Thursday, 30 October 2008

MA teaching next year

I teach economics on a Master's course at the University of Westminster in London. The course title is MA Economic and Governmental Reform, and runs from September to September. We are presently recruiting for next year's course.

The course requirements are listed on its website, although there is some flexibility. Unavoidable ones are:

1. Reasonable English (or things won't make sense)
2. A first degree with some relevance to the topic, or a degree and relevant work experience
3. A job, or potential job, in government (people from NGOs have historically also performed well)
4. Willingness to work hard (or things will not be enjoyable)

African applicants are most welcome and have good course records. Information on the course and obtaining funding is on the website. The course, like most in the UK, is expensive (£10,000), so students usually have applied for scholarships first. Early application is recommended.

Bretton Woods revisions

There are plans for revision of the Bretton Woods institutions (the IMF and World Bank) following the difficulties encountered by developed countries in the recent credit crunch. A conference is planned for the end of the year, I believe.

The Bretton Woods institutions are actually today subject to less criticism than in the past. The senior personnel is less controversial and more technocratic, their predictions have been lauded, and they have acted on - perhaps superficially - many of the criticisms lobbed in their direction for the last two decades.

The difference between the international response to developing country problems in the 1980s and developed countries problems today is marked. In the 1980s, the Bretton Woods institutions were inflexible and developing countries changed their policies; today, developed countries get the Bretton Woods institutions to change. It doesn't seem to me that developing countries were less or more responsible for their predicaments than developed countries are today. The difference lies in the power balance.

Ever thus, I suppose, and probably the 1940s BW structures are obsolescent, but the difference between then and now is still illustrative.

A twin to Feldstein-Horioka?

The Feldstein-Horioka paradox is that savings rates and investment rates in a country tend to be correlated even if the country has totally open borders for capital flows. One would expect capital to move to where the highest rates of return are, so why should there be a strong relation between national savings and investment in the country? The debate was active in the 1980s, and various papers have explained it to a degree, but I do not know whether it was ever fully answered or people just moved on leaving it incompletely resolved.

I recently came across an analogous empirical observation in open economy macroeconomics, where international exporters tend to price their goods in foreign currency when exporting. It is not obvious whether they would do so, as they may prefer to price in their own domestic currency and accept fluctuations in demand rather than fluctuations in exchange rate returns from foreign currency pricing, and there has been some theoretical debate as to which would be more logical. Published empirical observation indicates, as it does with Feldstein-Horioka, that national considerations predominate and foreign currency pricing applies.

The evidence is preliminary, but still fascinating in terms of describing the continued importance of the nation state, which often works uneasily with capitalism's operation.

Environment and its analogy to money

I mentioned a while back that environmental economic analysis should be as sophisticated and innovative as the Keynesian or monetarist revolutions had been. I am dissatisfied with approaches that work out the costs of future environmental damage and calculate its discounted value, because they seem inadequate to analyse or respond to the problem of global warming in particular, which could threaten life and civilisations.

Reading the sales pitch for the WWF Living Planet Report yesterday (here - downloading the full report into browsers instead of saving seems to lock them up, so beware), I came across the phrase

"[the possibility of a] financial recession pales in comparison to the looming ecological credit crunch"

which is true, to such an extent that the effects of recession are scarcely of the same expected order of magnitude. But the economic implications of the phrase - which seems rhetorical, rather than analytical - made me sit up.

Money is not a good like other goods, because it is present in almost all markets for goods. When a supply and demand diagram is drawn for, say, peanuts, the missing variable which is implicitly used but not explicitly included is money. No modern macroeconomic model could exclude money determination alongside and separate from aggregate good determination. Its properties are different, and critical for market operation.

So it is with the environment, most clearly through global warming. The effects of global warming will pervade almost every future market in goods, and it should be analysed on a multiple simultaneous approach to macroeconomics alongside aggregate goods and money. I do not know what its properties are, but its economic characterisation is certainly distinct from the other two. The recognition of its permeation is a first step towards finding the characterisation.

I think that the abstract representation is that goods like environmental use lie at the base of the economic pyramid on which everything else is built, and they move upwards to support production and consumption in other goods. The manner in which they do so is idiosyncratic to the good, so carbon dioxide release is generated and affects other production differently from other base goods like money, water, or oil. Oh, to be able to carry this analysis through!

