Should managers refrain from and investors ignore noisy dividend surprises? Some experimental evidence

Journal of Economics and Finance * Volume 18, Number 3 �9 Fall 1994 * Pages 343-356

Should Managers Refrain From and Investors Ignore Noisy Dividend Surprises ? Some Experimental Evidence

Steven Peterson a n d Dan Salandro

ABSTRACT

A series of experiments is conducted in an asset market that contains a high productivity firm and a low productivity firm. Managers' compensation is a positive function of the market determined value of the firm. Investment decisions are made endogenously and are private information to the managers. The results of the experiments indicate that managers signal earning's information via noisy dividend announcements that result in suboptimal investment decisions. A manager's overinvestment in the signal does not generate significant increases in managerial compensation. The noisy signal does not pay off and in fact would result in a tendency for the market to underpredict earnings. This implies that even in the presence of suboptimal contracts between the managers and the firms, managers are not overcompensated. Thus, in these experiments the signal does not "solve" the dividend puzzle.

Introduction

Recent empirical studies have supported the hypothesis that dividend changes convey information to the market and affect common stock prices. 1 In this scenario, dividends may signal information that shareholders could not acquire in an otherwise efficient market. This signalling hypothesis maintains that managers possess information about the firm's furore prospects not available to the shareholders. 2 The dividend announcement provides information to allow the market to estimate the

Steven Peterson is Assistant Professor of Economics, Virginia Commonwealth University, Richmond, VA. Dan Salandro is Assistant Professor of Finance, Virginia Commonwealth University, Richmond, VA.

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JOURNAL OF ECONOMICS AND FINANCE Volume 18 Number 3 Fall 1994

firm's unobserved current earnings, to form an expectation of future earnings and therefore, value the firm.

For managers whose compensation is tied to the share-price performance of the firm, there is an incentive to "run" up the price by paying too large a dividend (Miller and Rock 1985). Thus, to potential investors, dividend surprises constitute a noisy signal. Market participants must separate the "permanent" component of the dividend surprise corresponding to managers' deviations from an "optimal" investment scheme (the manager's inside information) from the part corresponding to transitory (shock) movements in the firm's earnings. The rational market participant desires to discard the transitory component and base the investment decision on the expected future permanent change in the firm's earnings. Hence, the idea of signal extraction.

Managers reallocate funds from investment to the dividend presumably to influence the market's perceptions of earnings that subsequently enhance managers' compensation. In this paper, a signal extraction model is developed to construct forecasts for firms' earnings conditional on the expected level of manager-generated inside information. The predictions of the model are then compared with firms' actual earnings performance. The results are used to evaluate three points of interest: (1) Do managers convey information via noisy dividend signals and if so (2) is it of any value to managers as measured by manager compensation and (3) how precise are forecasts of firms' earnings given the level of noise in the dividend signals. Tests are conducted using data obtained in a series of experimental asset markets. 3. Experimental data are used because of the control the experimenter can exert over the various probability distributions that determine the underlying market fundamental and other variables of interest. The analysis is also of practical interest because the earnings predictions of the signal extraction model can be likened to the (hypothetical) forecasts of rational investors. 4 The following section presents a brief description of the experimental design and the forecasting problem. In section three, several specifications of the forecasting model are derived and estimated. A discussion of the empirical results appears in section four. Concluding remarks are presented in section five.

The Experimental Design and the Forecasting Problem

The basic experimental design is a 15 period asset double-auction with five minute trading periods similar to the design presented in Smith, Suchanek, and Williams (1988). There are, however, several innovations in the present design. For example, Smith, et al. study a market for a single asset. In the present design there are two assets permitting trade in the shares of two firms. Second, the underlying market fundamentals are endogenously determined through the decisions of two managers (one for each firm). These managers make dividend and investment decisions in each period in an attempt to maximize their respective payoff functions. These payoff functions are linear in the market value of the firm. Investment decisions generate

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Should Managers Refrain From and Investors Ignore Noisy Dividend Surprises?

earnings for each firm through two distinct, but well defined, stochastic production functions (one high productivity and one low productivity firm). Third, differences in productivity, along with the endogenous dividend decision, generate implicit signalling costs to the managers of each firm. This is quite different from the product signalling scenario studied in Miller and Plott (1985), where subjects were provided a menu of exogenously determined signalling costs. So whereas Miller and Plott, and Smith, et al. firmly anchor the underlying market fundamental, the design presented below provides an opportunity to study trade in a competitive market environment in which the underlying fundamental can be altered given the investment and dividend decisions of managers.

