7.2.1 Estimation of the simulation
As a very useful reference point, it is advisable to rst run a VAR(3) estimation on the above simulation given by Figure 6.2, i.e. on the system 6.1 using the corresponding calibration.7 The coirfs resulting from this estimation are expected to deliver a benchmark against which the ensuing real samples might be compared. The universal average eect of the PoG seems well exposed in the upper central graph of Figure 7.2.
Figure 7.2: Simulating the classical growth model: Coirf matrix based on a VAR(3) model.
Likewise, the average eect of the PoP appears quite nicely depicted in the upper right graph.
Both eects are statistically signi cant, with the PoG on a ve percent level and the PoP on a one percent level. As suggested, the positive lagged eect of the PoLD of birth rate on GDP per capita growth after one generation cannot be captured in the bottom left graph, when using a maximum lag length of three. Instead, the contemporaneus annual eect of the PoDR is signi cantly displayed in the same graph at period zero, since it is not distorted in this simulation by a permanently operating eect of the PoLD.
7 To provide some additional variation on the variable death rate, the right hand side of the second dierence equation of eq. (4) is supplemented by adding an annual shock t∼ U (−0.005, 0.005).
7.2.2 Britain 15412010
The computed coirfs from running the VAR(3) model on the British data are displayed in Figure 7.3. The eect stemming from the PoP is roughly in line with that of the simulated model. The reaction of birth rate to a shock in GDP per capita growth is already positive and signi cant on a one percent level in the rst period, indicating a quick fertility adjustment, and accumulates in magnitude over the subsequent periods. With regard to the PoG, a death rate shock does not induce birth rate to react after one period. After four years, however, the positive eect becomes statistically signi cant on a ve percent level, providing evidence of a positive causal relationship and pointing to a lagged fertility decision.8
Figure 7.3: Britain 15412010: Coirf matrix based on a VAR(3) model.
Although the eect of the PoDR is signi cantly measured in year zero after a shock in birth rate, the subsequently displayed response until year ve might have been distorted by the PoLD.
While in the simulated impulse response the negative contemporaneous eect of the PoDR seems to have accumulated over the subsequent periods, this accumulation is neutralized in the British sample, suggesting that a positive (potentially long-run) eect of birth rate on GDP per capita growth has been captured by additional residual correlation.
8 In the simulation of chapter three, a lag of one year was used. However, this assumption can be easily relaxed by assuming a fertility lag of up to four years.
7.2.3 Stacked model using international data
Mitchell's international historical statistics oer data on vital rates and GDP per capita for 94 economies. Out of these, 55 economies exhibit simultaneous data on the three variables over at least three consecutive years. However, with an average number of approximately 70 observations, the impulse responses of most of these 55 eligible countries can, when individually tested, not be expected to give su ciently reliable evidence of the classical model. On the other hand, if they could be estimated collectively, the number of observations would rise to 3,911. For that purpose, the individual countrylevel data are stacked into one sample, leaving space for three missing values between subsamples such that the last observation of the preceding and the rst observation of the succeeding country are not related to each other.
Figure 7.4: 55 economies 18152010: Coirf matrix based on a VAR(3) model.
The resulting coirfs displayed in Figure 7.4 match those of Figure 7.3 relatively well. However, as the stacked sample includes observations between the years 1815 and 2010 only, while the English sample ranges from the year 1541 to 2010, the former is suspected to mainly include information on the regime of economic developement. It is therefore not surprising that the eect of the PoG is remarkably pronounced compared to the British model, while that of the PoP is smaller in magnitude, suggesting time-varying eects. Moreover, the higher persistence in the variable GDP per capita growth rate is in line with the suggestion that its mean was close to zero during the regime of stagnation and increased sustainably during the regime of development. However, as in the British sample, it remains puzzling why the fertility decision seems to be lagged by an
additional year in the case of the PoG as compared to the eect of the PoP. Finally, in contrast to the simulation where we have merely employed the eect of one cohort on the subsequent GDP per capita growth, the eect of the PoDR seems to have been neutralized by the PoLD such that no signi cant eects can be observed. In any case, both analyses of the British historical data as well as of the more recent international data record qualitative and quantitative evidence of a universal pattern of birth rates, death rates and GDP per capita growth and strong support for the universality of the PoG and the PoP.