That Is Not My Dog : Why Doesn't the Log Dividend-Price Ratio Seem to Predict Future Log Returns or Log Dividend Growths?

Campbell and Shiller’s “accounting identity” implies that the log dividend-price ratio (LDPR) predicts either returns or dividend growths, but neither is significantly predictable, a well-known puzzle. Existence of the long-term mean LDPR is an important assumption behind the accounting identity, but it appears that the LDPR is declining over time and therefore the long-term mean does not exist. However, the identity works well in our sample. The dividend growths (but not returns) are predictable in longer samples, but results vary by subsample. We conclude that the puzzle comes from lack of power: The first-order characteristic of stock returns is noise