All experimental sessions were conducted using the Cal-Tech MUDA 5 program installed on a network of IBM personal computers at Virginia Commonwealth University (VCU). The subject pool consisted of eighty students recruited from graduate and upper level undergraduate courses in the School of Business at VCU. Since none had any prior trading experience, considerable time and effort were invested in the initial training of the subjects. The training included the MUDA computerized instructional module to familiarize subjects with the trading mechanics as well as an oral reading of an extensive set of written instructions. Throughout, effort was made to ensure that all subjects had a full understanding of the objective functions, trading mechanics, and trading parameters. Of course, this task became easier as subjects gained experience.

This paper utilizes the results of 16 sessions (usually with ten subjects per session). All subjects participated in at least two sessions. Sessions were arranged and recruited to control factors such as trading experience and learning effects.

A typical session would involve ten subjects and proceed with instructions (or a review of the instructions). Subjects would then log onto their computers and two subjects would be randomly chosen as managers for the two firms. The rest would become traders. Each trader's screen displayed private information that included a portfolio consisting of cash-on-hand and shares of one, or both, firms. 6 During each trading period, traders could submit bids and offers for shares allowing for the possibility to earn capital gains or losses. At the end of each period, shares held in inventory earned dividends announced by the firms' managers prior to trading. At the end of period 15, traders were paid in cash for the amount of their dividend earnings and ending cash-on-hand.

When the two managers were chosen, one manager was randomly assigned control of the high productivity firm and the other, the low productivity firm. In essence, these managers were lent control of these firms for 15 periods. In the initial setup period (before period one), control was assumed in both cases of a firm currently pursuing the Fisher optimal level of investment (described below). Managers could then pursue any investment/dividend policy they chose thereafter, but in the last period they had to return control of these firms in the same condition as in the setup period. That is, they were required to invest at the Fisher optimal level in period 15. Any amount short of the optimal level of investment had to be made up out of the

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manager's payoff. This provided managers with a disincentive to run up the value of the firm in later periods by paying out all earnings in the form of dividends.

The following example illustrates the manager's decision problem. For Firm 2 (high productivity) the production function is specified as:

X,§ = 5 In(I,) + ez, (1)

with Firm 1 (low productivity) having the production function:

X,+ 1 = 4.5 In(I,) + el, (2)

where X t+l are the end-of-period earnings generated from present investment and the eit for i= 1,2 are independent random draws from two mean-zero triangular distributions and represent random ~hocks to each firm's earnings s t r e a m . 7 U s i n g

Firm 2 as an example, and given that shocks have zero expected value, then the Fisher-optimal investment level is given by comparing the risk-adjusted rate of return on assets to the marginal productivity of investment:

XZt.1 = l + r (3) 511, = 1 + r

which reduces to the optimal level I* = $5 since there is no time value of money in the experiment (r=0). Thus, managers optimally choose I t so that the expected marginal return to the value of the firm generated by an extra dollar in investment is identical to giving that dollar away to shareholders in the form of a dividend. Clearly, the higher the marginal productivity, the more that can be paid out in the form of a dividend and yet still maintain the optimal investment level. In that sense, more productive firms have lower signalling costs. Thus, in these experimental markets, signalling costs are implicit and arise naturally from the decision making process with the notion of a signalling equilibrium arising naturally in the market as well.

