Deep learning in econometrics: theory and applications

Abstract

This thesis concentrates on implementing deep learning methodologies for econometrics. Among the supervised machine learning toolbox, deep neural networks are the most ubiquitous ones. By being the least restricted nonlinear functions that one could implement, deep learning models allow learning complex signals from the infinitely versatile big data. Recent evidence from the literature shows how, notwithstanding the well-known issues around neural networks specification for causal problems, deep learning methods (among other machine learning methodologies) can be regarded as a powerful nonparametric tool for addressing not only prediction but also causal problems. Chapter 2 develops a new methodology for detecting Granger causality in nonlinear multivariate time series using deep neural networks coupled with Lasso methods. After dfining the optimal neural network architecture by maximizing the transfer of information between input and output variables, the novel two-stage procedure applies a sparse double group lasso penalty function to detect Granger causality.

The methodology is applied to the Tobalaba network of renewable energy companies showing an increase in the connectivity among the network members after the introduction of the blockchain platform. Chapter 3 proposes a constrained maximization for the identfication of an optimal neural network architecture of a given size. The optimal architecture obtains from maximizing the minimum number of linear regions approximated by a deep ReLu neural network. A Monte Carlo simulation illustrates the optimal architecture's outperformance against cross-validated methods for linear and nonlinear prediction models. Chapter 4 proposes
a suitable method for constructing prediction intervals for the output of both deep and shallow neural networks. The proposed methodology adapts the extremely randomized trees method to construct ensembles of neural networks. The Monte Carlo simulation shows a good performance of the novel methodology not only in terms of out-of-sample uncertainty estimation but also in terms of out-of-sample accuracy. Finally, chapters 5 and 6 apply the novel deep learning methodologies proposed in the previous chapters to environmental economics.More specifically, chapter 5 uses ReLu deep neural networks to predict the CO2
emissions associated with Bitcoin mining showing that the fossil fuel emission associated with Bitcoin mining, for the year 2018, is higher than the annual levels of fossil fuel emissions of some U.S. states such as Maine, New Hampshire, and South Dakota. Lastly, chapter 6 uses both deep and shallow neural networks to construct environmental Engel curves for the U.S. for the years 1984 and 2012. The empirical results show that richer households pollute more, the pollution content of consumption increases at a lower rate than income, and that the pollution content of consumption grows at a decreasing rate. Finally, Appendix A, B,and C provide a brief theoretical introduction to feedforward, convolutional, and recurrent neural networks to allow the reader to understand the similarities and the differences between the different deep learning methods; and three different empirical applications (focused on
regression, image classification, and text generation) are implemented to show the strength and power of the different classes of deep networks.

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Identifiers

ORCID for Jose Olmo: orcid.org/0000-0002-0437-7812

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