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Responding to Risk and Uncertainty

Empirical Essays on Corporate Investment, Liquidity and Hedging Decisions

ISBN 978-91-7731-076-1 Doctoral Dissertation

in Economics Stockholm School of Economics Sweden, 2018

Responding to Risk and UncertaintyThomas Seiler 2018

Thomas Seiler

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Responding to Risk and Uncertainty

Empirical Essays on Corporate Investment, Liquidity and Hedging Decisions

ISBN 978-91-7731-076-1 Doctoral Dissertation

in Economics Stockholm School of Economics Sweden, 2018

Responding to Risk and UncertaintyThomas Seiler 2018

Thomas Seiler

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Responding to Risk and Uncertainty

Empirical Essays on Corporate Investment, Liquidity and Hedging Decisions

Thomas Seiler

Akademisk avhandling

som för avläggande av ekonomie doktorsexamen vid Handelshögskolan i Stockholm

framläggs för offentlig granskning torsdagen den 31 maj 2018, kl 13.15,

sal 120, Handelshögskolan, Sveavägen 65, Stockholm

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Responding to Risk and Uncertainty:

Empirical Essays on Corporate Investment,

Liquidity and Hedging Decisions

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Responding to Risk and Uncertainty:

Empirical Essays on Corporate Investment, Liquidity and hedging

decisions

Thomas Seiler

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Dissertation for the Degree of Doctor of Philosophy, Ph.D., in Economics

Stockholm School of Economics, 2018

Responding to risk and uncertainty: empirical essays on corporate investment, liquidity and hedging decisions

SSE and Thomas Seiler, 2018c ISBN 978-91-7731-076-1(printed) ISBN 978-91-7731-077-8(pdf)

This book was typeset by the author using LATEX.

Front cover:

Sunspire / Shutterstock.comc Printed by:

BrandFactory, Gothenburg, 2018 Keywords:

Policy Uncertainty; Ambiguity; Risk; Knightian Uncertainty; Investment;

R&D; Financial Constraints; Cash holdings; Hedging; Entrepreneurship;

Textual Analysis

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Foreword

This volume is the result of a research project carried out at the Department of Economics at the Stockholm School of Economics(SSE).

This volume is submitted as a doctoral thesis at SSE. In keeping with the policies of SSE, the author has been entirely free to conduct and present his research in the manner of his choosing as an expression of his own ideas.

SSE is grateful for the financial support provided by the Jan Wallander and Tom Hedelius Foundation which has made it possible to carry out the project.

G¨oran Lindqvist Richard Friberg

Director of Research Professor and Head of the Stockholm School of Economics Department of Economics

Stockholm School of Economics

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Acknowledgements

I thank my supervisor, Richard Friberg, for his continuous guidance and sup- port. Richard always had an open door for me, listened to my ideas, and pro- vided constructive and careful feedback to my drafts. From Richard, I learned how to transform a research idea into a working paper and, finally, into a pub- lication. His advice was invaluable for me throughout my Ph.D.

I am also very grateful to Lars Persson, with whom I co-authored a pa- per in this dissertation. Lars taught me how simple mathematical models can shed light on important issues which are otherwise easily overlooked. In my discussions with Lars, I have learned a lot about what it means to be a good researcher.

I also thank J¨orgen Weibull, whose courses in mathematics and game the- ory have been eye-openers to me. I am grateful to Mark Voorneveld who taught me how to think like a mathematician. I am indebted to Alexander Ljungqvist whose steady feedback has substantially improved my paper on pol- icy uncertainty.

Many more people deserve to be mentioned for having accompanied me as colleagues, friends or advisors on at least part of my Ph.D. journey: Mag- nus and Malin Ahl, Alberto Allegrucci, Adam Altmejd, Niklas Amberg, Juan Carlos and Anna Andresen Peter with Mauricio and Rodrigo, Roman Bo- bilev, Evelina Bonnier, Julian Boulanger, Andrea Camilli, Serena Cocciolo, Paul Elger, Albin Erlansson, Clara Fernstr¨om, Eleonora Freddi, Jos´e-El´ıas Gal- legos Dago, Marta Giagheddu, Selene Ghisolfi, My Hedlin, Emma Heiken- sten, Markus Ibert, Siri Isaksson, Mathias Ivanovsky, Aljoscha Jannsen, Thomas Jansson, Camilla Elwing Johansson, Alla Khalitova, Matilda Kilstr¨om, Ritva Kiviharju, Nadiia Lazhevska, Benjamin Mandl, Svante Midander, Matti Mit- runen, Elin Molin, Jonna Olsson, Andreas P¨ahler, Andrea Papetti, Elle Parslow, Claudia Robles Garcia, Yingjie Qi, Fredrik Runel¨ov, Rustem Sadykov, Mark Sanctuary, Rickard Sandberg, Christofer Schr¨oder, Sreyashi Sen, J´osef Sigurds-

