KİŞİ BAŞINA DÜŞEN GELİRİN STOKASTİK YAKINSAMASI: KIRILMALI LM VE RALS-LM BİRİM KÖK TESTLERİNDEN YENİ KANITLAR

Abstract

Ülkeler arasında kişi başına gelir düzeylerinde yakınsamanın gerçekleşmesi durumunda, uzun vadede ülkeler arasındaki ekonomik eşitsizliklerin azalacağı ileri sürülmektedir. Bu çalışmada Carlino ve Mills (1993) tarafından geliştirilen stokastik yakınsama hipotezini test etmek için LM ve RALS-LM birim kök testleri kullanılarak E7 ülkelerinde kişi başına düşen gelir yakınsaması incelenmiştir. Geleneksel birim kök testlerinde hataların normal dağılmaması limit dağılımını etkilemediği için genellikle dikkate alınmamakta ve hataların normal dağılmama bilgisi göz ardı edilmektedir. Ancak bu durum normal olmayan hatalar içinde yer alan bilgilerin yararsız olduğu ve göz ardı edilmesi gerektiği anlamı taşımamaktadır. Çalışmada, LM testine normal olmama bilgisi eklenerek daha yüksek güce sahip RALS-LM birim kök testleri kullanılmaktadır. Bu testler, zaman serisi verilerinin önemli bileşenlerini dikkate alınmasını ve kullanılmasına olanak tanımaktadır. Özellikle RALS-LM birim kök testleri, örnek birim sayısının kısıtlı olması durumunda birim kök testinin gücünün arttırma yeteneği nedeniyle oldukça avantaj sağlamaktadır. Birim kök testi sonuçlarına göre, kişi başına düşen nispi GSYİH için stokastik yakınsama hipotezi 7 ülkenin 4’ünde geçerlidir. Bulgular, Endonezya, Hindistan, Meksika, Türkiye’nin gelirlerinin zaman içinde birbirine yakınsadığını göstermektedir. Buna göre, ülkelerin gelirleri birbirinden bağımsız değildir ve gelecekteki gelirleri tahmin edilebilir. Brezilya, Çin ve Rusya için elde edilen bulgular ise, gelir serilerinin durağan olmadığını göstermekte; dolayısıyla bu ülkelerde şoklar uzun vadeli etkiler yaratmaktadır. Bu nedenle, gelir yakınsamasının sağlanabilmesi için uygulanacak politikalar kalıcı etkiye sahip olacaktır.

Keywords

• Yakınsama
• Gelir
• RALS birim kök
• Yapısal Kırılma

STOCHASTIC CONVERGENCE OF PER CAPITA INCOME: NEW EVIDENCE FROM LM AND RALS-LM UNIT ROOT TESTS WITH BREAKS

Abstract

It is suggested that if countries' convergence occurs, inequality will decrease in the long term. This study examined the convergence of per capita income in E7 countries using LM and RALS-LM unit root tests to test the stochastic convergence hypothesis developed by Carlino and Mills (1993). In traditional unit root tests, the non-normal distribution of errors is generally not taken into account because it does not affect the limit distribution, and the information about the non-normal distribution of errors is ignored. However, this does not mean that the information included in the non-normal errors is useless and should be ignored. The study uses RALS-LM unit root tests with higher power by adding non-normality information to the LM test. These tests allow the important components of time series data to be considered and used. In particular, RALS-LM unit root tests provide considerable advantages due to their ability to increase the power of the unit root test when the number of sample units is limited. According to the unit root test results, the stochastic convergence hypothesis for relative GDP per capita is valid in 4 out of 7 countries. The findings show that the incomes of Indonesia, India, Mexico, and Türkiye converge over time. Accordingly, the incomes of the countries are not independent from each other, and their future incomes can be predicted. The findings for Brazil, China, and Russia indicate that the income series are non-stationary; therefore, shocks have long-term effects in these countries. As a result, any policies aimed at achieving income convergence would need to have permanent and long-lasting impacts.