In the setup period, investment for Firm 2 is I* = $5 so earnings are equal to ($8.05 + e) to start the experiment. Assume for the moment that e=0. The manager's decision then is to make an investment/dividend decision to maximize the value of the firm. s However, neither the investment decision, nor earnings (nor the shock) are revealed to the market. This constitutes the source of the information asymmetry. (Managers seek to signal the productivity of the firm and the market ascertains this attribute through the dividend announcements). Suppose the manager chooses the optimal level of investment for period 1. Then the dividend payout is automatically determined (there are no retained earnings) to be $3.05. Since there are ten shares of Firm 2 outstanding at all times, then the expected dividend per share would be $0.305 given I*. Thus, holding a share for say, all 15 periods, would generate approximately $4.57 thereby establishing the present value of Firm 2 in period 1. Expected dividend value would then fall off by $0.305 in each succeeding period. 9 All of this is public knowledge.

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It is straightforward to see that when e is nonzero, and assuming that managers still choose I*, then announced dividends and expected dividends differ only by the earnings shock. Therefore, dividend surprises are equivalent to the shock to the firm's earnings stream and managers simply would be passing that information along to the market. This, we refer to as the optimal signal.

However, when managers do not pursue I*, the dividend surprise will differ from and the signal sent to the market is a noisy one. Participants are fully aware of the

incentives for managers to inflate the signal at the expense of pursuing the optimal investment policy as well as the potential for firm failure in such instances. The problem is, although the market knows the nature of the surprise in the signal, they do not know its composition. Hence, it is the noisy signal which obstructs the market's valuation of each firm. This formed the basis of the Miller and Rock (1985) game-theoretic argument of suboptimal levels of investment.

After both managers make their investment/dividend decisions to begin period one, the dividends are announced and recorded on a blackboard at the front of the room. Period one trading then commences. During that time, managers locate the nonstochastic part of their earnings for the upcoming trading period (conditional on the investment decision) from the tables given in the instructions. The experimenter would thenreveal the random component ~ privately to each manager who, in turn, would calculate total earnings and make a new investment/dividend decision before beginning trade in period two. This process was then repeated for all 15 periods. At the close of each period, traders would record the announced dividends on shares held in their portfolios and managers would record one-half of the closing bid in their respective markets.

In sum, two managers make investment and dividend decisions in the presence of stochastic earnings shocks in an attempt to maximize share value. The market uses the information contained in the dividend announcements to discriminate between and value each firm. They know intrinsic value through expected dividends but not necessarily which firm is which. Thus, while intrinsic value is given by the expected stream of dividends, extrinsic value is given by the perceived stream of dividends. Though these two streams may not be equal, in a rational expectations equilibrium (REE) they would differ only by the amount of the realized shocks given that managers follow the rule I*.

Finally, for the control groups, the experimenter took over the roles of the managers. In these markets, dividends are (secretly) exogenous since the Fisher optimal investment policy I* was always followed and, hence, the exogenous shock E was simply passed along in the form of the dividend surprise. Trading then proceeded as usual. The market, of course, did not know the investment policy being pursued and hence, was unaware that the signal contained no noise.

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Empirical Models

The problems associated with the extraction of the signal from the dividend announcement can be illustrated in the context of the firm's sources and uses constraint with no external financing. In this approach, dividends plus investment (uses) must equal earnings (sources) rewritten as:

D, = X, - I , ( 4 )

where Dt, Xt, and I t are dividends, earnings, and investment levels respectively in period t. If X t and I t are unobserved, then dividend announcements signal net earnings. Furthermore, from the previous section:

X, = F(It_ ,) + , t (5) I, = l* + v,

where F is assumed to be a continuously differentiable production function (displaying diminishing returns). Here, e t is assumed to be an independently- distributed-random disturbance representing the shock to earnings which is assumed uncorrelated with v t, and v t represents departures from the optimal level of investment, I*. Though various specifications for v t can be entertained, we assume with no loss of generality that v t is independently distributed with zero expected value. Below, we demonstrate that v t represents the noise in the signal.