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vi RESPONDING TO RISK AND UNCERTAINTY

son, Stefan Schubert, Melinda S¨uveg, Yue Tang, Domenico Viganola, Max Viskanic, Simon Wehrm¨uller, and Abalfazl Zareei.

I wish to thank the Jan Wallander and Tom Hedelius Foundation and the Ann-Margret och Bengt Fabian Svartz Stiftelse. Without their financial sup- port, I would not have been able to pursue my passion for research.

Last but not least, I want to thank my partner Susanne Burri, my family, and friends back home for their unwavering support throughout my Ph.D.

Stockholm, March 21, 2018 Thomas Seiler

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Contents

1 Policy Uncertainty and Investment 11

1.1 Introduction . . . 12

1.2 Data . . . 16

1.2.1 Overview . . . 16

1.2.2 Firm-level economic policy uncertainty . . . 18

1.3 Policy uncertainty and corporate investments . . . 24

1.3.1 Empirical approach . . . 24

1.3.2 The average effect of policy uncertainty on investment 26 1.3.3 Financial frictions and the uncertainty-investment re- lation . . . 28

1.4 Validation, robustness and sensitivity tests . . . 33

1.4.1 Informativeness of disclosure data . . . 34

1.4.2 Robustness to alternative explanations . . . 37

1.4.3 Results using constant index weights . . . 40

1.4.4 Sensitivity to financial constraints and investment mea- sures . . . 42

1.5 Conclusions . . . 46

Appendix 49 1.A Variable definitions . . . 49

1.B Data extraction and matching algorithm . . . 50

1.C Measures for aggregate policy uncertainty . . . 52

1.D Search expressions for exposure measures . . . 53

1.E Additional figures and tables . . . 55

Bibliography 62

vii

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viii RESPONDING TO RISK AND UNCERTAINTY

2 Risk and ambiguity in 10-Ks 67

2.1 Introduction . . . 68

2.2 Related literature . . . 70

2.3 Development of hypotheses . . . 74

2.4 Data and empirical strategy . . . 77

2.4.1 Data sources . . . 77

2.4.2 Measures of risk and ambiguity . . . 78

2.5 Ambiguity and risk: description and validation . . . 80

2.5.1 Summary statistics and cross-secional patterns . . . 81

2.5.2 Relation to credit ratings . . . 85

2.5.3 Financial constraints . . . 87

2.6 Ambiguity and risk: cash holding and derivatives . . . 89

2.6.1 Empirical strategy . . . 89

2.6.2 Cash holding . . . 91

2.6.3 Derivatives use . . . 97

2.6.4 Reverse causality? . . . 101

2.7 Conclusions . . . 103

Appendix 105 2.A A presentation of the model in greater detail . . . 105

2.A.1 A discussion of robustness . . . 106

2.A.2 Adding risk to the model . . . 108

2.B Additional data details . . . 108

2.C Additional validation: relation to market beta . . . 110

2.D Details on Form 10-K Data. . . 112

2.E Index definition details . . . 115

Bibliography 118 3 Optimism under uncertainty 125 3.1 Introduction . . . 126

3.2 Empirical motivation . . . 129

3.2.1 Data . . . 129

3.2.2 Measuring risk, uncertainty and optimism . . . 131

3.2.3 Empirical results . . . 132

3.3 Base model . . . 136

3.3.1 Entry pattern and optimism . . . 138

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CONTENTS ix 3.3.2 How optimistic entrepreneurship may increase welfare 144 3.4 How optimistic entrepreneurs compete in the product market 147

3.4.1 How some but not too much optimism improves prof- its and welfare . . . 151 3.5 Conclusions . . . 155

Appendix 157

Bibliography 161

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Introduction

Uncertainty is a pervasive aspect of modern economic life. While this insight has a long tradition in economic thinking that goes back to at least John May- nard Keynes and Frank Hyneman Knight, the motivation for writing this the- sis was primarily a personal one. Shortly after the height of the financial crisis of 2008, I graduated from university and started to work in the strategy unit of a large financial institution. At the time, what had started as a financial crisis in the US had already morphed into an economic crisis in much of the world and was about to transform into a political crisis in Europe.

