Department of Economics. Working Papers

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1 10ISSN SIMON FRASER UNIVERSITY Department of Economics Working Papers An Experimental Examination of Asset Pricing Under Market Uncertainty Taylor Jaworskiy and Erik Kimbrough December, 2012 Economics

2 An Experimental Examination of Asset Pricing Under Market Uncertainty Taylor Jaworski Erik O. Kimbrough Abstract In a novel laboratory asset market, traders buy and sell shares of a monopolist while observing its price and transaction history in real-time. Dividends are based on the profitability of the monopolist, also an experimental subject. Despite dividend uncertainty resulting from both monopolist behavior and imperfect information about product market fundamentals, the present value of the dividend stream provides the best estimate of observed asset prices. We compare our data to previous experimental asset markets in which dividends were drawn from a known discrete distribution. While we still detect some mispricing, asset price bubbles are significantly smaller when dividends depend on an observable market process. JEL Classifications: C91, D84 Keywords: Asset Markets, Uncertainty, Experimental Economics The authors thank the International Foundation for Research in Experimental Economics Small Grants Program for providing funding for this project and providing useful comments on an early version of our ideas. We also thank the Economic Science Institute at Chapman University for the use of their laboratory. Cary Deck, Martin Dufwenberg, Shengle Lin, Ryan Oprea, Dave Porter, Andrew Smyth, and participants in seminars at the Southern Economic Association Annual Conference and the Luxembourg School of Finance provided useful feedback. We acknowledge the able assistance of Jennifer Cunningham in recruiting subjects and running the experimental sessions, and Kyle Bjordahl for programming (and re-programming) our software. All remaining errors are our own. Department of Economics, University of Arizona. tjaworski@gmail.com Corresponding Author: Department of Economics, Simon Fraser University. ekimbrough@gmail.com.

3 I Introduction In financial markets, information about the value of a firm is gradually revealed as traders observe the actions of managers and receive feedback on the firm s profitability. In a class of asset pricing models, firm value is derived from (rational) expectations about the future dividend stream provided to shareholders. These models often assume that dividends are generated by a random process with a known distribution (or that share values follow a random walk). However, fundamentally, financial market investments reflect beliefs about the behavior of people, e.g., employees, managers, and CEOs, who are themselves reacting to information about the state of the firm and the market. Thus, traders of a single firm s stock must form expectations about the firm s future profitability, taking into account both the randomness of future events and the decisions of managers. How the resulting uncertainty affects the informational efficiency of asset markets (i.e., how closely asset prices correspond to asset values) is an important open question. We report the first experimental asset markets (that we know of) in which asset values depend on the behavior of a firm in a linked product market. In a standard experimental asset market, traders buy and sell shares of a finitely-lived asset that pays a dividend at the end of each period. Dividends are drawn from a known discrete distribution and the tendency of these markets to produce substantial price bubbles is well documented (e.g. Smith, Suchanek and Williams 1988). Surprisingly, despite extensive replications of, and variants on this design, no previous studies have used real market activity, to determine the dividend process that underlies fundamental value. In our environment, an experimental subject sets prices as a product market monopolist selling units of an identical good to a sequence of demand-revealing robot buyers and may 1

4 change his price in real-time as buyers approach and choose whether to buy. We record the transaction history over 15 periods in this market, and replay the data to asset traders who own shares of the firm. This design allows us to perform multiple replications of asset market trading on data from a single product market to reduce the impact of idiosyncratic asset market behavior. Traders in the asset market may buy and sell shares as information about the dividend is revealed in the product market s transaction history. At the end of each trading period, each share pays a dividend equal to the monopolist s total profit divided by the number of shares available. In two treatments, we vary the production costs faced by the monopolist to observe whether asset prices accurately reflect the underlying value of a share. Our design moves experimental asset market research in a direction that more nearly approximates the problem faced by traders in financial markets. The tradeoff is that the expected impact of the additional uncertainty we induce on contract prices is not immediately obvious. In the standard asset market environment, the expected value of the asset is painstakingly communicated to traders. Therefore, uncertainty only exists with respect to the actions of other traders. With the introduction of a market-based dividend, traders also face uncertainty about present and future product market conditions. While this uncertainty is eventually resolved by continued observation of the firm, traders must make decisions prior to this resolution if they hope to profit from their trades. On the other hand, the gradual revelation of information about the value of a share via regular updates on the transaction history of the firm may provide a source of common expectations and subdue speculative tendencies. For our empirical analysis, we collect data on 18 experimental asset markets, and we 2

5 compare observed prices to benchmarks for asset value analogous to the benchmark used in previous work. We observe significant deviations between each period s closing price and share value in only 8 of 18 markets, suggesting that despite fundamental uncertainty about the value of a share, the market regularly aggregates information about the firm into a price that reflects underlying value. Moreover, in direct comparisons with a database of 34 previous asset market experiments, our market-based dividend process leads to shorter, smaller and less intense bubbles, even among inexperienced subjects. This finding is robust to varying the underlying product market structure. Thus, well-known results on the prevalence of bubbles may be partly due to the distinctive nature of the dividend processes typically employed in these asset markets. II Literature Review According to the efficient markets hypothesis, asset prices will fully reflect the underlying value of a share. Empirical analysis based on comparisons of national stock market data with observed dividends yields mixed results (Fama 1970; Shiller 1981; Blanchard and Watson 1982; Diba and Grossman 1988; and West 1988), so to evaluate this hypothesis, some researchers have turned to the laboratory. Smith, Suchanek, and Williams (1988; hereafter SSW) and many others show that a bubble-crash price pattern is a recurring feature of a particular multi-period asset market environment. Bubbles emerge in early trading periods, inflate rapidly, and crash when traders expectations converge so that prices reach fundamental value in the final periods. In a standard laboratory asset market, the dividend process is similar to the configuration used by SSW in which share returns are independent of economic activity: at the end of each trading period, each share pays an amount chosen by a single draw from a known discrete 3

