4.6.1 An exogenous shock in fertility
Consequently, having shown that Malthus suggested that the principle of population displayed its full power to increase merely in theory, it should be asked by what forces its pressure has been attenuated, or checked, in reality. Stating in his second proposition that
population invariably increases where the means of subsistence increase, unless prevented by some very powerful and obvious checks,22
he implicitly determined the conditions under which population would not hit the limits of sub-sistence. Having exhaustively determined productivity as the ratio of production to population, the pressure of population could only be relaxed by either increasing the means of subsistence
Y or by checking powerfully and obviously population N. To advance the latter remedy, we will rst have to exhaustively de ne the checks to population, employing again the de nition of a change in population, i.e. ∆N = B − D.
Mr. Malthus has divided the checks to population [N] into the preventive and the positive.
The rst are those which limit fecundity, the second those which decrease longevity. The rst diminish the number of births [B], the second increase that of deaths [D]. And as fecundity and longevity are the only elements of the calculation, it is clear that Mr. Malthus's division is exhaustive.23
Hence, the three dinstinct remedies eligible for mitigating the pressure of population and con-sequently raising the level of productivity are positive checks, increasing the means of subsis-tence and preventive checks. It has been argued that neither positive checks nor increasing production are in the case of an unrestricted principle of population capable of releasing the pressure of population permanently and therefore raising productivity in the long run. When thus excluding these options as potential forces toward a more permanent increase in production per capita, it remains to evaluate the nal option, i.e. to reduce the pressure of population by checking the number of births preventively and to conclude that the preventive checks are solely responsible for the escape from the Malthusian trap. It is regularly overlooked that this result follows directly from one of Malthus' most crucial illustrations.
In an endeavour to raise the proportion of the quantity of provisions to the number of consumers in any country [y = Y/N], our attention would naturally be rst directed to the increase of the absolute quantity of provisions [Y ]; but nding that, as fast as we did this, the number of consumers [N] more than kept pace with it, and that with all our exertions we were still as far as ever behind, we should be convinced, that our eorts directed only in this way would never succeed. It would appear to be setting the tortoise to catch the hare.
Finding, therefore, that from the laws of nature we could not proportion the food [Y ] to
22 Malthus (1826), book I, chapter II.
23 Senior (1836), p. 141.
the population [N], our next attempt should naturally be, to proportion the population to the food. If we can persuade the hare to go to sleep, the tortoise may have some chance of overtaking her.24
Although often portrayed as a pessimist, Malthus saw the improvement of the individual eco-nomic situation as a very real possibility. Evidently, if population growth is restricted, the power of population will not be fully exerted. Moreover, if and only if the power of population is em-banked, a situation is created in which production can possibly outrun population, generating per capita growth. Logically, apart from the positive checks, the only feasible way by which
the hare could be persuaded to go to sleep was to propose birth control and hence to check population preventively.
It is not in the nature of things that any permanent and general improvement in the condition of the poor can be eected without an increase in the preventive check; and unless this take place, either with or without our eorts, everything that is done for the poor must be temporary and partial. [. . . ] This is a truth so important, and so little understood, that it can scarcely be too often insisted on.25
According to Malthus, the preventive checks include any action aecting the number of births, which reduces the maximum rate of fertility. Analogously to the case of the positive checks, he advised employing the level of the birth rate to measure the operation of the preventive checks, as this was the only way to exhaustively capture the preventive checks:
The preventive check is perhaps best measured by the smallness of the proportion of yearly births to the whole population.26
Accordingly, wherever the preventive checks are strong, the birth rate will be observed to be low and vice versa.
Applying the foregoing considerations, it ought to be the decisive argumentation of a uni ed growth theory that only with the onset of the fertility decline population was increasingly pre-vented from eating up productivity gains, hence enabling economic growth in terms of GDP per capita. Moreover, this work intends to support the idea that the main distinction between the two regimes can be be reduced to their contrasting modes of population control. In particu-lar, with the onset of the fertility decline, the era of stagnation characterized by positively checked periodic overpopulation displayed by high death rates is replaced with a modern growth regime, because a potentially abundant part of the population is constantly preventively checked, i.e. via birth control, measured by low birth rates. We may therefore answer to the above mentioned skeptical economist: Yes it's true we observe increasing GDP per capita and at the same time decreasing population growth. But this does not contradict Malthus, it is part of his story. An increase in the preventive check causes population growth to decline which is in turn an immediate cause for the increase in productivity.
