing its growth to the limits of short-term possibilities so that people will keep borrowing to fund projects and expenditure even if they are likely to face bankruptcy in the medium term. Faced with recessionary pressures from rising oil costs which are a cause of imported inflation, the economy keeps straining until the extra tension brought by the oil costs forces the economy into a sharper decline than usual. One can keep adding to the neo-classical framework, and only reject it when its complexity becomes preposterous relative to its non-orthodox competitors.

Non-orthodox theories are generally more sophisticated than neo-classical theory, and many of the competitors to neo-classical theory are probably right in the sense that they describe reality more fully. For example, the post-Keynesian discussion of inside and outside debt probably gives a more complete description than neo-classical financial macrotheory. However, many classical works have the colossal advantage of being so simple that they are empirically testable, even if their proponents do not always test them. The few leading post-Keynesian papers and books I have seen do not test much if at all, and their specifications, whilst plausible, cannot be rejected relative to other theories because they are not readily able to be tested with available data or current econometrics. Increased sophistication is nice, but not worth it if it means taking a theory on trust.

Monday, 14 April 2008

I say! Three African news stories lead on TV

I say! Stories about the Kenyan coalition government (story 1), Zimbabwe's election (story 2), and Tanzania's stage of the Olympic torch relay (story 4 or 5) lead the UK news this morning. The other two stories were about rice prices in developing countries and a traffic accident in Latin America involving Britons, so the news felt like an edition of "What's happening in the developing world today?"

Having said that, it was the 1 a.m. news on a specialist news channel, so I may have been the only person to have seen this advance for developing world news reporting.

Institutional theory about consultancies

I don't know if it exists, but if it doesn't it should, and if it does it isn't widely applied. I am talking of course - well ok not "of course", not even slightly - about the institutional theory of consultancies.

A repeated problem with consultancies reported by users and in formal reports is that their advice seems to reflect whatever will please whoever is paying them. It is sometimes not in the interests of their paymasters, and often not in the interest of the recipient of the advice if they differ from the commissioner.

So some theoretical designs which separate the consultants from the paymasters - for example, that consultants work on a rotational basis, so only receive payment from one organisation once - would help to improve the general performance of consultants. Other design improvements are no doubt feasible.

Saturday, 12 April 2008

"Introductory" textbooks

University students should be aware of the meaning of "introductory" in their "introductory" textbooks. When they come across "Introductory monetary policy models" it is often not introductory in the sense of assuming no knowledge (advanced undergraduate knowledge can be assumed) or that the information is old (often the information is up-to-date, or just a decade old) or that it is easy (the difficulty is frequently close to professional standards).

What "introductory" often means is "If you read and understand completely this book and another book of similar thickness probably labelled 'further introductory' then you will be able to read much of what is published by academics for academics".

Hope that clears up the meaning of "introductory".

Preoccupation with unit root tests

While I am talking about lagged models...
The textbook by Maddala, "Introduction to Econometrics", discusses unit roots and other tests of goodness of fit for time series models. The author expresses his opinions more freely than some other introductory textbook authors, and seems to disparage the heavy emphasis on unit root testing vis-a-vis other tests of goodness of fit. It is an interesting point; I might go further and look at the whole emphasis on lagged terms throughout economics because of the reasons in my two last posts.

Lagged terms in econometrics

My last post argued that the lagged term in growth models indicates that growth is incompletely understood and may only be capable of rough estimation. Come to think of it, lagged terms should usually be a warning about incomplete theoretical knowledge, or insufficient empirical data or specification in models. This warning rings quite loud in economics since lagged terms are so ubiquitous.

Wednesday, 9 April 2008

Lags and holes in growth models

It is usual in empirical growth models to include a lag term for income. So the model looks like:

natural log of income this year = a + b*natural log of income last year + other terms like the amount of capital and knowledge in the country

a and b are constants. b is usually found to be less than one, so that writing the equation as
ln(income at t / income at t-1) = a + (b-1)*ln(income at t-1) + other terms
shows that as income increases, the rate of growth slows down, other things being equal.

