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Modelling real GDP per capita in the USA: cointegration test

  • Kitov, Ivan
  • Kitov, Oleg
  • Dolinskaya, Svetlana

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 original series have unit roots and their first differences have no unit root. 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. The VECM provides consistent, statistically reliable, and significant estimates of the coefficient in the cointegrating relation. 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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 2739.

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Date of creation: 2007
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Handle: RePEc:pra:mprapa:2739
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  1. Ivan, Kitov, 2006. "Exact prediction of inflation in the USA," MPRA Paper 2735, University Library of Munich, Germany.
  2. Ivan O. Kitov, 2008. "Real GDP per capita in developed countries," Papers 0811.0889, arXiv.org.
  3. Ivan O. Kitov, 2008. "GDP growth rate and population," Papers 0811.2125, arXiv.org.
  4. Carl Chiarella & S. Gao, 2002. "Type I Spurious Regression in Econometrics," Working Paper Series 114, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
  5. Ivan O. Kitov, 2005. "Modelling the overall personal income distribution in the USA from 1994 to 2002," Working Papers 07, ECINEQ, Society for the Study of Economic Inequality.
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