Growth Rate Of The GDP Per Capita Revisited. The Results From 2007, 2009, And 2012 Revisited

Appendix. The model

Let me repeat the major features of our concept describing the evolution of real Gross Domestic Product (GDP). The principal claim is simple – the growth rate, g(t), of real GDP per capita, G(t), is driven by the attained level of real GDP per capita and the change in a country dependent on a specific age population, Ns. The growth rate of the real GDP per capita in developed countries is characterized by a constant annual increment, A. All fluctuations around this constant increment can be explained by the change in the number of people of the country-specific age: 

g(t) = dlnG(t)/dt  = A/G(t) + 0.5dlnNs(t)/dt                                                                      (1) 

Equation (1) is a quantitative model that has been constructed empirically and proved statistically by cointegration tests.

In economic statistics, usually, the relative growth rate is published, as represented by dG(t)/G(t)=dlnG(t). For the sake of simplicity, we assume that the second term in (1) is zero. Accordingly, the economic system under study is in a stationary or inertial growth, i.e. A/G(t) is “the inertial growth” as in physics. The adults between 15 and 64, i.e. in the working-age population, can be also considered as living in a stationary regime since no dramatic organic and functional changes happen to their life process out of the margins of natural variations.  

For the inertial growth, the real GDP per capita grows as a linear function of time: 

g(t) = dlnG(t)/dt(given dNs(t) = 0)   = A/G(t)

G(t) = At + C                                                                                                                     (2)

where G (t) is completely equivalent to the inertial growth, Gi(t), i.e. the first component of the overall growth as defined by (1).  Relationship (2) defines the linear trajectory of the GDP per capita, where C=Gi(t0)=G(t0) and t0 is the starting time. In the regime of inertial growth, the real GDP per capita increases by the constant value A per time unit. Relationship (3) is equivalent to (2), but holds for the inertial part of the total growth: 

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