Sargan and Hausman tests in growth models

I have a low success rate in finding good instruments to use in the GMM system and GMM difference estimation methods for growth models. These methods assume that some equations connect the parameters and observed values in a model. Even if the data seems to have a reasonable fit to a model, the equations are more demanding than just a good visual fit, and subsequent testing can reject the application of the method to the model. It is important to note, as I have in recent posts, that what is being tested is not just whether the model is acceptable, but whether the method conditions and model jointly apply.

Why bother with the methods, if they impose extra conditions which are not intrinsically in the model? Well, less demanding methods such as OLS may incorrectly estimate the parameters, so even though the model is OK according to the method and the method is applicable, the output is not good. What would be best is a method with low intrinsic demands in addition to the model, and which produces accurate results, but for growth models the method does not seem to have been devised yet.

And so to instruments. These are observed data used in the equations alongside the parameters, and can be just about anything. We can test whether the instruments are satisfying the equations, but generally I find that they are unlikely to satisfy them. The rejection is probabilistic; any model can generate data which could satisfy the equations, but for most models the chances of getting the data by chance is extremely remote. I try to ensure that the instruments would be compatible with the data around 90 percent of the time. Common tests are known as the Sargan and Hausman tests.

The problem is frequent among researchers. The theoretical literature reports how difficult it is to find instruments which fulfil the conditions, and many applied researchers avoiding reporting the Sargan or Hausman tests at all when using the GMM estimators. I looked at two of the few empirical growth research papers which report in full their statistics, and which discuss in depth their instrument selection. Neither of them ensure, even across a small number of specifications, that the 90 percent condition is met; in fact even a 95 percent condition is not met.

The rejection indicates misspecification of the model-method. It is not surprising, as the underlying growth models and method conditions are linearisations of the true, complex, and probably unknowable economic generators. So I think that Sargan and Hausman rejection at 90 percent is not the end of model-methods.

Monday, 27 October 2008

ANC potential split

Several high profile members of the ANC, the ruling party in South Africa, have seceded from the party and are looking at setting up a new political opposition. The events follow internal disputes which saw the replacement of its leader and president, and the resignation of much of the cabinet.

The split may be viewed in terms of a division which often happens in modern capitalist economies, where two major parties form that are broadly aligned with the right and left sides of the ideological divide in their countries. The division occurs in all major Western powers, for example, and even frequently occurs in state capitalist, directed economies.

Although there are some exceptions, many of the secessionists and critics are identified with more pro-business wing of the party, and many of the loyalists are identified with the more pro-distribution wing, all relative to South African norms. The events may be interpreted through personality clashes or tribal politics or responses to corruption, all of which have happened in recent times in South Africa. But the persistence of the right-left split across so many countries suggests that another occurrence in South Africa is at least partially driven by the same factors as elsewhere.

Here are two final observations. First, economic influence on political structures is always impressive to observe; second, the outcome would be helpful for South African democracy and help to calm the fears of many of its citizens.

The natural integration of African economies

The leaders of three trading African blocs have agreed on a mutual free trade zone last Wednesday in Kampala. They have also agreed to work towards further economic integration in the near future.

The integration is a natural outcome of Africa's development. As incomes rise, the demand for goods beyond subsistence production rises, and regional production offers lower travel costs than more distant production. Sufficiently large demand encourages international specialisation and consequent lowered costs. More stability in politics decreases the economically hazardous effects of international conflict. Trade integration gives increased weight in negotiations at world trade bodies.

Thursday, 23 October 2008

Instrument selection is an extra modelling equation

I mentioned in a September post that when a growth model is prepared, a well-designed empirical estimation method can still find adequate estimation coefficients despite the incompleteness of the growth model. In a sense, the model is the equations plus the estimation method.

Here is another example. Instrumental variable estimation is a way of avoiding biases in estimation if the determinant variables are correlated with the error term. Ordinary Least Squares estimation gives biased estimates of a in the equation y=a.x+error if x is correlated with the error term.

