Informational price cascades and non-aggregation of

asymmetric information in experimental asset markets

Jason Shachat∗

Anand Srinivasan†

February 25, 2013

Abstract

We report on experimental markets in which asymmetric information abjectly fails to ag-

gregate. Prices have zero correlation with fundamental values. Prices aren’t highly volatile,
rather they lock in to home grown norms we call informational price cascades. Our results
contrast those of previous experiments testing fully revealing rational expectations equilib-
rium under asymmetric information and others examining social learning in asset markets
with a rational market maker. We also show that price cascades are robust to giving the
same private signal to two traders, and information partially aggregates when each private
signal is revealed to half of the traders.

JEL classification: C92, D82, G12

Keywords: Information cascade; information aggregation; experiment; asset market

∗
Corresponding Author.Wang Yanan Institute for Studies in Economics, and MOE Key Laboratory in
Econometrics, Xiamen University. jason.shachat@gmail.com
†
Department of Finance, NUS Business School, and Risk Management Institute, National University of
Singapore. bizas@nus.edu.sg
1 Introduction

Ideally, asset markets perform important functions such as directing capital to the greatest
wealth creating opportunities, facilitating the efficient sharing of risk, and the accurate in-
corporation of diversely held information into market prices. This last function is commonly
referred to as information aggregation and has theoretical foundations in the hypotheses of
rational expectations (Lucas, 1972) and efficient markets (Grossman, 1976). Traditional tests
of whether information aggregates in financial markets have relied upon indirect inferences
usually in the form of testing for profitable trading strategies based on public information.
However, since the market’s information set is never available to the researcher, it is not
possible to directly test for information aggregation using real market data. In contrast, with
controlled laboratory experiments, the experimenter has the ability to observe and control the
market’s information set. Therefore, such experiments are well suited to evaluate information
aggregation. One strand of literature (Plott and Sunder, 1988; Forsythe and Lundholm,
1990; Barner, Feri, and Plott, 2006) finds strong support favoring information aggregation
with short lived assets traded in continuous double auctions. A second strand of literature
conducts experiments on variations of the rational herding model developed by Bikhchandani,
Hirshleifer, and Welch (1992), with the theoretical prediction that individuals would ignore
their private information resulting in informational cascades. Several experimental studies
(Anderson and Holt, 1997; Celen and Kariv, 2004; Goeree, Palfrey, and Rogers, 2007; Alevy,
Haigh, and List, 2007) confirm the theoretical prediction that information fails to aggregate,
and this lack of aggregation is due to cascades and herding. A key institutional feature in
these studies is a market maker who exogenously sets a constant price for the asset.
Avery and Zemsky (1998) reformulate the Bikhchandani, Hirshleifer, and Welch (1992)
model with a market maker who adjusts this price according to Bayes rule. They show
that this change results in full information aggregation and no information cascades.1 Sub-
sequent experimental studies (Sgroi, 2003; Cipriani and Guarino, 2005, 2009; Drehmann,
1
The prediction of full information aggregation occurs only under some conditions.

1
Oechssler, and Rider, 2005) confirm this prediction and report greatly reduced herding and
informational cascade formation, and correspondingly high levels of information aggregation.
We conduct asset market experiments that synthesize these two strands of literature; we
adopt the asset and corresponding information structure of Bikhchandani, Hirshleifer, and
Welch (1992) and we use the continuous double auction for trading. While accommodating
flexible prices, our setting differs from Avery and Zemsky (1998) and related experiments as
it adheres to the principle of decentralized information (Hurwicz, 1972). A trader’s portfolio
holdings and adjustments, information regarding dividends, and her identity when taking
market actions are all private information. Consequently, traders can only learn from the
observation of public market data such as contract prices and limit orders in the open book.
Replacing social learning - through the direct observation of others actions - with market
learning - through the observation of anonymous market actions - leads to a dramatic change
in the informational efficiency of the market.
The most dramatic change is that we observe zero information aggregation when in-
formation signals are private information. In our first set of experiments, we consider an
asset market where participants trade a contingent claim asset with two between-subject
treatments: public information in which each signal is observed by all traders, and private
information in which each signal is revealed to one trader (with traders taking turns at being
this insider.) We use a dynamic asset market structure similar that that used in Palfrey and
Wang (2012).2 In the private information treatment, there is no information aggregation,
which manifests in surprising fashion. Within an experimental session, trades quickly lock
into a single price and subsequent contract prices substantially deviate rarely. We refer to
this phenomenon as an informational price cascade because the lock-in price has zero corre-
lation with the fundamental value of the asset and further arriving private information does
not get incorporated into the market. The persistence of these informational price cascades
is quite strong; within a session, these price norms carry across the conclusion of one asset’s
2
We use this to study information aggregation in contrast to their focus on speculation.

2
life to a new market repetition in which subjects’ endowments are reset and a new - but
identical - contingent asset is traded.
Despite market prices failing to incorporate newly arrived private information, we don’t
observe accompanying strong herding in terms of individuals’ portfolio adjustments. Some
subjects do adjust the number of assets they hold conditional upon their private signals and
increase their earnings, but there is great variance in these two measures. One might suspect
that insiders will wait before acting on their private signals, but that is only half the story.
Forty-four percent of the time, an informed trader participates in one of the first two trades
that occurs after she receives her private signal, while about thirty percent of the time, the
informed trader does not make a contract in that period.
So how is it these portfolio adjustments do not lead to information leaking into market
prices? The sequential arrival of asymmetric information to the market creates a longer lived
asset (in discrete time), relative to assets traded in the typical continuous double auction
information aggregation experiments. In studies such as Plott and Sunder (1988), assets
typically live for one trading period and all asymmetric information regarding it’s value is
endowed to traders prior to the period. In contrast, our markets start with a common prior
for asset value and over the course of trading, a sequence of eight informative signals are
received; producing an asset that lives for nine-periods with no dividends other than its
terminal value. This creates opportunities for noise traders to cloud the inference of the
information that may be revealed by informed trading. In particular, these noise traders
allow informed traders to exploit their private information without perturbing a market
price norm.
An obvious question is how robust are the informational price cascades that we report?
Motivated by models of partial aggregation (Diamond and Verrecchia (1981), Kyle (1985),
Holden and Subrahmanyam (1992), and Foster and Viswanathan (1996)), we make two
important modifications in the experimental design for the private treatment. First, we
create a new treatment where each signal is given to two subjects. By doing this, we remove

3
the information monopoly held by the informed trader. We do not find any effect of removing
this monopoly on information aggregation. In another treatment, we give each signal to four
subjects. We find partial aggregation in this treatment, supporting the prediction in some
of the above models on the importance of the fraction of informed traders for information
aggregation.3
The rest of the paper proceeds as follows. In Section 2, we present the experimental
design and motivate the hypotheses to be tested. In Section 3, we present the results of
the main treatments and empirical analysis. In Section 4, we examine the robustness of the
results to alternative treatments. In Section 5, we present our conclusions. Importantly, we
discuss potential explanations of our results as well as relate our findings to prior literature
in this last section.