Suppose now that an earnings forecast is desired to value a particular firm. Our information set consists of I*, the firm's investment history, and the current period dividend signal. Substituting the definitions contained in (5) into the sources and uses constraint given by (4) yields:

O =F( t t_ l )_ I* + (6 t_v t ) (6)

In equation (6), the signal provided by D t is equal to the expected dividend plus an error component. The component e t represents the error associated with using only the previous level of investment to forecast earnings (see equation 5), while v t accounts for departures from the optimal level of investment. The signal is therefore noisy with the surprise given by:

D _ [ F ( I t _ I ) _ I * ] = ( e _v, ) (7)

W h e n , I t and X t eventually become known (i.e., before period t+ 1) then this new information can be used in a recursive fashion to calculate the proportion of (e t - vt) which is due to the earnings shock. This proportion is the correlation between e t and (e t - vt), that is, the coefficient in a regression of e t o n (e t - v t ) , v i z . ,

= - v,) (8 )

where f~ is estimated using ordinary least squares:

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fl = cov[e,(~,- v t) ]fvar(et- v ,) =o2J(o2 E + O2v)

This correlation goes to zero in the limit as the variance in the noise (and therefore, the variance in the insider information), vt, gets arbitrarily large, or as the variance in the earnings shock goes to zero. The latter implies that deviations in the signal from expected value are due only to the variance in departures from the optimal investment level and not to any shock to earnings. On the other hand, as oZv increases, the "noise" swamps the information in the signal and again, B approaches zero. In this case, the information contained in the dividend surprise has no forecasting value over lagged investment. A coefficient equal to unity, on the other hand, implies that the dividend surprise contains only the information contained in the earnings shock.

Substituting for et and (et - vt) in equation (8) from the definitions given in equations (5) and (6) and rearranging terms gives:

X, = F(It_l) + .[3(0 t - I F ( I t _ l ) - I*]) (9)

which suggests that the best forecast of earnings in period t is the nonrandom part of earnings (deterministic earnings) from the previous period updated by a fraction B of the dividend surprise. Notice that the term in square brackets is the expected dividend~

Consider, now, the experimental control group discussed above for which investment was always optimal. For this set of experiments, the surprise is equivalent to et. In this case, all of the surprise is accounted for by the earnings shock (since there is no deviation from I*) and 13 is equal to unity. Therefore, when equation (9) is estimated for a set of experiments where the signal is indeed optimal, earnings should be perfectly predicted since there is no insider information, and hence, no signalling noise.

On the other hand, when investment is endogenously determined, the restriction that investment equals I* is nonbinding. In this case, the power of the model to predict earnings, will be inversely related to the level of the suboptimality in investment. The reason is that period-to-period deviations from I* are private information and known only to managers and so, confusion exists about the source of the dividend surprise. Rejection of the null hypothesis, H0: B = i, would imply the existence of significant noise and hence, inside information.

We also hypothesize that the predictive power of the model will be poorer the greater the variance of the earnings shock because the latter contributes to the variance in the dividend surprise. As mentioned previously (see footnote 7), the distributions for the various earnings shocks are treatment variables and so, findings pertaining to this hypothesis will also be discussed below.

Additional tests are conducted by comparing the difference between the firm's actual per-period earnings and the earnings that would be predicted assuming managers have no inside information. This prediction is equivalent to the predicted

349


value which would arise from the imposition of the restrictions that i3 t = 13 2 = 1 in the regression:

Xt = ~1 F(Itl) + fJ2(Dr - [ F ( I t , ) - I*]) + I x, (10)

These restrictions generate rational forecasts under the assumption that managers choose the investment level I*. Put differently, we ask what earnings forecasts would evolve assuming managers did succeed in fooling the market.

Finally, we test whether managers gain from the creation of inside information by examining the correlation between manager payoffs and the noise component of the signal (by treatment). Results from these tests are presented in Table 1 and Table 2.

Discffssion of Results

The two columns labeled I in Table 1 present the least squares estimates of equation (10) using data obtained from the four experiments (60 periods in all) where investment levels were determined exogenously for both firms.l~ The signal in the market for these two firms is uncontaminated since there is no deviation from I*. As expected, these results indicate that earnings are perfectly predicted by the dividend surprise because the surprise contains only the information in the earnings shocks. We thereby fail to reject the set of linear restrictions imposed on equation (i0) that B~ =i32= I at any level of significance.

