University of Southern California Dissertations and Theses

Essays in behavioral and entrepreneurial finance

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Essays in behavioral and entrepreneurial finance

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Content ESSAYS IN BEHAVIORAL AND ENTREPRENEURIAL FINANCE
by
Aleksandar Giga
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ECONOMICS)
August 2016
Copyright 2016 Aleksandar Giga
To my family, for their unwavering love and support. Beskrajno vam hvala.
ii
Acknowledgments
This was a long and arduous journey, but one from which I thrived, in large part due to all the
wonderful people I met along the way. To some I owe a huge debt of gratitude. First among them
is my advisor, Fernando Zapatero. He taught me much and more, and enabled me to explore
my interests and simply enjoy my research. He was always ready to bounce ideas no matter
how unconventional they sounded. He supported each and every one of my various research
undertakings and was tolerant to my repeated failures, all throughout being a constant source of
encouragement. I never left his office without a fresh dose of optimism.
Next, I express my deepest gratitude to Juan Carrillo and Isabelle Brocas. They taught me eco-
nomics, how to run experiments well, and how to write good research papers. Most importantly,
they instilled the scientific rigor in me. Juan’s door was always open, much to my advantage (and
a bit less to his). I am honored to have been their student and hope that one day l will live up to
their standard.
I would also like to thank Arthur Korteweg for being part of my dissertation committee and
guiding me through my project on entrepreneurial finance. I am grateful to Giorgio Coricelli
and David Solomon for their service on my qualifying committee. I am indebted to everyone at
LABEL for helping with the experiment and for enduring my countless presentations and still
providing me with useful feedback each time. Your contribution is invaluable. My special thanks
goes to Mallory Montgomery, Diego Vilán, and Ashish Sachdeva for numerous challenging dis-
cussions. They made me a better economist. I thank the USC’s Department of Economics for the
financial and Young Miller, Morgan Ponder and Fatima Perez for the administrative support.
iii
Lastly, and most importantly, I will be forever grateful to my family - my father Lazar, my
mother Gordana, and my brother Vojislav. Without their loving support and patience, I would
not have had the luxury to follow my passion, and to be where I am today would have been
simply impossible.
iv
Table of Contents
Dedication ii
Acknowledgments iii
List of Tables vii
List of Figures viii
Abstract ix
Chapter 1: Risk Aversion in a Dynamic Asset Allocation Experiment 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Classification of subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4.1 Econometric model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4.2 Constrained choices: willingness to borrow and short sell . . . . . . . . . . . 13
1.4.3 Classification of subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.3.1 Unconstrained subjects . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.3.2 Constrained subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.5 Behavioral anomalies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.5.1 Path dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.5.2 Gain/loss asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.5.3 Classification of behavioral types . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.6 Testing the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.6.1 Out-of-sample predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.6.2 Risk type predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.7 Aggregate risk attitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Chapter 2: Skewness Seeking in a Dynamic Portfolio Experiment 31
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.2 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.2.1 Treatment 1: benchmark portfolio allocation (NoBet) . . . . . . . . . . . . . . 35
2.2.2 Treatment 2: allocation in the presence of a skewed asset (Bet) . . . . . . . . 37
2.2.3 Treatment 3: skewed asset with feedback (Bet&Box) . . . . . . . . . . . . . . 38
2.2.4 Payments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.3 Risk attitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
v
2.4 Betting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.4.1 General betting behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.4.2 Effects of wealth and end of path . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.5 Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.5.1 Wealth and feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.5.2 Effect of feedback on bet purchases . . . . . . . . . . . . . . . . . . . . . . . . 52
2.5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Chapter 3: Firm Financing in Equity Crowdfunding 56
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.2 Equity Crowdfunding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.4.1 Correlates to Funding Success . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.4.2 Early and Late Funding Raised . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Bibliography 76
Chapter A: Appendix A 82
Chapter B: Appendix B 91
vi
List of Tables
1.1 Risk types as a function of risk aversion parameters. . . . . . . . . . . . . . . . . . . 8
1.2 Number of subjects affected by the constraints. . . . . . . . . . . . . . . . . . . . . . . 13
1.3 Risk attitude of the unconstrained subjects. . . . . . . . . . . . . . . . . . . . . . . . . 16
1.4 Risk estimates: a comparative analysis with Holt and Laury (2002) . . . . . . . . . . 17
1.5 Risk attitude of constrained subjects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.6 Consistency in classification - early paths vs. late paths . . . . . . . . . . . . . . . . . 24
1.7 Type frequency - early paths vs. late paths . . . . . . . . . . . . . . . . . . . . . . . . 25
1.8 Risk attitude of representative agents . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.1 Behavior following feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.1 Funding Campaigns Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.2 Management Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.3 Product Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.4 Firm General Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.5 The Likelihood of Raising Funds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.6 The Amount of Raised Funds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.7 The Effect of Early on Later Funding Raised . . . . . . . . . . . . . . . . . . . . . . . 75
B.1 Consistency in classification - early periods vs. late periods . . . . . . . . . . . . . . 91
B.2 Type frequency - early periods vs. late periods . . . . . . . . . . . . . . . . . . . . . . 91
vii
List of Figures
1.1 Screenshot of path 1 - period 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2 Estimated parameters of the 81 unconstrained subjects . . . . . . . . . . . . . . . . . 15
1.3 Out-of-Sample Fit (100 repetitions) - HARA vs. Random . . . . . . . . . . . . . . . . 23
1.4 Out-of-Sample Fit (100 repetitions) - HARA vs. CRRA . . . . . . . . . . . . . . . . . 24
1.5 Estimated parameters of representative agents (81 unconstrained subjects) . . . . . 27
1.6 Out-of-Sample Fit (100 repetitions) - HARA vs. CRRA . . . . . . . . . . . . . . . . . 29
2.1 Screenshot of path 1 / period 4 in NoBet treatment . . . . . . . . . . . . . . . . . . . 36
2.2 Screenshot of path 3 / period 1 in Bet treatment . . . . . . . . . . . . . . . . . . . . . 38
2.3 Screenshot of path 4 / period 5 in Bet&Box treatment . . . . . . . . . . . . . . . . . 39
2.4 Average proportion of wealth in asset A (Bet and Bet&Box treatments) . . . . . . . 40
2.5 Comparison of subjects’ allocation of risk across treatments . . . . . . . . . . . . . . 41
2.6 Risk allocation and bet purchases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.7 Frequency of bet purchase over time . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.8 Distribution of stopping times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.9 Standard deviation of portfolio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.10 Frequency of bet purchase by wealth level . . . . . . . . . . . . . . . . . . . . . . . . 46
2.11 Frequency of bet purchase by period and treatment . . . . . . . . . . . . . . . . . . 47
2.12 Last period effect and wealth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.13 Frequency of bet purchase in the last period . . . . . . . . . . . . . . . . . . . . . . . 48
2.14 Distribution of lookups in the population . . . . . . . . . . . . . . . . . . . . . . . . 50
2.15 Lookups in Min, Ave and Max boxes by wealth quintile . . . . . . . . . . . . . . . . 51
2.16 Betting frequency by wealth quintiles and lookup when lead vs. lag . . . . . . . . . 53
3.1 Early and Late Funding Raised . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
B.1 Out-of-Sample Fit - HARA vs. CRRA in early vs. late periods . . . . . . . . . . . . . 92
viii
Abstract
This dissertation is a collection of studies on investments and investment behavior. The first
two chapters, products of collaboration with my advisors, Isabelle Brocas, Juan Carrillo, and Fer-
nando Zapatero, describe investment behavior in an experiment in dynamic portfolio allocation
problems. Chapter 3 studies early-stage firms’ financing campaigns.
In chapter 1, my coauthors and I analyze a controlled laboratory experiment we conducted,
where subjects dynamically choose their portfolio allocation between a safe and a risky asset.
We first derive analytically the optimal allocation of an expected utility maximizer with HARA
utility function. We then fit the experimental choices to this model to assess the risk attitude of
our subjects.
Despite the substantial heterogeneity across subjects, decreasing absolute risk aversion and
increasing relative risk aversion are the most prevalent risk types, and we can classify more than
50% of the subjects in this combined category. We also find evidence of increased risk taking after
a gain but the effect is small in magnitude. Overall, our robustness tests show that the behavior
of subjects is generally well accounted for by the HARA expected utility model.
Finally, the analysis at the session level suggests that the behavior of the representative agent
is less heterogeneous and closer to (though statistically different from) constant relative risk aver-
sion.
In chapter 2, we analyze results from a controlled laboratory experiment in which subjects
dynamically choose to allocate their portfolio between (i) a safe asset, (ii) a risky asset and (iii) a
skewed asset with negative expected value (a “bet"), in an environment where they can sometimes
choose to acquire some information about the performance of their peers.
ix
We find three distinct groups of individuals: 16% of subjects never buy the bet, 29% of subjects
learn not to buy the bet and 55% subjects persist purchasing the bet throughout the experiment.
Among the latter group, purchases are most frequent when subjects are rich and when it is their
last opportunity.
Our subjects are also interested in the wealth of others, especially relative to theirs. Indeed, a
subject with low, medium and high wealth has a preference for finding out what is the minimum,
average and maximum wealth in the session, respectively. We also find that subjects buy more
bets when they are richer and (unexpectedly) learn that their peers outperform them.
The preference for skewness studied in chapter 2 drew my attention to an asset class where
positive skewness is arguably the largest - start-up equity. Entrepreneurial finance is therefore
the topic of chapter 3, where I analyze firms of entrepreneurs that seek funds through equity
crowdfunding, a relatively new source of financing whereby individuals and businesses solicit
funds from a broad audience usually through an internet platform. This is the most comprehen-
sive study of equity crowdfunding to date. I find that firms with larger and more experienced
management tend to raise more funds. Furthermore, I find that the amount of financing in the
early stage of the campaign has no effect on further funding.
x
Chapter 1
Risk Aversion in a Dynamic Asset
Allocation Experiment
1.1 Introduction
Understanding risk is of paramount importance in economics and finance. From a microeconomic
perspective, the behavior of entrepreneurs crucially depends on their risk preferences. From a
macroeconomic perspective, the risk attitude of the representative agent shapes investment and
capital accumulation.
The goal of the study is to design a task that provides a reliable assessment of the risk attitude
of individuals in a controlled yet comprehensive and realistic financial environment. To this purpose,
we conduct a laboratory experiment where subjects choose how to invest their wealth between
two assets, one safe and one risky, during 15 investment paths. The subject (she) starts a path
with an initial endowment, which she allocates between the assets. After observing the returns
of the assets, she is asked to reallocate her wealth, and the new returns are observed. This
dynamic process lasts for 10 periods, after which her final payoff is recorded and a new path is
started with the same initial endowment as the previous path. Overall, each subject makes 150
investment decisions with different levels of wealth.
In this experimental setting, we address the following questions. First, are our subjects similar
in their risk attitudes or do we observe substantial heterogeneity? Second, can we fit the data
well using a structural estimation of an expected utility model? If so, how general should the
specification of the utility function be and what are the most prevalent risk attitudes? Third and
related, do we observe frequent and/or severe deviations from neoclassical theory? Fourth, if
we analyze the data at the session level, how does the behavior of the “representative agent"
compares to that of subjects taken individually?
1
To answer these questions, we first derive analytically the optimal portfolio allocation of an
expected utility maximizer who has a general, two-parameter hyperbolic absolute risk aversion
(HARA) utility function. Given this analytical characterization, we can structurally estimate the
absolute and relative risk aversion parameters of our subjects using the 150 choices made in the
experiment.
We find that our experimental subjects are highly heterogenous. At the same time, some
risk attitudes are more prevalent than others. Most individuals increase the total amount of
wealth invested in the risky asset as their wealth increases (decreasing absolute risk aversion
or DARA). They also decrease the fraction of wealth invested in the risky asset as their wealth
increases (increasing relative risk aversion or IRRA). Overall, more than half of our subjects can
be confidently classified in the combined DARA-IRRA category, the risk attitude conjectured by
Arrow (1971) to be most natural among investors.
Our robustness checks show that the HARA utility function is consistent and has good pre-
dictive power in out-of-sample analysis. We find a statistically reliable relationship between the
investment decision and the set of independent variables. Also, when we estimate the parame-
ters using a subsample (either 8 paths randomly chosen or the first 5 periods of all paths) we can
predict well the behavior in the complementary subsample. Finally, if we restrict attention to a
constant relative risk aversion utility function (CRRA) the accuracy of our estimates suffer sig-
nificantly for one-third of our population and not significantly for the rest. This provides mixed
support for CRRA, the utility function most commonly employed in theoretical and empirical
studies. On the one hand, it has a lot of appeal due to its simplicity and convenience. On the
other hand, it may yield biased estimates of individual risk attitudes for a non-negligeable subset
of the population.
We also find some evidence of biases. A few subjects (19%) change their risk taking behavior
over time. More significantly, 44% of subjects exhibit a gain/loss asymmetry. Of these, the vast
majority (39%) take more risk after a gain and only 5% take more risk after a loss. Overall, many
subjects exhibit some anomaly. However, these are small in magnitude which is why, despite
their presence, the expected utility model performs well.
2
Finally, we conduct an aggregate analysis. For each session, we compute the per capita wealth
in each period and endow a fictitious “representative agent" with this amount. We find that,
just like the majority of our individuals, representative agents are typically best captured by a
DARA-IRRA risk type. However, their types are less heterogeneous and closer to constant risk
aversion than those of individuals. This suggests that restricting to CRRA functions when we
study aggregate behavior may be a reasonable approximation.
Before proceeding to the analysis, we present a brief literature review. Methods to elicit risk
attitudes abound in economics. Perhaps the most widely employed technique is the “list method"
proposed by Holt and Laury (2002), hereafter [HL]. In this elegant procedure, subjects are offered
choices between two lotteries, where each lottery is identified by two possible outcomes and one
probability. By varying the stakes and probabilities, one can assess the subjects’ risk attitudes as
a function of wealth. The method is fast, intuitive and easy to implement. It offers an excellent,
simple measure to compare risk attitudes across individuals. It has been extended in several
directions either to improve the precision of estimates (Andersen et al. (2006), Maier and Ruger
(2010)) or to obtain a more efficient algorithm (Wang et al. (2014)). Other risk elicitation designs
have been proposed by Becker et al. (1964), Binswanger (1980), Hey and Orme (1994), Eckel and
Grossman (2008) and Sokol-Hessner et al. (2009) among others.
1
However, simplicity comes at the expense of a design that is not intended (and therefore not
suitable) to provide a precise measure of risk preference of individuals endowed with a general
utility function. For example, the [HL] procedure assumes CRRA utility so, by construction, it
cannot assess the changes in the percentage of risk taking as a function of wealth. It also provides
only interval estimates of the parameter, so it is difficult to assess the fit of the data to the utility
specification and to challenge the model.
The risk attitudes have been explored in dynamic settings too, most notably in the game show
“Deal or No Deal". For example, Post et al. (2008) find that the Expected Utility Theory cannot
explain the contestants’ decisions well and point that previous outcomes play a significant role in
the choices of participants. They assume a CRRA functional form, however. Andersen et al. (2008)
summarize this strand of the literature. In their own laboratory replication of the "Deal or No
1
For surveys of empirical and experimental elicitation procedures and results, see Harrison and Rutström (2008),
Charness et al. (2013) and Friedman et al. (2014).
3
Deal", they do not constrain their estimation to a single parameter EUT model. Estimating average
risk preferences, they find overall moderate levels of risk aversion with evidence suggesting IRRA.
Described above, our methodology has a number of advantages. First and foremost, we can
structurally estimate an asset allocation model based on a rich utility function for each individual
subject. We can also determine the loss in predictive and explanatory power when we restrict to
simpler utility functions. Second, we can measure standard errors of individual estimates and
assess the fit of the data. We can also study the structure of the noise and its relation to wealth
levels. And third, our dynamic framework is useful for measuring any behavioral anomaly due
to repeated exposure to risk. We can detect any gain/loss asymmetry in behavior and determine
whether a subject changes her risk attitude over the course of the experiment.
Given the dynamic asset accumulation nature of the experiment, the paper also relates to the
experimental literature on portfolio allocation. Levy (1994) proposes a non-structural analysis
to study risk attitudes in a market experiment, and finds support for DARA but not for IRRA.
In Rapoport (1984) and Rapoport et al. (1988), subjects invest in securities and a safe asset in a
dynamic setting, and find evidence in favor of IRRA and against CARA or CRRA. Other related
individual asset allocation experiments test whether subjects allocate portfolios efficiently (Kroll
et al. (1988), Kroll and Levy (1992), Sundali and Guerrero (2009)).
Last, our results on path-dependence of choices and gain/loss asymmetry are related to the lit-
erature that highlights behavioral anomalies in choice under uncertainty. Discrepancies between
observed behavior and theoretical predictions may come from errors in choices (Jacobson and
Petrie (2009)), frequency of feedback (Gneezy and Potters (1997); Thaler et al. (1997)), reference
dependent preferences (Koszegi and Rabin (2006, 2007); Abeler et al. (2011); Knetsch and Wong
(2009); Ericson and Fuster (2011); Sokol-Hessner et al. (2009)), or disappointment aversion (Choi
et al. (2007); Gill and Prowse (2012)) among other reasons. Our design is not intended to test for
specific behavioral anomalies, nor to fit behavioral models. However, like in Thaler and Johnson
(1990), we find that prior gains (losses) decrease (increase) risk aversion for many of our subjects.
The article is organized as follows. In section 1.2, we present the theoretical framework. In
section 1.3, we describe the experimental setting. In section 1.4, we present the econometric model
and the results of the classification analysis. In section 1.5, we investigate behavioral anomalies.
In section 1.6, we study the explanatory and predictive power of our expected utility model. In
4
section 1.7, we provide an aggregate analysis of the data. In section 1.8, we offer some concluding
remarks.
1.2 Theory
Consider the following complete markets, continuous-time, dynamic portfolio choice problem.
At each instant t, an agent (she) allocates her wealth X(t) between two assets, a risky asset A and
a safe asset B. At t = 0, her initial wealth is X(0) = x
0
> 0. The temporal horizon is finite and
equal to T. The agent can reallocate her portfolio at each instant t until date T, time at which
she enjoys the accumulated wealth X(T). Therefore, at each t, she maximizes the expected utility
of wealth at time T. We assume that the agent’s preferences are characterized by the general
Hyperbolic Absolute Risk Aversion (HARA) utility function with two parameters, g and h, first
applied by Merton (1971) to a dynamic portfolio allocation. Formally:
U(X)=
1g
g