2 Experimental Design

2.1 Asset structure, market institution, and protocols

Consider a simple asset a that lives for nine periods and possesses no value other than a final
dividend d(a). Market participants hold a common prior that this final dividend is either
zero or one dollar with equal probability. To test for information aggregation, we introduce
informative, but imperfect, signals about the dividend value before periods two through
nine. Each signal is an independent realization of the following probability experiment. If
the dividend is one dollar, the signal is a draw from an urn containing eight red (R) chips
and four (B) black chips. On the other hand, if the dividend is zero, the signal is a draw
from an urn with four red chips and eight black chips. Thus, the probability of drawing
a red chip conditional on a one dollar dividend is two-thirds, Pr(R|d(a) = 1) = 2/3, and
the probability of drawing a red chip conditional on a zero dollar dividend is one-third,
3
Bossaerts, Frydman, and Ledyard (2013) also find that information aggregation is impacted by the
fraction of informed traders.

4
Pr(R|d(a) = 0) = 1/3. For any sequence of realized signals, the Bayes rule calculation for
the posterior probability that d(a) = 1 reduces to 1/ 1 + 2−k , where k is the number of R

less the number of B signals. For the relevant values of k, Table 1 provides the corresponding
posterior probabilities that d(a) = 1, or in other words, the conditional expected value of
the dividend, E [d(a)|k]. For our purposes, the fundamental value of a at every point in time
is its expected value conditional upon all realized signals up to that point.

Table 1: Expected dividend conditional on #R − #B

#R − #B 0 1 2 3 4 5 6 7 8
E [d(a)] 0.50 0.67 0.80 0.89 0.94 0.97 0.98 0.99 1.00
#R − #B 0 -1 -2 -3 -4 -5 -6 -7 -8
E [d(a)] 0.50 0.33 0.20 0.11 0.06 0.03 0.02 0.01 0.00
Expected values are rounded to the nearest one hundredth.

We populate the market for the asset a with eight traders, endowing each trader with
five dollars of currency and five units of the asset. For all nine periods in the life of the asset,
traders have the opportunity to buy and sell the asset amongst themselves via a continuous
double auction. During a market period, traders can take the following actions: submit bids
to purchase, submit asks to sell, make market sales (agreeing to sell at the current highest
bid), and make market buys (agreeing to purchase at the current lowest ask). While these
actions are for a single unit, traders can submit multiple bids and asks, and make multiple
purchases and sales within a period. When a market period closes, all remaining bids and
asks expire. Short sales are not allowed, nor can traders borrow money.4
We conducted all of our sessions in the National University of Singapore (NUS) Depart-
ment of Marketing’s Behavioral Research Computer laboratory.5 We executed the continu-
ous double auction trading mechanics using the Marketlink software application for running
market experiments (Cox and Swarthout, 2006), publicly available at the Econport web-
4
Further details of the trading institution are included in the experimental instructions available from
the authors upon request.
5
This laboratory is especially designed to conduct research experiments with individual computers housed
in private carrels that prevent subjects from viewing each other’s computer screens and also discourage
communication between subjects.

5
site (http://www.econport.org). We augmented the computerized trading procedures with
hand-run protocols to induce the various information treatments.
We recruited participants through e-mails to the undergraduate majors in the NUS De-
partment of Economics and undergraduate majors and Master of Business Administration
students from the NUS School of Business. Participants were told the experiment would last
approximately two and a half hours, received a ten Singapore dollar payment for showing
up on time, and privately paid any money earned in the experiment at its conclusion. All
amounts in the experiment, and in this description, are in Singapore dollars. There was no
conversion between experimental and local currencies. Each subject participated in only one
session.
Every experimental session had eight subjects. A session started with a public reading
of the instructions, which each subject had a printed copy of, followed by a practice market
consisting of three trading periods (the earnings from which subjects were not paid). Subjects
then participated in a sequence of three markets for which they earned money. Each of these
markets consisted of nine 90 second trading periods. Prior to period one, the subjects could
observe us toss a coin that determined the asset’s dividend value and the composition of the
urn. However, the outcome of the coin toss was not shown to the subjects. After period
nine, we announced the realized dividend value, and a subject’s earnings for that market
was her final currency balance plus the number units of the asset she held at the conclusion
of trading, multiplied by the dividend value. All subjects had common knowledge of this
structure. Note that there was no carry over of currency or asset units across markets, and
a subject started each market with a new endowment. A subject’s total payment was the
show-up fee and the sum of her earnings in the three markets.

2.2 Informational treatments

Our experimental treatments concern how signals were disseminated to the subjects. The
following list provides the treatments and the implementing protocols. Note that the relevant

6
protocols were common knowledge to all subjects within a treatment and fully disclosed in
the publicly read instructions.

1. Public Information (PUB): All subjects publicly observed every signal. Prior to
trading in periods two through nine, a single chip was drawn at random in view of
the subjects. The color of the chip was shown to all traders and then returned to
the urn. At the conclusion of market period nine, after the value of the dividend was
announced, we allowed subjects to verify the contents of the urn.

2. Private Information (PVT): We used the same protocols as the PUB treatment
with the following modifications. In each market, subjects were randomly and anony-
mously ordered one through eight to determine the sequence of informed traders. Prior
to trading in periods two through nine, the color of the randomly selected chip was
only revealed to that period’s informed trader. To preserve anonymity, an envelope was
distributed to every subject. The informed trader’s envelope contained a slip of paper
with the color of the selected chip written on it, and all other envelopes contained a
slip of paper with the printed word ‘None.’ The envelopes were recollected after the
subjects inspected the contents.

The principal statistical tests rely on differences between these two treatments (PUB
and PVT). Nevertheless, we perform two further treatments with a view to identifying the
robustness of the results. These two treatments are also motivated by models of partial
aggregation that suggest that having multiple insiders or a greater fraction of traders with
inside information should improve information aggregation.6

3. Private Information with Two Informed Traders (2SIG): This treatment fol-
lowed the same protocols as the PVT treatment except that we revealed each signal
to two subjects rather than one. The subjects were formed into four anonymous and
randomly ordered pairs. The ordered pairs took turns being the informed trader pair
6
See Holden and Subrahmanyam (1992) and Foster and Viswanathan (1996).

7
 Table 2: Experimental design
Treatment Acronym Markets Show-Up Fee Sessions
Public Information PUB 3 S$10 8
Private Information PVT 3 S$10 8
Private Information with
2SIG 3 S$10 4
Two Informed Traders
Private Information with
4SIG 3 S$10 4
Four Informed Traders

for periods two through five. Within a pair, the two subjects did not know each other’s
identity. Then, for periods six through nine we generated a new random set of pairs.
Thus, a subject knew that she would observe one of the first four signals, and then ob-
serve another signal from the set of the last four signals. Further, she knew that when
she observed a draw from the urn, exactly one other subject simultaneously observed
the same draw.

4. Private Information with Four Informed Traders (4SIG): This treatment was
the same as 2SIG except that four subjects rather than two observed each draw. In
this case, the eight subjects were divided into random groups of four for the market
period pairs two/three, four/five, six/seven, and eight/nine. Thus, a subject knew she
observed the draw once in each of those pairs of market periods, and that exactly three
other subjects observed the same draw.

We adopted a between subject experimental design: each experimental session was ex-
posed to a single information treatment. Table 2 provides details regarding our experiment
design such as the number of sessions per treatment and the acronyms will use for each
treatment.
Before discussing some of the motivations and hypotheses generated by the differences
between these treatments, let’s consider some of the constants. Note that the set of feasible
allocations is the same across the four treatments: the same number of traders each endowed
with five units each of currency and assets. Second, the total information content of the

8
market does not vary as there are exactly eight independent draws from the urn with identical
timing. With a constant set of feasible allocations and information structure, the rational
expectations equilibrium is the same for every market in all treatments.

