Abstract
It is argued if xt ~ I(1) and yt ~ I(1), then running a regression xt on yt would produce spurious results because e t would generally be I(1). However, there may exist a ‘b’ such that e t = x t - by t is I(0), then running a regression x t on y t would not produce spurious results. This special case of two integrated time series is known in the literature as cointegration. In this particular case, x t and y t are said to be cointegrated. In our review of the development of the concept of cointegration, we identified that the underlying reason for this special case to arise is the proposition that if x t ~ I(d x ), y t ~ I(d y ), then z t = bx t + cy t ~ I(max(d x ,d y )). In this research, we offer evidence against this proposition.
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Notes
The knowledge that in response to the financial and economic crisis of 2007–2009, economists are open for re-evaluating alternative approaches to neoclassical paradigm gave us an additional strength to carry out this research (Neck 2014).
See Temin (2013) for an eloquent description of how or why economic history vanished both from the faculty and the graduate program at Massachusetts Institute of Technology (MIT), and subsequently its cost consequences to current economic education and overall societal scholarship.
Data files are available from the corresponding author upon request.
The anomalies that arise from the use of panel unit root tests are taken up separately.
According to the Bureau of Labor Statistics (BLS), which reports labor force statistics at the state level as well as at the federal level for the United States, labor force is the sum of employed and unemployed. It follows that the first difference of labor force is literally equal to the sum of the first difference of number of people employed and the first difference of number of people unemployed.
References
Cuthbertson, K., Hall, S. G., & Taylor, M. P. (1992). Applied econometric techniques. London: Philip Allan.
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.
Dickey, D. A., & Fuller, W. A. (1981). Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica, 49(4), 1057–1072.
Elder, J., & Kennedy, P. E. (2001). Testing for unit roots: what should students be taught? Journal of Economic Education, 32(2), 137–146.
Elliott, G., Rothenberg, T. J., & Stock, J. H. (1996). Efficient tests for an autoregressive unit root. Econometrica, 64(4), 813–836.
Engle, R. F., & Granger, C. W. J. (1987). Co-integration and error correction: representation, estimation, and testing. Econometrica, 55(2), 251–276.
Fuller, W. A. (1976). Introduction to statistical time series. New York: Wiley.
Granger, C. W. J. (1981). Some properties of time series data and their use in econometric model specification. Journal of Econometrics, 16(1), 121–130.
Granger, C. W. J. (1986). Developments in the study of cointegrated economic variables. Oxford Bulletin of Economics and Statistics, 48(3), 213–228.
Granger, C. W. J., & Newbold, P. (1974). Spurious regressions in econometrics. Journal of Econometrics, 2(2), 111–120.
Hamilton, J. D. (1994). Time series analysis. Princeton: Princeton University Press.
Harris, R. I. D. (1992). Testing for unit roots using the augmented Dickey-Fuller test: some issues relating to the size, power and lag structure of the test. Economics Letters, 38(4), 381–386.
Hendry, D. F. (1980). Econometrics – alchemy or science? Economica, 47(188), 387–406.
Hendry, D. F. (1986). Econometric modelling with cointegrated variables: an overview. Oxford Bulletin of Economics and Statistics, 48(3), 201–212.
Kennedy, P. E. (2003). A guide to econometrics. Cambridge: MIT Press.
Luitel, H., & Mahar, G. (2015a). A short note on the application of Chow test of structural break in US GDP. International Business Research, 8(10), 112–116.
Luitel, H., and Mahar, G. (2015b). Why most published results on unit root and cointegration are false. Ethical Economic Support Occasional Newsletter of the Association for Integrity and Responsible Leadership in Economics and Associated Professions, December 22, 2015.
Luitel, H., and Mahar, G. (2016). Testing for unit roots in autoregressive-moving average of unknown order: critical comments. In Mimeo, Algoma University, February 2016.
Moosa, I. (2011). The failure of financial econometrics: assessing the cointegration “revolution”. The Capco Institute Journal of Financial Transformation, Applied Finance # 32.
Neck, R. (2014). Austrian economics today. Atlantic Economic Journal, 42(2), 121–122.
Nelson, C. R., & Plosser, C. R. (1982). Trends and random walks in macroeconomic time series. Journal of Monetary Economics, 10(2), 139–162.
Phillips, P. C. B. (1987). Time series regression with a unit root. Econometrica, 55(2), 277–301.
Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75(2), 335–346.
Royal Swedish Academy of Science (2003). Time-series econometrics: cointegration and autoregressive conditional heteroskedasticity. Advanced information on the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel 8 October 2003.
Said, S. E., & Dickey, D. A. (1984). Testing for unit roots in autoregressive-moving average of unknown order. Biometrika, 71(3), 599–607.
Schwert, G. W. (1989). Tests for unit roots: a monte carlo investigation. Journal of Business and Economic Statistics, 7(2), 147–159.
Taylor, A. M. R. (2000). The finite sample effects of deterministic variables on conventional methods of lag-selection in unit root tests. Oxford Bulletin of Economics and Statistics, 62(2), 293–304.
Temin, P. (2013). The rise and fall of economic history at MIT. Massachusetts Institute of Technology, Department of Economics, Working Paper Series, Working Paper 13–11, June 5, 2013.
Acknowledgments
The research was presented at the 85th Annual Meetings of the Southern Economic Association, November 21-23, 2015, New Orleans, USA and the 49th conference of the Canadian Economics Association during Thursday, May 28, 2015 - Sunday, May 31, 2015, in Toronto, Canada. We thank Afshin Amiraslany, Murshed Chowdhury, Brandon Mackinnon, Mariana Saenz and session participants in the above conferences for their helpful comments and suggestions. We also thank three anonymous referees for their comments and suggestions.
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Luitel, H.S., Mahar, G.J. Algebra of Integrated Time Series: Evidence from Unit Root Analysis. Int Adv Econ Res 22, 199–209 (2016). https://doi.org/10.1007/s11294-016-9577-9
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DOI: https://doi.org/10.1007/s11294-016-9577-9