Inflation illusion or no illusion: what did pre- and post-war data say?

Campbell and Vuolteenaho (CV, 2004) empirically decompose the S&P 500's dividend yield from 1927 to 2002 to derive a measure of residual mispricing attributed to inflation illusion. They argue that the strong positive correlation between the mispricing component and inflation is strong evidence for the inflation illusion hypothesis. We find evidence for structural instability in their prediction equation for the excess return. We apply the same decomposition approach to the data before and after 1952, and find that the correlation between inflation and the mispricing component is close to zero in the post-war period, when inflation and the dividend yield are strongly positively correlated. The post-war data do not support the inflation illusion hypothesis as the explanation for the positive correlation between inflation and dividend yields.