Modelling real GDP per capita in the USA: cointegration test

TL;DR

This paper presents a nonlinear two-component model for US real GDP per capita, testing its cointegration with the number of 9-year-olds, and finds a strong cointegrating relationship that explains economic deviations.

Contribution

It introduces a novel nonlinear model linking GDP growth to the population of 9-year-olds and demonstrates its cointegration with actual GDP data using advanced econometric tests.

Findings

Cointegration between measured and predicted 9-year-old population exists.

VAR model achieves R2=0.95 in fitting the data.

Deviations from economic trend are driven by changes in 9-year-old population.

Abstract

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.