A big problem with this model, which emerges even if pure economic analysis is ignored, is the amount of theoretical omission implied by the lagged term. There is no information why the lagged term occurs, it just occurs and is important. Why does growth slow down if people get richer? There is slowdown because of declining returns from capital and labour, but surely these are already included in the model? Why is a model like ln income = a + b*capital + d*education not sufficient?

One of the major empirical models (the MRW model, discussed in the "disproportionately useful" series in this blog) presents a derivation why the lag term occurs. It is essentially a statistical outcome of the instantaneous model ln income = a + b*capital + d*education, together with an equation for accumulating capital over time. However, the assumptions in the derivation have been tested and found to be unlikely. So even if the lagged model is correct for some reason, it probably isn't because of the MRW derivation and its assumptions.

Personally, I would say that some of the reason for slowing growth as countries become richer is because of technological convergence. When countries are poor, they lag behind other countries in technology and can receive significant economic benefit from technological transfers from abroad. As their income catches up, along with technology, they can receive fewer benefits from transfers.

Technological transfers do not explain the whole story, or the technological leaders would show no dependence on the lagged term. In fact, in the original MRW paper, OECD incomes show less dependence on the lagged term than poorer countries' incomes, but there is still significant dependence.

I would guess that network construction accounts for part of the explanation for the lagged term. That is, when countries are poor, people can easily find people who want to buy things and who can sell them things they want. As countries become richer, these opportunities become harder to find, as many of the sales links are already established. The probability of success in a random hunt for a new sales partner declines over time under a simple model with a fixed number of people in an economy and a fixed number of possible sales between them. This network construction could explain why income falls over time, and has a neat mathematical representation.

A difficulty with this explanation is that network formation is difficult to observe. While the model does develop a precise functional form of convergence, so that the model could be tested indirectly through implied model misspecification, the form would depend on the way that networks are built and the testing may be complex.

Sunday, 6 April 2008

Cross-country dominance

This year's winner of the men's world 12,000 metre cross country championship was no surprise, as the Ethiopian champion had won five times previously. He followed a tradition of dominant winners; in the 1990s, one Kenyan won five times, and a few years before him, another Kenyan won five times too.

It is curious that cross-country lends itself to such consistent dominance by a single person. There is so much which changes from race to race and which can go wrong, like different terrain, harsh weather, lost shoes, and falling over. The more standardised track racing shows greater variation in its results.

Friday, 4 April 2008

God's bits of wood float to London

My last post argued that class formation may cut across ethnic lines. Familiarity with the ideas of class certainly cut across borders in the novel God's Bits of Wood, by Senegalese author Ousmane Sembene. It describes a strike in 1940s West Africa, through the characters involved in the long struggle.

I grew up in class-conscious 1970s and 1980s Britain, with one of nation's major strikes happening on the street outside my house. The characters in the novel, particularly the left-wing urbanites, sounded like people not from the decades ago in a different continent, but my friends and acquaintances. Sembene wrote not just about his own region - although he would be celebrated as one of its greatest novelists - but for all people who had experienced social class one way or another.

Enough capitalism in Burundi?

A few years ago, I wrote a paper which proposed that "the IMF is not capitalist enough in Burundi". The title was a bit vague, being intended to capture several ideas at once, and did not have a great reception. Today, I would break it up into several precise hypotheses which align more with academic expectations for publication, something like:

1. Structural adjustment packages are not associated with significant increases in domestic saving rates (and then I'd identify which exact policies in the packages are best at promoting domestic saving)
2. The number of people earning in the second, third, and fourth quantiles (between 20 percent and 80 percent of the total income earned in the country) does not increase in countries with structural adjustment programs
3. Industrial organisations (whether trade union, managerial, or proprietorial in orientation) increase more quickly in some other economic policy regimes than under structural adjustment.

Conjecture 1 has received support from existing published evidence. The other two are to be tested, although IMF programs have been accused, with empirical evidence, of leading to a static economy which is not conducive to wealth creation among low to middle earners. The failure to promote saving would lead many development economists to call for more "capitalism".

