[Introduction] The remarkable phenomenon of bubbles and crashes in laboratory asset markets was first

discovered and reported in Smith et al (1988). Subsequent research inquired about the robustness

of the phenomenon and how it might be explained. One interpretation of the data is that public

knowledge of rationality is lacking in the subjects, which leads to a type of individually rational,

bubble creating speculation as part of an attempt to acquire capital gains. A different

interpretation is that subjects begin with a type of confusion or mistaken understanding about this

particular environment and that such “irrationality” at the individual level initiates the bubble,

which could be sustained by a lack of common knowledge of rationality even after all confusion

becomes removed during the process of participating in the market. This paper explores these

two ideas through the study of experiments in which a capital gains tax is imposed that makes

speculation for capital gains unprofitable except under extreme circumstances

Lei, Vivian

Noussair, Charles

Plott, Charles R.

Caltech Authors - Main

DIVISION OF THE HUMANITIES AND SOCIAL SCIENCES
CALIFORNIA INSTITUTE OF TECHNOLOGY
PASADENA, CALIFORNIA 91125
ASSET BUBBLES AND RATIONALITY: ADDITIONAL EVIDENCE FROM
CAPITAL GAINS TAX EXPERIMENTS
Vivian Lei
Charles Noussair
Charles R. Plott
1 8 9 1
C
A
L
IF
O
R
N
IA
 I
N
S T
IT U T E O F T
E
C
H
N
O
L
O
G
Y
SOCIAL SCIENCE WORKING PAPER 1137
June 2002
 1
Asset Bubbles and Rationality: Additional Evidence From Capital 
Gains Tax Experiments 
 
Vivian Lei, Charles Noussair and Charles Plott* 
June 2002 
 
1. Introduction 
The remarkable phenomenon of bubbles and crashes in laboratory asset markets was first 
discovered and reported in Smith et al (1988).  Subsequent research inquired about the robustness 
of the phenomenon and how it might be explained.  One interpretation of the data is that public 
knowledge of rationality is lacking in the subjects, which leads to a type of individually rational, 
bubble creating speculation as part of an attempt to acquire capital gains.  A different 
interpretation is that subjects begin with a type of confusion or mistaken understanding about this 
particular environment and that such “irrationality” at the individual level initiates the bubble, 
which could be sustained by a lack of common knowledge of rationality even after all confusion 
becomes removed during the process of participating in the market.  This paper explores these 
two ideas through the study of experiments in which a capital gains tax is imposed that makes 
speculation for capital gains unprofitable except under extreme circumstances. 
The experiments of Smith et al. created continuous double auction markets for assets with 
a lifetime of a finite number of periods (typically 15 or 30 periods). Each unit of the asset paid a 
dividend in each period, and the dividend was typically the only source of intrinsic value. The 
dividend paid was identical for each trader and the dividend process was common knowledge to 
all traders. Smith et al. (1988) observed that these long-but finitely lived assets tended to trade at 
prices much higher than their fundamental values for much of the life of the asset and that their 
prices tended to crash as the end of the asset’s life approached. This pattern was observed despite 
the fact that there were no rational expectations equilibria in which prices could deviate from 
fundamental values. Subsequent experimental studies (King et al., 1993; Van Boening et al. 1993; 
Camerer and Weigelt, 1993; Porter and Smith, 1995; Fisher and Kelly, 2001, Lei et al., 2001 and 
Noussair et al., 2001) have replicated the bubble phenomenon and shown it to be robust to 
changes in the structure of the dividend process, the rules of exchange, and the number of assets 
traded in the market.  
                                                                 
