Most empirical growth models are not theoretically complicated. For example, one may be based on the assumption that output is
Output = A * Capital ^ a * Labour ^ (1-a)
or, dividing by labour,
Output per person = A * Capital per person ^ a
where A and a are constants. If one takes logs in the equation, then subtracts the same equation in the previous time period, one gets
ln output p.p.(t) - ln output p.p. (t-1) = a*(ln capital p.p. (t) - ln capital p.p. (t-1))
The left hand side is approximately equal to (output(t)- output(t-1))/(output(t)), which can be shown by using the Taylor expansion for ln (1+{output(t)/output(t-1) - 1}). The term is thus approximately equal to the growth in output, and we have a model
growth in output p.p. = a*growth in capital p.p.
The model has ignored many aspects of the economy, such as alternative production functions, differences across countries, aggregate demand, changes across time, other influences on growth, and influences of growth on changes in capital.
Yet the empirical testing of the model has been reasonably successful. One of the reasons is that the empirical testing does much of the clean-up work for the model. For example, if we test
growth in output p.p. =
a*growth in capital p.p. + country specific constant + time specific constant + error
the error will often be robustly estimated, so handling wide fluctuations in the quality of the fit and the direction of the model's bias. The country and time specific constants capture factors which may dwarf the explanatory power of the basic model. The estimation will frequently employ methods to handle endogeneity of variables, which allows for the possible omission of other relations between the variables in the model.
In short, if a growth model is assessed to be an empirical success, it is usually the model and the estimation method which are the successes.
Monday, 8 September 2008
Thursday, 4 September 2008
Endogenous growth through technological innovation
As a further point to make on the last post, the tentative results imply that growth could be sustained indefinitely rather than heading to a steady state, although it would slow through diminishing returns to capital. Indefinitely here means a few decades, since economies could change hugely in the period rendering the model invalid. Pretty short time period for "indefinitely"!
My estimations indicate that having a higher proportion of the world's computers and researchers tends to increase growth, and that other countries cannot obtain, in the short term, the growth benefits associated with their ownership just by transferring technology from abroad. Thus, there seems to be a definite advantage with being a technological pioneer, which may help to explain the ability of economically advantaged countries to sustain their growth over time.
My estimations indicate that having a higher proportion of the world's computers and researchers tends to increase growth, and that other countries cannot obtain, in the short term, the growth benefits associated with their ownership just by transferring technology from abroad. Thus, there seems to be a definite advantage with being a technological pioneer, which may help to explain the ability of economically advantaged countries to sustain their growth over time.
The coefficient on the lagged income term in technological growth models
Estimations of the growth model
income growth per person = constant0
+ constant1*income last period
+ constant2*capital accumulation
+ constant3*education increase
+ constant4*technological transfer from abroad
+ error
typically find constant1 less than zero if constant4 is set to zero before the estimation begins. So as income increases, growth declines.
If technological transfers are allowed and constant4 is estimated rather than set to zero, then my recent estimations have found constant1 to be very small, and may be positive or negative. It would seem that technological transfers account for much of the reason why growth is estimated to be lower in rich countries than in poor countries, when cross-sectional or panel data estimation is used. It also helps to explain why time series for economically leading individual countries often do not show such marked declines in their growth as would be expected from estimations.
The results are sensitive to the estimation method, and so are quite tentative at the moment.
income growth per person = constant0
+ constant1*income last period
+ constant2*capital accumulation
+ constant3*education increase
+ constant4*technological transfer from abroad
+ error
typically find constant1 less than zero if constant4 is set to zero before the estimation begins. So as income increases, growth declines.
If technological transfers are allowed and constant4 is estimated rather than set to zero, then my recent estimations have found constant1 to be very small, and may be positive or negative. It would seem that technological transfers account for much of the reason why growth is estimated to be lower in rich countries than in poor countries, when cross-sectional or panel data estimation is used. It also helps to explain why time series for economically leading individual countries often do not show such marked declines in their growth as would be expected from estimations.
