For theoretical and statistical reasons, it is important to decompose some series into dual components in order to understand their permanent and temporary movements as well as their dual co-movements. This study, therefore, aims to introduce the dual adjustment approach for the nonstationary macroeconomic variables. In line with this aim, the concept of common Hodrick-Prescott (HP) trend and a simple test for the existence of such relationship (Common HP trending) are also provided. The dual adjustment approach provides an alternative to the cointegration analysis for some cases, e.g., consumption function, by relaxing the implicit assumption of the singular adjustment in cointegration analysis. Our empirical results indicate that while personal consumption expenditure and disposable income are not cointegrated in the US over the period 1929e2017, these variables have a common HP trend. Additionally, it is shown that there is some evidence of dual adjustment in the behavior of US aggregate consumption.
Ash, J.C.K., Easaw, J.Z., Heravi, S.M., Smyth, D.J., 2002. Are hodrick-prescott ‘forecasts’ rational? Empir. Econ. 27, 631e643.
Balke, N.S., Fomby, T.B., 1997. Threshold cointegration. Int. Econ. Rev. 38, 627e645.
Baltagi, B.H., 2008. Econometrics, fourth ed. Springer, New York.
Baxter, M., King, R.G., 1999. Measuring business cycles: approximate band-pass filters for economic time series. Rev. Econ. Stat. 81 (4), 575e593.
Berenguer-Rico, V., Gonzalo, J., 2014. Summability of stochastic processes: a generalization of integration for non-linear processes. J. Econom. 178, 331e341.
Beveridge, S., Nelson, C.R., 1981. A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of business cycle. J. Monetary Econ. 7, 151e174.
Bierens, J.H., 2000. Nonparametric nonlinear cotrending analysis, with an application to interest and inflation in the United States. J. Bus. Econ. Stat. 18, 323e337.
Campbell, J.Y., Mankiw, N.G., 1989. Consumption, income, and interest rates: reinterpreting the time series evidence. In: Blanchard, O.J., Fischer, S. (Eds.), NBER Macroeconomics Annual. The MIT Press, Cambridge, MA, pp. 185e216.
Centoni, M., Cubadda, G., 2011. Modeling comovements of economic time series: a selective survey. Statistica 71, 267e294.
Chapman, D.A., Ogaki, M., 1993. Cotrending and the stationarity of the real interest rate. Econ. Lett. 42, 133e138.
De Jong, R.M., Sakarya, N., 2016. The econometrics of the Hodrick-Prescott filter. Rev. Econ. Stat. 98, 310e317.
Dornbusch, R., Fischer, S., Startz, R., 2012. Macroeconomics, eleventh ed. McGrawHill.
Du Toit, L., 2008. Optimal HP Filtering for South Africa. Stellenbosch Economic Working Papers. Department of Economics. Stellenbosch University.
Enders, W., 2015. Applied Econometric Time Series, fourth ed. Wiley.
Enders, W., Siklos, P.L., 2001. Cointegration and threshold adjustment. J. Bus. Econ. Stat. 19, 166e176.
Engle, R.F., Granger, C.W.J., 1987. Cointegration and error correction: representation, estimation and testing. Econometrica 55, 251e276.
Engle, R.F., Kozicki, S., 1993. Testing for common features. J. Bus. Econ. Stat. 11, 369e380.
Flavin, Ma, 1993. The excess smoothness of consumption: identification and interpretation. Rev. Econ. Stud. 60, 651e666.
Friedman, M., 1957. A Theory of the Consumption Function. Princeton University Press, Princeton.
Granger, C.W.J., 1993. What we are learning about the long run? Econ. J. 103, 307e317.
Granger, C.W.J., 2004. Empirical Modeling in Economics: Specification and Evaluation. Cambridge University Press, Cambridge.
Granger, C.W.J., Lee, T.-H., 1989. Multicointegration. Adv. Econom. 8, 71e84. Granger, C.W.J., Ter€ asvirta, T., Patton, A.J., 2006. Common factors in conditional distributions for bivariate time series. J. Econom. 132, 43e57.
Grant, A.P., Thomas, L.B., 1999. Inflationary expectations and rationality revisited. Econ. Lett. 62, 331e338.
