Thursday, 31 July 2008

Lagged income and the omitted accumulating variables in a MRW production function

In the MRW production function, production per person y at a particular time is given by


where k is physical capital per person, h is human capital per person, and A, a, and b are constants. A is meant to capture the average effect of all other terms influencing production.

The dynamics of y are introduced by many authors through assuming that capital accumulates as Dk = s.y(t-1) - p.k(t-1), where s and p are constants, y(t-1) is y at time t-1, and Dk=k(t)-k(t-1). This equation allows y to be replaced by A.k(t-1)^a.h(t-1)^b, so that if Dk=0, we can solve for a value of k which means that there is no further change in y from capital accumulation. We could assume a similar expression for human capital and solve it to find a pair of (k,h) which ensures that y is unchanged forever, or only experiences random shocks which are corrected by the same adjustment processes.

So if k and h are changed - either from outside the system, for example because of foreign direct investment or immigration, or because of capital accumulation - then output adjusts instantly to the inputs. The accumulating equations are the sources of adjustment in the economy, and do not moderate the speed of output response to new inputs. There is a problem here, because one might expect some delay as output adjusts to the new inputs. New markets might have to be set up to sell the goods, or people's expertise might have to be included in the productive process.

We could enter a new factor n in the production equation to allow for the effect of all other accumulating variables:


There are many possible omitted accumulating variables, so that the constant c would vary a great deal between two different economies. Taking logs and differencing gives


If we are going to estimate in an equation, we need some proxy variable for Dlnn. It is probably unobservable and certainly difficult to observe, so finding a proxy can be awkward. But we have the lagged income term, y(t-1). This has a neat property that

correlation(Dlnn, y(t-1)) =
(Cov(Dlnn, c.lnn) + other terms which are probably less important)/ Var(Dlnn).Var(y(t-1))

So if the first covariance term is large relative to the variation in income and in the accumulation, ie if the n variable is a strong accumulator, this term will be close to unity and y(t-1) will be a good proxy for the change in lnn. This is a likely reason why the lagged income term is so helpful in growth regressions. Our explanation differs from the criticised linearisation-around-a-steady-state theory of the origin of the lagged term, or the also criticised proxy-for-technology theory of origin. Unlike them, our explanation gives a very clear reason why the lagged term is unstable.

Equipment for African research

When preparing economic research papers, there are many doh! moments where one realises that one of the assumptions or methods used much earlier was wrong, and the whole thing has to be reworked. Happily, in theoretical analysis, it is usually just a matter of adjusting a few formulae and the rest of the reworking is automatic, and in applied analysis, frequently the computer programs supplied at most universities just need a few tweaks and everything else follows.

For applied analysis without computer programs, the reworking can be painful. I know it all too well. It can multiply the time taken for a research project many times. In African universities where necessary equipment for economic and other scientific research is either missing or rationed, the resulting delays in research must be frustrating.

The problem is longstanding in Africa. In the 1930s and 1940s when several (primarily Francophone, given their educational system) African writers were producing works comparable with those of their European contemporaries, I think it is fair to say that there were few, if any, scientists from the occupied continent who could match the best of the West. I may be ignorant of African history here, but surely the lack of equipment would have seriously hindered their scientific production.

Monday, 28 July 2008

Growth theory's predictive limitations

In several major papers on economic growth, the estimates of convergence to steady states vary between two percent and eight percent each year. That means that every year, the difference between current and potential income reduces by between two percent and eight percent, where economic potential is determined by capital per person and education per person. At two percent narrowing every year, within forty years the difference should have halved, while at eight percent, the difference will halve within a decade.

The potential for many developing countries is also estimated to be higher than developed countries since their savings rate can be much higher (which provides an estimate of capital, at least once the country reaches its steady state). So why are these developing countries not already far richer than the West? They have generally had at least a decade of capitalist growth, but are still generally quite poor.