* Lei: University of Wisconsin-Milwaukee, Milwaukee, WI 53201; Noussair: Emory University, 1602 
Mizell Dr. Atlanta, GA 30322; Plott: California Institute of Technology, Pasadena, CA 91125. 
 2
Such price bubbles have been attributed to the lack of common knowledge of rationality of 
market participants and the resulting incentive to speculate (Smith 1994; Plott, 1991). 
Alternatively, Lei et al. (2001) claim that errors in decision making contribute to bubble 
formation. The claim is that even after traditional amounts of training and testing residual 
confusion can remain in some subjects and leads to mistakenly believe that aggressive buying of 
the asset for profitable resale is a good strategy.  The Lei et al.  argument  rests on the fact that in 
markets in which purchase for resale is not possible, the bubble and crash pattern also occurs. 
Higher than predicted transaction volumes suggest many of the errors arise from the fact that the 
asset market is the only activity available in the experiment, and that subjects have a tendency to 
participate actively in the experiment in some manner, even when they do not fully understand 
the decision situation.  
In this paper, we report further evidence that errors in decision-making are a primary source 
of bubbles. We construct markets similar in structure to those in which bubbles and crashes are 
observed. The only difference is that a capital gains tax of 50% is in force. The tax is in effect a 
tax on speculation. There is no reason to suppose that the tax would reduce the number of 
decision errors. On the contrary, if it serves to complicate the decision task before the subjects, it 
might indeed increase the incidence of errors. If the tax eliminates or substantially reduces bubble 
formation, it would provide strong evidence that bubbles are predominantly speculative in nature, 
rather than caused by errors. However, the presence of bubbles despite the tax would be 
consistent with the conjecture of Lei et al. (2001) that errors are an important factor in bubble 
formation.1 As we report below, bubbles do arise in the presence of the tax, and traders pay taxes 
that are very substantial relative to their total earnings. 
  
2. Procedures 
The procedures we employ are identical (except for the presence of the tax) to those used in 
the OneMarket treatment of Lei et al. (2001) and are known to produce market bubbles and 
crashes when no capital gains tax is in effect. The data reported here consist of three sessions, 
conducted at Purdue University between November and December 1997. Subjects, who were all 
undergraduates recruited from introductory economics courses at Purdue University, were 
                                                                 
1 Unlike the robustness tests considered previously, a capital gains tax, set at 50% in our experiment, 
creates a specific disincentive to purchase for resale. Although an individual trader may be able to make a 
profit by speculating, the existence of the tax and the constant-sum payoff characteristic of the market 
meant that the group as a whole received lower earnings when speculation occurred. Note that a capital 
gains tax differs from a tax on each transaction, as implemented by King et al. (1993). Unlike our capital 
gains tax, their tax penalized every transaction without regard to any capital gain a price appreciation might 
have caused.  
 3
inexperienced with asset market experiments. Subjects were free to buy and sell an asset, called 
X, in a continuous double auction market. The market was created using the MUDA computer 
program developed at the California Institute of Technology by Hsing Yang Lee and Charles 
Plott. Transactions were in terms of an experimental currency called “francs,” convertible to US 
dollars at the end of the experiment at a rate of 130 francs to 1 dollar. The three sessions are 
labeled here as Captax1-3. In Captax1 and 2, seven subjects, and in Captax 3 eight subjects, were 
present.  
At the beginning of each session, subjects received instruction in the mechanics of making 
purchases and sales with the MUDA computer program. Afterward, the experimenter read the 
instructions describing the asset market, and administered a quiz to verify  subjects’ 
comprehension of the dividend process. There followed a practice period, which did not count 
toward subject earnings. After the practice period, inventories of X and working capital, the cash 
balance available to make purchases of X, were initialized to 10 units and 5000 francs 
respectively, and the asset market was opened. Sales of X added to working capital and purchases 
reduced working capital. 
Excluding the practice period, there were 12 trading periods in each session. Each period 
lasted 4 minutes.2 The inventories of both X and working capital were carried over from period to 
period starting from period 1 (we refer to the practice period as period number zero). Each unit of 
the asset paid a dividend at the end of each period. The dividend depended on a coin flip and in 
each period had a 50% chance of equaling 20 francs, and a 50% chance of equaling 40 francs. 
The coin was flipped in each period and thus the dividend draws were independent. Therefore the 
expected dividend paid on each unit of X was 30 francs per period and 360 francs over an entire 
twelve period session. In addition to the above information, each subject had a sheet indicating 
the expected total dividend from holding a unit of X from the current period to the end of the 
experiment. In period t, the expected dividend stream equaled 30*(13 – t), where t º {1,..,12} 
denotes  the current period. 
Subjects’ earnings came from two sources: dividend payments and capital gains. Capital 
gains were equal to the difference between the end-of-period and beginning-of-period working 
capital. In the Captax sessions, a tax on capital gains was imposed at the end of each period. The 
tax rate was 50% if a subject’s capital gains were positive, and zero if they were negative. Since 
there was no tax levied on dividends, each subject’s period earnings were equal to dividends on 
all units of X in his inventory plus the after-tax capital gains or minus capital losses. The capital 
                                                                 
