The Log-Linear Return Approximation, Bubbles, and Predictability
研究了Campbell-Shiller对数线性收益近似的误差上界，发现即使在爆炸性泡沫下近似仍很准确，并表明常数预期收益的泡沫模型可解释股息价格比对股票收益的可预测性。
Abstract 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 that have explosive conditional expectation, and we investigate the magnitude of the approximation error in those cases. We find that, surprisingly, the Campbell-Shiller approximation is very accurate even in the presence of large explosive bubbles. Only in very large samples do we find 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.