2.3 Major Hypotheses

In terms of hypotheses development, we will progress from full revelation of all information
in a rational expectations setting to successively lower degrees of information revelation. In
our setting, the rational expectation equilibrium is that, for every possible history of signal
realizations, the equilibrium price equals the expected dividend and excess demand for the
asset is zero. Implicit in the zero excess demand condition is that each market participant
calculates the expected dividend conditioning upon all market signals observed by any market
participant, not just the signals she observes. Radner (1979) showed that such fully revealing
equilibrium are generically rational expectations equilibrium in finite state settings like ours.

Hypothesis 1. Rational Expectations Equilibrium: Market prices equal the fundamental

value as defined by all realized market signals.

There are two effects governing the price dynamics in the rational expectations equilib-
rium. First, informational efficiency dictates whenever a participant observes a new market
signal, the change in value results in a perfectly correlated change in price. Second, there is
price efficiency such the price level always equals the market fundamental value. A market
outcome can fail to be price efficient - and thus failing to implement a rational expectation
equilibrium - but still have informational efficiency. For example, consider a market dynamic
in which price adjustments are exactly one-half of any change in fundamental value. While
this would fail price efficiency, there still remains a clear one-to-one mapping between the
path of market prices and the sequence of realized signals. If prices moved in the above man-
ner, a market participant could perfectly infer signals in the private treatment as though
they were being publicly revealed, despite the lack of price efficiency. Our second hypothesis
relaxes the assumption of price efficiency and only addresses correlation efficiency.

9
Hypothesis 2. Correlation efficiency: The correlation between market prices and funda-
mental value is one.

Next, we relax the above efficiency concept even further, by recognizing that the market
prices of assets may be influenced by trader’s biases in judgment (Hirshleifer, 2001). In
particular, the rational expectations equilibrium for our experiment relies heavily on the
assumption that conditional probabilities are updated according to Bayes rule when mar-
ket signals are realized. Past experimental studies have shown that asset prices generated
in markets are not immune to evaluation errors such as base rate fallacy (Ganguly, Kagel,
and Moser, 2000), the representative heuristic (Camerer, 1987), or both (Palfrey and Wang,
2012). For our next hypothesis, we suppose that whatever systematic judgment errors sub-
jects make, they are the same in all the treatments. This allows us to consider the PUB
treatment as our baseline, and if information aggregates when it is asymmetric, then market
prices should all follow the same data generating process.

Hypothesis 3. Comparative efficiency: Pricing dynamics are the same in all treatments.

From a theoretical standpoint, the above hypotheses essentially modify the full infor-
mation rational expectations hypothesis to one in which participants are allowed to deviate
from rationality in terms of how they use information to update their beliefs and the cor-
responding impact this has on equilibrium prices. However, it assumes that such judgment
biases have no effect on the ability of the market to aggregate diffuse information.
Next, motivated by the seminal paper on rational herding by Bikhchandani, Hirshleifer,
and Welch (1992), if individuals do not act according to their signals, then the market price
will not reveal any information and the prices will be in the form of an informational cascade.
To the extent that cascades are present, this would also imply that information aggregation
will be significantly lower in the private treatment relative to the public treatment. In fact,
with a cascade, information aggregation should be zero subsequent to the onset of a cascade.

10
Hypothesis 4. Informational Cascade: Prices in the private treatment will be in the form
of informational cascades where prices do not reveal any information.

Avery and Zemsky (1998) modify the social learning model developed by Bikhchandani,
Hirshleifer, and Welch (1992) to learning from asset market prices, by allowing a rational
market maker to set the price in a way that reflects the information that can be inferred
by an outsider from its holder. In this case, they show prices again become fully revealing
and we recover the rational expectations equilibrium. Thus, if is simply the mechanism of
flexible prices that makes actions fully revealing of signals, we should not see any cascades
and one of hypotheses 1, 2, or 3 should hold.

3 Empirical analysis

3.1 Graphical Analysis of the PUB and PVT treatments

We start with a presentation of contract prices and paths of fundamental value for the PUB
and PVT sessions. Figures 1 and 2 are 8×3 array of graphs, with rows corresponding to
experimental sessions and the columns to the three market sequence within a session. The
horizontal axis of each market graph measures time, the vertical lines indicate market period
closings. A dot represents a contract by its time stamp and price (the vertical axis value).
The step function tracks the fundamental value given realized urn draws and is calculated
according to Table 1. At the top of each period, we give the total number of trades within
that period.
To illustrate the differences in pricing dynamics between the PUB and PVT treatments
we compare a typical session of each. Consider session PUB4 in the fourth row of Figure 1.
Trading in Market 1 starts with a possible bubble. In the first three periods there are several
trades exceeding the maximum possible dividend of one dollar. It turns out the dividend
in this market is zero, every signal was black, and the fundamental value correspondingly
decreases each period. While the adjustments of prices track this value, the actual level

11
 Figure 1: PUB treatment sessions; contract prices and fundamental value
Market 1 Market 2 Market 3
15 6 5 8 3 0 1 2 5 4 9 4 5 7 5 4 4 3 5 6 6 4 6 3 3 4 6
0.0 0.5 1.0 1.5
x x
PUB1

3 5 7 2 3 6 4 2 6 3 2 3 0 2 2 4 1 1 1 1 1 2 2 1 2 2 1
0.0 0.5 1.0 1.5
PUB2

5 7 9 10 6 6 6 7 7 4 3 6 7 4 7 3 4 6 2 2 6 7 4 2 2 2 2
0.0 0.5 1.0 1.5
PUB3

9 10 9 10 6 4 2 3 4 10 6 3 2 3 3 5 5 6 6 4 6 5 4 3 2 3 0
0.0 0.5 1.0 1.5
PUB4

1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9
Market 1 Market 2 Market 3
9 5 2 9 8 3 11 11 8 10 8 8 4 8 6 5 7 9 11 2 3 5 8 11 10 8 3
0.0 0.5 1.0 1.5
PUB5

8 10 7 2 4 5 2 3 12 9 4 5 6 3 5 3 4 13 2 4 3 2 0 4 5 7 15
0.0 0.5 1.0 1.5

x
PUB6

9 8 12 12 11 8 4 5 2 7 4 5 4 0 4 2 3 4 4 3 3 5 5 4 4 3 7
0.0 0.5 1.0 1.5
PUB7

18 13 13 9 7 6 9 3 2 5 4 1 2 4 1 8 4 9 5 4 2 2 5 4 3 3 4
0.0 0.5 1.0 1.5
PUB8

1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9

12
 Figure 2: PVT treatment sessions; contract prices and fundamental value
Market 1 Market 2 Market 3
19 15 11 9 12 16 7 12 12 10 12 8 14 6 11 6 9 12 11 5 12 18 14 8 9 5 5
0.0 0.5 1.0 1.5
x
PVT1

