Recognition of Future News in Earnings and Price Bubbles in Experimental Asset Markets

Abstract

In this article, we use an experimental approach to examine the effect of reporting regimes on asset prices. We examine four different reporting regimes: the no recognition (NR) regime where no expected future cash flows are recognized; the full recognition (FR) regime where both the expected good news and expected bad news pertaining to the next period cash flows are recognized in current earnings; the good news recognition (GR) regime where only the expected good news pertaining to the next period cash flows are recognized in current earnings; and the bad news recognition (BR) regime where only the expected bad news pertaining to the next period cash flows are recognized in current earnings. We find that the NR, BR, and GR regimes are associated with more intense asset price bubbles than the FR regime. We also find that between the BR and GR regimes, the BR regime is associated with more intense asset price bubbles than the GR regime. Our findings shed insights about how biased (non-neutral) reporting regimes could affect the price formation process.

Keywords

asset price bubbles fundamental values recognition of future news neutral accounting fair value accounting

Introduction

A common phenomenon in asset markets is the run-up in prices (i.e., asset price bubbles) followed by crashes.¹ Legislators, regulators, and capital market participants have argued that stock price boom and bust cycles are exacerbated by accounting rules for reporting corporate performance. For example, the stock market crash of 2007 has been attributed to the fair value or mark-to-market accounting—an accounting rule that is premised on the unbiased/neutrality principle. Critics of fair value accounting argue that mark-to-market accounting introduces undesirable volatility in asset prices, which in turn affect real decisions.² The financial crisis in 2007 and the ensuing criticism of fair value accounting resulted in the Financial Accounting Standards Board (FASB) temporarily suspending fair value recognition requirements. Bowen, Khan, and Rajgopal (2009) document that the stock market reacted positively to the suspension of fair value accounting, suggesting that fair value accounting may not be desirable in a crisis.³ This evidence highlights the concerns of regulators and others about the role of accounting in stock price bubbles and crashes. However, there is little systematic evidence on whether and how the recognition of expected future outcomes such as fair values in the reported earnings exacerbates or attenuates stock market bubbles. Our study examines this issue using the experimental approach.

Experimental laboratory asset markets have been used in earlier studies to get insights into stock market bubbles. In their seminal study, Smith, Suchanek, and Williams (1988) document bubbles in laboratory asset market setting and find that in treatments with all or a majority of experienced traders, the price formation process exhibits less bubbles. Based on this finding, they attribute asset market bubbles to the behavior of inexperienced traders violating rational expectation. Lei, Noussair, and Plott (2001) examine whether asset market bubbles are attributable to lack of common knowledge or to individual behavioral characteristics and provide evidence consistent with bubbles being attributable to individual’s behavioral characteristics.⁴ We use the laboratory asset market to examine the effect of different accounting reporting regimes on the formation of stock market bubbles.

We differentiate the reporting regimes based on the recognition of expected future cash flows in the current period earnings because asset prices are determined by expectations of future cash flows.⁵ We simulate periodic cash flow realizations using a two-step random walk process. In any given period, in addition to the current period cash flow realization, the researchers have information about the first-step outcome. The first-step outcome provides information on whether the next period cash flows are expected to be higher or lower than that of the current period cash flow realization, that is, good news or bad news. Then conditioned on the first-step outcome, the actual realization of cash flow occurs in the next period. As such, in any given period the reported earnings can incorporate none, or part, or all of the information on the next period cash flows based on the first step of the random walk process.

In particular, we examine four reporting regimes. In the full recognition (FR) regime, both the expected good news and expected bad news about the next period cash flows are recognized in the current reported earnings. More specifically, in the FR regime, the reported earnings is the average of the expected value of next period’s cash flow based on the first-step outcome and the current period’s cash flow realization. In the good news recognition (GR) regime, only the expected good news pertaining to the next period cash flow is recognized in the current period reported earnings; and similarly, in the bad news recognition (BR) regime, only the expected future bad news pertaining to the next period cash flows is recognized in the current period reported earnings. More specifically, in the GR (BR) regime, the reported earnings is the average of the expected value of next period’s cash flows and the current period’s cash flow realization if the expected value of the next period cash flow is higher (lower) than the current period’s cash flow realization; otherwise, the current period reported earnings is the current period’s cash flow realization. In the no recognition (NR) regime, the future cash flows are not recognized in the current period reported earnings.

The conceptual framework project of the International Accounting Standards Board (IASB; 2013) emphasizes representational faithfulness as the recognition criterion. For example, QC 14 of IASB prescribes unbiasedness as follows: “A neutral depiction is not slanted weighted, emphasized, de-emphasized or otherwise manipulated to increase the probability that financial information will be received favorably or unfavorably by users.” Accordingly, neutrality implies that the recognition criteria should apply symmetrically to good news and bad news as in the FR and NR regimes. Compared with the FR and NR regimes, the GR and BR regimes are upward biased and downward biased, respectively, and are hence non-neutral.

