The adjustment of dividends to permanent earnings.

I. Introduction

A fundamental issue in corporate finance is whether dividend changes convey information about future earnings of the firm. There is an extensive literature in finance and accounting which discusses this issue.(1) However, these studies have yielded puzzling results. Studies using the event-study methodology and the cross-sectional regression approach have usually found a significant relationship between dividend changes and subsequent earnings. On the other hand, empirical studies on time-series regression by Watts [32] and Gonedes [8] have found that dividends convey little information about subsequent earnings.

Most of the previous studies have examined the relationship between dividends and reported earnings or the relationship between dividends and analyst earnings forecasts. However, as Nakamura and Nakamura [26] suggested, dividend changes may be related to the permanent earnings of the firm. If managers have superior information to investors on future earnings, they should be able to form more precise estimates of permanent earnings. Managers may then use dividends as an instrument to reflect their beliefs about the likely changes in permanent earnings. Thus, consistent with Lintner's [19] observations, an increase in current earnings which reverses in subsequent periods would typically not elicit a dividend change, whereas an increase in earnings that is expected to persist would lead to a dividend change.

The use of reported earnings figures, rather than permanent earnings, in the empirical examination may explain the puzzling results documented in previous dividend studies. If managers indeed determine dividends based on their forecasts of permanent earnings, empirical investigation using either reported earnings or short-run forecasts will be subject to a serious measurement error. This measurement problem could distort the empirical relationship in dividend-earnings studies.

In this paper, we propose a permanent earnings model to explain the corporate dividend behavior. The model is an extension of the previous partial adjustment models of dividends by Lintner [19], Brittain [4], Fama and Babiak [6], and Lee, Wu and Djarraya [18]. Specifically, we introduce a formation process of permanent earnings expectations similar to that suggested by Nakamura and Nakamura [26], into the dividend model.(2) Unlike Nakamura and Nakamura [26], our model permits a direct test of market rationality. Furthermore, we introduce a more general specification of earnings expectations. The type of expectations formation proposed here is consistent with the rational expectations hypothesis developed initially by Muth [25] and tested by Mishkin [23], Hoffman and Schmidt [12], Gregory and Veall [10] and Lovell [20]. Our specification of expectations formation represents an improvement over the past work by Waud [33]. (3)

Our empirical results have important implications for dividend models. Recently, rational signalling models proposed by Miller and Rock [22], and John and Williams [13] have been constructed to explain the information effect of dividends. These models show that dividends convey the manager's private information to the market and the market participants rationally revise their expectations for future earnings according to the dividend information released by the manager. However, there is to date no direct test performed at the corporate level on the rational expectations-permanent earnings hypothesis. Our main contribution is that we provide a direct joint test on both market rationality and the information contend of dividends.

The remainder of this paper is dividend into five sections. Section II provides a fairly general treatment of the dividend adjustment process with a rational expectations-permanent earnings specification. Section III provides a test of rationality. Section IV discusses the estimation procedure. Section V reports our major empirical results. Section VI compares our model with others in the literature. Finally, section VII summarizes the findings of this paper.

II. Rational Expectations, Permanent Earnings, and the Dividend Adjustment Process.

Consider the following partial adjustment model for dividends (1) [Mathematical Expression Omitted] where [Mathematical Expression Omitted] is the desired dividend payment in time t, [Lambda] is the speed of adjustment coefficient with 0 < [Lambda] < 1, and [[Mu].sub.t] is the error term. The partial adjustment model hypothesis that the firm only partially adjusts its past dividend to the target level [Mathematical Expression Omitted] in each period. The amount of adjustment depends of the value [Lambda] which is affected by a firm's investment opportunities, stock investors' preferences, marginal income tax rates, and transaction costs. The adjustment of dividends also reflects the confidence of the management in the prospect of future earnings. The constant term [Alpha] reflects the reluctance of managers to reduce dividends; a positive [Alpha] implies that managers desire to maintain a gradual growth in dividends.(4) The error term [[Mu].sub .t] is included in (1) to capture the implementation error and other noise.