6 distribution in which each outcome is equally likely. To explain the frequent occurrence of bubbles in this environment, previous research considers the impact of divergent or incorrect initial expectations (Caginalp, Porter, and Smith 2000; Haruvy, Lahav, and Noussair 2006), the role of traders market experience (Van Boening, Williams, and LaMaster 1993; Dufwenberg, Lindqvist, and Moore 2005), and the initial endowment of cash and shares (Caginalp, Porter, and Smith 1998). While experience typically dampens bubbles, Hussam, Porter, and Smith (2008) show that varying the dividend distribution and introducing additional liquidity can rekindle asset market bubbles even among experienced subjects. Attempts to eliminate mispricing by altering the market institution have revealed the bubble-dampening effect of futures contracts (Porter and Smith 1995; Noussair and Tucker 2006) and short sales (King, Smith, Williams, and Van Boening 1993; Haruvy and Noussair 2006). In an attempt to disentangle the joint effects of speculative trading and trader irrationality, Lei, Noussair, and Plott (2001) restrict traders to be either buyers or sellers, so that traders are unable to engage in speculation. In this restrictive environment, they nevertheless observe bubbles and conclude that mispricing is due to trader irrationality. In a different vein, to control for price variability resulting from uncertainty about an asset s future value, Noussair, Robin and Ruffieux (2001) report asset market experiments in which fundamental value is constant over the life of the asset, and they too find evidence of significant mispricing. Recent experiments by Kirchler, Huber and Stockl (2011) suggest that mispricing in standard implementations of both declining- and constant-fundamental value environments results from subject confusion because they are able to eliminate bubbles by reframing the experiment so that shares represent claims to an exhaustible resource rather than stocks. In this paper, we design an experimental asset market in which traders observe the costs, pricing decisions, and profits of a monopolist firm as it is approached by a sequence of buyers, 4

7 which together with the known total number of shares, determines the dividend per share. Thus, the dividend depends directly on the actions of a firm. This process introduces dividend uncertainty since traders observe the firm in real time and can only imperfectly forecast future profits. 1 From the point of view of the experimenter, it is straightforward to calculate the expected value of a share, but the actual dividend process faced by traders determined by the pricing decisions of another experimental subject is unknown (and unknowable). While we are skeptical that traders behavior can be solely attributed to confusion or irrationality, 2 our results provide additional support for the idea that the context of asset trading is an important determinant of the informational efficiency of the market. By inducing dividends with a market process, our design creates a trading environment nearer to that faced by traders in financial markets, and our results indicate that this context significantly reduces mispricing. III Experimental Design The experimental design consists of two separate environments: a product market and an asset market. In each of 15 trading periods, 60 demand-revealing robot buyers enter the product market in sequence and attempt to buy a single unit of a fictitious good from a monopolist who may change his posted price at any time. We collect data in four product market sessions, two in which the monopolist faces a constant cost of production in each period, and two in which costs vary cyclically across periods, though the monopolist is unaware of these facts in both treatments. We record the real-time pricing and transaction 1 Lin and Rassenti (2011) report under-reaction of prices to new information in a recent experiment in which traders buy and sell shares of a risky (but not uncertain) asset that pays a terminal dividend, the value of which is slowly revealed over the course of the trading period. 2 It only takes one confused trader to create self-confirming expectations of price increases among the other traders, which may be sufficient to inflate a bubble. 5

8 history for each monopolist so that we can replay the entire history to traders in the asset market. In the asset market, 9 traders buy and sell shares of an asset that pays dividends based on the decisions of the product market monopolist. Specifically, the cumulative profit earned on sales to all buyers in a period determines the dividend paid per share of the asset. We replay the product market data to traders as they buy and sell shares of the firm in the asset market. In each period, they observe the monopolist s cost, and as each buyer enters the market, they observe the posted price and the accumulated profit in real-time. Thus, information about the value of the dividend trickles in over the course of a trading period, and all uncertainty about the dividend has been resolved by the end of a period. Like a monopolist in the product market, traders face fundamental uncertainty about the future conditions of supply in the product market. Thus, they must form asset value expectations based on inferences about the future behavior of the monopolist in the shadow of uncertainty about future market conditions. 3 The remainder of this section describes the design of the product and asset markets in detail. III.A The Product Market In each product market session, one subject acts as a monopolist seller of a fictitious, made-to-order good in 15, 60-second periods of a posted offer market populated with fully demand-revealing robot buyers (see e.g. Deck and Wilson 2003, 2006). 4 The seller observes his costs for the period and sets an initial market price; then throughout the period, that price 3 Note that decisions in the asset market have no bearing on outcomes in the product market, so our environment models a situation in which the firm is not an active trader of its stock. 4 We chose a monopoly for the product market, rather than a duopoly, to abstract away from the effects product market competition may have in this setting. However, as we note in the conclusions, it will be interesting to extend this environment to the case of many firms. 6

9 can be costlessly adjusted in response to buyers decisions. Since we are primarily concerned with the data output from the product market for purposes of generating a dividend in the asset market, we reserve detailed description of the subject interface and experimental procedures for Appendix I and instead highlight the relation between the product market and the dividend process. In each trading period t T = {1, 2,..., 15}, the monopolist faces a constant per unit marginal cost c t. Fixed costs are assumed to be 0. Each second, one prospective buyer n N = {1, 2,..., 60}, approaches the monopolist attempting to purchase a single unit of the good. Each buyer s value for one unit, v n, is randomly drawn from a uniform distribution with support [v L, v H ]. Each buyer faces a posted price p n that may be adjusted at any time by the monopolist. 5 Hence, for each buyer in a period, the monopolist earns profit p n c t if p n v n π n,t = 0 otherwise (1) and the total profit earned by the monopolist in period t is n N π n,t 0. At the end of each period, product market monopolists observe their total accumulated profit up to that point in the experiment. Before the next period begins, they set an initial price. Once the price is set, the next period begins, and this process continues until the end of the session. Note that monopolists were unaware that their decisions would be observed in later asset market sessions. 5 We restrict the seller to set the price at or above the current marginal cost. 7