6 6 8 5 7 3 3 5 4 4 5 4 4 3 6 5 0 8 2 0 7 1 2 2 1 6 3
0.0 0.5 1.0 1.5
PVT2

17 17 13 21 11 18 11 11 7 11 12 13 15 10 14 4 13 13 8 7 6 7 4 14 9 5 7
0.0 0.5 1.0 1.5
PVT3

8 4 17 8 12 12 9 8 5 16 12 12 12 9 9 8 3 3 9 8 4 10 6 5 8 5 12
0.0 0.5 1.0 1.5
PVT4

1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9
Market 1 Market 2 Market 3
10 5 10 3 5 6 1 2 5 12 5 5 1 2 4 1 0 0 3 3 5 5 5 2 3 3 5
0.0 0.5 1.0 1.5

xxx x
PVT5

4 10 6 10 3 5 5 5 10 5 5 4 7 6 3 5 5 5 3 5 3 6 7 8 5 3 7
0.0 0.5 1.0 1.5
PVT6

10 3 3 4 3 2 2 3 3 7 11 5 4 1 1 2 0 5 7 8 3 3 3 4 1 4 5
0.0 0.5 1.0 1.5
PVT7

11 11 10 11 7 5 5 7 2 8 12 7 6 4 3 3 0 3 5 5 1 5 1 6 5 3 4
0.0 0.5 1.0 1.5

x x
PVT8

1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9

13
of transaction prices approach fundamental value only around Period 7. This is consistent
with other studies that generally document that subjects do not perfectly update according
to Bayes rule (Grether, 1980; Camerer, 1987; Charness and Levin, 2005; Palfrey and Wang,
2012). In Markets 2 and 3, as the subjects gain experience, we find successively smaller and
shorter duration bubbles, which is consistently found in other experimental studies (Smith,
Suchanek, and Williams, 1988; Dufwenberg, Lindqvist, and Moore, 2005; Haruvy, Lahav,
and Noussair, 2007). Subsequently, the trends of prices and values are similar, although
with some noise.
The PVT6 session, the sixth row of Figure 2, has markedly different price dynamics.
In Market 1, prices almost always exceed fundamental value, but never exceed one dollar.
More importantly, there is no obvious responsiveness of prices to value. As the markets
progress, the transactions lock in to a trading price unrelated to the value, and fail to adjust
to subsequent changes in value. We refer to such a price lock-in as an informational price
cascade. Consistent trading at such a home grown price norm makes it very difficult to
for market participants to infer the private - but valuable - information observed by others.
Also, it is quite remarkable how this price cascade, and those in all but one of the other
PVT sessions, span across market incidences even though it is common knowledge that
endowments are reset and asset dividends are drawn anew.

3.2 Univariate Evaluation of Informational and Pricing Efficiency

We proceed to quantify the informational efficiency, or the apparent lack of, suggested by
visual inspection of the data. As implied by Hypothesis 2, a basic indication that prices
incorporate information should be a positive correlation between price and fundamental
value. Table 3 presents simple univariate correlations of fundamental value and each trade
price stratified by treatment and market repetition. This correlation is computed using all
transactions within each trading period and the fundamental value.
The correlations are virtually zero in the PVT sessions, while strictly positive and in-

14
 Table 3: Correlation between all trade prices and value: PUB and PVT

Market 1 Market 2 Market 3 Overall

Public signal Correlation 0.29 0.66 0.88 0.54
Observations 473 338 291 1102
P-value 0.00 0.00 0.00 0.00
Private signal Correlation -0.03 -0.11 0.05 0.01
Observations 576 473 399 1448
P-value 0.53 0.02 0.37 0.61

creasing in the PUB sessions. In the public sessions, the correlation rises from 0.29 in Market
1 to 0.88 in the final market. This suggests that learning allows the public market partici-
pants to infer the pricing model much more efficiency but not in the private treatment. The
hypothesis that the correlation is zero is soundly rejected in all the markets. In contrast, the
PVT correlations are not significantly different from zero in Markets 1 and 3, and negative
in Market 2; this is no measurable improvement across markets. These individual transac-
tion price-fundamental value correlations support the general notion that prices in the PUB
treatment respond to signals whereas prices in the PVT treatment do not.

Result 1. Hypothesis 2, and information aggregation, fails in the PVT treatment; the cor-
relation between price and value is zero However, in the PUB treatment the correlation
approaches one in the latter stages of a session.

The presented correlation measures capture the degree to which prices adjust with
changes in fundamental value; however, they do not inform to how well prices match the
fundamental value, i.e., price efficiency. We use two metrics of pricing inefficiency to measure
differences between the PUB and PVT treatments.
First, we define pricing inefficiency as the absolute value of the deviation of price from
value expressed as a percentage of value. With perfectly price efficient markets, this should
equal zero and larger values would imply greater degrees of inefficiency. Panel A in Table 4
reports averages of this inefficiency for various price measures. For the PUB treatment, the
Market 3 pricing inefficiency is around 50% whereas in the PVT treatment, it is around 140%.
Second, to ensure that these results are not driven by large errors in the closing periods for

15
which the fundamental value approaches zero, we also report the simple average absolute
deviation, without scaling by value in the denominator. The results using this second measure
of inefficiency (Table 4, Panel B) shows a similar pattern but greatly increased efficiency.
Using the closing price in panel B, we see a similar pattern that was indicated by the
correlation analysis with reduced inefficiency in the third market for the public treatment,
but no such trend in the private treatment.

Table 4: Inefficiency measures

|Price-Value|
Panel A: Pricing inefficiency measure = Value

Overall Market 1 Market 2 Market 3

PUB Mean Price 70% 129% 29% 50%
Median Price 68% 121% 29% 51%
Close Price 65% 109% 32% 53%
PVT Mean Price 131% 165% 84% 141%
Median Price 132% 168% 81% 145%
Close Price 128% 157% 96% 130%
p-value Mean Price 0.02 0.62 0.00 0.00
Median Price 0.02 0.51 0.00 0.00
Close Price 0.01 0.44 0.01 0.01
Naive Pricing 98% 119% 66% 107%
Panel B: Pricing inefficiency measure = |Price-Value|
Overall Market 1 Market 2 Market 3
PUB Mean Price 18% 29% 14% 12%
Median Price 18% 28% 13% 12%
Close Price 18% 26% 15% 12%
PVT Mean Price 27% 29% 23% 29%
Median Price 28% 31% 23% 29%
Close Price 27% 29% 25% 27%
p-value Mean Price 0.00 0.83 0.00 0.00
Median Price 0.00 0.41 0.00 0.00
Close Price 0.00 0.42 0.00 0.00
Naive Pricing 20% 20% 19% 21%

As a basis of comparison, we compute a benchmark by calculating the level of inefficiency

had all trades occurred at the price of fifty cents, which we call naive pricing. As can be
seen, the PUB treatment has lower inefficiency than naive pricing, more so in Markets 2
and 3. In contrast, the PVT treatment has greater inefficiency than naive pricing, implying
price cascades are less price efficient than an equilibrium in which no information is given to
participants.

16
3.3 Multivariate Evaluation of Informational and Pricing Efficiency

The above univariate results suggest that the PVT markets have significantly less information
aggregation and greater price inefficiencies that the PUB markets. However, this does not
provide credence to prices being unbiased as well as correlated with fundamental value in the
PUB treatment. Nor does the lack of correlation indicate that there are information price
cascades of the nature that we speculate occur in PVT sessions. To provide further evidence
on the first three hypotheses - rational expectations (hypothesis 1), correlation efficiency
(hypothesis 2), and comparative efficiency (hypothesis 3), we consider the following simple
model for determination of price changes.

