The UN's IRIN news service is reporting a full spectrum of opinions on the recent Congolese-Rwandan military cooperation in DR Congo's East. Many analytical and normative opinions are reported, varied as required by the complexity of the Congolese conflict.

My own tuppence worth is on the high risk and potential returns the two sides have taken in the arrangement. Congo approves the entry of Rwandan troops, against whom they have been fighting directly or by proxy; Rwanda removes and detains the general who is perceived to have represented it loyally. It seems that the governments see no permanent friends or enemies, only permanent interests. I hope that this is the beginning of the war's end for the Congolese people.

## Friday, 30 January 2009

### Maternal mortality as entirely preventable

UNICEF has published its report "The State of the World's Children 2009". The report's webpage says that one in seven women in Niger die during childbirth in their lifetime. That much is well-known; the statistic that in Ireland, the figure is only one in 48,000 is what caught my attention. I didn't know that maternal mortality is entirely preventable, like polio or smallpox, and has been prevented in a fairly rich European country. I thought it might be more persistent.

### Earth versus space chess match

For all readers who are interested in chess or space travel, there is an Earth versus astronaut match on at the moment here. People can vote for the Earth's move at the website and anyone can take part, I think. The astronaut is considering his move presently.

Earth as black is a pawn up after some queenside tactics and looks like it has an advantage, although our king is still in the centre. It is only a couple of moves from consolidation, but the astronaut may be able to open things up quickly along the centre files.

Earth as black is a pawn up after some queenside tactics and looks like it has an advantage, although our king is still in the centre. It is only a couple of moves from consolidation, but the astronaut may be able to open things up quickly along the centre files.

## Tuesday, 27 January 2009

### A small non-parametric model of a company’s decision to adopt a knowledge-specific technology #1

## Thursday, 22 January 2009

### Growth and the assertion of African military power

The Congolese army has just initiated a joint action with Rwandan troops against Rwandan rebels operating in Congo. It follows a Congolese-Ugandan initiative last month against Ugandan rebels also operating within Congo. I wonder whether growth of government economic capacity could be partially responsible for the increased assertiveness of state militaries.

Most African countries have been growing rapidly in recent years, and one would expect government income from taxes and domestic debt issues to rise as well. It may rise as a proportion of total income, because a larger economy is more likely to use large amounts of fixed physical capital, which is easier to tax and monitor than itinerant labour. Further, a smaller proportion of government income will come from aid and so governments have fewer constraints on their expenditure choices from conditionalities, and they will be freer to spend on military affairs. They may also be freer because of growing international competition from non-Western countries for African governments’ goodwill.

By comparison, rebel groups may experience relatively slower growth in their income because they do not benefit to the same extent from these changes. Further, their bases are often in rural areas, and developing countries have been found frequently to experience less growth in their agricultural sectors than in their industrial and service sectors. Thus, rebels’ available revenue is shrinking relative to that of states.

I looked at changes in government military expenditure on the Stockholm International Peace Research Institute (sipri.org) internet site, available free to the public. They say “SIPRI military expenditure data are entirely based on open sources, and as much as possible on official data”, and it is possible that underreporting or inaccuracies are present. Subject to this caveat, here is the data. DR Congo expenditures have more than doubled in constant prices since 1996 in absolute terms, and also risen as a proportion of GDP. Ugandan expenditures rose by 50 percent between 1997 and 2007, although relative to GDP it remained constant. Rwandan expenditure fell in absolute and proportionate terms. It should be noted that Rwanda does not have a domestic insurgency to the extent of Uganda and DR Congo. Two other perennially militarily involved countries in the region, Sudan and Chad, have also seen large increases in military expenditure.

So there is evidence of increased military equipping of the state. It is possible that the changes may lead to less contest to state authority from domestic rebel groups, with which Africa has been plagued in the last half century, but increased clashes between states as they become the only actors able to challenge each other’s might.