Traditionally, the target dividend [Mathematical Expression Omitted] is linked to current earnings in the empirical investigation as in Lintner [19] and Watts [32]. It is commonly assumed that [Mathematical Expression Omitted] = [Upsilon] [Y.sub.t] where [Upsilon] is the target payout ration and [Y.sub.t] is current earnings. Given this relation, requation (1) can be rewritten as (2) [Mathematical Expression Omitted]

There are two problems with this simple partial adjustment model. First, the model implicitly assumes that dividends are related to current earnings. However, it is more likely that managers would determine [D.sub.t] based on the estimate of permanent earnings in time t. Second, the partial adjustment model assumes that the lagged earnings will not affect current dividends. This assumption is not appropriate. Empirical evidence by Fama and Babiak [6] has shown that the likelihood of raising the current dividend per share increases as firms have consecutive earnings increases. In Fama and Babiak's study, 65.8 percent of the firms in the sample increase dividends in the next period when there is a one-period earnings increase. The proportion of the firms raising dividends increases to 74.8 percent when firms have two consecutive earnings increases; to 80.7 percent when firms have three consecutive earnings increases. Despite these findings, the possible effects of lagged earnings on the current dividends have been ignored by many previous dividend studies using the partial adjustment model.(5) In the following, we propose an alternative model to resolve these two problems.

Lintner was one of the first to suggest that dividend changes are related to permanent earnings changes. Nakamura and Nakamura [26] and Marsh and Merton [21] provided some evidence to support this hypothesis. Healy and Palepu [11] also found that dividend initiations and omissions provide information to investors on earnings for several years subsequent to the dividend announcement. The results of these studies imply that managers have superior information to investors on future earnings. As such, managers will be able to form more precise estimates of permanent earnings. Managers would then increase dividends in response to an increase in permanent earnings.

Following Nakamura and Nakamura [26] we assume that the desired dividends, [Mathematical Expression Omitted], are related to the permanent earnings [Mathematical Expression Omitted], according to (3) [Mathematical Expression Omitted] where [Upsilon] is the long-run target payout ratio, and (4) [Mathematical Expression Omitted] where [E.sub.t] is the conditional expectations operator given the information set I(t) available to the manager in period t, i.e., [E.sub.t] ([Y.sub.t]) = [Mathematical Expression Omitted] for j = 1,2,. . . . As in Nakamura and Nakamura [26] we assume that I(t) includes [Y.sub.t] the current earnings, and the dividend decision is made after the current earnings is known to the manager. The definition of a permanent variable as in (4) has been adopted in the literature. For instance, Flavin [7] used a similar specification in a study of the relationship between consumption and permanent income. In [Mathematical Expression Omitted] represents the present value of all future discounted earnings expected by the manager and therefore, is the intrinsic value of the firm expected by the manager in time t. The firm's permanent earnings perceived by the manager are stated as the return on the expected intrinsic value of the firm in time t. The parameters b and a in (4) are the manager's discount factor and the rate of return on the intrinsic value of the firm, respectively.

Substituting (3) into (1) yields [Mathematical Expression Omitted] or (5) [Mathematical Expression Omitted]

The model in (5) is similar to that in Nakamura and Nakamura [26]. In order to complete the dividend adjustment model, it is necessary to process of earnings generation. Assume that earnings [Y.sub.t] follows an autoregressive (AR) process of order M < T is the number of the observations such that [Mathematical Expression Omitted] or (6) [Mathematical Expression Omitted] where [[Epsilon].sub.t]] is a white-noise, and [Beta](L) = 1 - [[Beta].sub.1]]L-,..., [Mathematical Expression Omitted]. If managers are rational, they will form expectations that are optimal forecasts of the future earnings conditions making use of all information available to them. Then from Sargent [31, 306] we can relate permanent earnings to current and past earnings as follows: (7) [Mathematical Expression Omitted] where [Beta](b) = 1 [[Beta].sub.1] b - [[Beta].sub.2] [b.sup.2], ... [Mathematical Expression Omitted] and [c.sub.i] is introduce to simplify the notation for the coefficients of [Y.sub.t-i-1].