The results are sensitive to the estimation method, and so are quite tentative at the moment.
Religious affiliation and women's workforce participation
As a possible partial answer to the question raised in the last post of factors which have influenced increased women's economic participation, the rise in secularisation of society may be one. A paper in a leading economic journal in 2003 ("People's Opium? Religion and Economic Attitudes") found that people who were actively religious or even just raised religiously were more likely than non-religious people to think that:
1. When jobs are scarce, men should have more right to a job than women
2. Women should have children in order to be fulfilled
3. Being a housewife is just as fulfilling as working for pay
4. A university education is more important for a boy than a girl
The authors split the results by religion for questions 1 and 4, and find that Muslims tend to agree most with them, followed by Hindus, then Catholics, and then Protestants. Members of the smaller religions have wide variation in their opinions. There may be some advantage in religious expansion through supporting the views, perhaps through increasing family size. Being an atheist significantly lowers agreement with the statements. Women have obtained more prime ministerial and presidential positions in countries with the large religions as the largest belief systems than in formally atheist countries or countries associated with smaller religions, so there may be some political-economic trade off or internal social tensions at work.
The paper is not available online, but the survey data it is based on is free at http://www.worldvaluessurvey.org/. There is considerable variation by country, and some of the results can be surprising. The data covers much more than just attitudes to women or religion.
1. When jobs are scarce, men should have more right to a job than women
2. Women should have children in order to be fulfilled
3. Being a housewife is just as fulfilling as working for pay
4. A university education is more important for a boy than a girl
The authors split the results by religion for questions 1 and 4, and find that Muslims tend to agree most with them, followed by Hindus, then Catholics, and then Protestants. Members of the smaller religions have wide variation in their opinions. There may be some advantage in religious expansion through supporting the views, perhaps through increasing family size. Being an atheist significantly lowers agreement with the statements. Women have obtained more prime ministerial and presidential positions in countries with the large religions as the largest belief systems than in formally atheist countries or countries associated with smaller religions, so there may be some political-economic trade off or internal social tensions at work.
The paper is not available online, but the survey data it is based on is free at http://www.worldvaluessurvey.org/. There is considerable variation by country, and some of the results can be surprising. The data covers much more than just attitudes to women or religion.
Granger causality between growth and women's education
Here's a little evidence from Burkina Faso on the Granger causality between per capita economic growth and women's education, or to put it another way, whether economic growth happens first or women's education happens first. The examination contributes a little to the question of whether women's rights are to any extent a product of capitalist expansion directly or whether women's rights are the product of social changes generated outside of capitalism, in the sense of not being the result of demands by profit maximising companies. The latter interpretation does not exclude the possibility that the social changes have been enabled by capitalist social structure changes.
Two models are empirically tested. Estimation 1 is
Growth in a country =
constant1
+ constant2 * growth in a country some time ago
+ constant3 * women in primary education as a percentage of total people in primary education the same time ago
+ error
and estimation 2 is
Percentage of women in primary education =
constant4
+ constant5 * percentage of women in primary education some time ago
+ constant6 * growth in a country the same time ago
+ error
If growth has a positive effect on women's participation in education, then the constant6 will be positive, and conversely if it is negative. If the evidence is weak, then constant6 will be insignificant, that is, estimated with much uncertainty in the results. If women's participation has a positive effect on growth, similar statements apply to constant3.
I focussed on Burkina Faso because it has increased its women's participation in education from 36.9 percent in 1980 to 42.2 percent in 2002, so has some variation in its figures allowing for more precision in estimation. Western countries generally have had constant levels over the same period, and data was not available from the sources used (annual 1980-2002, from the UN and Penn World Tables) over earlier periods. A larger number of countries could have been used, but would have increased the time for data preparation. Burkina Faso also has avoided very severe social and economic dislocation during the period under consideration, which would distort the data.