X
1g
+h

g
(1.1)
with the following restrictions:
g6= 1,
X
1g
+h> 0 and h = 1 if g=¥
This family of utility functions is rich in the sense that it encompasses utility functions with
absolute and relative risk aversion that are increasing, constant or decreasing depending on the
risk parameters g and h.
2
The agent exhibits decreasing absolute risk aversion (the empirically
most plausible case) when¥ < g < 1 and constant absolute risk aversion when g! +¥ or
g!¥. She exhibits increasing, constant and decreasing relative risk aversion when h > 0,
h = 0 and h< 0, respectively.
The price of the safe asset B(t) evolves as follows:
dB(t)= rB(t)dt (1.2)
2
A more general specification of the HARA utility function is: U(X)=
1g
g

bX
1g
+h

g
. In our case, the parameter
b is not identified and cannot be estimated.
5
where r > 0. The price of the risky asset A(t) follows a geometric brownian motion with drift
m (> r) and diffusion s (> 0). Formally:
dA(t)= mA(t)dt+sA(t)dW(t) (1.3)
where W(t) is a brownian motion. Let p(t) be the amount of wealth allocated to the risky asset
A at date t. The wealth X(t) grows as follows:
dX(t) = p(t)mdt+p(t)sdW(t)+[X(t)p(t)] rdt
= [X(t)r+p(t)(m r)] dt+p(t)sdW(t)
At each date t, the agent solves the following problemP:
P : max
p
E[U(X(T))]
s.t dX(t)=[X(t)r+p(m r)]dt+p(t)sdW(t)
X(0)= x
o
Given the complete market assumption and the specification of utility and asset returns, our
problem has a closed-form solution which we summarize in the next result.
Proposition 1 If markets are complete and time is continuous, the optimal amount allocated to the risky
asset at date t when the accumulated wealth is X(t) is:
ˆ p(t)=
m r
s
2

X(t)
1g
+h e
r(Tt)

(1.4)
Proof. It follows a standard martingale argument (proof available upon request).
The amount allocated to the risky asset depends on the current wealth X(t), the investment
horizon left T t, the returns of the assets and the risk aversion parameters. The model predicts
that it increases in the current wealth if the agent exhibits decreasing absolute risk aversion (g<
1). The allocation depends on current wealth irrespective of how wealth has been accumulated in
the past. Finally, ˆ p(t) increases (respectively, decreases) as time passes when h> 0 (respectively,
h< 0). Note thath = 0 corresponds to the CRRA specification, where the agent invests a constant
6
proportion of her wealth in the risky asset irrespective of the level of wealth and the horizon left
to invest.
The risk attitude of each agent is defined by both her absolute risk aversion (ARA) and her
relative risk aversion (RRA): increasing (I), constant (C) or decreasing (D) in wealth. These are
determined by the (g,h) parameter combination of the individual, which from now on will be
called her “type". Equation (1.4) has predictions for each type in terms of the amount of wealth
invested in the risky asset. First, all types with a DARA component increase the risky investment
as wealth increases. Of these, an agent with decreasing relative risk aversion (DARA-DRRA type)
is willing to short-sell when her wealth is low ( ˆ p(t) < 0 when X(t) is small). By contrast, an
agent with increasing relative risk aversion (DARA-IRRA type) is willing to borrow when her
wealth is low ( ˆ p(t)> X(t) when X(t) is small). Second, types with a IARA component decrease
the risky investment as wealth increases. Of these, an agent with increasing relative risk aversion
(IARA-IRRA type) will invest a positive amount of wealth in the risky asset only when her wealth
is low.
Note that the closed-form solution for the optimal portfolio choice requires a complete mar-
kets assumption, otherwise it cannot be characterized analytically. Therefore, if we impose the
extra restriction ˆ p(t) 2 (0, X(t)), then the inability to invest unrestrictedly both now and in
the future affect current decisions. Nevertheless, some of the qualitative properties of the solu-
tion remain. In particular, agents represented by DARA, CARA and IARA utility functions will
respectively choose to invest more, the same and less total amounts in the risky asset as their
wealth increases. Similarly, agents represented by DRRA, CRRA and IRRA utility functions will
respectively choose to invest a larger, an equal and a smaller fraction of their wealth in the risky
asset as their wealth increases.
Table 1.1 summarizes the risk types as a function of h and g and given the parametric restric-
tions in the utility function. It shows which types are likely to be constrained and for which
wealth levels (indicated by * and **). It also shows how investment varies with wealth.
7
g< 1 g> 1 g=¥ g=+¥
h< 0 DARA-DRRA* — — —
h = 0 DARA-CRRA — — —
h> 0 DARA-IRRA** IARA-IRRA** CARA-IRRA** CARA-IRRA**
¶ ˆ p/¶X> 0 ¶ ˆ p/¶X< 0 ¶ ˆ p/¶X = 0 ¶ ˆ p/¶X = 0
* ˆ p = 0 for small X and ˆ p = X for large X; ** ˆ p = X for small X and ˆ p = 0 for large X
Table 1.1: Risk types as a function of risk aversion parameters.
1.3 Experimental Design
The main objective of the paper is to study the dynamic portfolio choice of agents in a controlled
laboratory setting. To this purpose, we design a dynamic investment problem that follows as close
as possible the setting of the theory section. Subjects in the experiment allocate wealth between
a safe and a risky asset during 15 investment paths consisting of 10 periods each. The experiment
consists of 13 sessions run in the Los Angeles Behavioral Economics Laboratory (LABEL) at the
University of Southern California.
3
Each session has between 7 and 10 subjects for a total of
120 recruited subjects, of which 3 are omitted from the analysis due to software malfunction.
All subjects participate in three treatments. The first treatment corresponds to the paradigm we
study in this chapter. Results of the other treatments are reported in chapter 2.
Each subject (she) starts each path in period 1 with an endowment of $3, which she allocates
between two assets, a risky asset A and a safe asset B. After period 1 ends, each subject earns
a return on her portfolio and moves to period 2. She then reallocates her portfolio and earns
new returns. This process continues for a total of 10 periods. After period 10, the investment
path ends and the subject’s final payoff in that path is recorded. Each subject then moves to the
next investment path, where her endowment is reset to $3. Subjects have 10 seconds to make
their decision in period 1 of each path and 6 seconds in periods 2 to 10. They all begin and
end investment paths at the same time. Finally, all subject go through 15 paths for a total of 150
choices. Subjects know at the beginning of the experiment the number of paths and periods in
path they will go through.
3
For information about the laboratory, please visit http://dornsife.usc.edu/label.
8
The return of the safe asset B is 3% while the return of asset A is drawn from a Normal dis-
tribution with mean 6% and standard deviation 55%.
4
The parameters do not change throughout
the experiment. The draw of the return is presented in the form of a multiplier, that is, the num-
ber that multiplies the allocation to that asset. All participants in a session are subject to the same
draws, which makes it possible to analyze the aggregate portfolio of each session (see section
1.7). At the same time, we make clear to each subject that her return is in no way affected by the
allocation decision of the other subject.
Figure 1.1 provides a screenshot that describes what a subject sees in a given period of a path.
Current wealth is represented by the vertical bar positioned above the current period number
(period 4 in this example). When gray, the bar is not active and the wealth is not allocated to
either asset. Subjects need to click on the bar to activate it and move a horizontal slider to divide
their current wealth between assets A and B. The upper portion of the bar represents the money
invested in A and the lower portion represents the money invested in B. The figures on the
right side of the bar show the allocation, which can be displayed either in percentage or in dollar
terms. To facilitate her reasoning, each subject may change the display of the allocation at any
time between percentage in each asset (box labeled “ % ") and total amount in each asset (box
labeled “ $ "). After the period expires, returns are applied and subjects move to the next period.
A new bar with a height corresponding to the new wealth appears to the right of the previous
one for the new period and becomes inactive again. Subjects need to reactivate it to choose a new
allocation, otherwise they earn no interest in that period and their account just carries over. This
helps prevent subjects’ inertia and a bias towards any status quo allocation. Level of inactivity in
our experiment was negligible. Subjects observe bars to the left of the current one (periods 1 to 3
in this screenshot) that reminds them of their past allocations and returns. These bars accumulate
up to period 10, and then are reset for the new path. Finally, the left hand side of the screen has a
summary information of the main ingredients of the experiment: (i) the current path and period;
(ii) a reminder of the mean and standard deviation of returns of assets A and B; (iii) the time left
to make a choice in the current period; (iv) the accumulated wealth in the current path; and (v)
the multiplier of assets A and B in the last period of the current path.
4
This (unrealistically high) standard deviation ensures enough volatility in returns for interesting wealth effects
and comparative statics.
9
Figure 1.1: Screenshot of path 1 - period 4.
This dynamic wealth allocation problem is challenging and may require substantial learning.
To deal with this issue, we employ a highly illustrative 40 minute instructions period using
a neutral language with numerical examples, videos, 5 practice paths and a quiz to test the
subjects’ understanding (instructions can be found in appendix A). In addition, to help with the
cognitive strain, we add a projection bar placed on the right end of the screen (see Figure 1.1). The
projection bar tells the subject what she would expect if she were to keep her current investment
strategy until the last period. The bar shows the potential accumulated earnings from asset B
and identifies the 20th, 50th and 80th percentile of the earning distribution from asset A. As the
participant changes her allocation the projection bar automatically adjusts.
5
At the end of the experiment we collect answers to education, demographic and income
related questions as well as their own description of the strategies employed. Each participant
receives a $5 show-up fee and her final earnings in the final period of one randomly selected path.
Participants are also compensated for participating in the two other treatments. The total length
5
We carefully explain the function of the bar by simulating potential period-by-period trajectories of wealth coming
from a given allocation strategy. The simulation ends each trajectory with a dot, creating a probability distribution of
dots. We then draw a parallel between that probability distribution and the projection bar that the subjects see on their
screen.
10
of the experiment, including the subsequent treatments, is around 2 hours and the average payoff
is $23, with a maximum payoff of $244.
Note that the experimental design follows closely the theory with two important differences,
both introduced for technical reasons. First, choices are made in discrete time, with only 10 deci-
sions per path. Continuous time is difficult to implement in an experimental setting.
6
Even if
time was continuous, real choices still occur in discrete time given the time it takes to evaluate
options and implement decisions. Second, we do not allow our participants to borrow or short
sell, which means that markets are incomplete. Borrowing and short selling are difficult to imple-
ment experimentally since they may result in taking money away from participants. Our data
analysis takes this restriction into account.
1.4 Classification of subjects
Our first objective is to test how well the expected utility theory fits the data and to determine
which subjects exhibit systematic departures. We adopt a structural approach and estimate the
risk parameters (g,h) of each subject assuming they behave according to the expected utility
theory model. We then test for biases. This approach is used to classify our subjects according to
their risk type as well as their likelihood to exhibit a behavioral anomaly.
1.4.1 Econometric model
According to equation (1.4) –and subject to the above mentioned caveats of incomplete markets
and discrete time– expected utility theory predicts that the portfolio allocation and wealth vary
over time according to the following system:
8
>
<
>
:
ˆ p(t)=
m r
s
2

X(t)
1g
+h e
r(Tt)