Keywords

• Convergence
• Income
• RALS unit root
• Structural Break

References

1. Ayala, A., Cunado, J., & Gil-Alana, L. A. (2013). “Real Convergence: Empirical Evidence for Latin America.” Applied Economics, 45(22), 3220-3229.
2. Barro, R. J., & Sala-i-Martin, X. (1992). “Convergence.” Journal of political Economy, 100(2), 223-251.
3. Barro, R. J., & Sala-i-Martin, X. (1995). “Economic Growth”. New York: McGraw-Hill.
4. Barro, R. J., & Sala-i-Martin, X. (2004). Economic Growth (2nd ed.). MIT Press.
5. Ben-David, D. (1996). “Trade and Convergence Among Countries.” Journal of International Economics, 40(3–4), 279–298.
6. Benabou, R. (1996). “Inequality and Growth.” NBER macroeconomics annual, 11, 11-74.
7. Bernard, A. B., & Durlauf, S. N. (1995). “Convergence in International Output”. Journal of Applied Econometrics, 10(2), 97–108
8. Beyaert, A., & García-Solanes, J. (2014). “Output Gap and Non-linear Economic Convergence.” Journal of Policy Modeling, 36(1), 121-135.

9. Carlino, G. and Mills, L. (1993). “Are US Regional Economies Converging? A Time Series Analysis.” Journal of Monetary Economics, 32, 335-46.
10. Cellini, R., & Scorcu, A. E. (2000). “Segmented Stochastic Convergence across the G-7 Countries.” Empirical Economics, 25, 463-474.
11. Ceylan, R., & Abiyev, V. (2016). “An Examination of Convergence Hypothesis for EU-15 Countries”. International Review of Economics & Finance, 45, 96-105.
12. Chang, T., Chang, H. L., Chu, H. P., & Su, C. W. (2006). “Is Per Capita Real GDP Stationary in African Countries? Evidence from Panel SURADF Test.” Applied Economics Letters, 13(15), 1003-1008.
13. Chong, T. T. L., Hinich, M. J., Liew, V. K. S., & Lim, K. P. (2008), “Time Series Test of Nonlinear Convergence and Transitional Dynamics.” Economics Letters, 100(3), 337-339.
14. Coe, D. T., & Helpman, E. (1995).” International R&D Spillovers.” European Economic Review, 39(5), 859–887
15. Dawson, J. W., & Strazicich, M. C. (2010). “Time-Series Tests of İncome Convergence with two Structural Breaks: Evidence from 29 Countries.” Applied Economics Letters, 17(9), 909-912.
16. Dawson, J. W. & Sen, A. (2007). “New Evidence on the Convergence of İnternational İncome from a Group of 29 Countries.” Empirical Economics, 33, 199–230. de Mello, L., & Perrelli, R. (2003). “Growth Equations: A Quantile Regression Exploration.” The Quarterly Review of Economics and Finance, 43(4), 643–667.
17. Dickey, D. A., & Fuller, W. A. (1979), “Distribution of the Estimators for Autoregressive Time Series with a Unit Root.” Journal of the American Statistical Association, 74(366a), 427-431.
18. Durlauf, S. N. (2003). The Convergence Hypothesis after 10 Years. Social Systems Research Institute, University of Wisconsin.
19. Erdal, L., & Turan, T. (2012). “Türkiye’de Makroekonomik Dengesizliklerin Büyüme Üzerindeki etkisi.” Anadolu Üniversitesi Sosyal Bilimler Dergisi, 12(2), 11–30.
20. Eryer, A. (2023). “Yakınsama Hipotezinin Test Edilmesi: E7 Ülkelerinden Ampirik Kanıtlar.” Mehmet Akif Ersoy Üniversitesi Uygulamalı Bilimler Dergisi, 7(2), 245-255.
21. Evans, P., & Karras, G. (1996). “Convergence Revisited.” Journal of Monetary Economics, 37(2), 249-265.
22. Fleissig, A., & Strauss, J. (2001). “Panel Unit‐Root Tests of OECD Stochastic Convergence.” Review of International Economics, 9(1), 153-162.
23. Friedman, M. (1992). “Do Old Fallacies Ever Die?” Journal of Economic Literature, 30, 2129–32.
