KaydedilenlerDerginizi ekleyin

Dergiler / Ekonomi Politika ve Finans Araştırmaları Dergisi / 2024 / Cilt: 9 Sayı: 4

Yeşil Tahvil Endeksinin Tahmini için Yapay Zeka Destekli Makine Öğrenme Yöntemleri: Karşılaştırmalı Bir Analiz

Artificial Intelligence-Assisted Machine Learning Methods for Forecasting Green Bond Index: A Comparative Analysis

Yunus Emre Gür(FIRAT ÜNİVERSİTESİ)0000-0001-6530-0598
Ahmed İhsan Şimşek(FIRAT ÜNİVERSİTESİ)0000-0002-2900-3032
Emre Bulut(FIRAT ÜNİVERSİTESİ)0000-0002-2884-1405
Sayfa
628–655
Yayın Tarihi
2024-12-31
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Bu çalışmanın, literatürde doğrudan karşılaştırılabilir benzer çalışmaların sınırlı olması nedeniyle alana önemli bir katkı sağlayacağı düşünülmektedir.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:Bu çalışmanın temel amacı, yeşil tahvil endeks değerlerini yapay zeka destekli farklı makine öğrenmesi modelleri ile tahmin ederek literatüre katkıda bulunmaktır.
📊
Temel Bulgular & Veri:Çeşitli kaynaklardan bir araya getirilen, 1 Haziran 2021 ile 29 Nisan 2024 tarihlerini kapsayan veriler, eğitim ve test kümelerine ayrılmış ve her biri için standart ön işlemler gerçekleştirilmiştir.
💡
Sonuç & Katkı:Bu çalışmanın, literatürde doğrudan karşılaştırılabilir benzer çalışmaların sınırlı olması nedeniyle alana önemli bir katkı sağlayacağı düşünülmektedir.
🔬Tür:Literatür & Derleme Çalışması
📍Kapsam:2021 Verileri
⚙️Değişkenler:Yeşil Tahviller · Makine Öğrenmesi · Rasyonel Kuadratik Gauss Süreci Regresyonu

Özet

Bu çalışmanın temel amacı, yeşil tahvil endeks değerlerini yapay zeka destekli farklı makine öğrenmesi modelleri ile tahmin ederek literatüre katkıda bulunmaktır. Çeşitli kaynaklardan bir araya getirilen, 1 Haziran 2021 ile 29 Nisan 2024 tarihlerini kapsayan veriler, eğitim ve test kümelerine ayrılmış ve her biri için standart ön işlemler gerçekleştirilmiştir. Modelin bağımlı değişkeni, küresel finans piyasalarındaki yeşil tahvillerin performansını izleyen ve çalışma için kapsamlı bir ölçüt görevi gören Küresel S&P Yeşil Tahvil Endeksi'dir. Eğitilen makine öğrenmesi modellerinin (Random Forest, Doğrusal Regresyon, Rasyonel Kuadratik Gauss Süreci Regresyonu (GPR), XGBoost, MLP ve Doğrusal DVM) performansını değerlendirmek ve karşılaştırmak için değerlendirme ölçütleri olarak RMSE, MSE, MAE, MAPE ve R² kullanılmış ve en iyi performans gösteren model Rasyonel Kuadratik GPR modeli olmuştur. SHAP analizinin son bölümü modelin tahminlerini etkileyen başlıca faktörleri ortaya koymaktadır. Modelin DXY (ABD Doları Endeksi), XAU (Spot Altın Fiyatı) ve MSCI (Morgan Stanley Capital International) gibi makroekonomik göstergelere büyük önem verdiği görülmektedir. Bu çalışmanın, literatürde doğrudan karşılaştırılabilir benzer çalışmaların sınırlı olması nedeniyle alana önemli bir katkı sağlayacağı düşünülmektedir.