∆Psmt = α + β∆Vsmt + smt , (1)

where s denotes the session number (one through eight), m the market repetition (one
through three), and t the trading period (two through nine). In this equation, ∆P is the
change in price (mean, median or closing) from period t-1 to period t, and ∆V is the
corresponding change in value.
Under Hypothesis 1 of Rational Expectations Equilibrium, we should find that α equals
zero and β equals one. Under Hypothesis 2, α need not be zero, as this would simply
imply a lack of matching between the mean changes of price and the mean changes of value.
What would be the implication for β? In particular, if the volatility of the dependent
and independent variables were equal, then by the definition of the regression coefficient, a
correlation coefficient of one would imply that β should also be one. On the other hand, if
this were not true, the correlation could be one, but β can be different from one. For testing
hypothesis 2, we use this less restrictive test of correlation efficiency. If we reject correlation
efficiency with the weaker hypothesis test of β different from zero, this is a strong rejection.
Under comparative efficiency, we should find that β for the public and private treatments
should be equal.

17
 Table 5: Price difference regressions (Equation 1) using mean, median, and closing price
Panel A: PUB treatment
Independent Variables ∆(Mean Price) ∆(Median Price) ∆(Closing Price)
0.460 0.393 0.397
∆Vsmt
0.081 *** 0.066 *** 0.068 ***
Intercept -0.020 -0.016 -0.017
0.010 * 0.008 * 0.008 *
Observations 183 183 183
R2 0.15 0.18 0.17
Wald test of equality of 33.93 37.25 36.13
α=0 and β = 1
Probability > χ2 <.0001 <.0001 <.0001

Panel B: PVT treatment

Independent Variables ∆(Mean Price) ∆(Median Price) ∆(Closing Price)
-0.011 -0.051 -0.047
∆Vsmt
0.082 0.064 0.057
Intercept -0.022 -0.024 -0.025
0.011 * 0.009 *** 0.008 ***
Observations 182 182 182
R2 0.00 0.00 0.00
Wald test of equality of 3.77 7.54 10.13
α=0 and β = 1
Probability > χ2 0.151 0.023 0.006
*, **, and *** indicate 10%, 5%, and 1% levels of significance respectively. Standard errors
are in italics. These two conventions holds throughout the paper.

Table 5 gives the results of these tests for both the PUB and PVT treatments. First, we
confirm our first result there is no information aggregation in the PVT sessions as β is not
significant in this case. However, in the PUB treatment β is significant but we can reject
the null hypothesis that it is one. Also note that the intercept term is different from zero in
both treatments, and a joint test that α = 0 and β = 1 is rejected as well. Hence, we have
our second result.

Result 2. We reject the rational expectations equilibrium in both the PUB and PVT treat-
ments.

The specification of Equation 1 and the associated hypothesis on its parameter values
impose both informational efficiency - i.e., there exists a one-to-one relationship between

18
the changes in prices and fundamental value - and price efficiency. We now consider an
alternative empirical specification that better delineates these two efficiencies. Motivated in
part from the results in Figure 1, where it appears that public markets react with a lag, we
modify the empirical specification to model price levels rather than changes in price.

Psmt = αs + β0 ∆Vsmt + β1 ∆Vsm,t−1 + β2 Psm,t−1 + smt (2)

Apart from including the lagged change in value as an explanatory variable, another
important change in this specification relative to the previous one is that we include session
specific intercepts, αs . Given that the intercept captures the average pricing error, allowing
it to vary across sessions could possibly increase the magnitude of the slope coefficients. A
second more important reason for allowing for session specific intercepts is that it will allow
us to test for the possibility of informational price cascades.
Tables 6 and 7 present the results of estimating Equation 2 separately for the PUB and
PVT treatments. For considering the appropriate data for the dependent variable, we report
the results of using the mean, median and closing price as different dependent variables.
These estimations, and subsequent ones, are estimated by feasible generalized least squares
with session specific variances because we generally reject the hypothesis of equal variances
in each session for both the PUB and PVT treatments.7 We also test, but do not report, for
autocorrelations using the Breusch-Pagan test and do not find evidence for autocorrelation
in the error terms for all our presented specifications.
With respect to the PUB treatment (Table 6), we find a significant effect for change
in value for both the current period, ∆Vsmt , as well as for the previous period, ∆Vsmt−1 ,
suggesting delayed impact of information on prices. Approximately only fifty percent of
the change in fundamental value resulting from a urn draw is realized in the current price,
7
The null hypothesis of homoscedasticity is not rejected in all specifications. For example, in the PUB
treatment with mean price as the dependent variable, homoscedasticity is not rejected. Likewise, for the
PVT treatment with closing price, the hypothesis of equal session specific variances is not rejected. However,
to be consistent, we choose the same method of estimation for all specifications.

19
 Table 6: PUB treatment price level regressions (Equation 2)
Independent Variable Mean Median Closing
Price Price Price
0.491 0.466 0.468
∆Vsmt
0.091 *** 0.072 *** 0.072 ***
0.308 0.321 0.347
∆Vsm,t−1
0.085 *** 0.066 *** 0.067 ***
0.907 0.955 0.946
Psm,t−1
0.042 *** 0.035 *** 0.035 ***
0.038 0.007 0.010
Intercept
0.029 0.024 0.024
Observations 159 159 159
2
R 0.78 0.86 0.85
Wald stat. all αi = 0 8.02 6.75 6.81
Probability > χ2 <.431 0.564 0.557

while another thirty percent of this change in value is incorporated by the price of the
subsequent period. The estimates for the coefficient on lagged price range from 0.91 to 0.96.
Each of these estimated coefficients is significantly different from 1 and standard tests reject
the presence of a unit root.8 Note that the intercept is insignificantly different from zero
for the public market, suggesting that adding the lagged change in value allows a greater
explanatory power. Further, using a specification with session-specific intercepts, a Wald
test fails to reject that hypothesis the session specific intercepts are jointly equal to zero.
Next, in Table 7, we examine the estimation results for the PVT treatment, and find
a dramatic departure from the PUB treatment results. In particular, the coefficients of
change in value in the current period, ∆Vsmt , and the lagged change in value, ∆Vsmt−1 , are
statistically insignificant. Thus, neither current information nor lagged information has any
effect on prices. The impact of the lagged price is also significantly lower relative to the
PUB treatment. The R2 values are also much lower relative to the PUB market with values
between 61% and 77%. Overall, the results of this subsection with alternative empirical
specifications suggest the following results.
8
Due to the small number of observations in each session, these unit root tests are conducted by taking
all the end of period observations of each treatment and stacking them together.

