Nonlinear growth in a long-run perspective

Abstract

This study analyses the pattern of long-run growth of a cross-section of countries, adopting the distribution dynamics approach. The relationship between growth rates and income levels appears first increasing and then decreasing, indicating the existence of different growth regimes.

Notes

¹ Sample M1 includes: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Italy, The Netherlands, New Zealand, Norway, Sweden, UK, USA. With respect to the 16-country sample of Baumol (1986) (considered for the period 1870–1979), Sample M1 includes New Zealand and excludes Switzerland and Japan. Also, while Baumol considered labour productivity we focus on GDP per capita.

² The nonparametric estimation is performed using the statistical package included in Bowman and Azzalini (1997). We use the standard setting suggested by the authors (i.e. optimal normal bandwidth with weighted observations) and refer to Bowman and Azzalini (1997) for more details. Data and codes are available on the authors’ websites (www-dse.ec.unipi.it/faschi and www-dse.ec.unipi.it/lavezzi/index.html).

³ Note that the variability band displayed in Figure 1 is not a proper confidence band (see Bowman and Azzalini, 1997, p. 76).

⁴ Details on the analytical aspects are available from the authors upon request. For a similar model see Fiaschi and Lavezzi (2002).

⁵ With small changes, i.e. 6500 ± 500, 12,000 ± 500, 0.5% ± 0.25% and 2.5% ± 0.25%, we obtain similar results.

⁶ We estimate transition probabilities by , where n _i is the number of observations in state i, and n _ij is the number of transitions from state i to state j. Norris (1997), pp. 56–57, shows that these estimates are the maximum likelihood estimates of the true transition probabilities. Fiaschi and Lavezzi (2002) contains more details on all methodological aspects of our approach.

⁷ These ‘modified’ transition probabilities simply refer to each (stochastic) submatrix corresponding to an income level. E.g. the value is obtained by summing and . Tests of equality between and, respectively, and return the following p-values: 0 and 0. Details on hypothesis testing are in the appendix of Fiaschi and Lavezzi (2002).

⁸ Tests of equality between and, respectively, and return the following p-values: 0 and 0.