Abstract

The main objective of this study is to contribute to the literature by forecasting green bond index with different machine learning models supported by artificial intelligence. The data from 1 June 2021 to 29 April 2024, collected from many sources, was separated into training and test sets, and standard preparation was conducted for each. The model's dependent variable is the Global S&P Green Bond Index, which monitors the performance of green bonds in global financial markets and serves as a comprehensive benchmark for the study. To evaluate and compare the performance of the trained machine learning models (Random Forest, Linear Regression, Rational Quadratic Gaussian Process Regression (GPR), XGBoost, MLP, and Linear SVM), RMSE, MSE, MAE, MAPE, and R² were used as evaluation metrics and the best performing model was Rational Quadratic GPR. The concluding segment of the SHAP analysis reveals the primary factors influencing the model's forecasts. It is evident that the model assigns considerable importance to macroeconomic indicators, including the DXY (US Dollar Index), XAU (Gold Spot Price), and MSCI (Morgan Stanley Capital International). This work is expected to enhance the literature, as studies directly comparable to this research are limited in this field.

🔖

Bu Makaleye Atıf Yap

Gür, Y. E., Şimşek, A. İ., Bulut, E. (2024). Yeşil Tahvil Endeksinin Tahmini için Yapay Zeka Destekli Makine Öğrenme Yöntemleri: Karşılaştırmalı Bir Analiz. Ekonomi Politika ve Finans Araştırmaları Dergisi, Cilt: 9 Sayı: 4, 628–655. https://doi.org/10.30784/epfad.1495757

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (78)