Equations (6) and (7) express the stochastic process of [Mathematical Expression Omitted] as a function of the stochastic process of [Y.sub.t]. Notice that [Mathematical Expression Omitted] depends on [Y.sub.t], [Y.sub.t-1], ..., [Y.sub.-M+1] via the coefficients that partly reflect the stochastic process of (6) governing [Y.sub.t]. For example, if we set [Beta](L) = 1 [Mathematical Expression Omitted], then (6) and (7) become (8) [Mathematical Expression Omitted] (9) [Mathematical Expression Omitted]

Also, the sign of [c.sub.i], i = 1,2,3,4 could be either positive or negative depending on the value of the underlying parameters (a, b and [Beta]'s).(7)

Substituting (7) into (5) gives (10) [Mathematical Expression Omitted] where [[Mu].sub.t] is assumed to follow a fourth-order autoregressive process (11) [Mathematical Expression Omitted] with a white-noise [v.sub.t]. The fourth-order autoregressive process is usually successful in eliminating serial correlation from quarterly time series data. Assume that [Mathematical Expression Omitted] where [Mathematical Expression Omitted] If the dividend equation in (10) is a true reduced form, the covariance term, [Sigma], will be zero. Marsh and Merton [21] have suggested that the function of dividends with respect to permanent earnings is a true reduced form. Even if the dividend equation is not a reduced form, the restriction on the covariance term will not invalidate the test statistic since the model includes only a one-period-ahead earnings forecasts [23, 17]. Equations (6) and (10) can be estimated by the nonlinear weighted least squares (NWLS) described in Mishkin [23].

The system of equations (6) and (10) provides an empirical framework for examining the dividend adjustment process and for testing the validity of the rational expectations-permanent earnings hypothesis. In the following section, the test procedure is discussed.

III. Test for Rationality

The unconstrained version of (10) can be written as (12) [Mathematical Expression Omitted] where [Mathematical Expression Omitted] at [Mathematical Expression Omitted]. The rational hypothesis is valid if (6) and (12) satisfy the rationality constraints that [Mathematical Expression Omitted] for all i's (i = 1, ...,). The equality restrictions imposed for the rationality can be tested by the likelihood-ration (LR) test. The LR statistic is (13) [Mathematical Expression Omitted] which is distributed asymptotically as [Mathematical Expression Omitted], where q is the number of constraints, [L.sup.c] is the likelihood of the estimated constrained system of (6) and (10), and [L.sup.u] is the likelihood of the estimated unconstrained system where the constraints of [Mathematical Expression Omitted] for all i's are not imposed. Equation (12) can also be rewritten as (14) [Mathematical Expression Omitted] where [Mathematical Expression Omitted]. Note that the unconstrained system of (6) and (14) contains 2M + 6 parameters [Mathematical Expression Omitted] while the constrained system of (6) and (10) contains M + 9 paramaters [Mathematical Expression Omitted] so that there are M - 3 restrictions to be tested. That is q = M - 3.

If the nonlinear weighted least squares is used to estimate (6) and (10), the likelihood ratio statistic reduces to (15) [Mathematical Expression Omitted] where [SSR.sup.c] is the sum of the squared residuals from the constrained system, [SSR.sup.u] is the sum of squared residuals from the unconstrained system, and T is the number of observations. Note that [SSR.sub.c] and [SSR.sub.u] in (15) are based on the transformed version of the model which accounts for the autocorrelation in [[Mu].sub.t].(8) The rational expectations hypothesis is accepted if the LR statistic is less than the [Mathematical Expression Omitted] value. For a cross-sectional sample which includes many firms, acceptance of the rational expectations hypothesis requires that the majority of firms follow this type of expectations formation process. Thus, the hypothesis is supported if the sample median of [Mathematical Expression Omitted] statistics is below a critical value.

IV. Estimation Procedure

A nonlinear least squares method is used to estimate the system of equations (6) and (10). There are several reasons for conducting the estimation with the nonlinear least squares regression [28]. First, the full information maximum likelihood method is computationally cumbersome when there are a large number of paramaters to be estimated. Second, it is easier to impose the necessary restrictions for the covariance of error terms by using the nonlinear least squares regression. Third, the nonlinear least squares permits an easy correction of the degree-of-freedom problem for the small sample. The constrained and unconstrained systems of equations (6) and (10) have different degrees of freedom. This difference in the degree of freedom becomes a serious problem when the sample size is small. Therefore, a correction for the difference in the degrees of freedom is necessary for a more reliable test. The procedure for the correction of the degree of freedom will be discussed later. For these reasons, a NWLS method is used for the parameter estimation.