10 III.B The Asset Market Each asset market session is composed of 9 subjects who trade shares of a finitely lived asset for 15 periods in a continuous double auction market. 6 At the beginning of each 15- period asset market, all subjects receive identical endowments of 1000 cents in cash and 4 shares of the asset. Since traders experience is well-known to play an important role in price formation, each session consists of two 15-period asset markets so that we collect observations on subjects when they are completely inexperienced and after one market s worth of experience. Figure 1 shows the computer interface for the asset market. Cash may be exchanged for shares and vice versa by submitting bids to buy and offers to sell in the Market Order Book. Any new bid (offer) must improve upon the current highest bid (lowest offer) in the market. Subjects with sufficient cash can always buy at the current lowest offer by clicking the Buy button, and subjects with sufficient shares can always sell at the current highest bid by clicking the Sell button. 7 As traders enter bids and make offers to sell, the computer ensures that the sum of a trader s bids does not exceed his available cash and that the number of offers to sell does not exceed his available shares. When a transaction occurs, the share is transferred from the Seller to the Buyer in exchange for cash equal to the accepted price. Then, the transacted bid or offer is removed from the market order book and the highest (lowest) of the remaining bids (offers) becomes the new Buy (Sell) price. A trader s cash and share endowment is displayed in the upper-left corner of the screen. As a trader buys and sells shares, his current cash and share 6 An alternative trading institution is the uniform-price sealed-bid-offer call market. Previous studies find that the two institutions yield similar patterns of bubble and crash (Van Boening, Williams, and LaMaster 1993; Caginalp, Porter, and Smith 2000; Haruvy, Lahav, and Noussair 2007). 7 We do not allow subjects to sell shares short; nor do we allow them to borrow cash. 8

11 holdings update to reflect his current positions. Each trading period lasts for 180 seconds, and at the end of a period, each share of the asset yields a dividend. The dividend per share in each period of our market is determined by dividing the total profit of the product market monopolist in that period by the total number of shares. Figure 2 displays the screen observed by asset market traders at the end of a period. The Asset Math pane displays the monopolist s total profit, the dividend per share, and the trader s total dividend earnings in the period. Dividends are added to each trader s cash endowment for the following period, and the market order book is cleared. Once subjects have reviewed their earnings and indicate that they are ready to go on, the next trading period begins. This process continues until the 15 th period ends, at which point the market closes, the final dividend is paid, and the assets are worth nothing. III.C Integrating the Product and Asset Markets Subjects trading in the asset market observe the accumulation of profit in the product market in real time and may use this information to determine at what prices they are willing to buy and sell shares of the asset. In practice, observation means that in each period, the asset market traders learn the outcome of each prospective buyer s arrival in the product market by observing the panel labeled Firm A Market Info in Figure 1. In order to make our market comparable to previous asset market experiments (while shielding our product market sellers from abject boredom by reducing the time they had to spend in the lab), we replay the product market session at 1/3 speed (i.e. one buyer arrives every 3 seconds 180-second periods) so that asset market traders in period t may observe p n, c t, and π n,t v n p n for each buyer n N. As each buyer arrives in the market, the Sale bar either 9

12 flashes green to indicate that a transaction occurred or remains blank to indicate that the buyer chose not to purchase. Accumulated profit is displayed so that after the arrival of the j th buyer, the box labeled Total Profit displays j n=1 π n,t, and we also provide subjects with the ratio of consummated product market transactions to j. Prior to the session, we inform asset traders about the values v L and v H so they know whether each p n is feasible. Given this information, subjects may trade shares of the asset continuously as they observe the outcomes in the product market. Finally, each share in the asset market pays a dividend based on a proportion of the firm s total profit at the end of each period in the product market. Specifically, if S is the total number of shares in the asset market, the dividend d t, in period t is given by: d t = n N π n,t S 0 (2) The structure of the product market outlined above (i.e., the number of potential buyers, the distribution of buyer values, and the seller s marginal cost) defines the price-setting problem faced by the seller. And from the point of view of the experimenter, the profit maximization problem can be solved using standard techniques, and the solution implies the expected value of the dividend. Since the number of remaining periods is finite and always known, it also implies the fundamental value of the asset in each period. The next subsection derives two benchmarks for the value of a share. 10

13 III.D The Value of a Share In the product market experiments, firms have incomplete information about the distribution of buyer values 8 and about future costs, so solving for an equilibrium price from the point of view of our subjects would require making unjustifiable assumptions about beliefs. Nevertheless, with the benefit of full information, it is straightforward to compute the equilibrium price charged by a risk-neutral, profit-maximizing monopolist: p t = v H + c t 2 (3) This price provides a benchmark against which we can judge to what degree our monopolist firms earned the profits that were potentially available to them, which we will refer to as fundamental value (F V ). Given the equilibrium price, when the seller faces N buyers, the expected profit per period is: [ E n N π n,t ] = P r(v n,t p t )(p t c t )N = ( v H c t 2 ) 2 v H v L N (4) and the F V of the firm is the total expected profit of a firm that lives for T periods: F V = E(Π) = t T ( v H c t 2 ) 2 v H v L N (5) 8 They know only the maximum possible buyer value and that all values are at least 0. For present purposes, it is unimportant whether firms have perfect information because the role of the product market is simply to generate a dividend process that can be replayed to the asset traders. 11

14 Therefore, the initial fundamental value of one share of the asset is f = F V, and the S fundamental value of a share in period t is just the expected value of the dividend for the remaining periods: f t = T t=t ( v H c t 2 ) 2 v H v L N (6) However, the realized value of the asset (which is the true value of a share traded in our asset market) is derived from the drawn values of the buyers and the firm s actual pricing decisions, which may or may not be in equilibrium. Thus, the realized value (RV ) of the firm is given by: RV = Π = t T π i,t (7) i I And the realized value of a share is just r = t T d t. We define the realized value of a share in period t as the sum of as yet unrealized dividends: r t = T t=t d t (8) These two measures constitute alternative metrics for evaluating the informational efficiency of the asset market. Under a version of the rational expectations hypothesis that typically sets the standard of comparison in experimental asset markets, the price of a share of the asset should be equal to the future expected dividend stream of the asset. However, since traders face uncertainty about (1) seller behavior and (2) future seller costs in the product market, it is unclear what should be the source of these expectations. Our metrics, 12