  1. Abakah, E.J.A., Tiwari, A.K., Sharma, A. and Mwamtambulo, D.J. (2022). Extreme connectedness between green bonds, government bonds, corporate bonds and other asset classes: Insights for portfolio investors. Journal of Risk and Financial Management, 15(10), 477. https://doi.org/10.3390/jrfm15100477
  2. Ampomah, E.K., Qin, Z. and Nyame, G. (2020). Evaluation of tree-based ensemble machine learning models in predicting stock price direction of movement. Information, 11(6), 332. https://doi.org/10.3390/info11060332
  3. Bisht, R.K. and Bisht, I.P. (2022). Investigation of the role of test size, random state, and dataset in the accuracy of classification algorithms. In H. Sharma, V. Shrivastava, K.K. Bharti and L. Wang (Eds.), Communication and Intelligent Systems (pp. 715-726). Singapore: Springer Nature Singapore. https://doi.org/10.1007/978-981-99-2100-3_55
  4. Black, A.J., Klinkowska, O., McMillan, D.G. and McMillan, F.J. (2014). Forecasting stock returns: Do commodity prices help? Journal of Forecasting, 33(8), 627-639. https://doi.org/10.1002/for.2314
  5. Blossier, B., Bryan, K.R., Daly, C.J. and Winter, C. (2017). Shore and bar cross-shore migration, rotation, and breathing processes at an embayed beach. Journal of Geophysical Research: Earth Surface, 122(10), 1745–1770. https://doi.org/10.1002/2017JF004227
  6. Boughrara, H., Chtourou, M., Ben Amar, C. and Chen, L. (2016). Facial expression recognition based on a mlp neural network using constructive training algorithm. Multimedia Tools and Applications, 75, 709-731. https://doi.org/10.1007/s11042-014-2322-6
  7. Bouri, E., Çepni, O., Gabauer, D. and Gupta, R. (2021a). Return connectedness across asset classes around the COVİD-19 outbreak. International Review of Financial Analysis, 73, 101646. https://doi.org/10.1016/j.irfa.2020.101646
  8. Bouri, E., Demirer, R., Gupta, R. and Wohar, M.E. (2021b). Gold, platinum and the predictability of bond risk premia. Finance Research Letters, 38, 101490. https://doi.org/10.1016/j.frl.2020.101490
  9. Breiman, L. (2017). Classification and regression trees. London: Routledge.
  10. Broadstock, D.C. and Cheng, L.T.W. (2019). Time-varying relation between black and green bond price benchmarks: Macroeconomic determinants for the first decade. Finance Research Letters, 29, 17-22. https://doi.org/10.1016/j.frl.2019.02.006
  11. Chai, S., Chu, W., Zhang, Z., Li, Z. and Abedin, M.Z. (2022). Dynamic nonlinear connectedness between the green bonds, clean energy, and stock price: The impact of the COVİD-19 pandemic. Annals of Operations Research, 1-28. https://doi.org/10.1007/s10479-021-04452-y
  12. Chen, S., Tao, F., Pan, C., Hu, X., Ma, H., Li, C., … and Wang, Y. (2020). Modeling quality changes in pacific white shrimp (litopenaeus vannamei) during storage: Comparison of the arrhenius model and random forest model. Journal of Food Processing and Preservation, 45(1), e14999. https://doi.org/10.1111/jfpp.14999
  13. Chen, Y., Rogoff, K. and Rossi, B. (2010). Can exchange rates forecast commodity prices? Quarterly Journal of Economics, 125(3), 1145-1194. https://doi.org/10.1162/qjec.2010.125.3.1145
  14. Cortes, C. and Vapnik, V. (1995). Support-vector networks. Machine Learning, 20, 273-297. https://doi.org/10.1007/BF00994018
  15. Çetin, D.T. (2022). Green bonds in climate finance and forecasting of corporate green bond index value with artificial intelligence. Journal of Research in Business, 7(1), 138-157. https://doi.org/10.54452/jrb.992368
  16. D’Amato, V., D’Ecclesia, R. and Levantesi, S. (2022). ESG score prediction through random forest algorithm. Computational Management Science, 19(2), 347-373. https://doi.org/10.1007/s10287-021-00419-3
  17. Devereux, M.B. (2008). Much appreciated? The rise of the Canadian Dollar, 2002-2008. Review of Economic Analysis, 1(1), 1-33. https://doi.org/10.15353/rea.v1i1.1477
  18. Dorfleitner, G., Utz, S. and Zhang, R. (2022). The pricing of green bonds: External reviews and the shades of green. Review of Managerial Science, 16, 797-834. https://doi.org/10.1007/s11846-021-00458-9
  19. Dutta, A., Bouri, E. and Noor, H. (2021). Climate bond, stock, gold, and oil markets: Dynamic correlations and hedging analyses during the COVİD-19 outbreak. Resources Policy, 74, 102265. https://doi.org/10.1016/j.resourpol.2021.102265
  20. Dutta, A., Kumar, S.S. and Basu, M. (2020). A gated recurrent unit approach to bitcoin price prediction. Journal of Risk and Financial Management, 13(2), 23. https://doi.org/10.3390/jrfm13020023