OLS estimation was used, which is consistent for large amounts of data; we have 22 years worth, so the results should be reasonably accurate.
For estimation 1, constant3 is positive over all time lags. The first significant coefficient comes at time lag 6, when both constant2 and constant3 are significant at ten percent. A delay for the effect of increased female educational participation on growth to be evident would be expected. Thus, per capita growth appears to be positively associated with earlier increased female educational participation in Burkina Faso.
For estimation 2, constant6 varies between positive and negative signs depending on the time lag, and never comes near to significance at ten percent. Thus, economic growth does not seem be associated with future increased female participation in education in Burkina Faso, and increased participation seems likely to have been caused by other reasons. The results suggest that pure economic growth considerations - which may proxy for corporate profitability - have not influenced women's participation to any great extent in the country.
The results are an indication of the degree of influence capitalism exerts in Burkina Faso, and the importance of other social factors in effecting a major change in policy. Burkina Faso is still a pre-capitalist society to a great extent, and it would interesting to see whether the results translate to other countries and different measures of women's equality, and in particular to more capitalist societies. It would be surprising if economic growth seems to exert no influence on women's equality, since capitalist development is clearly a huge influence on society and possibly the principal one. If it is not significant, then the question arises of what social influences have been significant enough to effect apparently large changes in women's social participation over a very brief historical period.
Two models are empirically tested. Estimation 1 is
Growth in a country =
constant1
+ constant2 * growth in a country some time ago
+ constant3 * women in primary education as a percentage of total people in primary education the same time ago
+ error
and estimation 2 is
Percentage of women in primary education =
constant4
+ constant5 * percentage of women in primary education some time ago
+ constant6 * growth in a country the same time ago
+ error
If growth has a positive effect on women's participation in education, then the constant6 will be positive, and conversely if it is negative. If the evidence is weak, then constant6 will be insignificant, that is, estimated with much uncertainty in the results. If women's participation has a positive effect on growth, similar statements apply to constant3.
I focussed on Burkina Faso because it has increased its women's participation in education from 36.9 percent in 1980 to 42.2 percent in 2002, so has some variation in its figures allowing for more precision in estimation. Western countries generally have had constant levels over the same period, and data was not available from the sources used (annual 1980-2002, from the UN and Penn World Tables) over earlier periods. A larger number of countries could have been used, but would have increased the time for data preparation. Burkina Faso also has avoided very severe social and economic dislocation during the period under consideration, which would distort the data.
OLS estimation was used, which is consistent for large amounts of data; we have 22 years worth, so the results should be reasonably accurate.
For estimation 1, constant3 is positive over all time lags. The first significant coefficient comes at time lag 6, when both constant2 and constant3 are significant at ten percent. A delay for the effect of increased female educational participation on growth to be evident would be expected. Thus, per capita growth appears to be positively associated with earlier increased female educational participation in Burkina Faso.
For estimation 2, constant6 varies between positive and negative signs depending on the time lag, and never comes near to significance at ten percent. Thus, economic growth does not seem be associated with future increased female participation in education in Burkina Faso, and increased participation seems likely to have been caused by other reasons. The results suggest that pure economic growth considerations - which may proxy for corporate profitability - have not influenced women's participation to any great extent in the country.
The results are an indication of the degree of influence capitalism exerts in Burkina Faso, and the importance of other social factors in effecting a major change in policy. Burkina Faso is still a pre-capitalist society to a great extent, and it would interesting to see whether the results translate to other countries and different measures of women's equality, and in particular to more capitalist societies. It would be surprising if economic growth seems to exert no influence on women's equality, since capitalist development is clearly a huge influence on society and possibly the principal one. If it is not significant, then the question arises of what social influences have been significant enough to effect apparently large changes in women's social participation over a very brief historical period.
