forecasting accuracy of alternative dividend models

FORECASTING ACCURACY OF

ALTERNATIVE DIVIDEND MODELS

CHENG-FEW LEE, K. THOMAS LIAW, and CHUNCHI WU

ABSTRACT

Lee, Wu and Djarraya (1987) show that the traditional dividend models as represented by the partial adjustment, adaptive expectations, myopic policy and residual theory are all special cases of their proposed integrated model. Their empirical results indicate that the integrated model explains the firm’s dividend decision process rather well. Despite that the integrated model is superior to other dividend models in terms of ex post performance, the forecasting accuracy of the model is still to be investigated. The purpose of this paper is to examine the forecasting accuracy of alternativedividend models. The empirical results suggest that forecasting accuracy can be improved if the integrated model is first used to identify the dividend adjustment process and then the identified dividend model is used to forecast future dividends.

I. INTRODUCTION

Lee, Wu and Djarraya (1987) propose an integrated model to investigate firm’s dividend behavior. They show that the traditional dividend models such as the partial adjustment

Direct all correspondence to: Chunchi Wu, Syracuse University, School of Management, Syracuse, N.Y. 13244 l Cheng-Few Lee, Rutgers University l K. Thomas Liaw, St. John’s University

International Review of Economics and Finance, 1(3):261-270 Copyright 0 1992 by JAI Press, Inc. ISSN: 1059-0560 All rights of reproduction in any form reserved.

261

262 CHENG-FEW LEE, K. THOMAS LIAW, and CHUNCHI WU

process (Lintner, 1956; Fama and Babiak, 1968), information content hypothesis (Ang, 1975 and Laub, 1976), and the residual theory (Higgins, 1972) are all special cases of the integrated model. Their results suggest that firm’s dividend adjustment process can be better identified by the integrated model. In particular, the integrated model is capable of explaining the dividend behavior of firms with different characteristics.

While the integrated model seems to be able to explain firm’s ex post dividend behavior, it is important to examine the predictive ability of the integrated model and other competing dividend models. Furthermore, it will be interesting to see whether firm’s dividend behavior changes over time. The integrated model provides an excellent framework for examining the intertemporal pattern of firm’s dividend behavior because of its ability to distinguish different corporate dividend decisions.

In this paper, we attempt to compare the forecasting accuracy of alternative dividend models and examine the stability of alternative dividend behavior over time. The rest of this paper is organized as follows. The next section briefly outlines the alternative dividend models including partial adjustment, myopic policy, residual theory, adaptive expectations, and the integrated model. Also, the criteria for identifying firm’s dividend behavior and the corresponding reduced forms to be estimated are presented. The third section documents the regression results and then compares forecasting accuracy among different dividend models, We find that the prediction errors for adaptive expectations and the integrated models would be higher if fitted by the partial adjustment process. Finally, the last section summarizes the main findings and concludes the paper.

II. ALTERNATIVE DIVIDEND MODELS

In this section, we briefly outline the alternative dividend models examined in the paper.

Empirical estimates of the parameters and forecasting of dividends follow in the next section.

We begin with the partial adjustment model. The partial adjustment process can be

characterized as

(1)

and

Dt-Dt_, =a+h(@ -Dt_l)+ut (2)

Equation (1) indicates that the firm’s desired dividend payment L$ is determined by the

target payout ratio(r) and thecurmnt net income (E,). Equation (2) states that the amount

of dividend will adjust to the new level gradually, depending on the speed of adjustment (A). In equation (2), cx is a constant term which was originally added by Lintner to test whether managers are more reluctant to cut dividends than to raise them.

The adaptive expectations model hypothesizes that the current dividends are related to the expected future net income, i.e.,

Forecasting Accuracy of Alternative Dividend Models 263

DI=rI$+E, (3)

Dt is the current dividends, r is the target payout ratio, Ef is the expected long-run

income, and E, is the error term. The expected income at time f is determined by

E;=hE,+(l -a)& (4)

where 6 is the coefficient of expectations. Under such a formation, expectations are updated each period by a fraction of the discrepancy between the current income and

the previous expected income, i.e., the current expectations are derived by modifying previous expectations.

