  A two-component model for the evolution of real GDP per capita in the USA is
presented and tested. The first component of the GDP growth rate represents an
economic trend and is inversely proportional to the attained level of real GDP
per capita itself, with the nominator being constant through time. The second
component is responsible for fluctuations around the economic trend and is
defined as a half of the growth rate of the number of 9-year-olds. This
nonlinear relationship between the growth rate of real GDP per capita and the
number of 9-year-olds in the USA is tested for cointegration. For linearization
of the problem, a predicted population time series is calculated using the
original relationship. Both single year of age population time series, the
measured and predicted one, are shown to be integrated of order 1. The
Engel-Granger approach is applied to the difference of the measured and
predicted time series and to the residuals or corresponding linear regression.
Both tests show the existence of a cointegrating relation. The Johansen test
results in the cointegrating rank 1. Since a cointegrating relation between the
measured and predicted number of 9-year-olds does exist, the VAR, VECM, and
linear regression are used in estimation of the goodness of fit and root
mean-square errors, RMSE. The highest R2=0.95 and the best RMSE is obtained in
the VAR representation. Econometrically, the tests for cointegration show that
the deviations of real economic growth in the USA from the economic trend, as
defined by the constant annual increment of real per capita GDP, are driven by
the change in the number of 9-year-olds.