Most African countries have been growing rapidly in recent years, and one would expect government income from taxes and domestic debt issues to rise as well. It may rise as a proportion of total income, because a larger economy is more likely to use large amounts of fixed physical capital, which is easier to tax and monitor than itinerant labour. Further, a smaller proportion of government income will come from aid and so governments have fewer constraints on their expenditure choices from conditionalities, and they will be freer to spend on military affairs. They may also be freer because of growing international competition from non-Western countries for African governments’ goodwill.

By comparison, rebel groups may experience relatively slower growth in their income because they do not benefit to the same extent from these changes. Further, their bases are often in rural areas, and developing countries have been found frequently to experience less growth in their agricultural sectors than in their industrial and service sectors. Thus, rebels’ available revenue is shrinking relative to that of states.

I looked at changes in government military expenditure on the Stockholm International Peace Research Institute (sipri.org) internet site, available free to the public. They say “SIPRI military expenditure data are entirely based on open sources, and as much as possible on official data”, and it is possible that underreporting or inaccuracies are present. Subject to this caveat, here is the data. DR Congo expenditures have more than doubled in constant prices since 1996 in absolute terms, and also risen as a proportion of GDP. Ugandan expenditures rose by 50 percent between 1997 and 2007, although relative to GDP it remained constant. Rwandan expenditure fell in absolute and proportionate terms. It should be noted that Rwanda does not have a domestic insurgency to the extent of Uganda and DR Congo. Two other perennially militarily involved countries in the region, Sudan and Chad, have also seen large increases in military expenditure.

So there is evidence of increased military equipping of the state. It is possible that the changes may lead to less contest to state authority from domestic rebel groups, with which Africa has been plagued in the last half century, but increased clashes between states as they become the only actors able to challenge each other’s might.

## Monday, 19 January 2009

### Congolese rebel split continues. Possibly.

There are reports that the members of the Congolese CNDP rebel group who recently split from the main group are to integrate into the main Congolese army. But then again, there have been other reports that the splinter group was to reintegrate into the CNDP.

The parties involved may know what is going on, but I don’t. There is some first hand information on the conflict on the CNDP website . At the time of writing, the French language half of the site has a little more information than the English half. The website of their primary enemy, the FDLR, is here. The local French language newspaper Le Phare used to be good when I was trawling for Congolese information, so perhaps they can penetrate the jungle.

The parties involved may know what is going on, but I don’t. There is some first hand information on the conflict on the CNDP website . At the time of writing, the French language half of the site has a little more information than the English half. The website of their primary enemy, the FDLR, is here. The local French language newspaper Le Phare used to be good when I was trawling for Congolese information, so perhaps they can penetrate the jungle.

### Instruments, generalised transformations, and ring theory

I proposed last week that the procedure used in a recent paper for testing convergence could be split into several stages. The first stage was to transform the equations under consideration into a form where only a small set of quantities are present and those quantities can be analysed exactly with available data. I suggested that mathematical group theory may be applicable to examine which quantities could be derived.

With slightly more reflection, I think that mathematical ring theory may be a better tool than group theory, in view of the transformations used being both additive and multiplicative. In maths terms, the quantity derived represents an ideal, and the largest number of quantities which can be simultaneously estimated is the size of the maximal ideal of the ring consisting of the original equations under multiplication and addition. The size of the quotient ring may help to determine this maximum number; I am not familiar enough with ring theory to say for sure. The ring less the maximal ideal (the minimal ideal is the name I presume) is the set of inestimable elements, at least while the maximal ideal elements are estimated. The maximal ideal may not be unique.

The ring analysis can apply to conventional examination of identification in two stage least squares, where each endogenous variable should have at least one instrumental variable allocated to it, and no subset of n endogenous variables should have less than n instruments allocated to it. The required row non-degeneracy of the instrument-endogenous variable cross-product is the same as the requirement that the rows of the matrix span a space of dimension equal to the number of endogenous variables. Equivalently, under addition, the instrumental variables should cover a space equal to the space covered by the endogenous variables. If they cover a smaller subspace, its dimension indicates the maximum number of endogenous variables whose coefficients can be estimated.