24. Furuoka, F. (2018). “Income Convergence in the ASEAN-5 Countries.” International Journal of Business and Society, 19(3), 554-569.
25. Ghosh, M., (2013). “Regional Economic Growth and İnequality. In Liberalization, Growth and Regional Disparities in India.” India Studies in Business and Economics series, 17–45, Springer India.
26. Gylfason, T. (2001). “Natural Resources, Education, And Economic Development.” European Economic Review, 45(4–6), 847–859.
27. Hawksworth, J., Cookson, G. (2006). "The World in 2050”. PricewaterhouseCoopers.
28. Holmes, M. J. (2002). “Convergence in İnternational Output: Evidence from Panel Data Unit Root Tests.” Journal of Economic Integration, 826-838.
29. Im, K. S. (1996). Least Square Approach to Non-Normal Disturbances (No. 9603). Faculty of Economics, University of Cambridge.
30. Im, K. S., Pesaran, M. H., & Shin, Y. (2003). “Testing for Unit Roots in Heterogeneous Panels.” Journal of Econometrics, 115(1), 53-74.
31. Im, K. S., & Schmidt, P. (2008). “More Efficient Estimation Under Non-Normality When Higher Moments Do Not Depend on The Regressors, Using Residual Augmented Least Squares.” Journal of Econometrics, 144(1), 219-233.
32. Im, K. S., Lee, J., & Tieslau, M. A. (2014). “More Powerful Unit Root Tests with Non-Normal Errors.” In Festschrift in Honor of Peter Schmidt (pp. 315-342). Springer, New York, NY.
33. Islam, N. (1995). “Growth Empirics: A Panel Data Approach.” The Quarterly Journal of Economics, 110(4), 1127–1170.
34. Ivanovski, K., Awaworyi Churchill, S., & Inekwe, J. (2020). “Convergence in Income Inequality across Australian States and Territories.” Social Indicators Research, 148(1), 127-142.
35. Konat, G., Gökçe, M., & Kızılkaya, F. (2019). “AB Ülkelerinin Yakınsaması: SURADF VE SURKSS Birim Kök Testi.” EKOIST Journal of Econometrics and Statistics, (31), 63-75.
36. Lee, J., & Strazicich, M. C. (2003), “Minimum Lagrange Multiplier Unit Root Test with Two Structural Breaks.” Review of Economics and Statistics, 85(4), 1082-1089.
37. Lee, J., & Strazicich, M. C. (2004), Minimum LM Unit Root Test with One Structural Break. Manuscript, Department of Economics, Appalachian State University, 33(4), 2483-2492.
38. Lee, H., & Hur, M. (2021). “Non-normal Errors or Nonlinearity? Performance of Unit Root Tests.” Applied Economics, 53(52), 6094-6103.
39. Lee, H., Meng, M., & Lee, J. (2011). “How Do Nonlinear Unit Root Tests Perform with Non Normal Errors?.” Communications in Statistics-Simulation and Computation, 40(8), 1182-1191.
40. Lima, M. A., & Resende, M. (2007). “Convergence of Per Capita GDP in Brazil: An Empirical Note”. Applied Economics Letters, 14(5), 333-335.
41. Li, Q., & Papell, D. H. (1999). “Convergence of İnternational Output: Time Series Evidence for 16 OECD Countries.” International Review of Economics and Finance, 83, 267–280.
42. Lin, P. C., & Huang, H. C. (2012). “Convergence in İncome İnequality? Evidence from Panel Unit Root Tests with Structural Breaks.” Empirical Economics, 43, 153-174.
43. Maddala, G. S., & Wu, S. (1999). “A Comparative Study of Unit Root Tests with Panel Data and a New Simple Test.” Oxford Bulletin of Economics and Statistics, 61(S1), 631-652.
44. Mankiw, N. G., Romer, D., & Weil, D. N. (1992). “A contribution to the empirics of economic growth”. Quarterly Journal of Economics, 107(2), 407–437.
45. Mello, M. (2011). “Stochastic Convergence across U.S. States.” Macroeconomic Dy-namics, 15:160–183
