Threshold detection and anlaysisMARS methodology in macroeconomics and public health

Resumo

In this thesis, we employ and develop a highly flexible methodology to detect thresholds in macroeconomic relationships such as the Taylor Rule and Okun’s law. We also interdisciplinarily apply it in one of the most serious current concerns in Public Health: the bacterial resistance to antibiotics. One of our purposes is to provide estimations to encourage the debate to guide the design of Macroeconomic and Public Health policies. Both these macroeconomic relationships and the bacterial resistance to antibiotics show evidence of nonlinearity and the possible existence of thresholds. Friedman's Multiple Adaptive Regression Splines (MARS) methodology let us detect these behaviors, allowing data select and estimate the optimal model. The flexibility and nesting capacity of MARS not only permit to estimate multiple thresholds without imposing previously what variables contain them and how many thresholds but also allows estimating them in interaction effects. We deeply describe the iterative algorithms that compose MARS that tackle problems of concurvity and unnecessary complexity of the model in its selection and estimation; and its ability to adequately fit the underlying model; and we develop an implementation protocol to take into account characteristics of data and associations. We also provide an important methodological innovation: a procedure to estimate confidence intervals of each threshold detected by MARS. Regarding the Taylor rule, we develop a theoretical model that highlights possible thresholds in the Taylor rule. We estimate the Taylor rule for the Federal Reserve of the United States and we detect thresholds both in the inflation rate, in the output gap, and in the interaction between both, as well as in the effect of Volcker's presidency. This more complete characterization of the Taylor rule constitutes another of the innovations of this thesis. We also estimate the Taylor rule for ECB using our protocol. We detect thresholds both in the output gap and in the inflation rate, and we provide their respective confidence intervals. Our estimation demonstrates ECB takes economic activity into account more than it officially declares, and reacts more intensively to inflation deviations once they have sufficiently exceeded the official target of 2%. Regarding Okun's Law, we propose a simple theoretical model that provides a basis to the empirical nonlinearity. In addition, it opens the debate to consider that nonlinearity comes out from a combination of firms risk aversion hypothesis with institutional rigidity hypothesis or with hoarding labour hypothesis; instead of exclusively considering one of them. We use the protocol to estimate Okun's Law for four countries in Europe: Spain, Germany, the Netherlands and France, also controlling a possible effect of the crisis in the Eurozone. Despite not previously imposing a number of thresholds, our results support the existence of a single threshold for each country, but at significant different positions. On the one hand, the Okun’s Law for Spain exhibits steeper slopes than those from the central countries. In addition, the differences between the coefficients below and above the threshold are consistent with the firms risk aversion hypothesis. Likewise, the significant differences between threshold positions contribute to the debate that a combination of firms risk aversion with institutional rigidity is more important Spain while in the other countries it seems to be the combination with hoarding labour hypothesis. In addition, we note that periods of economic crisis in Euro zone affect Okun’s law in France. In light of all these results, our analysis brings both theoretical and empirical innovations in the Okun’s law debate. Finally, facing the worrisome threat to Public Health that constitutes antimicrobial resistance, considering the current interest and its nonlinearity and possible thresholds, we estimate these associations in five European hospital centers in a multidisciplinary study. It leads us to adapt the estimation protocol to very different time series and to contribute in a practical way in the detection of thresholds in the intensity of antibiotic use. This helps to guide the design of Public Health policies. Based on the Levy’s hypothesis that resistance to antibiotics could be associated with the intensity of use exceeding certain thresholds, our estimates detect these thresholds in hospitals and primary care centers. We provide confidence intervals that facilitate support to health policy recommendations about restricting the use of antibiotics. It represents a fundamental methodological innovation. We hope that these results can humbly contribute to shed some light on the design of public policies to face the current challenges in Macroeconomics and Public Health.