Thursday, 29 May 2008

Developing country growth models should look outwards

Just finished reading another paper on growth theory. The conclusion of the paper was that growth is unpredictable in developing countries and the classical descriptors of growth - capital accumulation, labour accumulation, education accumulation - are very poor at predicting rapid economic expansion.

The conclusion is familiar from other papers. The interpretation on results is often that growth is due to idiosyncratic or unknowable causes. This deduction is related to the idea that the missing features of growth lie primarily within economies, since if the causes were international then idiosyncracy would be improbable. The "within economy" hypothesis uses the same theoretical approach, if not the identical variables, to the classical model which the papers themselves find to be empirically inadequate.

The within economy hypothesis is in itself inadequate to explain one of the salient facts of economic growth's history, that developed countries grew far slower than today's fastest growing developing countries when they were in comparable "within country" states. The observation in one of my earlier posts about the instability of the lagged term coefficients across countries is empirical demonstration of the fact.

Both of these observations could be explained if the presence of today's developed countries is responsible for much of the faster growth rates for developing countries. The explanation is the obvious one, is compatible with core economic theory, and has early empirical support in the significance of variables such as openness and technology transfer in models which bother to include them.

Growth models should no longer look inwards, but outwards.

Removing the lag term as a modelling objective

I've presented some arguments and data recently on why the lagged income term in growth models is an indicator that the basic modelling might not be up to much. I would still use a lagged term in my models for the reasons that 1) it captures, badly, the effect of omitted and probably unobservable variables and 2) everyone else uses it. However, removing the lagged term whilst maintaining or improving the basic fit of the model is a good goal for modelling and variable choice.

Sunday, 25 May 2008

Sub-Saharan book production

On the UN data website, there is information on how many books are published in different countries. The data on Sub-Saharan countries is patchy, with only a dozen or so countries present. It can be found at

I am not sure whether to believe the data, as some of the figures are so small. Ghana for example in 1998 is recorded as having published just seven books, while Togo apparently published just five. Perhaps their authors choose to publish outside the country for subsequent import back in. Something looks strange when you compare with Malawi's figure of 120 books in 1996. There are also healthy publication industries in DR Congo and Ethiopia, and some of their books crop up in UK bookshops.

Butare, Texas

One of the features on my website (admittedly, it is courtesy of Google Maps) is the ability to see photos for places in Africa. You can go to, then click on the interactive map option, then select the "more" menu, then tick photos. Photos appear all over the continent.

If you zoom into Rwanda (between DR Congo and Tanzania) there is a photo for Butare, in the south of the country. The photo can be found directly at

I think that Butare could be twinned with so many small towns around the world in so many eras - it has the look of British seaside towns today, of US mid Western towns in the 19th century, of French North African colonies in the 1950s, of southern Spanish towns in the early part of the 20th century. What do you think?

Investing in Africa is back

My website Investing in Africa is back online. It was offline for a few weeks while some hosting administration was performed. No further interruptions are planned.

Friday, 23 May 2008

Monte Carlo simulations as standard

Many of the estimation methods used in econometrics produce a biased result when applied to real datasets. In other words, if you want to know what value b is, the estimate tends to be b + some other constant value.

The theoretical understanding of the methods is imperfect, so we do not always know how much the bias is, and we therefore can't correct for it. Monte Carlo estimation gives a way of finding out without having perfect theoretical knowledge. It works by simulating lots of data from a model where you know the parameter values, then you apply the estimation method to the data and get estimated parameter values, then you subtract the real values from the estimated ones and you get your estimated bias. There is an assumption here (ergodicity, meaning convergence of sampled values to real ones) but it is not too restrictive.

It is unusual for papers to report corrections for their estimates based on Monte Carlo simulation, and much more usual to report estimates from different estimation methods. That's OK, but biases can be persistent across different methods, so it is not as comforting to get similar estimates as authors say.

So: here's to Monte Carlo reporting.

Rwanda embassy attempted arson

There was a reported attempted arson attack at the Rwandan embassy last week ( The report describes the context of how four Rwandans are due to be deported from the UK for suspected involvement in the 1994 genocide.

I find the arson particularly worrying because of the implication for events in Rwanda. Activities by expatriates in the UK can indicate imminent unrest in their native lands. Prior to the outbreak of conflict in Cote d'Ivoire, posters in French were stuck up in London calling for action against an Ivoirian political leader. Rwanda is in a more tense situation than Cote d'Ivoire was, with the Rwandan militias responsible for the killings in 1994 still at large just over the border in Western Congo and with a refugee civilian population accompanying them. They have been there for fourteen years without anyone being able to reach an adequate resolution for the region, and the possibility of their re-entry in Rwanda is not insignificant.

