History or path dependence in mixed-Poisson growth: Brazil, 1822-2000, and USA, 1869-1996, with an estimate of the world mixing distribution at start-up

The growth empirics of two separate but related issues are studied. In the first, the annual data on GDP per person (GDPpp) for Brazil, 1822-2000, and the US, 1869-1996, were converted into arrival times for innovations defined as permanent increments to GDPpp of given size (e.g. 3%). We say an economy exhibits history dependence if its arrival times can be shown to come from a homogenous Poisson process, that is, with a constant mean arrival rate of innovations (the Poisson parameter, λ). Brazil’s growth trajectory since 1822 is shown not to be history dependent in this sense, though both its truncated series, 1889-2000, and the US, 1869-1996, passed the tests. Brazil’s stagnation in the mid to late 19th century, when coupled to its growth spurt in the 20th, is the suggested reason for the failure. The second study uses the Summers-Heston data for 134 economies in 2000 to estimate a discrete, theoretical distribution for the λ at start-up in 1800, based on the (unproved) assumption that each economy drew an arrival rate from this “mixing” distribution and stayed with it. The results show that if innovations are assumed to be big, rare events, then the world mixing distribution will be skewed, and all the λ drawn at start-up will be almost equal and thus the dispersion of incomes across nations 200 years later will then be due only to random variations along paths generated by the same homogenous Poisson process.