20
 Table 7: PVT treatment price level regressions (Equation 2)
Independent Variable Mean Median Closing Stationary
Price Price Price Price
-0.066 -0.054 -0.040
∆Vsmt
0.075 0.061 0.054
0.046 0.059 0.061
∆Vsm,t−1
0.072 0.058 0.051
0.328 0.566 0.564
Psm,t−1
0.084 *** 0.068 *** 0.065 ***
0.259 0.175 0.177 0.40
α1
0.041 *** 0.035 *** 0.033 ***
0.330 0.215 0.216 0.49
α2
0.056 *** 0.045 *** 0.042 ***
0.358 0.234 0.235 0.54
α3
0.051 *** 0.043 *** 0.040 ***
0.397 0.247 0.250 0.57
α4
0.058 *** 0.046 *** 0.044 ***
0.396 0.255 0.244 0.58
α5
0.064 *** 0.052 *** 0.049 ***
0.441 0.297 0.297 0.68
α6
0.066 *** 0.055 *** 0.051 ***
0.609 0.385 0.380 0.89
α7
0.085 *** 0.069 *** 0.065 ***
0.446 0.272 0.282 0.60
α8
0.073 *** 0.062 *** 0.059 ***
Observations 159 159 159
2
R 0.61 0.73 0.77
Wald stat. all αi equal 32.660 19.720 22.810
Probability > χ2 <.0001 0.006 0.002

Result 3. We reject correlation efficiency (hypothesis 2) for the PVT treatment. We reject
that the comparative aggregation of the PUB and PVT treatments are equal (hypothesis 3).

3.4 Evidence of Price Cascades

The previous sub-section presented strong evidence that information aggregation fails ab-
jectly in the PVT treatment. Recall from section 3.1 that prices in the private treatment
tend to visually lock on to a price norm that tends to persist across sessions, and is un-
correlated with fundamental value. Next, we present analysis that the multivariate results

21
presented earlier in Table 7 are also consistent with price cascades, thus providing formal
statistical evidence consistent with the visual interpretation of the figures earlier.
From Table 7, we observe that session specific intercept for every single session in the
PVT treatment is significantly different from zero. Further, the intercepts are also different
from each other. Specifically, this result suggests that prices in the PVT treatment are
session specific mean reversion processes. The corresponding stationary points are the home
grown price norms at which informational price cascades form. Let’s consider the stationary
price for a PVT session, denoted Ps . Once an informational price cascade forms, i.e. a
stationary point reached,
Psmt = αs + β2 Psmt−1 + smt .

If one takes expectations on both sides, then one has the following

αs
E[Psmt ] = .
1 − β2

Thus, a non zero positive intercept implies the presence of a long run steady state price
as long as β2 is less than one. We report the calculated stationary price for each session in
the last column of Table 7. In our calculation of the stationary price, we use the coefficients
from the regression on the median price because it always results in a value that lies between
the same calculations based upon the mean and closing price regressions. Note that the
difference between these calculated values is never more than five cents. In summary, the
fact that every PVT session specific intercept is significantly positive provides strong evidence
of informational cascades. Thus, not only do we document lack of information aggregation,
we provide a possible mechanism for the presence of lack of aggregation, namely that there
are information price cascades. We summarize the regression analysis with the statement of
our next two results.

Result 4. The non-aggregation of information in the PVT treatment manifests itself as

informational price cascades. Hypothesis 4 is supported.

22
 We conduct a variety of robustness checks of these results that are available from the
authors on request and provided in the SSRN version of the paper. These include analyzing
the impact of bubbles as well as experience results on information aggregation. The main
finding is that accounting either for bubbles or experience, does not alter the result of zero
aggregation of information in the PVT treatment.

3.5 Actions of Informed Traders

We now shift from the analysis of prices to addressing some natural questions regarding the
informed traders’ actions. For example, given the presence of informational price cascades,
do traders simply disregard their private information and select asset holdings independent
of their private information, in other words, do they herd? Do traders act upon their
information when they receive it, or are they strategic and delay trading in order to not
reveal and better exploit it? If traders successfully adjust their portfolios to take advantage
of their information, how do they do so without leaking information into the market and
breaking a price cascade? Lastly, what proportion of the trades have the informed trader as
a counterparty?

3.5.1 Portfolio adjustments

If subjects exploit informational advantages, we should expect to see the final number of
asset units held to differ conditional on whether a subject observed a Red or Black draw.
On the other hand, if subjects simply herd we should see no such differences. In Table 8, we
report the average number of asset units held at the conclusion of a market conditional upon
market number and signal type observed, as well as the standard deviation for each of these
statistics. Using the endowment of five units of the assets as a benchmark, on average those
who receive a Black signal reduce their holdings by approximately one unit and those who
receive a Red signal add about one unit. This would suggest subjects are not herding, except
the standard deviations are quite large and we can’t reject the hypothesis that average final

23
asset holdings are the same for both Black and Red signal receivers.

Table 8: Average final asset units holdings conditional upon signal

Signal Market 1 Market 2 Market 3 Total

Black 4.64 3.72 4 4.13
Stand. dev. 3.58 3.52 3.84 3.65
Red 5.39 6.06 6.37 5.92
Stand. dev. 3.88 4.27 4.46 4.17
Total 5.00 5.00 5.00 5.00
Stand. Dev. 3.55 3.97 4.52 4.01

It turns out the high standard deviations in asset holdings arise from an important
heterogeneity in how subjects choose portfolios. In Figure 3, we plot the empirical CDF’s
of asset holdings conditional on receiving a Red or Black signal. There are several features
worth noting. First, the support for both distributions is quite large; zero to thirteen for
those who observe a Black signal, and zero to fifteen for those whose observe a Red signal.
There many people choosing corner solutions, such as the twenty percent of the Black signal
receivers and ten percent of the Red signal receivers who hold no units of the asset. Finally,
casual inspection suggest the empirical CDF of Red first order stochastically dominates that
of Black. We quantify this conclusion with a nonparametric hypothesis test suggested by
Barrett and Donald (2003) which rejects the absence of first order stochastic dominance
for any plausible level of significance.9 Evidently some traders adjust their portfolios based
upon their signals and benefit, while at the same time there is overall tremendous variation
in portfolio adjustments.

3.5.2 Timing of insider trades

How are some subjects able to use their private information to make profitable portfolio
adjustments without transmitting this information to the market? One conjecture is that a
subject may wait to act on such information so as to not transmit the signal by her actions,
9 mn 0.5
The test-statistic is z ∗ ( m+n ) where m and n are the number of observed Black and Red draws
respective, and z is the absolute of maximum difference between the two empirical CDF’s. The p-value of
this statistic is exp(−2 ∗ z 2 ).

24
Figure 3: Empirical CDF of final asset holdings for Red and Black signal receivers, dashed line for
Black

1.00

0.75
Prrobability

0.50

0.25

0 00
0.00
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Final asset holdings

and thus erodes its value (Foster and Viswanathan, 1994, 1996). As we will demonstrate,
this conjecture is partially wrong as many informed subjects quickly trade upon receipt of
their information. However, it turns out they are able to do so with impunity, because many
of the other subjects, who are not informed, are also engaging in trades. This creates a
large amount of noise trades that dilutes the informational content of the insider’s market
actions.10
Let’s consider how fast a subject makes a trade after observing a draw from the urn.
Figure 4 plots the empirical cumulative probability of the contract at which the period’s
informed trader makes her first transaction within the period. Surprisingly, many subjects
act quickly, about twenty-four percent are a party to the first contract, and almost twenty
percent more make their first trade as a party to the second contract of the period. On the
other hand, slightly over thirty percent of the subjects do not make any trade in the period
that they are the informed trader. Clearly, subjects utilize the endogenous timing of when
10
While trading by uninformed (noise) traders may appear to violate the no-trade theorem of Milgrom and
Stokey (1982), this is not actually the case as one important necessary condition is the presence of complete
markets. In fact, as shown by Blume, Coury, and Easley (2006), arrival of new information would generate
trade in incomplete markets.