A little evidence against the AR(1) growth model

My last few posts have complained about the AR(1) lagged growth model (that's the one that says
income per person this year = a * income last year + b * other terms + error term,
a and b being constants) on theoretical grounds. I said that stability might be a problem. Here's a little evidence that it is.

I ran estimates for Niger (a low income country), China (a rapidly growing country), and the US (a large economically leading country) on a growth model like the one above. Income was measured as log of gdp per person, and there was one other term, log of capital investment. I used five year growth periods since 1959, so had ten data points for each. I used OLS to make the whole process quick and easy, so there are bias issues discussed below.

Niger had an autoregressive 'a' coefficient of 0.22, China had 1.04, and the US had 0.84. I Chow-tested the equality of the Niger and US values, getting a p-value of .06. The equality of the US and China means had a p-value of 0.001.

Now using OLS to estimate AR(1) should bias down the coefficients in these small samples, with the US affected more than Niger, and China affected more than the US since closeness to unity increases bias. So the range of 'a' coefficients is likely to be even larger.

I am not sure of the direction of standard deviation bias, and the t-test might not be entirely correct for estimation, but the Chow values are large enough to be confident that the true tests would indicate that the autoregressive parameters are not stable from country to country. Yes, there are a lot of caveats, but my point holds. In fact, inspecting several countries, it doesn't seem that the parameters are stable within countries over time either.

Monday, 19 May 2008

Limits of fungibility

Fungibility in aid describes the situation where a country gives aid to a developing country intended for a particular purpose, and the receiving government reduces its own expenditure on the purpose. So no more money gets spent on the purpose such as healthcare than before, which may not be what the donor intended.

There is a limit here. The receiving government can only reduce its expenditure to zero, so if the donor government is very generous, it does not matter so much if the receiving government diverts its own budget. The recipient country will still have an increase in money intended for the purpose.

I have neglected the possibility that the recipient government will reduce its future spending too after a single year's donation, but it seems likely that it would not be able to do so indefinitely without encountering domestic opposition. Broadly speaking, donor governments can design aid programs using exact targeting to reduce fungibility's problems.

Technology transfers and growth

Excellent news.

My preliminary regressions work. They show that technology transfers between countries have a significant positive effect on growth. The results are so preliminary and rough that I would not put much faith in them, but the wheels have started turning.

An interesting and equally rough side result is that being technologically disadvantaged is not enough for technology transfers to occur and cause growth; in fact being technologically disadvantaged is likely to persist and harm growth. I haven't added many correlates of technological development into the regression, so the results may vanish when I do.

Why dummies and lags are problems in growth theory, addendum

During my polemic last week against dummies and lags in growth theory, I covered some of the problems, but neglected to mention that their presence makes the resulting model unstable to future changes in circumstances. So if one of the determinants hidden in the dummy or the lagged term changes, then the model starts behaving in an unexpected way. It is the same problem as confronted economics in the 1970s with the apparent breakdown in the Phillips curve relationship and revision of the underlying methodology for deriving such relations.

Thursday, 15 May 2008

Right angles in econometrics

I mentioned a week ago that the Generalised Method of Moments puts orthogonality relations (expressions stating that two vectors are at right angles to each other) at the centre of econometric estimation. In the spirit of advancement, I have tried to see whether perceiving econometric proofs and analysis in visual terms could be used more widely. It's not much of a study, only having lasted a week and concentrating on orthogonality.

Nevertheless, some of the results are encouraging. Considering the geometry behind the simple orthogonality relation a.b=0 (understandable by rotating axes and then using cos90=0) makes the two-way interaction between operations such as differentiation and the resulting econometric equations much clearer. I find it helps if in viewing the equations, one sees at the same time the proof of (a.b=0 is equivalent to perpendicularity). It's a trivial thing but helps a lot. The idea of differentiation as a projection also follows, and it is quite fun to imagine how the projected space gets rotated around at each successive differentiation.

The orthogonality approach also helps with the infinitesimal analysis which crops up in econometric proofs. The relation |x+y|<|x|+|y|, often used to show the term on the left hand side tends to zero by showing the two right hand ones do, is easy to show in Euclidean space (that's the one that describes our world) by projecting lines at right angles and using cos<=1. In more complex mathematical space, the equation seems to be equivalent (at least conceptually) to having projections shorter than the original line. So using the proof is like constructing a triangle and watching two of the sides contract, forcing the third one to contract.

