Teoría de la rentabilidad

7.3.1 Alternative British dataset

In the following, robustness checks are conducted with respect to alternative data, logged vari-ables, alternative orderings of the varivari-ables, countryspecic estimations and the hypothesis of timevarying coecients. Firstly, since Clark's macroeconomic aggregates for Britain have not been fully accepted by many economic historians, the VAR(3) model will also be applied to the Broadberry et al. dataset of GDP per capita. The resulting coirfmatrix displayed in Appendix 11.3 yields a very similar pattern to the matrix using the Clark dataset. Likewise, the eects of the PoG and the PoP are signicant after four periods, while the immediate eect of the PoDR and the lagged eect of the PoLD cannot be identied. Although, therefore, the Broadberry et al. data suggest no stagnation during the seventeenth and eighteenth century, they conrm the observability of the classical (Malthusian) theory of population as well.

7.3.2 Using logged birth rates

Furthermore, in the theory of production it has been argued that there exists an exponential relationship  instead of the linear relationship employed in our simulations  between birth rate and GDP per capita growth. This feature can be accounted for by replacing the absolute value of the birth rate with the logged birth rate and estimate the VAR(3) model on the British data as well as on the international stacked data again, based on this new variable. As is shown in Appendix 11.3, this reestimation does not greatly change the above results, as the PoG and PoP remain well observable even when using logged birth rates.

7.3.3 Using an alternative variable ordering

Thirdly, we evaluate the impact of a dierent variable ordering on the PoG and the PoP. The resulting coirfs are again displayed in Appendix 11.3.

Firstly, if the ordering of the three variables is so arranged that the birth rate still precedes the death rate ⁽

), the coirfs from the corresponding autoregressions remain relatively unchanged. Accordingly, it does not play a large role, whether GDP per capita growth is allowed to aect the birth rate in the same year, since the correlation (the contemporaneous eect)

between the two variables is in any case very small. However, when making use of the possibility that the death rate is allowed to aect the birth rate contemporaneously, as is shown in the graphs resulting from the dierent orderings⁽ be identied. Although the eect of the PoP is well in place, a strong negative (contemporaneous) correlation between birth rate and death rate outweighs the PoG. Consequently, we argue that the original ordering with the birth rate as rst variable and the death rate as second variable is valid and crucial in measuring the PoG.

7.3.4 Estimation on a Country-level

Fourthly, the robustness of the PoG and the PoP will be checked on a countrylevel. Since the number of parameters of the above VAR(3) model amounts to 36 when including a vector of intercepts, it does not seem reasonable to evaluate economies with less than seventy observations on death rate, birth rate and GDP per capita growth rate. For this reason, merely all available countrylevel time series providing at least seventy observations on the three variables are em-ployed for empirical evaluation. The remaining twenty countries, including Britain, are listed in Appendix 11.3. Following the above estimation procedure, it should be kept in mind that the resulting coirfs are naturally suspected to be less signicant due to the smaller sample sizes. The correspondingly estimated coecients of the PoG and the PoP after four years are displayed in Table 7.2, also including the two above British cases for comparison.

Astonishingly, in spite of the small sample sizes and with the exception of Denmark, each of the 19 economies display a positive coecient in the case of the PoG as well as for the eect of the PoP in addition to the signicant ndings in the British cases. What is more, 17 out of 40 tests (excluding the British data by Broadberry et al.) display signicant coecients. These results suggest that even very small samples may be capable of providing evidence for the two principles sustaining our conclusions from the stacked model. For a more detailed examination of the stability of the eects, the national coirfs with veyear time horizon are also displayed in Appendix 11.3.

7.3.5 Time-varying eects

Finally, when accounting for the time-varying eects of the PoG and the PoP, the classical theory of population suggests that the PoG grows stronger whereas the PoP grows weaker during the transition to growth. Again following Nicolini (2007), a straightforward way to measure the evolution of the corresponding eects on the birth rate, which are supposed to increasingly respond to the declining level of the death rate, is to split up the British sample into an early period of economic stagnation and high mortality and a late period of economic growth and low mortality and to compare the respective coirfs. As, in accordance with the stylized facts, the growth take-o corresponds to the fertility decline, 1815 is chosen as the cuto year, as it exhibits the maximum value and a structural break for birth rates. However, with the rst sample

Table 7.2: Cumulative orthogonalized impulse response of b in % 4 periods after a one standard deviation shock in d and gy. All 20 countries with more than 70 observations are displayed.

Principle of Population Great preventive Check

country gy → b(4) d → b(4) obs

arg 0.039 0.018 97

au 0.018 0.077** 75

aus 0.035 0.115*** 133

can 0.052 0.039 100

chil 0.097 0.064 99

den -0.027 0.075*** 179

n 0.051 0.172*** 147

fra 0.076*** 0.059*** 182

ger 0.148*** 0.089*** 122

hun 0.161*** 0.038 72

ita 0.057 0.035 102

jap 0.005 0.066* 109

net 0.015 0.067** 91

nor 0.008 0.077*** 128

nz 0.013 0.024 76

rom 0.034 0.043 79

spa 0.074** 0.003 91

swe 0.053 0.108*** 146

swi 0.017 0.047** 78

ukc 0.146*** 0.060** 467

ukb 0.092*** 0.060*** 467

*** indicates signicance at 1% level, ** at 5% level, * at 10% level.

employing 271 observations and the second sample using 192 observations only, the outcome can again merely be considered as indicative evidence.

Figure 7.5: Britain: The evolution of PoG, PoP, PoDR and positive checks. Upper sample 15411815. Lower sample 18152010.

Figure 7.5 illustrates the evolution of the PoG and the PoP respectively from left to right. In the upper row, coirfs are given for the timespan 15411815, the bottom row displaying responses for the period 18152010. First, the eect attributed to the PoG grows in size and signicance over time, suggesting an increasing direct mortality eect as is predicted from the theory. Secondly, the impact of the PoP sharply decreases over time. While indicating a strongly positive conversion rate of GDP per capita growth into birth rate in the early sample, the eect seems to entirely disappear in the later period. This diminishing income eect is in line with the increasing operation of indirect mortality eects. However, as it seems implausible to argue that the eect of the PoP completely vanished after 1815, the extremely low values of the coirf might be owed to distortions resulting from the small sample size. Thirdly, the relatively unchanged coirf that is supposed to capture the constant eects of the PoDR and the PoLD substantiates the theoretical predictions and sustains the robustness of the estimation method.

7.4 A Critical Note on the Prevailing Measurement of Preventive