The required operations (addition) for instrumental variable identification are fewer than for the convergence transformation (addition and multiplication) so in this ring theory viewpoint, the latter may be considered one example of a theory generalising the transformations of instrumental variable estimation.

With slightly more reflection, I think that mathematical ring theory may be a better tool than group theory, in view of the transformations used being both additive and multiplicative. In maths terms, the quantity derived represents an ideal, and the largest number of quantities which can be simultaneously estimated is the size of the maximal ideal of the ring consisting of the original equations under multiplication and addition. The size of the quotient ring may help to determine this maximum number; I am not familiar enough with ring theory to say for sure. The ring less the maximal ideal (the minimal ideal is the name I presume) is the set of inestimable elements, at least while the maximal ideal elements are estimated. The maximal ideal may not be unique.

The ring analysis can apply to conventional examination of identification in two stage least squares, where each endogenous variable should have at least one instrumental variable allocated to it, and no subset of n endogenous variables should have less than n instruments allocated to it. The required row non-degeneracy of the instrument-endogenous variable cross-product is the same as the requirement that the rows of the matrix span a space of dimension equal to the number of endogenous variables. Equivalently, under addition, the instrumental variables should cover a space equal to the space covered by the endogenous variables. If they cover a smaller subspace, its dimension indicates the maximum number of endogenous variables whose coefficients can be estimated.

The required operations (addition) for instrumental variable identification are fewer than for the convergence transformation (addition and multiplication) so in this ring theory viewpoint, the latter may be considered one example of a theory generalising the transformations of instrumental variable estimation.

## Thursday, 15 January 2009

### African of the Year 2008

Nigeria's Daily Trust newspaper has awarded the African of the Year 2008 award to Congolese doctor Dr. Denis Mukwege. It looks richly deserved for his work at the Panzi Hospital in Bukavu.

From the award page:

"Dr. Denis Mukwege is a gynecologist who specializes in reconstructive surgeries on victims of rape in the war-torn Democratic Republic of Congo. His hospital, Panzi Specialist Hospital, has become a refuge for these unfortunate victims over the years.

According to the United Nations, 27,000 sexual assaults were reported in 2006 in South Kivu Province alone, and that may be just a fraction of the total number across the country. The justice system and the military still barely function, and United Nations officials say Congolese government troops are among the worst offenders when it comes to rape. Large swaths of the country, especially in the east, remain authority-free zones where civilians are at the mercy of heavily armed groups who have made warfare a livelihood and survive by raiding villages and abducting women for ransom.

It is in this environment that Dr. Denis has had to keep up his practice. His continued efforts at putting these women back together physically and mentally is what has, above everything else, made it impossible not to acknowledge him as the Daily Trust African of the Year for 2008."

From the award page:

"Dr. Denis Mukwege is a gynecologist who specializes in reconstructive surgeries on victims of rape in the war-torn Democratic Republic of Congo. His hospital, Panzi Specialist Hospital, has become a refuge for these unfortunate victims over the years.

According to the United Nations, 27,000 sexual assaults were reported in 2006 in South Kivu Province alone, and that may be just a fraction of the total number across the country. The justice system and the military still barely function, and United Nations officials say Congolese government troops are among the worst offenders when it comes to rape. Large swaths of the country, especially in the east, remain authority-free zones where civilians are at the mercy of heavily armed groups who have made warfare a livelihood and survive by raiding villages and abducting women for ransom.

It is in this environment that Dr. Denis has had to keep up his practice. His continued efforts at putting these women back together physically and mentally is what has, above everything else, made it impossible not to acknowledge him as the Daily Trust African of the Year for 2008."

### Results, theories, and metatheories in convergence estimation

I read Phillips and Sul's "Transition modeling and econometric convergence tests" today. The authors' recent work has been vaunted as state-of-the-art for analysing convergence of quantities like countries' incomes. Their paper is available online through Google Scholar.

My interest in the paper was threefold. Firstly, the paper's tests are useful in themselves. Secondly, I wanted to see the theoretical methods used, with a view to adopting them elsewhere. Thirdly, I wanted to see whether the methods could be considered as part of larger theories with more general application.