2 Period 12 in CapTax2 lasted only two minutes. 
 4
gains tax was levied “on paper” and thus did not reduce the working capital available for 
purchases. 
 
3. Results 
The principal result of our study is that the capital gains tax does not eliminate price bubbles. 
Figure 1 shows the time series of median transaction prices in each period of the three sessions 
compared to the fundamental value, and to the maximum and minimum possible realizations of 
the dividend stream. All three sessions have at least six consecutive periods in which the median 
price is greater than the fundamental value, and two of the sessions have at least five consecutive 
periods in which the median price is higher than the maximum possible realization of the 
dividend stream. 
  
   [Figure 1: About Here] 
 
The magnitudes of the bubbles under Captax are comparable to those observed in previous 
studies. King et al. (1993) suggest several measures to measure magnitude. Three of these 
measures are Price Amplitude, Normalized Deviation, and Turnover. The Price Amplitude is 
defined as the difference between the peak and the trough of mean period prices relative to the 
fundamental value, normalized by the initial fundamental value. In other words it equals maxt{(Pt 
-f t)/f1} - mint{(Pt - f t)/f1}, where Pt and f t equal the average transaction price and fundamental value 
in period t, respectively. In our markets f t = 30*(13 – t). The normalized deviation is the sum, 
over all transactions, of the devia tions of prices from the fundamental value, divided by the total 
number of shares outstanding. It equals ∑t∑i|Pit – f t|/(TSU*100), where Pit is the price of the ith 
transaction in period t and TSU equals the total stock of units.3 Turnover is defined as the total 
volume transacted over the session divided by the total stock of units. In our sessions, all three 
measures reach levels that are comparable to those observed in other studies (see Porter and 
Smith, 2002, for a summary of the values of the measures in other studies).  
 
     [Table 1: About Here] 
 
                                                                 
3 We use the formula ∑t∑i|Pit – ft|/(TSU*100). In contrast, many other authors do not divide by 100. This is 
because their prices are measured as dollars and  ft typically takes on values between 0 and $3.60. In our 
markets, in which trade takes place in experimental currency,  ft takes on values in the range of 0 to 360 
francs. Thus, to have a comparable measure of the normalized deviation, we divide by 100 for our data. .   
 5
In the three sessions, overall revenue from capital gains taxes equaled 24.9%, 47.0% and 
53.4% percent of the overall expected dividend stream of the total stock of units in sessions 1-3 
respectively. Thus the tax failed to prevent price bubbles, even when it imposed very substantial 
costs on traders.  
 