Gonzalo, J., Granger, C.W.J., 1995. Estimation of common long-memory components in cointegrated systems. J. Bus. Econ. Stat. 13, 27e35.
Haldrup, N., Kruse, R., Terasvirta, T., Varneskov, R.T., 2013. Unit roots, nonlinearities € and structural breaks. In: Hashimzade, N., Thornton, M.A. (Eds.), Handbook of Research Methods and Applications in Empirical Macroeconomics. Edward Elgar, Cheltenham, UK, pp. 61e94.
Hansen, B.E., 1995. Rethinking the univariate approach to unit root testing: using covariates to increase power. Econom. Theor. 11, 1148e1171.
Hodrick, R.J., Prescott, E.C., 1980. Postwar US Business Cycles: an Empirical Investigation. Carnegie Mellon University Discussion Paper, p. 451.
Hodrick, R.J., Prescott, E.C., 1997. Postwar business cycles: an empirical investigation. J. Money Credit Bank. 29, 1e16.
Harris, R., Sollis, R., 2003. Applied Time Series Modelling and Forecasting. Wiley, Chichester.
Ismihan, M., 2016a. A useful framework for linking labor and goods markets: Okun's law and its stability revisited. Rev. Keynes. Econ. 4, 175e192.
Ismihan, M., 2016b. Trend-Tar Models. Unpublished Paper.
Ismihan, M., Küçüker, M.C., 2017. _ Ikili uyarlanma yaklas¸ ımı: Türkiye için yatırım fonksiyonu uygulaması [The dual adjustment approach with an application to the investment function for Turkey] (in Turkish). Presented in the National Economics Symposium XIX, Organized by Turkish Economic Association (TEA), Girne, North Cyprus, November 3-4, 2017.
Kozicki, S., 1999. Multivariate detrending under common trend restrictions: implications for business cycle research. J. Econ. Dynam. Contr. 23, 997e1028.
Kydland, F.E., Prescott, E.C., 1990. Business Cycles: Real Facts and a Monetary Myth. Federal Reserve Bank of Minneapolis Quarterly Review. Spring, pp. 3e18.
Maddala, G.S., Kim, I.-M., 1998. Unit Roots, Cointegration and Structural Change. Cambridge University Press, Cambridge.
Mankiw, N.G., 2013. Macroeconomics, eighth ed. Worth Publishers, New York.
MacKinnon, J.G., 1991. Critical values for cointegration tests. In: Engle, R.F., Granger, C.W.J. (Eds.), Long-Run Economic Relationships: Readings in Cointegration. Oxford University Press, Oxford, pp. 267e276.
Mills, T.C., 2003. Modeling Trends and Cycles in Economic Time Series. Palgrave Macmillan, New York.
Morley, J., 2009. Non-linear time series in macroeconomics. In: Meyers, R.A. (Ed.), Encyclopedia of Complexity and Systems Science. Springer, pp. 5325e5348.
Neftci, S.N., 1984. Are economic time series asymmetric over the business cycle? J. Polit. Econ. 92, 307e328.
Nelson, C.R., Plosser, C.I., 1982. Trends and random walks in macroeconomic time series: some evidence and implications. J. Monetary Econ. 10, 139e162.
Pedersen, T.M., 2001. The Hodrick-Prescott filter, the Slutzky effect, and the distortionary effect of filters. J. Econ. Dynam. Contr. 25, 1081e1101.
Phillips, P.C.B., 2003. Laws and limits of econometrics. Econ. J. 113, C26eC52.
Phillips, P.C.B., Jin, S., 2015. Business Cycles, Trend Elimination, and the Hp Filter. Cowles Discussion Paper No. 2005. Yale University.
Ravn, M.O., Uhlig, H., 2002. On adjusting the Hodrick-Prescott Filter for the frequency of observations. Rev. Econ. Stat. 84, 371e375.
Stock, J.H., 1988. A reexamination of Friedman's consumption puzzle. J. Bus. Econ. Stat. 6, 401e409.
Stock, J.H., Watson, M.W., 1988. Testing for common trends. J. Am. Stat. Assoc. 83, 1097e1107.
Vahid, F., Engle, R.F., 1993. Common trends and common cycles. J. Appl. Econom. 8, 341e360.
White, H., Granger, C.W.J., 2011. Consideration of trends in time series. J. Time Econom. 3, 1e38.