15 which we refer to as fundamental value (f) and realized value (r) capture this tension. 9 Below, we test which of these metrics provides a better benchmark for trading behavior, which in turn depends on the information available to traders. III.E What Are Traders Told? It is useful to review the information that traders in the asset market receive during the instructions or have displayed to them through their computer interface during the experiment. First, traders are told that each asset market session will last 15 periods. Second, the computer interface always displays the current period, the time remaining in that period, the trader s current cash and asset holdings, and the history of asset market transactions for that period. Third, the computer interface also shows current conditions in the product market: the monopolists current selling price and cost, accumulated profit, and the number of completed sales out of the number of possible sales. Fourth, at the end of each period, traders are shown the monopolist s profit for that period, the per-share dividend, and the total payout to the trader based on the per-share dividend and asset holdings. During the instruction phase, we also provided information on the range of buyer values in the product market (i.e., Each buyer has a randomly assigned, privately known value for the good between 50 and ), although we were not explicit that the distribution was uniform. 10 Our motivation for this approach was previous work in the standard version of the multi-period asset market environment, where traders are typically found to respond 9 While we realize this terminology is nonstandard, we think it captures the flavor of the difference between these two metrics. In a real sense, a share is fundamentally worth its expected value in equilibrium, but to what extent this value is realized depends on the behavior of the monopolist. 10 An oversight on our part provided the asset traders with slightly more information than the monopolists, as monopolists were not informed of the lower bound of the value distribution. As noted above, the lack of information is not a problem for our results because we want to observe how closely asset prices track share value, whether the monopolist prices optimally or not. 13

16 more strongly to knowledge gained through experience than information transmitted by the experimenter. Therefore, after reading the instructions aloud, subjects participate in: 1) three practice periods in which they cannot trade assets and they simply observe product market behavior and how the monopolist s profit is used to calculate the dividend, and 2) two more practice periods in which they may gain experience trading the asset. IV Treatments and Hypotheses The parameter choices for the product market sessions determine our baseline and treatment conditions in the asset market sessions. Since the purpose of the experimental design is to study whether asset prices will reflect information about the product market firm, we fix demand and our treatments vary the firm s marginal cost. Therefore, for all product market treatments, buyer values are drawn from the uniform distribution [v L, v H ] = [50, 250], and we alter market structure by altering unit costs. 11 We chose cost parameters in the product market so that the fundamental value of an asset, if held for the entire experiment, is the same in both treatments. In the baseline sessions, the marginal cost of the product market firm is the same in each period. We refer to these asset markets as constant sessions and the underlying product markets as P M Constant sessions. Specifically, c t = 150 t {1, 2,..., 15} = f constant = In our other treatment, the firm s marginal cost varies across periods as follows: the firm s costs take one of three values in each period c t {High, Middle, Low} = {182, 150, 126}. In particular, 11 We also could have varied demand to produce the same effect, but we chose to alter costs for the purposes of explaining the process to our product market sellers and transmitting the information clearly into the asset market. 12 In these two product market sessions, from the perspective of the monopolist, values were actually distributed U[25, 125] and marginal cost was fixed at 75. To increase the value of the dividend, we then multiplied all values, prices and costs by 2 before inputting the data into the asset markets. Note that given our parameters, this transformation does not change our predictions. We employed this transformation rather than re-running the sessions due to our budget constraint. 14

17 costs change every 3 periods to create a cyclical environment (Middle High Middle Low Middle) such that f variable = f constant = 312.5, but the expected per period dividend is lower when costs are high and higher when costs are low. We refer to these asset markets as variable sessions and the associated product markets as P M V ariable sessions. Each asset market session consists of two 15-period markets. Within the constant and variable conditions, the underlying product market parameters are identical. However, the realized profits in the two 15-period markets are based on the pricing decisions from two different (experimental) product market firms. Since asset market subjects trade shares with dividends based on one product market session when they have no experience and another when they have already been through a 15-period asset market, we refer to the two underlying product market sessions with the constant parameters as P M Constant I (for inexperienced) and P M Constant E (experienced); similarly, the variable product market sessions are called P M V ariable I and P M V ariable E. We conduct four asset market sessions in the constant treatment (8 total markets) and five sessions under variable conditions (10 total markets). Individual markets in the constant condition are referred to as Constant I1, Constant E2, etc., where the number is a unique session-in-treatment identifier that refers to the order in which we ran the sessions, and we define labels similarly for the variable condition. Fundamentally, our experiment is motivated by ambiguous results in previous empirical tests of the efficient markets hypothesis (cf. section 2 above). Experimental methods have provided a controlled means of evaluating the informational efficiency of asset markets and the impact of initial conditions and policy on mispricing, but in our view the decoupling of asset and product markets in standard experimental tests left a substantial gap between the problems faced by traders in the lab and the field. While our design cannot fully bridge that 15

18 gap, we think it provides a step in the right direction. One might argue that basing our asset market dividends on only 4 product markets (2 per treatment) reduces the generalizability of the results, but we chose to trade off comparability between sessions against the possibility of introducing a greater variety of dividend processes. Moreover, the claim that efficient markets will yield asset prices reflecting firm value does not depend on the particular firm or the characteristics of the industry. We compare observed prices to both fundamental value (derived from theoretical considerations) and realized value (which results from the actual decisions of the product market monopolist). Under a strong form of the efficient markets hypothesis, asset prices will fully reflect the value of a share. While evidence from earlier experiments suggests that bubbles are likely, we hypothesize that the introduction of product market activity as a focal point for traders expectations will dampen this tendency and eliminate bubbles. As a corollary, we hypothesize that bubbles will be smaller in our environment than in the standard asset market experiments. Finally, our treatments allow us to compare the effects of real-time product market information on asset prices when underlying economic conditions are both fixed and variable. When the product market is changing, the task of coordinating expectations becomes increasingly difficult. Hence, if our first hypothesis is falsified, then we hypothesize that the additional uncertainty resulting from variable conditions in the product market will exacerbate the bubble. 16