Part of the problem is with omitted variables, which account for much of the growth. Misspecification in assuming a country constant and constant autoregressive parameter in the growth equation when the true autoregressive parameter is variable across countries leads to overestimates of growth at low levels of income and underestimates at high levels, as demonstrated in one of my earlier posts. And standard estimation methods based on GMM tend to overstate growth generally in misspecified AR(1) models.

Selection of non-autoregressive parameters in GMM under misspecification

Here's an observation about the behaviour of the GMM estimates in a misspecified AR(1) model. The estimated model is

y(t) = a.y(t-1) + b.x(t) + error

while the real generating process is

y(t) = a(i).y(t-1) + b(i).x(t) + error.

The a(i) and b(i) vary across groups. I showed on 14th July that if the b(i)=b=0 for all i, then GMM selects an a estimate near the top of the range of the a(i). This post discusses what happens if the bs are not zero.

My procedure for analysis is that one takes the standard formula for an OLS estimate of the a and b parameters, then plugs in the misspecified formulae, and rearranges the formulae a wee bit to make the expressions look like weighted averages. If the b(i)s are all the same, then no matter what the behaviour of the as, the estimate for b is unbiased. If the b(i)s vary, then the estimator tends to select the parameters from the series with the highest xs, and the lowest autoregressive parameters.

I haven't worked this analysis through the GMM System and Difference estimators, but suspect that the behaviour will be the same, as the OLS is a variant of GMM. Cross-country growth theory empirics often use these GMM estimators, so the estimates will tend to be near the top of the range across countries for the lagged autoregressive parameter, and the non-autoregressive parameters will tend to come from low autoregressive parameter countries.

The next couple of sentences are more conjectural. Given that the majority of growth tends to be explained outside the augmented classical determinants of capital and education accumulation, countries whose growth is substantially explained by these determinants may be among the low growth countries with low autoregressive parameters. Thus, the non-autoregressive parameters may be near the top of the range too, and growth is likely to be overstated by the estimates.

Thursday, 24 July 2008

What sort of technology promotes growth best?

The theoretical and empirical finding in many works on growth and technology is that technology is most effective in promoting growth when it is suitable for the education level in a country. Thus, sending biotechnology laboratory equipment to a country where no-one can read is unlikely to promote growth as much as sending tractors. My own current studies find that if, in a particular year, a poor country has far fewer computers per person than other countries, their subsequent growth isn't affected much. On the other hand, if they have fewer telephones in a particular year, their future growth tends to be higher than if not, other things being equal. A plausible explanation is that technology catch-up is occurring; transfers of telephone technology are usually both feasible and suitable for the education levels in a poor country, whereas computer technology transfers are often just feasible.

But there is a caution on this interpretation. A gap affects growth through its influence on transfers. Thus the causality of effect on growth is gap-->transfers-->growth. The "inappropriate for education" hypothesis states that the second stage breaks down. But in low income countries, the first stage may also break down for certain goods, for a variety of reasons.

The meaning of technology, reprise

In a post from the Monday before last I defined technology as

"physical capital with a high level of education or knowledge required in use or maintenance."

The technology level might be defined as this education or knowledge, technological transfers as changes in technology by virtue of foreign influences, and technological gaps as the difference in technological levels between two countries.

These definitions sound like they might be OK, but encounter problems when one tries to use them in a production function. For example, with the famous (MRW) production function, we have

Output per person = A*capital per person^alpha*education per person ^beta

where A, alpha, and beta are constants. The technology level is a measure of education, so presumably education per person should be decomposed into something like

Output per person = A*capital per person^alpha
*(technology-relevant education per person) ^beta1
*(non-technology-relevant education per person)^beta2

where beta1 and beta2 are new constants. But then, how would the (non-technology relevant education per person) variable be defined? And if the technology changes, how should education be repartitioned? Furthermore, if we look at the original MRW production function, it is apparent that all education helps to increase the output of physical capital, so all education could be defined as the technology level, and our definition is weak.

