Crimes Against Campbell-Shiller -- by Itzhak Ben-David, Alex Chinco

The Campbell and Shiller (1988) log-linear approximation is widely viewed as a model-free accounting identity that always holds: in sample, in expectation, and under arbitrary subjective beliefs. None of these claims is true. The formula is far from automatic even in realized data. Many companies do not pay dividends, making the calculation ill-defined. For dividend payers, the results are not always what they seem. The formula registers buybacks and new issuance as phantom cash-flow shocks. Taking expectations comes with its own complications. Researchers see the forward-looking version of Campbell-Shiller as a dynamic Gordon model, but this interpretation requires investors to consistently think in present-value terms and to know the cap rate with basis-point precision. Both are strong assumptions that do not always hold in the data. Finally, the formula generically fails under arbitrary subjective beliefs. The exceptions represent knife-edge cases where forecast errors obey a precise adding-up condition. Insisting that Campbell-Shiller always holds makes it harder to learn about the true pricing model in the many cases where it does not.