Design-features of bubble-prone experimental asset markets with a constant FV

Experimental asset markets with a constant fundamental value (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {\textsc {fv}}$$\end{document}FV) have grown in importance in recent years. A methodological examination of the robustness of experimental results in such a setting which has been shown to produce bubbles, however, is lacking. In a laboratory experiment with 280 subjects, we investigate whether specific design features are sufficient to influence experimental results. In detail, we (1) vary the visual representation of the price chart, and (2) provide subjects with full information about the FV process. We find overvaluation and bubble formation to be reduced when trading prices are displayed at the upper end of the price chart. Surprisingly, we do not find any effects when subjects have full information about the FV process. Electronic supplementary material The online version of this article (10.1007/s40881-019-00061-5) contains supplementary material, which is available to authorized users.


A Additional Figures and Tables
presents the calculation of all market variables used in the main text.
Notes: Pt -(volume-weighted) mean price in period t; F Vt -fundamental value in period t; F V -mean fundamental value in the market; T -total number of periods; t * -peak period (i.e., period with the highest price); k ∈ [1, t − 1] -number of periods before the peak period; l ∈ [1, T − 1] -number of periods after the peak period; log-return of a trade: Rt,j = ln(Pt,j/Pt,j−1); total number of trades in period t: Nt; average log return in period t: Rt; price of sell order j at the end of period t: St ,j ; price of buy order j at the end of period t: Bt ,j . All variables above are calculated on the market level.    Table 1 in the Appendix).
In Table A3 we provide details on individual market results for each bubble measure in all four treatments.   In Table A4 summarizes subject demographics between all four treatments and p-values for differences across treatments. Female represents the percentage share of female subjects; Age is subjects' age in years; Semesters of study is the average of subjects' study time in semesters; Experience represents subjects' experience with participating in laboratory experiments (0 = "This is my first experiment.", 1 = "1 to 5 experiments", 2 = "6 to 15 experiments", 3 = "more than 16 experiments"); Risk attitude general is the average value to the question "In general, are you willing to take of to you avoid taking risky decisions?" [Likert-scale ranging from 0 (avoid taking risky decisions) to 10 (willing to take risky decisions)]; Risk attitude investments is the average value to the question "With respect to investments, are you willing to take of to you avoid taking risky decisions?" [Likert-scale ranging from 0 (avoid taking risky decisions) to 10 (willing to take risky decisions)]; CRT score is the number of correct answers (out of 4) of a 4-question Cognitive Reflection Test (?) as proposed by ?. The column "p-values" reprents p-values from Kruskal-Wallis equality-of-populations rank tests between treatments.