The paper tests the convergence of quantities y(i,t) which can be expressed as the product of a time specific function and a country specific function. The country function can also vary over time. The idea is to take ratios across countries to get rid of the time specific component, then look at variances across groups. If the ratio's variance is going to zero over time, we have convergence. A tidy equation follows from the expansion of the ratio which allows for regression testing.

Here is the general methodology used:

1. Transform the base equation to get an expression dependent on only one key quantity. Expand the expression into a familiar form.

2. Determine asymptotics.

3. Apply moment conditions.

Here are candidate metatheories corresponding to each stage. The list is by no means exclusive or exhaustive, and other taxonomies could be made.

1. A theory classifying all transformations of base equations into expressions dependent only on quantities of interest. Perhaps group theory from pure mathematics may help here.

2. Weiner process theory.

3. GMM analysis.

I would like to bring recent work on estimation into a similar classification and so combine the theories in a systematic way. Have to see how it goes.

My interest in the paper was threefold. Firstly, the paper's tests are useful in themselves. Secondly, I wanted to see the theoretical methods used, with a view to adopting them elsewhere. Thirdly, I wanted to see whether the methods could be considered as part of larger theories with more general application.

The paper tests the convergence of quantities y(i,t) which can be expressed as the product of a time specific function and a country specific function. The country function can also vary over time. The idea is to take ratios across countries to get rid of the time specific component, then look at variances across groups. If the ratio's variance is going to zero over time, we have convergence. A tidy equation follows from the expansion of the ratio which allows for regression testing.

Here is the general methodology used:

1. Transform the base equation to get an expression dependent on only one key quantity. Expand the expression into a familiar form.

2. Determine asymptotics.

3. Apply moment conditions.

Here are candidate metatheories corresponding to each stage. The list is by no means exclusive or exhaustive, and other taxonomies could be made.

1. A theory classifying all transformations of base equations into expressions dependent only on quantities of interest. Perhaps group theory from pure mathematics may help here.

2. Weiner process theory.

3. GMM analysis.

I would like to bring recent work on estimation into a similar classification and so combine the theories in a systematic way. Have to see how it goes.

### How does a neoclassical growth model fail in a non-classical world?

A neo-classical growth model assumes that income growth is primarily determined by output supply constraints, in the form of limits on capital, labour, and other factor inputs. Income distribution and macroeconomic flows are not generally modelled. Its predictions come under stress in today's economy where growth seems to be influenced by these factors, both domestically and internationally.

A neoclassical model may have a production function of the form y=A.k^b where y is output per person, k is capital per person, and A and b are constants. The production function is not the neoclassical part, having been used in Keynesian models and saying nothing about the flow of income. It is the other equations expressing dynamics which characterise the model as neoclassical or not. A neoclassical growth model may have dk/dt = s.y where t is time and s is a constant, so capital accumulation is independent of everything apart from the previous production. On differentiating the production function with respect to time we get dy/dt.df/dy = dk/dt.A.b.k^(b-1), and we can then substitute dk/dt and k from the production function and accumulation function to get dy/dt in terms of y alone.

We can alternatively posit an accumulation function dk/dt = s.y.I(y < c) for an indicator function I equal to one if y is less than a constant c and zero otherwise. We may be trying to capture a demand effect, where people only want or can afford goods up to a certain level of production, and then stop buying so companies in response stop accumulating (k is assumed to be the only factor of production here). Under this accumulation equation, we would have an identical growth equation up to y=c, then suddenly the neo-classical equation for dy/dt in terms of y would stop working.

One could find other examples.

A neoclassical model may have a production function of the form y=A.k^b where y is output per person, k is capital per person, and A and b are constants. The production function is not the neoclassical part, having been used in Keynesian models and saying nothing about the flow of income. It is the other equations expressing dynamics which characterise the model as neoclassical or not. A neoclassical growth model may have dk/dt = s.y where t is time and s is a constant, so capital accumulation is independent of everything apart from the previous production. On differentiating the production function with respect to time we get dy/dt.df/dy = dk/dt.A.b.k^(b-1), and we can then substitute dk/dt and k from the production function and accumulation function to get dy/dt in terms of y alone.