19 V Procedures All subjects were recruited from the undergraduate population of a medium-sized private university in the United States. In total, we recruited 85 subjects: 4 product market and 81 asset market participants were recruited for 1 hour and 2.5 hours, respectively. We conducted 4 product market sessions of 1 subject each and 9 asset market sessions of 9 subjects each. The past experience of product market participants was unrestricted while asset market participants had never participated in an asset market experiment. Upon arriving at the laboratory, subjects were seated at visually isolated computer terminals. In the product market sessions, subjects read through self-paced instructions. In the asset market sessions, a monitor read the instructions aloud while subjects followed along on their computer screens. Subjects were free to ask questions at any point during the experiment. Copies of the instructions are available in Appendix II below. The instructions were divided into two parts. In the first part, subjects learned about the dividend process and how they would receive information about the behavior of the firm. After this part, asset market participants took part in three observation periods, in which they familiarized themselves with the dividend process by observing the profit stream of a simulated firm in the Firm A Market Info panel. The realizations of profit from each buyer and the accumulated profit in each period were translated into a dividend as described above, and subjects were shown how these dividends were added to their cash according to Figure 2. Next, the monitor read the subjects a second set of instructions that described how to submit bids, offers and initiate trades in the asset market. Upon completion of these in- 17

20 structions, subjects took part in two unpaid practice periods in which they traded assets and familiarized themselves with the experimental interface in Figure 1. After the practice periods, the monitor reviewed a summary sheet reiterating the major points in the instructions. If subjects had no more questions, the first of two 15-period markets began. At the completion of the first market, subjects observed their total earnings. Once subjects indicated that they were ready to go on, the experiment was restarted and the monitor began the second 15-period asset market. Subjects were paid in USD based on their decisions in the experiment plus a $7 show-up payment. On average, subjects earned $25.94 in the product market sessions and $38.35 over two markets in the asset market sessions (min = $1.25, max = $77.50), excluding the show-up payment. Asset market sessions lasted approximately 150 minutes and product market sessions around 45 minutes. VI Results Figure 3 displays time series of posted price along with the profit-maximizing price for each period of the P M Constant sessions (3a-b), and the P M V ariable sessions (3c-d). Figure 4 displays the path of fundamental (f) and realized value (r) of assets derived from each of the product market sessions. Figure 4a shows f and r for the P M Constant sessions, and figure 4b shows the same data for the P M V ariable sessions. Table I displays the dividend in each period of each product market treatment, which together sum to the realized value. In both treatments, the realized value of an asset is less than the fundamental value because product market monopolists charge prices consistently lower than the profit-maximizing price. 18

21 Our results test a number of different hypotheses about price formation. Two potential outcomes of the market process in this environment could be considered informationally efficient (in the sense of prices correctly representing the value of a share): (1) subjects trade at prices equal to fundamental value or (2) they accurately react to the endogenous flow of market information and price according to the realized dividend stream. To compare observed prices to these metrics, we report regressions of mean and closing contract prices on fundamental and realized value. 13 VI.A Determinants of Asset Prices Let P i,t be the mean (closing) contract price in period t of the i th market, and let f i,t and r i,t be the fundamental and realized value of an asset in period t of market i. We estimate the following linear models with market fixed effects (s i ) and standard errors clustered by experimental session: P i,t = α 0 + β 0 f i,t + s i + ε i,t (9) P i,t = α 1 + β 1 r i,t + s i + ε i,t (10) If asset prices reflect fundamental value, then α 0 + s i = 0 in (9) and β 0 = 1. Similarly, if asset prices reflect realized value, then α 1 + s i = 0 and β 1 = 1. Result 1 Mean and closing contract prices are significantly different from fundamental value ( β 0 1). However, in 8 (10) of 18 markets, mean (closing) contract prices in each period 13 Closing prices provide a particularly interesting case because by the final transaction most of the information from the product market could, in principle, be incorporated into dividend expectations. Thus, we might expect these to be most accurate. We also ran the same regressions using the median price, but we do not report them since the results are no different than those for the mean. 19

22 are not significantly different from realized value (i.e. α 1 + s i = 0 and β 1 = 1). Evidence: Columns 1 and 2 of Table II report estimates of equation (9) where the dependent variables are mean and closing contract prices, respectively. First, Wald tests reject the hypothesis that the estimates of β 0 are equal to one (p-values are and , respectively). Thus, fundamental value (f) does not appear to account for asset prices in this environment. Columns 3 and 4 report analogous estimates of equation (10). In both columns, Wald tests indicate that estimates of β 1 are not statistically different from one (p-values are and , respectively). Thus, in general, observed contract prices over time are driven by product market dividend realizations. However, this indicates only that the level of prices moves with the change in future expected dividends. The average price level may still be above (or below) realized value (r) if α 1 + s i 0. Thus, in equation (10) for each market i we test the hypothesis that the sum of the market fixed effect and the constant term (which is the fixed effect for market 1) are equal to 0. Using mean prices, we reject this hypothesis (p-value < 0.1) in 10 of our 18 markets, 6 of which come from the variable treatment, which suggests that many of our markets trade at mean prices greater than realized value. However, if we compare realized value to closing prices, which better capture the information aggregated over the course of a trading period, we reject the null hypothesis in only 8 of the markets, 6 of which are from the variable treatment. This provides evidence that many of our markets eventually aggregate information about the value of a share into the market price. Figure 5 displays the deviation of mean contract price from realized value by period for each session in the Constant treatment. Panel (a) shows deviations for inexperienced subjects, and panel (b) shows the same data for once-experienced subjects. Figure 6 displays the same deviations for the variable treatment. From the figures it is clear that a non- 20

23 negligible subset of our experimental asset markets display the familiar bubble and crash pattern observed in previous asset market literature. Thus, we also explore to what extent our environment displays predictable price dynamics similar to those observed in previous asset market experiments. VI.B Price Adjustment One hypothesis for the presence of asset price bubbles is that traders form endogenous expectations of capital gains. To estimate the impact of such expectations on price dynamics, SSW formulate what they call the lagged Walrasian adjustment hypothesis, which predicts that price changes in period t are driven by excess demand in period t 1, i.e., traders incorporate market activity into their notion of share value. Under this hypothesis, when prospective buyers submit many bids that are rejected by sellers, prices will increase in the following period as buyers adjust their price expectations upward and increase their subsequent bids. Similarly, the presence of excess supply, in the form of relatively many rejected asks, indicates to prospective sellers that they should reduce their subsequent asking prices. To test this hypothesis, SSW ask whether a count of lagged excess bids predicts the direction and magnitude of next period price movements. In their markets displaying a bubble and crash pricing pattern, they find strong evidence that a market thick with bids relative to asks tends to display increasing prices and that a relative thinning of bids (indicating sellers desire to unload assets) precedes the eventual crash. We analyze whether price movements in our asset markets can be described by the same Walrasian mechanics. Assuming constant absolute risk aversion (CARA) and the absence of expected capital gains, SSW use the Arrow-Pratt measure of the risk premium to demonstrate that the expected change in price is equal to the expected dividend plus compensation for the average 21