Similar problems arose when I tried to define technology as the part of total factor productivity due to education. After playing around with various definitions, I think the following set works and captures the main content of the theory of scientific technology transfers:

"An economy’s technology level is defined non-uniquely as a measure of the scientific processes employed when using or maintaining aggregate physical capital. A technology gap is the difference in the technology levels between two economies. Technology transfer is defined to be an inflow to an economy from another economy, whether of knowledge or physical capital or another quantity, which change the scientific processes employed in use or maintenance of physical capital."

The definitions do not overlap with definitions of other variables, so the technology level can be entered into production functions without creating problems of determining the residual parts of variables which are not captured by technology levels. They allow for neat theoretical expressions of production functions including technology which embed many other production functions in them, whether they have included technology's effects or not.

Monday, 21 July 2008

Recession or cycle?

There is lots - lots and lots - of talk in the UK at the moment of an economic recession. High oil prices are blamed for much of the problem, no doubt accurately. But will it be a recession? There is another candidate, a long term shift in the growth of the UK and other Western economies.

Recessions in the 1970s or early 1980s followed oil price hikes when the OPEC cartel raised its prices. The UK emerged from the recession following price reductions. This time, oil price increases are caused (as I mentioned in my last post) in large part by increased global demand from emerging countries whose economic size will soon be comparable with the combined size of current developed nations. This demand won't be reversed barring major global economic downturns when all countries will be in trouble, so the UK and the West will have to adjust to higher prices permanently. These prices have been associated with recessions in the past. So, the West may have to move along with slower growth for a longer period.

There will be an upswing eventually. It relies on the emerging countries wanting to buy Western goods, innovating and transferring technology to the West, and generally acting as Western countries do today. This shift takes time, so the current downturn in the UK economy may be less of a business cycle-type recession, and instead one of the longer cycles which economic historians have identified.

High oil prices do not always prevent global warming

Occasionally it is stated that high oil prices may prevent global warming since people will not want to buy so much oil. That is true if high oil prices were caused by suppliers raising their prices. But the current increase in prices is caused in large part by increased global demand. As demand increases, oil prices go up, but so does the amount consumed. So demand led oil price increases is an indicator that global warming is likely to increase.

The IMF and new open economy macroeconomics

The IMF is soon to have a new economic counsellor. The position coincides with its research directorship. The counsellor (Olivier Blanchard) is a leading figure in new open economy macroeconomics (NOEM), as was a former high profile occupant in the late 1990s (Kenneth Rogoff).

The IMF's commitment to leading NOEM figures is interesting in terms of the direction it seems to want to move its research. Very roughly, NOEM papers have attempted to model economies starting from the behaviour of individual consumers and companies, then aggregate the behaviours to get a behaviour for a whole economy, then combine them with other (often one other) economies with the same underlying behaviour to see what happens. Their markets tend to exhibit classical behaviour on a small scale but Keynesian behaviour on large scales.

NOEM may be viewed as a step towards perfection of the neo-classical synthesis, which attempts to combine Keynesian and classical views of economies. Other schools of thought reject the neo-classical synthesis for various reasons. One point of concern I have about NOEM, even though it is impressive and has begun to attract some appealing empirical estimation, is that it is necessarily limited by the speed at which innovations in it emerge. I am not an expert on the field, but I do not think debt is adequately incorporated in NOEM models yet. So even with the full NOEM literature, much is uncertain about one of the world economy's major challenges.

Friday, 18 July 2008

The future course of the oil price

I don't much like supply and demand diagrams, because from a mathematics point of view, they are irritating. The determinant quantity should be on the x-axis, not the y-axis. They are fiddly and look like 18th century schoolbooks on geometry. And what self-respecting economist draws things to sort out their understanding?

Very occasionally, they are fab. Like in determining the future course of the oil price. There is a lot of conjecture about whether the oil price will increase to $200 dollars a barrel by the end of the year. That's where a simple supply and demand diagram can be helpful.

