The economic crisis in Argentina around year 2002 provides a unique opportunity for Econophysics studies. The available data on individual income are analyzed to show that they correspond to non stationary states. However, the rather restricted size of the data survey imposes difficulties that must be overcome through a careful analysis, for a reliable use. A new method of data treatment is presented that could be helpful in theoretical studies.
The empirical data on individual income distribution presents, for every country, two special features. One of them is the tail of the distribution, which is linear in a logarithmic graph and the other is the stability of the shape of the distribution, which changes very slowly over time and shows no appreciable differences in consecutive years. The first of these characteristics has been the subject of numerous studies [2 -4] since first observed by Pareto, more than 100 years ago [5]. The Pareto tail of the cumulative distribution follows a power law of the type
where α is the Pareto index, whose value is usually around 2. A notable feature of the Pareto tail that allows for a differentiation from the rest of the distribution is the change in the value of the slope with the economic situation [1]. The second indicates that the income distribution is in a quasi-stationary state, which enables model calculations based on obtaining distribution functions corresponding to steady states. This is the central assumption underlying the models developed by the Kolkata school and other researchers [6][7][8][9]. The model, based on the kinetic theory of ideal gases has been extremely successful in accounting for the main features of empirical data by introducing a saving propensity factor in the transactions between pairs of agents [10]. The model has been extensively studied and is able to reproduce the main features of the empirical distribution [11,12].
Since both theory and empirical data correspond to stationary situations, none of them provides information on the evolution of income and factors affecting it. This would require the availability of statistical information obtained in an economy undergoing a major perturbation in a very short period that resulted in a rapid transfer of resources between the various groups that compose it, leading to a distribution out of equilibrium and evolving towards a new steady state.
A recent case, unique from the great crises in the first half of the 20 th century has been the economic and financial collapse that occurred in Argentina in 2002 and that developed within months.
This article will examine critically the individual income data from Argentina in the years around the 2002 crisis, in order to explore the potentiality of its use in Econophysics studies.
A succinct account on the economic crisis in Argentina, which peaked in the period December 2001 -June 2002 will serve to put the subject in perspective. It could also seem familiar to those acquainted with the present situation in Europe. Briefly, until the end of 2001 the price of local currency (the peso) was linked to the U.S. dollar in a 1:1 ratio, and there was free convertibility between the two currencies, so that all transactions were made with any of them. The rapidly deteriorating economic situation due to the overwhelming foreign debt, led to a crisis that ended with a default and the collapse of the financial system. The end of convertibility and the deterioration of the value of money quickly exceeded government expectative, reaching a ratio of 1:4, to finally stabilize at around 1:3. This resulted in a rapid, massive transfer of resources between various sectors, mainly associated with the sudden change of the local currency value. The rapid rise in unemployment and the consequent increase in poverty led the government to take palliative measures. Slowly, compared with this process, the economy evolved to a new state of equilibrium.
An analysis of the evolution of a system like this requires, from the point of view of Econophysics, empirical data of high quality and reliability.
In Argentina, through the statistical studies office, INDEC, the government collects and compiles data on population and economy through surveys on selected samples. Although statistically significant, they are necessarily limited in size. This feature establishes a difference with the empirical data from those countries where each resident must complete an annual declaration of income, which provides a very large database. One of the problems that arises from a small sample originates in the low value of the cumulative probability of the Pareto tail, which starts at typical to values below 1%, so if the database is small, this tail is not sufficiently sampled.
Individual income data, either theoretical or empirical, are usually presented as the cumulative distribution function (CDF), as in Figure 1, or the probability density function (PDF). If the amount of data is low, it seems better to use the CDF. However, in most of the curve, corresponding to the low and medium income sectors, the CDF is relatively insensitive to changes in the economic situation while the tail of the distribution may not be adequately represented. This seems to be the case in the income distribution of Argentina in years 2000 and 2001, where the change of slope that indicates the onset of the Pareto tail is not detected (Figure 1) although it
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