We study in detail the log-linear return approximation introduced by Campbell
and Shiller (1988a). First, we derive an upper bound for the mean approximation
error, given stationarity of the log dividend-price ratio. Next, we simulate various
rational bubbles which have explosive conditional expectation, and we investigate
the magnitude of the approximation error in those cases. We …nd that surprisingly
the Campbell-Shiller approximation is very accurate even in the presence of large
explosive bubbles. Only in very large samples do we …nd evidence that bubbles
generate large approximation errors. Finally, we show that a bubble model in which
expected returns are constant can explain the predictability of stock returns from
the dividend-price ratio that many previous studies have documented.