We can alternatively posit an accumulation function dk/dt = s.y.I(y < c) for an indicator function I equal to one if y is less than a constant c and zero otherwise. We may be trying to capture a demand effect, where people only want or can afford goods up to a certain level of production, and then stop buying so companies in response stop accumulating (k is assumed to be the only factor of production here). Under this accumulation equation, we would have an identical growth equation up to y=c, then suddenly the neo-classical equation for dy/dt in terms of y would stop working.

One could find other examples.

## Monday, 12 January 2009

### Applications for MA Economic and Governmental Reform at the University of Westminster

Here's another reminder about applying and getting funded for the MA Economic and Governmental Reform at the University of Westminster.

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 (linked here), 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 performance 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.

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 (linked here), 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 performance 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.

### Causality between growth, investment, and education

The relation between economic growth, investment, and education is interesting in all causal directions. On one hand, the determinants of economic growth are studied widely; on the other, the impact of economic growth on its determinants indicates the extent of influence economic outcomes exert on the allocation of resources. If high growth tends to lead to high education rates at the same time as education leads to growth, it would seem that society tends to adjust its resource allocation to promote further growth. A slightly longer route of influence might have education leading to increased investment and then investment leading to increased growth; in which case higher education might be demanded by the providers of investment.

Here is a VAR analysis of the relations

X1 = (B0,B1,B2,B3)*(1,L.X1,L.X2,L.X3)' + normal zero mean error

where X1, X2, and X3 are the three variables and ' denotes transpose. L. denotes their first lags. The analysis is for three European countries, and three African countries. Data is from the Penn World Tables and Barro and Lee, dating back to 1960 and grouped in five year sets.

In all countries, either education or investment is associated with future increased growth; their lack of individual significance or their negative signs may indicate collinearity. In all countries education is associated with increased future investment share; it may be that education encourages investment.

In the European countries, investment is associated with increased future education, as would be expected in a growth motivated society. In two of the African countries, investment is associated with lower future education; the link between growth and education provision seems weaker. It is possible that business has less lobby power on the state, or does not require a high level of education, or education is a national priority to compensate for low investment.

Click to enlarge:

Here is a VAR analysis of the relations

X1 = (B0,B1,B2,B3)*(1,L.X1,L.X2,L.X3)' + normal zero mean error

where X1, X2, and X3 are the three variables and ' denotes transpose. L. denotes their first lags. The analysis is for three European countries, and three African countries. Data is from the Penn World Tables and Barro and Lee, dating back to 1960 and grouped in five year sets.

In all countries, either education or investment is associated with future increased growth; their lack of individual significance or their negative signs may indicate collinearity. In all countries education is associated with increased future investment share; it may be that education encourages investment.

In the European countries, investment is associated with increased future education, as would be expected in a growth motivated society. In two of the African countries, investment is associated with lower future education; the link between growth and education provision seems weaker. It is possible that business has less lobby power on the state, or does not require a high level of education, or education is a national priority to compensate for low investment.

Click to enlarge:

## Thursday, 8 January 2009

### Congolese rebel split

There are uncertain and volatile reports emerging of a split in the CNDP rebel group in DR Congo. The CNDP is a dominant force in the East, and I briefly assumed that the split would be with members who are more willing to work for peace. My mistake. The BBC is reporting the secessionist as a hardliner, nicknamed the Terminator. How long have I been studying Central Africa?

### Country groups for diffusion of different technologies

This post looks at the historic patterns of diffusion by country for various technologies. It uses principal components analysis to combine variables measuring each country’s technology level into a new set capturing most of the variation in as few variables as possible. These new variables are then stated in terms of their main country variable components. For example, if 50 percent of data variation in the prevalence of personal computer use is captured by the variables

0.4 x Italian rate + 0.7 x US rate + small contributions from other countries

0.5 x Canadian rate + 0.8 x UK rate + small contributions from other countries

we would identify personal computer use as described by the shared expansion in groups consisting of Italy and the US on one hand, and Canada and the UK on the other.