dX(t)= [X(t)r+ ˆ p(t)(m r)] dt+ ˆ p(t)sdW(t)
6
For the challenges and some creative solutions on how to implement continuous time decisions in experimental
settings, see Friedman and Oprea (2012). Furthermore, see Duffie and Protter (1992) for a theoretical discussion on
convergence of discrete-time processes to continuous-time ones.
11
The parameters g and h can be estimated from the first equation using least squares fitting. Since
our data is obtained in discrete time, we consider the discrete version of the model. For each
individual, in each path i and at each period t, we observe the current wealth X
i,t
and the chosen
allocation of this wealth to the risky asset p
i,t
. Let F
t
= e
r(Tt)
, our structural econometric model
given HARA utility isM
HARA
:
p
i,t
= aX
i,t
+ b F
t
+ u
i,t
(1.5)
where a=
mr
s
2
(1g)
, b=
(mr)h
s
2
and u
i,t
N(0,s
2
u
) is an error term.
7
Given a and b, the parameters
g and h are identified. In the next section, we classify the risk attitude of our subjects by fitting
this model to their decisions.
Note that a myopic decision-maker would maximize the instantaneous expected utility
E[U(X(t))] at each period t. This problem has a simple closed-form solution: the optimal allo-
cation in the risky asset is obtained by replacing e
r(Tt)
with 1 in the equilibrium equation of
Proposition 1. For our data, e
r(Tt)
2 [0.7, 1]. This value is close enough to 1 to make the
myopic model almost indistinguishable from the forward-looking model. Such feature of the
design could potentially be a drawback if the objective was to test for forward-looking behavior.
However, the problem is sufficiently relevant that a test of optimal choice is interesting indepen-
dently of whether we consider the myopic or the forward-looking approach. We will therefore
not report any results for the myopic model.
8
Notice that for an accurate estimation, we need enough variation in wealth within subjects.
In half of our sample, the 5th and 95th percentile of wealth are around $1 and $15, respectively.
For the other half of the sample, the range extends from $1 to $20. Although these figures are not
excessively large, the dispersion is important enough to obtain reliable estimates of absolute and
relative risk aversion.
Lastly, our structural model is well specified only if subjects do not systematically invest all
their wealth in the safe or the risky asset. In other words and as explained before, the structural
model is misspecified for the subjects who are significantly affected by the inability to short sell
7
We relax the assumptions on the error term’s distribution later (see subsection 1.4.3.1).
8
We conducted the same analysis based on the myopic model and we did not find any qualitative changes in the
classification of our subjects.
12
or borrow. This poses a challenge. On the one hand, treating the data as if all choices are interior
amounts to place too much weight on the constrained choices, which biases the interpretation of
the parameters and the residuals of the regression. On the other hand, eliminating the constrained
choices from the analysis biases the estimated parameters as well. The solution we propose is to
classify separately the subjects who hit the bounds often and those who do not.
1.4.2 Constrained choices: willingness to borrow and short sell
Our first task is to determine empirically which subjects are affected by the inability to short-sell
(i.e, to set p
t
< 0) and/or borrow (i.e, to set p
t
> X
t
). For the large majority of our subjects the
pressure to short-sell or borrow is low. At the aggregate level, subjects invest all their wealth in
the safe asset 2.2% of the time and in the risky asset 8.2% of the time.
9
At the individual level,
there is heterogeneity in behavior. Table 1.2 shows the distribution of subjects as a function of
their likelihood to hit the constraints.
% trials
(0%, 10%] (10%, 20%] (20%, 100%] Total
Hit p
t
= 0 only 10 0 0 10
Hit p
t
= X
t
only 24 3 8 35
Hit p
t
2f0, X
t
g 13 11 14 38
p
t
2(0, X
t
) always n/a n/a n/a 34
Table 1.2: Number of subjects affected by the constraints.
Only 34 subjects never hit a constraint. However, if we combine these subjects with those who
hit the constraints no more than 10% of the time we can account for 81 individuals, or 69% of
the sample. In what follows, we call these subjects ‘unconstrained’. Of the remaining subjects, 11
would have liked to borrow and 25 would have liked both to borrow and short sell. We call these
subjects ‘constrained’.
10
9
A choice is defined as non-constrained (interior) when the allocation to the risky asset is bigger than 2% and
smaller than 98% of the wealth.
10
We considered other more conservative thresholds for the division between constrained and unconstrained subjects
and found similar results.
13
1.4.3 Classification of subjects
1.4.3.1 Unconstrained subjects
Our next task consists in estimating the risk aversion parameters (g,h) of the subjects for which
the econometric modelM
HARA
is well specified, that is, the 81 unconstrained subjects who either
never or rarely hit the short selling and borrowing constraints. EstimatingM
HARA
presents a few
challenges. Given our observations are repeated measures for the same subject and given wealth
is following a stochastic process, we need to be careful about issues that arise naturally in this
time series framework and that may contradict the underlying assumptions required to use the
least squares method.
First, the error term should have a constant variance. We run a standard OLS on each individ-
ual’s dataset and apply the White test to detect the presence of heteroscedasticity. We find that
the variance of the residuals increases with the level of wealth for 73 out of the 81 unconstrained
subjects (at the 5% significance level) and is constant for the rest.
11
Second, error terms should be uncorrelated across periods. We test for serial correlation for
each participant by looking at the residuals of the OLS regression, denoted by ˆ u
i,t
. Note first that
an error at period t 1 applied to the amount invested in the risky asset at that period affects the
wealth level at period t. Therefore, regressors are not independent of the error term. To account
for this, we use the Breusch-Godfrey test which allows explanatory variables not to be strictly
exogenous. Formally, we consider the regression:
ˆ u
i,t
= b
0
+b
1
X
i,t
+b
2
F
t
+r ˆ u
i,t1
+ v
i,t
where the X
i,t
and F
t
components account for weak exogeneity and v
i,t
are assumed to be i.i.d.
with normal distributionN(0,s
2
v
). We use robust standard errors in our test. We find first
11
Of the 73 heteroscedastic subjects, 41 choose the percentage display more than 80% of the time and only 24 choose
the absolute amount display more than 80% of the time. By contrast, of the 8 homoscedastic subjects, 3 choose
the percentage display more than 80% of the time and 4 choose the absolute amount display more than 80% of the
time. Since the vast majority are heteroscedastic, the evidence is not sufficient to conclude a positive relationship
between reasoning in percentage terms and exhibiting increased volatility with wealth. However, it is an interesting
and intuitive possibility worth of future exploration.
14
order serial correlation (r > 0) for 63 out of 81 subjects. To correct for heteroscedasticity and
autocorrelation, we run the OLS regression with Newey-West standard errors.
Figure 1.2 displays the estimated(g,h) risk parameters of the 81 unconstrained subjects using
the structural modelM
HARA
presented in equation (1.5). Table 1.3 reports the relative and abso-
lute risk aversion attitudes based on the estimated parameters. We observe substantial hetero-
geneity in risk attitudes. At the same time, there is a concentration in the upper left quadrant:
the vast majority of subjects are DARA ( g< 1 for 84% of subjects) and IRRA (h > 0 for 70% of
subjects). Overall, 54% of subjects are willing to increase their total investment in the risky asset
and decrease the fraction of investment in the risky asset as their wealth increases. These are
the DARA-IRRA subjects (g < 1 and h > 0) conjectured by Arrow (1971) to be the empirically
most plausible types. By contrast, the simple one parameter specifications commonly used in the
literature do not capture well the risk attitude of many of our subjects: only 15% of our subjects
are CARA (g!+¥) and 16% are CRRA (h = 0).
12
Figure 1.2: Estimated parameters of the 81 unconstrained subjects
12
For our classification, we use CARA and CRRA as the null hypotheses which may over-classify subjects in those
categories.
15
Risk attitude No. of subjects
DARA-DRRA 11
DARA-CRRA 13
DARA-IRRA 44
IARA-IRRA 1
CARA-IRRA 12
Total 81
Table 1.3: Risk attitude of the unconstrained subjects.
A natural question is to determine how these results compare to the existing estimates in the
literature such as, for example, Holt and Laury (2002), hereafter [HL]. To address this issue, we
estimate our structural model assuming the familiar functional form:
˜
U(X)=
X
1x
1x
used in [HL]. In this case, the solution to the problemP described in section 1.2 is well-established
in the literature. Indeed, the agent invests a constant fraction of wealth in the risky asset:
ˆ p(t)=
1
x
m r
s
2
X(t).
Analogously to our strategy in section 1.4.1, we estimatex from the following econometric model:
p
i,t
= cX
i,t
+n
i,t
(1.6)
where c =
mr
xs
2
and n
i,t
N(0,s
2
n
) is an error term. Let us call this modelM
CRRA
. We compare
our estimates of x to those in [HL]. Because of the way the experiment is designed, [HL] only
gives range estimates for the parameter x. Table 1.4 summarizes the proportion of subjects who
fall in each of the six ranges of x in our model (M
CRRA
) as well as in the low stakes ($0.10 to
$3.85, HL-low) and high stakes ($2 to $77, HL-high) treatments of Holt and Laury (2002).
Our estimates are substantially more concentrated than in [HL]. Only 11% of our subjects
exhibit risk-neutrality or risk-loving preferences (x < 0.15) as opposed to 34% and 19% in [HL-
low] and [HL-high] respectively. Unlike [HL], we also find no evidence of high (0.97 x < 1.37)
or extremely high (1.37 x) risk aversion. Overall, we have twice as many subjects as [HL] in
16
Risk Aversion HL-low HL-high M
CRRA
x< 0.15 .34 .19 .11
0.15 x< 0.41 .26 .19 .61
0.41 x< 0.68 .23 .23 .27
0.68 x< 0.97 .13 .22 .01
0.97 x< 1.37 .03 .11 .00
1.37 x .01 .06 .00
no. of subjects 175 150 81
Table 1.4: Risk estimates: a comparative analysis with Holt and Laury (2002)
the expected range (88% against 49% and 42% in 0.15 x < 0.68, which [HL] label as slightly
risk averse and risk averse). These differences are important. They are partly due to differences
in the design of the two experiments and partly due to the misspecification of the CRRA utility
function in our experiment (and possibly in theirs as well). However, the results do not seem in
contradiction. They also highlight the advantages of a rich experimental setting to better estimate
risk aversion and a two-parameter specification to capture the heterogeneity present in the relative
risk aversion of subjects.
1.4.3.2 Constrained subjects
Next, we study the risk attitude of the 36 subjects who, according to the analysis in section 1.4.2,
are constrained by their inability to borrow and short sell. As noted before, the tendency to invest
all wealth in the safe or the risky asset should depend on the amount of wealth. We first assess
how wealth affects their probability of hitting each bound. More specifically, we estimate a probit
regression on the following two models:
p
max
i,t
= b
max
0
+ b
max
1
w
i,t
+e
max
i,t
p
min
i,t
= b
min
0
+ b
min
1
w
i,t
+e
min
i,t
where p
max
i,t
takes a value of 1 if p
i,t
= w
i,t
and 0 otherwise, and where p
min
i,t
takes a value of 1 if
p
i,t
= 0 and 0 otherwise. We establish an effect when b
max
1
or b
min
1
are different from zero at the
5% significance level.
17
We find three distinct groups of individuals. The “constrained IRRA" group comprises 28 sub-
jects, who invest their entire wealth in the risky asset when their wealth is low enough (b
max
1
< 0)
or invest their entire wealth in the safe asset when their wealth is high enough (b
min
1
> 0) or both.
This behavior is consistent with IRRA, although it can also be compatible with risk neutrality for
low enough wealth levels.
13
The “constrained irregular" group comprises 7 subjects who exhibit
an irregular and volatile behavior with no discernible patterns or statistically significant effects.
Finally, the “constrained DARA-DRRA" group comprises 1 subject who invests his entire wealth
in the safe asset when his wealth is low enough (b
min
1
< 0) and in the risky asset when his wealth
is high enough (b
max
1
> 0), a behavior consistent only with DARA-DRRA. The result (which is the
analogue of Table 1.3 for the constrained subject sample) is summarized in Table 1.5.
Risk attitude No. of subjects
Constrained IRRA 28
Constrained irregulars 7
Constrained DARA-DRRA 1
Total 36
Table 1.5: Risk attitude of constrained subjects.
Overall, just like for the unconstrained subjects, there is substantial heterogeneity among the
constrained subjects. A majority of subjects (78%) exhibit increasing relative risk aversion with
more than half of them exhibiting also decreasing absolute risk aversion.
Finally, we use our questionnaire to study the correlation between risk attitude and demo-
graphics. We find an over-representation of males in the population of subjects who are affected
by the inability to borrow (i.e., hit often the p
t
= X
t
constraint). More precisely, out of our full
sample comprising 49 males and 68 females, 33% of the males (16) and 18% of the females (12)
are in the Constrained IRRA group. Among the unconstrained subjects, the distributions of types
in the male and female populations are not significantly different.
13
Of these subjects, 15 are best classified as DARA-IRRA, 10 are best classified as CARA-IRRA, and the remaining 3
are best classified as IARA-IRRA.
18
1.5 Behavioral anomalies
So far, we have assumed that the expected utility model is “correct" and classified the risk attitude
of our subjects assuming their behavior is consistent with a HARA utility function. Several studies
have reported behavioral anomalies in decision-making under risk and uncertainty. One notable
anomaly is the tendency of subjects to repeat choices that have generated gains in the past and
avoid choices that have generated losses in the past. In a financial setting, it translates into
repeating risky investments after a gain and moving wealth into safe assets after a loss, even
when draws are known to be i.i.d. (Thaler and Johnson (1990)). A second and related anomaly is
a disproportionate preference to avoid losses relative to acquire gains. One way to describe this
behavior is through prospect theory, in which subjects evaluate their options via a reference point
(Kahneman and Tversky (1979)). In a financial setting, the reference point can be the current
wealth or any other heuristic. From a dynamic perspective, the reference point is likely to change
over time, suggesting that a certain degree of time dependence may be observed.
14
Our goal in this section is to determine if there are systematic biases in choices due to dynamic
considerations rather than to test specific models or fit specific parametric functions. In our
dynamic expected utility model, negative or positive shocks at t 1 affect wealth at t and therefore
the investment decision at t. The risk attitude of each subject determines how she should respond
to positive or negative shocks. To test whether subjects react differently after a positive or a
negative shock, or whether time dependence is present, we need to control for any effect that
emerges naturally from the model. To do so, we study the residuals of our corrected least squares
regression in the group of the 81 unconstrained subjects that are fitted with theM
HARA
model.
We explore their behavior as a function of the path, and the returns obtained in the period
immediately before. The results are reported in the next two sections.
14
The literature usually uses status-quo or lagged status-quo as natural candidates for the reference point. Koszegi
and Rabin (2006, 2007) model the reference point as an expectation. As noted earlier, a recent strand of the literature
has tested and supported that hypothesis. Unlike these experiments, our design is not suitable for controlling or
revealing subjects’ expectations. Therefore, we cannot test the endogenous reference point theory without confounds.
19
1.5.1 Path dependence
To test for path-dependence, we run the following regression:
ˆ u
i,t
= b
0
+aI
path>8
i,t
+b
1
X
i,t
+b
2
F
i,t
+r ˆ u
i,t1
+ v
i,t
(1.7)
where I
path>8
i,t
is a dummy variable that takes value 1 if the observation is from a late path (9 to
15) and 0 otherwise. The regression shows no evidence of path-dependence for 63 subjects (at
the 5% significance level). Among the remaining 18 subjects, 9 exhibit a positive a parameter,
indicating more risk-taking behavior over time than predicted by the model. The other 9 subjects
exhibit a negativea parameter, indicating less risk-taking over time than predicted by the model.
15
A possible explanation is that subjects learn about their preferences over time and adapt their
behavior gradually. To investigate this issue further, we run a regression with squared residuals
as the dependent variable in order to assess whether the decisions of subjects become more
precise over time. We find that among the 18 subjects with path-dependency, 1 subject commits
more mistakes over time (decreasing precision) and none commits fewer mistakes over time.
Finally, in order to get a better sense of the magnitude of the path-dependency, we look at the
a-coefficient of the 18 subjects with a statistically significant effect. The largest positive and
negative coefficients are a = 0.56 and a =0.51, meaning that the error in the estimation due
to path-dependency is relatively small. To summarize, 22% of the individuals show statistically
significant path-dependency, but small in magnitude.
1.5.2 Gain/loss asymmetry
To check whether subjects react differently after a loss or a gain, we run the regression:
ˆ u
i,t
= b
0
+aI
gain
i,t
+b
1
X
i,t
+b
2
F
i,t
+r ˆ u
i,t1
+ v
i,t
where I
gain
i,t
is a dummy variable that takes value 1 if the subject starts the period t after a gain
at t 1 and 0 if she starts it after a loss at t 1 (we use the White-Huber standard errors to
15
The results are similar when we run the regression: ˆ u
i,t
= b
0
+aPT
i,t
+b
1
X
i,t
+b
2
F
i,t
+r ˆ u
i,t1
+ v
i,t
, where the
independent Path variable PT takes values from 1 to 15.
20
account for heteroscedasticity). Our data shows no reaction to previous gains or losses beyond
the model prediction for 30 subjects (at the 5% significance level). Among the remaining 51
subjects, the vast majority (46 subjects) exhibit higher residuals after a gain. So, consistent with
the findings in Thaler and Johnson (1990), these subjects take more risks after a gain than after
a loss. The remaining 5 subjects exhibit the opposite pattern. We then study the magnitude
of the a-coefficient for the subjects with a significant overreaction to previous outcomes. All 5
subjects who take more risks after a loss have a small coefficient: jaj < 0.48. Among the 46
subjects who take more risks after a gain, 40 have a small overreaction ($1 or less) and 6 have a
more substantial one (between $1 and $4). In summary, many subjects (57%) exhibit excessive
risk-taking after gains but, except for some notable exceptions (7% of subjects), the overreaction
is, once again, small in magnitude.
1.5.3 Classification of behavioral types
Finally, when we compare the two sets of anomalies we find that they mostly involve differ-
ent subjects. Indeed, 6 subjects exhibit different risk taking behavior in the latter paths of the
game (path dependence), 39 subjects exhibit an effect of past period outcomes on current choices
(gain/loss asymmetry), and only 12 subjects exhibit both anomalies. Subjects with one or both
anomalies are present in all the risk-type categories described in Table 1.3. The remaining 24
subjects can be confidently classified as expected utility maximizers.
In conclusion, anomalies are prevalent. Residual behavior can be attributed to systematic
biases that are not captured by the structural model. On the other hand, anomalies are spread
among subjects and small in magnitude, so we can fit the data to the expected utility model
reasonably well. In the next section, we provide a more in-depth investigation of the fit of our
model.
1.6 Testing the model
The objective of this section is to explore the validity of the HARA specification, both overall
and in comparison to the one-parameter CRRA specification. We restrict our attention to the 81
21
subjects whose behavior can be fitted to our structuralM
HARA
model. To assess the general good-
ness of fit of our structural model, we first conduct F-tests to determine whether the proposed
structural relationship between the risky investment at each period and the set of independent
variables is statistically reliable. We find that it is for all 81 subjects. Furthermore, according to
the Akaike Information Criterion comparison (AIC),M
HARA
outperformsM
CRRA
for all but 7
subjects.
16
1.6.1 Out-of-sample predictions
We probe the matter further and ask whether we can predict the behavior of our subjects based on
the observation of their choices in a subset of trials. More specifically, we pick 8 paths at random
to estimate the parameters of theM
HARA
model and then use the estimates to predict choices
on the remaining 7 paths. We repeat the exercise 100 times. For each repetition we calculate the
Mean Absolute Error:
17
MAE
HARA
=
å
7
i=1
å
10
t=1
jp
i,t
˜ p
HARA
i,t
j
70
where ˜ p
HARA
i,t
is the prediction ofM
HARA
on decisions in the 7 validation paths.
As a benchmark, we first compare the out-of-sample fit of HARA to a model where fit deci-
sions are made at random for the same 7 validation paths. More specifically, we calculate:
MAE
RND
=
å
7
i=1
å
10
t=1
jp
i,t
˜ p
RND
i,t
j
70
where ˜ p
RND
i,t
is an amount drawn from a uniform distribution in [0, X
i,t
]. Figure 1.3 shows the
mean, 10th percentile, and 90th percentile of the ratio
MAE
HARA
MAE
RND
of 100 repetitions for our 81
subjects, sorted by the mean of the ratios, from smallest to largest. The ratio is intended to
describe how much betterM
HARA
explains behavior in comparison to a naïve random model.
The ratio is below 1 for all subjects and below 0.5 for 73% of subjects, suggesting (not surprisingly)
16
The h parameter ofM
HARA
is estimated to be zero for these 7 subjects, implying de-facto constant relative risk
aversion. If we use the Bayesian Information Criterion (BIC), there are 4 more subjects for whichM
CRRA
outperforms
M
HARA
. The estimated h parameter is zero or close to zero for all 11 subjects.
17
We conducted the same analysis with the root mean square error measure (RMSE) instead of the MAE and
obtained similar results.
22
that for the vast majority the HARA specification performs substantially better out-of-sample than
the random specification.
Figure 1.3: Out-of-Sample Fit (100 repetitions) - HARA vs. Random
Next, we ask a more relevant question: how much predictive power do we lose by considering