Here's the diagram. The demand curve for global oil is the lower line. As the world economy expands by say 6% a year, the quantity demanded increases by 6% at every price assuming that the new growth is supported by the same oil requirements as the old growth. The demand curves are assumed to be linear; we are interested in short term changes around the equilibrium point, so the assumption is OK. The supply curve is vertical as oil output is not quickly increased, but the curve can slant a bit without changing the analysis.

If demand keeps increasing every year by 6%, then gradually the demand curve will move towards the horizontal, and it will do this more slowly every year. If you think about it, an infinite number of years would be required to reach the horizontal, so it would have to slow down eventually. The price increases also decline if demand increases are the same each year, as the price moves gradually towards its value at the intercept.

The maximum market driven growth in prices (as opposed to politically caused growth) will occur somewhere between now and the time at which world economic growth is at its maximum. Given China and India's path to growth, that time is probably some date in the next thirty years, and the maximum growth is unlikely to be far higher than it is today. So the maximum increase in oil prices is unlikely to be more than its current rate of 25% a year in the near future, at least until supply starts to run out. From the diagram, a gentle rise in price would be expected once supply does dwindle.

Now the change in price depends on the heights and slants of the curves, so a detailed analysis would be required to assess exactly the change in price over time. What we have is recent price change information. Part of the change is a premium due to political events and risk, but they are so closely intertwined with oil pricing that we might say that they should be considered permanent influences on the price. Around 10% growth would be expected in the second half of the year, bringing the oil price to between 140 and 150 dollars a barrel by the end of the year. Oil price is a politically influenced quantity, so there is considerable uncertainty of course, but $145 is my market-based estimate.

Water, the pinnacle of the economic pyramid

There was a news story last year about how inflation in China had spiked because of the price of pork if I remember correctly. It was strange - you have an emerging economic and political superpower, whose economy is heavily disturbed by the price of a single meat. Now the UK is undergoing a similar hike in inflation because of rises in the prices of food and oil.

The inflation spikes really bring out the inverted pyramid-like nature of an economy. For all the complexity and diversity of production in most of the economy, what underpins everything are a few essential commodities whose supply does not vary much.

Some environmentalists have indicated that wars may occur over water in the future. The assertion is credible. Petroleum we can do without, even if our standard of living falls; we can change to cheaper diets, at least in the rich countries; but water supplies, taken for granted in most of the developed world, are at the sharp pinnacle of the pyramid.

UK security involvement in Nigeria

There has been unfavourable coverage given in the Nigerian and UK media to possible UK security involvement in the Niger Delta ( Lots of other commitments were also discussed in the meeting of the two national premiers this week, but it is the training and advisory support for security that has attracted the attention. Apparently, France has also made a similar offer to Nigeria (

British petroleum companies have interests in the Niger Delta, and production has been halted by attacks by local militias who want increased control over oil revenues from the region, where much of Nigeria's oil wealth is concentrated. British involvement would be commercially motivated, and at best morally neutral; much of the oil wealth has been allegedly (with much documentation) stolen by corrupt leaders in the past, and Nigeria's elections have been heavily criticised for fraud and violence (

Personally, I do not support secessionist groups which spring up whenever oil is discovered in their region, but the social context in the Niger Delta makes me more sympathetic towards the Delta insurgents. As I looked for information on the British involvement on, I came across these other stories from the Nigerian press, which put a context on the activity. Perhaps there is some journalistic licence, but the stories are consistent with others coming out of the country:

"WOMEN of Obodogugu-Ogume community in Ndokwa area of Delta State protested naked, yesterday, while no fewer than eight persons, including a policeman have been shot by armed youths in a renewed orgy of violence between the community and the people of Emu-Ebendo over negotiations with an oil company..."