The political crisis in Europe erupted because public debt in some Euro- pean markets started to be perceived as untenable. This perception introduced a non-negligible risk of the Eurozone falling apart should the necessary po- litical adjustments to stabilise the monetary union not be made in time. A break-up of the Eurozone would have had substantial economic and political consequences, most of which were difficult to foresee and almost impossible to quantify. Situations like this raise a host of questions: how should compa- nies in such settings make their investment decisions, adapt their liquidity and hedging policies, and how should they think about entering new markets? It is this type of questions that I address in my dissertation.

The dissertation consists of three chapters, all covering different aspects of decision-making under uncertainty. Each chapter starts with an individual abstract and introduction. Readers that are pressed for time might find it easiest to learn about the content of the individual chapters by directly consulting these abstracts(see pages 11, 67, and 125). The current introduction includes a broader, more personal take on what I think is the main contribution of each chapter and why I believe the underlying research question is well worth addressing.

In the first chapter, I investigate how economic policy uncertainty affects the firm’s investment decision. Economic policy uncertainty refers to uncer-

1

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2 RESPONDING TO RISK AND UNCERTAINTY

tainty about when and how policies may change and how the changes may impact the business environment. Policy uncertainty was put forward as a po- tential explanation for the sluggish economic recovery after the crisis of 2007.

The sluggish recovery in the US was particularly puzzling, because the fundamentals for renewed economic growth were in place by 2010. Around that time, I discovered the working paper version of Baker et al.(2016). A key contribution of this paper is to provide aggregate measures of economic policy uncertainty based on the analysis of newspaper articles for a large number of advanced markets. A striking aspect of this new data was that historically, policy uncertainty and measures of economic activity were strongly negatively correlated. In particular, policy uncertainty increased substantially in 2008 and remained high thereafter. From this, many observers concluded that policy uncertainty wascausing lower investment rates.

To establish whether economic policy uncertainty indeed depresses eco- nomic activity, it is key to control for aggregate or industry-specific shocks.

Such shocks are likely to both increase policy uncertainty and to simultane- ously decrease investment rates. The intuition is simple: once something bad happens, politicians will begin to act. They will thereby create policy uncer- tainty when investment rates are already depressed anyway. To identify the effect of uncertainty on investment, we need to control for the initial negative shock that drives both variables. This is difficult to achieve with just aggregate data, but could be done quite easily with firm-level data through the inclusion of time fixed effects in the typical investment regressions.

A key contribution of my first chapter is to suggest a novel approach to measure variation in policy uncertainty at the firm-level. I suggest to combine information from the textual analysis of mandatory corporate risk disclosure with the aggregate measures of policy uncertainty across different policy classes from Baker et al.(2016) to construct a firm-level measure of policy uncertainty.

My approach relies on two key ideas. First, individual firms might be ex- posed to a different degree to different policy classes. For example, a firm in the defense industry might be exposed to fiscal policy uncertainty, but less so to uncertainty related to healthcare regulation. I measure how important an individual policy class is to a firm by text-mining the firm’s mandatory risk dis- closure section in its annual report. Second, uncertainty about different policy classes evolves differentially over time. We might be uncertain to a different de- gree about where monetary policy is heading than we are uncertain about the

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INTRODUCTION 3 future path of healthcare regulation. For the US, aggregate measures of policy uncertainty across a number of policy classes are available from Baker et al.

(2016).

In combination, the variation in exposure to policy classes and the vari- ation in the degree of uncertainty across policy classes leads to variation in policy uncertainty at the firm-level. Equipped with this type of data, I am able to better address the endogeneity problems inherent in estimating the effect of policy uncertainty on investment than has been possible in the previous liter- ature.

I find that a doubling of economic policy uncertainty significantly reduces capital expenditure, but R&D — an other main form of investment – does not respond to policy uncertainty when controlling for industry-specific shocks.