25
to take market actions in diverse ways.

Figure 4: Empirical CDF of Insider’s first contract: PVT

Empirical CDF of Insiders First Contract  

1.00
0.90
0.80
0.70
Probability

0.60
0.50
0.40
0.30
0.20
0.10
0.00
1 2 3 4 5 6 7 8 9 10 11 12
Sequence number of contract in period

3.5.3 Noise versus informed trading

For a transaction to reveal information it must have the informed trader as a counterparty,
we examine how likely this is. To do this, we classify any trade between two non-informed
traders as a noise trade; any other trade - which must involve the informed trader - we
classify as informed. Figure 5 plots trades according to this classification with the order of
the trade within a given period - the idea being to examine whether there is an intra-period
trend in the informativeness of trades.
The figure exhibits two features. First, a large proportion of trades (conditional on the
order of trading within the period) are noise trades, i.e., trades where both participants do
not have any information in the given period. For example, for the first trade in any given
period, about seventy-five percent are noise trades. This pattern continues for most trades.
Thus, non-informed traders would have difficulty in inferring the direction of the signal given
the large fraction of noise trading in the market. This happens regardless of the order of the
trade, thus, the last trade in a period is not much more likely to be informed relative to the

26
 Figure 5: Count of informed and noise trades according to trade number in period
200
180 Informed
160 Noise
140
120
100
80
60
40
20
0
1 2 3 4 5 6 7 8 9 10 >10

first trade.
The result that noise traders can reduce information aggregation is also empirically ob-
served in Bloomfield, O’Hara, and Saar (2009), where they have a treatment where traders
are explicitly paid for creating noise trades. This reduces efficiency of the market in terms of
pricing do not result is cascades of the type we document here. While noise trading is not a
treatment variable in our experiment, it does emerge as a large fraction of the total number
of trades, and is an important behavioral component of price cascades.

4 Experimental tests on the fragility of price cascades

The informational price cascades in our PVT sessions are quite prominent and unexpected.
Hence, there is likely some skepticism about whether such phenomenon are general or re-
stricted to the specific circumstances of the experimental design. In an attempt to address
this issue, we earlier identified two possible limitations in our experimental design section:
information monopoly of the signal for each trader, and the fraction of traders who observe
the signal. With respect to the number of traders observing the signal; one conjecture is
that price cascades rely upon there being a monopoly for each signal, and creating any
competition for informational rents and induces full information aggregation (Holden and
Subrahmanyam, 1992, 1994). A second conjecture is that increasing the ratio of informed

27
traders to non-informed traders will reduce the amount of noise trade, suggesting a contin-
uous increase in the rate of information aggregation. Prior experimental work, for example,
Schnitzlein (2002) using a quote driven market finds support for the monopoly effect with
quick aggregation when two traders are given similar (and perfectly revealing) information
on the final value of the asset. On the other hand, using a continuous double auction setting
but with a single round of trading, Bossaerts, Frydman, and Ledyard (2013) document that
the fraction of insiders have an impact on speed of information aggregation, as well as the
efficiency of the final price at the end of trading.

4.1 Impact on informational price cascades

Again, we start by considering time series plots of all trade prices and fundamental value
for both the 2SIG and 4SIG sessions, Figures 6a and 6b. Casual inspection of the 2SIG
plots clearly reveals price cascades that span across multiple markets in three out of four
of the sessions, and a possible price cascade in Market 2 of the remaining session. This
suggests that removing the monopoly of the informed trader is not sufficient to preclude the
formation of price cascades. In contrast, we don’t observe any multi-period price cascades
in the 4SIG sessions. Although there is some suggested price inertia in the early periods of
some markets, and often - but not always - the movement of price is towards fundamental
value in later periods of the market. This movement from a price norm early in the market
towards fundamental value later in the market suggests that having one-half the subjects
observe each signal, and subsequently, subjects information reaching a sufficiently precise
level, breaks the cascade phenomenon.
Next, in Table 9, we quantitatively evaluate the presence of information aggregation by
examining the correlation between all contract prices and fundamental value. The evidence
is quite negative for information aggregation in the 2SIG treatment. Overall, the correlation
is virtually zero, and when conditioning upon the market number we have no increasing
trend, and two out of three markets exhibit negative correlation.

28
Figure 6: 2SIG and 4Sig treatment sessions: contract prices and fundamental value
2SIG Sessions
Market 1 Market 2 Market 3
18 19 13 9 7 7 8 5 8 6 6 7 4 5 6 6 6 5 6 6 5 5 2 4 3 1 6
0.0 0.5 1.0 1.5
2SIG1

10 11 11 10 13 5 6 8 6 12 10 13 2 3 4 2 1 1 11 4 5 1 7 2 2 3 8
0.0 0.5 1.0 1.5
2SIG2

12 9 5 3 6 6 5 1 7 8 6 4 4 4 4 2 1 3 5 4 4 2 2 4 3 10 5
0.0 0.5 1.0 1.5
2SIG3

8 7 3 8 6 9 8 2 6 11 4 6 6 4 4 3 5 6 9 8 11 6 2 3 9 4 6
0.0 0.5 1.0 1.5

x
2SIG4

1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9

4SIG Sessions
Market 1 Market 2 Market 3
16 7 4 7 4 8 3 4 5 7 5 6 6 4 4 5 3 6 6 2 1 6 5 8 13 6 3
0.0 0.5 1.0 1.5
4SIG1

20 17 14 17 14 13 9 12 10 14 12 18 12 13 18 24 19 9 25 13 20 10 11 12 11 7 12
0.0 0.5 1.0 1.5

x xx
4SIG2

9 11 13 13 12 12 13 16 11 12 17 8 13 18 6 4 10 8 15 10 12 6 4 9 5 20 13
0.0 0.5 1.0 1.5
4SIG3

6 11 7 8 10 14 13 11 10 14 13 12 8 5 8 10 7 9 7 7 8 3 4 4 7 8 6
0.0 0.5 1.0 1.5

xx
4SIG4

1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9

29
 Table 9: Correlation between all trade prices and value: 2SIG and 4SIG

Market 1 Market 2 Market 3 Overall

2SIG Correlation -0.30 0.29 -0.10 -0.02
Observations 285 184 178 647
P-value 0.00 0.00 0.18 0.59
4SIG Correlation 0.10 0.62 0.51 0.36
Observations 384 367 319 1070
P-value 0.05 0.00 0.00 0.00

On the other hand, there is significant and positive correlation for all three markets and
overall for the 4SIG treatment; and we see higher correlations in Markets 2 and 3 versus
Market 1. However, these levels are lower than those for the PUB treatment. Thus, the
2SIG treatment appears to exhibit zero information aggregation like the PVT treatment,
and the 4SIG treatment seems to generate partial information aggregation relative to the
PUB treatment.
To further corroborate this, we ran the same empirical specifications in terms of price
difference (Equation 1) and price levels11 (Equation 2) and report the results in Table 10
and 11, respectively.12 First, we find that 2SIG results are similar to those of the PVT
treatment. In the price difference and price level regressions, the coefficients for change in
fundamental value are never significant. Further, price level regressions in Table 10 show that
2SIG prices are a session specific mean reversion processes, with stationary prices at which
cascades form. The results for 4SIG reveal that information starts to aggregate and price
responds to new information and the corresponding change in value, albeit not as strongly
as the PUB treatment. The coefficient for ∆Vsmt is significant in both price difference and
level regressions, but we note an interesting variation in its value depending upon the price
measure used. For mean and median price, the coefficient is roughly half the of the value
estimated in the PUB treatments; however, when closing price is used the coefficient is
11
In this case, we report regressions without the ∆Vsmt−1 variable. With only four sessions in each
treatment, we wished to utilize as much data as possible, and the coefficient was not significant in unreported
regressions.
12
In unreported results, we perform all the alternative tests including examining the impact of bubbles
and learning on information aggregation, and find no effects.