B Additional Results: Beliefs about Prices and Trading Behavior
In each period, we elicited subjects' beliefs about the average market price in the following three periods. This procedure allows us to analyze how participants' expectations about future price developments relate to trading behavior and thus drive market prices.
Result B1. We detect strong beliefs about increasing prices across all subjects in treatments base and floor, as well as for the most optimistic traders across all treatments. Support: Following ? and ?, we run least squares regressions with market-fixed effects to detect belief dynamics. We calculate differences between subjects' price beliefs and past period prices (P m,t−1 ) according to the following equations, BeP opt m,t,t+k = OPT(F m,t,t+k ) − P m,t−1 ; with k = 0, 1, 2; where F m,t,t+k is the average belief for period t + k, elicited in period t, among all subjects in market m (BeP is an acronym for "Beliefs about Prices"). OPT(F m,t,t+k ) describes the optimists' beliefs -that is, the second-highest price belief (85-percentile) in a market. We then subtract the past period's average market price P m,t−1 and estimate the following regression model: y m,t,t+k = α + m,t ; k = 0, 1, 2 with y m,t,t+k being a generic placeholder for either BeP m,t,t+k or BeP opt m,t,t+k . As we aim to explain differences between treatments in the price run-ups, we restrict our analysis in this part to periods before or at the peak period in each market, i.e., t ≤ t * , and test each treatment separately for significance. A positive intercept indicates beliefs about future prices being higher than last period's average market price, i.e., subjects expect prices to further increase in the next periods. Notes: BeP m,t,t+k detects speculative motives by comparing average beliefs about future market prices up to t + 2, elicited in period t (market average), with the average market price of the last period. BeP opt m,t,t+k applies only the two highest beliefs in each period. In each market, only periods before or at the price peak, t ≤ t * are considered; this leads to different sample sizes across treatments. * , * * , and * * * represent double-sided tests' p-values smaller than .10, .05, and .01. One observation with implausible price beliefs of 3,000 Taler was dropped in Treatment floor.
In the left panel of Table A5, showing the estimation results with average beliefs (BeP m,t,t+k ), we observe positive intercepts in treatments base and floor which indicates that subjects expect prices to increase. However, ? and ? show that the most optimistic traders' beliefs in each period (BeP opt m,t,t+k ) are the ones who drive market prices. Estimating the same model in Eq. (6) for optimists' beliefs only, we find that beliefs are considerably higher than last period's prices in all treatments (see right panel of Table A5). Testing for differences between treatments in multivariate regressions with treatment dummies, we find that belief dynamics regarding optimists are statistically indistinguishable between treatments. Considering all subjects, we only observe marginally lower values of BeP m,t,t+k in info than in base. 11 As a rationality check, to test whether the price beliefs of the most optimistic/pessimistic traders also translate into trading behavior, we investigate the change of asset holdings per period between optimists and pessimists prior to the peak period of each market. Across all treatments, we find that optimists buy more assets prior to the bubble peak than pessimists.
Thus, optimists' price beliefs do translate into trading behavior and, therefore, drive prices. 12 Table A6 shows estimates from random effects regressions on Beliefs about Prices with treatment dummies (top panel) as well as pairwise Wald-tests for differences between treatments (bottom panel).  As a rationality check, we run ordinary least squares regressions for differences in periodto-period changes in asset holdings between optimists and pessimists in all pre-peak periods separately for each treatment (see Table A7). In particular, we regress the change in asset holdings per period on the binary variable optimist indicating 1 for optimists and 0 for pessimists. 13 We find significantly positive coefficients in each treatment with the highest value for base. Here, we estimate that optimists buy on average 0.80 assets per period while pessimists sell on average 1.09 assets. Thus, we find that having comparatively optimistic price beliefs is conducive to buying more assets than subjects with comparatively pessimistic beliefs. In price run-ups, optimists are indeed the ones who drive prices upwards. Notes: Dependent variable: Period-to-period change in asset holdings. optimist is a dummy variable indicating whether a subject is among the two most optimistic traders -that is, whether her price forecasts are on average among the two highest -in her respective market across all pre-peak periods. If optimist = 0 the respective subject's price forecasts are on average among the two lowest across all pre-preak periods and she is therefore classified as a pessimist. Clustered standard errors on the subject-level are provided in parentheses. * , * * , and * * * represent double-sided tests' p-values smaller than .10, .05, and .01.

C Instructions of the Experiments
All experimental studies and supplementary questionnaires described in this paper were conducted in German. In the following we display the translated versions. The original versions in German language are available upon request.

Description of the Game
This experiment is designed to evaluate economic decision making. Your task is to indicate which of the 25 boxes on the decision-screen (on the next page), which are arranged in five rows and five columns, you would like to select. Under one of these boxes will be placed a

Payment
Your payment is dependent on whether the bomb is under a selected box or not. If the bomb is not under a box which you selected, you get a payment of 40 Cents per selected box, but if the bomb is under a box you will not get a payment for this experiment.

Information for your payment
The reversing of the boxes will be after the second experiment. You will see the screen with your selected boxes again and with a click on "reverse selected boxes" you will see if you have selected the box with the bomb (indicated by red color). You will see your total payment of this experiment on the bottom right of the screen.

Important Information
• You can select and deselect boxes as often as you like.
• You have 240 seconds for your decision.
• The reversing of the boxes will be after the second experiment.

C.2 Experimental Instructions for the Market Experiment
In the following, text parts included only in Treatment info are in italics. Text parts in standard font are identical for all treatments.