We run eight trading sessions, two each with two different cash flow realizations for each of the four regimes. Each trading session spans 50 periods with about 40 traders. To avoid issues of framing, we do not label the reporting regimes in our experiment instructions—we provide a description of how the reported earnings are computed.

We expect traders to make adjustments to reported earnings in reporting regimes where partial information about the future cash flows is provided as in the GR and BR regimes. In these regimes, the traders are likely to de-bias the earnings or incorporate their subjective probability assessment of good and bad news in the BR and GR regimes, respectively. Similarly, traders are likely to make adjustments to incorporate their subjective probability assessment about future cash flows in the NR regime. These adjustments are noisy and thus are likely to exacerbate asset price bubbles. In essence, relative to the other regimes where future information is either not made known (NR) or provided in a biased manner (BR and GR), we expect the traders to make the least amount of adjustments to incorporate their subjective view of the future in the FR regime. Based on these arguments, we expect the least asset price bubble in the FR regime.

In the BR and GR regimes, we expect the traders to undo the downward and upward biases in the reported earnings, respectively. These adjustments to undo biases are likely to be more in the BR regime than in the GR regime due to optimism bias. Optimism bias is defined as the overestimation of the probability of good future prospects and underestimation of the probability of bad future prospects, and has been documented in psychology, biology, and finance (Barefield & Comiskey, 1975; Calderon, 1993; Sharot, 2011; Slovic, 2000; Slovic, Finucane, Peters, & MacGregor, 2002; Weinstein, 1980, 1982). In particular, if the traders are optimistic about the future prospects of the firm, they are more likely to attribute the downward bias in the BR regime to non-recognition of expected future good news and are less likely to attribute the upward bias in the GR regime to the non-recognition of expected future bad news. Thus, the optimism bias is likely to exacerbate the asset price bubble in the BR regime compared with the GR regime.

Alternatively, traders could exhibit more risk seeking in the BR regime than in the GR regime, because traders are likely to be willing to hold larger amounts of the risky asset in the BR regime in anticipation that the next period’s cash flows from the risky asset are likely to be high. In contrast, the next period’s expected cash flows are likely to be lower in the GR regime. This differential expectation of future cash flows is likely to lead to a greater demand for the risky asset in the BR regime than in the GR regime. Thus, we expect a larger asset price bubble in the BR regime compared with the GR regime.

Following Stöckl, Huber, and Kirchler (2010), we use seven metrics to measure the intensity of asset price bubbles: price amplitude (PA), total dispersion (TD), average bias (AB), Hassels R² (HR²), duration, relative absolute deviation (RAD), and relative deviation (RD). For each reporting regime, we compute the intensity of asset price bubble. PA measures the trough-to-peak change in market price relative to the fundamental value normalized by the initial fundamental value. TD (AB) is the sum of the absolute (signed) deviations of prices from fundamental values. HR² is the R² of the regression of the price and fundamental value, and thus is an inverse measure of price deviation. DUR is the maximum number of consecutive periods that the difference between the price and fundamental value increases and is indicative of the length of bubbles. RAD (RD) is similar to TD (AB) and measures the average absolute (signed) level of deviation of prices from the fundamental value. The fundamental values in each period are computed as the realized cash flows discounted by the risk-free rate (4%).

Consistent with our prediction, we find that the FR regime exhibits the smallest asset price bubble based on the PA, TD, AB, RAD, and RD measures, but not so based on the HR² and DUR measures. The HR² measure captures the variance in prices that is explained by the fundamental value, that is, the realized cash flows; and thus, even if the prices are negatively correlated with the fundamental value the R² can be high. The DUR measure captures the momentum and as such may not capture the intensity of the bubble. Thus, overall our evidence suggests that the FR regime exhibits the lowest asset price bubble. The BR regime exhibits the largest asset price bubble followed by the NR and GR regimes. Our debriefing survey of the traders shows that in the FR (NR) regime compared with the other regimes, traders place more (less) weight on current as well as historical earnings. Collectively, our results suggest that deviations from neutral recognition could lead to asset market bubbles—and more so with the downward biased reporting regimes than upward biased reporting regimes.⁶

The remainder of the article is organized as follows. Section “Experiment Design and Empirical Expectations” describes the experimental design. Section “Results and Discussion” provides and discusses the results. The last section provides concluding remarks.

