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.
Tuesday, 8 July 2008
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) + c.education(t) + 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.
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) + c.education(t) + 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.
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!
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?
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.
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) + c.technology change (t-1) + error1
technology change(t) = d+ e.technology 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.
growth(at time t) = a+ b.growth(t-1) + c.technology change (t-1) + error1
technology change(t) = d+ e.technology 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.
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