a simple, one-parameter CRRA specification instead of the richer, two-parameter HARA specifi-
cation? We follow the same procedure as before with theM
CRRA
model instead of theM
HARA
model. More precisely, we calculate the Mean Absolute Error:
MAE
CRRA
=
å
7
i=1
å
10
t=1
jp
i,t
˜ p
CRRA
i,t
j
70
where ˜ p
CRRA
i,t
is the prediction ofM
CRRA
on decisions in the 7 validation paths. Figure 1.4 shows
the mean, 10th percentile, and 90th percentile of the ratio
MAE
HARA
MAE
CRRA
of 100 repetitions for our 81
subjects.
The mean of ratios is smaller than 1 for 61 subjects (75%). Half of these subjects have mean
ratios below 0.9 and at least 90% of repetitions below 1, which suggests that the improvement of
HARA over CRRA is substantial for 37% of subjects and minor for the other 38%. Among the
remaining 20 subjects for whom CRRA performs better out-of-sample (25% of the population), the
mean ratio is above 1.1 for only 1 subject. Notice also that 11 out of those 20 subjects are specified
as having constant relative risk aversion by the HARA model (h = 0), so the similarity between the
23
Figure 1.4: Out-of-Sample Fit (100 repetitions) - HARA vs. CRRA
out-of-sample predictions of the two models is expected for those individuals. Overall, HARA
improves significantly out-of-sample predictions over CRRA for one-third of the sample and
performs similarly for the other two-thirds.
1.6.2 Risk type predictions
Our second prediction exercise consists in determining whether the risk type obtained from the
data in one sample is consistent with the risk type obtained in the complement. If they are not,
it might be because of learning or a preference change. To do so, we divide our sample into
“early paths" (first 8 paths) and “late paths" (last 7 paths). We then estimate the risk types of
the individuals in each subsample following the same methodology as before, and look at the
consistency in the classification of subjects across datasets. The results are reported in Table 1.6.
Type consistency by paths Frequency
Consistent Full - Early - Late 46
Consistent Full - Early 21
Consistent Full - Late 11
Inconsistent 3
Total 81
Table 1.6: Consistency in classification - early paths vs. late paths
24
In line with previous results, we find that subjects are fairly consistent between early and late
paths. Of the 81 subjects, 46 have the same risk type across all samples, 32 are consistent on the
full sample and one subsample, and only 3 subjects have different risk types in all samples. Table
1.7 presents the risk aversion attitude of subjects in the full sample as well as the early path and
late paths subsamples.
Full sample Early paths Late paths
DARA-DRRA 11 12 10
DARA-CRRA 13 14 23
DARA-IRRA 44 38 33
IARA-IRRA 1 1 1
CARA-IRRA 12 16 14
Table 1.7: Type frequency - early paths vs. late paths
The proportions of the different risk types are, to a large extent, preserved in all samples:
there is a majority of DARA-IRRA (between 41% and 54%), virtually no IARA-IRRA, and some
representation of the other three types. The most notable difference between samples is the
increase in CRRA types at the expense of IRRA types. However, we do not want to excessively
emphasize this conclusion as it may be partly due to a statistical effect: with fewer observations
per subject in each subsample it may be more difficult to reject the null hypothesis of constant
relative risk aversion.
Overall, the expected utility model performs well in our sample. Subjects do not change risk
types dramatically over the course of the experiment and it is possible to predict with reasonable
accuracy their behavior after observing the choices in the first paths. In appendix B, we perform
a similar predictive analysis where the sample is divided between “early periods" (first 5 of
each path) and “late periods" (last 5 of each path) and also obtain consistent risk types across
subsamples.
1.7 Aggregate risk attitudes
In this section, we perform the same classification exercise as in section 1.4.3 except that we
conduct the analysis at the session level rather than at the individual level. Indeed, recall that our
experiment consists of 13 sessions with 7 to 10 participants each for a total of 117 subjects. The
25
No. of sessions
Risk attitude Unconstrained All
(81 subjects) (117 subjects)
DARA-DRRA 2 1
DARA-CRRA 3 2
DARA-IRRA 8 10
IARA-IRRA 0 0
CARA-IRRA 0 0
Total 13 13
Table 1.8: Risk attitude of representative agents
design permits an objective measure of aggregate wealth because participants are subject to the
same shock (the stochastic return of the risky asset in each period of each path is identical for all
participants within a session). Instead of summing all the wealth accumulated by subjects in each
period, we adopt a per capita specification which allows us to identify the risk preferences of the
“representative agent". This approach makes the results of the individual and session analyses
comparable.
By aggregating wealth, the per-capita investment is always interior. We can therefore fit our
structural modelM
HARA
to the data. The results of the White test indicates the presence of
heteroscedasticity in all sessions. The Breusch-Godfrey test reveals first-order serial correlation in
8 of the 13 sessions. As in the analysis of section 1.4.3, we correct for both heteroscedasticity and
serial correlation using the Newey-West standard errors and estimate the risk parameters g and
h to obtain the risk types of the representative agent in each session. We conduct this analysis
using the data from the 81 unconstrained subjects so we can draw a comparison between the
individual and the representative agent cases (as a robustness check, we also run the analysis
using the full sample of 117 subjects and obtain similar results). Figure 1.5 displays the analogue
of Figure 1.2 for the session level analysis, that is, the estimated (g,h) risk parameters of the 13
representative agents of our experiment when the 81 unconstrained subjects are considered. For
visual comparison we keep the size of the x- and y-axis identical in both figures. Table 1.8 reports
the analogue of Table 1.3, that is, the relative and absolute risk aversion attitudes based on the
estimated parameters, when the analysis is conducted on the unconstrained subjects and on the
full sample, respectively.
26
Figure 1.5: Estimated parameters of representative agents (81 unconstrained subjects)
All sessions exhibit decreasing absolute risk aversion and the considerable majority exhibit
also increasing relative risk aversion. There is no evidence of CARA and only some evidence of
CRRA (3 sessions). When we add the constrained agents to the analysis, relative risk aversion
increases but types remain similar. Overall, the comparison between Figures 1.2 and 1.5 suggests
a similar distribution of types at the individual and session level: in both cases, DARA-IRRA
accounts for more than half of the observations and IARA-IRRA are non-existent. We notice,
however, two important differences. First, there are no CARA types at the session level (all
estimates of g are below 1). Second, even when we look only at the DARA types, the estimates
are substantially more dispersed at the individual than at the session level: h2 (17, 21) vs.
h2(7, 12) and g2(1.2, 0.9) vs. g2(0.2, 0.9). The parameter h is, on average, also higher for
individuals.
The larger dispersion and higher average ofh at the individual level is important, as it suggests
that wealth effects are weaker– and therefore that CRRA (h = 0) is a better approximation– for
the representative agent than for the individual data. This results from the combination of two
effects. One is purely statistical: by mixing IRRA with DRRA subjects we obtain an aggregate
behavior close in magnitude to (even if statistically different from) CRRA. The second is perhaps
more subtle: DRRA agents accumulate on average more wealth than IRRA agents and therefore
27
end up having more weight on the average behavior. So, even though there are fewer DRRA than
IRRA individuals, their impact in the economy is larger.
We check for evidence of behavioral anomalies at the aggregate level by replicating the analy-
sis of section 1.5. There is very little evidence of path-dependence: only 3 sessions show an effect
and the magnitudes are small. By contrast, we find that all 13 sessions exhibit an asymmetry
between gains and losses, with a higher residuals after a gain. The representative agent is there-
fore taking more risk after a gain than after a loss, consistent with Thaler and Johnson (1990), but
the magnitude of the anomaly is, once again, small.
We next explore the out-of-sample predictive properties of the model by performing the same
analysis as in section 1.6.1. Again as a benchmark, we compare HARA to random choice. For
all 13 representative agents, the ratio
MAE
HARA
MAE
RND
is below 0.5 in at least 90% of the repetitions. This
means that the improvement of HARA over random choice is greater for the representative agent
than for the individual analysis, which implicitly suggests that some of the subjects’ deviations
cancel each other out.
We then analyze how HARA compares to CRRA. Figure 1.6, the analogue to Figure 1.4, shows
the mean, 10th percentile, and 90th percentile of the ratio
MAE
HARA
MAE
CRRA
of 100 repetitions for the 13
representative agents. The mean ratio is virtually 1 for 8 sessions and between 0.5 and 0.8 for
the other 5 sessions. This means that, just like for the individual analysis, the out-of-sample
predictions of the HARA model significantly improve those of CRRA for one-third of the sample
and they are very similar for the rest.
18
When we divide the sample between early paths and late paths, as we did in section 1.6.2 for
the individuals, we find that the representative agent has the same risk type across all samples in
7 sessions (4 DARA-IRRA and 3 DARA-CRRA). Of the remaining 6 sessions, 2 sessions show the
same type in the full and early paths subsample and 4 sessions show the same type in the full
and late paths subsample. Overall, representative agents are generally consistent across paths,
a result which is not surprising given the type-consistency of the majority of individuals in our
sample.
18
When we include the constrained subjects, we find a larger improvement of HARA over CRRA. This is due mostly
to the fact that the vast majority of the constrained subjects exhibit IRRA behavior.
28
Figure 1.6: Out-of-Sample Fit (100 repetitions) - HARA vs. CRRA
To sum up, according to the individual level analysis, estimating a two-parameter HARA
utility function rather than a one-parameter CRRA utility function helps improving the estimation
of one-third of individuals. The same is true for the session level analysis. The point estimates,
however, are substantially more concentrated and closer to constant relative risk aversion in the
latter than in the former.
1.8 Conclusion
In this paper, we report the results of an experiment where 117 subjects dynamically choose their
wealth allocation. Assuming a HARA utility function, we first construct a structural dynamic
choice model which we then use to estimate the absolute and relative risk aversion of the partic-
ipants. Although technically more complex, this method has the advantage of providing more
accurate estimates than traditional risk elicitation techniques.
Even though we find substantial heterogeneity in behavior, decreasing absolute risk aversion
and increasing relative risk aversion are the most prevalent subtypes, and we can confidently
classify more than half of the subjects in the combined DARA-IRRA category. We also find
evidence of increased risk taking after a gain but the effect is small in magnitude, and the behavior
29
of subjects is generally well accounted for by the expected utility model. Finally, our design allows
us to perform an aggregate analysis. We find that the representative agent in most sessions is
also best represented by DARA-IRRA. However, the estimated risk types at the session level are
substantially more concentrated and closer to constant risk aversion than the risk types at the
individual level, suggesting that CRRA may be a reasonable approximation for representative
agents.
Recent papers have argued that risk attitudes are volatile and difficult to pinpoint (see Fried-
man et al. (2014) for a survey). Our analysis suggests that if the experimental setting is rich
enough, it is possible to accurately estimate (stable) risk preferences. This result is encourag-
ing given the paramount importance for microeconomic theory in understanding risk choices in
financial, insurance and environmental settings, just to name a few. At the same time, we also
find that in the session level analysis the risk-type estimates are relatively close to (though sta-
tistically different from) constant relative risk aversion. Again, this is an encouraging result as
it suggests that macroeconomic theories based on the CRRA utility function capture reasonably
well the risk characteristics of the representative agent.
30
Chapter 2
Skewness Seeking in a Dynamic
Portfolio Experiment
2.1 Introduction
The behavior of economic agents under risk is known to often depart from the predictions of
the classical expected utility theory. In particular, the tendency to invest in skewed assets with
negative expected value is a pervasive behavioral anomaly. Lotteries, race-tracks, and financial
markets, provide evidence of skewness seeking behavior.
1
However, little is known as to why
this occurs, whether preferences for skewness are an intrinsic trait of some individuals, whether
there are more likely to show in conjunction with specific circumstances, and/or whether they
are driven by social concerns. For instance, it has been evidenced that the demand for lotteries
increases at the last minute in race-track betting (McGlothlin (1956); Ali (1977); Asch et al. (1982))
suggesting that observed preferences for skewness might be triggered by certain events. It is
also known that subjects in experiments sometimes react to relative concerns and may buy more
lottery tickets when they feel poorer than their peers (Haisley et al. (2008); Dijk et al. (2014)).
This indicates that observed preferences for skewness may not be intrinsic, but rather tied to
social comparisons. The objective of this study is to design a controlled laboratory experiment
that generates two potential triggers of skewness seeking behavior: an option to act at different
dates including a final date and the possibility of social comparisons. We then analyze how these
options affect investment decisions. More precisely, we want to answer the following questions.
How pervasive are preferences for skewness in the population and can frequent exposure help
1
For evidence of skewness seeking in lotteries and race-track betting see Garrett and Sobel (1999) and Golec and
Tamarkin (1998), respectively. For proposed evidence in the financial markets, see Mitton and Vorkink (2007), Kumar
(2009), Boyer et al. (2009), Bali et al. (2011), Green and Hwang (2012), Conrad et al., (2013), and Boyer and Vorkink
(2014).
31
individuals realize the low (in our design, negative) expected value of such investment? Is the
“last hour" effect an anomaly specific to race betting or do we observe a last period effect irre-
spective of the unit of time? Are social concerns driving to some extent preferences for skewness?
To address these questions, we design a dynamic portfolio allocation experiment in which
each subject (she) allocates money at each date between different types of assets. We consider a
within-subject design with three treatments. In the first (NoBet) treatment, the subject allocates
wealth between a safe asset and a risky asset with higher expected payoff. It is a control treat-
ment designed to elicit and structurally estimate the risk attitude of subjects. The results of this
treatment are analyzed in chapter 1 and used for comparison in this chapter whenever relevant.
2
In the second (Bet) treatment subjects can also buy “a bet" (a third, skewed asset with negative
expected payoff) in each period. In the third (Bet&Box) treatment, subjects are given the option
to obtain feedback about the wealth level of other participants in the session at specific points in
time. More precisely, they can choose to learn the minimum, average or maximum current wealth.
They can also choose to remain ignorant. In all treatments, feedback regarding the returns of all
assets is provided at the end of each period. We address our three questions of interest and we
obtain three main results.
First, we find that a small subset of our subjects (16%) never purchase the bet perhaps because
they understand that it has negative expected value. Some others (29%) buy the bet at first but
stop purchasing it half-way through the experiment. Finally, about half of the subjects (55%)
purchase bets throughout the entire experiment. This echoes the results from other experiments
in the literature that evidence preference for skewness. Testing higher order-risk preferences
(prudence and temperance), Deck and Shlesinger (2010), Brünner et al. (2011), Ebert and Wiesen
(2011) and Ebert (2015) find preference for skewness. In these studies, subjects are offered pairs
of lotteries with the same mean and variance but different degrees of skewness. Many subjects
choose options with higher skewness. Grossman and Eckel (2012) and Astebro et al. (2014)
also find skewness seeking behavior in experiments with modified multiple price list paradigms.
Lastly, in the asset market experiments of Ackert et al. (2006) and Huber et al. (2014), subjects
2
For overviews regarding static empirical and experimental risk elicitation procedures, see Harrison and Rutström
(2008), Charness et al. (2013), and Friedman et al. (2014). Dynamic experimental frameworks have been used in Kroll et
al. (1988), Kroll and Levy (1992), Levy (1994), Sundali and Guerrero (2009), and in game show replications summarized
by Andersen et al. (2008)
32
exhibit stronger initial overpricing of skewed assets. However, none of theses studies have scope
for learning about one’s own reaction to the outcome of the lottery. The dynamic aspect of our
experiment allows us to investigate the robustness of the preference for skewness, and it shows
that such preferences are indeed quite robust. At the same, it also suggests that a non-negligible
fraction of subjects learn to avoid these gambles, so that estimates of the preference for skewness
based on one or a limited number of gamble opportunities may be biased upwards.
Second, subjects who buy the skewed asset during the entire experiment exhibit a strong last
period effect, with purchases two to four times higher in the last opportunity they have (period
10 of their investment paths) than in any other one (periods 1 to 9 of their investment paths).
As reviewed earlier, an increase in betting on long-shots in the last race of the day has been
observed in the field (McGlothlin (1956); Ali (1977); Asch et al. (1982)) and our study shows that
the effect can also be generated in a controlled laboratory setting.
3
This suggests that a behavioral
bias might be at play in dynamic situations, where a preference for skewness is developed over
time. Furthermore, we find that the effect is strongest when subjects accumulate highest levels
of wealth but it is also present in the mirror image case of lowest levels of wealth. The results
are consistent with loss aversion, characterized by Kahneman and Tversky (1979) and Thaler and
Johnson (1990), whereby bettors who have lost or not accumulated much wealth may try to catch
up at the end of the day. It also supports the intuitive idea that subjects who accumulate large
amounts of cash are more willing to bet with house money.
Third, our subjects are very curious about the wealth of others. They mostly choose to learn
what is the highest wealth in the session. However, this choice is strongly affected by their own
performance. Indeed, when a subject accumulates low, medium and high wealth, she typically
looks for feedback regarding the minimum, average and maximum wealth in the session, respec-
tively. Interestingly, subjects tend to buy more bets when they discover that they are lagging,
in particular if this information is unexpected - an individual with relatively high wealth who
discovers that her wealth is below the average in the session. This result is consistent with the
existing literature. For example, Haisley et al. (2008) find that participants buy more lottery tickets
when they are primed to feel they have relatively low income. Dijk et al. (2014) show that lower
3
It is worth noting that in a recent empirical study using a much larger sample size of horse races, Snowberg and
Wolfers (2010) show that this effect, albeit present, is statistically insignificant. However, drawing stimuli from a real
day of racing, one experimental study by McKenzie et al. (2016) still finds a significant last race effect.
33
ranked individuals in an asset allocation game invest relatively more in skewed assets while the
reverse holds for higher ranked individuals. Finally, Schwerter (2013) shows that subjects take
more risk when they lag against the earnings of assigned peers.
4
The paper is organized as follows. In section 2.2, we describe the experimental setting. In
section 2.3 we present the basic results on portfolio allocation between the safe and risky asset.
In section 2.4, we discuss the general propensity to purchase the skewed asset and the effects of
wealth and end of period. In section 2.5, we study the willingness to obtain information on the
performance of others. In section 2.6, we offer some concluding remarks.
2.2 Experimental Design
We study the dynamic portfolio choice of agents when a skewed asset is present and how their
investment decisions among the different assets is affected by relative concerns. The experiment
consists of 13 sessions run in the Los Angeles Behavioral Economics Laboratory (LABEL) at the
University of Southern California.
5
Each session has between 7 and 10 subjects for a total of 120
recruited subjects, of which 3 are omitted from the analysis due to software malfunction. All
subjects participate in three treatments presented always in the same order. In the first treatment
(hereafter NoBet), subjects allocate wealth between two assets, a ‘safe’ and a ‘risky’, during 15
investment paths consisting of 10 periods each. The results of this treatment are reported in chapter
1. The second treatment (hereafter Bet) is similar except that, in each period, subjects can also
invest in a third asset, the bet, which costs $1 and gives a return of $20 with probability 0.04.
The third and last treatment (hereafter Bet&Box) is identical to the Bet treatment, except that
subjects can obtain feedback in designated periods. More precisely, they are given the option
to check either the minimum wealth (hereafter Min), the average wealth (hereafter Ave), or the
maximum wealth (hereafter Max) among all participants in the session. We report here the
results of treatments Bet and Bet&Box and compare them with the results obtained in the NoBet
treatment whenever relevant.
4
See also Kuziemko et al. (2014) who show more risk taking by the subject in the last place and Schoenberg and