The estimation procedure is given as follows: First, the constrained system of (6) and (10) is estimated by setting the estimate of the covariance matrix, [Sigma] [Caret], equal to an identify matrix, I. Then, an initial estimate of the covariance [Sigma] of the residuals is obtained for the constrained system, where [Mathematical Expression Omitted] and [SSR.sub.6] and [SSR.sub.10] are the sum of squared residuals from the constrained system of (6) and (10) as explained in footnote 8. Second, the system of equations is estimated by the nonlinear weighted least squares based on the estimated covariance matrix and a new [Sigma] [Caret] is obtained from the resulting residuals. Third, the iteration procedure is continued until there is little change in the [Sigma] [Caret] matrix. The estimates from this iterating estimation procedure will converge to the maximum likelihood estimates as the number of iterations gets larger. An IMSL Fortran subroutine ZXMIN is used to compute the nonlinear weighted least squares.

For the unconstrained system, equation (14) is estimated separately by the nonlinear weighted least squares where the weighted is the same as the weighted used in the last iteration of the constrained system for equation (10). Equation (6) is estimated by the ordinary least squares (OLS). Note that equation (14) cannot be estimated by OLS because of autoregressive errors. The parameters in (14), [Mathematical Expression Omitted], are obtained by minimizing, [SSR.sub.14] in footnote 8. Since [SSR.sub.14] is nonlinear in the parameters, the nonlinear least squares should be employed for the estimation [14, 296]. The same weight as in the constrained system is used to correct the difference in the degree of freedom as indicated above. The LR statistic based on this correction will be more conservative in that it would be less likely to reject the null hypothesis. Details about this procedure can be found in Mishkin [23].

A problem associated with the use of the AR process in (6) is the determination of the appropriate order M. One naive strategy for choosing the order is to exclude the lagged earnings variables whose coefficients are not significantly different from zero. However, this strategy yields a very short order: one quarter for most cases in the sample of this study. In this paper, we set the order of lags to four quarters since previous studies [18; 23] have shown that in general four lag variables are sufficient for the forecasting purpose. We have checked the effect of this restriction and found that the impact of this imposition on earnings forecast appears to be minimal. We have compared the forecast ability of the autoregressive model with an order of four with that of an alternative model with an order of 28.(9) We found that for most of the sample firms the improvement in prediction is only marginal (less than three percent in most cases). This is because the the coefficients of earnings lagged for more than five periods are generally indistinguishable from zero. Thus, for practical purposes, the earnings process is appoximated well by the AR model with four lags. Another practical consideration is related to the structure of the dividend model. The definition of permanent earnings implies that within the reasonable range of a and b values, the effect of any earnings variables lagged for more than four periods on the estimation will be negligile. Shortening the order of lagged earnings greatly reduces the computational complexity and allow us to focus on testing rationality and dividend adjustment.(10)

V. Data and Empirical Results

Quarterly earnings and dividends were obtained from the COMPUTSAT tape over the 1965--1986 period. Earnings and dividends per share were adjusted for stock splits. Firms not paying dividends for more than three consecutive years were dropped.(11) The final data set includes 179 firms with no missing values for earnings and dividends during the study period.(12)

Table I summarizes the distribution of parameter estimates, Durbin-Watson (DW) statistics, and LR statistics. The median and mean of the LR statistics are equal to 3.966 and 4.390, respectively, and the standard error of the mean is 0.295. More than 75 percent of the firms do not reject the null hypothesis of rationally at the one percent significance level with one degree of freedom ([[Chi].sub.1, .01] =6.63). The dispersion of the LR statistics is measured by the interquartile range (upper quartile - lower quartile) which is 4.221, or measured by the standard deviation which is 2.618. The LR statistics in Table I suggests that most firms make use of the available information in generating their estimates of permanent earnings. For the majority of the firms, earnings forecasts follow a formation process consistent with the theory of rational expectations.

The coefficient estimates of the lagged earnings variables in the forecasting equation (8) are reported in columns one to four in Table I. Some lagged variables have negative coefficients. As expected, the effects of lagged earnings decline over time with the earnings in the past two periods dominating the effects on earnings forecasts. The cross-sectional distribution of average asymptotic t-statistics for [Beta] estimates are reported in columns 18 to 21. The median estimates of [[Beta].sub.1] and [[Beta].sub.2] for the lagged earnings are significant.