Monday, 1 September 2008
Record reductions in track records
One of my interests is track athletics, and I am fascinated by reductions in world record times over distances. It impresses me most when there are major reductions in the records, since the record holder has not just been fit and naturally gifted, but has had the mental toughness to do something no-one has come near to before, and in doing so moved the whole sport forward.
Wikipedia has lists of world record progressions from this page; in all events beyond 800 metres, African men feature prominently. The women are less prominently featured, which could be for several reasons. The most substantial recent record reductions by African men are the 1.4 second reduction in the 1500 metres in 1998; the 4.5 second reduction in the 3000 in 1996; the 11 second reduction in the 5000 in 1995; and the minute reduction in the half-marathon in 1993. These would all be the equivalent of a reduction of more than 0.05 second over 100 metres. The 5000 metre reduction is the equivalent of 0.14 seconds off the 100 metres time, and is the largest percentage reduction here. Given when it occurred, in a frequently competed event, and the subsequent competition to reduce it further, it is arguably the most impressive revision of a track record in recent years.
Wikipedia has lists of world record progressions from this page; in all events beyond 800 metres, African men feature prominently. The women are less prominently featured, which could be for several reasons. The most substantial recent record reductions by African men are the 1.4 second reduction in the 1500 metres in 1998; the 4.5 second reduction in the 3000 in 1996; the 11 second reduction in the 5000 in 1995; and the minute reduction in the half-marathon in 1993. These would all be the equivalent of a reduction of more than 0.05 second over 100 metres. The 5000 metre reduction is the equivalent of 0.14 seconds off the 100 metres time, and is the largest percentage reduction here. Given when it occurred, in a frequently competed event, and the subsequent competition to reduce it further, it is arguably the most impressive revision of a track record in recent years.
Recommendations for a start-up economy's institutions
I'm polishing a research paper at the moment, and don't have too many new results to report. So I thought that it would be a good time to consolidate some earlier results, and produce some recommendations for the economic institutions of a newly established country or newly autonomous region within a country:
1. Technology transfers from rich countries have a huge effect on economic growth. Getting students into foreign countries is often associated with growth, as are some forms of imports of technological goods. Poor countries are probably going to benefit more from transfers of less advanced technologies than of cutting edge ones, so building domestic industries accordingly might be a good idea.
2. A recent paper on growth found that presidents are frequently good for their economies for a decade, but their performance drops off afterwards. A four and a half year term for the government, possibly with limits on presidential or prime ministerial office of two terms, would seem to allow for changes before the performance falls.
3. Oil producing states may wish to create strong competitive meritocracies in promotions to government and senior administrative positions. Output in their economies responds less to educational accumulation than output in non-oil producing economies, so educational achievement is likely to be rewarded relatively poorly in the market.
4. Transparency and education in government are important for avoiding foreign investors gaining excessive returns in a country.
5. In dealing with foreign countries interested in gaining control over a country's resources, it may be possible to play the foreigners off against each to achieve greater benefits.
1. Technology transfers from rich countries have a huge effect on economic growth. Getting students into foreign countries is often associated with growth, as are some forms of imports of technological goods. Poor countries are probably going to benefit more from transfers of less advanced technologies than of cutting edge ones, so building domestic industries accordingly might be a good idea.
2. A recent paper on growth found that presidents are frequently good for their economies for a decade, but their performance drops off afterwards. A four and a half year term for the government, possibly with limits on presidential or prime ministerial office of two terms, would seem to allow for changes before the performance falls.
3. Oil producing states may wish to create strong competitive meritocracies in promotions to government and senior administrative positions. Output in their economies responds less to educational accumulation than output in non-oil producing economies, so educational achievement is likely to be rewarded relatively poorly in the market.
4. Transparency and education in government are important for avoiding foreign investors gaining excessive returns in a country.
5. In dealing with foreign countries interested in gaining control over a country's resources, it may be possible to play the foreigners off against each to achieve greater benefits.
Subscribe to:
Posts (Atom)