The Marsh-Merton Model of Managers' Smoothing of Dividends - Shiller, Robert J. (American Economic Review, 2016)
The fact that firms seem to follow an earnings payout policy that results in a dividend stream has often been brought up in criticism of the variance inequality tests that I used (1981a) to call into question the simple efficient markets model. It seems that the smoothing lowers the variance of detrended real dividends, and this may account for the apparent inadequacy of dividends movements to account for price movements. The fact that the present value of actual dividends p* is itself a moving average of dividends d, and hence a smoothed version of dividends, is also brought up in criticism of the inequality that involves p*. However, dividend smoothing or the smoothing implicit in p* does not pose any problems for the theoretical volatility inequalities. As long as (real detrended) price p is the present value of expected (real detrended) dividends d, then the dividends, whether they are smoothed or not, must move enough according to the measures in the inequalities if the price movements are to be justified. Terry Marsh and Robert Merton (1986) use arguments relying on the above-noted smoothing relations to show a sense in which, for sample variances, the variance inequalities in my paper may be thought of as reversed. Marsh and Merton model the behavior of those decision makers who set the level of dividends; the model (13) in their paper is a dividend smoothing model. Moreover, the proof of their Theorem 2 also makes use of the smoothing implicit in p*. However, the feature of the model that causes the variance inequalities to be invalidated is not the smoothing per se, but the nonstationarity in dividends that is induced by the particular dividend smoothing rule (13). Substituting their equation (13) into their equation (2) and then into their equation (1), we find