The median of [Lambda] estimates is 0.317 and the median t-statistic is 3.25. The mean of the estimated adjustment coefficient [Lambda] is 0.438 while its average t-statistic is 4.91. The results suggest that the dividend adjustment generally takes approximately three quarters to complete.

The median of the estimated target payout ratio, [Gamma], is 0.335 and the median t-statistic is 2.5. The mean of [Gamma] estimates is 0.356 and its average t-statistic is 38.1. The estimates of [Alpha] are not always positive. A positive [Alpha] suggests that a firm is more reluctant to reduce than to raise dividends. As shown in Table I, about 75 percent of the firms have a positive [Alpha]. However, only slightly less than 25 percent of [Alpha] estimates are significant. The mean (median) of [Alpha] is 0.005 (0.002) and its mean (median) t-statistics is 0.71 (0.92). The mean (median) of b estimates is 0.373 (0.315) while its mean (median) t-statistics is 16.22 (0.58). The mean (median) of a estimates is 0.414 (0.441) while its mean (median) t-statistics is 12.43 (4.68).

The mean (median) of DW statistics for [[Mu].sub.t] in (10) is 1.936 (1.977) and its standard error is 0.209.(13) The mean (median) of DW statistics for [[Epsilon].sub.t] in (8) is 1.855 (1.955) and its standard error is 0.439. More than 90 percent of the firms do not reject the null hypothesis that the autocorrelations in (10) and (8) are zero. The results suggest that the fourth-order AR process for the error term in (11) and the choice of four lagged variables for the AR process in (8) have successfully eliminated the problem of serial correlation. The median and mean autoregression coefficients ([[Rho].sub.1] to [[Rho].sub.4] are all positive. The value of [[Rho].sub.4] is relatively large and significant compared to the remaining three autoregressive coefficients. The relatively high fourth-order autocorrelation was also found previously. The distribution of [R.sup.2] for the dividend equation indicates that the values of this goodness-of-fit measure are generally very high.

To see whether the adjustment pattern of dividends differs by industry, we classified our sample firms into different groups based on both two-digit and four-digit SIC codes. The average [Lambda] values were then obtained for each industry group. However, the test statistics did not show any significant difference between industry groups. We also grouped firms into different sizes using both total asset and equity values. Again, the speed of adjustment did not differ significantly between large and small firms although the average [Lambda] values were generally greater for larger firms. Thus, the results did not indicate that the dividend adjustment pattern differs by industry and size.

Overall, our tests support the hypothesis of rational expectations-permanent earnings. We have shown that corporate dividends exhibit a systematic time-series behavior that is well described by the rational expectations-partial adjustment dividend model. Consistent with the dividend information hypothesis, the results indicate that the information conveyed by dividend changes is strongly related to permanent earnings. The result are also consistent with the contention that managers posses superior information about future earningsa and use the earnings information to obtain superior estimates for permanent earnings. Managers then use these permanent earnings estimates to determine dividend payments. Thus, dividend changes are related to information on earnings prospect. Finally, our tests provide direct evidence that supports the hypothesis of rationality implicity assumed in rational signalling models.

IV. Comparison of Our Model with Others in the Literature

In this section, we compare our test with those of Watts [32] and Gonedes [8]. We show that the structure of our model is more suitablee for testing the hypothesis of dividend information content. As a result, our model explains corporate dividend behavior better than other models. In contrast to Watts and Gonedes's findings that dividends convey little information about subsequent earnings, our result document a strong relation between dividend changes and expected future earnings. Therefore, dividends appear to provide important about the manager's future earnings expectations.

Since Modigliani and Miller [24] proposed the information hypothesis of dividens, researchers have tried to answer the question whether dividends convey future earnings information. Modigliani and Miller suggested that earnings consist of permanent and transitory components and dividends serve as surrogate for the former. Therfore, dividends may convey information for expected future earnings for the firm. Modigliani and Miller labeled this hypothesis as "the informatio content of dividends." Thus, the original rationale for the conveyance of information through dividends is that managers may use dividends as the medium to reflect their permanent earnings exepectations rather than current earnings which are often subject to random fluctuations.