I don't know if this approach will turn out to be an inefficient conceptual tool, but it avoids making proofs seem either repetitively drawn from someone else's work, or drawn magically from a bag of symbols. It is possible that leading mathematicians have the spatial perception buried in their subconscious, or they may work completely differently.

Clearing out the dummies in growth theory

Economic growth theory is the study of what makes countries grow and how quickly they do it. It has been heavily studied in the last twenty years, and there are many different definitions and proposals associated with it.

Some of the ideas do not appeal to me because they seem to embed ignorance within the model. I've talked in an earlier post about how I often dislike lagged income terms in models such as
income this year = 1.06*income last year + other terms. The reason is that income does not magically appear this year because it existed last year, but rather because, for example, the networks which existed last year continue to exist this year. Income last year is a proxy term, and has all the inaccuracy associated with them.

The complaint I have about some other growth theoretical models is similar. For example, the inclusion of regional dummies, where different parts of the world have different potential income levels just because of where they are, gets me down. If a region has a dummy, then research should treat it as a transition model for quick replacement by models including more meaningful variables like climate, history, or politics. I have similar concerns about models with multiple equilibria, although they may have intrinsic value in exceptional circumstances such as for handling hysteresis where income depends on the timing of past economic development.

Tuesday, 13 May 2008

Stuck on and with Earth

I like science fiction, but have costing concerns about warp-drive.

In your typical science fiction film or series, the heroes travel around planets and galaxies. Let's say it costs $10 billion to get a spaceship between planets, just on running costs. That's the amount raised by a million people producing a non-consumed surplus of $10,000 per year. So the whole planet of six billion could produce enough for 6,000 one way trips per year, assuming everyone wanted to pay for them. Even with 1,000 people travelling on a big spaceship, it is clear that only a small proportion of the world's population would get to travel on them.

So people are going to be staying on Earth for a long time. And (here's the morality bit) let's all look after this planet of our's and not ruin it with global warming and stuff.

The huge economic burden on science

Science has a major role in modern economics. Its innovation is one of leading sources of economic growth, and according to some models it will be the only major source of growth in the future. It is largely responsible for increasing the length of human life, and is expected to save the world from global warming.

It's a big burden, and science is not certain to live up to it.

More to life than war in Burundi

Burundi's conflict hobbles on with a recent outbreak of fighting ( between a rebel group and government forces. It has been fifteen years since the group first raised arms, although there have been periods of ceasefire.

Burundi's economic potential - indeed its delivered performance - should put it on a better path than constant conflict. The chance of war is reduced by economic growth, and war's persistence is discouraging for those people who concentrate on economic aspects of societies as means of increasing the happiness of their citizens. Some analyses of the tensions in the country hardly mention economics at all.

The important idea here is that the chance of war is reduced. Economics does not determine every facet in a society, but its effect works constantly and in most circumstances. Burundi's fighting today is probably less fierce than it would have been if the economy had been worse.

Thursday, 8 May 2008

Picking international champions

Some governments used to support individual companies with a view to helping them become successful. They were known as national champions. The record was mixed, and today governments tend to concentrate more on providing a good business environment for all companies.

There may be lessons for Western governments in their development policy. They often identify foreign leaders as being worthy of celebration, with potential for embarrassment if they do not live up to their billing. As with industrial policy, the record is mixed. Often, a country's institutions, generally a product of its people and history, should be celebrated rather than the leaders.

The obvious change in development policy would be to avoid identifying with particular leaders, but instead provide support for the emergence of good governance. So instead of giving selected leaders social and other benefits, Western countries might outlaw bribery by their own companies or make market access contingent on human rights standards.

The idea is very vague, but it might have legs. I have no data on whether it would be successful.

Successful academic papers are like hampers

I spend a lot of time reviewing academic papers, and some of them have been reviewed in the "disproportionately useful" series here. I've reached some conclusions about what makes a successful academic paper, and will explain it with a picnic analogy.

A standard published academic paper will have a few new results, enough to keep an existing area of research going, but does not pioneer. It is like a basket taken on a picnic, with some tolerable jam in it and maybe some warm salad.

A good published academic paper will have more new results, and perhaps innovates within an area. It is like a hamper taken on a picnic, with lots of food for everyone, and containing a few favourites.