The desired dividends are likely to be determined by the target payout ratio and the expected income. In a world with information uncertainty, managers would estimate future income based on their inside information and adjust dividends to the desired level. The expectation for future income is important for the dividend decision. In the presence of adjustment lag, managers must form expectations about future income before they can make decisions on dividend payout. Conversely, when there is no adjustment lag, expectations for future income are generally irrelevant since managers can always respond to any changes in earnings conditions immediately. In addition, it is also assumed that equations (2) and (4) hold. Under these assumptions, the integrated model can now be derived

D,=a6+(2-h-6)D,, - (1 - A.)( 1 - 6)D,_2 + AGE, + u, - (1 - 6)u,_i (5)

where D, is dividend payments at time t, Et is net earnings at time t, CL is a constant, 6 is

the coefficient of expectations, his the speed of adjustment coefficient, r is the dividend payout ratio, and ur is the disturbance term.

Equation (5) states that the current dividends are related to current net earnings and the past dividends. The relationship is nonlinear in parameters which include both speed-of-adjustment coefficient hand adaptive expectations coefficient 6. The value of h depends on firm’s investment opportunities, investor’s preferences, marginal income tax rates and transaction costs. The value of 6 depends on the persistence of expected future earnings. The value of 6 will be close to one if the expected earnings change is permanent. On the other hand, 6 will be close to zero if the expected earnings change is transitory.

The integrated model in equation (5) allows us to classify companies into various dividend behavior groups according to parameter estimates. The dividend adjustment process is represented by the integrated model if Q and h are both significantly different from, but fall between, zero and one. The firm’s dividend behavior is explained by the adaptive expectations process if h is not significantly different from one and 6 is significantly different from zero. It is a partial adjustment process if 6 is not significantly different from one and h is significantly different from zero. The firm adopts a myopic policy if both h and 6 are not significantly different from one. On the other hand, the dividend decision is based on the residual theory if both h and 8 are not significantly


Table 1. Alternative Dividend Models

Dividend Model Parameter Estimates Reduced Form

(A) Integrated Model 0 < 6,hcl D,-a6+(2-h-6)D,-t-(l-h)(l-G)D,_2

+ AbE, + rc, - (1 - 6)rr,_~

(B) Adaptive expectations A = I,6 l 0 Q-(1 -6)D,_, +r6E,+u,-(1 -@I(,._,

(C) Partial adjustment 6=1,X20 D, - u + (1 - h)D,_l + AE, + u,

(D) Myopic policy h=6=1 D,-rE,+u,

(E) Residual theory h=b=l,r=O

(F) others the remaining companies

different from one and t- is not significantly different from zero. The remaining companies are classified as others. These groupings of companies and the corresponding reduced forms are summarized in Table 1. As shown in Table 1, the current dividends are influenced by the current earnings and the dividends paid in the past two periods

under the integrated model. This is because both cost of adjustment and information uncertainty exist. The partial adjustment model states that firms usually seek to maintain stable dividend payouts by changing them each year by only a portion of the change determined by earnings in conjunction with the target payout ratios. The adaptive expectations hypothesis states that dividends convey information about future earnings expected by management. For the myopic policy, the amount of dividends is determined by the target payout ratio and the current earnings. Finally, the residual theory holds that firms should finance as many acceptable investment projects as possible with equity capital since internal financing is cheaper than external financing. Dividends are therefore a residual that reflect the amount left over from earnings after investment projects ate financed by equity capital.


Table 2. Grouping of Companies Mean and Standard Deviation of the Estimated Structural Parameters’

Dividend Process Cltmijied (IS a 8 h r Rz

Integrated model (11 firms)

Adaptive expectations (19 firms)

Partial adjustment (10 firms)

Myopic policy (7 firms)

0.187 0.638

(0.07) (0.10)

0.301 0.562

(0.25) (0.23)

0.220 0.951

(0.14) (0.19)

0.407 0.813

(0.35) (0.40)

0.916 0.535

(0.27) (0.17)

0.592 0.838

(0.22) (0.27)

0.643 0.617

(0.12) (0.13)

0.580 0.695

(0.15) (0.17)

0.756 0.499

0.658 0.669

0.448 0.489

(0.40) (0.14)

0.319 0.691

(0.19) (0.32)

0.437 0.640

(0.36) (0.23)

0.399 0.721

(0.26) (0.32)

Notes: ‘Numbers in parentheses are standard deviations of the estimated coeffkients.

