We often discuss the evolution of real GDP (per capita) in developed countries and built a quantitative model, which includes two terms – inertial growth with constant annual increment of GDPpc and the change in a specific age population. We have presented a number of growth models for various developed counties and validated them with new data. The last revision was around ten years ago, and it is a good opportunity to look at the model with data for the previous decade. It is also important that all relevant data undergo regular revision back into in the past, actually decades.
The original model for the U.S. links the change rate of real GDP per capita, dlnG/dt, to the change in the number of 9-year-olds, dlnN9/dt, and the reciprocal value of the attained level of GDP per capita, A/G:
dlnG/dt= A/G + 0.5dlnN9/dt (1)
where A is an empirically derived constant. One can rewrite (1) relative to N9 and obtain the following equation in a discrete form:
N9(t) = N9(t-1)[2.0( dlnG - A/G) + 1] (2)
where dt=1 year.
The upper panel of Figure 1 presents the result of the N9 modeling between 1960 and 2005. The agreement between the measured and predicted N9 is excellent, and we have shown that these time series are cointegrated. Our model has passed all rigorous econometric (Johansen and Engle-Granger) tests and can be used for GDP forecasts when the quality of population estimates is good enough. Here, we update the data set using the most recent release of population and real GDP data. The lower panel of Figure 1 shows the updated curves. The predicted number of 9-year-olds has a short but intensive spike between 2003 and 2008, which dropped to the predicted level in the 2008 recession. The same Johansen and Engle-Granger cointegration tests applied to the new measured and predicted time series of 9-year-olds. Both tests confirm that these two time series are cointegrated, and thus, the linear regression is valid and defines the link between them. Simple linear regression is not the best choice for the predicted and measured number of 9-year-olds in Figure 1. One has to retain in mind the measurement errors in both time series. Considering the fact that the GDP difference test in (2) is very sensitive to the accuracy of annual GDP pc estimates and often revisions to the population estimates, we could give a conservative estimate of the measurement error is 20% of the annual GDP pc estimate. For this error, the Rsq=0.91. It is worth noting, that the predicted N9(t) value is the integral of the GDPpc-related difference, while the measured N9 is an instant measurement and the next measured N9 does not depend on the previous one. Therefore, the number of 9-year-olds is a fully independent variable, and it defines the long-term (integral) behaviour of the GDP per capita.
We do not know the reason behind the absence of the spike in the measured population data, but it is clear that the postcensal data for a single-year-of-age population are smoothed. The raw population data is not available. The measured GDP growth between 2003 and 2007 in the USA was intensive, and we have no indication that these data are somehow corrupted.
The updated model indicates that the deviations from the inertial growth in the USA (and likely in all developed countries) are related to the change in 9-year-olds. This might be the age when some financial operations are started by parents in view of future education. This might be the age when additional saving starts and the economy gets a changing fresh portion.
Figure 1. Upper panel: Measured number of 9-year-olds (open circles) in the U.S. and that predicted from real GDP per capita (solid circles) for the period between 1960 and 2005. Lower panel: Same as in the upper panel for the period between 1960 and 2019.
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