At the back of my mind when writing the original paper was the idea that under capitalism there would be class formation in Marx's tradition of workers forced to work to pay their bills and a middle class who can live off the profits generated by their capital (probably left wing economists would like to say more than this). Then, these classes would cut across the ethnic groupings which have created conflict in Burundi, and ethnic conflict may decline.

There are a lot of assumptions in this argument, and I would sharpen it today into something like "In countries with a large section of the society earning above sub-subsistence wages, or earning in the middle three income quantiles (a less pure characterisation of the bourgeoisie), industrial disputes are more common and ethnic disputes less common". The statement is then testable, though measures of industrial disputes may only be available for rich countries, and characterising disputes - wars, say - as ethnic in origin may be tricky because of the frequent political agitation which uses ethnicity as a cover for other motives.

In much of Africa, there is the emergence of a wealthy elite and highly uneven distribution of income, so there will be a large experiment in the next few decades on whether income stratification reduces the likelihood of ethnic conflict. However, domestic capital accumulation still is missing from many countries, even those with rising inequality, so it is not an experiment in capitalism in its usual Western form.

Wednesday, 2 April 2008

Inflation's a bit odd anyway

Well, it is. An economy is going along nicely, growing at record rates, but then stop, everyone, inflation is ten percent, so we will have to hike interest rates and slow down the economy. Sorry, poor and rich alike, you'll have to wait for a few more decades before reaching your potential wealth, no matter how hard you are willing to work for it.

All because inflation is too high. Or, prices are increasing too quickly. Or, the artifice termed money which is used to denominate the economy has acquired a particular abstract mathematical quality which results in the economy breaking down if it is sustained.

It is like this: you have a car whose engine overheats if it goes faster than ten miles an hour. The smart solution is not to limit the speed to ten miles an hour, but to invent a cooling system. Someone should invent a cooling system for the economy.

It may be argued that the economy can grow rapidly without inflation if there is productivity growth rather than just frenzied economic activity, which is true. But frenzied economic activity still leads to real economic growth, and it would be nice to have it without having to slam down the brakes. If the problem is money creation through debt issue, so that inflation is not the problem in itself but the debt accompanying it, and the growth is likely to be evened out by future contractions, then that should be dealt with directly, rather than by inflation targeting primarily. At least the difficulties should be named correctly.

I think I have assumed the "capitalism in itself can cause inflation" point noted in my last post, and that's OK.

What inflation rate should a developing country have?

I am sometimes asked what inflation rate a developing country should have. It is not an easy question to answer. The answer is highly likely to be between zero and ten percent per year in normal situations, but no-one expects an answer of 48 percent anyway as that would expose the country to hyperinflation and have some grave problems in itself. And even 48 percent might be a good inflation rate if it has been above 1000 percent for the last few years.

Usually it is a difficult question. The developing country might have an inflation rate of six percent for the last few years - should the government put in an effort to bring it down to three percent?

Good practice in analysis would start by looking at the quality of the data. Inflation data can be misreported and be higher than the real rate. If the government is targeting two percent in real rates, then the reported data rate for targeting may be four percent. If a reported data rate of two percent is targeted, then the real rate may be zero percent.

There are some general considerations which should be analysed for determining the most suitable rate for a country. Economists have listed them at length, and I will describe just a few, though I might put a more extensive analysis toolkit in my next macroeconomics course for students. The considerations include: how many people in the economy have fixed incomes such as pensions which are reduced by inflation; how stable the inflation rate is; how good businesses and the workforce are at adjusting to the inflation rate without escalating it; and what the risk of hyperinflation is.

A zero or even very low rate of inflation may not be a great target because inflation is linked to government and bank decisions to issue money. These decisions, by virtue of their redistribution effect, can result in increased economic growth. To take an extreme example: suppose all the money in the economy is in the hands of one person, who won't spend it. The government prints money, gives it to everyone apart from the one person, and they spend it. Output increases.

Another reason for zero or extremely low inflation being a less than sparkling idea is that capitalist activity can generate inflation itself. Entrepreneurs may raise their prices hoping to increase profits, or out of fear that their suppliers will increase prices and their net profits will decline. The mechanism here is less clear cut than the money creation route, but probably still occurs. In developing countries, squashing capitalist activity merely to get very low inflation would be unfortunate.