Measuring complexity in Brazilian economic crises

RESEARCH ARTICLE Measuring complexity in Brazilian economic crises Letı́cia P. D. Mortoza, José R. C. Piqueira* Laboratório de Automaçãoe Controle/Escola Politécnica, Universidade de São Paulo, Avenida Prof. Luciano Gualberto, travessa 3 - 158, São Paulo-Brazil * a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 OPEN ACCESS Citation: Mortoza LPD, Piqueira JRC (2017) Measuring complexity in Brazilian economic crises. PLoS ONE 12(3): e0173280. https://doi.org/ 10.1371/journal.pone.0173280 Editor: Boris Podobnik, University of Rijeka, CROATIA Abstract Capital flows are responsible for a strong influence on the foreign exchange rates and stock prices macroeconomic parameters. In volatile economies, capital flows can change due to several types of social, political and economic events, provoking oscillations on these parameters, which are recognized as economic crises. This work aims to investigate how these two macroeconomic variables are related with crisis events by using the traditional complex measures due to Lopez-Mancini-Calbet (LMC) and to Shiner-Davison-Landsberg (SDL), that can be applied to any temporal series. Here, Ibovespa (Bovespa Stock Exchange main Index) and the “dollar-real” parity are the background for calculating the LMC and SDL complexity measures. By analyzing the temporal evolution of these measures, it is shown that they might be related to important events that occurred in the Brazilian economy. Received: October 28, 2016 Accepted: February 4, 2017 Published: March 16, 2017 Copyright: © 2017 Mortoza, Piqueira. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: Data are available from Ibovespa at http://www.bmfbovespa.com.br/ pt_br/produtos/indices/indices-amplos/. As the site is opened, click on the Ibovespa window and go to “Serie Retroativa do Ibovespa. The exchange rate can be viewed at http://www4.bcb.gov.br/pec/ taxas/port/ptaxnpesq.asp?id=txcotacao. As the site is opened, choose period and choose “dolar dos EUA”. Funding: The authors received no specific funding for this work. Competing interests: The authors have declared that no competing interests exist. 1 Introduction For the last forty years, complex thinking has influenced many research areas [1] contributing to model problems related to the onset of surprising or catastrophic events such as traffic jams, crowd behavior, tsunamis and earthquakes [2]. Consequently, the concept of complexity has been largely debated [3], with generality implying the prevalence of qualitative arguments [4]. In this scene, concerning to computer science, Shannon [5] and Kolmogorov [6] proposed similar and useful complexity measures. In terms of economic applications, fractal dimension measures were proposed by Mandelbrot [7], which are largely used to characterize economic time series [8], including different fractal measures adaptable to different patterns of series [9]. Another well spread line of reasoning applied to economic problems is the Dynamical System’s approach, aiming to detect order and chaos in processes [10]. Although the common sense is that complexity is a relative concept [11], López-Ruiz, Mancini and Calbet proposed a global measure for complexity by using the entropy definition, which is referred to as the LMC measure [12]. PLOS ONE | https://doi.org/10.1371/journal.pone.0173280 March 16, 2017 1 / 12 Complexity and Brazilian crises Additionally, Shiner, Davison and Landsberg, by slightly changing the LMC definition, proposed the SDL measure [13] and both, LMC and SDL, are satisfactory to measure complexity for many problems [14]. Concerning economy, these measures are barely used [15] although they could be useful to model crises by the analysis of their temporal evolutions [16], as it was shown in former work; moreover they could be used as an alternative to the analysis of the tails of statistical distributions [8, 17]. Here, slightly modified versions of the LMC and SDL measures are proposed for temporal series. Then, considering that capital fluxes are determinant to the economic health of an emerging country [18], oscillating drastically due to several political, social and economic changes, Brazilian macro-economical data are analyzed by calculating the LMC and SDL complexity measures, aiming to identify how their behavior is connected to crisis events. The chosen data are Ibovespa (Bovespa Stock Exchange main Index) and the “dollar-real” parity, generating the LMC and SDL complexity measures temporal series that are studied in five critical periods of the Brazilian economy. Since the end of dictatorship regime in 1985, Brazil has been alternating short cycles of economical phases, with macroeconomics indicators oscillating, apparently commanded by the political changes. To delineate the Brazilian political events, the analysis starts with José Sarney’s term, between 1985 and 1990, which is considered the transition period between dictatorship and democracy and in which several stabilization plans were practiced, such as freezing prices, causing an increase in demand and a strong monetary black market. In 1990, Fernando Collor de Mello was democratically elected and applied the “Collor” plan, radically freezing the financial assets, creating the “commercial-dollar”, a parallel to the existing fluctuating rates. Latter, the “Collor” plan-II was enforced based on freezing prices [17]. The Collor plans promoted important changes in the Brazilian economy, mainly opening the market to foreign capital and privatizing important service companies formerly controlled by the state. Corruption suspicions and a bad economic scenario caused the impeachment of the president (Fernando Collor de Mello) who was replaced in September, 1992. A new stabilization plan was designed (“Real” plan), and started to be applied in 1993, with a new currency, linked to the dollar quotation and implying a strong inflation decrease [17]. The exchange policy was pressed and, in 1999, the Brazilian currency was finally allowed to have free fluctuations, with a strong initial devaluation. The data sampling presented here starts from this period on, considering that the economic policy did not suffer any additional change. Between 1999 and 2003, liberal ideas, mainly represented by the new president Fernando Henrique Cardoso, governed the country and a satisfactory economic equilibrium was reached; however, with timid social actions. Supported by ideas regarding social justice and the democratic distribution of gains, the Labor Party, represented by Luiz Inacio Lula da Silva was elected in 2003, governing up to 2011. This period was characterized by optimism and, consequently, the Labor Party, represented by Dilma Roussef, was elected again in 2011 and in 2016. During Dilma’s s (...truncated)