The columns labeled II, III, and IV in Table 1 present the estimates of equation (10) when investment is determined endogenously and the earnings shocks are obtained from distributions bounded by _ $1.00, 5: $1.50, and _+ $2.00 respectively. Since managers may now choose suboptimal investment levels in an attempt to mislead the market in its perception of the firm's earnings, then rejection of the above set of restrictions is evidence contrary to the manager's credibility concerning adherence to the Fisher-optimal investment strategy.

In all cases, the coefficient 132 is significantly less than one indicating that the signal is noisy and that the rational forecaster discounts or is unable to fully utilize the dividend surprise when estimating the firm's earnings. The F-statistics in row 4 e~sily reject the joint hypothesis H0: h i = h E = 1 at any reasonable significance level.

Summary statistics on the noise level, earnings shocks and dividend surprises are presented in the last six rows of Table 1. The dividend surprises are illustrated graphically according to earnings shock treatment in Figure 1. Dividend surprises are shown to increase as the level of earning shock increases. Noise levels, which are measured relative to I*, indicate that managers of the low productivity firm (Firm 1) invest less than the optimal level and managers of the high productivity firm (Firm 2) tend to overinvest. Though managers of Firm 1 have a clear incentive to underinvest, the actions of the managers of Firm 2 are puzzling to the extent that it appears they have foregone opportunities to pay higher dividends. This result is Iargely due to the actions of a few managers of Firm 2 who overinvested large

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T A B L E 1

Regression results for estimations of earnings forecasts using experimental

data. The following equation was estimated: ~

Xt = 3IF(I t - t ) + 32(D t - [F(It-I) - I ' ] ) + /z t

Panel A: Firm 1

I II III IV

~2

N

F(d,N)

Noise, v t (020

Shocks, e t (o2~)

Dividend Surprise &)

1.00

1.00

60

0.0047 0.206

0.0047 0.206

1.0117 1.013 1.0007 (0.0097) (0.0118) (0.0135)

0.323 0.261 0.465 (0.1035) (0.103) (0.099)

60 60 60

22.13 26.29 15.28 (2,58) (2,58) (2,58) -0.587 -0.404 -0.614 0.563 1.151 0.945

0.079 0.082 0.019 0.243 0.364 0.546

-0.033 -0.066 -0.144 0.336 0.527 0.684

Panel B: Firm 2 I II III IV

fll

~2

N

F(d,~

Noise, v t (ozv)

Shocks, e t (o2,)

Dividend Surprise (o -z)

1.00

1.00

60

0.0967 0.2047

0.0967 0.2047

1.016 1:0016 1.003 (0.0068) (0.0070) (0.0167)

0.096 0.440 0.076 (0.075) (0.1108)) (0.1021)

60 60 492

80.01 14.04 41.06 (2,58) (2,58) (2,47)

0.912 0.866 -1.49 2.572 0.685 4.42

0.146 -0.037 -0.0026 0.2116 0.271 0.645

-0.0872 -0.145 -0.759 0.645 0.298 2.328

i All figures in parentheses are standard error terms. Columns I present the coefficient estimates when the Fisherian optimum investment level is imposed ex ante. Columns II, III, and IV present the coefficient estimates when the earnings shock are drawn from distributions with upper and lower hounds of +$1.00, +$1.50 and +$2.00 respectively.

z In one experiment the manager bankrupt the firm after the fourth period of trading.

amounts. Because of this action, the noise variances are much higher for Firm 2. The connection between low values for g2 and high levels of variance in the noise

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component is strong and also consistent with the theory; the signal is too contaminated to be of any predictive value and hence the proportion of the signal (f~2) representing the information is low. We therefore reject the hypothesis that managers follow the Fisher-optimal investment policy. It is also true that, with the exception of the experiments in which investment was exogenously optimal, the noise variance is higher than the earnings-shock variance in every case. Therefore, not only do managers generate significant noise levels, but they generate levels whose variance exceeds the variance in shocks to their production.