"The trouble with Nigerian youths has been highlighted by the death of a dozen or more applicants for jobs at the Nigeria Immigration Service last Saturday. Many jobseekers died from exhaustion during a 3-4km marathon race to determine their physical fitness before they could take part in a written test. Others were victims of stampedes at the venues where millions of unemployed youths were chasing a few hundreds of jobs."

"The Chief of Defence Staff, General Owoye Azazi, yesterday told the Senate ad-hoc committee on the Green Tree Agreement that the former president, Chief Olusegun Obasanjo, did not consult the military before the cession of Bakassi Peninsula to Cameroon. General Azazi also told the panel that the fighting between Nigeria and Cameroon over Bakassi is courting the attention of France and would likely result into war, giving the recent pact between France and Cameroon."

Monday, 14 July 2008

The meaning of technology

Technological capital is intuitively easy to understand, as it is things like computers and advanced manufacturing processes. A working definition might be physical capital with a high level of education or knowledge required in use or maintenance. International technological transfers might be defined correspondingly as adoption of physical or intellectual capital from overseas which increase the technological capital in an economy.

The definitions work, but they have often not been used in the economic growth literature. It is quite common to define technology as total factor productivity - the output of the economy divided by the value of its inputs, particularly physical capital, educational capital, and labour. This definition means that technology could include many things which do not seem very technological, such as a stable political environment.

However, it does have the advantage that the interaction between education and total factor productivity can be investigated. If total factor productivity is heavily influenced by technology defined by my criteria - goods requiring a high educational content for use - then one would expect that there should be a high correlation between education and total factor productivity. Some writers have found that the relation exists, and I think that the hypothesis of a link was made at least as early as the 1960s.

A few other writers do use measures of technology transfer which could coincide with my definition, although they may not state the broad definition.

Why GMM selects high parameters in misspecifications

My earlier posts have described how within group OLS, difference GMM, and system GMM estimators select parameters from the high end of the range b(i) when they are estimating a model like

y(i, t) = a(i) + b.y(i, t-1) + error,

(y(i,t) is data for group i at time t, a(i) is a constant for each group, and b is a constant within and across groups)

when the true generating process is

y(i, t) = a(i) + b(i).y(i, t-1) + error

(b(i) is a constant within groups).

It's a feature of GMM, particularly where the weighting matrix is the identity matrix. Within groups OLS is an instance of GMM, so is covered by the same theory.

If we look at the main moment conditions for any of the estimators, they are

E(y*error)=0 or E((change in y)*error)=0 or E(y*(change in error))=0.

There's a slight difference for system and difference GMM when dealing with homoscedastic errors.

Take the first moment condition, applicable to OLS. GMM sets equal to zero sums of terms of the form

y(i,t-1) * (y(i,t) - b*y(i,t-1) - c(i)).

We can replace y(i,t) with its true generating process to get

y(i,t-1) * (b(i)*y(i,t-1) - b*y(i,t-1) + error).

When the b(i) are positive, y(i, t) will in the long run almost certainly be larger when b(i) is larger. It follows that b will tend to the highest of the b(i), since this parameter has more weight in the equation. The expected tendency is monotonic upward as sample sizes increase.

The original GMM recommended optimal weighting matrix may help to correct for the tendency, but is often not used in the growth literature, and the misspecification means that no parameter is more accurate than another although the impression it gives may be more useful. I think that Wald test estimation between two subsets of the data may also be distorted - high standard errors combined with selection of high parameter values from the ranges may give an artificial impression that two different regions of the world have the same generating processes.

Thursday, 10 July 2008

Which accumulation matters most for growth?

It is often argued that East Asia's rapid economic growth is down to two features primarily, the rapid accumulation of capital and labour in the market economy. But there are others who argue that productivity growth has been important for them. There are still others who argue for the importance of transfer of technological knowledge, not just in East Asia's growth but global growth.

Sorting the last issue out has been hampered by limited empirical studies on the role of technological transfer in growth. My recent work jumps into the lacuna, and there are some useful results emerging.

