This is another way to characterize the mismatch in the persistence properties of the EPRR and consumption growth.
In response, some researchers test for fractional integration (Granger, 1980; Granger and Joyeux, 1980; Hosking, 1981) in the EARR and EPRR.
EPRR and EARR do not contain a unit root per se but are mean-reverting and very persistent.
For example, a threshold model might permit the EPRR to be approximately a random walk within [+ or -] 2 percent of some long-run equilibrium value but to revert strongly to the [+ or -] 2 percent bands when it wanders outside the bands.
EPRR adjusts in a nonlinear fashion to a long-run equilibrium level using a logistic smooth transition autoregressive (LSTAR) model and monthly U.
The estimated ESTR model for 1960:Q1-1978:Q1 is not consistent with a stationary real EPRR for any inflation rate, and the estimated LSTR model for 1979:Q1-2004:Q4 is consistent with a stationary EPRR only when the inflation rate moves above approximately 3 percent.
In summary, recently developed econometric procedures provide some evidence of threshold behavior or nonlinear cointegration in the EPRR in certain industrialized countries.
The filtered probability estimates show that the EPRR was likely in the middle regime from 1961-73, the low regime from 1973-81, and the high regime from 1981-86.
The breaks correspond to a decrease in the mean EPRR in 1966/1967, a further decrease in 1972, and a sharp increase in 1980.
Rapach and Wohar (2005) extend the work of Caporale and Grier (2000) and Bai and Perron (2003) by applying the Bai and Perron (1998) methodology to the EPRR in 13 industrialized countries using tax-adjusted nominal long-term government bond yield and CPI inflation rate data for 1960-98.
Caporale and Grier (2005) find that political regime changes associated with changes in the party of the president or control of Congress do not affect the mean EPRR after controlling for inflation.
EPRR using quarterly long-term government bond yield and CPI inflation rate data for 1980-95, allowing for two breaks in the mean of the EPRR.