Experiment Design and Empirical Expectations

Asset Market

The traders participating in the experiment are volunteers drawn from a pool of undergraduate and graduate business students. Each trader is initially endowed with US$250,000 of cash (risk-free asset) and 100 shares of stocks (risky assets).⁷ Cash balances earn a deterministic risk-free return of 4% per period.

The stock generates cash flow in each period that is determined by a two-step random walk process without drift. In each period, in the first step one of two equally likely states, “Positive” or “Negative,” is chosen randomly (by the program), where each state has a probability of .50. Conditioned on the Positive or Negative state, in the second step the realized cash flow per share for the period can either be higher (UP) or lower (DOWN). If the state is Positive, then the probability of UP is .9; and correspondingly, if the state is Negative then the probability of DOWN is .9. The realized cash flow in a period is given by 1.25 × Previous period cash flow per share when the realization is UP; and 0.75 × Previous period realized cash flow per share if the realization is DOWN. This process is illustrated in Figure 1. The vertical line in Figure 1 indicates the time when reported earnings are released to the traders. We use the two-step random walk cash flow generation process as the basis for all the reporting regimes. For all the reporting regimes, we start with US$100 cash flow per share.

Figure 1.

Reported earnings: The two-step random walk process of cash flow realization.

The earnings reporting regimes and the information provided to the traders are described in the next section. All traders are informed about the random walk process for cash flow realization and the way the earnings information is computed for their regime. At the beginning of every period, before the commencement of trading, each trader is provided with earnings information derived by applying the accounting recognition rule. At the end of each trading period, the reported earnings proportional to their shareholdings are added to the traders’ cash balance.

Each trader is allowed to submit a limit order to buy and/or sell shares that specifies the number of shares and the maximum purchase/minimum sale price per share. The trader could also submit a null order if he or she does not want to trade in that period. Once all the orders are placed, the bids and asks are aggregated into a pseudo-demand and supply function, respectively; and the intersection of the demand and supply function determines the market-clearing asset price. Specifically, the market-clearing price is such that it maximizes the number of trades and in the case of multiple market-clearing prices, the lowest one gets selected.

At the end of the final trading period, the stock’s terminal value is determined by the terminal period cash flow capitalization model, that is, the present value of the terminal period cash flow discounted at the risk-free rate (final period cash flow over the risk-free rate). Thus, at the end of the final period, the traders’ portfolio value is the sum of their cash holding and the stock holding valued at the terminal value. Till the end of the trading periods, the measurement of the portfolio value is in experimental currency units. At the end of the final trading period, each participant is paid in cash an amount that is proportional to the total portfolio value including both the cash and stock holdings plus an initial show-up fee.⁸

The experimental setting is an across-subject design in that the four reporting regimes are run on different cohorts of traders. For each reporting regime, the experiment is conducted twice (in two sessions) on different cohorts of traders to reduce the attribution of the results to any particular cohort. Overall, we ran eight trading sessions with 50 trading periods each with the number of trading periods specified at the beginning of the experiment for each session.

Information and Accounting Regimes—The Treatment

We examine the following four reporting regimes:

NR: The current period realized cash flow is reported to all the traders. No information is provided about the next period’s expected cash flow. This is the no-information regime and is similar to the asset market of Smith et al. (1988) with common value.

FR: In this regime, the expected cash flow conditional on the first step of the random walk process, that is, the next period’s “Positive” or “Negative” state, is aggregated with the realized current period cash flow. The next period expected cash flow is computed over the probabilities of the second step, that is, UP or DOWN. More specifically, if the Positive state has occurred in the first step, then the expected next period cash flow is given by $E (C_{t + 1} | Positive) = p (1 + x) C_{t} + (1 - p) (1 - x) C_{t}$ , where C_t is the cash flow in period t, p is the probability of the UP state in the second step, and E(.) is the expectations operator. Similarly, if the Negative state has occurred, then the expected next period cash flow is given by $E (C_{t + 1} | Negative) = (1 - p) (1 + x) C_{t} + p (1 - x) C_{t}$ . In particular, p and x are set at .9 and 0.25, respectively. The current period earnings reported in the FR regime is the average of the expected next period cash flow and the current period realized cash flow. As such, the reported earnings amount includes both the good news (Positive) and bad news (Negative) information in an aggregated form. The FR regime is neutral in the sense that both the good news and the bad news are incorporated in reported earnings.

GR: In this regime, the reported earnings is the average of current period cash flow and the expected cash flow of subsequent period if the expected subsequent period cash flow is greater than the current period cash flow. If the expected subsequent period cash flow is less than the current period cash flow, the reported earnings is the current period cash flow. In effect, the reported current period earning contains only the good news but not the bad news; the earnings report is biased upward.