‘Numbers in row (1) are the estimates assuming II, is serially independent and numbers in row (2) art results

when n, is autocorrelated

Residual theory (1 firm)

Others: (32 firms)

Overall sample (80 firms)

(1)’

a2

(1)

(2)

(1)

(2)

(1)

(2)

(1)

(2)

(2)

(1)

(2)

-0.125

(0.20)

-0.085

(0.16)

-0.024

(0.33)

0.053

(0.24)

0.053

(0.18)

0.081

(0.29)

0.164

(0.34)

0.249

(0.55)

0.378

0.588

-0.057

(0.15)

-0.030

(0.16)

0.020

(0.24)

0.028

(0.27)

0.653

(0.18)

0.662

(0.18)

0.555

(0.26)

0.514

(0.26)

0.457

(0.20)

0.459

(0.20)

0.365

(0.12)

0.359

(0.11)

0.165

0.125

0.554

(0.29)

0.534

(0.32)

0.534

(0.25)

0.517

(0.27)

0.987

(0.02)

0.981

(0.03)

0.923

(0.10)

0.909

(0.12)

0.900

(0.11)

0.903

(0.10)

0.875

(0.13)

0.881

(0.12)

0.699

0.727

0.927

(0.11)

0.921

(0.12)

0.923

(0. IO)

0.918

(0.11)

vt = u, - (1 - 6)U(_1.

vt will be serially correlated if ur is normal, identically and independently distributed

and 6 is not equal to one. Under these circumstances, it can be shown that ordinary least

squares estimators are inconsistent and that the structural regression coefficient, a, I, 6

and r can be identified but can not be estimated due to the unobservable uI. On the other

hand, if vt is normal and independently distributed, then 6 and h cannot be identified.

To obtain consistent and unique estimates, the Marquardt’s nonlinear least squares

regression method was used to estimate the structural parameters of equation (5). The


Table 3. Dividend Models: Mean and Standard Deviation of the Estimated Structural Parameters1

a d h r R2 SPR2

Integrated model (1? -0.125 0.187 0.638 0.652 0.987 3.73 (11firms) (0.20) (0.07) (0.10) (0.18) (0.02) (4.95)

(2)2 -0.085 0.301 0.562 0.662 0.981 3.31

(0.16) (0.25) (0.23) (0.18) (0.03) (4.28)

Adaptive expectations: (1) 0.162 0.617 0.895 0.888 (19 firms) (0.10) (0.36) (0.12) (2.07)

(2) 0.196 0.532 0.897 0.805

(0.13) (0.20) (0.13) (1.97)

Partial adjustment (1) 0.040 0.487 0.472 0.895 20.87

(lOfirms) (0.20) (0.22) (0.20) (0.11) (25.7 1)

(2) 0.042 0.510 0.472 0.901 20.05

(0.22) (0.26) (0.20) (0.10) (23.77)

Myopic policy (1) 0.367 0.878 151.84

(7 firms) (2) (0.10) (0.10) (185.85)

0.323 0.911 152.24

(0.09) (0.09) (185.93)

Notes: ‘Numbers in parentheses are standard deviations of the estimated coefftcients.

*Numbers in row (1) are the estimates assuming n, is serially independent and numbers in row (2) are results when n, is autocotrelated

average values of parameter estimates reported in Lee, Wu, Djarraya (1987) were used

as the starting values. Table 2 reports the results of regression estimates assuming Ut is serially correlated.

We perform statistical tests on the competing hypotheses (A) to (F) listed in Table 1. In

testing parameter estimates, we use a 5% significance level. Companies are classified

into one of the six groups (see Table 1) according to test results on the parameter

estimates of equation (5). There are 11 firms characterized by the integrated model, 19

firms explained by the adaptive expectations model, 10 firms by the partial adjustment

process, 7 firms by the myopic policy and 1 firm by the residual theory. A list of

companies for each group is provided in Appendix A. After identifying firm’s dividend behavior, we next use the integrated model, adaptive

expectations, partial adjustment, and the myopic model to estimate the structural

parameters for the firms in each corresponding group. Table 3 reports the mean and

standard deviation of the estimated structural parameters for each dividend model. We also estimate the models for the case when ut is serially independent. The results

are also reported in Tables 2 and 3. The estimates are similar to those obtained by assuming serial correlation. In brief, the myopic theory and the partial adjustment model

provide a lower payout ratio (r) than the other two models. The means of the expectations