4. Concluding Remarks 
We find that the imposition of a capital gains tax fails to eliminate the possibility of a 
bubble.4 Two of our three markets exhibited sustained transaction prices far in excess of 
fundamental values. Furthermore, the observed measures of the magnitude of bubbles yield 
values typical of markets without a capital gains tax.  While we report behavior of only three 
markets, the data are sufficient to establish the point. The possible existence of bubbles in the 
presence of the capital gains tax is clearly established.  We are in agreement with previous 
authors who have shown the bubble phenomenon to be robust to changes in trading rules thought 
to discourage bubble formation. The presence of bubbles and crashes and the high revenue 
generated by the tax in our data is consistent with the conjecture of Lei et al. (2001) that errors are 
an important factor in bubble formation.  
When taken with experiments reported elsewhere, these data are part of what appears to be an 
emerging pattern.  The robustness of the bubble phenomenon appears to be in fact a reflection of 
the robustness of the decision errors to different treatments.  Given the nature of the issue it is not 
clear what information would be gained from additional  experiments conducted in the same way 
as those reported here. The exact source of subject confusion is not likely to be exposed by more 
data gathered under the same procedures.  Instead, changes in instructions and procedures might 
produce more insights. 
  
 
References 
 
                                                                 
4 We recognize that there are many alternative methods of implementing a capital gains tax, other than 
the one we chose. One possibility is to have the tax paid on each individual sale rather than on changes in 
overall cash balances. The purchase price of a unit could be calculated on either a first-in-first-out or a last-
in-first-out basis. However, a system of this type would place a far greater computational burden on the 
subjects, and we do not see how such a system might be more effective in suppressing price bubbles than 
the system we have studied. We believe that the empirical patterns we observe here are so strong, and the 
robustness of the bubble phenomenon so well established, that altering the structure of the tax would not 
qualitatively change the result. 
 
 6
Camerer C. and K. Weigelt (1993) “Convergence in Double Auction Markets for Stochastically-
Lived Assets”, in The Double Auction Market: Institutions, Theories, and Evidence, D. Friedman 
and J. Rust, Eds. Addison-Wesley Publishing Company. 
 
Fisher, E., and F. Kelly (2000), “Experimental Foreign Exchange Markets”, Pacific Economic 
Review, 5, pp. 365-387. 
 
King R., V. Smith, A. Williams, and M. Van Boening  (1993), “The Robustness of Bubbles and 
Crashes in Experimental Stock Markets,” in Nonlinear Dynamics and Evolutionary Economics, I 
Prigogine, R. Day and P. Chen eds. Oxford University Press.   
 
Lei, V., C. N. Noussair and C. R. Plott (2001), “Non-Speculative Bubbles in Experimental Asset 
Markets: Lack of Common Knowledge of Rationality vs. Actual Irrationality”, Econometrica, 
69(4): pp. 831-859.  
 
Noussair, C., S. Robin, and B. Ruffieux (2001), “Price Bubbles in Laboratory Asset Markets with 
Fundamental Values”, Experimental Economics, 4(1): pp. 87-105. 
 
Plott, C. (1991), “Will Economics Become an Experimental Science”, Southern Economic 
Journal, pages 901-919. 
 
Porter, D., and V. Smith (1995), “Futures Contracting and Dividend Uncertainty in Experimental 
Asset Markets,” Journal of Business, 68(4): pp. 509-541. 
 
Porter, D., and V. Smith (2002), “Price Bubbles”, in the Handbook of Experimental Economics 
Results, C. Plott and V. Smith. Eds. forthcoming. 
 
Smith, V. (1994), “Economics in the Laboratory,” Journal of Economic Perspectives, 8(1): pp. 
113-131. 
 
Smith, V., G. Suchanek, and A. Williams (1988), “Bubbles, Crashes and Endogenous 
Expectations in Experimental Spot Asset Markets,” Econometrica, 56: pp. 1119-1151. 
 