BR: In this regime, the reported earnings is the average of current period cash flow and the expected cash flow of subsequent period if the expected subsequent period cash flow is less than the current period cash flow. If the expected subsequent period cash flow is more than the current period cash flow, the reported earnings is the current period cash flow. In effect, the reported earning includes only the bad news but not the good news; the earnings report is biased downward.

A couple of additional points are noteworthy in our experiment design. First, in our instructions to the traders, we simply describe the process by which earnings are determined and do not label the regimes using any terms with connotations being neutral or biased. We do this to mitigate effects of framing that have been shown to influence behavior of traders’ decision making (Andreoni, 1995; Sonnemans, Schram, & Offferman, 1998; Tversky & Kahneman, 1981). Online Appendix A shows the detailed instructions to the traders. Second, we choose two random realizations of the cash flow process (referred to later as “seeds”) that are derived from the same underlying random walk process and compute the reported earnings for the four recognition treatments, that is, NR, FR, GR, and BR for each of the two cash flow realizations. This ensures that the underlying process generating the cash flow is the same for all regimes. Furthermore, limiting the information about the future to one period and keeping p = .9 reduces the inter-regime differences in the reported earnings.⁹ This design increases the likelihood that the differences we observe in the price formation process are due to behavioral responses rather than due to informational differences among the different reporting regimes.¹⁰

Theoretical Considerations

As the earnings generation process is made known to the traders, we expect traders to adjust the earnings appropriately in estimating the underlying cash flows. In the absence of information, any adjustment is likely to deviate from the actual realization.¹¹ We expect the traders to make adjustments in the GR and BR regimes to incorporate their subjective probability assessments of bad news and good news, respectively. Such adjustments are likely to introduce more noise in the assessments and induce more heterogeneous beliefs among the traders. In a similar fashion in the NR regime, the traders are likely to assess the subjective probability of future information, which also can result in more heterogeneous beliefs. Traders in regimes with less than full information about the future are likely to use the past prices to assess the beliefs of the other traders, and thus trade on momentum strategies rather than reported earnings information.¹² This is likely to result in less intensive asset price bubbles in the FR regime compared with the NR, GR, and BR regimes.

Research in the psychology, biology, and finance literatures has shown that people overestimate the probability of positive events and underestimate the probability of negative events (Barefield & Comiskey, 1975; Calderon, 1993; Sharot, 2011; Slovic, 2000; Slovic et al., 2002; Weinstein, 1980, 1982). In our context, such bias can manifest as a stronger subjective tendency to increase rather than decrease the estimate of the future cash flow. When traders try to back out the realized cash flow from reported earnings, their inferences are likely to differ across the BR and GR regimes. Specifically, in the BR (GR) regime, the traders make adjustments to “correct” the reported earnings by undoing the downward (upward) bias in the reports. However, the traders’ optimism bias could induce an overcorrection in the BR regime by overestimating the likelihood of improved cash flows; while not doing so in the GR regime. This could result in euphoric price increases under BR regime but only relatively cautious price increases under GR regime, resulting in more deviation from the fundamental value in the BR regime compared with the GR regime.¹³

An alternative explanation is that the traders are more risk seeking in the BR regime than in the GR regime. That is, traders are likely to be willing to hold larger amounts of the risky asset in the BR regime, where the next period’s expected cash flows are likely to be higher than in the GR regime, where the next period’s expected cash flows are likely to be lower.¹⁴ Irrespective of whether behavioral bias or risk preferences lead to greater demand for the stock, we expect the asset price bubble to be more intense in the BR regime compared with the GR regime.

Sessions

All the subjects participate in a practice session before the actual experiment to be familiar with the experimental set-up, that is, cash flow and reported earning processes and the trading process. As mentioned earlier, for each reporting regime, we conduct 2 experimental sessions. In all, we conduct 8 trading sessions. For each session, only one reporting regime is used and traders are not allowed to participate in multiple sessions. There were 38 and 43 traders participating for the 2 NR regime sessions; 44 and 42 traders for the 2 FR regime sessions; 30 and 42 for the 2 GR regime sessions; and 41 and 47 for the two BR regime sessions. Online Appendix A contains the instructions provided to the traders for each regime: NR, FR, GR, and BR. Online Appendix B illustrates the screenshots of the trader windows.