In a system GMM regression for a fifty year panel of all countries around the world and with five year country growth as a dependent variable, investment has seven percent average effect, education has an insignificant coefficient at a 0.2 p-value, so does population growth, so does the lagged income term, and the gap in telephones per person compared with the United States has a 12 percent effect. Average effects are calculated as estimation coefficients times the variable mean over the whole dataset. It is a bit rough, and the results will change with different estimation methodologies. But it is noticeable that the effect of a technology gap contributes more to growth than capital accumulation. The presence of a lagged income term removes some of the possibilities that the technology gap is picking up the effect of missing variables.

In fact, the presence of a lagged income term is not theoretically necessary. If it is omitted, the results are telephone gap has a 10% effect, investment 8%, education 7%, and population growth is insignificant.

If change in telephones per person is used instead, with no lagged term, the results are telephones per person change 7% effect , investment 5%, education is insignificant, population growth is insignificant. If change in computers per person is used, the results are computers per person change 1% effect, investment 10%, education -4%, population growth -4%.

If the data is restricted to Africa, and change in telephones per person is used, the fit is pretty good, with telephone per person change having 6% effect, investment 8%, education 15%, population growth 18%. I'm a bit sceptical about the value of the population growth results in developing countries as mentioned in my post last week. If lagged income is included, the results are telephone change 8% effect, investment 5%, education is insignificant, population growth 16%, lagged income 87%. I included a constant in the estimations, which help to explain the large effect of the lagged income, as the constant is large and negative.

If the data is restricted to South East and East Asia only without a lagged term, change in telephones per capita is insignificant as is population growth, investment has 6% effect and education has -23% effect. It is plausible that education's effect is negative because of the inclusion of communist states in the data, who educated highly but did not have market systems for much of the time. With the lagged income term, only investment is significant at 10 percent.

Well, there are lots of caveats to be made here, but it seems that capital accumulation has been the leading explanation for growth in South East and East Asia, but globally technology transfers are as important as the other forms of accumulation.

Research paper content: a student guide

My earlier post on research paper structuring described how many economic research papers are structured. This post talks a little about the content of papers. It may help to keep the ideas coming when writing papers and essays.

The structure of many research papers, as mentioned, is along the lines of

1. Research questions
2. Their importance
3. Other people's work
4. Plan
5. Theory
6. Applied specification
7. Empirical method
8. Inputs
9. Outputs
10. Discussion in the paper's context
11. Discussion in a wider context

The structure also often repeats internally within sections.

The sections typically contain small advances for the whole paper, followed by extensive consolidation relative to earlier sections. So, in the inputs section for example, the use of a particular source of data will be discussed, in terms of content like:

whether it provides good data to help answer questions (relating to metasection 1)
whether other people have used the data before (relating to metasection 3)
the innovations in the current paper's usage (relating to metasection 3)
how it is inserted in an empirical specification (such as by averaging, or removing poor quality data, or that sort of thing) (relating to metasection 6)

and so on. All the discussion emerges from a single statement like "we will use World Bank data". Similarly in the outputs section, a results table might be discussed in terms of

whether questions are answered
whether the specification has influenced the results
whether theory is correct
if there are any changes when the data source changes

and so on. Usually the discussions are relative to sections which have already been undertaken, for obvious reasons of comfort for the reader.

The points above do not complete research papers by themselves, but they help avoid the "my research paper is complete at 200 words but has got to be 20000 words" feeling.

Tuesday, 8 July 2008

Neglecting India

China's economic growth and potential attracts a huge amount of attention in the popular and economic literature. Its neighbour India attracts much less, despite growth not far behind and a similarly sized population. The latter observation is the important one. In a capitalist economy, other things being equal, economic output is determined solely by the number of people producing in it. India's economic potential is much the same as China's, and it is getting there just a bit later. Given time, measured in a lifetime or two, its economy will be larger than that of the United States or Western Europe barring global catastrophe.