The data is from a new dataset entitled HCCTAD by Comin and Hobijn, available here. The dataset covers the ownership and use of around 30 technological products, both capital and consumer goods, for 23 developed countries for the last 250 years (with breaks). My analysis is restricted to the current members of the G7 leading industrialised countries.

The summarised results are in the table. The table shows the existence of clear diffusion groups in capital goods, but much more homogeneity in the spread of consumer goods. It may be that the conditions which determine capital good consumption are more internationally variable than consumer demand preferences.

0.4 x Italian rate + 0.7 x US rate + small contributions from other countries

0.5 x Canadian rate + 0.8 x UK rate + small contributions from other countries

we would identify personal computer use as described by the shared expansion in groups consisting of Italy and the US on one hand, and Canada and the UK on the other.

The data is from a new dataset entitled HCCTAD by Comin and Hobijn, available here. The dataset covers the ownership and use of around 30 technological products, both capital and consumer goods, for 23 developed countries for the last 250 years (with breaks). My analysis is restricted to the current members of the G7 leading industrialised countries.

The summarised results are in the table. The table shows the existence of clear diffusion groups in capital goods, but much more homogeneity in the spread of consumer goods. It may be that the conditions which determine capital good consumption are more internationally variable than consumer demand preferences.

## Sunday, 4 January 2009

### Technology may stay when the money leaves

The skills and knowledge of foreign companies can help to develop a country, and if they transfer to domestic companies, could remain after the foreign companies leave. One macroeconomic mechanism for the transfers occurred to me today when reviewing the literature on exchange rates.

The exchange rate research suggests a mechanism by which long run domestic income could be raised by a change in domestic money. It works like this:

1. Domestic money is inflated a little

2. Consumption rises because prices domestically and internationally are sticky in the short term

3. Some of the consumption is on foreign bonds

4. Prices adjust in the long term

5. The purchased bonds continue to pay interest.

The sequence amounts to a transfer from the foreign country to the domestic country. There are analogous transfers when looking at one country alone, such as where small unexpected inflationary increases can result in a financial transfer from producers to consumers. Incidentally, a systematic attempt by government to exploit the mechanism is likely to result in retaliation and a possible inflationary spiral.

Back to technology, which could be inserted in the mechanism to take the place of bonds in a direct way, although the other stages have to be adjusted a little. The new mechanism for technology spread could be:

1. Domestic money is deflated a little (equivalently, foreign money could be kept as reserves)

2. Foreign consumption rises

3. Some of the expenditure is on foreign direct investment, and technology transfer results

4. Prices correct in the long term

5. The technology transfer remains

I think this mechanism may not rely exclusively on price stickiness, and so may able to be exploited more systematically. Exporting countries which maintain artificially low exchange rates may be doing just that.

I am not sure whether the approach should be considered a gain to the technology receiver at the expense of the technology sender, even if the sending country would not choose the approach from all possible money-mediated outcomes. Although the strategy creates new competition for the sender in the long run, it also promotes the development of the receiver so that they may become partners on a more equal, profitable basis. Underpricing of developing countries' currencies may - on this narrow measure - be Pareto optimal.

The exchange rate research suggests a mechanism by which long run domestic income could be raised by a change in domestic money. It works like this:

1. Domestic money is inflated a little

2. Consumption rises because prices domestically and internationally are sticky in the short term

3. Some of the consumption is on foreign bonds

4. Prices adjust in the long term

5. The purchased bonds continue to pay interest.

The sequence amounts to a transfer from the foreign country to the domestic country. There are analogous transfers when looking at one country alone, such as where small unexpected inflationary increases can result in a financial transfer from producers to consumers. Incidentally, a systematic attempt by government to exploit the mechanism is likely to result in retaliation and a possible inflationary spiral.