Results and Discussion

Figure 2 provides the difference in reported earnings for the FR, BR, and GR regimes compared with that of the NR regime. Specifically, for each reporting regime, we average the reported earnings across the two seeds of cash flows in each period, and then take difference between FR and NR regime, or between GR and NR regime, or between GR and NR regime. The line labeled “ $E (FR) - E (NR)$ ” is the FR regime earnings averaged over the two seeds minus the NR regime earnings averaged over the two seeds for each period. Similarly, the line labeled “ $E (BR) - E (NR)$ ” [“ $E (GR) - E (NR)$ ”] − is the BR [GR] regime earnings averaged over the two seeds minus the NR regime earnings averaged over the two seeds for each period. The difference between the GR and NR regimes’ reported earnings, that is, the line labeled “ $E (GR) - E (NR)$ ” shows that the reported earnings in the GR regime conveys good news compared with the NR regime. Correspondingly, the difference between the BR and NR regimes’ reported earnings, that is, the line labeled “ $E (BR) - E (NR)$ ” shows that the reported earnings in the BR regime conveys bad news compared with the NR regime. The difference between the FR and NR regimes’ reported earnings, that is, the line labeled “ $E (FR) - E (NR)$ ” shows that the reported earnings in the FR regime conveys both good news and bad news as compared with the NR regime.

Figure 2.

Difference in reported earnings relative to that of the NR regime.

Table 1 reports the descriptive statistics of cash flow realizations, reported earnings, and market prices across different regimes. For each reporting regime, we first average these variables across the two seeds of cash flows in each period t. The statistics reported here are based on these averaged values. The mean (median) cash flow realizations are 214 (197) and are the same across the reporting regimes by design. The mean (median) reported earnings in the NR, FR, GR, and BR regimes are 214, 214, 225, and 204 (197, 209, 213, and 193), respectively. Similar to Figure 2, compared with the NR regime, the GR regime conveys good news, that is, has higher mean and median earnings compared with all the other regimes; and the BR regime conveys bad news, that is, has lower mean and median earnings compared with all the other regimes. The FR regime on average has earnings statistically similar to that of the NR regime because it provides both good and bad news.

Table 1.

Descriptive Statistics.

Variable	NR regime			FR regime			GR regime			BR regime
Variable	Mean	Median	SD	Mean	Median	SD	Mean	Median	SD	Mean	Median	SD
AvC_t	214	197	108	214	197	108	214	197	108	214	197	108
AvE_t	214	197	108	214	209	104	225	213	111	204	193	100
AvP_t	12,542	11,750	6,638	7,660	8,225	2,978	10,201	9,575	5,050	16,326	12,000	14,206
AvFV_t	5,359	4,916	2,697	5,359	4,916	2,697	5,359	4,916	2,697	5,359	4,916	2,697
AvP_t/AvE_t	68	55	48	46	30	39	51	40	29	82	50	62

Note. Variable definitions: For each regime, the average cash flow (AvC_t), average reported earnings (AvE_t), average price (AvP_t), and average fundamental value (AvFV_t) in period t are computed by averaging over the two sessions, that is, cash flow seeds. Fundamental value in period t is cash flow discounted by the risk-free interest rate (4%). P/E is the price-to-earnings ratio computed as the AvP_t / AvE_t. NR regime is the no recognition regime. FR regime is the full recognition regime. GR regime is the good news recognition regime. BR regime is the bad news recognition regime. See Figure 1 for the reported earnings in the four regimes and the cash flow realization process.

Choosing the probability p = .9 ensures that the first step in the random walk process is informative. Furthermore, because the first step being informative, the averaging of realized current period and expected next period cash flows makes the reported earnings roughly similar to the cash flow realizations in all the regimes. This helps ensure that the bubbles that we document are not driven by the differential information content across the regimes. In effect, if traders used the reported earnings as a surrogate for cash flows they would have been close to the fundamental value. However, as the traders do not know the cash flow realizations, they are likely to adjust the reported earnings and/or use past prices instead of reported earnings to make their trading decisions.

The mean (median) prices for the NR, FR, GR, and BR regimes are 12,542, 7,660, 10,201, and 16,326 (11,750, 8,225, 9,575, and 12,000), respectively. The mean and median prices are the lowest in the FR regime and highest in the BR regime. The mean (median) price-to-earnings ratios (P/E) for the NR, FR, GR, and BR regimes are 68, 46, 51, and 82 (55, 30, 40, and 50), respectively. The mean and median price-to-earnings ratios are also the lowest in the FR regime and highest in the BR regime (not for the median), primarily because the bias in earnings tends to exacerbate the ordering of prices. This provides an initial indication that the asset market price bubble is the lowest in the FR regime and highest in the BR regime, and is consistent with our expectation. However, compared with the fundamental value mean (median) of 5,359 (4,916) the mean and median prices in all regimes exhibit a price bubble.