The neglect perhaps arises from greater familiarity with India than China and less sense of threat in the West. India's ties with the West should not be dismissed lightly; they may be among the last and greatest gifts of the British Empire back to Britain and its interests. Consider an India which had been highly politically repressive in the last century and which today naturally aligned itself with dictatorial regimes in Asia and elsewhere. India's democracy tips the political and economic balance in favour of non-repressive states, and will keep it that way as the world's economy expands. Global warming may be the most important single determinant of the world's future, so to weaken Bismarck's statement about the United States in the 19th Century, the most important political fact for the future of the world may be that India speaks English.

Biases in common estimation methods

The GMM System estimator and other estimators of the AR(1) model have been tested many times in the academic literature in clinical situations where data is generated from Monte Carlo models which look like y(t)=a + b.y(t-1) + group constant + error. They are also frequently used in testing complex applied models such as y(t) = a + b.y(t-1) + other covariates + group constant + error.

I was interested in testing the performance of the estimators in Monte Carlo situations, but facing a complexity of data similar to that of the applications. So I generated data for a hundred countries, based on a model

income per person (t) = a + b.income(t-1) + + d.investment(t) + e.population growth(t-1 to t) + f.changes in the number of telephones per person (t-1 to t) + error.

The various variables are given common proxies: ln(gdp per capita), years of education, and investment/GDP.

The starting points for the countries were those actually observed over the last forty years, that is, I used as the starting data for the Monte Carlo simulations the actual country data for the first year that sufficient data was available for any estimation to be viable. The synthetic data was generated subsequently by Monte Carlo using the parameters and standard errors from the within groups estimator of the base data and updated on a period by period basis, so that the right hand side variables could themselves be updated from their own Monte Carlo sequences based on the parameters of OLS estimates (for example from investment(t) = g + h.investment(t-1) + i.income(t-1) + error).

The final Monte Carlo data was then put through the estimation methods. For the GMM estimators, both the theoretically optimal instrument set (which Sargan tests on GMM SYS comprehensively rejected) and optimal tests (according to Sargan) were tried. The results below are representative.

As you can see, the GMM DIF has good estimates compared with the generating model, and the within groups OLS is pretty good too. The GMM SYS is less good, though the signs are correct. I am not sure why.

Friday, 4 July 2008

Population growth as a poor proxy for capitalist workforce growth

It is common in papers on economic growth to proxy capitalist workforce growth by the growth of the overall population.

This assumption yields a good approximation in developed countries with stable populations and birthrates. In countries where the capitalist workforce is swollen by people coming out of subsistence farming and moving into paid labour, the assumption could be dreadful. Since most developing countries have exactly such a workforce, the assumption requires urgent revision. It is likely to overstate the estimated effects on economic growth of other forms of accumulation.

Research paper structuring: a student guide

Part of the difficulty of reading and writing research papers is knowing where to get started with them. Even smart students with lots to say can struggle to begin or maintain their impetus.

The problem in economics should be less than in some other disciplines. Modern economics is primarily scientific in its approach and methods, and the structure of research papers (though not always the content, thankfully!) is highly standardised. Although I do not mark down papers which deviate from academic structuring so long as the student shows evidence of being able to make the structure take whatever form they wish, many markers do reduce grades and students may find the following points helpful for that and other reasons.

A typical theoretical or empirical paper in a leading journal usually is structured overall according to a form like:

1. Statement of research questions answered
2. Their importance
3. Other people's work on the questions
4. Plan
5. Theory
6. Specification of applied theory
7. Method of applied analysis
8. Inputs to analysis
9. Outputs from analysis
10. Interpretation of results in the model's context
11. Interpretation of results in the wider context

The structures are usually fairly clear from chapter headings, although not all of them occur in every paper. Their internal repetition within research papers and their subsections should not be understated. For example, in the section on the method of applied analysis, the structuring might go:

A research question from the earlier theoretical work (analogy to section 1)
Statement of other people's applied approaches to the question (analogy to section 3)
Statement of methods to use (analogy to section 7)
Comments on theoretical and other aspects of the methods (analogy to section 8)
Rationalisation of usage (analogy to section 10)
Robustness checks (analogy to section 11)

Even within paragraphs the structure can occur. For example, when a paper is discussing someone else's research paper, their research questions might be stated, then their method, then their results, then the limitations of the work. That's sections 1, 7, 9, and 11.

