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Economic Forecasting with Many Predictors University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Doctoral Dissertations Graduate School 5-2017 Economic Forecasting with Many Predictors Fanning Meng University of Tennessee, Knoxville, [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_graddiss Part of the Econometrics Commons, International Economics Commons, Macroeconomics Commons, Management Information Systems Commons, and the Management Sciences and Quantitative Methods Commons Recommended Citation Meng, Fanning, "Economic Forecasting with Many Predictors. " PhD diss., University of Tennessee, 2017. https://trace.tennessee.edu/utk_graddiss/4483 This Dissertation is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a dissertation written by Fanning Meng entitled "Economic Forecasting with Many Predictors." I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the equirr ements for the degree of Doctor of Philosophy, with a major in Economics. Luiz R. Lima, Major Professor We have read this dissertation and recommend its acceptance: Celeste Carruthers, Eric Kelley, Georg Schaur, Christian Vossler Accepted for the Council: Dixie L. Thompson Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) Economic Forecasting with Many Predictors A Dissertation Presented for the Doctor of Philosophy Degree The University of Tennessee, Knoxville Fanning Meng May 2017 c by Fanning Meng, 2017 All Rights Reserved. ii Dedication This dissertation is dedicated to my beloved husband, Zhihao Hao, and my dearest son, Junqi Hao, for their support over these years. And I am also grateful to my parents and parents-in-law for taking care of my little boy during the days I’m away. iii Acknowledgements I would like to sincerely thank my advisor Dr. Luiz R. Lima for leading me onto the road of being a professional researcher. I also want to express my deep gratitude to Dr. Georg Schaur, Dr. Celeste Carruthers and Dr. Christian Vossler for their guidance and support on my research. Special thanks to Dr. Christian Vossler and Dr. Williams Neilson for their help with my sick leave requirements in Spring 2014 and Fall 2015. I would also like to thank Dr. Eric Kelley for serving on my committee and offering valuable comments on my research. Many thanks to Sherri Pinkston and Juliana Notaro for their wonderful assistance on many administrative issues. I want to express my appreciation to the whole Economics Department at Haslam College of Business for providing me the precious opportunity to achieve my academic goal. iv Abstract The dissertation is focused on the analysis of economic forecasting with a large number of predictors. The first chapter develops a novel forecasting method that minimizes the effects of weak predictors and estimation errors on the accuracy of equity premium forecasts. The proposed method is based on an averaging scheme applied to quantiles conditional on predictors selected by LASSO. The resulting forecasts outperform the historical average, and other existing models, by statistically and economically meaningful margins. In the second chapter, we find that incorporating distributional and high- frequency information into a forecasting model can produce substantial accuracy gains. Distributional information is included through a quantile combination approach, but estimation of quantile regressions with mixed-frequency data leads to a parameter proliferation problem. We consider extensions of the MIDAS and soft (hard) thresholding methods towards quantile regression. Our empirical study on GDP growth rate reveals a strong predictability gain when high-frequency and distributional information are adequately incorporated into the same forecasting model. The third chapter analyzes the wage effects of college enrollment for returning adults based on the NLSY79 data. To improve the estimation efficiency, we apply the double-selection model among time-varying features and individual fixed effects. The empirical results on hourly wage predictions show evidences towards the superiority v of double-selection model over a fixed-effect model. Based on the double-selection model, we find significant and positive returns on years of college enrollment for the returning adults. On average, one more year’s college enrollment can increase hourly wage of returning adults by $1:12, an estimate that is about 7:7% higher than that from the fixed-effect model. vi Table of Contents 1 Out-of-Sample Return Predictability: a Quantile Combination Ap- proach1 1.1 Disclosure.................................1 1.2 Introduction................................1 1.3 Econometric Methodology........................4 1.3.1 The `1-penalized quantile regression estimator.........7 1.3.2 An alternative interpretation to the PLQC forecast......8 1.3.3 Weight selection.......................... 