One explanation might be that firms have little reason to delay R&D projects when policy uncertainty idiosyncratically increases because this makes them lose the race for new discoveries against their competitors. However, the re- sults on R&D are shakier than the capital expenditure results, because includ- ing industry-specific time-shocks in the regressions absorbs most of the varia- tion in the R&D measures which are centered in a small number of industries.

Having established a negative relation between policy uncertainty and cap- ital expenditure, I explore the channels that might drive this relation. Most of the previous empirical literature has identified the “wait-and-see” channel as an important driver of the investment-uncertainty relation. The Firms delay their investment projects when uncertainty increases so they canwait and see what happens. I instead investigate the role of financial frictions in amplifying the effect of policy uncertainty on investment.

In theory, financial frictions can amplify the effect of uncertainty on invest- ment by increasing the default probability of exposed firms. This is because fi- nancial frictions render firms financially constrained. When constrained firms are exposed to higher uncertainty, they become more likely to default, which will lead them to reduce their investment by more than financially uncon- strained firms in the same situation. While this channel is theoretically well- established, empirical evidence on its importance is still scarce.

Empirically, I find the sensitivity of capital expenditure to policy uncer- tainty is significantly amplified for firms that are likely to be financially con- strained ex-ante. To the extent that R&D expenditure responds to policy un- certainty at all, the effect seems to operate primarily through a financial fric-

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4 RESPONDING TO RISK AND UNCERTAINTY

tions channel. To understand the magnitude of the relation between invest- ment and policy uncertainty, it is thus important to take into account the in- teraction between uncertainty and financial markets.

The finding that financial frictions are important to an understanding of the magnitude of the investment-uncertainty relation suggests that reducing financial frictions might be a viable path to reduce the negative effects of policy uncertainty on investment. This insight contrasts with the mostly implicit policy recommendation in the literature to date. If policy uncertainty affects investment primarily by inducing firms to wait and see with investments until uncertainty recedes, then it might make sense to reduce policy uncertainty as much as possible. For example, it might be better to implement a bad policy quickly so as to create certainty, rather than to suffer through the prolonged period of uncertainty it can take to come up with a good policy. By contrast, my findings suggest that politicians might be able to take their time to work out sound policies if, in the meantime, financial frictions can be reduced.

The second chapter in this thesis is co-authored with Richard Friberg and investigates the flipside of the investment-uncertainty relation, namely the de- cision to build precautionary savings and to use hedging to protect one’s invest- ments. In particular, we are interested to what extent the distinction between risk and ambiguity matters for corporate liquidity and hedging decisions. Fol- lowing Knight(1921), decision problems with known probabilities (risk) are sometimes distinguished from those where no objective probability distribu- tion exists(ambiguity). In the standard models of decision-making under un- certainty used in economics and finance, agents maximize their expected utility irrespective of whether objective probabilities are available(Morgenstern and Von Neumann, 1944) or not (Savage, 1954). The distinction between risk and ambiguity is thus mute.

But this standard modelling approach has been criticized on behavioral and conceptual grounds alike. From a behavioral perspective, Ellsberg(1961) proposed two ingenious experiments that subsequently habe been extensively tested in the laboratory.1 The experimental results suggest that, contrary to the

1Ellsberg intended to criticise expected utility theory on normative grounds. His thought experiments are designed to persuade us that a rational person would sometimes not want to choose in a way that is consistent with expected utility theory. However, the experiments later became an important building block of descriptive criticisms of expected utility theory.

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INTRODUCTION 5 standard model, subjects maintain different attitudes towards risk and ambigu- ity(Camerer and Weber (1992) for an early overview; also Camerer (1998)).2 From aconceptual perspective, Schmeidler(1989) argues that it should be pos- sible to distinguish the amount and quality of information that leads to certain beliefs being formed. Modelling beliefs as probability distributions over out- comes does not allow us to formally express such notions.3

Unease with treating subjective and objective probabilities equivalently in a decision problem has led to a surge in theoretical models of ambiguity(see Schmeidler (1989), Gilboa and Schmeidler (1989), Bewley (2002), Klibanoff et al.(2005), Chateauneuf et al. (2007)). A string of recent papers investigate models of ambiguity averse decision makers and test predictions mainly in the lab(see Etner et al. (2012) for a survey of the literature). A handful of articles have used models of ambiguity averse agents to examine asset price determi- nation and investment behavior (see for instance Epstein and Wang (1994);

Nishimura and Ozaki(2007); Miao and Wang (2011)). The abundance of rig- orous theoretical and experimental work on the topic stands in contrast to the lack of empirical field work.