In their extensive studies, Watts [32] and Gonedes [8] examined whether dividends contain information about future earnings. They found that dividends convey very little information about subsequent earnings of the firm. However, there are two potential problems for their methodology. First, both studies tested the hypothesis of dividend information by relating dividend changes to subsequent reported earnings changes. As Modigliani and Miller noted, dividends convey mainly permanent earnings information. Therefore, it is quite possible to find a weak relationship between reported earnings changes and dividend changes, because reportd earnings figures may not be an accurate reflection of real (permanent) earnings. Second, the procedure which Watts and Gonedes used to identify unexpected dividend information may not be appropriate. Both studies examined whether unexpected dividends reflect future earnings changes. Gonedes used a dividend model similar to equation (2) to identify the unexpected dividend information (the residual component [[MU].sub.t] while Watts used equation (2) and another model with an additional lagged earnings explanatory variable. The extended model used by Watts is as follows: (16) [Mathematical Expression Omitted] where [Z.sub.t] is a residual term. Watts reported his test using (16) while noting that the results are substantially the same under both models (2) and (16). After the unexpected dividend information ([[MU].sub.t] or [Z.sub.t]) was identified, test were then performed to see whether unexpected dividends were related to subsequent earnings changes ([[Delta] [Y.sub.t] + 1 = [Y.sub.t] + 1 - [Y.sub.t]). (14) For example, Watts estimated the following regression: (17) [Mathematical Expression Omitted] where [W.sub.t] + 1 is a residual term.

The procedure used by Watts and Gonedes to identify dividend information content may be responsible for their weak result. As Watts [32, 208-11] indicated, the estimation of the manager's expectations for future earnings using either (2) or (16) could be obscured by the noise in these two models. This is particularly the case when the manager's expectation of future earnings is misspecified. According to Watts [32] the correct dividend model can be written as (18) [Mathematical Expression Ommitted] where [Mathematical Expression Omitted] is the manager's expectation of earnings in t + 1 and [MU.sub.t], is the error term. Watts assumed that the manager's earnings expectation can be expressed as (19) [Mathematical Expression Ommitted] where [Delta], reflects the earnings information available only to the manager in time t. Substituting (19) into (18), Watts obtained the following relationship: (20) [Mathematical Expression Ommitted] Thus, the residual term in (16) can be rewritten as (21) [Z.sub.t] = [Delta] [Gamma] [[Delta].sub.t] + [U.sub.t] which includes the manager's expectation for future earnings and a noise term [U.sub.t]. This statistical problem may have caused the insignificance of [[Theta].sub.1] in (17). Watts's test is also subject to another problem. The dependent variable in (17) is the reported earnings change in t + 1, which is a very poor proxy for the manager's real earnings expectation. This could further weaken the regression result as reflected by the low average [R.sup.2] (.114) in Watts's study. One way to resolve these problems would be to specify the manager's earnings expectations [Mathematical Expression Omitted] accurately as in our equation (4) and conduct a test directly based on the correct model in (18).

In a way our methodology represents an improvement over Watts's procedure. First, our analysis avoids the problem of earnings expectations measurement by substituting the permanent earnings measure for reported earnings figures. Second, we directly test the hypothesis of dividend information content originally proposed by Modigliani and Miller. More, specifically, instead of using Watts's two-step procedure, we directly link dividend changes to expected future earnings changes as indicated in equations (4) and (5) by allowing a more flexible earnings generating process and imposing a rationality condition. This contrast sharply Watts and Gonedes's procedure. In their study, Watts and Gonedes implicity assumed that the earnings in t + 1, [Y.sub.1] + 1, summarize the information about expected future earnings [Y.sub.1] + 1 + j, j > 0 [8, 37]. The credibility of their test will therefore depend on the validity of this assumption. It is quite clear that this assumption may not be appropriate if earnings are subject to short-term fluctuations or measured with errors. In contrast, we directly related dividend changes to a consistent measure of long-term permanent earnings expectations. Furthermore, our model permits a test of rationality while Watts and Gonedes did not perform such a test to check the validity of their assumption regarding earnings expectations. The test of rationality is crucial for the examination of dividend information content. Presumbly, in order to test whether dividends convey information about expected future earnings, we need to specify a formation process of future earnings expectations consistent with rationality.

