The Global Financial Crisis, starting in 2007, served as a reminder of the serious impact that imbalances originating in financial markets can have on economic growth. The aftermath of this economic shock with the ensuing recession continues to concern policymakers to this day. The subsequent period characterized by subdued growth and few but severe recessions gave rise to the importance of linkages between economic policy and risk management. The connection between this idea and the relevance of financial variables for analyzing growth risks is established by Adrian et al. (2019). They employ quantile regressions to examine the conditional distribution of future GDP growth and find that its left tail is exposed to substantially more volatility over time than the right tail. Moreover, they find that financial conditions for the US measured by the National Financial Conditions Index (NFCI) can serve as a relevant predictor of downside risk to conditional future economic growth.
This thesis examines some machine-learning based variable selection methods that have been largely unexplored in the GaR context. The focus is on generating higher predictive power compared to the model by Adrian et al. (2019) rather than on analyzing economic relationships. The approaches described here are easy to apply and can help to automate the selection of variables for GaR estimation instead of having to manually choose relevant indicators. In detail, the LASSO method is used in the quantile regression context (Belloni and Chernozhukov 2011; Li and Zhu 2008), as well as the Adaptive (Wu and Liu 2009) and Relaxed LASSO (Meinshausen 2007), two of its modifications. In addition, the Elastic Net method is investigated as a compromise between Ridge and LASSO regression.
To test the performance of these models, a backtesting exercise is conducted based on US data ranging from 1986 to 2019. The out-of-sample analysis is performed under the expanding and rolling window approach. For evaluation of the models, some of the backtesting tools used by Brownlees and Souza (2019) to perform a similar analysis for volatility models in the GaR context are utilized. In this regard, the following research question is formulated: Can the machine learning-based models improve the predictive power measured by the introduced backtesting tools for the investigated period compared to the quantile regression base model?
Table of Contents
1 Introduction
2 The Concept of Growth-at-Risk
2.1 Literature Overview
2.2 Quantile Regression
2.3 LASSO Quantile Methods
2.3.1 LASSO Quantile Regression
2.3.2 Relaxed LASSO Quantile Regression
2.3.3 Adaptive LASSO Quantile Regression
2.3.4 Elastic Net Quantile Regression
2.4 Backtesting
3 Empirical Analysis
3.1 Data
3.2 In-Sample Analysis
3.3 Out-of-Sample Analysis
3.3.1 Expanding Window Results
3.3.2 Rolling Window Results
3.3.3 Variable Selection in Out-of-Sample Analysis
3.4 Discussion
4 Conclusion
Objectives and Research Focus
The primary objective of this thesis is to enhance the predictive power of Growth-at-Risk (GaR) models by applying machine learning-based variable selection techniques. The work centers on evaluating whether penalized quantile regression methods, such as LASSO and its variants, can outperform the benchmark model formulated by Adrian et al. (2019), which relies on aggregate indicators of financial conditions.
- Comparison of machine learning-based variable selection methods in the GaR context.
- Evaluation of LASSO, Relaxed LASSO, Adaptive LASSO, and Elastic Net quantile regressions.
- Backtesting performance analysis using expanding and rolling window approaches.
- Investigation of variable selection patterns across different quantiles and time horizons.
Excerpt from the Book
2.3 LASSO Quantile Methods
To accommodate a large number of estimators, it is necessary to go beyond the classic QR method as described before. Several GDP growth indicators might be correlated with each other, as they represent overlapping information. Including many of these variables in a QR model could consequently lead to problems with multicollinearity which is connected with unstable estimators. Under these circumstances, small changes in the data can greatly alter the estimators. In addition, with too many predictors in the model overfitting can occur. While this does not pose a problem for in-sample analyses as the tick loss function is still minimized, in out-of-sample analyses overfitted models perform poorly. This is due to the imprecisely estimated coefficients, which cannot be generalized to new data.
To keep the flexibility of the QR approach and tackle the issues arising with high-dimensional data and multicollinearity, regularization methods such as the LASSO and Elastic Net, used for shrinking coefficients and selecting variables, can be employed. In this chapter, the LASSO approach in the quantile context, two well-known modifications of it, the relaxed and adaptive LASSO, and Elastic Net are described.
Summary of Chapters
1 Introduction: Provides the context of the Global Financial Crisis and introduces the Growth-at-Risk (GaR) concept, highlighting the need for advanced variable selection in predicting economic downturns.
2 The Concept of Growth-at-Risk: Formally introduces the GaR framework, outlines quantile regression methodology, and details various penalized methods, including LASSO, Relaxed LASSO, Adaptive LASSO, and Elastic Net, while discussing backtesting.
3 Empirical Analysis: Conducts an analysis on US data (1986-2019) using various models, evaluating them against the benchmark through in-sample and out-of-sample tests, and discussing the variable selection results.
4 Conclusion: Synthesizes the findings, noting that while penalized methods provide insights, the benchmark often performs strongly in specific extreme downside quantiles, and emphasizes the conditional applicability of the proposed models.
Keywords
Growth-at-Risk, GaR, Quantile Regression, Machine Learning, LASSO, Adaptive LASSO, Elastic Net, Variable Selection, Backtesting, GDP growth, Financial instability, Forecasting, Predictive power, Macrofinance, Econometrics
Frequently Asked Questions
What is the core focus of this Master Thesis?
The thesis focuses on improving the predictive accuracy of Growth-at-Risk (GaR) models by replacing aggregate index-based approaches with machine learning-based variable selection methods that automatically identify relevant individual economic indicators.
Which specific statistical methods are compared in this work?
The work systematically compares the benchmark Quantile Regression (QR) model against penalized variants: LASSO Quantile Regression, Relaxed LASSO, Adaptive LASSO, and Elastic Net Quantile Regression.
What is the primary motivation for introducing these machine learning methods?
The primary motivation is to overcome limitations in existing GaR literature, specifically the reliance on aggregate indices like the National Financial Conditions Index (NFCI) and the issue of dealing with a vast number of potential economic predictors.
How is the model performance evaluated?
Model performance is rigorously tested through backtesting protocols using both expanding and rolling forecasting windows, with evaluation metrics including empirical coverage, average prediction length, and tick loss.
Does the machine learning approach lead to superior results?
The results show mixed performance; while penalized models often show improved results in specific periods (e.g., during the Global Financial Crisis) or for higher quantiles, the benchmark QR model remains highly competitive for the most extreme downside risks.
What role does the Global Financial Crisis play in the analysis?
The thesis uses the period surrounding the 2008 crisis to explicitly analyze how well the different models capture major economic shocks and subsequent recoveries, highlighting specific strengths and weaknesses of the proposed penalized methods compared to the benchmark.
Which variables were identified as most relevant for GaR prediction?
The empirical findings highlight that variables such as house prices, corporate debt-to-GDP, and crude oil prices are frequently selected as significant indicators for lower downside quantiles in the US data.
Are there limitations to the interpretation of the coefficients in these models?
Yes, due to the shrinkage nature of LASSO-based methods, the thesis notes that economic interpretability should be handled with caution, as the primary goal is primarily focused on accurate out-of-sample prediction.
- Arbeit zitieren
- Franz Lennart Wunderlich (Autor:in), 2022, Machine Learning in the Growth-at-Risk Context. A Comparison of Predictors, München, GRIN Verlag, https://www.grin.com/document/1274858