The main goal of the second chapter is to investigate whether the distinc- tion between risk and ambiguity helps to understand real world corporate de- cision making. We find that cash holdings are higher for firms ranking higher on our ambiguity index, while hedging is more prevalent among firms ranking high on our risk index. Interestingly, the correlations we identify in our data between risk, ambiguity, cash holding and hedging are in line with straight- forward extensions of standard models of liquidity management. We take this as evidence that the distinction between risk and ambiguity is not just an in-

2There is also some evidence using field data that is at least consistent with wide-spread am- biguity aversion. See Barseghyan et al.(2013) for a recent contribution and a good overview of the available evidence.

3Imagine you can bet on one of two coins coming up heads. The first one you have extensively tested, thrown it thousands of times, so that you know it is a fair coin. The second coin looks like the first coin, but you have never thrown it before. You might be willing to assume it has a 50% probability of coming up heads too. However, your belief over the second coin is based on considerably less information than the belief over the first coin. This difference is not reflected in your probabilistic assessment, but potentially important if you need to bet on one of the coins coming up heads.

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6 RESPONDING TO RISK AND UNCERTAINTY

teresting distinction to understand individual decision making in the lab, but might also be important to understand actual firm-level decisions.

The third chapter in this thesis looks at the problem of firm formation and is intended to speak primarily to the literature on entrepreneurship. It is based on joint work with Lars Persson. A key puzzle in the entrepreneurship literature is why people become entrepreneurs in the first place. The return distribution of such a career choice is not attractive: while some entrepreneurs do exceptionally well, most do not. Despite this, entrepreneurship is a wide- spread phenomenon.

Different explanations for this observation are conceivable. Entrepreneur- ship might be involuntary, because no other career options are open. Alterna- tively, entrepreneurs might be more risk-loving than other parts of the popula- tion. Or they might hold skewed beliefs about their own abilities, the abilities of others, or their chances of success more broadly. Potentially, they might also just have an inherent taste for being an entrepreneur. In this chapter, we suggest an explanation for why people become entrepreneurs that is related to the distinction between risk and ambiguity introduced in the previous chapter.

Our key assumption is that becoming an entrepreneur is primarily a deci- sion under ambiguity and not under risk. To illustrate this we use automatic text-analysis on specific sections of US annual reports and show that young companies describe the risks they face in ambiguous rather than risky terms.

The older they get, however, the less likely they are to use ambiguous terms to describe their risk environment. Similarly, younger firms use a more positive tone in their forward-looking statements than older firms. In combination, these findings suggest that young firms face ambiguity, rather than risk, and that the management of younger firms tends to look at the upside within this ambiguity rather than at the downside.

In the first part of the paper, we introduce a simple model of entrepreneurial entry with ambiguity-sensitive agents to check whether it has the potential to reproduce the empirical facts just described. Indeed, we find that under ambi- guity, optimistic entrepreneurs enter markets where expected profit maximiz- ers would not enter, providing a rationale for our empirical findings.

In the second part of the paper, we proceed to investigate how ambiguity sensitive agents perform in product market competition. We show that op- timism under ambiguity helps entrepreneurs to act more boldly and achieve higher profits in product market competition. Sometimes it is even the case

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INTRODUCTION 7 that only optimistic, but not too optimistic, entrepreneurs can profitably en- ter a market. This leads to positive effects on the consumer rent, and because entry is profitable, to society as a whole.

The key point that this paper adds to the entrepreneurship literature is that behavioral mistakes might be individually and socially beneficial because be- havioral biases can act as a commitment device in strategic interactions. Opti- mism in the face of ambiguity helps entrepreneurs to commit to a more aggres- sive strategy in competition. This pushes up overall supply and reduces prices, which benefits consumers. At the same time, an entrepreneur that is more optimistic in the face of ambiguity achieves a higher market share than less op- timistic entrepreneurs. If this optimism is not too excessive, the entrepreneur will actually be able to achieve a higher profit than otherwise possible. Overall, with some, but not too much optimism, it is possible that an outcome obtains where the consumer as well as the entrepreneur profit and welfare in the econ- omy goes up, even though the entrepreneur commits a mistake from the point of view of standard expected utility theory.