Background of the experiment
This experiment replicates an asset market in which 8 traders can trade assets of a fictitious company over 20 periods, where each period lasts for 120 seconds. You receive an initial endowment of 20 assets and 560 Taler (experimental currency, converted to EUR at the end of the experiment). Your asset and Taler holdings carry over from one period to the next. Your asset and Taler holdings cannot drop below zero.
To familiarize you with the software and the trading mechanism, there will be 2 trial periods, which are not relevant for your final payment.
Information on the market architecture and your tasks as a trader

1) Trading
Participating in the market as a trader you can sell and buy assets. Trade is accomplished in form of a continuous double auction. That is, every trader can buy as well as sell assets. You can submit as many buy and sell orders (with at most 2 decimal places) as you like. You have to specify the number of stocks you want to trade for every order.
If you buy assets, your Taler holdings will be decreased by the respective expenditures (price x quantity) and the number of assets will be increased by the quantity of newly bought assets.
Inversely, if you sell assets, your Taler holdings will be increased by the respective revenues (price x quantity) and the number of assets will be decreased by the quantity of newly sold assets. Please note that you can only buy (sell) as many assets as are covered by your Taler (asset) holdings -this includes also your active offers in the market.
Each share held at the of a trading period will pay a dividend, which amounts to 1.20 Taler or 1.60 Taler per share with equal probability. The randomly selected dividend is the same for each share and is newly determined each period. Additionally, you receive interest payments of 5% on your current Taler holdings. These dividend and interest payments are added to your Taler holdings.
At the end of the experiment the units you own are bought back by the experimenter at a buyback price of 28 Taler per share.
At the beginning of each new period you receive an income of 100 Taler. This will be added to your Taler holdings. Example for the calculation of the dividend and your asset and Taler holdings: Suppose you begin the experiment with 560 Taler in cash and 20 assets. If you make no purchases or sales, the interest earnings will be 28 Taler, that is 560 × 0.05 = 28 Taler. If the randomly determined dividend turns out to be 1.20 Taler, the total dividend income will be 20 × 1.20 = 24 Taler. These 28 + 24 = 52 Taler, as well as your income of 100 Taler, will be added to your Taler holdings at the end of the period. Hence, your initial endowment at the beginning of the next period will be 6 assets and 712 Taler ( 560 + 52 + 100).

2) Predictions
Additionally to your trading activity you will be asked to predict the development of market prices over the three subsequent periods. Exceptions are the penultimate period with two predictions and the last period with one prediction.
If your prediction is within +-5% of the average market price in the corresponding period, your earnings from the three predictions are 50 Taler each. That is, you can earn a maximum of 150 Taler for your predictions in each period. These earnings will be added to your Taler holdings at the end of the last period.

Calculation of your payment
At the end of the experiment, your payment as a trader is calculated as follows: The number of assets you hold are bought back by the experimenter at the end of the experiment (after period 20). You will receive 28 Taler for each asset you hold. The total amount is added to your final cash (Taler) holdings. Additionally, your earnings from all your predictions will be added to your Taler holdings.
Final Wealth in Taler = asset holdings * 28 Taler + Taler holdings + income from market predictions Your earnings from this experiment will then be converted to EUR using a conversion rate of 1 Euro for 400 Taler.

Trading Screen
Price chart of the current period Submit BUY order: you have to enter the offered price and quantity. Trading does not take place until another participant accepts your offer.
Overview of your current holdings in asset and cash (Taler) SELL: You sell the entered quantity at the price of the offer with the blue background. If you enter a higher quantity than offered in the blue box, you sell the offered quantity at most.
List of all orders to SELL from all traders your own offers are in blue. The highlighted offer is the best offer, i.e. the least expensive one for a buyer.
Liste of all orders to BUY from all tradersyour own offers are in blue. The highlighted offers is the best offer, i.e. the most expensive one for a seller.
Submit SELL order: analogous to "Submit BUY order" (see above).
BUY: You buy the entered quantity at the price of the offer with the blue background. If you enter a higher quantity than offered in the blue box, you buy the offered quantity at most.

History Screen
Dividend per share (1.20 oder 1.60 with a probability of 50% each)

Number of shares x Dividend
Your Taler holdings including shares valued at the current market price Taler holdings x 5 % Price Chart displaying average prices of previous periods