 7
Van Boening, M., A. Williams, and S. LeMaster (1993), “Price Bubbles and Crashes in 
Experimental Call Markets”, Economics Letters, 41, pp. 179-185.  
 8
 
Table 1. Bubble Measures, All Sessions 
 
 
 
Turnover Amplitude Normalized 
Deviation 
Captax1 1.357 0.988 1.876 
Captax2 3.614 2.124 7.914 
Captax3 3.563 1.647 8.607 
 
 
 9
Figure 1. Time Series of Median Transaction Prices by Period, All Sessions
0
100
200
300
400
500
600
1 2 3 4 5 6 7 8 9 10 11 12
P e r i o d
Captax1 Captax2 Captax3 Fundamentals Maximum Dividend Minimum Dividend
 


English

Asset Bubbles and Rationality: Additional Evidence from Capital Gains Tax Experiments

DIVISION OF THE HUMANITIES AND SOCIAL SCIENCES
CALIFORNIA INSTITUTE OF TECHNOLOGY
PASADENA, CALIFORNIA 91125
ASSET BUBBLES AND RATIONALITY: ADDITIONAL EVIDENCE FROM
CAPITAL GAINS TAX EXPERIMENTS
Vivian Lei
Charles Noussair
Charles R. Plott
1 8 9 1
CA
LI
F
O
R
N
IA
 
IN
S T
IT U T E O F
 T E C
H
N
O
LO
G
Y
SOCIAL SCIENCE WORKING PAPER 1137
June 2002
 1
Asset Bubbles and Rationality: Additional Evidence From Capital 
Gains Tax Experiments 
 
Vivian Lei, Charles Noussair and Charles Plott* 
June 2002 
 
1. Introduction 
The remarkable phenomenon of bubbles and crashes in laboratory asset markets was first 
discovered and reported in Smith et al (1988).  Subsequent research inquired about the robustness 
of the phenomenon and how it might be explained.  One interpretation of the data is that public 
knowledge of rationality is lacking in the subjects, which leads to a type of individually rational, 
bubble creating speculation as part of an attempt to acquire capital gains.  A different 
interpretation is that subjects begin with a type of confusion or mistaken understanding about this 
particular environment and that such “irrationality” at the individual level initiates the bubble, 
which could be sustained by a lack of common knowledge of rationality even after all confusion 
becomes removed during the process of participating in the market.  This paper explores these 
two ideas through the study of experiments in which a capital gains tax is imposed that makes 
speculation for capital gains unprofitable except under extreme circumstances. 
The experiments of Smith et al. created continuous double auction markets for assets with 
a lifetime of a finite number of periods (typically 15 or 30 periods). Each unit of the asset paid a 
dividend in each period, and the dividend was typically the only source of intrinsic value. The 
dividend paid was identical for each trader and the dividend process was common knowledge to 
all traders. Smith et al. (1988) observed that these long-but finitely lived assets tended to trade at 
prices much higher than their fundamental values for much of the life of the asset and that their 
prices tended to crash as the end of the asset’s life approached. This pattern was observed despite 
the fact that there were no rational expectations equilibria in which prices could deviate from 
fundamental values. Subsequent experimental studies (King et al., 1993; Van Boening et al. 1993; 
Camerer and Weigelt, 1993; Porter and Smith, 1995; Fisher and Kelly, 2001, Lei et al., 2001 and 
Noussair et al., 2001) have replicated the bubble phenomenon and shown it to be robust to 
changes in the structure of the dividend process, the rules of exchange, and the number of assets 
traded in the market.  
                                                                 