Table 4. Mean and Standard Deviation of the Estimated Structural Parameters for Different Dividend Behavior Models’

Group r a A 6 Number of Finns

1. Integrated model

2. Adaptive expectations model

3. Partial adjustment model

4. Other

5. Overall sample

0.378

(0.23)

0.476

(0.29)

0.442

(0.45)

0.418

(0.19)

0.435

(0.27)

0.031 0.445 0.121 25

(0.07) (0.15) (0.07)

0.082 1.060 0.082 19

(0.15) (0.27) (0.07)

0.008 0.139 0.931 11

(0.02) (0.11) (0.18)

0.012 0.214 0.201 25

(0.05) (0.10) (0.17)

0.036 0.478 0.232 80

(0.09) (0.35) (0.28)

Note: ‘This is from Table 4a of Lee, Wu, and Djarraya (1987). The numbers in parentheses are the standard

deviations of the estimated ccefftcients in each group. The parameters are from regressions which assume ut is serially independent. A 5% significance level is used in grouping the companies.

and speed of adjustment coefficient (6 and A) are about the same or reasonably close.

The R2 values of the integrated model are generally higher than the others. Table 4 documents the results of Lee, Wu, and Djarraya (1987). Their study period

covers 1962-1978. The eighty firms covered in their study were selected based on the same criteria described in the beginning of this section (it should be noted that their sample and the one examined in this paper are different). Groups (D), (E) and (F) were lumped into one group because of small number of units. The overall sample reveals that the mean of the target payout ratio, r, is equal to 0.435. The constant term, a, has a mean of 0.036. The estimated speed of adjustment, I., is 0.478, which suggests that the adjustment generally takes two periods to complete. The mean coefficient of expectations is 0.232. The parameters in each group can be interpreted in a similar manner.

The parameter estimates of the dividend models vary among this study and Lee, Wu, and Djarraya’s (1987). We find some differences between the results in Table 2 (this study) and in Table 4 (Lee, Wu, and Djarraya’s). For the integrated model, the average h value has increased somewhat (from 0.445 to 0.638) in our sample. The average payout

ratio appears to be higher in Table 2 (0.653) than that in Table 4 (0.378). It is difficult to have a precise comparison for the results in Tables 2 and 4 because the sample firms in these two studies are different. The difference in the estimates of average payout ratios could result from sample variation. Also, over time some firms may increase dividends. Turning to the adaptive expectations model, we find that the average 6 value increases significantly, particularly for the case when uI is independent. For the partial adjustment model, the average hvalue has also increased substantially (from 0.139 to 0.535). Again, the difference in the estimates of the partial adjustment coefficients could be due to either the difference in the sample selection or the increase in dividend adjustment speed. For


Table 5. Comparison of Forecasting Accuracy’

Made1 SPR’ SPR2 if Predicted by Partial Adjustment

Integrated model (l? 3.73 12.59

(4.95) (10.36)

(2)2 3.31 13.13

(4.28) (11.23)

Adaptive expectations (1) 0.89 5.86

(2.07) (8.20)

0.81 6.11

(1.97) (9.01)

Myopic policy (1) 151.84 27.05

(185.85) (30.85)

(2) 152.24 22.95

(185.93) (30.95)

Notes: ‘Numbers in parentheses are standard deviations of the estimated coefficients.

2Numbers in row (1) are the estimates assuming U, is serially independent and

numbers in row (2) are results when U, is autocorrelated.

the remaining models, the values of 6 and h have generally increased. The overall results for the speed-of-adjustment and adaptive expectations coefficients suggest that recently firms have reacted more quickly to changes in financial and business conditions. The

quicker response to changing financial and business conditions is expected because of the increasing costs of being out of the equilibrium. Today, performance of firms and securities are closely monitored by the security analysts and investment advisories. This tends to push firms to react to changes in market conditions as quickly as possible to avoid penalty of being out of the equilibrium.

Next, we turn to dividend forecasting. The estimated parameters are used to forecast dividend payments in 1985. The forecasting values of dividends are compared with the actual dividend payments in 1985. Following Fama and Babiak (1%8), the standardized prediction error is defined as

Standardized Prediction Error (SPR)

actual D in 1985 - predicted D in 1985 = standard deviation of changes in dividends 1966-1984

where D is dividend payment. We report the distribution of the standardized prediction errors in the last column of

Table 3. The averages of the squared standardized prediction errors are 3.73,0.89,20.87 and 151.84 for the integrated model, adaptive expectations, partial adjustment and myopic models, respectively.