Back to technology, which could be inserted in the mechanism to take the place of bonds in a direct way, although the other stages have to be adjusted a little. The new mechanism for technology spread could be:

1. Domestic money is deflated a little (equivalently, foreign money could be kept as reserves)

2. Foreign consumption rises

3. Some of the expenditure is on foreign direct investment, and technology transfer results

4. Prices correct in the long term

5. The technology transfer remains

I think this mechanism may not rely exclusively on price stickiness, and so may able to be exploited more systematically. Exporting countries which maintain artificially low exchange rates may be doing just that.

I am not sure whether the approach should be considered a gain to the technology receiver at the expense of the technology sender, even if the sending country would not choose the approach from all possible money-mediated outcomes. Although the strategy creates new competition for the sender in the long run, it also promotes the development of the receiver so that they may become partners on a more equal, profitable basis. Underpricing of developing countries' currencies may - on this narrow measure - be Pareto optimal.

### Income and prices as technology spread co-determinants

Here is an illustration of one of the pitfalls of measuring how technology spreads across countries. It concerns the relation of income and technology prices, which are sometimes tested as possible co-determinants of the technology level in a country, such as:

Computers per person = a*national income + b*computer cost + c*other variables

where a and b are scalar constants and c is a vector constant. National income and computer cost are collinear, their constants being connected through the Slutsky equation:

deltaQuantity/deltaPrice =

deltaQ(U fixed)/deltaPrice - quantity*deltaQuantity/deltaIncome

where delta means partial differentiation, and Q(U fixed) denotes the quantity minimising costs for a particular level of consumer satisfaction (this is the usual taught formulation of the Slutsky equation and is a bit unappetising but I do not regularly teach it so don't have any better approach - apologies). The equation means

change in quantity =

change due to substitution with other goods because of relative price changes

+ change due to lower total purchasing power as the cost rises.

In the computer example, it becomes

b = Substitution effect (which is always negative) - a*quantity.

The collinearity should theoretically be recognised and corrected for when estimating, but it isn't always. Of interest here is interpreting a result from a recent paper looking at computer and internet dissemination which finds b is small and a is large (after adjusting quantity, price, and income to be in comparable units). For b to be small, the substitution effect would have to be small. Plausibly it is in poor countries (computers and the internet are not wanted much no matter how their price varies?) and in rich countries (computers and the internet may be cheap to begin with or have no substitutes?). Additionally, a*quantity would have to be small, which means that the quantity must be small since a has been found to be large. It probably is small in developing countries, but not in developed countries.

So the observed finding of small price effect and large income effect may indicate misspecification, collinearity, or income proxying for omitted variables.

Computers per person = a*national income + b*computer cost + c*other variables

where a and b are scalar constants and c is a vector constant. National income and computer cost are collinear, their constants being connected through the Slutsky equation:

deltaQuantity/deltaPrice =

deltaQ(U fixed)/deltaPrice - quantity*deltaQuantity/deltaIncome

where delta means partial differentiation, and Q(U fixed) denotes the quantity minimising costs for a particular level of consumer satisfaction (this is the usual taught formulation of the Slutsky equation and is a bit unappetising but I do not regularly teach it so don't have any better approach - apologies). The equation means

change in quantity =

change due to substitution with other goods because of relative price changes

+ change due to lower total purchasing power as the cost rises.

In the computer example, it becomes

b = Substitution effect (which is always negative) - a*quantity.

The collinearity should theoretically be recognised and corrected for when estimating, but it isn't always. Of interest here is interpreting a result from a recent paper looking at computer and internet dissemination which finds b is small and a is large (after adjusting quantity, price, and income to be in comparable units). For b to be small, the substitution effect would have to be small. Plausibly it is in poor countries (computers and the internet are not wanted much no matter how their price varies?) and in rich countries (computers and the internet may be cheap to begin with or have no substitutes?). Additionally, a*quantity would have to be small, which means that the quantity must be small since a has been found to be large. It probably is small in developing countries, but not in developed countries.

So the observed finding of small price effect and large income effect may indicate misspecification, collinearity, or income proxying for omitted variables.

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