* Lei: University of Wisconsin-Milwaukee, Milwaukee, WI 53201; Noussair: Emory University, 1602 
Mizell Dr. Atlanta, GA 30322; Plott: California Institute of Technology, Pasadena, CA 91125. 
 2
Such price bubbles have been attributed to the lack of common knowledge of rationality of 
market participants and the resulting incentive to speculate (Smith 1994; Plott, 1991). 
Alternatively, Lei et al. (2001) claim that errors in decision making contribute to bubble 
formation. The claim is that even after traditional amounts of training and testing residual 
confusion can remain in some subjects and leads to mistakenly believe that aggressive buying of 
the asset for profitable resale is a good strategy.  The Lei et al.  argument  rests on the fact that in 
markets in which purchase for resale is not possible, the bubble and crash pattern also occurs. 
Higher than predicted transaction volumes suggest many of the errors arise from the fact that the 
asset market is the only activity available in the experiment, and that subjects have a tendency to 
participate actively in the experiment in some manner, even when they do not fully understand 
the decision situation.  
In this paper, we report further evidence that errors in decision-making are a primary source 
of bubbles. We construct markets similar in structure to those in which bubbles and crashes are 
observed. The only difference is that a capital gains tax of 50% is in force. The tax is in effect a 
tax on speculation. There is no reason to suppose that the tax would reduce the number of 
decision errors. On the contrary, if it serves to complicate the decision task before the subjects, it 
might indeed increase the incidence of errors. If the tax eliminates or substantially reduces bubble 
formation, it would provide strong evidence that bubbles are predominantly speculative in nature, 
rather than caused by errors. However, the presence of bubbles despite the tax would be 
consistent with the conjecture of Lei et al. (2001) that errors are an important factor in bubble 
formation.1 As we report below, bubbles do arise in the presence of the tax, and traders pay taxes 
that are very substantial relative to their total earnings. 
  
2. Procedures 
The procedures we employ are identical (except for the presence of the tax) to those used in 
the OneMarket treatment of Lei et al. (2001) and are known to produce market bubbles and 
crashes when no capital gains tax is in effect. The data reported here consist of three sessions, 
conducted at Purdue University between November and December 1997. Subjects, who were all 
undergraduates recruited from introductory economics courses at Purdue University, were 
                                                                 
1 Unlike the robustness tests considered previously, a capital gains tax, set at 50% in our experiment, 
creates a specific disincentive to purchase for resale. Although an individual trader may be able to make a 
profit by speculating, the existence of the tax and the constant-sum payoff characteristic of the market 
meant that the group as a whole received lower earnings when speculation occurred. Note that a capital 
gains tax differs from a tax on each transaction, as implemented by King et al. (1993). Unlike our capital 
gains tax, their tax penalized every transaction without regard to any capital gain a price appreciation might 
have caused.  
 3
inexperienced with asset market experiments. Subjects were free to buy and sell an asset, called 
X, in a continuous double auction market. The market was created using the MUDA computer 
program developed at the California Institute of Technology by Hsing Yang Lee and Charles 
Plott. Transactions were in terms of an experimental currency called “francs,” convertible to US 
dollars at the end of the experiment at a rate of 130 francs to 1 dollar. The three sessions are 
labeled here as Captax1-3. In Captax1 and 2, seven subjects, and in Captax 3 eight subjects, were 
present.  
At the beginning of each session, subjects received instruction in the mechanics of making 
purchases and sales with the MUDA computer program. Afterward, the experimenter read the 
instructions describing the asset market, and administered a quiz to verify  subjects’ 
comprehension of the dividend process. There followed a practice period, which did not count 
toward subject earnings. After the practice period, inventories of X and working capital, the cash 
balance available to make purchases of X, were initialized to 10 units and 5000 francs 
respectively, and the asset market was opened. Sales of X added to working capital and purchases 
reduced working capital. 
Excluding the practice period, there were 12 trading periods in each session. Each period 
lasted 4 minutes.2 The inventories of both X and working capital were carried over from period to 
period starting from period 1 (we refer to the practice period as period number zero). Each unit of 
the asset paid a dividend at the end of each period. The dividend depended on a coin flip and in 
each period had a 50% chance of equaling 20 francs, and a 50% chance of equaling 40 francs. 
The coin was flipped in each period and thus the dividend draws were independent. Therefore the 
expected dividend paid on each unit of X was 30 francs per period and 360 francs over an entire 
twelve period session. In addition to the above information, each subject had a sheet indicating 
the expected total dividend from holding a unit of X from the current period to the end of the 
experiment. In period t, the expected dividend stream equaled 30*(13 – t), where t º {1,..,12} 
denotes  the current period. 
Subjects’ earnings came from two sources: dividend payments and capital gains. Capital 
gains were equal to the difference between the end-of-period and beginning-of-period working 
capital. In the Captax sessions, a tax on capital gains was imposed at the end of each period. The 
tax rate was 50% if a subject’s capital gains were positive, and zero if they were negative. Since 
there was no tax levied on dividends, each subject’s period earnings were equal to dividends on 
all units of X in his inventory plus the after-tax capital gains or minus capital losses. The capital 
                                                                 