30
almost the same as the PUB treatments. The suggests, with half of the subjects informed,
there is movement of prices towards fundamental value within a market period.

Table 10: 2SIG and 4SIG price difference regressions

2SIG 4SIG
Variable Closing Median Mean Closing Median Mean
Price Price Price Price Price Price
-0.087 0.011 -0.053 0.507 0.212 0.178
∆Vsmt
0.065 0.008 0.015 0.176 *** 0.015 *** 0.013 ***
-0.022 -0.013 -0.013 -0.039 -0.053 -0.051
Intercept
0.009 ** 0.008 0.015 0.023 * 0.015 *** 0.013 ***
Numb. of obs. 96 96 96 96 96 96
R2 0.02 0.00 0.00 0.08 0.04 0.04

Table 11: 2SIG and 4SIG price level regressions

2SIG 4SIG
Variable Closing Median Mean Stationary Closing Median Mean
Price Price Price Price Price Price Price
0.811 0.730 0.255 0.741 0.963 0.997
Psm,t−1
.127 *** .117 *** .117 ** .089 *** .065 *** .058 ***
-0.103 -0.003 -0.108 0.415 0.205 0.175
∆Vsmt
.053 .066 .088 .174 ** .116 * .099 *
0.067 0.151 0.483 0.56 0.118 -0.032 -0.051
α1
.090 .082 * .085 *** .065 * .048 .042
0.163 0.245 0.687 0.91 0.179 -0.011 -0.045
α2
.119 .113 ** .113 *** .095 * .069 .061
0.141 0.205 0.585 0.76 0.093 -0.035 -0.055
α3
.104 .094 ** .096 *** .072 .053 .045
0.097 0.140 0.417 0.52 0.163 -0.029 -0.045
α4
.071 .064 ** .072 *** .076 ** .057 .049
Numb. of obs. 96 96 96 96 96 96
R2 0.76 0.81 0.57 0.56 0.78 0.82
Wald statistic for 8.22 6.23 25.47 1.91 0.27 0.09
all αi equal
Probability > χ2 0.042 0.101 <.001 0.591 0.966 0.992

Note that in both these treatments, apart from breaking the monopoly and increasing
the fraction of insiders, we also increase the precision of the signals of each insider. Other
theoretical literature suggests that increasing the precision of insiders may induce better
aggregation, for example, see Diamond and Verrecchia (1981), Vives (1995). In unreported
results, we try to establish if there are effects of increased precision beyond those due to

31
breaking the monopoly and increased fraction of insiders. However, the current experimental
set up is not able to detect any effects.

5 Conclusion

We conclude by discussing how our study and findings relate to the existing experimen-
tal literature, and suggesting future directions of inquiry. Our initial premise asked if the
long lived asset, and accompanying long sequence of informative private information, of
Bikhchandani, Hirshleifer, and Welch traded in a market with decentralized private infor-
mation leads to full information aggregation or informational cascades. They were strong
precedents that the information should aggregate in our experiment. In particular, in the
social learning literature, it’s been robustly shown theoretically (Avery and Zemsky, 1998)
and experimentally (Drehmann, Oechssler, and Rider, 2005; Cipriani and Guarino, 2005)
that allowing for rational market makers, who endogenously set prices, information fully ag-
gregates. Further, in experimental tests of fully revealing rational expectation equilibrium,
information robustly aggregates and efficient pricing occurs with homogeneous preferences,
one-period lived assets, and aggregate certainty (Plott and Sunder, 1988). In studies that
follow the same Plott and Sunder design except environments with aggregate uncertainty,
such as Forsythe and Lundholm (1990) and Bruguier, Quartz, and Bossaerts (2010), infor-
mation aggregation and the rational equilibrium solutions do not perform as well, although
still better than competing theories.
There are a couple of studies that test the fully revealing rational expectation equilib-
rium with longer lived assets and dynamically arriving private information. Copeland and
Friedman (1987, 1991) examine information aggregation in a four period asset market in
which a different subset of subjects learn the true dividend state each period. While they
find imperfect adherence to the rational expectations equilibrium, the rational expectation
equilibrium still outperforms alternative models. In Barner, Feri, and Plott (2006), there is

32
a three period lived asset with four possible dividend levels. Subjects are partitioned and
each period an element of the subject partition is informed of one of the non-realized states;
hence aggregate certainty is achieved in the last period of the market. Each subject partition
always has multiple traders so there is no treatment like our PVT one. With this structure,
they find much more support for the rational expectation equilibrium and information ag-
gregation hypothesis than we do.13 The above suggest that aggregate uncertainty leads
to reduced informational efficiency, but typically not enough to reject the fully revealing
rational expectations equilibrium in favor of alternative equilibrium models.
A second potential reason for the lack of aggregation in our experiment, in contrast to
social learning experiments, is the endogenous timing of trades. The only effort we are aware
of that incorporate flexible prices with endogenous timing is the experimental study by Park
and Sgroi (2012) in which subjects are provided signals of heterogeneous strength prior to
trading. Their focus however is on the effects of differentially precise signals and its impact
on the actions of insiders. However, it should be noted that a subject can make at most two
transactions and therefore is still different from the experiment in this paper.
This complete freedom for timing of trades creates a large amount of trading, both for
insiders as well as for noise trades. Theoretically, we know that this timing option should
create partial aggregation (Kyle, 1985) but not cascades. Empirically, Bloomfield, O’Hara,
and Saar (2009) observe that when the number of non-informed traders increases price
efficiency is reduced when the realized value is far from the prior expected value, but price
efficiency increases when that difference is small. Further, informed traders tend to wait
until the latter part of the period to trade. While we do not observe a temporal pattern
of insider trading within a round, and noise trading is not a treatment variable in our
experimental set up, we document similar results except that in our set up this actually
leads to cascades. Thus, the endogenous timing option for insider trading appears also be
13
However, there are significant pricing inefficiencies as they do find some mirages (price moving the
opposite direction of the signal) and bubbles (price moves in the direction suggested by the signal but to the
price above the fundamental value).

33
an important ingredient for informational cascades.
We have demonstrated that market and social learning are not equivalent, and one should
be careful in extrapolating the results of social learning models to asset markets. However,
our results also suggest new questions. Is there either an equilibrium or behavioral founda-
tion for the price cascade phenomenon? In terms of further experimental inquiry there are
several avenue of interesting inquiry including sequences of shorter lived assets, settings with
aggregate certainty, and would public signals along side private ones trigger price responses
that cause information to flow back into the market. Finally, can price cascades be observed
in equity markets? Clearly such mis-pricing would be important but difficult to identify.

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