Figure I: Dividend sur 4

3-

2

- 2 -

- 3

- d

I I I

3rises for treatments

3

- 3 "

I I I IV

I-IV

I I I I l l IV

Firm I Firm 2

note: four treatments - exogenous followed by endogenous

Perhaps more interesting is the fact that managers' alleged attempts to alter the market's assessment of firm value fails consistently. The situation can be characterized in the context of a noncooperative game in which management deviates from the socially optimal solution (choose I = I*) because the market expects the optimal level of investment. This would be especially appropriate for the managers of Firm 1. If the market is fooled, then the market, at least temporarily, over- estimates the value of the firm. In a signalling equilibrium however, the market would take managers' incentives to cheat into consideration (see, for example, the Miller and Rock (1985) discussion). Nonetheless, it is clear from the results presented in Panel A of Table 2, that if forecasts are formed as managers would like, earnings are not over-estimated. Indeed, they are underestimated all of the time.U For example, the market underestimates actual earnings for firm 1 by amounts ranging from 11 cents to 16 cents depending on the earning shock treatment variable.

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TABLE 2

Panel A: Differences between actual earnings for different levels of earnings shocks and restricted earnings forecasts based on the assumption of no inside information I. All figures in parentheses are t-statistics.

Firm 1 Firm 2

I II III IV I II III IV

--- 0.1124 0,148 0.163 [ --- 0.234 0,1089 0.308 (1.217) (1.607) (1.766) ] (2.116) (1.533) (1.585)

Panel B: Mean differences between actual manager payoffs and expected dividends (REH prediction o f manager payoffs) in cents. All figures in parentheses are t-statistics.

I II III IV I II III

12.633 19.55 -4.912 1.575 4.45 -15.98 -33.21 (1.105) (2.738) -0.695) (0.277) (0.328) (-1.356) (-5.923)

N 60 60 59 58 60 59 60

IV

-32.05 (-4,728)

50

Panel C: Results for estimations to determine whether managerial compensation and deviation from the optimal investment levels are related. The fol lowing equation is estimated.

I II III

0.6155 -0,322 (1.615) (1,157)

-0.107 0,067 (1.122) (1.014)

pay~ = ~ + flv t + ~t

IV I

-0,266 --- (-1.126)

0.072 0.0089 (1.228) (0.328)

II IH IV

0.955 0.5612 -0.7463 (2.22) (1.436)) (-3.89)

-0,188 -0.153 0.1013 (-2.686) (-2,326) (2.358)

Columns labeled I, II, III and IV represent the experiments with exogenously determined investment levels, and earnings shock drawn from distributions bounded by +$1.00, :1:$1.50

and +$2.00 respectively.

From Panel B in Table 2, it is also clear that managers' payoffs are either significantly less or no different than payoffs measured relative to the rationally expected dividend value. Thus the market does not respond to deviations from the optimal investment level. The lone exception occurs for managers of Firm 1 with the low variance earnings shock where the payoff is 19.55 cents higher than the rationally expected dividend value, i.e., the rational expectations hypothesis (REH) prediction of manager's payoffs (regression II in Panel B). Results from signalling theory would suggest however, that low productivity firms stand to gain most from this behavior. This exception notwithstanding, payoffs do not appear to be significantly positively related to the level of noise (Panel C). On the contrary, for Firm 2 managers who have overinvested, (treatment II and III), payoffs are significantly negatively related to the level of noise.

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The basic conclusion forthcoming from these results is that attempts to deviate from the optimal level of investment, thereby creating this so-called insider information and noisy dividend signals, does not produce over-estimates of firms' earnings by an otherwise rational market. Nor does this behavior generate above- average manager compensation. It only appears to result in suboptimal resource allocations.

Summary

This paper presents the results of a series of experiments conducted in an asset market which trades securities in two firms with different productivity levels. Managers are randomly chosen and. they provide the investment decisions for the firms. These levels are known only to the managers. Manager compensation is a positive function of the market determined value of the firm. The results of the experiments indicate that managers signal earnings information via a noisy dividend announcement which results in suboptimal investment levels. The noisy signal does not pay off to the managers and a rational outsider forecasting earnings would systematically under-value the earnings of the firm. The level of under-prediction of earnings is larger the higher the variance of the firm's earnings shocks. Managers of the low productivity firms under-invest as predicted by Miller and Rock (1985). It also is observed that only managers of low-productivity firms which experience low variance earnings shocks are able to enhance their compensation by creating inside information, i.e., deviations from the optimal level of investment. This result implies that one should look to low productivity firms in the market for significant under-investment. Likewise, it implies that it would behoove the more established and relatively high productivity firms to avoid this type of competition simply because the activity does not pay off.