  21. Ehlers, T. and Packer, F. (2017). Green Bond Finance and Certification. BIS Quarterly Review, September 2017, 89–104. Retrieved from https://www.bis.org/quarterlyreviews/index.htm?m=158
  22. Gao, P., Zhang, R. and Yang, X. (2020). The application of stock index price prediction with neural network. Mathematical and Computational Applications, 25(3), 53. https://doi.org/10.3390/mca25030053
  23. Gao, Y. and Zhang, J. (2023). Investigating financialization perspective of oil prices, green bonds, and stock market movement in COVİD-19: Empirical study of E7 economies. Environmental Science and Pollution Research, 30(23), 64111-64122. https://doi.org/10.1007/s11356-023-26808-6
  24. Gevorkyan, M.N., Demidova, A.V., Demidova, T.S. and Sobolev, A.A. (2019). Review and comparative analysis of machine learning libraries for machine learning. Discrete and Continuous Models and Applied Computational Science, 27(4), 305-315. https://doi.org/10.22363/2658-4670-2019-27-4-305-315
  25. Ghoshray, A. and Pundit, M. (2021). Economic growth in China and its impact on international commodity prices. International Journal of Finance & Economics, 26(2), 2776-2789. https://doi.org/10.1002/ijfe.1933
  26. Hao, J. and Ho, T.K. (2019). Machine learning made easy: A review of scikit-learn package in python programming language. Journal of Educational and Behavioral Statistics, 44(3), 348-361. https://doi.org/10.3102/107699861983224
  27. Harrell, F.E. (2015). Regression modeling strategies: With applications to linear models, logistic and ordinal regression, and survival analysis. Berlin: Springer.
  28. Hong, H. and Yogo, M. (2012). What does futures market interest tell us about the macroeconomy and asset prices? Journal of Financial Economics, 105(3), 473-490. https://doi.org/10.1016/j.jfineco.2012.04.005
  29. Hung, N.T. (2021). Green bonds and asset classes: New evidence from time-varying copula and transfer entropy models. Global Business Review. Advance online publication. https://doi.org/10.1177/09721509211034095
  30. Huynh, T.L.D., Hille, E. and Nasir, M. (2020). Diversification in the age of the 4th industrial revolution: The role of artificial intelligence, green bonds and cryptocurrencies. Technological Forecasting and Social Change, 159, 120188. https://doi.org/10.1016/j.techfore.2020.120188
  31. Idilbi-Bayaa, Y. and Qadan, M. (2021). Forecasting commodity prices using the term structure. Journal of Risk and Financial Management, 14(12), 585. https://doi.org/10.3390/jrfm14120585
  32. Jabeur, S.B., Mefteh‐Wali, S. and Viviani, J. (2024). Forecasting gold price with the XGBoost algorithm and SHAP interaction values. Annals of Operations Research, 334(1-3), 679-699. https://doi.org/10.1007/s10479-021-04187-w
  33. Jia, H. (2021). Deep learning algorithm-based financial prediction models. Complexity, 2021, 560886. https://doi.org/10.1155/2021/5560886
  34. Kehoe, M., Chun, K.P. and Baulch, H.M. (2015). Who smells? Forecasting taste and odor in a drinking water reservoir. Environmental Science & Technology, 49(18), 10984-10992. https://doi.org/10.1021/acs.est.5b00979
  35. Lebelle, M., Jarjir, S.L. and Sassi, S. (2020). Corporate green bond issuances: An international evidence. Journal of Risk and Financial Management, 13(2), 25. https://doi.org/10.3390/jrfm13020025
  36. Li, G., Liu, X., Wang, M., Yu, T., Ren, J. and Wang, Q. (2022). Predicting the functional outcomes of anti‐LGI1 encephalitis using a random forest model. Acta Neurologica Scandinavica, 146(2), 137-143. https://doi.org/10.1111/ane.13619
  37. Li, W., Yin, Y., Quan, X. and Zhang, H. (2019). Gene expression value prediction based on XGBoost algorithm. Frontiers in Genetics, 10, 1077. https://doi.org/10.3389/fgene.2019.01077
  38. Liu, D., Zhang, X., Zheng, T., Shi, Q., Cui, Y., Wang, Y., … and Liu, L. (2021). Optimisation and evaluation of the random forest model in the efficacy prediction of chemoradiotherapy for advanced cervical cancer based on radiomics signature from high-resolution T2 weighted images. Archives of Gynecology and Obstetrics, 303(3), 811-820. https://doi.org/10.1007/s00404-020-05908-5
  39. Liu, Y., Chen, H., Zhang, L., Wu, X. and Wang, X.J. (2020). Energy consumption prediction and diagnosis of public buildings based on support vector machine learning: A case study in China. Journal of Cleaner Production, 272, 122542. https://doi.org/10.1016/j.jclepro.2020.122542