Haruvy (2012) who show that in market experiments the price of the asset is higher when the traders are informed
about the best performer than when they are informed about the worst performer (however and despite the effect on
market prices, they could not find a significant difference in risk taking between leaders and laggards).
5
For information about the laboratory, please visit http://dornsife.usc.edu/label.
34
2.2.1 Treatment 1: benchmark portfolio allocation (NoBet)
In the NoBet treatment, each subject (she) starts each path in period 1 with an endowment of
$3, which she allocates between two assets, a risky asset A and a safe asset B. After period 1
ends, each subject earns a return on her portfolio and moves to period 2. She then reallocates her
portfolio and earns new returns. This process continues for a total of 10 periods. After period
10, the investment path ends and the subject’s final payoff in that path is recorded. Each subject
then moves to the next investment path, where her endowment is reset to $3. Subjects have 10
seconds to make their decision in period 1 of each path and 6 seconds in periods 2 to 10 of each
path. They all begin and end investment paths at the same time. Finally, all subjects go through
15 investment paths for a total of 150 choices. Subjects know at the beginning of the treatment
the number of paths and periods ahead.
The return of the safe asset B is 3% while the return of asset A is drawn from a Normal dis-
tribution with mean 6% and standard deviation 55%.
6
The parameters do not change throughout
the experiment. The draw of the return is presented in the form of a multiplier, that is, the num-
ber that multiplies the allocation to that asset (so the multiplier of asset B is always 1.03 whereas
the mean multiplier of asset A is 1.06). All participants in a session are subject to the same draws
but we make clear to each subject that the draw of the return of the risky asset is in no way
affected by her past allocation decision or by the allocation decision of the other subjects.
Figure 2.1 provides a screenshot that describes what a subject sees in a given period of a path.
Current wealth is represented by the vertical bar positioned above the current period number
(period 4 in this example). When gray, the bar is not active and the wealth is not allocated to
either asset. Subjects need to click on the bar to activate it and move a horizontal slider to divide
their current wealth between assets A and B. The upper portion of the bar represents the money
invested in A and the lower portion represents the money invested in B. The figures on the right
side of the bar show the current allocation. To facilitate their reasoning, subjects may change the
display of the allocation at any time between percentage in each asset (box labeled “ % " as in this
screenshot) and total amount in each asset (box labeled “ $ "). After the period expires, returns
are applied and subjects move to the next period. A new bar with a height corresponding to the
6
This (unrealistically high) standard deviation ensures enough volatility in returns for interesting wealth effects
and comparative statics.
35
Figure 2.1: Screenshot of path 1 / period 4 in NoBet treatment
new wealth appears to the right of the previous one for the new period and becomes inactive
again. Subjects need to reactivate the bar in order to choose a new allocation, otherwise they earn
no extra earnings in that period and their account just carries over. This helps prevent subjects’
inertia and a bias towards a status quo allocation. Level of inactivity in our experiment was
negligible. Subjects observe bars to the left of the current one (periods 1 to 3 in this screenshot)
that reminds them of their past allocations and returns. These bars accumulate up to period 10,
at which point earnings are recorded and a new investment path is started in period 1 with the
endowment reset to $3. Finally, the left hand side of the screen has a summary information of the
main ingredients of the experiment: (i) the current path and period; (ii) a reminder of the mean
and standard deviation of returns of assets A and B; (iii) the time left to make a choice in the
current period; (iv) the accumulated wealth in the current path; and (v) the multiplier of assets A
and B in the last period of the current path.
This dynamic wealth allocation problem is challenging and may require substantial learning.
To deal with this issue, we employ a highly illustrative 40 minute instructions period using
a neutral language with numerical examples, videos, 5 practice paths and a quiz to test the
subjects’ understanding (instructions can be found in appendix A). In addition, to help with the
36
cognitive strain, we add a projection bar placed on the right end of the screen (see Figure 2.1). The
projection bar tells the subject what she would expect if she were to keep her current investment
strategy until the last period. The bar shows the potential accumulated earnings from asset B
and identifies the 20th, 50th and 80th percentile of the earning distribution from asset A. As the
participant changes her allocation the projection bar automatically adjusts.
7
As stated above, the results of the NoBet treatment are extensively analyzed in chapter 1. In
particular, we structurally estimate the risk attitude of the subjects assuming they are expected
utility maximizers and discuss the frequency and severity of behavioral biases. These findings
form a benchmark for comparison when we add a skewed asset (Bet treatment) and the possibility
of observing the earnings of other subjects (Bet&Box treatment).
2.2.2 Treatment 2: allocation in the presence of a skewed asset (Bet)
After completing the NoBet treatment, subjects move to the Bet treatment, which introduces
two changes to the environment described in section 2.2.1. First, subjects go through 10 (rather
than 15) investment paths of 10 periods each, for a total of 100 new choices. Second and most
importantly, we add a new asset C, the "bet", which costs $1 and yields $20 with probability
0.04 (naturally, in the experiment we never refer to this asset as a “bet"). Figure 2.2 presents the
screenshot from the Bet treatment, which is identical to Figure 2.1 except for the lower left corner
where asset C is introduced.
Asset C is purchased by clicking on the button below the description of its cost and potential
return. Subjects can buy at most one bet per period. If they have less than $1 in their account,
they cannot afford the bet and the box button is grayed out and inactive. If they buy a bet, the
cost is withdrawn from the other two assets keeping constant the proportion invested in assets A
and B. Overall, subjects make two decisions per period: whether to buy a bet (asset C) and how
to allocate the rest of the money between assets A and B. Subjects learn the outcome of the bet
at the same time as the returns of assets A and B, that is, at the end of the period. Subjects are
informed that bets are independent across individuals and across periods, in contrast with the
7
We carefully explain the function of the bar by simulating potential period-by-period trajectories of wealth coming
from a given allocation strategy.
37
Figure 2.2: Screenshot of path 3 / period 1 in Bet treatment
return on asset A which is the same for all subjects in a given a period. They go through one
practice path before commencing the Bet treatment.
2.2.3 Treatment 3: skewed asset with feedback (Bet&Box)
Feedback is provided in the Bet&Box treatment. More specifically, the environment is identical to
the Bet treatment, with one exception. In periods 5 and 9 of each path, 3 boxes labeled ‘Lowest’,
‘Average’ and ‘Highest’ appear on the lower left corner of the subjects’ screens (see Figure 2.3).
These boxes contain information about the minimum, the average, and the maximum amount
held currently by the subjects in the session. They do not disclose the identity of those subjects.
Subjects may open only one box at the time it is offered and may decide to not open any.
Overall, in periods 5 and 9, subjects make three decisions: whether to obtain feedback about
earnings of subjects in the session, whether to purchase the bet, and how to allocate the rest of
the money between assets A and B. In the other periods, subjects make only the second and the
third decision, just like in the Bet treatment.
38
Figure 2.3: Screenshot of path 4 / period 5 in Bet&Box treatment
2.2.4 Payments
At the end of the experiment we collect answers to education, demographics and income related
questions as well as their own description of the strategies employed. Each participant receives a
$5 show-up fee and her final earnings in the final period of two paths, one path randomly selected
from the NoBet treatment and one path randomly selected from the Bet and Bet&Box treatments.
Sessions last for 2 hours and the average payoff is $23, with a maximum payoff of $244.
2.3 Risk attitudes
As mentioned in the introduction, the main purpose of the paper is to analyze how the presence of
a skewed asset and information regarding the wealth of other subjects affects risk taking behavior
in a controlled environment. However, it is instructive to start the analysis of the data by studying
the subjects’ allocation of wealth between the risky and safe assets (A and B) in the Bet and
Bet&Box treatments, and to compare their choices with those obtained in the NoBet treatment.
There are at least two reasons why the results of such comparison must be taken with a grain of
salt. First, the investment environment is complex, so we expect some learning over the course of
39
the experiment about the implications of the different choice allocations as well as the subject’s
own risk tolerance. Differences in choices across treatments may simply reflect such knowledge
acquisition. Second, even though a risk-neutral or risk-averse individual should never buy the
skewed asset C in the Bet and Bet&Box treatments, we do observe purchases of the bet (see
section 2.4). Buying a bet (or simply being offered a bet) is likely to affect the allocation of wealth
between the other two assets. Naturally, this is not to say that we expect choices across treatments
to be uncorrelated.
Figure 2.4 presents a histogram with the average proportion of wealth allocated by each subject
to the risky asset A in the Bet and Bet&Box treatments. Half the individuals put between 40%
and 60% of their wealth in the risky asset and very few choose to put all their wealth in one
asset. On average we observe more investments in the safe than in the risky asset, consistent with
reasonable levels of risk aversion (see chapter 1).
Figure 2.4: Average proportion of wealth in asset A (Bet and Bet&Box treatments)
40
Next, we compare wealth allocation across treatments. Figure 2.5 presents for each subject the
average proportion of wealth allocated to the risky asset in treatment 1 and in treatments 2 and 3
pooled together (left). It also presents the standard deviations of the portfolios (right)
8
.
Figure 2.5: Comparison of subjects’ allocation of risk across treatments
We note a remarkable correlation across treatments both in the average proportion of wealth
allocated to each asset and in the standard deviation of the allocations.
9
It suggests that subjects
behave consistently over the course of the experiment and that the levels of risk identified in
the analysis of the NoBet treatment (see chapter 1), apply reasonably well also to the Bet and
Bet&Box treatments.
There are two final remarks regarding the relationship between risk allocation across treat-
ments. First and as depicted in Figure 2.6, the subjects’ risk attitude in the NoBet treatment is
largely uncorrelated with their propensity to buy bets in the Bet and Bet&Box treatments. As we
will see in section 2.4, subjects who invest in the skewed asset do not exhibit eccentric risk atti-
tudes with their remaining wealth. Second, the average standard deviation of the portfolio choice
of all subjects in the experiment is 0.27, 0.32 and 0.30 for the NoBet, Bet and Bet&Box treatments,
8
The standard deviation is calculated using the ex-ante variances of all the assets and their respective weights in
the portfolio.
9
The correlations between the Bet and Bet&Box treatments are also high (0.86 for the average allocation to the risky
asset and 0.79 for the standard deviation).
41
respectively. As explained below, the differences in standard deviations across treatment are, to a
large extent, a consequence of the differences in bet purchases.
Figure 2.6: Risk allocation and bet purchases
2.4 Betting
We shall note to begin with that asset C has negative expected value so a risk-neutral or risk-averse
expected utility maximizer should never buy a bet.
10
From the behavior in the NoBet treatment
(and in accordance with previous research) we found that no subject exhibits risk-loving attitudes
(see chapter 1). We should therefore expect zero or minimal levels of bet purchases. Furthermore,
since a risk-loving attitude is necessary for the willingness to buy asset C, any expected utility
maximizer subject who purchases that asset should invest the remaining of her wealth in the risky
asset A. Indeed, that asset has higher expected return and higher variance than the safe asset B.
10
Note that asset C return is independent from other assets’ returns, thereby bringing no diversification benefits
42
2.4.1 General betting behavior
Figure 2.7 depicts the aggregate frequency of bet purchases over time conditional on subjects
having the option to buy them (in 3.9% of the observations, subjects have less than $1 and there-
fore could not afford the bet). Contrary to the theoretical predictions, we find that 6.3% of the
available bets are purchased. We notice, however, a significant decline in the number of bets pur-
chased over time: 8.1% in the Bet treatment against 4.5% in the Bet&Box treatment. The trend
is decreasing over the course of the Bet treatment and stabilizes afterwards, suggesting that in
aggregate terms subjects realize that the bet is not profitable.
Figure 2.7: Frequency of bet purchase over time
Interestingly, out of the 1416 bets purchased over the two treatments, subjects put more than
98% of the remaining wealth in the risky asset only in 96 occasions. This indicates that subjects
do not behave as risk loving expected utility maximizers.
11
There is a large heterogeneity in betting behavior among our subjects. We can informally
classify subjects into three groups. There are 19 subjects who never bet (group 1 or G1), 34
11
Also, only two subjects exhibit this behavior more or less consistently: one purchases a total of 9 bets and in 8 of
these instances puts all the remaining wealth in the risky asset whereas the other purchases 6 bets and in 4 of these
instances puts all the remaining wealth in the risky asset.
43
subjects who bet a few times and stop purchasing bets before the end of the Bet treatment (group
2 or G2), and 64 subjects who bet in both parts (group 3 or G3). Figure 2.8 shows the distribution
of stopping times, that is, the last path where a subject chooses to bet (histogram, axis on the left)
and, for each subject, the total number of bets bought before stopping (filled circle, axis on the
right). The majority of subjects in G2 bet only a few times before stopping (4.7 on average per
subject). By contrast, many subjects in G3 bet often (19.6 on average) and keep betting throughout
the entire experiment. These subjects also purchase more bets in the Bet treatment than subjects
in G2 (11.6 on average).
Figure 2.8: Distribution of stopping times
To understand further the differences in behavior, we compute the standard deviation of the
portfolio of each subject in each treatment. Figure 2.9 reports the average results by group.
Although the differences in variance across groups in the NoBet treatment are statistically sig-
nificant, the levels are very similar ( 0.24, 0.28 and 0.27). When comparing across treatments, we
notice that for G1 the variance is constant for the entire experiment, for G2 it increases between
NoBet and Bet and then levels down in Bet&Box, and for G3 it increases and then stays up.
Overall, variance mimics the evolution of bet purchasing behavior in the different groups, which
44
suggests that when subjects invest in asset C they do not change significantly the allocation of
their remaining wealth between assets A and B.
Figure 2.9: Standard deviation of portfolio
We also investigate whether the outcome of the bet (win vs. loss) has an impact on the behavior
immediately after, and find no effect. One possible reason is that very few bets are won (only
2.9% over all purchased) and only 27 subjects experience at least one win. In particular, no subject
in group 2 ever won, which also possibly accounts for their behavior in the third treatment.
However, even in group 3 where bets are sometimes won, the percentage of bet purchases at
t+ 1 following a bet win and a bet loss at t are high and remarkably similar (35% vs. 37%). By
contrast, the percentage of bet purchases at t+ 1 after no bet at t is very low (4%). Overall, there
is persistence in behavior (bet is followed by bet and no bet is followed by no bet) and it does not
seem to depend on the outcome of the bet.
2.4.2 Effects of wealth and end of path
Subjects in our experiment buy more bets when they are richer. To see this, we study within-
subject heterogeneity in bet purchases as a function of wealth. More precisely, for each individual
45
we remove the observations where she has less than $1 (and therefore cannot buy a bet) and
group all her other observations in wealth quintiles. We then determine the frequency of bet
purchases when her wealth falls in each of these quintiles.
12
Figure 2.10 depicts this information
separately for the Bet and Bet&Box treatments. In both treatments, the frequency of bet pur-
chases is significantly higher when subjects are in their top wealth quintile (p-value = 0.000 for
all pairwise comparisons between the top quintile and the other quintiles). Interestingly, it is also
significantly higher in the bottom quintile compared to the second and third in the Bet treatment
(p-value = 0.000 and 0.003, respectively), indicating a tendency in that treatment to invest in the
skewed asset when wealth is “extreme."
13
However, the fact that this happens only in the Bet
treatment prevents us from drawing further conclusions.
Figure 2.10: Frequency of bet purchase by wealth level
Perhaps the most striking result of our analysis is the tendency of subjects to buy bets in the
last period of every path, a feature that persists throughout the experiment. This is illustrated in
12
We opt for a within-subject quintile analysis to avoid confounding wealth heterogeneity with subject heterogeneity.
13
Further analysis suggests that the G3 group, subjects that bet in the Bet&Box treatment, reduces bet purchases in
low wealth cases. This is why do not observe higher betting propensity for the lowest wealth quintile in the Bet&Box
treatment.
46
Figure 2.11 which shows that the bet frequency is significantly higher in period 10 than in any
other period (p-value = 0.000 for a test of comparison between bet frequency in period 10 and
any of the earlier periods, overall and by treatment).
Figure 2.11: Frequency of bet purchase by period and treatment
A possible explanation for this trend is that subjects bet more at the last minute simply because
they are richer at that point. After all, wealth substantially accumulates over the periods of a
path. However, we find that the last period effect is independent of wealth. Figure 2.12 depicts
the frequency of bet purchases in periods 8, 9 and 10 by wealth quintile, as defined previously. A
test of differences reveals that the last period effect is present in all wealth quintiles, although the
effect is smaller in the highest one (p-values< 0.005 for tests of comparisons between periods 9
and 10 in all quintiles and between 8 and 10 in quintiles 1 to 4).
This effect is largely responsible for the increase in the standard deviation of portfolios we
discussed earlier in treatments Bet and Bet&Box compared to NoBet. The left graph of Figure
2.13 shows that for the last two treatments subjects increase significantly the volatility of their
portfolio in the last period. The right graph of Figure 2.13 describes portfolio volatility by wealth
quintile and treatment. Consistent with the previous result, the increase in volatility is mostly
due to last minute betting among the poorest subjects (quintiles 1 and 2).
47
Figure 2.12: Last period effect and wealth
Figure 2.13: Frequency of bet purchase in the last period
To investigate this effect further, we run the following linear probability model (LPM) for each
of the 79 individual who purchase 3 or more bets:
Y
it
= c+b
w
W
it
+b
x
X
it
+e
it
where Y
it
is a dummy variable indicating whether subject i buys the bet at period t or not, W
it
is her endowment at period t and X
it
is a dummy variable for period 10. We find that about
48
one-third of the subjects (28 out of 79) bet significantly more in the last period (at the 5% level).
The majority of these subjects (23) belong to G3.
2.4.3 Summary
There are three main results regarding investment in the skewed asset. First, there is a non-
negligible amount of “betting" which decreases significantly over the course of the experiment:
some subjects never try the gambling option, some like it all along, while others, likely realizing
its low return, stop purchasing it. This suggests that studies based on one (or few) opportunities
for skewed investments may provide an upward biased estimate of the willingness of individuals
to undertake gambles. Second, bet purchases are higher when subjects are wealthy, consistent
with the idea that the subject gambles when it constitutes only a small fraction of money, and
wisely invests the rest. Third and perhaps most strikingly, betting increases significantly in the
last period of each path in both the Bet and Bet&Box treatments and for all wealth levels. A
possible explanation is that subjects realize that asset C has low expected value and want to avoid
the compounding effect of buying it early in the path. However, our design does not allow for a
test of this hypothesis.
2.5 Feedback
We now analyze how the possibility of observing the payoffs of other subjects affects the portfolio
allocation in the game. Recall that subjects make independent decisions, so they should not be
affected by any information about the performance of their peers. Feedback collection depends
on whether we think there is a (small) cost of opening boxes or a (small) benefit of satisfying
curiosity. Either way, it should not affect subsequent choices.
We find that the vast majority of our subjects open a box whenever the option is available:
2158 out of the 2340 available times (92%). Subjects open boxes with equal frequency in periods
5 and 9 and in all investment paths. The distribution of the number of boxes open by subject is
represented in Figure 2.14. Only 2 subjects never open a box and two-thirds of subjects open a
box every single time.
49
Figure 2.14: Distribution of lookups in the population
Remember that subjects can obtain information about the lowest (Min), Average (Ave) or
highest (Max) payoff currently held by an individual in the session, although they never learn the