It remains to be seen whether data collected from naturally occurring markets would generalize the results presented in this paper. Presumably, estimation of the underlying market fundamental, earnings shocks, and optimal investment levels would be relatively elusive. Perhaps a more promising extension of the research presented here would involve a similar experimental study with more that two firms in the market and a broader array of treatment effects.

NOTES

This research was supported in part by the Grant-In-Aid Program for Faculty of Virginia Commonwealth University. All errors are the responsibility of the authors.

1. Empirical studies include Aharony and Swary (1980), Asquith and Mullins (1986), Brickley (1983), Handjinicolaou and Kalay (1984), Jayaraman and Shastri (1988) among others.

2. See for instance, Miller and Rock (1985), Bhattacharya (1979), Williams (1988), and John and Williams (1985) for discussions relevant to dividend signalling.

354


3. In essence, this experimental market is designed as a multi-period version of the theoretical treatment developed in Miller and Rock (1985). A detailed discussion follows in section II.

4. Expectations are rational in the sense that agents' forecasts optimize over the relevant information sets. See, for example, Sargent (1987), ch. 10.

5. MUDA (Multiple Unit Double Auction) was developed by Charles R. Plott, Hsing Yang Lee (Cal-Tech), and Alonzo Johnson (Southern University).

6. All portfolios were initialized according to the present values of the firms and were identical in value though perhaps different in composition.

7. For each session, the width of the distribution was predetermined so that the two shocks were drawn from independent distributions with upper and lower bounds (for both firms) given by either +$1.00, +$1.50, or +$2.00. These constituted treatment effects which will be discussed below.

8. Managers receive one-half of the closing bid in each period as their payoff. The closing (standing) bid was used rather that the average contract price due to the fact that the latter depended on contracts being struck in each period. Sometimes this did not occur. In addition it was felt that the standing bid most accurately measured the market's perception of share value.

9. Similarly for Firm 1, I* = $4.50, expected earnings are then $6.77 and the expected dividend per share given I* and ten shares is $0.227. Thus, expected dividend value is approximately $3.40 in period 1 for shares of Firm B.

10. For all experiments in which investment was exogenously determined, earnings shocks were drawn from a triangular distribution with mean zero and range 5:$1.00

11. Managers would like to think that the market believes that no noise is injected into the signal. In such a case, the market would then forecast earnings using a restricted version of equation (10) with the restrictions that gl = 132 = i.

REFERENCES

Aharony, Joseph, and Itzhak Swary. "Quarterly Dividends and Earnings Announcements and Stockholder's Returns: An Empirical Analysis." Journal of Finance 35, no. 1 (March 1980): 1-12.

Asquith, Paul, and David W. Mullins, Jr. "Signalling With Dividends, Stock Repurchases, and Equity Issues." Financial Management 15, no. 3 (1986): 27-44.

Bhattacharya, Sudipto. "Imperfect Information, Dividend Policy, and 'The Bird in the Hand' Fallacy." Bell Journal of Economics 10, no. 1 (Spring 1979): 259-270.

Bricldey, James A. "Shareholder Wealth, Information Signalling and the Specially Designated Dividend." Journal of Financial Economics 12, no. 2 (August 1983): 187-210.

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Handjinicolaou, George, and Avner Kalay. "Wealth Redistribution or Change in Firm Value: An Analysis of Returns to Bondholders and Stockholders Around Dividend Announcements." Journal of Financial Economics 13, no. 1 (March 1984): 35-64.

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John, Kose, and Joseph Williams. "Dividends, Dilution, and Taxes. A Signalling Equilibrium." Journal of Finance 40, no. 4 (September 1985): 1053-1070.

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Miller, Ross M., and Charles R. Plott. "Product Quality Signaling in Experimental Markets." Econometrica 53, no. 4 (July 1985): 837-872.

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Should managers refrain from and investors ignore noisy dividend surprises? Some experimental evidence