  40. Lundberg, S.M. and Lee, S-I. (2017). A unified approach to interpreting model predictions. Paper presented at the 31st Conference on Neural Information Processing System. Long Beach, CA, USA. Retrieved from https://proceedings.neurips.cc/paper/2017/file/8a20a8621978632d76c43dfd28b67767-Paper.pdf
  41. Lundberg, S.M., Erion, G.G. and Lee, S.I. (2018). Consistent individualized feature attribution for tree ensembles. ArXiv, abs/1802.03888. https://doi.org/10.48550/arxiv.1802.03888
  42. Maneejuk, P., Zou, B. and Yamaka, W. (2023). Predicting Chinese stock prices using convertible bond: An evidence-based neural network approach. Asian Journal of Economics and Banking, 7(3), 294-309. https://doi.org/10.1108/ajeb-08-2023-0080
  43. Marín-Rodríguez, N.J., González-Ruiz, J.D. and Botero, S.B. (2022). Dynamic relationships among green bonds, CO2 emissions, and oil prices. Frontiers in Environmental Science, 10, 992726. https://doi.org/10.3389/fenvs.2022.992726
  44. Montaño, J., Coco, G., Antolínez, J.A.Á., Beuzen, T., Bryan, K.R., Cagigal, L., … and Vos, K. (2020). Blind testing of shoreline evolution models. Scientific Reports, 10(1), 2137. https://doi.org/10.1038/s41598-020-59018-y
  45. Muñoz, P., Orellana‐Alvear, J., Willems, P. and Célleri, R. (2018). Flash-flood forecasting in an andean mountain catchment-Development of a step-wise methodology based on the random forest algorithm. Water, 10(11), 1519. https://doi.org/10.3390/w10111519
  46. Naeem, M.A., Mbarki, I., Alharthi, M., Omri, A. and Shahzad, S.J.H. (2021). Did COVİD-19 impact the connectedness between green bonds and other financial markets? Evidence from time-frequency domain with portfolio implications. Frontiers in Environmental Science, 9, 657533. https://doi.org/10.3389/fenvs.2021.657533
  47. Pentoś, K., Mbah, J.T., Pieczarka, K., Niedbała, G. and Wojciechowski, T. (2022). Evaluation of multiple linear regression and machine learning approaches to predict soil compaction and shear stress based on electrical parameters. Applied Sciences, 12(17), 8791. https://doi.org/10.3390/app12178791
  48. Pinkus, A. (1999), Approximation theory of the MLP model in neural networks. Acta Numerica, 8, 143–195. https://doi.org/10.1017/S0962492900002919
  49. Rasmussen, C.E. (2003). Gaussian processes in machine learning. In O. Bousquet, U. von Luxburg and G. Rätsch (Eds.), Summer school on machine learning (pp. 63-71). Berlin: Springer.
  50. Reboredo, J.C. (2018). Green bond and financial markets: Co-movement, diversification and price spillover effects. Energy Economics, 74, 38-50. https://doi.org/10.1016/j.eneco.2018.05.030
  51. Reboredo, J.C. and Ugolini, A. (2020). Price connectedness between green bond and financial markets. Economic Modelling, 88, 25-38. https://doi.org/10.1016/j.econmod.2019.09.004
  52. Ren, Z., Yang, K. and Dong, W. (2020). Spatial analysis and risk assessment model research of arthritis based on risk factors: China, 2011, 2013 and 2015. IEEE Access, 8, 206406-206417. https://doi.org/10.1109/access.2020.3037912
  53. Sadorsky, P. (2021). A random forests approach to predicting clean energy stock prices. Journal of Risk and Financial Management, 14(2), 48. https://doi.org/10.3390/jrfm14020048
  54. Shahhosseini, M. (2021). Improved weighted random forest for classification problems. In T. Allahviranloo, S. Salahshour and N. Arica (Eds.), Progress in intelligent decision science (pp. 42-56). Papers presented at the 4th International Online Conference on Intelligent Decision Science (IDS 2020), Istanbul, Türkiye. https://doi.org/10.1007/978-3-030-66501-2_4
  55. Shapley, L.S. (1953). A value for n‐person games. Contribution to the Theory of Games, 2. Princeton: Princeton University Press
  56. Sharma, H., Harsora, H. and Ogunleye, B. (2024). An optimal house price prediction algorithm: Xgboost. Analytics, 3(1), 30-45. https://doi.org/10.3390/analytics3010003
  57. Simsek, A.I. (2024). Improving the performance of stock price prediction: A comparative study of random forest, XGBoost, and stacked generalization approaches. In N. Geada, R. Sood, and A. Sidana (Eds.), Revolutionizing the global stock market: Harnessing blockchain for enhanced adaptability (pp. 83-99). https://doi.org/10.4018/979-8-3693-1758-7.ch005