24 risk preference: ( P i,t P i,t 1 ) = E(d i,t ) + ε i,t, where ε i,t is a measure of average risk preference. Then to introduce endogenous expectations of capital gains via the Walrasian adjustment hypothesis, they construct the following measure of excess demand: let B i,t be the number of bids to buy submitted in period t of market i, and let A i,t be the number of asks submitted by sellers. Then excess demand is defined as B i,t A i,t. To compute the impact of excess demand on price adjustment, we estimate separate regressions for each asset market: ( P i,t P i,t 1 ) = α 2 + β 2 (B i,t A i,t ) + ε i,t (11) Thus, under the aforementioned assumptions, our estimate of α 2 should equal the average dividend, and a positive and significant estimate of β 2 will indicate that prices respond to lagged excess demand by increasing when excess demand is positive and decreasing when excess demand is negative. The magnitude of the estimate indicates the speed of adjustment (or the rate at which the bubble inflates and deflates). Result 2 Walrasian adjustment accounts for price movements in our environment, particularly when we observe price bubbles. Evidence: Table III displays the estimation results of equation (11) separately for each session. In general, the results show that sessions with notable bubble and crash patterns (e.g. V ariable I4, Constant I1, and Constant E2) also exhibit large coefficients of Walrasian adjustment, though the majority of our markets have coefficients insignificantly different from 0. Furthermore, in those sessions that do not exhibit the bubble and crash pattern (e.g. Constant E1, Constant E3, and all V ariable E markets), the estimated constant T t term is insignificantly different from E(d) = dt, which provides further evidence that T 22

25 market fundamentals are frequently reflected in asset prices. VI.C Impact of the Market-Based Dividend Behavior in our markets may differ in important ways from previous experiments because our market-based dividend process provides constant feedback about the expected value of the dividend in a given period. Since traders observe as the monopolist accumulates profits, they may find it easier to forecast dividends and also more difficult to find buyers who are overly optimistic about the future value of a share. Thus, we might observe smaller than usual bubbles. On the other hand, our dividend process introduces two kinds of uncertainty about the value of a share: (1) strategic uncertainty about the decisions of the product market monopolist, and (2) parameter uncertainty about the monopolist s future conditions of supply and demand. Introducing uncertainty into the dividend process may impact pricing in either direction. For example, traders may be averse to uncertainty and thus less likely to trade (and less likely to pay high prices); however, this uncertainty may also reduce the ability of traders to correctly form price expectations, and make them more susceptible to herd-like behavior, potentially exacerbating price bubbles. To understand the impact of market uncertainty on asset pricing, we obtained data from a large set of experimental asset markets reported in previous research. 14 Our database consists of statistics collected from 52 asset market experiments. The database includes our 18 markets along with 34 other markets, all of which employ the standard dividend process of SSW. Using this database, we evaluate the effect of our market-based dividend process on 14 In addition to the 18 new markets reported here, our data includes: (1) 4 markets with inexperienced traders from Smith, Van Boening, and Wellford (2000) employing a continuous double auction trading institution (hereafter cda), (2) 6 cda markets, 3 experienced and 3 inexperienced, reported in Van Boening, Williams, and LaMaster (1993), (3) 18 markets, 9 experienced and 9 inexperienced, reported in SSW, and (4) 6 unpublished cda markets, 3 experienced and 3 inexperienced, from a replication of SSW performed at George Mason University in 2007 by Shengle Lin. 23

26 asset price bubbles in markets employing the continuous double auction trading institution. To facilitate comparison across experiments we compute the following four normalized bubble characteristics (Hussam, Porter, and Smith 2008): 1. Amplitude measures the trough-to-peak change in market asset value relative to share value. Formally, A = max{(p t r t )/E : t = 1,..., 15} min{(p t r t )/E : t = 1,..., 15}, where P t is the mean contract price in period t; r t is the value of the asset in period t; and E is the expected dividend value over the life of the asset. 2. Duration captures the consecutive number of periods in which market price increases relative to share value. Formally, D = max{m : P t r t < P t+1 r t+1 < < P t+m r t+m }. 3. Turnover measures trading activity in each market session. Formally, T = V t is trade volume in period t and S is the total number of shares. t Vt S, where 4. Market Value Amplitude is the normalized market value of trade. Formally, M = max{[(p t r t )/E]V t : t = 1,..., 15} min{[(p t r t )/E]V t : t = 1,..., 15}. 15 To assess the impact of a market-based dividend process, the V ariable treatment, and subject experience on the nature of bubbles, we employ seemingly unrelated regression (SUR) to estimate a system of four equations. The dependent variables are the four bubble characteristics described above, and the independent variables in each equation are dummy variables for the market-dividend process and the V ariable treatment. We also include a dummy variable for once-experienced sessions and interact the once-experienced dummy with each of the other variables. The excluded group includes subjects in the continuous double auction trading institution with a stochastic (non-market) dividend process and no experience. The results are reported in Table IV. 15 Computing amplitude, duration and market value amplitude in our sessions relative to fundamental value, f, instead of realized value, r, does not substantially alter our results, except that the sign of the estimated coefficient on Duration switches. This effect is due to the fact that market prices are actually below fundamental value in many cases since they nearly track realized value, and the definition of duration does not depend on whether prices deviate in a positive or negative direction. 24

