Concluding Remarks on the Empirics of the Theory of Production

The above ndings strongly support the validity of the employed SolowModel without tech-nology and thus yield strong evidence of the simultaneous operation of the classical principles of labor division and of diminishing returns provided by equation 3.6. If there exists an equally strong negative contemporaneous eect (PoDR) and a positive lagged eect (PoLD) of popula-tion growth on GDP per capita growth over the subsequent periods, a change in the populapopula-tion growth rate will obviously negatively eect GDP per capita growth, as has been impressively conrmed by the data as follows.

Evaluating annual data on 104 countries over a period of 55 years, 34 countries over a period of 65 years and 10 countries over a period of 114 years, our estimations imply that a birth rate reduction from 4% to 1%  as is often observed in developed countries  raises production per capita by the factor sixteen. If these results are correct, the historically observed decline in fertility can account for the largest part of the historically experienced sustainable rise in production per capita. Moreover, our estimations suggest that the production elasticity of broad capital lies in the range (0.60, 0.75), suggesting a production elasticity of population in the range (0.25, 0.40), which has often erroneously been calculated to lie in the interval (0.66, 0.75).

Although employing a quite dierent approach, the results are roughly in line with those of Mankiw et al. (1992) and Ashraf et al. (2013), providing supportive evidence of the neoclassical growth model. Further research will be required to conrm the idea that an appropriate form of the aggregate production function is approximated by Y (K, H, N) = K^1/3H^1/3N^1/3.

A calculation of γ may alternatively be conducted by using the production exhaustion theorem to determine the income share of population. To this end, we would have to employ average unskilled labor wages or minimum wages with regard to the whole population (which may in fact be termed geographical wages or population wages) and to compute their income share (1- γ) on total GDP. This share should be found to lie in the interval (0.25, 0.40). Moreover, while this empirical exercise provided a relatively simple approach to productivity, adhering to Cobb and Douglas' method of attack, the model might be extended by accounting for a fourth constant production factor  land  that is not subject to accumulation and depreciation. This

7 See footnote 5 for our empirical denition of constancy. The longest series (fourty years) displaying a constant birth rate is given by the UKdata.

may imply that even the density of the population is relevant in determining development and that population growth exhibits diminishing returns in the long run. Finally, since physical and human capital accumulation of a country are sometimes strongly encouraged by foreign investments, future research on the topic may allow for a varying national savings rate. These external adjustments toward an ecient international division of labor may account for the remaining unobserved variation in our regressions.

In summary, the empirical evaluations of the last two chapters reported a signicant positive shortrun eect of GDP per capita growth on the variable birth rate, a signicant positiveshort run eect of death rate on birth rate and a signicant negative longrun eect of birth rate changes on GDP per capita growth. All these results point toward the correctness of the four principles of classical economics and support the valid use of the classical unied growth model, which has moreover been found to be able to illustrate the stylized facts of a transition from an economic regime of stagnation, exhibiting high rates of births and deaths, to an economic regime of development, exhibiting steadily decreasing rates of births and deaths. Accepting these results as suciently mirroring reality, we will in the last chapter use the classical unied growth model to summarize and discuss its implications and to speculate about the future economic development suggested by this model.

Implications of Classical Unied Growth Theory

120

Speculations on a Future Regime of Stagnation

9.1 The Recent Development

To assess the potential future economic development, we will continue the above line of thought that an early regime of stagnation is, in every economy, followed by a regime of development as long as mortality decreases. The left graph of Figure 9.1 extends the time horizon of Figure 6.1 by adding the most recent years of British history. Firstly, it is worth remarking that the death rate had achieved a low sustainable level of 0.125 as far back as the 1920s and has only slightly decreased since. Secondly, the birth rate roughly adjusted to the death rate during the 1970s and seems to have settled on a constant low level close to, but higher than the death rate. For better visualization, the presumed demographic transition from a weakly preventively checked toward a strongly preventively checked economy is stylized in the right graph of Figure 9.1.

Figure 9.1: Left graph: British return to stagnation: Birth rate (blue), death rate (red) and GDP per capita (green) 18022016. Right graph: Stylized fact return to stagnation.

Sources: GDP: Clark (2009) for 18001871, Mitchell (2013) for 18712010, Vital Rates: Wrigley and Schoeld (1981) for 18001871, Mitchell (2013) for 18712010.

121

Thirdly, British real GDP per capita has slowed down to nearstagnation since the year 2007.

Projecting this development into the future decades might suggest an additional stylized fact which remains to be evaluated, namely the return to what has lately been termed secular stagnation, which is illustrated by the last regime late stagnation in the right graph of Figure 9.1. This idea of a new era of stagnation is sustained when extending the simulation by another one hundred periods, supposing a constant death rate (see Figures 9.2 and 9.3). We should, however, keep in mind that our simulation used a single labor division lag of merely fteen years, whereas our estimations suggested a continuous labor division lag of approximately 65 years. The next section will give a short outline of the eects, the decisive operation of the great preventive check principle of generation is supposed to have on future population growth and growth in production according to our classical unied growth theory.

Figure 9.2: A simulation of a constant future death ratein growth rates (birth rate (blue), death rate (red), GDP per capita growth rate (light green)).

Figure 9.3: A simulation of a constant future death rate in level variables (population (orange), production (blue) and GDP per capita (green)).