OLS can be characterised in terms of the orthogonality condition E(x.error)=0. Then the estimate of a is x.y/x.x, and inserting the value of y and taking expectations shows this formula is unbiased if the orthogonality condition holds. The corresponding orthogonality condition for instrumental variables is that E(v.error)=0 where v is the instrumental variable, and the estimator is v.y/v.x.

The orthogonality approach is neat, but it is also helpful to consider the structure of the estimator as the projection of y on v divided by the projection of x on v. The derivation of instrumental variable estimators is given in many econometrics textbooks, often in terms of estimation when simultaneous equations give rise to the single observed relation. This happens when two variables can interact in more than one way, and the error term becomes correlated with the observed determinant variable.

Selection of an instrumental variable gets rid of the bias and selects one form of interaction between the variables, that which acts through the instrumented variable. So changing instruments can not only alter the biases on an estimated coefficient, but also change what is being modelled. It is like introducing a new equation into the model.

Debt changes' effects on growth

I posted a few weeks ago suggesting that economic growth may be increased when consumer debt is increased, and reduced when debt is decreased. The idea is that debt helps to fund consumer demand, so businesses can make and sell more goods. When the debt is repaid, the opposite happens.

I have investigated the proposition empirically using a particular form of debt, borrowing by governments from abroad. The mechanisms here are possibly different from the one described above, as government priorities and economic interests are distinct from the general public's. The specification is for countries with

growth in income per person
= a0 + a1*lagged growth in income per person + a2*change in capital per person
+ a3* average change in national external debt/GDP + zero mean error

Five year periods are used, and estimation is by GMM system with the levels equation instrumented by all variables lagged three periods and more, and the difference equation instrumented by growth in income lagged three periods and more. Results are split by continent. Data is for developing countries and is from UN sources and the Penn World Tables. The results are shown in the table, with ***, **, and * meaning significance at five percent, ten percent, and 15 percent.

The African data shows that debt increases have often been associated with lower growth. But then, so have debt reductions (debt reductions are negative debt changes, so their positive coefficient translates to negative growth). The coefficients are not significantly different from zero, however. The same pattern is observed with countries in Latin America.

In Asia, the pattern is different. Increases in debt are associated with lower growth, while decreases are associated with higher growth. The mechanism is apparently different from the one described at the start of the post. It is possible that Asian countries are involved in anticyclical policies, or that borrowing is accompanied by or anticipatory of difficult economic circumstances, and repayment of debt occurs during recoveries. Perhaps borrowing in Africa and the Americas is less associated with stabilisation.

Monday, 20 October 2008

Satellite watching in Africa

This post is off the economics topic, but if you are in Africa and interested in science, you might like it. There is a website which displays the path of human made satellites across the African night. The site has Nairobi as the reference point for viewing, and shows (from the ISS link) that the International Space Station will be visible for three minutes between 04.22 and 04.25 tonight (20th October) for example. Other satellites are visible at different times, not all at 4 o'clock in the morning! The viewing point can be changed to your location. The satellites move quickly, like a really distant aeroplane.

The success of growth models in an unstable global economy

I worry about the predictive accuracy of many common growth models in the current economic circumstances. Questions about their performance are important, as their predictions are useful in helping countries to adopt policies and change their characteristics in order to promote rising incomes, and are also helpful in anticipating the global changes that a country's enrichment brings. Different approaches to growth models are an active area of economic research.

The problem with many growth models is that their foundations are prefabricated. A major strand of analysis assumes that changes in an economy's output is determined solely by changes in productive factors, and those factors obey rigid rules of change themselves. Another major strand is exclusively empirical, which allows the inclusion of a very large number of determinant variables, but ignores how those determinants are themselves determined or how they influence growth. Sophisticated estimation methods allow the models to produce reasonable fits to past data despite the relative ignorance of fundamentals.

It seems fairly clear that if a major change occurs in the underlying interaction between growth and its determinants, then the models may not be such a good fit to future data. In particular, if a major structural change occurs which has no precedent in past data, the model predictions may be weak. This vulnerability of models without foundations has been observed in the past, when high inflation and unemployment coincided in the 1970s leading to a rejection of a hypothesised trade-off between them in all circumstances. Consequently, a major break in the analytical tradition occurred with a shift towards macromodels with detailed foundations. The modelling approach continues today, although it has not been applied so extensively to growth models, with exceptions who have also attempted empirical estimation. The approach is brave, in view of the uncertainty and probable early failure. One recent paper takes several macroeconomic equations derived from microfoundations and estimates them as a separate system away from the rest of the derived equations.