  58. Soltani, H., Taleb, J., Ben Hamadou, F. and Boujelbène-Abbes, M. (2024). Using machine learning to forecast clean energy, commodities, green bonds and ESG index prices: How important is financial stress? EuroMed Journal of Business, Advance online publication. https://doi.org/10.1108/EMJB-12-2023-0341
  59. Su, M., Zhang, Z., Zhu, Y., Zha, D. and Wen, W. (2019). Data driven natural gas spot price prediction models using machine learning methods. Energies, 12(9), 1680. https://doi.org/10.3390/en12091680
  60. Sun, J., Yu, H., Zhong, G., Dong, J., Zhang, S. and Yu, H. (2020). Random shapley forests: Cooperative game-based random forests with consistency. IEEE Transactions on Cybernetics, 52(1), 205-214. doi: 10.1109/TCYB.2020.2972956
  61. Tsui, A.K. and Zhang, Z. (2021). Trading macro-cycles of foreign exchange markets using hybrid models. Sustainability, 13(17), 9820. https://doi.org/10.3390/su13179820
  62. Tu, C.A., Rasoulinezhad, E. and Sarker, T. (2020). Investigating solutions for the development of a green bond market: Evidence from analytic hierarchy process. Finance Research Letters, 34, 101457. https://doi.org/10.1016/j.frl.2020.101457
  63. Verma, R.K. and Bansal, R. (2023). Stock market reaction on green-bond issue: Evidence from Indian green-bond issuers. Vision, 27(2), 264-272. https://doi.org/10.1177/09722629211022523
  64. Wang, J., Tang, J. and Guo, K. (2022a). Green bond index prediction based on CEEMDAN-LSTM. Frontiers in Energy Research, 9, 793413. https://doi.org/10.3389/fenrg.2021.793413
  65. Wang, Z., Dong, W. and Yang, K. (2022b). Spatiotemporal analysis and risk assessment model research of diabetes among people over 45 years old in china. International Journal of Environmental Research and Public Health, 19(16), 9861. https://doi.org/10.3390/ijerph19169861
  66. Wei, P., Zhou, J., Ren, X. and Taghizadeh-Hesary, F. (2024). The heterogeneous role of economic and financial uncertainty in green bond market efficiency. Review of Accounting and Finance, 23(1), 130-155. https://doi.org/10.1108/RAF-07-2023-0202
  67. Wilamowski, B.M. (2009). Neural network architectures and learning algorithms. IEEE Industrial Electronics Magazine, 3(4), 56-63. Retrieved from https://ieeexplore.ieee.org/
  68. Wu, K., Chai, Y., Zhang, X. and Zhao, X. (2022). Research on power price forecasting based on pso-xgboost. Electronics, 11(22), 3763. https://doi.org/10.3390/electronics11223763
  69. Xi, B. and Jing, H. (2021). Research on the impact of green bond issuance on the stock price of listed companies. Kybernetes, 51(4), 1478-1497. https://doi.org/10.1108/k-12-2020-0900
  70. Xia, Y., Ren, H., Li, Y., Xia, J., He, L. and Liu, N. (2022). Forecasting green bond volatility via novel heterogeneous ensemble approaches. Expert Systems with Applications, 204, 117580. https://doi.org/10.1016/j.eswa.2022.117580
  71. Yadav, M.P., Tandon, P., Singh, A.B., Shore, A. and Gaur, P. (2022). Exploring time and frequency linkages of green bond with renewable energy and crypto market. Annals of Operations Research. Advance online publication. https://doi.org/10.1007/s10479-022-05074-8
  72. Yue, Y., Wu, Y.C., Wang, P. and Xu, J. (2021). Stock price prediction based on XGBoost and LightGBM. E3S Web of Conferences, 275, 01040. https://doi.org/10.1051/e3sconf/202127501040
  73. Zaki, J., Nayyar, A., Dalal, S. and Ali, Z.H. (2022). House price prediction using hedonic pricing model and machine learning techniques. Concurrency and Computation: Practice and Experience, 34(27), e7342. https://doi.org/10.1002/cpe.7342
  74. Zazoum, B. (2022). Solar photovoltaic power prediction using different machine learning methods. Energy Reports, 8, 19-25. https://doi.org/10.1016/j.egyr.2021.11.183
  75. Zheng, H., Yuan, J. and Chen, L. (2017). Short-Term load forecasting using EMD-LSTM neural networks with a Xgboost algorithm for feature importance evaluation. Energies, 10(8), 1168-1188. https://doi.org/10.3390/en10081168
  76. Zhou, X. and Cui, Y. (2019). Green bonds, corporate performance, and corporate social responsibility. Sustainability, 11(23), 6881. https://doi.org/10.3390/su11236881
  77. Zhu, Y., Duan, S., Fu, Z. and Liu, Z. (2022). Stock price crash warning in the chinese security market using a machine learning-based method and financial indicators. Systems, 10(4), 108. https://doi.org/10.3390/systems10040108
  78. Zou, L., Zheng, B. and Li, X. (2017). The commodity price and exchange rate dynamics. Theoretical Economics Letters, 7(6), 1770-1793. https://doi.org/10.4236/tel.2017.76120