Figure 3 shows the price-to-earnings (P/E) ratios for the four regimes over the 50 trading periods. As we run two sessions of different cash flow realizations for each of the four regimes, we compute the average trading price and fundamental value per period over the two sessions for each period t. As the trading session approaches the end, price-to-earnings ratio is roughly 25 for all the four regimes; note that the fundamental value in each of the four regimes is 25 times the earnings. This result suggests that traders understand that the fundamental valuation is based on cash flow realizations and trade near that value when there are few trading periods left. In other words, the deviations from fundamental value seem to be driven by speculation in trading when future trading opportunities are perceived to be abundant and the traders feel that they can “unload” the stock and lock in the trading profits.

Figure 3.

Price-to-earnings (P/E) ratios.

The P/E(NR), P/E(FR), P/E(GR), and P/E(BR) lines in the graph break the price-to-earnings ratio of 50 in periods 6, 38, 22, and 21, respectively, and reach a high value of 220, 160, 160, and 230 roughly around periods 42 and 43. This shows that the asset price bubble is the lowest in the FR regime and highest in the BR regime, which is consistent with the hypothesis.

The differential price-to-earnings ratios across the BR and GR regimes reveal that when traders are aware of a biased recognition of only future bad news, they become more speculative in trading than when there is biased recognition of only future good news. This asymmetry cannot be explained by behavioral responses that are symmetric in bad news and good news. This suggests an optimism bias which, in conjunction with biased loss recognition, generates more speculation. Under BR regime, traders overestimate the likelihood of the accounting report masking future good news. This leads to the speculation that good news will get released later and the prices are bid up on speculation. In contrast, under GR regime, traders do not overestimate the likelihood of the accounting report masking future bad news. This does not lead to a fear that bad news will get released which prevents speculative selling taking place. Therefore, the fall in prices as a result of decrease in reported earnings in the GR regime is modest, whereas the increase in prices as a result of increases in reported earnings in the BR regime is excessive.

In Table 2, we follow Stöckl et al. (2010) and compute seven measures that are used in the literature to provide aggregate measures of the intensity of asset price bubble. As we run two sessions of different cash flow realizations for each of the four regimes, we compute the average trading price and fundamental value per period over the two sessions for each period t. These measures are defined in Panel A of Table 2.

Table 2.

Price Bubble Measures of Reporting Regimes.

Panel A: Price Bubble Measures Definitions.
Measure	Definition
Price amplitude	$PA = [Max (\frac{Av P_{t} - AvF V_{t}}{AvF V_{1}})] - [Min (\frac{Av P_{t} - AvF V_{t}}{AvF V_{1}})] .$
Total dispersion	$TD = \sum_{t = 1, N} \| Av P_{t} - AvF V_{t} \| .$
Average bias	$\begin{matrix} \begin{matrix} AB = \frac{1}{N} \sum_{t = 1, N} (Av P_{t} - AvF V_{t}) . \end{matrix} \end{matrix}$
Hassels R²	$H R^{2} = R^{2} of OLS regression of Av P_{t} = a + b AvF V_{t} + error .$
Duration	$\begin{matrix} \begin{matrix} DUR = Max (N : Av P_{t} - AvF V_{t} < Av P_{t + 1} - AvF V_{t + 1} < \dots < Av P_{t + (N - 1)} - AvF V_{t + (N - 1)}) . \end{matrix} \end{matrix}$
Relative absolute deviation	$\begin{matrix} RAD = \frac{1}{N} \sum_{t = 1, N} \| Av P_{t} - AvF V_{t} \| / \| AvF V_{t} \| . \end{matrix}$
Relative deviation	$\begin{matrix} RAD = \frac{1}{N} \sum_{t = 1, N} \frac{Av P_{t} - AvF V_{t}}{\| AvF V_{t} \|} . \end{matrix}$

Panel B: Price Bubble Measures for the Reporting Regimes.
	NR regime	FR regime	GR regime	BR regime
PA	8.47	4.08	6.30	15.85
Rank PA	III	I	II	IV
TD	366,695	135,089	249,760	565,816
Rank TD	III	I	II	IV
AB	7,182	2,301	4,842	10,966
Rank AB	III	I	II	IV
HR ²	0.23	0.16	0.35	0.42
Rank HR²	III	IV	II	I
DUR	8	12	5	16
Rank DUR	II	III	I	IV
RAD	1.37	0.50	0.93	2.11
Rank RAD	III	I	II	IV
RD	1.34	0.43	0.90	2.05
Rank RD	III	I	II	IV

Note. Variable definitions: For each regime, the average reported earnings (AvE_t), average price (AvP_t), and average fundamental value (AvFV_t) in period t are computed by averaging over the two sessions, that is, cash flow seeds. Fundamental value in period t is cash flow discounted by the risk-free interest rate (4%). NR regime is the no recognition regime. FR regime is the full recognition regime. GR regime is the good news recognition regime. BR regime is the bad news recognition regime. See Figure 1 for the reported earnings in the four regimes and the cash flow realization process. The rank row indicates the intensity of price bubble ranked I (IV) indicates the lowest (highest) intensity.