The observations above should take a bit of the worry out of writing research papers. There's still the content to find though!

Chinese bank funding: another short account

I mentioned in a previous post that I think that understanding the methods of savings mobilisation in China and East Asia generally is important for understanding their growth and other people's potential growth. There's another account of the mobilisation on the World Bank website.

The description argues that although the bank sector is deep and wide in China, it has not been very important in growth because the Chinese state which owns most of the banks does not make loans for strictly profit based reasons, and many of them are badly performing. It points to data showing that in provinces where the banking sector is deep, growth is lower. This argument would seem to support the idea that it is internal savings which are funding corporate growth. The argument does raise the question of why people deposit in banks so much if they are that unprofitable - wouldn't it be more sensible to invest in companies?

Generating full Solow data

I'm spending much time setting up a Monte Carlo program which will generate reasonable data for global growth models. When testing estimation methods, many papers have looked at very simple data from models like Y(t)=a + b.Y(t-1) + error. My model introduces endogenous variables in the right hand side too, for multiple countries and time periods.

It doesn't sound too complex, but when one tries to implement it, there are complexities of what sort of standard errors should be used, how to generate the endogenous terms, and so on. Sometimes simple tasks demonstrate many different knots such as the differences between prediction standard error (the uncertainty in the difference between a model's predictions and expected observed data) and the forecast standard error (the uncertainty between a model's predictions and actual observed data, so the prediction error plus the data's error). Another point the task has clarified is why so many papers on growth do not report any constants in their regressions. It would seem to be because the country specific constants are not zero mean, so if they are not reported then the country specific constants are meaningless. It is not a great reason.

Tuesday, 1 July 2008

VAR growth estimates

I ran vector autoregressive (VAR) models for per capita technology measures and growth across countries a few days ago. These models look like

growth(at time t) = a+ b.growth(t-1) + change (t-1) + error1
technology change(t) = d+ change (t-1) + f.growth(t-1) + error2

where a, b, c, d, e, and f are constants. Technology change was measured as per capita change in the number of telephone lines and cell phones.

This plain VAR is a swizz, since the estimates are the same as for OLS, although the standard errors are not as accurate. ARIMA estimation of the same model is not great either, since the exact estimates are usually replaced by the outcomes of numerical optimisation.

Anyway, the estimates of the parameter c are generally negative across countries. I was a bit disappointed at first, as my hypothesis is that greater changes in technology lead to increased growth. But on reflection, the results do not reject the hypothesis. Growth (t-1) and technology change (t-1) are themselves highly correlated, so their two effects are not easily distinguished particularly over short time periods. Furthermore, there is an omitted variable, income, which is correlated with both growth and technology change. However, the correlation is probably far higher with growth usually, so that if growth(t) is small then growth(t-1) is probably small from the omitted variable bias, whereas technology (t-1) is not certain to be small. So growth(t-1) tends to attract a positive bias from the omitted variable, whereas technology gets a negative one.

This argument is roughly right I think but there may be a few caveats and it would better be expressed in mathematical terms.

I had hopes for my VAR estimates on a per country basis, but the two problems mentioned make things difficult. At their heart is the limited number of time periods commonly used in growth regressions, itself caused by the five year averaging in many research approaches including the one above. Adding many other covariates in the model makes the estimates highly uncertain because only five to seven datapoints are available by country, and the estimates in a limited period VAR estimation are perhaps severely biased too. They are probably not even consistent. It is no wonder panel data estimation, for all its faults, has gained ascendancy.