24 Malthus (1826), book IV, chapter III.
25 Malthus (1826), book IV, chapter XIII.
26 Malthus (1826), book II, chapter XI.
4.6.2 An exogenous shock in fertility in the neoclassical model
Using a neoclassical framework, this section illustrates mathematically and graphically that sus-tainably increasing productivity is predominantly the result of reducing too high fertility toward a lower level. This result is broadly in line with Galor (2011), who suspects that a substitution of child quality for child quantity backed the takeo toward a sustained path of economic devel-opment. In particular, Ashraf et al. (2013) nd a negative eect of fertility on GDP per capita that can account for about 10% of long-run growth.27 The classical framework here outlined argues that the historical reduction of fertility can almost completely explain economic longrun development.
It has commonly been argued that the neoclassical growth model used in chapter three is incom-plete as it does apparently not account for the historically observed increases in productivity.
As we have seen, this claim often overlooks the eect stemming from a potential decrease in the birth rate as was depicted in the structural equation of chapter three:
gyt,j = γ
1 − γ(ln bt−j− ln bt) (4.1)
While a higher birth rate reduces the steadystate value of productivity, we nd that an ex-ogenous decrease of the birth rate is wellquali ed for causing productivity growth during the transition between two steady states. More explicitly, as is depicted in Figure 4.4, a continuously decreasing birth rate from bt−j toward btis expected to yield continuous productivity growth, as in this case the right hand side of equation 4.1 will be positive.28 The advanced theory suggests that economic development is, in this case, caused solely by the bene cial eects from the PoLD outweighing the detrimental eects of PoDR.
Figure 4.4: A population slowdown in the Solow model.
27 The perhaps most recent evaluation of this argument is provided by Chatterjee and Vogl (2018).
28 A result that has been con rmed by a number of studies on economic development including Sachs and Malaney (2002).
Furthermore, from the observed stylized facts it can be derived that population growth formerly seemed to outperform growth in production, causing stagnation, whereas in more recent times population growth is observed to have slowed down, oering the potential for economic devel-opment. Obviously, our neoclassical model ts perfectly into this framework, as it provides a wellestablished theory by which a decreasing birth rate is essential to allow productivity to in-crease. Consequently, the negative causal relationship from birth rate to productivity exhibited by the interrelation between PoDR and PoDL continues to operate over the whole time span under consideration and may provide the missing link between Galor's second and third stylized facts. To account for a more precise timing and magnitude of the relation between birth rate and GDP per capita growth, the parameters γ and j will be empirically estimated in chapter seven.
4.6.3 Simulation of a fertility decline
Recapitulating the above ndings, the impact of a simple exogenous fertility decline on produc-tion and populaproduc-tion can be simulated by introducing a negative trend lt into the population equation of our simpli ed model of stagnation as follows:
gyt = α1bt−15− α2bt+ gy15 bt= α3bt−1+ α4gyt−1 + α0glt
dt= α5dt−1
(4.2)
Table 4.1: Calibration of the system of 4.2
α1 α2 α3 α4 α5 α0 b0 d0 gy0 gy15 l see Table 3.1 0.4 see Table 3.1 0.020-0.001t
As is illustrated in Figure 4.5 and Figure 4.6, an exogenously modeled decline in the birth rate raises growth in production per capita by reducing population growth, due to not inspite of
the continued operation of the three classical principles. Although productivity reacts with an exponential increase, the impact of the birth rate is not strong enough to account for the observed British sixteenfold increase in GDP per capita, which is partly owed to the usage of the level of the birth rate instead of the logarithmized birth rate. Nevertheless, since we have so far neglected the eect of a decreasing death rate on population by holding mortality on a constant high level, the parallel decrease in production and population during the nal periods of the simulation is not in line with the stylized facts. We will therefore deal with the mortality decline in the next chapter.
Figure 4.5: A simulation of an exogenous fertility decline in growth rates (birth rate (blue), death rate (red), GDP per capita growth rate (light green)).
Figure 4.6: A simulation of an exogenous fertility decline in level variables (population (orange), production (blue) and GDP per capita (green)).