We next use the partial adjustment model as benchmark to estimate the other groups and predict dividend payments in 1985. The squaredstandardized prediction errors are,


when the other groups were fitted by the partial adjustment process, reported in Table 5. For the myopic policy group, the partial adjustment model can provide a better prediction of future dividends. However, for adaptive expectations and the integrated model, the forecasting errors are higher if fitted by the partial adjustment process.

Results indicate that the partial adjustment and myopic models perform very poorly in predicting future dividend movements. Although the adaptive expectations model has the lowest prediction error, the predictive ability of the integrated model appears to be very reasonable. As shown in Table 3, the mean and the standard deviation of prediction errors of the integrated model are much smaller than the partial adjustment and myopic models. Also the explanatory power (in terms of R2) of the integrated model is higher than the adaptive expectations model and the model can be used to distinguish different firm’s dividend behavior.

IV. CONCLUSIONS

The integrated model is used to identify firm’s dividend adjustment process: adaptive expectations, partial adjustment, myopic policy, residual theory, and others. We then use the identified model to estimate parameters of the corresponding firm group. We find that parameter estimates are time varying.

We further compare prediction errors among the alternative dividend models. For the myopic policy group, the partial adjustment model provides a better prediction of future dividends. However, for adaptive expectations and the integrated models, the forecasting errors would be higher if fitted by the partial adjustment process. In general, the explanatory power and forecasting ability of the integrated model appears to be reasonably good.

APPENDIX List of Companies

A. The Integrated Model C. Partial Adjustment Process

1. Schering-Plough

2. Lubrizol Carp

3. American Petrofina

4. Witco Corp

5. Coming Glass Works

6. Reynolds Metals Company

7. Eastern Company

8. Pitney-Bowes Inc.

9. Singer Company

10. Thomas & Betts Corporation

11. Textron Inc.

I

1. San Carlos Milling

2. Newmont Mining Corp

3. Homestake Mining

4. Rarer Group

5. Exxon Corp

6. Foote Mineral Company

7. Dover Corporation

8. American Standard Inc.

9. Tecumseh products Company

IO. Maytag Company


B. The Adaptive Expectations

1. Callahan Mining Corporation

2. Campbell Red Lake Mines

3. Wilson Brothers

4. DuPont

5. British Petroleum

6. Imperial Oil Ltd.

7. Mobil Corporation

8. Pennzoil Company

9. Ideal Basic Industries Inc.

10. Copperweld Corporation

11. Kaiser Aluminum & Chemical Corp.

12. Stanley Works

13. Caterpillar Inc.

14. Ingersoll-Rand Company

15. E-Systems Inc.

16. Chrysler Corporation

17. Mickelberg Corpaation 18. MCA 19. Dravo Corporation

D. Myopic Policy

1. Atlas Const. Mining & Develop.

2. Heileman Brewing Inc.

3. Domtar Inc.

4. New York Times Company

5. McGraw-Hill Inc.

6. DeSota Inc.

7. General Motors Corporation

E. Residual Theory

1. Asarco Inc.

ACKNOWLEDGMENT

We thank the referee, the editor, and participants of the finance seminar at St. John’s University for valuable comments and suggestions.

REFERENCES

Ang, J.S. “Dividend Policy: Informational Content or Partial Adjustment?’ Review of Economics and Stufistics, 57 (1975): 65-70.

Fama, E.F. and Babiak, H. “Dividend Policy: An Empirical Analysis.” Journal of American Statis?ical Associution, 63 (1968): 1132-l 161.

Higgins, R.C. “TheCorporate Dividend Saving Decision.” Journal ofFinancial undQuantitufive Analysis, 7 (1972): 1531-1538.

Laub, P.M. “On Informational Content of Dividends.” Journal of Business, 49 (1976): 73-80. Lee, C.P., Wu, C., and Djarraya, M. “A Further Empirical Investigation of the Dividend

Adjustment Process.” Journal of Econometrics, 35 (1987): 267-285. Lintner, J. “Distribution of Income of Corporations. ” American Economic Review, 46 (1956):

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forecasting accuracy of alternative dividend models

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