# Desarrollo de aplicaciones de sistemas dinámicos y econométricos a problemas económicos

- Juan Luis Martín Suárez

- Antonio Aníbal Golpe Moya Director
- Emilio Congregado Ramírez de Aguilera Director

Defence university: Universidad de Huelva

Year of defence: 2017

- Inés Herrero Chair
- Antonio Jesús Sánchez Fuentes Secretary
- María Concepción Román Diaz Committee member

Type: Thesis

## Abstract

This thesis is a compendium of works in three different lines. The first one dedicated to exploring both theoretically and empirically the use of graphs of visibility in the analysis of temporal series. Thus, in the face of the traditional analysis techniques used to date macroeconomic time series with the objective of analyzing summits and valleys and analyzing the depth and amplitude of the different cyclic phases, this thesis develops applications of the theory of Graphs to series analysis following the approach opened by Lacasa et al. At the same time as making a theoretical contribution on one of the indexes most commonly used in the measurement of resilience. Thus, this contribution arises from the need to arbitrate some mechanism to avoid the lack of sensitivity of the index when the timerai series has a verynigh number of observations. All these ideas and algorithms are applied to the analysis of two types of economic series for the North American economy: those of the gross domestic product and the series of energy consumption. The choice of these series is not arbitrary insofar as it is a question of making an alternative approach, so that its value must be made in a key way compared with the techniques traditionally used for these issues. For this reason, we opted to approach a classical series, which is dated by the NBER as well as being the object of numerous studies and analyzes, as well as the North American energy consumption series that have been the object of a profuse analysis in the Field of the Energy Economics. The visibility graph (VGA) algorithm allows the transformation of a time series into a complex network in a very simple way. The study of the topological properties of the network contributes knowledge about the behavior of the series, as the graph inherits many of its properties. In Chapters 2 and 3 we proceed to transform the temporal series corresponding to the total energy consumption and by type of source and the quarterly rate of change of the GDP of the USA in a graph and apply the theory of complex networks to study it. The resulting approach, when applied to different metrics, shows results that are quite in line with those obtained with traditional algorithms, so that it can be concluded that these applications provide quite useful representations for forecasting and tracking. This part closes with a question related to the analysis of the time series, and more specifically with the capacity of absorption of a shock by the series. In particular, it is analyzed as one of the most commonly used indices to measure resilience, shows a certain insensitivity when the sample size is large. To address this problem, a digression and theoretical input is made that can correct this bias. The third part provided empirical evidence supporting a stylized fact observed in some economies with regard to the business ownership rates development: after a long-decline in the rate of self-employment and since 1978, self-employment rates appeared to increase in many industrialized countries in such a way that the trend of self-employment rates seemed to show a structural shift in terms of a revival (U-shape) or at least a stabilization (L-shape). To this end, they developed an empirical model in which estimates of dif- ferent functional forms of the relationship between the "equilibrium" self- employment rate and the GDP per capita allowed them to infer the shape of this relationship for 23 OECD countries. In their empirical model, the equilibrium self-employment rate was obtained using some assumptions about the relationship between self-employment, unemployment, labour incomes and some lags structures. Opposite to this approach, we propose to test the U/L-shape hypothesis using statistical methods: i) first, decomposing the self-employment rate into their two components -i.e. the cyclical and natural components, and, ii) using a recent econometric approach for detecting the presence of structural breaks (Kejriwal and Perron, 2010). In this way, the U-shape hypothesis is tested for 23 OECD countries, using data on GDP per capita and the natural self-employment rate component (a proxy for the "equilibrium" self- employment rate) over the period 1972- 2008. Our results only provide a partial support for the U-shape hypothesis: for 15 out of 23 countries we find a significantly positive relation between GDP per capita and the natural self-empioyment rate. Our results suggest that, notwithstanding the rise of self-employment observed in many countries over the last few decades, economies of scale and scope continue to play an important role in many advanced economies The fourth part of the thesis addresses issues related to the use of numerical methods and the development of applications that can be used in teaching the modeling of economic dynamics. In particular, two trials are presented. The first one is an essay of modeling and programming of dynamic problems through systems of differential equations solved through numerical methods. In particular, the study of the behavior of a bacterial mass in a controlled crop that presents analogies to the evolution and business survival is presented. The second presents two applications of a simulator of a basic version of the dynamic aggregate supply and demand model - the well-known neoclassical synthesis model - programmed in Excel that will allow a student of an Intermediate Macroeconomics course to know how they are formulated, solved And the results provided by the dynamical models versus the traditional benchmarking exercises that usually compose the bulk of the programming of a standard course of Macroeconomics of this level. It is intended that these applications serve the student to appreciate the power of dynamic models and the ability of these to reproduce cyclical adjustments in which the adjustment of the variables to their longterm values is far from a Gradual and linear adjustment.