27 Result 3 The market-dividend process significantly reduces bubble amplitude, duration, turnover and the market value of bubble amplitude. Evidence: The coefficients on the market-dividend dummy and interaction of the marketdividend dummy and the once-experienced dummy are given in rows 1 and 2 of Table IV, respectively. In row 1 the coefficient in each specification is significantly different from zero at at least the ten percent level. This suggests that the market-dividend process reduces the magnitude of asset market bubbles relative to sessions with a stochastic dividend process and subjects with no experience. The coupled effect of lower amplitude and less turnover drives the large estimated effect of the market-based dividend on market value amplitude. Finally, note that none of the interactions in row 2 are statistically significant, suggesting that effect of experience is no different for traders facing a market-dividend process. Result 4 The Variable treatment has no additional effect on any of the bubble characteristics. Evidence: Rows 3 and 4 of Table IV present the coefficients on the V ariable treatment dummy and its interaction with the once-experienced dummy, respectively. The V ariable treatment, with and without experience, exerts no additional influence on bubble characteristics. While the positive sign on the coefficients of amplitude and market value amplitude is consistent with the idea that increased uncertainty has a positive effect on bubble size, the effects are not statistically significant. This result suggests that strategic uncertainty about the decisions of the product market monopolist may override parameter uncertainty about the monopolist s future supply and demand conditions in our setting. Finally, as has been observed repeatedly, experience significantly reduces the magnitude of mispricing and the total market value of bubble trades. 25

28 VII Discussion We study the effect of a market-dividend process on asset price dynamics in experimental asset markets and contrast it with the stochastic dividend process used in previous research. In our environment, we observe instances of the bubble-crash pattern typical of experimental asset markets. However, when we compare our sessions directly to previous sessions that employ the stochastic dividend process, we find that the market-dividend process dampens asset market bubbles, even among inexperienced subjects. Moreover, while we observe price adjustment based on excess demand metrics that account for the endogenous development of (speculative) expectations of capital gains, particularly in our sessions that exhibit the largest degree of mispricing, our results suggest that for many of our sessions speculation is not driving observed contract prices. Instead, we find that closing contract prices in each period of our market-dividend sessions frequently reflect the underlying value of the asset. Our experiments generate asset market bubbles that are smaller, do not last as long, and are accompanied by less trading activity, than sessions with a stochastic dividend process that are otherwise similar. We attribute the dampening effect of the market-dividend process to two features of the experimental design, though our design does not allow us to disentangle their separate effects: (1) the arrival of real time information about the underlying profitability of the firm generating the dividend, together with (2) the important role of trading context in coordinating expectations. Real time resolution of strategic uncertainty in the product market provides a source of common expectations of the current period dividend which moderates the formation of bubbles, and this is reinforced by the trading context which emphasizes the role of a commonly-observed firm in the determination of dividend values. 26

29 In addition to shedding light on the role of a market-based dividend on asset market bubbles, this paper provides a new experimental platform for studying the interactions between product and asset markets. Since our design introduces multiple design changes to the well-known SSW environment, future research should consider designs that introduce the changes separately, e.g. isolating the impact of gradual information revelation about the value of the dividend on observed prices in the absence of strategic uncertainty about the behavior of a firm. In addition, our results suggest a number of important extensions. In particular, future research could consider the role of product market competition in asset pricing or whether asset prices will accurately reflect differences in firm profitability across different markets. In addition, in the current experiment, we only consider the one-way effect of product market profitability on asset market fundamental value. Extensions to this research could address the crucial role asset markets play in raising and allocating capital and the associated principal-agent concerns. For example, firms might offer stock to finance expansion of production (or cost reductions) in the product market. 27

30 References Blanchard, Oliver J. and Mark W. Watson Bubbles, Rational Expectations, and Financial Markets, in P. Wachtel, ed., Crises in Economic and Financial Structure, Lexington Books: Lexington, MA. Bruguier, Antoine, Steven R. Quartz, and Peter Bossaerts Exploring the Nature of Trader Intuition, Journal of Finance, 65(5), Caginalp, Gunduz, David Porter and Vernon L. Smith Initial Cash/Asset Ratio and Asset Prices: An Experimental Study, Proceedings of the National Academy of Sciences, 95(2), Caginalp, Gunduz, David Porter, and Vernon L. Smith Momentum and Overreaction in Experimental Asset Markets, International Journal of Industrial Organization, 18(1), Deck, Cary A. and Bart J. Wilson Automated Pricing Rules in Electronic Posted-Offer Markets, Economic Inquiry, 41(2), Deck, Cary A. and Bart J. Wilson Tracking Customer Search to Price Discriminate, Economic Inquiry, 44(2), Diba, Behzad T. and Herschel I. Grossman Explosive Rational Bubbles in Stock Prices? American Economic Review, 78, Dufwenberg, Martin, Tobias Lindqvist, and Evan Moore Bubbles and Experience: An Experiment, American Economic Review, 95(5), Fama, Eugene F Efficient Capital Markets: A Review of Theory and Empirical Work, The Journal of Finance, 25(2), Haruvy, Ernan, Yaron Lahav, and Charles N. Noussair Traders Expectations in Asset Markets: Experimental Evidence, American Economic Review, 97(5), Haruvy, Ernan and Charles. N. Noussair The Effect of Short-Selling on Bubbles and Crashes in Experimental Spot Asset Markets, Journal of Finance, 61(3), Hussam, Reshmaan N., David Porter, and Vernon L. Smith Thar She Blow: Can Bubbles Be Rekindled with Experienced Subjects? American Economic Review, 98(3), King, Ronald, Vernon L. Smith, Arlington W. Williams and Mark Van Boening The Robustness of Bubbles and Crashes in Experimental Stock Markets, in I. Prigogine, R. Day, and P. Chen, eds., Nonlinear Dynamics and Evolutionary Economics, Oxford University Press: Oxford, UK. 28