identity of that subject. We are interested in assessing the reasons why subjects decide to collect
feedback, why they choose a particular type of feedback, and how it affects their subsequent
behavior.
2.5.1 Wealth and feedback
Only 17 subjects open always the same box while the remaining 98 switch between boxes. A
natural possibility is that subjects care about their relative position within the population and
try to figure out how far they are from a position of interest. Some subjects may be intrinsically
more interested in checking some specific relative position (e.g., how far they are from Ave), while
some others may be willing to track their relative position as a function of their performance (e.g.,
check that they are not the poorest when they fear it might be the case, and figure out if they are
the wealthiest when they are likely to be). To test this hypothesis, we study lookup patterns of
50
subjects by wealth quintile.
14
Figure 2.15 depicts the mean and 95% confidence interval for the
fraction of lookups in each box.
Figure 2.15: Lookups in Min, Ave and Max boxes by wealth quintile
Subjects are systematically more likely to open Max than Ave and Ave than Min. This trend
holds independently of wealth levels. However, the likelihood of opening Min decreases with
wealth, the likelihood of opening Ave is hump-shaped in wealth, and the likelihood of opening
Max increases with wealth. This suggests that wealth levels drive lookups and that the two
hypotheses previously mentioned have some support: (i) subjects are intrinsically more interested
in finding out what is the maximum wealth currently held in the session and (ii) subjects are more
likely to look at the box they believe is closest to their own wealth. These results hold in both
periods in which feedback is possible and across groups.
15
14
Contrary to the previous quintile analysis, we now keep all observations of the individuals in the Bet&Box treat-
ment, including those in which wealth is smaller than $1.
15
To investigate more formally this effect we create three dummy variables (Min, Ave, Max) and regress each of
them separately on wealth and a number of control variables. We find that wealth has a significant positive effect on
Max lookup, no significant effect on Ave lookup, and a significant negative effect on Min lookup (results omitted for
brevity but available upon request).
51
2.5.2 Effect of feedback on bet purchases
The first noticeable result is that feedback has the immediate effect of reducing the overall betting
activity. Indeed, the percentage of bets purchased in Bet&Box is significantly higher in period
4 compared to period 5 (0.041 vs. 0.018, p-value = 0.001) and marginally higher in period 8
compared to period 9 (0.059 vs. 0.043, p-value = 0.074).
We next study whether the feedback obtained as a result of opening a box has an impact on
the subsequent decision to purchase a bet. To this purpose we consider a very simple binary
partition of feedback. For subjects who open the Min, Ave and Max boxes, we say they “lead",
if they learn that they are above minimum, above average and at maximum, respectively. By
contrast, we say they “lag" if they learn that they are at minimum, below average and below
maximum, respectively.
16
Figure 2.16 reports the percentage of times subjects bet when they lead
vs. lag as a function of the box they open. Consistent with the results in section 2.4, subjects
rarely bet when their wealth is low (first and second quintile) independently of the information
obtained. Subjects with average wealth (third quintile) who learn that they are below average
increase moderately their betting activity. Most of the increase, however, occurs for high levels
of wealth and unexpected news. In particular, a subject in the top quintile bets five times more
when she discovers that her wealth is below average.
17
Finally, we present a Probit regression of the probability of purchasing a bet on the type of
feedback obtained (lead or lag) controlling for the level of wealth, the box that has been opened
(Min, Ave, Max) and the different sources of heterogeneity. In particular, we capture the intrinsic
risk attitude with the average fraction of wealth invested in the risky asset in the NoBet treatment,
and we control for the period where the box is open (5 or 9). The results are presented in Table
2.1. Consistent with the evidence presented before, subjects are more likely to purchase bets
when their wealth is high and when they learn they are lagging behind. They also purchase more
bets in period 9 than in period 5. Once we control for these variables, the type of box open is
16
Obviously, a subject who opens Max is likely to be coded as “lag" even when she has high wealth a subject who
opens Min is likely to be coded as “lead" even when she has low wealth. In that respect, this is just one simple
(and imperfect) cut of the data. We have performed a similar analysis where we look at distance between wealth and
information and obtained similar conclusions.
17
There is also a big increase when she discovers that her wealth is at minimum as opposed to above minimum but
it is based on few observations and therefore not statistically significant.
52
Figure 2.16: Betting frequency by wealth quintiles and lookup when lead vs. lag
not predictive of bet purchases. Similar results (not reported here) hold when, instead of using
the lead/lag binary variable, we consider the actual difference between own wealth and wealth
revealed in the box.
Prob. of bet purchase
Lead -0.324 ** -0.304*
Wealth 0.043 *** 0.039 ***
Ave (dummy) -0.048 -0.038
Max (dummy) -0.336 -0.332
Period 9 (dummy) — 0.405***
% asset A in NoBet — -0.141
Constant -1.552*** -1.707 ***
*, **, ***: significant at the 10%, 5% and 1% level.
Table 2.1: Behavior following feedback
2.5.3 Summary
Our subjects are very curious about the performance of others. They have a preference to learn the
highest payoff of the population but they often decide as a function of their current performance:
low wealth subjects look more at Min, medium wealth subjects look more at Ave, and high wealth
subjects look more at Max.
53
On aggregate, opening boxes decreases the likelihood of betting. However, subjects who are
in an investment path where they accumulate equal or more wealth than they typically do and
nevertheless learn that they are below average significantly increase their tendency to buy the bet.
2.6 Conclusion
In this paper, we design a controlled laboratory experiment where subjects dynamically choose
to allocate their portfolio between a risky asset A, a safe asset B, and a skewed asset C. Many
subjects purchase the skewed asset over the course of the experiment despite its negative expected
payoff. However, we note substantial heterogeneity in bet purchases with the existence of three
distinct groups: subjects who never buy asset C (16%), subjects who learn not to buy asset C
(29%) and subjects who persist buying asset C (55%). Among the latters, purchases are more
frequent when the subject is richest (possibly because they can afford a cheap lottery) and, to a
lesser extent, when she is poorest (possibly as a chance to catch up). Purchases are also more
frequent in the last period of the path, when it is the last occasion to make a big impact.
We also analyze the effect of feedback and notice that subjects care about the performance
of others, especially in relation to their own wealth: subjects who accumulate little wealth are
relatively more interested to check whether they are the poorest while those who accumulate a
large wealth are more inclined to check whether they are the richest. Finally, subjects tend to take
riskier positions when they accumulate a high wealth and find out they are among the poorest
subjects in the population. Overall, our results suggest that skewed assets are valuable for some
individuals but purchased with caution. Also, subjects care about their relative performance and
sometimes act upon it.
We conclude with a few remarks hoping to open avenues for future research. First, we find
that the initial demand for a skewed asset drops, suggesting that the experience of lottery out-
comes affects its subsequent demand. This result should be instructive for future experiments
assessing preference for skewness. More broadly, it should be informative when estimating the
demand for financial products incorporating lottery-like features such as prize-linked savings
54
(PLS) accounts. These bank accounts offer savers to partially or entirely replace the interest pay-
ment on their principal with a lottery ticket.
18
In a lab experiment, Filiz-Ozbay et al. (2013)
find that PLS offers increase subjects propensity to save. According to our results, it would be
interesting and beneficial to investigate the long-term effects of PLS programs.
Second, the substantially higher purchases in the last period raise the question of what is
deemed to be the "last period", especially in the cases where the end point may not be a salient
feature of the investment cycle.
19
Next, we found that subjects sometimes (namely in the Bet treatment) tend to bet more often
when they are poor. Our design however does not allow to collect enough data at the individ-
ual level to further investigate this result. It would be interesting to design an experiment in
which subjects would have to face different levels of wealth exogenously to better measure the
relationship between wealth and betting attitude.
Lastly, we have found that subjects are mostly interested in checking their expected relative
position and that they resort to bets to catch up with this belief. The theory of inequality aversion
may offer an explanation, plausibly, in the narrow range of wealth only. Recently, Coibion et al.
(2015) has shown that low income households accumulated more debt in low income neighbor-
hoods compared to high-inequality neighborhoods before the recent financial crisis. This sug-
gests that low income households may have cared about their relative performance with respect
to households with similar income levels rather than inequality itself. This is reminiscent of our
finding, suggesting that a novel form of inequality aversion may impact behavior in both real
life and controlled settings. Comparing the behavior of experimental subjects in our Bet&Box
treatment when portfolio choices lead to large inequalities and when they do not should help
understand this issue further.
18
For an overview of prize-linked savings products, see Kearney et al. (2011)
19
For example, Thaler and Ziemba (1988) suggested that underperforming portfolio managers may take more long-
shot investments as the year draws to a close. For the analysis of investment funds on this topic, see Brown et al.
(1996) and Lin (2011).
55
Chapter 3
Firm Financing in Equity Crowdfunding
3.1 Introduction
Entrepreneurs often need external financing to carry out their projects and grow their firms. I
analyze firms of entrepreneurs that seek funds through equity crowdfunding, a relatively new
source of financing whereby individuals and businesses solicit funds from a broad audience
usually through an internet platform. In exchange, entrepreneurs offer financial stakes in their
businesses. In examining the data, I focus on two questions. First, what firm characteristics relate
to a higher chance of funding success? Second, does early funding success breed later success?
The first question is guided by the debate in the venture capital literature on the relative
importance of management compared to the business of the firm. This debate matters for
evaluating young firms as well as for understanding how are rents divided between the owners
of the human (management) and the non-human (physical) assets.
1
Furthermore, this "the
jockey vs. the horse" debate bears weight on a fundamental question in economics on what
constitutes a firm.
2
In the frameworks of Grossman and Hart (1986) and Hart and Moore (1990),
the non-human assets bind the firm together. Wernerfelt (1984) and Rajan and Zingales (2001),
among others, hold a different view that people can also be a critical resource around which the
firm forms.
Not many empirical studies of early-stage firms exist to answer the question. Kaplan et al.
(2009) follow 50 firms from inception to a few years after the IPO and find that the management
experiences frequent turnovers, while the business idea and the market the firm participates in
remains largely stable over time. The sample looks at successful cases only, however. Recently, in
1
Quindlen (2000) and Gompers and Lerner (2001) discuss the topic.
2
This question has been debated at least since Coase (1937). Gibbons (2005) reviews the theory.
56
a field experiment on one of the leading equity crowdfunding platforms, Bernstein et al. (2015)
find that the information on the human capital of the early stage firms is causally important for
investors initial interest in such firms.
This paper adds to the debate. From a sample of nearly 1500 firms raising funds on one of the
largest US equity crowdfunding platforms, I analyze the relationship between the fundamentals
that firms report and their funding campaign success. I proxy management by education and
experience levels, and product (or alienable assets, more broadly) by the product availability,
intellectual property, and the level of tangible and total assets. I find no evidence of relationship
between the success of raising funds and the product variables, while I find that previous
experience as well as management size positively correlates to the funding success.
Only two other studies evaluate the determinants of funding outcomes in equity crowdfund-
ing. Ahlers et al. (2015) analyze 104 offerings on an Australian platform and find that retaining
equity and detailing project risks increase the funding success. Vismara (2016) examines 271
projects listed on a British crowdfunding platform and finds that retaining equity and social
capital, as well as management size, positively relate to funding success. Compared to those
studies, the present study evaluates a much larger sample size with detailed information on firm
characteristics, making it the most comprehensive study of equity crowdfunding so far.
3
Unfortunately, the cross-sectional nature of the data does not allow me to claim causality.
I discuss the point in the section 3.4.3. Also, the crowdfunding investors are likely different
from professional investors. So, the evidence here points more to what these investors find
important in making their investment decisions than what may be optimal. Were the firms that
raise money this way to perform relatively well, the result would have broader implications. To
this date, due to the recency of the equity crowdfunding industry, there is no evidence of its
merit. Nevertheless, it is important to note that many investors looking for opportunities on
crowdfunding platforms belong to angel networks, and Kerr et al. (2014) present evidence that
some of these groups are successful in their investment choices. Furthermore, Mollick and Nanda
3
See Mollick (2014) for the analysis of crowdfunding that is not investment based.
57
(2015) show that the crowd’s funding decisions and expert valuations of theatre projects tend to
coincide. Also, the plays favored by the crowd alone do not have worse long-term outcomes than
those viewed favorably by both experts and the crowd.
My second question relates to the work on information cascades (Welch (1992) and Bikhchan-
dani et al. (1992)). Apart from non-equity crowdfunding studies (Zhang and Liu (2012), Burtch
et al. (2013), Agrawal et al. (2015), Colombo et al. (2015)), the amount of evidence in this regard
is scarce. Bernstein et al. (2016) find that investments of other notable investors had no effect on
crowd’s interest in the firm. Recently, Vismara (2015) followed 111 equity crowdfunding offerings
and finds that the number of early investors is important for subsequent success. However,
he does not control for firm fundamentals. In the present study, I test whether a higher early
campaigning success attracts higher subsequent funding. The data allows me to separate the
total funding raised in that reported within first 7 days of the crowdfunding campaign, and that
after. After controlling for the quality of firms, the evidence suggests no relationship between
early and late financing, much to the contrary of previous findings.
I dedicate the next section to a brief introduction of equity crowdfunding. In section 3.3,
I describe the platform and the data. Section 3.4 contains results. In section 3.4.1 I analyze
correlates of success in equity crowdfunding. Section 3.4.2 examines the relationship between
early and late investing. In section 3.4.3, I discuss the results. In section 3.5, I offer brief
concluding remarks.
3.2 Equity Crowdfunding
Crowdfunding is essentially a two-sided market with a platform as an intermediary. In equity
crowdfunding, as opposed to more widespread donation and reward-based crowdfunding,
the crowd looks for investment opportunities. This brings equity crowdfunding under a more
stringent regulatory framework that until very recently allowed only high income (wealth)
individuals to invest. On the other side of the platform are individuals and businesses looking to
58
finance their projects. As with any two-sided market, due to the network externality effects, the
success of a platform and the industry hinges on both sides’ willingness to enter the market. In
the next few paragraphs I summarize the economics behind equity crowdfunding mostly based
on a detailed survey available in Agrawal et al. (2014).
4
What are the incentives for agents to participate in equity crowdfunding? Young firms may
be drawn by the lower cost of capital. Crowd-investors may be willing to pay a higher price
for shares than more traditional investors, either because they cannot evaluate projects properly
or because they are deriving more than just the financial benefit from their investment (e.g.
investing in novel medical treatments or environment-friendly projects). Secondly, firms may
learn about the future demand for their product from a wide audience and get a feedback on how
to make the product better. By the same token, that same information can help entrepreneurs
abandon unpromising projects earlier. Lastly, a successful crowdfunding campaign may attract
follow-up rounds of financing.
On the other hand, entrepreneurs may shy away from crowdfunding because they do not
want to share their detailed project ideas too early too publicly. Also, they may be apprehensive
in dealing with so many investors as oppose to just a few (as in the case of banks, angels, and
VCs). With crowdfunding, firms also forego, at least initially, important expertise and guidance
that they would receive from professional investors.
Looking on the other side of the platform, why would anyone invest in crowdfunding? First,
it offers a new asset class that may provide some diversification benefits to investor’s overall
portfolio, or a small chance of an extraordinarily big return. The distribution of returns among
start-ups tends to be highly skewed. See Moskowitz and Vissing-Jorgensen (2002) and Hall and
Woodward (2010) for evidence. Therefore, preference for skewness may bring investors to an
equity crowdfunding platform. Second, and as mentioned above, investors may be seeking to
invest not only for financial gain but also for a cause they care about. Furthermore, they may
derive utility from participating in a development of a new product. Nevertheless, the sheer
4
For other surveys, see Schwienbacher and Larralde (2010) and Moritz and Block (2016)
59
uncertainty, asymmetry of information, and potential fraud might dissuade investors.
This can very well bring the industry to a market failure. If the investors look for very high
returns to compensate for the asymmetry of information and uncertainty, it may leave only the
very risky firms and lower quality projects on the other side of the platform, since the good firms
would seek better opportunities elsewhere. This in turn prompts investors to require even higher
returns, unraveling to market failure. Yet another source of market failure can be a coordination
problem where investors wait to see the decisions of other investors. In equilibrium, no one
invests.
Nevertheless, certain market design features, such as syndication and provision point mecha-
nism, arose in response.
5
And the industry is growing. In 2014 the global crowdfunding market
raised $16.2 billion up from $6.1 billion in 2013 (Belleflamme et al. (2015)). Equity-crowdfunding
accounts for only 1.1$ billion. However, the median campaign size is drastically bigger for equity
crowdfunding than for other types. Furthermore, a recent deregulation allowing non-accredited
investors to participate may further spark the growth of equity crowdfunding in the US.
3.3 Data
Data used in this analysis comes from EquityNet, an internet crowdfunding platform operating
since 2005 in Fayetteville, Arkansas. To raise funds, entrepreneurs open a profile on the platform.
There they state the basic information regarding their enterprise as well as the information on the
funding campaign. Furthermore, they may decide to fill out an in-depth business plan detailing
the management, products, markets, intellectual property, capitalization and financials of their
firm. The profile is available to all registered investors. But in order to share a business plan with
investors, entrepreneurs need to subscribe to EquityNet. This is the main source of income for
5
See Agrawal et al. (2016)
60
the platform, given that it does not take any transaction fees.
6
EquityNet does not represent a typical equity crowdfunding platform. Apart from not taking
a transaction fee, the platform does not guide the investment process. Transactions between
investors and entrepreneurs do not go through EquityNet. All of the information provided
by firms is therefore self-reported. Furthermore, I cannot observe the contract details, nor the
number or the identity of the investors on the platform that decide to buy stakes in the firms.
Needless to say, funds that a firm reports to have raised those does not necessarily come from an
EquityNet investor.
Also, it is important to note that the platform does not limit the length of the funding
campaign like many other platforms do, although they seem to last around 6 months. Fur-
thermore, the platform does not employ the provision point mechanism, whereby firms get
to keep the raised funds only if they surpass a preset threshold. This is employed to avoid
the coordination problem mentioned in section 3.2.
7
Putting it all together, it would be most
accurate to understand EquityNet as a very sophisticated ad platform for entrepreneurs to adver-
tise their business and funding campaigns, and leave a footprint of data for researchers to analyze.
The data I look at in this paper is the cross-sectional snapshot taken in March 2016. I
analyze firms that started seeking funds anywhere from March 2013 until the end of 2015.
Not all firms that opened accounts on EquityNet are in my sample, however. I eliminate
firms that do not state their funding goal or the type of financing they are looking for. Even