2 Period 12 in CapTax2 lasted only two minutes. 
 4
gains tax was levied “on paper” and thus did not reduce the working capital available for 
purchases. 
 
3. Results 
The principal result of our study is that the capital gains tax does not eliminate price bubbles. 
Figure 1 shows the time series of median transaction prices in each period of the three sessions 
compared to the fundamental value, and to the maximum and minimum possible realizations of 
the dividend stream. All three sessions have at least six consecutive periods in which the median 
price is greater than the fundamental value, and two of the sessions have at least five consecutive 
periods in which the median price is higher than the maximum possible realization of the 
dividend stream. 
  
   [Figure 1: About Here] 
 
The magnitudes of the bubbles under Captax are comparable to those observed in previous 
studies. King et al. (1993) suggest several measures to measure magnitude. Three of these 
measures are Price Amplitude, Normalized Deviation, and Turnover. The Price Amplitude is 
defined as the difference between the peak and the trough of mean period prices relative to the 
fundamental value, normalized by the initial fundamental value. In other words it equals maxt{(Pt 
-f t)/f1} - mint{(Pt - f t)/f1}, where Pt and f t equal the average transaction price and fundamental value 
in period t, respectively. In our markets f t = 30*(13 – t). The normalized deviation is the sum, 
over all transactions, of the devia tions of prices from the fundamental value, divided by the total 
number of shares outstanding. It equals åtåi|Pit – f t|/(TSU*100), where Pit is the price of the ith 
transaction in period t and TSU equals the total stock of units.3 Turnover is defined as the total 
volume transacted over the session divided by the total stock of units. In our sessions, all three 
measures reach levels that are comparable to those observed in other studies (see Porter and 
Smith, 2002, for a summary of the values of the measures in other studies).  
 
     [Table 1: About Here] 
 
                                                                 
3 We use the formula åtåi|Pit – ft|/(TSU*100). In contrast, many other authors do not divide by 100. This is 
because their prices are measured as dollars and  ft typically takes on values between 0 and $3.60. In our 
markets, in which trade takes place in experimental currency,  ft takes on values in the range of 0 to 360 
francs. Thus, to have a comparable measure of the normalized deviation, we divide by 100 for our data. .   
 5
In the three sessions, overall revenue from capital gains taxes equaled 24.9%, 47.0% and 
53.4% percent of the overall expected dividend stream of the total stock of units in sessions 1-3 
respectively. Thus the tax failed to prevent price bubbles, even when it imposed very substantial 
costs on traders.  
 
4. Concluding Remarks 
We find that the imposition of a capital gains tax fails to eliminate the possibility of a 
bubble.4 Two of our three markets exhibited sustained transaction prices far in excess of 
fundamental values. Furthermore, the observed measures of the magnitude of bubbles yield 
values typical of markets without a capital gains tax.  While we report behavior of only three 
markets, the data are sufficient to establish the point. The possible existence of bubbles in the 
presence of the capital gains tax is clearly established.  We are in agreement with previous 
authors who have shown the bubble phenomenon to be robust to changes in trading rules thought 
to discourage bubble formation. The presence of bubbles and crashes and the high revenue 
generated by the tax in our data is consistent with the conjecture of Lei et al. (2001) that errors are 
an important factor in bubble formation.  
When taken with experiments reported elsewhere, these data are part of what appears to be an 
emerging pattern.  The robustness of the bubble phenomenon appears to be in fact a reflection of 
the robustness of the decision errors to different treatments.  Given the nature of the issue it is not 
clear what information would be gained from additional  experiments conducted in the same way 
as those reported here. The exact source of subject confusion is not likely to be exposed by more 
data gathered under the same procedures.  Instead, changes in instructions and procedures might 
produce more insights. 
  