The different chapters in this dissertation all investigate different research questions. But there are nevertheless a number of unifying elements between them. Here, I will briefly mention two of them.

First, all three chapters touch upon how economic agents tend to respond to the risks and uncertainties that they face. Yet the different chapters touch upon this issue in conceptually opposed ways. In chapters one and two, I start from a theoretically motivated research question to then study empirically how a changing risk environment affects the investment, liquidity, and hedging de- cisions of firms. The empirical findings in these chapters can help theorists to effectively navigate the vast model space they face. In chapter three, this pro- cess is turned on its head. Starting from an empirical observation of how the types of risks faced by young and old firms differ, a theory of entrepreneurial decision-making is developed. This theory can help empiricists to better un- derstand some of the difficulties that they face when they want to answer ques- tions such as who becomes an entrepreneur, or what makes entrepreneurs suc- cessful. I believe that having a good understanding of what might matter in a decision situation from a theoretical point of view is a pre-requisite for good empirical work. At the same time, having a good grasp of the empirical facts is a necessary condition for solid and relevant theoretical work.

The second unifying element across all chapters is a methodological one.

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8 RESPONDING TO RISK AND UNCERTAINTY

All chapters rely on the application of automatic textual analysis methods to quantify large amounts of qualitative information in public firm disclosure.

Over the past decade a vast amount of data has become available via online repositories. With the right tool set, this allows us to answer novel empirical questions, and it allows us to revisit old questions from a new angle. All of this, I believe, offers great opportunities for future research. We are just at the beginning of this development.

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Bibliography

Scott R. Baker, Nicholas Bloom, and Steven J. Davis. Measuring economic policy uncertainty. The Quarterly Journal of Economics, 131(4):1593–1636, 2016.

Levon Barseghyan, Francesca Molinari, Ted O’Donoghue, and Joshua C. Teit- elbaum. The nature of risk preferences: Evidence from insurance choices.

American Economic Review, 103(6):2499–2529, 2013.

T. F. Bewley. Knightian decision theory: Part I. Decisions in Economics and Finance, 25(2):79–110, 2002.

Colin Camerer. Bounded rationality in individual decision making. Experi- mental Economics, 1(2):163–183, 1998.

Colin Camerer and Martin Weber. Recent developments in modeling prefer- ences: Uncertainty and ambiguity. Journal of Risk and Uncertainty, 5(4):

325–370, October 1992.

Alain Chateauneuf, J¨urgen Eichberger, and Simon Grant. Choice under un- certainty with the best and worst in mind: Neo-additive capacities. Journal of Economic Theory, 137(1):538–567, 2007.

Daniel Ellsberg. Risk, ambiguity, and the Savage axioms.The Quarterly Journal of Economics, 75(4):643–669, 1961.

Larry G. Epstein and Tan Wang. Intertemporal asset pricing under Knightian uncertainty. Econometrica, 62(2):283–322, 1994.

Johanna Etner, Meglena Jeleva, and Jean-Marc Tallon. Decision theory under ambiguity. Journal of Economic Surveys, 26(2):234–270, 2012.

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10 RESPONDING TO RISK AND UNCERTAINTY

Itzhak Gilboa and David Schmeidler. Maxmin expected utility with non- unique prior. Journal of Mathematical Economics, 18(2):141–153, 1989.

Peter Klibanoff, Massimo Marinacci, and Sujoy Mukerji. A smooth model of decision making under ambiguity. Econometrica, 73(6):1849–1892, 2005.

Frank H. Knight. Risk, uncertainty and profit. New York: Hart, Schaffner and Marx, 1921.

Jianjun Miao and Neng Wang. Risk, uncertainty, and option exercise. Journal of Economic Dynamics and Control, 35(4):442–461, 2011.

Oskar Morgenstern and John Von Neumann. Theory of Games and Economic Behavior. Princeton University Press, 3rd edition, 1944.

Kiyohiko G. Nishimura and Hiroyuki Ozaki. Irreversible investment and Knightian uncertainty. Journal of Economic Theory, 136(1):668–694, 2007.

Leonard J. Savage. The Foundations of Statistics. Dover Publications, 2nd edi- tion, 1954.

David Schmeidler. Subjective probability and expected utility without additiv- ity. Econometrica, 57(3):571–587, 1989.

References

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