A great published academic paper will have a high density of new results, and in a pioneering area. It is like a premium hamper, specially prepared for the purpose, and surprising everyone with its contents.

The hamper comparison isn't always perfect for a great paper as some of them present just a few important results. But it's picnic weather in London today, so there you go.

Tuesday, 6 May 2008

Principles common to business and aid allocation

There are some principles which are common to both business and aid allocation. One might be diversification, avoiding putting all the donor's or investor's money in a single recipient or region in case the project fails and there is no benefit to the commitment. Another might be avoiding sending new money to a failing project.

I wouldn't push the analogy too far, but businesspeople who are concerned about donating in the most effective way could use portfolio analysis techniques.

Business assistance in Africa

There has been a UK government call this morning for business to help with international development. Many businesspeople would like to help in the developing world if they could, but are not sure how to help. Working physically in a low income country is possible but not necessary, and there are few obvious avenues for private individuals to use their business skills there.

Local entrepreneurs and senior employees are often highly aware of the demands of business and may require similar skill building to UK managers, particularly on the international stage. Civil servants may also benefit from commercial awareness.

The highest possible impact of foreign business in development may involve facilitating and teaching about internal company capital accumulation. Information previously discussed on this blog suggests that it may be the principal source of China's sky high investment rate. The connection is so important that I will revisit the evidence presently.

Friday, 2 May 2008

Recessions in developing and developing countries

This post could be called SSA speaks to the IMF part 2, since it discusses briefly the South African bank governor's comments (mentioned in my last post) on the chance of recession in developing countries. Some of the risks he identified are experienced by developed countries too, such as balance of trade shocks from oil price hikes and a collapse in global demand for goods. Other risks, such as fluctuations in aid flows and droughts are more specific in their impact.

The effects of recessions similarly have shared and distinct features between the two regions. A point of difference which works in favour of developing countries is that an economic downturn, at least in the early stages, can mark a substantial slowdown in accumulation of capital goods, physical and technological. In developing countries, although physical capital accumulation may slow, still quite fast technological capital accumulation may continue for utilisation during a subsequent economic upturn. The point of difference is that intellectual capital transfers from developed countries to developing countries can continue for an extent even during a recession. So a downturn may be viewed as growth deferred, rather than lost.

The observation above does not cover all forms of deskilling and disaccumulation during a recession, and these may offset the potential for growth which builds up during a downturn.

SSA speaks to the IMF

The Governor of the South African Central Bank gave a statement at the IMF last month on behalf of twenty or so Sub-Saharan countries. The text is at

The Governor gave advice on the IMF's future, of a form more usual in the other direction: how the IMF can save money, how it should reduce staff numbers, how its voting arrangements should interact with its financial ones, how it should improve its operations, and so on. The pressure might be unpleasant for the IMF, but the advice was sufficiently general to allow for flexibility in its implementation. Moreover, the IMF is supragovernmental, and a monopolistic or an oligopolistic leader in provision of finance and advice to developing countries. It faces limited pressure from competition, so some demands from users are helpful in improving it.

GMM and econometrics teaching

My last post discussed the impact of GMM on econometrics theory. I would also add that the ideas behind GMM could also have an impact on econometrics teaching. The explanation is a bit technical.

In most econometrics courses, the teaching roughly follows the path that econometrics took during its discovery. So least squares is taught first, then variations on least squares, then more complex testing, then maximum likelihood estimation, and so on. Least squares is intuitively relatively appealing, so the students have an easy entry to the course. However, at some point, around the entry of two stage least squares or instrumental variables, the student has to shift from the intuitive graphical representation of least squares to the abstract representation of orthogonality. The effect is a little jarring, like cycling along at a fair rate, then peddling backwards and going down a side street some hundred metres back. If the student hasn't got the idea by then, they will struggle with the derivations of recent tests on bias in residuals, which often use orthogonality twice or more in their testing procedure.

Since GMM theory establishes the general applicability of orthogonality, it seems like a reasonable idea to introduce the whole econometrics theory with a discussion of it. Of course least squares' derivation can be retained, but it should act as a support for orthogonality in the introduction rather than being the centre of attention. The whole idea of orthogonality can be given a graphical representation for each of the types of estimator - it is only right angles in a suitable space after all, and even the founding paper of GMM could be portrayed in a child's cartoon, albeit a seriously dull one. Then the main sections of conventional analysis of each of the estimators and tests could occur.