The micro to macro approach might seem to be the best possible, but is far more demanding in the modelling, and it is uncertain whether the resulting analysis will contribute more than the cruder macroeconomic approach. The economy, after all, cannot stand still while economists find a perfect model to describe it. Critics in the 1960s were probably correct in many of their analytical qualifications of the neo-classical synthesis school of economics, but the neo-classical synthesis works reasonably well, can easily be understood, and became dominant. Interestingly, many of the universities which were the targets of criticism back then have pioneered the more sophisticated microfounded models of today, while other universities have championed the cruder macromodels, if not inventing them.

The current economic turmoil, and the global imbalances which produced it, seem to have no precedent in the last fifty years of data which is generally used for estimating growth models. It thus provides a stress test for macromodels to see whether they are up to the job, or whether they will have to be jettisoned in favour of microfounded growth models.

Thursday, 16 October 2008

Risk capital when there is no government guarantee

Risk capital calculation is a commonly used way of deciding how much money a financial company should put aside to cover its risks. Risk capital may be calculated by working out what losses the company could make and what the chances are of making those losses. Then all the losses are ordered with smallest first, and the chances of each are added up going from the start, so that a "cumulative loss distribution" is calculated. The smallest loss which has a cumulative percentage bigger than a certain value is identified, and the company puts aside money equal to that loss. So a company might say that it will put aside money which covers the 95 percentage point, meaning that 95 percent of the time it has enough money to pay its losses.

This way of allocating capital is neat in the way it fits in with profit calculations. A financial company might decide it wants to make 25 percent income per year on its capital, and as it knows what the capital is, it can charge customers based on its profit target. The approach also works for individual contracts.

An alternative interpretation of the capital would be that if a company makes losses larger than the capital, it will go bankrupt or at least have to ask its owners for more capital. However, this is not entirely true in the financial sector, since part of the upper five percent of losses would arise from systemic problems, meaning that many financial service companies would be threatened with bankruptcy at the same time. In those circumstances, it is reasonable to assume that the government would intervene. So the coverage of losses at the capital allocation level is effectively higher than 95 percent, say 99 percent.

However, if it becomes clear that a government can not or will not intervene to protect against systemic problems, financial service companies may put aside more capital to protect against the 99 percent losses themselves. The 99 percent point can be far higher than the 95 percent point, as the diagram shows:

The probability of loss is on the y-axis, the risk capital is on the x-axis. Allocating at the 95 percent point, the company puts aside risk capital equal to a. At the 99 percent point, the risk capital is the much larger b. Such long-tailed distributions of risk are common in finance.

I suspect that risk capital adjustment in the presence of uncertain government guarantees is playing a role in contracting credit in Western economies.

Functions of money and its buffering action

The operation of money is often described in terms of three of its functions, namely as a unit of account, a means of exchange, and a store of value. There are questions whether these functions are sufficient to describe all the economic operations of money in a modern society. For example, risk pooling, where different risks of economic loss are collected by one economic agent and the risk of extreme losses becomes less likely, is facilitated by money and certainly needs the three basic characteristics to operate but also requires that the pooling does not alter the riskiness of the underlying economic events. So risk pooling may be considered an additional, independent function of money.

The recent financial turmoil in the world's markets emphasise another function of money, as a buffer against the real economy. As the real economy is experiencing some event, it is generally considered possible in many circumstances to offset the event through adjustment of the money supply. A commonly occurring example is counter-cyclical fiscal and monetary policy where during a recession, government debt may rise and interest rates fall in order to help the economy recover. There are other examples in trade, government financing, and elsewhere in the economy.

In recent years, demand for world goods has been supported by the ready availability of credit in developed countries. With the debt crisis and the anticipated decline in aggregate demand and the world economy, it is possible that recent monetary supply has been pro-cyclical rather than anti-cyclical. However, it is also possible that monetary policy has been anti-cyclical for several years, buffering against a relatively low global aggregate demand for goods. The speed of monetary expansion has arguably been unhelpful, with monetary policy substantially defined relative to short term inflationary targets in independent central banks, longer term macroeconomic fluctuations being less important. However, the distribution of demand and other global imbalances make the judgement on monetary (and stabilising fiscal) policy difficult at the moment.

