Growth theory: Solow or Lucas?

I've just come across a new OECD economic working paper on growth theory: Solow or Lucas? Testing growth models using panel data from OECD countries. Authors Jens Arnold, Andrea Bassanini and Stefano Scarpetta test whether the growth experience of a sample of OECD countries over the past three decades is more consistent with the human-capital augmented Solow model of exogenous growth, or with an endogenous growth model à la Uzawa-Lucas with constant returns to scale to “broad” (human and physical) capital. Here's their methodology:

We exploit the different non-linear restrictions implied by these two models to discriminate between them. Using pooled cross-country time-series data, we specify our growth regression by imposing cross-country homogeneity restrictions only on  long-run  coefficients, while  letting  the  speed  of  convergence  and  short  term  dynamics  to  vary  across  countries.

Their conclusions?

The results suggest a strong effect of human capital accumulation: the estimated long-run effect on output of one additional year of education (about 6-9%) is also within the range of the estimates obtained in microeconomic analyses of the private returns  to  schooling. Our estimated speed of convergence is too fast to be compatible with the augmented Solow model, while is consistent with the Uzawa-Lucas model with constant returns to scale. This main finding is robust to several robustness tests. 

Comments

[David]

This is really terrific work, but I'd note one problem that makes comparison kind of 'unfair' (if such a thing as fairness exists in comparison of economic models). If you look at the laws of motion for human capital in their versions of Solow and Uzawa-Lucas the technology by which individual's 'invest' tells different stories. In the Solow model they posit that growth in human capital comes from savings of the final good, but then use years of education as its proxy. This proxy is a bit imprecise, as explained by Mulligan and Sala-i-Martin (2000), by assuming return to education is the same in every OECD country, and is especially troublesome when we are considering it in difference terms, as in the ECM.
Less technical, if human capital accumulates due to spending out of total production, shouldn't human capital be measured by some spending figure, perhaps labor income method? Basically, it's unit consistency.
In the endogenous-education model we have human capital growing by time devoted to education, and this seems consistent with approximating with a measure of time devoted, i.e. years of education. But then to estimate the law of motion, they assume a constant 'savings choice' of 1/3 of working life in school. However, in the Solow, saving towards education varied year-to-year. I'm still thinking about all the implications, but comparability of the motion implied by these two models with such different processes seems troublesome.
Especially when so much of the model's conclusions are based on the level and motion of this human capital thing, and the estimates lynch on this data about human capital. When they constrain the coefficient on the log stock to be 1, the actual level becomes quite important. It seems that along with this 'robustness' test, we need to consider the implications of its level being noisily estimated.

[Arthur Eckart]

I think, it's very difficult to accurately measure human capital, in cross country or intertemporal models, because of differences in quantity and quality, e.g. in education or output. Also, accumulation of human capital is a lifetime achievement (i.e. through education, experience, training, etc.) rather than only in school years. Moreover, investment in human capital has increasing or decreasing returns to scale depending on the individual. Nonetheless, the evidence suggests developing aggregate human capital has a permanent positive effect on aggregate growth, although it's a small piece of the equation (there are also negative growth factors).

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Abstract
( http://ideas.repec.org/p/pra/mprapa/2739.html )
A two-component model for the evolution of real GDP per capita in the USA is presented and tested. The first component of the GDP growth rate represents an economic trend and is inversely proportional to the attained level of real GDP per capita itself, with the nominator being constant through time. The second component is responsible for fluctuations around the economic trend and is defined as a half of the growth rate of the number of 9-year-olds. This nonlinear relationship between the growth rate of real GDP per capita and the number of 9-year-olds in the USA is tested for cointegration. For linearization of the problem, a predicted population time series is calculated using the original relationship. Both single year of age population time series, the measured and predicted one, are shown to be integrated of order 1 – the original series have unit roots and their first differences have no unit root. The Engel-Granger approach is applied to the difference of the measured and predicted time series and to the residuals or corresponding linear regression. Both tests show the existence of a cointegrating relation. The Johansen test results in the cointegrating rank 1. Since a cointegrating relation between the measured and predicted number of 9-year-olds does exist, the VAR, VECM, and linear regression are used in estimation of the goodness of fit and root mean-square errors, RMSE. The highest R2=0.95 and the best RMSE is obtained in the VAR representation. The VECM provides consistent, statistically reliable, and significant estimates of the coefficient in the cointegrating relation. Econometrically, the tests for cointegration show that the deviations of real economic growth in the USA from the economic trend, as defined by the constant annual increment of real per capita GDP, are driven by the change in the number of 9-year-olds.

____________________________________________________________

Abstract
( http://ideas.repec.org/p/pra/mprapa/2738.html )

Growth rate of real GDP per capita is represented as a sum of two components – a monotonically decreasing economic trend and fluctuations related to a specific age population change. The economic trend is modeled by an inverse function of real GDP per capita with a numerator potentially constant for the largest developed economies. Statistical analysis of 19 selected OECD countries for the period between 1950 and 2004 shows a very weak linear trend in the annual GDP per capita increment for the largest economies: the USA, Japan, France, Italy, and Spain. The UK, Australia, and Canada show a larger positive linear trend. The fluctuations around the trend values are characterized by a quasi-normal distribution with potentially Levy distribution for far tails. Developing countries demonstrate the increment values far below the mean increment for the most developed economies. This indicates an underperformance in spite of large relative growth rates.

[Lafayette]

David: "But then to estimate the law of motion, they assume a constant 'savings choice' of 1/3 of working life in school."

This is based upon the erroneous assumption that education starts and finishes early in life, it seems.

With globalization, once backward economies are playing a furious game of catch-up with the developed world, particularly in the un- and semi-skilled employment sectors. As a result, we should rethink the above assumption.

Can we really content ourselves with primary, secondary and post secondary education/training? Maybe for artisans/craftsmen. The unemployment rate for Plumbers and Electricians is very often lower than it is for System Analysts.

But, for other professions I submit that the training must be life-long. Furthermore, why assume that families must save for a child's education? In America the cost of a university education is enormous for a family with two children. Most European governments have seen the advantage of nationally subsidized Education (as well as Health Care) for all who wish to pursue it. It is only the US that is backwards in the matter.

Why burden families with the responsibility of paying for Education (or Health Care). Do we ask them to pay for their local police forces? The local firemen? Do we send them a bill for National Defense. No, these are considered Public Services available to all and paid for by National/State Tax Revenues.

Then why are Education and Health Care not included as well (in America)? Because it genuflects too often to the notion that "market always gets it right"? I suggest so.

Solow is looking at the matter solely from the American point-of-view. Which is incorrect, I maintain. The government should be paying for establishing and maintaining workforce skill sets. And, people who refuse to do so, and are amongst the unemployed, should be required to sharpen their skills -- perhaps even change professions.

If not, the government will be paying for the consequences of NOT establishing / maintaining them ... by resulting increased long-term Unemployment Rates (that lead to delinquency and crime as well.) The further consequence is a reduced standard of living for much of the population.

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