though this represents a large number of accounts (around 50,000 of them), these firms have
much more incomplete profiles and attract far less of investors’ attention. I further eliminate
firms that do not report their management and product information in their business plan.
6
EquityNet’s disclaimer: "The author(s) were provided a conditional license subject to strict confidentiality provi-
sions to certain data compiles for EquityNet. Any opinions, findings, conclusions or recommendations expressed in
this material are those of the author(s) and do not necessarily reflect the views of EquityNet." For more information
on EquityNet visit www.equitynet.com
7
By the end of 2015, the platform introduced a similar mechanism, where firms can report separately funds raised
and pledged funds, the funds likely to be committed if the goal is reached. I do not take this into account in my
analysis as the feature has become available only recently and it was not relevant for most of the firms in my sample.
I focus entirely on reported funds raised.
61
Admittedly, some firms with serious intentions of raising funds may decide to see how their
profile fares before they decide to pay the subscription and fill out the business plan.
8
However,
the information regarding the product and the management is critical to the analysis in this paper.
I also disregard firms that report being located outside of the United States or Canada,
firms that seek grants and royalties and those that either seek less than $1000 or more than
$100 million. I further count out firms that attempted multiple rounds of funding, as I cannot
know how much funds they raised in the initial round. Most importantly, among the remaining
firms I leave out 255 that had their profiles turned off at the time of data collection. I remove
these firms from the sample because I cannot tell with certainty whether the firm had ever
had the profile on or not. I assume that entrepreneurs that never publish their profiles have
little incentive to diligently fill out information regarding their firms, thereby likely biasing the
results. After the described sample selection, I am left with 1487 firms in the sample. To the
best of my knowledge, this is the largest sample size of any equity crowdfunding analysis thus far.
Table 3.1 shows descriptive statistics regarding the funding campaigns. Most companies sell
equity and, judging by the size of their funding goal, are looking for seed capital. More than
half of firms are seeking less than a $1 million, with a great majority seeking up to $5 million.
Target amounts are bigger than the ones reported in Ahlers et al. (2015) and Vismara (2016)
most likely due to the lack of the "all-or-nothing" mechanism which prompts entrepreneurs to
set more modest targets.
The distribution of funding outcomes is very skewed, a common occurrence in the crowd-
funding industry (Agrawal et al. (2014)). Nearly a half of the firms raise nothing. Of those that
do, most raise only a modest percentage of their target with only 21 firms reaching it. Given that
a firm can raise more than its target, I do not believe that there is less of an incentive for firms to
report being fully funded, although it certainly may happen. In that case, the number of fully
funded firms is downward biased. Also, note that 64.7% of the sample subscribed to EquityNet
8
Current monthly subscription to EquityNet costs $300 per month
62
at least once, allowing them to communicate with investors and share their business plan.
Funding Type (%)
Equity 73.0
Debt 12.2
Convertible Note 14.8
(> 0)
Obs. N Mean SD 10th 50th 90th
Funding Goal ($1,000) 1487 1487 2214.7 6209.8 75 595 5000
Funding Raised (%) 1201 656 25.6 41.4 2 12.5 60
Full Funding (#) 21
Subscribed to EquityNet (%) 64.7
Table 3.1: Funding Campaigns Descriptive Statistics
Table 3.2 describes firms’ management characteristics, some of which I use in the subsequent
analysis of the relationship between management and the funding success. When it comes to
CEOs highest education level, high school, university and graduate school are nearly equally
represented.
9
Most of the firms are small in management size with about 17% having more than 4
managers. This is comparable to what Ahlers et al. (2015) and Vismara (2016) find in their studies.
The average management experience refers to the average of the average of the firm’s
management team. The average management age is 45, while the average industry, management,
and start-up experience is 14.5, 16.6, and 10.2, respectively. The average number of previous
start-ups founded by the management is around 1.2, with more than half of the sample reporting
to have participated in founding at least one other still active company. Interestingly enough,
the majority of firms have experienced management. This may be because equity crowdfunding
draws in experienced management that feels they can gain less from the angel or the VC
9
If the firm has more than one person in management, I identify the CEO using their stated position (e.g. CEO or
President), years with the firm, and the order in which they were entered in the management section of the business
plan. I cannot identify the founder(s) of the firm.
63
professional advice. Alternatively, given the self-reporting and no strict guidance in how to fill
out the business plan, some of the figures may be inflated.
CEO Education (N=1487) (%)
High School 29.7
Undergraduate 36.0
Graduate 34.3
Management Size (N=1487) (%)
1 44.7
2 23.6
3 14.0
4 8.5
5 or more 9.2
Average Management Experience
N Mean SD 10th 50th 90th
Age 1474 45.5 10.9 31 46 59.5
Industry 1380 14.5 9.3 3 13.7 27.4
Management 1403 16.6 9.5 5 15.2 29
Start-up 1331 10.2 8.5 2 8 21
Previous start-ups (active) 1473 1.2 1.8 0 1 2.5
Table 3.2: Management Descriptive Statistics
Table 3.3 contains information regarding firms’ products and assets. I will use these variables
as proxies for non-human assets suggested by Grossman and Hart (1986) framework. At the
time of account creation, only 25.3 % firms had a product available. Nearly a half claim some
sort of intellectual property. However, only 6.9% have actual patents granted in the United
States. Most of the companies do not have revenue yet, nor assets, tangible or otherwise. Among
those that do, the average asset size is 110 thousand dollars and the average revenue is 210
thousand dollars. The distribution of assets and revenues is extremely skewed, however, with
firms reporting more than $3 million in revenue.
10
10
In the main analysis, I use the log transformations.
64
Product Available (%) 25.3
Patents, TM, or Copyrights (%) 41.6
Patents Granted in US (%) 6.9
(> 0)
Obs. N Mean SD 10th 50th 90th
Revenue ($1,000) 1376 349 2,174.9 9,315.6 6.5 209.7 3,370.2
Assets ($1,000) 1374 532 17,421.9 259,155.8 5 110 2,577.216
Tangible Assets ($1,000) 1374 243 2,342.84 17,113.5 2.5 76.3 2,043.6
Table 3.3: Product Descriptive Statistics
Lastly, table 3.4 describes general business characteristics of the firms in the sample. The
great majority of them are organized or plan to be organized as limited liability companies. This
is in contrast to a representative sample of newly founded US firms that tend to have a much
higher proportion of sole proprietorships (Robb and Robinson (2012)). However, this is expected
given that most of these firms sell equity and must therefore offer protection to their investors.
A larger proportion of companies are offering products than what is usual among young and
small firms. In the Kauffman survey (Robb and Robinson (2012)), around 85% of the newly born
firms offer services. In my sample, the figure is close to 50%.
11
Unlike the firms in the Kauffman
survey, this sample contains firms more varied in age. More than half of the sample was less
than 18 months old, but with a considerable amount of firms more than 5 years old - nearly 20%.
This may suggest that equity crowdfunding does attract some firms that have existed for some
time and were not able to attract other outside financing.
11
Around 40% of the firms in the sample report to operate in retailing, IT services, consumer or business products
and services. Other industries with notable representation include medical (biotech, pharmaceuticals, and healthcare),
media & entertainment, and software with around 10% of the sample each.
65
In terms of geographical location, the top 5 states by venture capital activity represent 41.8%
of the sample.
12
This speaks to the limitation of crowdfunding to bridge distances to locations
with less traditional financing.
13
Lastly, the median of workers employed is 3 with only a handful
of companies reporting a high number of workers. The actual number may be smaller if certain
firms double-count their management as workers.
Legal Status (N=1486) (%)
Corporation 42.4
Limited Liability Company 47.2
Partnership 1.3
Sole Proprietorship 6.9
Other 2.2
Product/Service (N=1487) (%)
Product 49.9
Service 36.6
Both 13.5
Age (N=1429) (%)
Not Yet Founded 21.2
up to 18 months 36.3
18M - 3Y 14.8
3Y - 5Y 9.5
5Y or more 18.19
Location (%)
CA, FL, TX, NY, MA 41.8
Other 58.2
(> 0)
Obs. N Mean SD 10th 50th 90th
Workers (#) 1427 1356 8.3 45.9 1 3 12
Table 3.4: Firm General Descriptive Statistics
12
See www.pwcmoneytree.com for the information on venture capital activity. The data comes from the Thomson
Reuters.
13
For the analysis of the effects geographical distances in crowdfunding see Agrawal et al. (2015) and Lin and
Viswanathan (2016).
66
3.4 Results
3.4.1 Correlates to Funding Success
To test whether management or product proxies relate to success in fundraising I run two sets of
analysis with different outcome variables. In the first one, for the dependent variable I use an
indicator variable that takes a value of one if the firm raised any funds. The results are presented
in Table 3.5. Given that the likelihood of raising a positive amount is a rather crude measure, I
also use the logarithm of the amount raised as an outcome variable.
14
The results for this set of
analysis are presented in Table 3.6. Apart from running the analysis on the full sample, I also
look at two particular subsets. One is the subset named "Equity Only" which excludes compa-
nies seeking debt. In the second subset, I only look at young firms - those less than 18 months old.
The variables shown in red proxy the quality of the management. I include the average
number of years of industry experience and experience in management, no. of previous start-ups
founded that are still active, and indicator variables for CEO’s undergraduate and graduate
education. One dimension of management experience, number of previous start-ups founded,
positively correlates to funding success. According to the far left column of table 3.5, a unit
increase in management’s average number of active start-ups founded relates to about 3%
increase in likelihood of raising any funds. Also, the same unit increase is related to a 22%
increase in the amount raised (table 3.6). The result seems to be robust across all subsamples.
15
Unlike experience, the education level does not seem to matter. In alternative specifications, I
used the proportion of managers holding graduates and undergraduates degrees as well as the
education level of the CEO. The results remained the same, pointing to no relationship between
funding success and management’s education level.
14
In order to make the logarithmic transformation, I replace a value of zero dollars to a value of one dollar for those
that raised no money.
15
Other specifications included the variables on average management age and start-up experience and showed
similar results.
67
Dep. Var Reported Funding Raised (0/1) Target (log)
Sample Equity Only Young Full
Spec. Probit Probit Probit OLS
N 1075 958 605 1312
Industry Exp. (y) -0.0002 -0.0039 0.0049 0.0073
(-0.03) (-0.70) (0.70) (1.50)
Exp. in Management (y) 0.0052 0.0038 0.0002 0.0175***
(0.97) (0.66) (0.03) (3.51)
Previous Start-ups (#) 0.0918** 0.0887** 0.0974** 0.0334
(2.43) (2.21) (1.99) (1.55)
Undergraduate (0/1) 0.1291 0.0874 0.1069 0.1126
(1.26) (0.79) (0.77) (1.17)
Graduate (0/1) 0.0652 0.0441 -0.0252 0.2019**
(0.62) (0.39) (-0.17) (2.04)
Management Size (#) 0.0973*** 0.0911*** 0.0471 0.1330***
(3.66) (3.29) (1.24) (5.77)
Product Available (0/1) -0.0222 -0.0313 -0.1277 0.0433
(-0.19) (-0.24) (-0.64) (0.39)
Revenue (log) -0.0039 -0.0065 0.0069 -0.0114
(-0.39) (-0.60) (0.40) (-1.25)
Patents, TM, Copyright (0/1) -0.0958 -0.1164 -0.0842 0.1166
(-1.07) (-1.24) (-0.70) (1.38)
Tangible Assets (log) 0.0075 0.0108 0.0153 0.0109
(0.75) (1.00) (0.92) (1.16)
Target (log) 0.0219 0.0399 0.0409
(0.73) (1.23) (1.00)
Subscribed (0/1) 0.0738 0.0364 0.1234 0.4284***
(0.76) (0.35) (0.98) (4.70)
Controls Yes Yes Yes Yes
*, **, ***: significant at the 10%, 5% and 1% level. Numbers in parentheses below the coefficient show the z-score (t-stat) for the Probit
(OLS) model. Units are in the parenthesis next to the variable name. Important Controls include: industry, location, funding type,
legal type, age, campaign starting quarter, number of workers. The reported coefficients are raw in the case of the Probit specification.
See the text for the interpretation of the effects.
Table 3.5: The Likelihood of Raising Funds
Overall, the results are in line with findings by Bernstein et al. (2016) and support the claim
by Rajan and Zingales (2001) that the firm’s critical resource may be human capital as well. This
study goes beyond previous studies and identifies experience as the more relevant dimension of
management.
68
In blue are the proxies for product traction: the indicator of product availability, size of the
revenue, the indicator for any patent, trademark or copyright ownership, and the size of tangible
assets. The results consistently show no significance of any of the product proxies, across all
the different specifications and sample subsets. In alternative specifications I used total assets
instead of tangible assets. I also used stricter definitions of owning intellectual property, namely,
an indicator function for whether a firm has a granted patent in the US. In all of these robustness
checks, results remain the same.
The results do not suggest that the product does not matter. Physical and intellectual
property assets and revenue generation may be poor proxies for the product potential at this
stage of development. Competition, potential customer base, or other, less quantifiable, aspects
of the business may be more relevant.
As in Ahlers et al. (2015) and Vismara (2016), management size shows strong positive
relationship to fund raising. An additional member of the management relates to a 3% increase
in the likelihood of raising any money, and to a 35% increase in the amount raised. Interestingly
enough, the relationship is insignificant for the subset of young firms. It is not clear what
management size actually represents. On the one hand, it may proxy for the size of the firm,
better than assets or revenue, since many firms have none. Or, alternatively, it may suggest
something about the maturity of the product. If a firm expands the management to include
positions such as the CFO or a marketing manager, it may mean that the firm’s product passed
the stage of concept, thereby reducing some of the uncertainty related to its prospects.
Last column of table 3.5 shows the determinants of target setting, an interesting question
in its own right. It is conceivable that the funding goal depends on how much money is
expected to be raised, which in turn depends on the firm fundamentals. Results corroborate
that. Targeted amount relates to a few firm characteristics including management experience,
size, and education. For the robustness check, I excluded the target from the first 3 specifications
in Table 3.5. The results remained largely unchanged. An added concern would be if the firms,
informed by initial state of their campaign, revise their funding targets. This may, in turn, change
69
the response of investors.
Note that I include an indicator for whether a firm has an EquityNet subscription or not.
Investors may be more informed about the firms with the subscription as those can deliver
their business plans easily through the platform. However, investors can obtain the information
outside of EquityNet.
16
Some of the other most relevant variables I control for include industry,
location, funding type, legal type, age, campaign starting quarter, and a number of workers. One
important variable absent from the analysis is the price of equity. Unfortunately, a large number
of entrepreneurs do not actually reveal how much of firm’s ownership would the targeted
amount represent. This is likely because it may prove costly to commit to a price beforehand.
3.4.2 Early and Late Funding Raised
In order to more precisely identify funds raised while a firm advertises on the platform,
EquityNet records the amount of money the firm reports raising within the first 7 days after
filling out the profile. EquityNet assumes that it is likely that firms raised these funds before
coming to EquityNet. In my analysis, I denote this part of the total funds raised as the early
funding. The remaining funds raised, that is, the difference between the total and the early
funding, I denote as the late funding. Figure 3.1 shows, in percentages, the decomposition of the
total funding raised, on early and late.
This decomposition allows me to test the effect of early impetus in raising funds on the later
one while controlling for the fundamentals of the firm. The results are presented in Table 3.7.
The relationship between early and late fundraising is positive but insignificant. This result
stands in contrast to Vismara (2015). More in line with results here, Bernstein et al. (2016) also
find that investors are not more likely to be interested in a firm if a prominent investor invested
in it.
16
Analysis based on just the subscribed sample shows the same result.
70
Figure 3.1: Early and Late Funding Raised
There are a couple of reasons why we should question the result presented here, however.
Firstly, from the Figure 3.1 we can observe that many firms with high early funding raised
tend to report raising little thereafter. It may happen that in these instances entrepreneurs are
less likely to update their profiles causing a measurement error in the data. Secondly, and
more importantly, there is no reason to believe that the price of the equity stays constant. It
may happen that later investors are attracted by early success but dissuaded to invest by an
actual, or assumed, higher price they may need to pay to buy a stake in the firm. Since I do
not observe the actual contracts or negotiations between the parties, I cannot reject this possibility.
More broadly, I can compare the results here with the ones in tables 3.5 and 3.6. Contrary
to the finding there, the number of previous start-ups has no effect on late funding raised, but
the years of experience in management do, albeit with not so strong statistical significance.
Management size shows a strong relationship to the late funding raised as it does to the total
funding raised. Lastly, I find that the firms that subscribe to EquityNet tend to raise more funds.
This result gives support to EquityNet’s model, but also suggest that indeed for most firms the
71
early amounts were likely raised before their access to the platform.
3.4.3 Discussion
To which extent can I make the causal inference that the results above show determinants of
successful fundraising? It may be the case that the funds raised were already invested before
arrival to EquityNet and used to form the fundamentals reported by the firm in its business plan.
Maybe the money raised was used to hire more managers prompting a positive relationship
between funding and management size. Due to the cross-sectional nature of the data, I cannot
tell which way the causality runs. This is especially worrisome in the section 3.4.1, where I
analyze the correlates of the total funding raised, since I cannot know how long before arriving
to EquityNet were the reported funds raised.
To the extent that the separation on early and late funding is valid, the issue of endogeneity
may be less pronounced in the following subsection. There, the significance of management
experience and its size remains, but start-ups founded do not affect the late funding raised and
experience in management shows a weak effect. Therefore, the results ought to be taken with
a grain of salt. Furthermore, the firms are likely investing in their fundamentals as they raise
funds. However, comparing the data to its earlier snapshot, I find that entrepreneurs tend to
be inert when it comes to updating their business plans, suggesting that the firm fundamentals
viewed are the ones stated by the firm at the beginning of the campaign.
The analysis in this paper disregards the other side of the platform - the investors. Even
though I cannot observe their investment decisions, I am able to observe the firms they are
interested in and that they communicate to. One of the next steps in my research agenda will be
to describe the clusters formed by investors based on their firm interest and examine how the
determinants of fundraising change across these clusters - a dynamic potentially concealed by
the aggregate analysis presented here.
72
3.5 Conclusion
In this paper, I analyze the funding success of small firms raising money through equity
crowdfunding. In terms of sample size and the amount of firm information available, this is the
most comprehensive analysis of equity crowdfunding to date. I find suggestive evidence that the
management, in particular its experience and size, play a role in funding success. I also find no
support for the case of informational cascades.
Speaking more broadly, any result out of the equity crowdfunding research hinges on the abil-
ity of the crowd in choosing the right investments. Therefore, the future research agenda needs to
address the performance of firms after they have raised funds through equity crowdfunding. Due
to privacy constraints, I am not able to identify and follow firms in my sample. Furthermore, it
may take some time before long-term outcomes, such as profits, sales, and exits, can be measured.
73
Dep. Var Reported Funding Raised (log)
Sample Equity Only Young
Spec. OLS OLS OLS
N 1075 958 605
Industry Exp. (y) -0.0044 -0.0200 0.0270
(-0.20) (-0.86) (0.96)
Exp. in Management (y) 0.0375* 0.0302 0.0163
(1.66) (1.27) (0.55)
Previous Start-ups (#) 0.2285** 0.2134** 0.1938**
(2.52) (2.30) (1.98)
Undergraduate (0/1) 0.6097 0.4276 0.4943
(1.40) (0.92) (0.88)
Graduate (0/1) 0.2580 0.2325 -0.2468
(0.57) (0.49) (-0.41)
Management Size (#) 0.3591*** 0.3246*** 0.1006
(3.48) (3.02) (0.70)
Product Available (0/1) 0.0799 0.0448 -0.1481
(0.16) (0.08) (-0.18)
Revenue (log) -0.0244 -0.0314 -0.0059
(-0.58) (-0.70) (-0.09)
Patents, TM, Copyright (0/1) -0.3383 -0.4371 -0.2800
(-0.90) (-1.11) (-0.57)
Tangible Assets (log) 0.0428 0.0581 0.0802
(1.01) (1.28) (1.20)
Target (log) 0.5008*** 0.5896*** 0.5674***
(3.93) (4.29) (3.41)
Subscribed (0/1) 0.6193 0.5431 0.8261
(1.48) (1.22) (1.60)
Controls Yes Yes Yes
*, **, ***: significant at the 10%, 5% and 1% level. Numbers in parentheses below the coefficient show the t-statistic. Units are in
the parenthesis next to the variable name. Important Controls include: industry, location, funding type, legal type, age, campaign
