Testing the Goodwin growth-cycle macroeconomic dynamics in Brazil

Abstract

This paper discusses the empirical validity of Goodwin's (1967) macroeconomic model of growth with cycles by assuming that the individual income distribution of the Brazilian society is described by the Gompertz-Pareto distribution (GPD). This is formed by the combination of the Gompertz curve, representing the overwhelming majority of the population (~99%), with the Pareto power law, representing the tiny richest part (~1%). In line with Goodwin's original model, we identify the Gompertzian part with the workers and the Paretian component with the class of capitalists. Since the GPD parameters are obtained for each year and the Goodwin macroeconomics is a time evolving model, we use previously determined, and further extended here, Brazilian GPD parameters, as well as unemployment data, to study the time evolution of these quantities in Brazil from 1981 to 2009 by means of the Goodwin dynamics. This is done in the original Goodwin model and an extension advanced by Desai et al. (2006). As far as Brazilian data is concerned, our results show partial qualitative and quantitative agreement with both models in the studied time period, although the original one provides better data fit. Nevertheless, both models fall short of a good empirical agreement as they predict single center cycles which were not found in the data. We discuss the specific points where the Goodwin dynamics must be improved in order to provide a more realistic representation of the dynamics of economic systems.Comment: 21 pages, 9 figures, 1 table, LaTeX. Minor changes to match corrected proofs. To appear in "Physica A

Tsallis statistics in the income distribution of Brazil

“…Both fitted parameters also present a cycling behavior in terms of one another similar to the cycles obtained in Ref. [11] through a substantially different analysis where the method of describing the income data range with two functions was applied. In addition, we noted a second order effect, not previously reported in the study of any other income samples, comprised of a periodic oscillation along the fitted straight line whose amplitude grows with increasing income values.…”

“…We propose using Tsallis statistics to represent the income distribution of the entire income data range, from the very poor to the super rich, by a single function, that is, without assuming a class division. We applied the Tsallis q-logarithm to the entire income data of the Brazilian individual income distribution yearly samples from 1978 to 2014 using the same data reducing techniques previously applied in other studies made with the personal income data of Brazil [3, 4,11]. This allowed us to study the time evolution of a single q parameter along a time span of almost four decades for the entire income distribution of a whole country, providing then new evidence of Tsallis functions' ability to adequately represent personal income of a whole country.…”

Testing a Goodwin model with general capital accumulation rate

“…Although addition of harmonics definitely improved the fit, there is no discussion on the theoretical properties or the impact on structural stability of the model. Recently, Moura and Ribeiro (2013) took a nonconventional route to estimate the Goodwin model, as well as an extension proposed by Desai, Henry, Mosley, and Pemberton (2006), using data for the Brazilian economy from 1981 to 2009. The novelty of their approach lies in the data construction for wage share and employment rate.…”

Oscillations in the Tsallis income distribution

“…where f (x) is the PDF [5,12]. The empirical suggestions that the income distribution can be modeled by the TD comes from the fact that when F(x) is obtained from income data and plotted in a log-log scale, its functional curve decreases as the income x increases.…”

“…Higher values of the Pareto index imply more uneven distribution of the personal income. The interesting detail is that this result has not been disputed by different investigations carried out since then, which considered several different samples obtained at different times for different populations in distinct countries or groups of countries [3][4][5][6][7][8][9][10][11][12][13], and references therein]. Despite its empirical success, the Pareto power-law does not work for the overwhelmingly majority, and less rich, part of the population.…”