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This paper uses a vector autoregressive model to decompose excess stock and 10-year bond returns into changes in expectations of future stock dividends, inflation, short-term real interest rates, and excess stock and bond returns. In monthly postwar U.S. data, stock and bond returns are driven largely by news about future excess stock returns and inflation, respectively. Real interest rates have little impact on returns, although they do affect the short-term nominal interest rate and the slope of the term structure. These findings help to explain the low correlation between excess stock and bond returns.
Campbell et al. (Mon,) studied this question.