46. Meng, M. (2013). Three Essays on More Powerful Unit Root Tests with Non-Normal Errors. The University of Alabama.
47. Meng, M., Im, K. S., Lee, J., & Tieslau, M. A. (2014). “More Powerful LM Unit Root Tests with Non-Normal Errors.” In Festschrift in honor of peter schmidt (pp. 343-357). Springer, New York, NY.
48. Meng, M., Lee, J., & Payne, J. E. (2016). “RALS-LM Unit Root Test with Trend Breaks and Non-Normal Errors: Application to the Prebisch-Singer Hypothesis”. Studies in Nonlinear Dynamics & Econometrics, 21(1), 31-45.
49. Narayan, P. K., & Popp, S. (2013). “Size and Power Properties of Structural Break Unit Root Tests.” Applied Economics, 45(6), 721-728.
50. Perron, P. (1997), “Further Evidence on Breaking Trend Functions in Macroeconomic Variables.” Journal of Econometrics, 80(2), 355-385.
51. Prodan, R. (2008), “Potential Pitfalls in Determining Multiple Structural Changes with an Application to Purchasing Power Parity.” Journal of Business & Economic Statistics, 26(1), 50-65.
52. Rodrik, D., & Subramanian, A. (2005). “From “Hindu Growth” to Productivity Surge: The Mystery of the Indian Growth Transition.” IMF Staff Papers, 52(2), 193–228.
53. Sala-i-Martin, X. X. (1996). “The Classical Approach to Convergence Analysis.” The Economic Journal, 106(437), 1019-1036.
54. Savacı, S., & Karşıyakalı, B. (2016). “Ülkeler Arası Gelir Yakınsaması Analizi: AB Ülkeleri ve Türkiye.” Akdeniz İİBF Dergisi, 16(33), 237-257.
55. Schmidt, P., & Phillips, P. C. (1992). “LM Tests for a Unit Root in the Presence of Deterministic Trends.” Oxford Bulletin of Economics and Statistics, 54(3), 257-287.
56. Sollis, R. (2009), “A Simple Unit Root Test Against Asymmetric STAR Nonlinearity with an Application to Real Exchange Rates in Nordic Countries.” Economic Modelling, 26(1), 118-125.
57. Solow, R. M. (1956). “A Contribution to the Theory of Economic Growth.” The Quarterly Journal of Economics, 70(1), 65–94.
58. Strazicich, M. C., Lee, J., & Day, E. (2004). “Are Incomes Converging among OECD Countries? Time Series Evidence with Two Structural Breaks.” Journal of Macroeconomics, 26(1), 131-145.
59. Swan, T. W. (1956).” Economic Growth and Capital Accumulation.” Economic Record, 32(2), 334–361.
60. Tıraşoğlu, M. (2013). “G20 Ülkeleri İçin Gelir Yakınsama Analizinin Panel Birim Kök Testleri İle İncelenmesi.” Yalova Sosyal Bilimler Dergisi, 3(6), 91-106.
61. Tong, T., Ortiz, J., Xu, C., & Li, F. (2020). “Economic Growth, Energy Consumption, and Carbon Dioxide Emissions in The E7 Countries: A Bootstrap ARDL Bound Test.” Energy, Sustainability and Society, 10(1), 1-17.
62. Tsionas, E. G. (2003). “Convergence Clubs and Spatial Externalities: A Bayesian Examination.” Studies in Nonlinear Dynamics & Econometrics, 7(3), 49-69.
63. World Bank. (2023). World Development Indicators. The World Bank. https://databank.worldbank.org/source/world-development-indicators
64. Yılancı, V., & Gökçe, E. C. (2020). “OECD Ülkelerinde Yakınsama Hipotezinin Geçerliliği: Kalıntılarla Genişletilmiş Panel Fourier SURADF Birim Kök Testi.” Sosyoekonomi, 28(44), 395-407.
65. Yilanci, V., Saridogan, E., & Artar, O. (2014). “A Stochastic Convergence Analysis for Selected East Asian and Pacific Countries: A Fourier Unit Root Test Approach.” Theoretical and Applied Economics, 18(598), 51-62.
66. Zhang, J., & Zhang, J. (2017). “Dual-track Reform and Transition: China’s Experience.” China Economic Journal, 10(2), 83–98.