Price amplitude (PA), introduced by Porter and Smith (1995), measures the trough-to-peak change in price relative to the fundamental value; and thus ignores price deviations in all the other periods. Total dispersion (TD), introduced by Haruvy and Noussair (2006), is a measure of the total magnitude of mispricing. Average bias (AB), introduced again by Haruvy and Noussair (2006), is a measure of the sum of signed values of mean price deviation from fundamental value and therefore provides a measure of overvaluation and/or undervaluation. If the resulting sum is positive (negative), the asset is overvalued (undervalued) on average. The main difference of AB from TD is AB sums up the signed value of price deviation, whereas TD sums up the absolute value of price deviation. In our setting where on average there is no undervaluation, both TD and AB measures will be similar other than for the scaling by 50 for the AB measure and captures the intensity of the asset price bubble.

HR ², introduced by Dufwenberg, Lindqvist, and Moore (2005), is intended to be an indicator of the goodness of fit between average prices and fundamental values. This is an inverse measure of price deviation. This measure is not directly indicative of the asset price bubble intensity—it is indicative of the extent to which traders utilize earnings information, even if they do so in a contrarian fashion. Duration (DUR), introduced by Porter and Smith (1995), is the maximum number of consecutive periods that the difference between the price and fundamental value is positive. This measure likely captures the intensity of the price bubbles when prices increase gradually. However, if prices increase very rapidly and remain at a high level that market will obtain a low duration score even though the intensity of the price bubble is high.

Stöckl et al. (2010) propose two additional measures to help cross-experiment comparison. These two measures are independent of number of periods and the fundamental values across different experiments. Relative absolute deviation (RAD) is similar to the TD measure; and relative deviation (RD) is similar to AB.

Panel B of Table 2 reports the results of the seven measures for each reporting regime. The FR regime exhibits the lowest asset price intensity for the price amplitude (PA), total dispersion (TD), average bias (AB), relative absolute dispersion (RAD), and relative deviation (RD) measures. However, the FR regime exhibits third-largest asset price bubble intensity for the duration (DUR) measure and the largest asset price bubble intensity for the HR² measure. The FR measure exhibits a high asset price intensity for the duration measure because of the gradual increase in prices albeit the increases are less dramatic (see Figure 3). This gradual increase could likely result in the lower explanatory power of earnings as a determinant of prices leading to a low HR². Stöckl et al. (2010) caution that the HR² measure may not be a good measure for measuring asset price bubbles. This is because although when price tracks fundamental value, HR² would be high, but even when price and fundamental value move in the opposite direction, HR² would also be high. In summary, five of the seven measures of the asset price bubble intensity indicate that the FR regime has the lowest asset price bubble, which is consistent with our expectations.

The BR regime exhibits the highest price intensity for the price amplitude (PA), total dispersion (TD), average bias (AB), relative absolute dispersion (RAD), duration (DUR), and relative deviation (RD) measures. Only the HR² shows that the BR regime has the lowest asset price bubble. Collectively, six of the seven measures indicate that the BR regime has the highest price bubble, which is consistent with traders exhibiting optimism bias. The BR regime having the highest value of HR² could be due to the cash flow realization seed decreasing for consecutive periods; however, the prices increase in these periods. This potential contrarian strategy adopted by the traders is consistent with the optimism bias. Overall, BR regime exhibits the largest asset price bubble (based on six measures) followed by the NR (based on six measures) and GR regimes (based on six measures). The FR regime exhibits the least asset price bubble (based on five measures).

We then perform a statistical test that helps provide a certain degree of confidence in our inferences that the FR regime exhibits the lowest asset price bubble. We test the number of consecutive periods that prices increase. That is, the dependent variable is coded 1 for period t if there are two consecutive periods including that of period t and 0 otherwise. Similarly, we use three and four consecutive increases in prices as well. We use the FR regime as the benchmark and include an indicator variable for the NR regime, GR regime, and BR regime. We estimate the model using logit, and the results are reported in Table 3.

Table 3.

Price Increase Runs in the Regimes.

