US inflation and interest rates fail KPSS and ADF tests but macroeconomists still use them (in levels) in VAR and DSGE models. Why? Some papers have used 'economic stationarity' and/or 'theoretical stationarity' to justify their use, but that is subjective, yeah?
Dear Emmanuel. I understand you are against using those variables as I(1) inside a VAR model, for instance. One can argue that those variables are I(0) from a simple plot and also by considering the problems behind the theoretical assumptions of the KPSS & ADF tests (and many more related tests). An important assumption behind those tests is the absense of covariates, which leads to the possibility of considering KPSS-like and ADF-like tests inside multivariate models, VAR models, say.
In fact, there exists an important branch of the Granger-causality-test literature that advises to follow Toda-Yamamoto (1995)'s procedure before testing for Granger Causality.
Besides these inference-related issues, Hsiao (2006) says that "nonstationarity does not invalid the classical concerns of structural equation modeling - identification and simultaneity bias. The same rank condition for identification holds for stationary and nonstationary data ..."
BUT then the key problem arises: the consistency of the VAR model's parameter estimates. Using a I(1) variable inside a VAR is not a problem: the real problem is how to estimate such a VAR model. Hsiao (2006) advises to use IV methods, but this is not the only way... As a conclusion, one can ask you, Emmanuel, about the specific estimation procedures followed in those papers you have read.
Useful references:
+Hsiao, Cheng (2006) Cowles commission structural equation approach in light of nonstationary time series analysis, IMS Lecture Notes-Monograph Series on Time Series and Related Topics 52, 173-192.
+Toda, H.Y. & P.C.B. Phillips (1991) Vector Autoregression and Causality: A Theoretical Overview and simulation Study, The University of Western Australia Working Pager No. 91-07 & Cowles Foundation Discussion Paper, Yale University.
+Toda, H.Y. & P.C.B. Phillips (1993) The spurious effect of unit roots on vector autoregressions, Journal of Econometrics 59, 229-255.
+Toda, H.Y. & P.C.B. Phillips (1993) Vector Autoregressions and Causality, Econometrica 61, 1367-1393.
+Toda, H.Y. & T. Yamamoto (1995) Statistical inference in vector autoregressions with possibly integrated processes, Journal of Econometrics 66, 225-250.
Despite failing KPSS and ADF tests, macroeconomists use US inflation and interest rates in levels in VAR and DSGE models because they capture important economic relationships and dynamics that are relevant for understanding monetary policy, inflation dynamics, and the overall functioning of the economy.