 
References 
 
                                                                 
4 We recognize that there are many alternative methods of implementing a capital gains tax, other than 
the one we chose. One possibility is to have the tax paid on each individual sale rather than on changes in 
overall cash balances. The purchase price of a unit could be calculated on either a first-in-first-out or a last-
in-first-out basis. However, a system of this type would place a far greater computational burden on the 
subjects, and we do not see how such a system might be more effective in suppressing price bubbles than 
the system we have studied. We believe that the empirical patterns we observe here are so strong, and the 
robustness of the bubble phenomenon so well established, that altering the structure of the tax would not 
qualitatively change the result. 
 
 6
Camerer C. and K. Weigelt (1993) “Convergence in Double Auction Markets for Stochastically-
Lived Assets”, in The Double Auction Market: Institutions, Theories, and Evidence, D. Friedman 
and J. Rust, Eds. Addison-Wesley Publishing Company. 
 
Fisher, E., and F. Kelly (2000), “Experimental Foreign Exchange Markets”, Pacific Economic 
Review, 5, pp. 365-387. 
 
King R., V. Smith, A. Williams, and M. Van Boening  (1993), “The Robustness of Bubbles and 
Crashes in Experimental Stock Markets,” in Nonlinear Dynamics and Evolutionary Economics, I 
Prigogine, R. Day and P. Chen eds. Oxford University Press.   
 
Lei, V., C. N. Noussair and C. R. Plott (2001), “Non-Speculative Bubbles in Experimental Asset 
Markets: Lack of Common Knowledge of Rationality vs. Actual Irrationality”, Econometrica, 
69(4): pp. 831-859.  
 
Noussair, C., S. Robin, and B. Ruffieux (2001), “Price Bubbles in Laboratory Asset Markets with 
Fundamental Values”, Experimental Economics, 4(1): pp. 87-105. 
 
Plott, C. (1991), “Will Economics Become an Experimental Science”, Southern Economic 
Journal, pages 901-919. 
 
Porter, D., and V. Smith (1995), “Futures Contracting and Dividend Uncertainty in Experimental 
Asset Markets,” Journal of Business, 68(4): pp. 509-541. 
 
Porter, D., and V. Smith (2002), “Price Bubbles”, in the Handbook of Experimental Economics 
Results, C. Plott and V. Smith. Eds. forthcoming. 
 
Smith, V. (1994), “Economics in the Laboratory,” Journal of Economic Perspectives, 8(1): pp. 
113-131. 
 
Smith, V., G. Suchanek, and A. Williams (1988), “Bubbles, Crashes and Endogenous 
Expectations in Experimental Spot Asset Markets,” Econometrica, 56: pp. 1119-1151. 
 
 7
Van Boening, M., A. Williams, and S. LeMaster (1993), “Price Bubbles and Crashes in 
Experimental Call Markets”, Economics Letters, 41, pp. 179-185.  
 8
 
Table 1. Bubble Measures, All Sessions 
 
 
 
Turnover Amplitude Normalized 
Deviation 
Captax1 1.357 0.988 1.876 
Captax2 3.614 2.124 7.914 
Captax3 3.563 1.647 8.607 
 
 
 9
Figure 1. Time Series of Median Transaction Prices by Period, All Sessions
0
100
200
300
400
500
600
1 2 3 4 5 6 7 8 9 10 11 12
P e r i o d
Captax1 Captax2 Captax3 Fundamentals Maximum Dividend Minimum Dividend
 


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Asset Bubbles and Rationality: Additional Evidence from Capital Gains Tax Experiments

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