	Dependent variable = two-period consecutive price increase	Dependent variable = three-period consecutive price increase	Dependent variable = four-period consecutive price increase
Intercept	−0.12	−0.74***	−1.19***
	(−0.61)	(−3.39)	(−4.87)
NR	0.54*	0.74**	0.93***
	(1.86)	(2.48)	(2.90)
GR	1.04***	1.21***	1.31***
	(3.44)	(3.99)	(4.11)
BR	0.94***	1.25***	1.40***
	(3.15)	(4.12)	(4.37)
Pseudo R² (%)	2.97	4.34	4.92
No. of dependent var. = 1	243	198	165
No. of dependent var. = 0	149	186	211
No. of total observations	392	384	376

Note. Dependent variable is equal to 1 if in period t, the two period, three period, and four period exhibit a consecutive price increase including period t, and 0 otherwise. NR is 1 if the observation belongs to the no recognition regime and 0 otherwise. GR is 1 if the observation belongs to the good news recognition regime and 0 otherwise. BR is 1 if the observation belongs to the bad news recognition regime and 0 otherwise. The model is estimated using Logit with the full recognition regime as the benchmark. Z values are reported in parentheses.

. **. *** present 10%, 5%, 1% significance levels, respectively.

When the dependent variable is an indicator for two consecutive period price increases, the coefficients on the NR regime, GR regime, and BR regime indicator variables are 0.54, 1.04, and 0.94 with z values of 1.86, 3.44, and 3.15, respectively (see column 1). When the dependent variable is an indicator for four consecutive period price increases, the coefficients on the NR regime, GR regime, and BR regime indicator variables 0.93, 1.31, and 1.40 with z values of 2.90, 4.11, and 4.37, respectively (see column 3). These results suggest that compared with the FR regime, all the other three regimes exhibit more price increase momentum and thus a higher price bubble as expected. Furthermore, comparing the BR regime with the GR regime, the BR regime exhibits more price increase momentum for longer periods of time. This result is consistent with the optimism bias.

Finally, we use the debriefing survey question responses that we conduct at the end of each experiment session to see how the traders regarded the importance of earnings across the regimes. For each reporting regime, we asked the traders to report the importance they placed on earnings and historical earnings in their trading decisions on a 6-point scale, with 1 indicating not important at all and 6 indicating very important. For each regime, we compute the weighted average importance by multiplying the response point with the proportion of traders who select that point. We then compare the weighted average importance score across different regimes. Figure 4 provides the results. Panel A (B) plots the weighted average importance on current (historical) earnings for each regime. Panels A and B of Figure 4 show that traders placed more (less) importance on current and historical earnings in the FR (NR) regime compared with the other three regimes. This is consistent with our premise that traders understand the informativeness of the underlying random walk process and that they use the neutral earnings more than the biased ones or the ones in which no future information is incorporated. Between the GR and BR regimes, Panel A shows that traders under the GR regime place more importance on current earnings than traders under BR regime, and vice versa in Panel B with respect to historical earnings. This is consistent with the notion that traders try to undo the bias in earnings in these regimes. Collectively, the debriefing survey responses provide a certain degree of confidence in corroborating our inferences.

Figure 4.

Traders’ debriefing questionnaire, use of earnings, and historical earnings for trading.

Concluding Remarks

In this article, we conducted an asset market experiment to examine the effect of reporting regimes on asset prices. We considered four reporting regimes: (a) the “NR” regime, where no expected future cash flows are recognized; (b) the “FR” regime, where both the expected good news and expected bad news pertaining to the next period cash flows are recognized in current earnings; (c) the “GR” regime, where only the expected good news pertaining to the next period cash flows are recognized in current earnings; and (d) the “BR” regime, where only the expected bad news pertaining to the next period cash flows are recognized in current earnings. The FR regime considers reported earnings incorporating future cash flow information in a symmetric fashion, that is, both good and bad news; while the GR and BR regimes are asymmetric in their recognition of good news and bad news, respectively. We run eight sessions, with two sessions for each of the four treatment regimes. There were roughly 40 traders in each session, and no trader participated in more than one session.

We expect traders to add more noise in the process of undoing the biases in reported earnings in the GR and BR regimes than in the FR regime. We also expect the less informative NR regime to result in greater noise than the FR regime. The noise in the process of “correcting” the information provided is likely to create more intense price bubbles in the NR, GR, and BR regimes compared with the FR regime. Consistent with this prediction, we found that the NR, BR, and GR regimes are associated with more intense asset price bubbles than the FR regime. We also found that between the BR and GR regimes, the BR regime is associated with more intense asset price bubbles than the GR regime. We attribute this asymmetric response to overoptimism in correcting for the negative reporting bias or to an apparently risk-seeking response to the biased information under the BR regime.

This study shows that bias in reporting can exacerbate asset market bubbles. This finding supports the call for neutral accounting by the IASB. However, our study does not consider the incentives for managers to bias information, that is, the supply-side effects of information. Future research could build upon our results by examining firms’ incentives for biasing information and how this interacts with accounting policies.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors acknowledge the financial support of the Hong Kong General Research Funding (Grant No. PolyU548810).

Notes

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