Dit – Dit-1 = ai + ci (D*it – Dit-1) + εit (1)
where Dt and Dt-1 are dividend payments at times t and t-1, D*it = riEit and r is the target payout ratio, and Et is the current year net profits. Thus, D*it are the current firm’s dividend payout if the firms dividend policy were based only on the target payout ratio ri as a fraction of net profits. The coefficient ci is a percentage representing the difference between the target dividend, D*it, and the dividend payout that occurred in the previous year: the coefficient shows the increase or decrease in dividend payout from the previous year, and Lintner called it the speed-of-adjustment factor. The constant ai has generally a positive value, implying that firms often find preferable to increase than to decrease dividends, and εit is an error term. Fama and Babiak (1968) applied the partial adjustment model of Lintner to a dataset of individual firms, while the previous work employed aggregate data. …show more content…
In their formulation, for a firm i in period t, they substitute D*it = riEit in (1): Dit – Dit-1 = ai + ci riEit – ci Dit-1 + εit (2) generating, Dit – Dit-1 = αi + λiDit-1 + βiEit + εit (3) where αi = ai, λi = – ci, and βi = ci ri. Thus, the model implies that firms have a target payout that is a fraction βi of their profits. Any difference between last period’s dividends and this target is reduced by a fraction, λi, each period. In this context, we refer to β as the target payout ratio and λ as the speed of adjustment or SOA. This latter parameter corresponds to the response of firms’ dividend policies to transitory earnings shocks. Large values for the SOA suggest an erratic dividend policy characterized by large changes driven by transitory shocks. Conversely, small values for the SOA suggest a smooth, persistent dividend policy characterized by insensitivity to earnings shocks and a desire to smooth the shock over many periods. Thus, the equation (3) measures dividend payout policy in terms of two parameters: the speed of adjustment coefficient (SOA), and the target payout ratio. The SOA shows how fast a firm adjusts its dividends to its target dividend: a high SOA means a low level of dividend smoothing, while a low SOA represents a high level of dividend smoothing by the firms under study. Fama and Babiak (1968) proposed a new model derived from that introduced by Lintner, and demonstrated that they could obtain more precise results. Their most successful models are: Dit – Dit-1 = λiDit-1 + βiEit + εit (4) Dit – Dit-1 = αi + λiDit-1 + β1iEit + β2iEit-1 + εit (5) Dit – Dit-1 = λiDit-1 + β1iEit + β2iEit-1 + εit (6) While equation (3) is directly used in Lintner’s paper, equations (4), (5), and (6) are those later introduced by Fama and Babiak. Equation (4) drops the intercept from equation (3), and equation (5) adds a new variable, β2iEi(t-1), for lagged earnings, in Lintner’s model, and equation (6), similarly to equation (4), goes further by dropping the intercept. Linter (1956) argued that the constant αi would be equal to zero for some firms in the sample, but it would usually have a positive signal, explicitly showing the managers reluctance to …show more content…
As in the general Lintner’s model, the lower the SOA, the higher the level of dividend smoothing in the sample. A high SOA would indicate that firms in the sample under study have a low level of smoothing. Leary and Michaely concluded that the Lintner’s model, as in equation (3), or models directly derived from that one, as those developed by Fama and Babiak (1968), are not accurately reflecting modern firms’ dividend payout policies. As a consequence, the SOA must be redesigned so that it can reflect more precisely firms’ payout