starting quarter, number of workers.
Table 3.6: The Amount of Raised Funds
74
Dep. Var Late Funding Raised (0/1) Late Funding Raised (log)
Spec. Probit OLS
N 977 991
Early Funding Raised (0/1) 0.0475
(0.46)
Early Funding Raised (log) 0.0152
(0.58)
Industry Exp. (y) -0.0114* -0.0272
(-1.75) (-1.50)
Exp. in Management (y) 0.0124* 0.0340*
(1.89) (1.82)
Previous Start-ups (#) 0.0107 0.0374
(0.46) (0.51)
Undergraduate (0/1 -0.0588 -0.2384
(-0.45) (-0.66)
Graduate (0/1) -0.0644 -0.1975
(-0.49) (-0.53)
Management Size (#) 0.0941*** 0.3487***
(3.44) (4.06)
Product Available (0/1) -0.0328 0.0027
(-0.22) (0.01)
Revenue (log) -0.0006 -0.0038
(-0.05) (-0.11)
Patents, TM, Copyright 0.1321 0.2533
(1.21) (0.81)
Tangible Assets (log) 0.0013 0.0029
(0.10) (0.08)
Target (log) 0.0186 0.1265
(0.47) (1.19)
Subscribed 0.8107*** 1.6605***
(5.70) (4.91)
Controls Yes Yes
*, **, ***: significant at the 10%, 5% and 1% level. Numbers in parentheses below the coefficient show the z-score (t-stat) for the Probit
(OLS) model. Units are in the parenthesis next to the variable name. Important Controls include: industry, location, funding type,
legal type, age, campaign starting quarter, number of workers. The reported coefficients are raw in the case of the Probit specification.
See the text for the interpretation of the effects.
Table 3.7: The Effect of Early on Later Funding Raised
75
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Chapter A
Appendix A
Note: The following instructions are accompanied by a slideshow presentation. Slides available
upon request.
We are about to begin. Please put your cell phones and other electronic devices in your bag
and do not use them until the end of the experiment.
Dear Participants,
Welcome and thank you for coming to this experiment. You will be paid for your participation,
in cash, at the end of the experiment. You will remain anonymous to me and to all the other
participants during the entire experiment; the only person who will know your identity is the
person in the other room who is responsible for paying you at the end. Everyone will be paid
in private and you are under no obligation to tell others how much you earned. The entire
experiment will take place through the computer terminals.
Let us begin with a brief instruction where you will be given the complete description of the
experiment and shown how to use the software. Please, pay attention to the instructions, as it is
important for you to understand the details of the experiment. There will be a quiz at the end
of the instructions that everyone needs to answer correctly before we can proceed to the actual
experiment. Participants who are unable to answer the quiz will not be allowed to participate
in the experiment. If you have any questions during the instruction period, raise your hand and
your question will be answered so everyone can hear. If any difficulties arise after the experiment
has begun, raise your hand, and an experimenter will come and assist you. If you cannot see the
entire projection screen, please come forward as it is important for you to see the entire screen.
Today, we will ask you to make investment decisions. Your final payment consists of a $5
show-up fee plus your investment earnings. Those earnings depend both on the choices you
make and on luck. The choices of other participants do not affect your payoff in ANY way, at
ANY point in the experiment and your choices do not affect their payoff. The entire experiment
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is split in 3 parts. I will now give you instructions for Part 1. You will get additional instructions
before Part 2 and Part 3.
PART 1
Let me first summarize the investment process and then we will go through each step in more
detail. You will start with an initial amount of money that you will be able to invest in two assets,
A and B. You will have 10 periods to invest. At each period you will decide how to allocate your
money between the two assets. At the end of each period, you will earn returns from that period’s
investment in each asset. The two assets will pay differently, and later in the instructions I will
explain what to expect from each asset. After period 10, the process ends and the computer will
record your final money amount. This process of 10 investment periods is called an investment
path. At the start of each path, your money will be reset to the initial amount.
In Part 1 you will complete 15 of these paths. Consequently, there will be 15 final amounts of
money, one for each path. The computer will randomly select one of these 15 final amounts. The
selected amount will be your payoff for Part 1. Are there any questions? Let me now walk you
through the procedure step by step.
The Initial Endowment: This is a screenshot of what you will see on your computer at the
beginning of each path, that is, in period 1 of each path. In each path you start with $3, this is
your initial endowment. This amount is displayed on the left side of the screen in the box labeled
“Account". It is also represented by the height of the bar in the middle of the screen. There is a
grid in the background to help you get a sense of the bar’s height.
Periods and Timing: As mentioned earlier a path is made of 10 periods, starting at 1 and
ending at 10. The sequence is displayed on the bottom of the screen and your current period is
displayed in the upper left corner. Each period is an opportunity for you to invest. A period ends
when the time runs out. You can see the timer on the left hand side. For the first period in each
path you will have 10 seconds to make your investment decision. For the other periods in the
path, that is, periods 2 to 10, you will have 6 seconds to make your investment decision.
Investing: Let me show you with a short video how to make your investment.
Step 1. Choose display. To start your investment, you first need to click on one of the two
boxes at the bottom, the ones labeled with percentage and dollar signs. These boxes control how
your allocation between assets A and B is displayed: in percentages or dollar terms. You have to
83
click one of the boxes in period 1 of each path. You can also change the display anytime simply
by clicking on the other box. Select whichever box you find convenient and change it anytime
you want.
Step 2. Activate the bar. Now you can activate the investment bar. Click anywhere on the
light gray bar to activate it. Notice when the bar is light gray it means that your money is not
invested in either asset. If the bar stays that way after the period ends, you will earn zero interest
on your money: the same amount will just be transferred to the next period.
Step 3. Choose the allocation. Once you activate the bar you will notice that it is split between
two colors: the top is light blue, and the bottom is gray. The top represents the amount of money
allocated to Asset A, and the bottom represents the amount of money allocated to Asset B. Now
you can see the display I previously mentioned. It shows how much money you have allocated to
A and B either in dollar or in percentage terms. This example shows the dollar display. You can
change the allocation between A and B in two ways: by holding the horizontal bar and moving it
up or down or by clicking on the bar, as you can see in the video. Once you are satisfied with the
allocation wait until the period ends.
Step 4. Proceed to the next period. When the period ends, a new gray bar will appear showing
you the new amount. Here is the transition from period 1 to period 2. Your new amount will
be the sum of the money you earned on both assets A and B and it will be shown on the left
where your initial money amount was displayed. The new height of the bar will also represent
this amount. Be aware that the background grid can be re-scaled to accommodate changes in the
bar, so pay attention to the figures written on the grid. The last period’s bar will become inactive
but you will still be able to see your past allocation between assets A and B. Remember that you
need to activate the bar and choose an allocation between A and B at every period, otherwise
you earn no interest. Here is a period 2 allocation process and the transition to period 3. Notice
how I changed the display from dollars to percentages. This process continues until period 10.
After period 10, the path ends. Here is a screenshot of one path end. Your final amount will be
shown in the box on the left and by the height of a green bar on the right. A message will appear
informing you that the path ended. You need to click the “OK" button to continue. A new path
will start shortly thereafter.
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Assets A and B: Let me show you what to expect from the investment in each asset. In the
upper left corner of your screen there is a box that reads “Asset A: mean return 6%, standard
deviation 55%"; “Asset B mean return 3%". These numbers show how your investment in each
asset grows and they will not change during the entire experiment.
Asset B: The 3% next to Asset B in the box means that, once the period ends, the amount
allocated to Asset B will grow by 3% for sure. The interest rate of 3% will not change throughout
the duration of the experiment. A reminder: money in Asset B is represented by the bottom,
GRAY portion of your active bar. Here is an example: if you have 2 dollars invested in B you will
have 2 dollars and 6 cents in the next period. If you keep that money in B you will then have 2
dollars and 12.2 cents the period after. You can think of your money in Asset B being multiplied
by 1.03. Note that 2 dollars is just an example. In the experiment you can choose any allocation
you want provided it does not exceed your total amount.
Asset A: Contrary to asset B, your return on asset A is uncertain. Technically, the return on
asset A has a Normal distribution with mean 6% and standard deviation 55%, as shown in the
upper left box. This means that asset A grows by 6% on average. However, it may be more or it
may be less. In particular, the growth rate could be negative. In this case the money you invested
in Asset A will shrink. Although the return can be negative, the amount of money you hold on
asset A can never go below zero. A reminder: money in Asset A is represented by the top, LIGHT
BLUE portion of your active bar.
Another way to think about the return on this asset is that the amount you put in asset A will
be multiplied by some positive number. On average, this number will be 1.06 which corresponds
to a 6% growth. Let us call this number a multiplier. If the multiplier is less than 1, it means that
your investment in Asset A shrinks. For example, if you allocate $2 to asset A and the multiplier
turns out to be 0.8, you will have $1.6 in the next period. If the multiplier turns out to be 1.5, you
will have $3 the next period. Here is a chart showing the probability of your multiplier being in a
given range. With 20% chance it will be somewhere between 0 and 0.67. With 30% chance it will
be somewhere between 0.67 and 1.06. With another 30% chance it will be somewhere between
1.06 and 1.7. Finally, with 20% chance it will be above 1.7. Once the period ends and you receive
the returns on your assets, the box on the left marked “Last Period Multiplier" will show what
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turned out to be the multiplier for asset A in that period. The box will show always 1.03 as the
multiplier for asset B.
Projection Bar: The returns from asset A obtained after several periods depend on many
factors. In order to help you get an idea of the range of outcomes, we placed a projection bar
at the end of the screen. Let me explain how the projection bar works. Suppose for example
that in the first period you invest $2 in Asset A. If you keep the returns on that same asset, how
much money will you have at the end of the 10th period? Observe what happens on the left hand
side of the graph. It is a simulation of your return. The vertical axis represents dollars and the
horizontal axis the periods. It begins with 2 dollars in the first period and it ends after 10 periods.
Here is one potential final amount of money. But it can also be this. Or this. Or this. Notice that
each time a path ends, we keep track where it lands by adding a dot on the right graph. Each
dot represents a possible final amount of money. If we run enough paths, all with $2 invested in
asset A, we will get a bunch of dots on the right end. The more dots each dollar region has, the
more likely your amount of money will end up there. And that’s exactly what the bar represents:
the likelihood of your earnings ending up in a certain amount.
Now look at the example in the picture. It is period 4. Look at the projection bar. For the
current investment strategy, the lower gray part is the projection of how much you will earn on
asset B if you don’t change the allocation between assets until the end of the path. In this case,
you will earn 1.89 dollars on asset B. This amount is for sure since there is no uncertainty on this
asset. The upper part shows the projected earnings on asset A if you don’t change the allocation
between assets until the end of the path. They correspond to the dots shown in the video. There
is a 20% chance that the final amount lands in the white area above the gray one, a 60% chance
that it lands in the dark blue area and another 20% chance that it lands above the dark blue area.
Finally, there is a thick line showing the median, in this example, 16 dollars and 64 cents. This
means that with a 50% chance your final amount will be somewhere below that number and with
a 50% chance it will be somewhere above that number.
Notice also from our demonstration that probabilities are different within a segment. For
example, receiving an amount above the dark blue area has a 20% chance, but within this 20%
it is more likely to be close to the dark blue area than further away. In other words, it is more
likely to get this payoff [point to the slide] than this payoff [point to the slide], although both are
86
possible. You can see this point more clearly on the frequency table. Based on the number of
circles, it is more likely that your payoff will end up here [point to the slide] rather than [point to
the slide] here, even though both of these areas correspond to the 20% region above the projection
bar.
Important Points:
1. The projection bar shows the likelihood of different final earnings at the end of the path
ASSUMING the amount you receive from each asset is reinvested in the same asset in all
the following periods. However, you can change the allocation between assets at every
period.
2. At each period, the projection bar recalculates the probabilities. If you move the cursor up
and down within a period, the bar shows instantly the new projection.
3. The multipliers on asset A are independent across periods. In other words, the multipliers
of previous periods will in no way impact the multiplier in the current period. For example,
if the multiplier in a previous period was very high, it does not mean it will be high again.
The new multiplier will simply follow the rules of uncertainty described before.
4. All the participants start and end the paths at the same time. The clock starts as soon as the
screen appears, so pay attention.
5. The multiplier for asset A in each period is the same for all participants. So, for example if
the computer chooses 2 as a multiplier in period 4, it means that all participants will have
their investment in asset A doubled.
Are there any questions? If not, let us proceed to 5 practice paths. What you earn on these
paths will not count towards your payment; these are meant only for you to familiarize yourself
with the entire process of allocating money between assets A and B. Feel free to explore as many
investment strategies as possible to better understand the different options.
Please double click on the icon on your desktop that says ABC STUDY. When the computer
prompts you for your name, type a 4 digit number that you can easily remember. Please do not
forget the number you typed. Then click SUBMIT and wait for further instructions.
87
Pay attention to the screen. The first practice path will be starting soon. Focus on understand-
ing how to choose the display between percentage and dollars, how to activate the bar, and how
to change the allocation between assets. Reminder: Once a path ends, you need to click the OK
button in order to proceed to the next path.
[START game] [Complete practice path 1]
You have now completed practice path 1. Are there any questions? Let’s proceed to practice
paths 2 and 3. Now try to explore different investment strategies to get a good understanding of
the investment process.
[Complete practice paths 2 and 3]
You have now completed 3 practice paths. Are there any questions? If not, we will proceed to
a short quiz. Please pay close attention to answering the questions, as you will not be permitted
to continue with the experiment if you do not answer the questions correctly. Raise your hand if
you have any question during the quiz.
[Complete quiz]
You have now completed the quiz. Let us proceed to the last 2 practice paths.
[Complete practice path 4 and 5]
You have now completed practice paths 4 and 5. Are there any questions? Before we start
please write down your ID on your record sheet in front of you. You will locate your ID on the
left side of your window bar. You will have to present the record sheet to get paid at the end of
the experiment. Did everyone right their IDs down?
Let me remind you how you will be paid for Part 1. At the end of the experiment, the
computer will randomly select one of the 15 paths and you’ll be paid the final amount you
earned in that path. Are there any questions? If there are any problems or questions from this
point on, raise your hand and an experimenter will come and assist you. We are ready to start
the experiment. Please pull out your dividers.
QUIZ (accompanied by a display print-out):
1. Look at the display on the paper in front of you. What is the current period?
(a) 1
(b) 2
88
(c) 6 (correct)
(d) 8
2. Had the person not chosen any allocation between assets A and B, how much would she
have in the next period?
(a) $1.44
(b) $4.16
(c) $5.60 (correct)
(d) $7.29
3. In this period, how much has the person invested in Asset A?
(a) $5.60
(b) $4.16 (correct)
(c) $1.44
(d) $0.81
4. Assume this person keeps reinvesting the returns of asset A in A and the returns of asset
B in B until the end of the path. Given the current allocation, how much money will this
person have in asset B after the path ends?
(a) $1.67 (correct)
(b) $1.44
(c) $1.03
(d) $7.29
5. Assume this person keeps reinvesting the returns of asset A on A and the returns of asset
B on B until the end of the path. Given the current allocation, how much money will this
person have in asset A after the path ends?
(a) $7.29
89
(b) $5.60
(c) $18.00
(d) Cannot be determined with certainty (correct)
6. Forget about the display. Imagine you invest $1 in Asset A and $1 in Asset B and suppose
the multiplier on Assets A and B are 2.00 and 1.03 respectively. How much money will you
have in the next period?
(a) $3.03 (correct)
(b) $4.00
(c) $5.03
(d) Cannot be determined from the information given.
90
Chapter B
Appendix B
We perform the same analysis as in section 1.6.2 except that we divide the sample into early
periods (first 5 of each path) and late periods (last 5 of each path). Notice that wealth is likely
to be lower in the early periods. We first confirm that intuition: wealth is on average $6.7 in the
last five periods compared to $3.9 in the first 5 periods for the 81 subjects inM
HARA
. With this
potential source of differences in mind, we present in Tables B.1 and B.2 the analogue information
of Tables 1.6 and 1.7 for the new subdivision of samples.
1
Type consistency by periods Frequency
Consistent Full - Early - Late 39
Consistent Full - Early 9
Consistent Full - Late 25
Inconsistent 8
Total 81
Table B.1: Consistency in classification - early periods vs. late periods
Full sample Early periods Late periods
DARA-DRRA 11 11 8
DARA-CRRA 13 27 20
DARA-IRRA 44 31 37
IARA-IRRA 1 1 1
CARA-IRRA 12 10 14
Not classified 0 1 1
Table B.2: Type frequency - early periods vs. late periods
As before most subjects are consistent between the full sample and at least one subsample,
though the number of inconsistent subjects is slightly higher than for the early/late paths division
1
The type “Not classified" in Table B.2 corresponds to individuals for which both the a and b coefficients in equation
(1.5) are zero.
91
(8 vs. 3). Risk attitudes are also similar between samples, with a large representation of DARA-
IRRA and an absence of IARA-IRRA. Also as before (and with the same caveat) there is an
increase in CRRA subjects at the expense of IRRA subjects.
We also conduct a similar out-of-sample prediction analysis as in section 1.6.1, except that we
estimate parameters on the first 5 periods of all paths and predict choices in the last 5 periods of
all paths. This is different than before not only in that the sample division is based on periods
rather than paths, but also in that we do not take subsamples randomly. The purpose is to
test whether extrapolating choices based on risk attitudes elicited in trials with low wealth is
meaningful to explain decisions in trials with high wealth.
We get that all but one subject have a ratio
MAE
HARA
MAE
RND
smaller than 1 and, as before, more
than two-thirds of subjects have a ratio smaller than 0.5 indicating, again not surprisingly, a large
improvement of HARA over random choice. We then present in Figure B.1 the analogue of Figure
1.4 to the new sample division, that is, the the ratio
MAE
HARA
MAE
CRRA
sorted by subjects from smallest to
largest.
Figure B.1: Out-of-Sample Fit - HARA vs. CRRA in early vs. late periods
The results are remarkably similar to those obtained in section 1.6.1. One-third of subjects
exhibit a considerable improvement of HARA over CRRA whereas the other two-thirds are sim-
ilar. The most notable difference is the existence of a few subjects (6) for which CRRA performs
92
better than HARA. Overall, the results confirm those in section 1.6: the estimated types are con-
sistent across subsamples (even when we use “low" wealth estimates to predict “high" wealth
choices) and a general utility function helps in the estimation for one-third of the individuals.
93

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Asset Metadata

Creator Giga, Aleksandar (author)

Core Title Essays in behavioral and entrepreneurial finance

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Economics

Publication Date 07/29/2016

Defense Date 05/10/2016

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag CRRA,equity crowdfunding,HARA,laboratory experiment,OAI-PMH Harvest,portfolio allocation,relative performance,risk aversion,skewed asset,startup financing

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Zapatero, Fernando (committee chair), Brocas, Isabelle (committee member), Carrillo, Juan D. (committee member), Korteweg, Arthur (committee member)

Creator Email aleks.giga@gmail.com,aleksang@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-285831

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