31 Kirchler, Michael, Jürgen Huber, and Thomas Stöckl. Forthcoming. Thar She Bursts Reducing Confusion Reduces Bubbles, American Economic Review. Kogan, Shimon, Anthony M. Kwasnica, and Roberto Weber Coordination in the Presence of Asset Markets, American Economic Review, 101(2), Lei, Vivian, Charles N. Noussair and Charles R. Plott Nonspeculative Bubbles in Experimental Asset Markets: Lack of Common Knowledge of Rationality vs Actual Irrationality, Econometrica, 69(4), Lin, Shengle and Stephen Rassenti Are Under- and Over-reaction the Same Matter? A Price Inertia Based Account, Economic Science Institute Working Paper, Chapman University, Orange, CA. Noussair, Charles, Stephanie Robin and Bernard Ruffieux Price Bubbles in Laboratory Asset Markets with Constant Fundamental Values, Experimental Economics, 4, Noussair, Charles, and Steven Tucker Futures Markets and Bubble Formation in Experimental Asset Markets, Pacific Economic Review, 11(2), Porter, David P., and Vernon L. Smith Futures Contracting and Dividend Uncertainty in Experimental Asset Markets, Journal of Business, 68(4), Shiller, Robert J Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends? American Economic Review, 71(3), Smith, Vernon L An Experimental Study of Competitive Market Behavior, Journal of Political Economy, 70(2), Smith, Vernon L., Gerry L. Suchanek, Arlington W. Williams Bubbles, Crashes, and Endogenous Expectations in Experimental Spot Asset Markets, Econometrica, 56(5), Smith, Vernon L., Mark Van Boening, and Charissa P. Wellford Dividend Timing and Behavior in Laboratory Asset Markets, Economic Theory, 16(3), Van Boening, Mark, Arlington W. Williams, and Shawn LaMaster Price Bubbles and Crashes in Experimental Call Markets, Economics Letters, 41(2), West, Kenneth D Bubbles, Fads and Stock Price Volatility Tests: A Partial Evaluation, Journal of Finance, 43,

32 Tables and Figures Period Fundamental Constant I Constant E Variable I Variable E Average Dividends rounded to the nearest cent. In the experiment, only the sum of dividends was rounded. Table I: Fundamental and Realized Dividends in Cents, by Product Market and Period 30

33 Mean Price Closing Price Mean Price Closing Price F V (0.167) (0.161) RV (0.242) (0.234) ConstantI (Intercept) (27.80) (26.80) (25.18) (24.36) ConstantI (1.77e-12) (2.31e-12) (1.19e-12) (1.13e-12) ConstantI (1.77e-12) (2.31e-12) (1.24e-12) (1.16e-12) ConstantI (1.77e-12) (2.31e-12) (1.23e-12) (1.16e-12) V ariablei (2.242) (2.161) (6.879) (6.655) V ariablei (2.242) (2.161) (6.879) (6.655) V ariablei (2.242) (2.161) (6.879) (6.655) V ariablei (2.242) (2.161) (6.879) (6.655) V ariablei (2.242) (2.161) (6.879) (6.655) ConstantE (0.993) (0.957) (7.734) (7.484) ConstantE (1.80e-12) (2.34e-12) (9.009) (8.717) ConstantE (1.77e-12) (2.31e-12) (9.009) (8.717) ConstantE (1.77e-12) (2.31e-12) (9.009) (8.717) V ariablee (2.242) (2.161) (9.106) (8.811) V ariablee (2.242) (2.161) (9.106) (8.811) V ariablee (2.242) (2.161) (9.106) (8.811) V ariablee (2.250) (2.169) (9.144) (8.847) V ariablee (2.242) (2.161) (9.106) (8.811) R N Standard errors in parentheses. + p < 0.10, p < 0.05, p < 0.01, p < Table II: Contract Prices and Asset Valuation 31

34 Session d t /T α 2 β 2 R 2 ConstantI ConstantI ConstantI ConstantI ConstantE ConstantE ConstantE ConstantE V ariablei V ariablei V ariablei V ariablei V ariablei V ariablee V ariablee V ariablee V ariablee V ariablee Significantly different from d t /T at p < 0.1, Wald tests. Significant at p < 0.1. Table III: Walrasian Price Adjustment, by Market 32

35 (1) (2) (3) (4) Amplitude Duration Turnover MV Amplitude MarketDividend (0.268) (0.961) (1.598) (5.512) M arketdividend Once (0.384) (1.154) (2.286) (7.885) V ariable (0.327) (1.172) (1.949) (6.722) V ariable Once (0.463) (1.658) (2.756) (9.506) Once (0.168) (-0.604) (1.003) (3.461) Intercept (0.112) (0.401) (0.666) (2.299) R N Standard errors in parentheses. Significant at p < 0.1, p < 0.05, p < Table IV: Seemingly Unrelated Regression Comparing Bubbles across Dividend Processes 33

36 Figure 1: The Asset Market Interface 34

37 Figure 2: The Asset Market Interface at the End of a Period 35

38 (a) PM_ConstantI (b) PM_ConstantE Price Price Eq. Price Cost (c) PM_VariableI (d) PM_VariableE Price Price Eq. Price Cost Period Period Figure 3: Posted Prices in the Product Market Sessions (a) PM_Constant (b) PM_Variable Cents FV RV_ConstantI RV_ConstantE Cents FV RV_VariableI RV_VariableE Period Period Figure 4: The Path of Fundamental and Realized Value by Treatment 36

39 (a) Inexperienced (b) Experienced Mean Price Minus Realized Value Constant_1 Constant_2 Constant_3 Constant_4 RV Mean Price Minus Realized Value Period Period Figure 5: Time Series of Deviation of Mean Share Price from Realized Value (Constant Treatment) (a) Inexperienced (b) Experienced Mean Price Minus Realized Value Variable_1 Variable_2 Variable_3 Variable_4 Variable_5 RV Mean Price Minus Realized Value Period Period Figure 6: Time Series of Deviation of Mean Share Price from Realized Value (Variable Treatment) 37

40 Appendix I: Product Market Interface The computer interface for the product market is shown in Figure A1. On the left portion of the screen the monopolist can access a vertical slider to set and change the posted price p i. At the beginning of each period, the monopolist selects an initial price and then clicks the green Set Initial Price button in the bottom left corner. Once the period begins, this price can be changed at any time by clicking on and moving the slider. The graph to the right of the slider displays the per-unit cost, c t, as a red line and the current posted price as a blue line. As buyers approach, a vertical line moves across the graph to provide a visual representation of how many buyers have arrived and how many remain. When each buyer approaches, the graph indicates the outcome by displaying a green-shaded arrows at the posted price when a transaction occurs and nothing otherwise. The Sales Log in the top-middle portion of the screen records the price faced by each buyer, whether a sale was made, and the seller s profit on each sale. To the right, the Status pane tracks the current number of sales and the total period and experiment profit. Finally, in the History pane, the seller observes the profit, number of sales out of the total possible sales, average sale price, and cost in each of the previous periods. At the end of each period, the bar along the bottom of the screen displays the total profit in the most recent period. At the end of a session the subject receives his or her total earnings in cash. Figure 7: The Product Market Interface 38