This post is a mish-mash as I am trying to sort out the issues myself, but I trust some half-decent idea has clambered from the mire.

Monday, 13 October 2008

Formal proof of the selection tendency in GMM difference

A few weeks ago, I gave an informal proof of the tendency for GMM difference estimation to select high a(i) parameters in a model y(i,t)=a(i).y(i,t-1)+b.x(i,t)+ v(t) where the i is a group indicator and t is a time indicator and v is a zero mean error, and the model is estimated assuming that the a(i)s are a constant a across groups. Here is a quick formal proof.

The GMM difference estimator is

alpha = Y(t-1)*M*Y(t)/Y(t-1)*M*Y(t-1)

where M is a matrix and the Y(t) denotes a stacked vector of the differences between y(t) and y(t-1). It is connected to Y(t) by the relation

Y(t)^ = (alpha(1).Y(1,t-1)^,alpha(2).Y(2,t-1)^,...,alpha(N).Y(N,t-1)^) + V(t)^

where the ^ denotes transposition, the Y(i,t) denotes a stacked vector of the components of Y(t) specific to group i, and the V(t) is a stacked version of the errors corresponding to Y(t). If we insert the expression in the GMM estimator we obtain

alpha = alpha' + Y(t-1)*M*V(t)/Y(t-1)*M*Y(t-1)

where alpha' is a weighted average of the set {alpha(i)} with coefficients summing to unity. As t--> infinity, the largest coefficients are expected to be on high alpha series since they will have the largest y series. Thus alpha' tends to be near the upper part of the alpha(i) range.

To complete the proof, we note that the second term has a denominator converging in probability to a constant, and a numerator converging in law to a normal distribution. Thus, the expression tends to a distribution equal to the ratio of the two and we can take expectations. E(M*V(t))=0 is the assumption of GMM difference, and the proof follows.

Instrument availability when there is misspecification

A misspecified model can mean that there are no error uncorrelated instruments available. For example, suppose that the generating model is y = a.x^2 + error while the estimated model is y = a.x + error, then as x goes up for any reason, so does the expected error. Thus any causal variable on x also increases the error in estimation as it rises, and any instrument is error correlated. I suppose that this is why instrument exogeneity tests are also known as misspecification tests.

Instrument selection when there are no good instruments

I mentioned last Thursday that my paper on technology transfers could be questioned on the result variability in the last few tables and the selection of foreign direct investment lags as instruments in the GMM estimations. The issues are more related than I had anticipated when preparing the paper.

Instrumental variables may be weakly correlated with their instrumented variables and/or may be highly correlated with the error term. Both are problems, but I had favoured weakly correlated, low error correlated instruments if no highly correlated, error correlation free instruments were available. However, recent econometrics literature indicates that quite severe bias problems and non-standard distributions of estimates can arise from using weak instruments.

So if no highly variable correlated, error uncorrelated instruments are available across the full set of specifications, I would use three different sets of instruments and mention the results in a robustness testing section of a research paper. The sets are:
1) the weakly correlated, error uncorrelated instruments
2) the strongly correlated, error correlated instruments
3) a set consisting of the optimal instruments for each individual specification, even if they change across the full complement of specifications

None of the sets are perfect - the third suffers from variable biases across specifications. But if they give similar results, probably qualitatively rather than quantitatively, then we can be more confident than when using the weakly correlated variables alone.

Thursday, 9 October 2008

Free, high quality econometric software

Much econometric software is expensive. Here's a link to some impressive econometric freeware which looks sufficient to perform most of the analysis in published applied economic papers.

It's nice of the authors to release it publicly.

Increasing tensions in Eastern DRC

There are reports of an increase in military and diplomatic conflict in Eastern Democratic Republic of Congo. The tension at the moment seems to be principally opposing the government of the DRC with a single rebel group, but there are many other parties who may or may not be involved on a long-term or day-to-day basis.