10 1.3.4 The forecasting data, procedure and evaluation........ 11 1.4 Empirical Results............................. 14 1.4.1 Out-of-sample forecasting results................ 14 1.4.2 Explaining the benefits of the PLQC forecasts......... 18 1.4.3 Robustness analysis: other quantile forecasting models.... 20 1.5 Conclusion................................. 22 2 Quantile Forecasting with Mixed-Frequency Data 24 2.1 Introduction................................ 24 2.2 The Econometric Model......................... 27 2.3 The Parameter Proliferation Problem.................. 30 2.3.1 Solutions to the Parameter Proliferation Problem....... 31 2.3.2 Soft Thresholding......................... 34 vii 2.3.3 Hard Thresholding........................ 37 2.4 Empirical Analysis............................ 38 2.4.1 Data................................ 38 2.4.2 Estimation Scheme and forecasting models........... 41 2.4.3 Forecast Evaluation........................ 43 2.4.4 Empirical Results......................... 43 2.4.5 Forecast Combination...................... 45 2.4.6 Robustness Analysis....................... 46 2.5 Conclusion................................. 48 3 Wage Returns to Adult Education: New Evidence from Feature- Selection 50 3.1 Introduction................................ 50 3.2 Data.................................... 52 3.3 Econometric Models........................... 54 3.3.1 Double-selection (DS) Regression................ 55 3.4 Empirical Results............................. 56 3.5 Conclusion................................. 58 Bibliography 60 Appendix 69 Vita 89 viii List of Tables A.1 Out-of-sample Equity Premium Forecasting ................ 72 A.2 Mean Squared Prediction Error (MSPE) Decomposition .......... 72 A.3 Frequency of variables selected over OOS : Jan 1967 − Dec 2013 ..... 72 A.4 Quantile Scores ............................... 76 B.1 Correlation coefficients among randomly selected lag predictors ...... 78 B.2 Stationarity test results ........................... 78 B.3 Description of variables ........................... 80 B.4 Out-of-sample forecast performance for GDP growth over 2001Q1−2008Q4: RMSFE and CW ............................. 81 B.5 Out-of-sample forecasts of GDP growth over 2001Q1 − 2008Q4: p-values of CW tests .................................. 83 B.6 Out-of-sample forecast performance for model combination over 2001Q1 − 2008Q4 ................................... 83 B.7 Performance of forecast combination models over 2008Q1 − 2012Q1 .... 85 C.1 Summary statistics of MSFE ........................ 86 C.2 Summary statistics of wage effects ..................... 87 ix List of Figures A.1 Cumulative squared prediction error for the benchmark model minus the cumulative squared prediction errors for the single-predictor regression forecasting models, 1967.1-2013.12 ..................... 70 A.2 Cumulative squared prediction error for the benchmark model minus the cumulative squared prediction errors for the FQR, FOLS, CSR and PLQC models, 1967.1-2013.12 ........................... 71 A.3 Scatterplot of forecast variance and squared forecast bias relative to historical average, 1967.1 - 1990.12 ..................... 73 A.4 Scatterplot of forecast variance and squared forecast bias relative to historical average, 1991.1 - 2013.12 ..................... 74 A.5 Variables selected by PLQC for quantile levels τ = 0:3; 0:4; 0:5; 0:6; 0:7 over OOS 1967.1-2013.12 ............................ 75 A.6 Cumulative squared prediction error for the benchmark model minus the cumulative squared prediction errors for the PLQC 1, AL-LASSO 1, RFC 1, and singe-predictor quantile forecasting models, 1967.1-2013.12 ..... 77 B.1 GDP growth rate over 1963Q1 − 2012Q1 ................ 79 B.2 Histogram of GDP growth rate over 1963Q1 − 2012Q1 ........ 79 B.3 The RMSFE comparison for multi-step ahead forecasts over 2001Q1−2008Q4. 82 B.4 The RMSFE comparison for multi-step ahead forecasts over 2008Q1−2012Q1. 84 C.1 Histogram for highest grade completed for the whole sample..... 86 C.2 Histogram for highest grade completed for the restricted sample... 87 x C.3 The fitted distribution of MSFE for DS and FE models....... 88 C.4 Wage effects of adult education..................... 88 xi Nomenclature AL-LASSO Asymmetric-loss LASSO
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