This paper develops and estimates a habit persistence consumption asset pricing model in which the sign of the equilibrium covariance between equity and bond returns depends on the reduced-form correlation between inflation and the output gap, the correlation between the federal funds rate and the output gap, as well as the equilibrium persistence of inflation.
CPV document in U.S. data, for a sample spanning 1979:Q3 to 2011:Q4, that (1) the correlation between inflation and the output gap changed sign from negative to positive; that (2) the correlation between the federal funds rate and the output gap changed sign, also from negative to positive; and that (3) the evidence of the sign change becomes statistically significant beginning in the late 1990s.