Our direct test of dividend information content appears to reduce substantially the effect of "noise" in Watts indirect two-step procedure. As indicated above, the residual variable [Z.sub.t] from (16) contains both a component of the manager's earnings expectations and the noise term. If the noise term is relatively large, the component of the manager's information will be obscured by the noise term. In contrast, our direct procedur is able to avoid this problem by separating the noise term from the manager's information in the dividend regression. This tends to improve test efficiency as evidence in our much higher t-statistics and [R.sup.2] values in the dividend regressions(15) On the basis of the statistical performance, our permanent earnings models seems to better describe the time-series relation between dividends and earnings.

VII. Summary

This paper considers explicity the formation of permanent earnings expectations in dividend adjustment. An adjustment model consistent with the rational expectations hypothesis is formulated to analyze corporate dividend behavior. The paper shows that the proposed rational expectations model is more general than previous models for examining the individual firm's dividend adjustment.

A nonlinear regression method is used to estimate the parameters of the model and test the validity of the rational expectations-permanent earnings hypothesis in dividend decision making. The partial adjustment model with rational expectations explains corporate dividend behavior very well. The results suggest that firms make use of the earnings information to form optimal estimates of permanent earnings, and that firms' dividend adjustment process is completed in about three quarters. The empirical results are consistent with the individend information hypothesis and market rationality, and therefore, provide support for rational signalling models. (1)Studies in this area include Pettit [209;30], was [32] Laub [17], Gonedes [8], Aharony and Dotan [1], Aharony and Swary [2], Eades, Hess and Kim [5], Kane, Lee and Marcus [15], Ofer and Siegel [27], Marsh and Merton [21], and Healy and Palepu [11]. (2)The partial adjustment model requires a specification of how the expected target is formed. As indicated by Gould [9] and Kennan [16], any model involving an adjustment lag requires a specification of expectations formation. (3)Waud [33] specified a static expectations formation in the dividend adjustment process. However, the adaptive expectations model impose a strong restriction on the process ofexpectations formation ; that is, the adaptive expectations model requires the expected future dividend target to be an exponentially weighted moving average (EWMA) of past earnings. (4)[Alpha] may be equal to zero. However, Lintner [19, 107] argues that this constant term (expected to be postive) should be included in (1) to reflect the greater reluctance to reduce than to raise dividends. (5)Exceptions are Nakamura and Nakamura [26], and Watts [32]. (6)We did not consider an ARMA process for the earnings equation because of the complications involved in the joint estimation and test of the proposed dividend model. It is known that an ARMA process can often be approximated by an AR process. (7)Nakamura and Nakamura [26] assumed that earnings follow a random walk with drift. Under this assumption, they derived a dividend model in which the coefficient of the lagged earnings variable is negative. In a way, our AR process is more than the random walk process. For instance, our earnings process in (8) will degenerate to random walk if [[Beta].sub.1] = 1, and [[Beta].sub.t-i] = O for i = 2, 3, and 4. (8)Let M = 4 and [Mathematical Expression Omitted] and [Mathematical Expression Omitted] where [Mathematical Expression Omitted] Then [Mathematical Expression Omitted] (9)We also used Akaike's [3] FPE procedure and found the order of lags for equation (6) can be as high as 28. (10)Since 0 < a, b < 1, lagging earnings for more than 4 periods will have only a negligible effect on the estimates of permanent earnings. (11)This data selection rule may cause a potential bias on the estimates. However, we do not feel that this would create a very serious problem because those firms not paying dividends for more than three consecutive years are mostly not paying dividends for the entire study period. (12)The original sample includes more firms than those reported. Some firms were dropped because of the convergence problem of the nonlinear regression. (13)DW statistics were computed based on the transformed models (in footnote 8) which explicitly consider the autoregressive terms. (14)Gonedes [8] focused on the effect of dividend information on portfolio returns. Strictly speaking, our test procedure is more similar to Watts [32]. (15)In Watts's study, the mean t-statistics of lagged dividend and earnings are - 2,379 and 3.488 which are much lower than our t-statistics for [Lambda] and [Gamma]. Also, the [R.sup.2] values are .584 and .114 for Watts's first and second-step regressions, respectively. The sum (.698) is still much lower than our average [R.sup.2] of .948. In Gonedes's study, the dividend regressions gives an average [R.sup.2] of .38.

References

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