At the heart of the conflict between the government and the rebels is the potential actions of a third group, who left Rwanda after the 1994 war and ethnic slaughter. The group certainly contains military from Rwanda, including but not exclusively some people who orchestrated and committed war-crimes. They probably have many civilians with them, who were not involved in the killing but fled in fear or from coercion in 1994. The rebel group is ideologically opposed to them and may be supported by the current Rwandan government; the third group is not ideologically supported by the DRC government, but state elements may have engaged commercially with it.

So there is the core problem of this part of the DRC conflict, and which may be the most important part of the whole conflict: a probably large mixed group of soldiers, mass murderers, and civilians who probably do not want to return to Rwanda and may not be safe there but are a cause of conflict in the DRC.

I hoped that one of the senior diplomats and politicians who retire in their dozens every year might find employment as a UN envoy to the region and have the skills and charisma necessary to solve the problem. It is clearly difficult, but is it insoluble on a political level? Time is passing without any real resolution, and given that military annihilation of one of the sides is most unlikely in the DRC geographical and social environment, the problem will remain. It is probable in the long term that changes in the socio-economic environment - increased wealth, for a start - will make the tensions fade, but can no-one solve the problem rather than wait for it to become less important?

Technology transfers' effect on growth

I have put my paper "Measuring the association of inter-country technological gaps with economic growth" on-line here.

On the upside it uses better measures of technological gap than the gdp gap used elsewhere, so the effects observed are more convincingly attributed to technology gaps. It may be the first paper to do so.

On the downside, only fourteen works are mentioned in references, the use of foreign direct investment as instruments may be open to debate, a couple of innovative ideas from outside the main topic are discussed but it may be better to keep entirely mainstream in the non-core parts of the work, and the coefficients in some of the tables near the end change a great deal between specifications. There are reasons for all of these, and other papers could be criticised for the same reasons, but a perfect paper would not have them.

Monday, 6 October 2008

Technology's economic characterisation

The effect on growth of technology gaps between two countries depends on the type of technology. So gaps in computers have different effects from gaps in telephones. I will post a research paper on Great Lakes Economics soon showing the different impacts.

The technologies could be characterised in terms of the effects, but it would be better to have more intrinsic determinants which could be included in a model to explain the different growth effects. Thus, a vector X of successful characterising determinants would satisfy

growth =
a.vector of change in basic output determinants + b.X + c.indicator vector of technology types + error

where a, b, and c are constant vectors, and c should be tested as statistically insignificant.

I am not sure what X should be.

Refining the inclusion of debt in a simple growth model

In a September 8th post, I proposed a growth model for a country

growth in output = a*growth in (1+d) + growth in F

where a is a constant, d is the share of debt in the national economy, and F is all other factors like capital and labour. The derivation is in the earlier post. The logic is that increased production will occur in response to demand increases, and production will fall in response to demand decreases.

The argument can be refined to make allowance for the dual role of debt in funding consumers and companies. As debt rises or falls it may have an impact on business' ability to fund itself, so that realisable output can fluctuate. We assume firstly that banks can create money through loans during times of credit expansion, and secondly that some borrowers will find it difficult to repay at times of credit contraction so that banks will see their loanable funds fall. Thus companies will be more credit constrained during times of credit contraction than expansion. Thus, the effect of debt repayment will not be neutral as in the first model - repaying debt does not undo the earlier debt-funded economic expansion near perfectly. Rather, the effect of the repayment is to undo the expansion and additionally contract the productive capacity of companies. So the net effect of the increased borrowing, if it cannot be repaid, should be to contract the economy.

The model does not imply that debt is a hindrance for the economy. In the model it is essential for funding companies. But unrepayable debt may be a hindrance.

An empirical specification following from the theory would be something like

change in output =
a * change in (1+d) * a zero-one indicator that d is increasing
+ b*change in (1+d) * a zero-one indicator that d is reducing
+ c * growth in F
+ error term

since growth in debt and contraction in debt may have different effects.

One could also split d into different ranges to see what size of debt is non-contractionary for an economy.

Thursday, 2 October 2008 tidied up

I've tidied up the website The commentary and news is easier to read, and I have tried to remedy the intermittent display problems. I will monitor the site to see if they return. Hopefully, they will not.