Essays on Decision Making over Time : Correlation
Neglect and the Labor Market Discrimination of Parents
Thèse
Ibrahima Sarr
Doctorat en économique
Philosophiæ doctor (Ph. D.)
Essays on Decision Making over Time: Correlation
Neglect and the Labor Market Discrimination of
Parents
ThèseIbrahima Sarr
Sous la direction de:
Charles Bellemare, directeur de recherche Sabine Erika Kröger, codirectrice de recherche
Résumé
Cette thèse, structurée en trois essais, se propose tout d’abord d’étudier de façon expérimentale et empirique les règles de décision utilisées dans le processus de décision avec une emphase sur l’inattention à la corrélation et ses conséquences sur les décisions prises, d’autre part la discrimination à l’embauche liée à la parentalité.
Un comportement prospectif rationnel fait nécessairement appel à une résolution de problèmes complexes impliquant le calcul des évaluations futures maximales attendues entre des options de choix (calculs Emax). Dans le premier essai, nous avons mené une expérience pour me-surer la proportion de participants capables d’effectuer ces calculs complexes ainsi que celle utilisant deux règles de calcul alternatives (sous-optimales) qui ignorent la corrélation entre les évaluations futures. La première règle alternative capte les participants qui effectuent des calculs Emax en ignorant la corrélation entre les éléments non observables dans l’ensemble d’informations. La seconde règle alternative est celle utilisée par les sujets calculant le maxi-mum des évaluations futures attendues (calculs maxE), similaires au modèle option-valeur de Stock and Wise (1990). Notre conception expérimentale exploite différentes structures de corrélation entre les évaluations futures pour séparer la part des sujets utilisant chaque règle. L’expérience a été menée sur un échantillon important et hétérogène de sujets, ce qui a permis de relier la propension à utiliser une règle donnée à un ensemble de caractéristiques socio-économiques. Nos résultats suggèrent que 28% des sujets sont capables d’effectuer des calculs Emax en exploitant la structure de corrélation, 20% des sujets effectuent des calculs Emax en ignorant la corrélation, tandis que 52% des sujets effectuent maxE calculs. De plus, nous constatons que la propension à utiliser une règle donnée varie, de manière significative, selon les niveaux d’éducation - les sujets les plus instruits sont beaucoup plus susceptibles d’effectuer des calculs maxE.
Le deuxième essai constitue une extension du premier essai. L’arrivée d’un enfant dans une famille engendre plus d’incertitudes poussant ainsi stratégiquement certains agents à éviter ou retarder la venue d’un premier enfant. Cette incertitude supplémentaire apportée par l’arrivée d’un enfant crée des conflits entre la parentalité et l’emploi, en particulier chez les femmes, qui préfèrent souvent sécuriser leur emploi avant de se tourner vers la parentalité. Conséquemment, le report de la première naissance est plus que jamais perceptible dans les sociétés actuelles. Dans le deuxième essai de cette thèse, nous nous donnons comme objectif d’explorer la manière dont les incertitudes liées au travail et les risques accrus d’infertilité associés au retard de maternité interagissent dans la formulation des décisions en matière de parentalité (timing et nombre d’enfants). A cet effet, nous avons développé un modèle de cycle de vie des décisions en matière d’offre de travail et de choix de parentalité et nous avons cherché à quantifier les effets de l’incertitude sur le marché du travail ainsi que de l’inattention à la corrélation sur le report de la première maternité. Nos paramètres estimés (préférences, équations salariales, qualité des enfants) sont conformes à la littérature existante. De plus, nos résultats suggèrent que la réduction des incertitudes liées au marché du travail augmenterait le nombre d’enfants et diminuerait l’âge à la première naissance quel que soit le niveau d’instruction (primaire, secondaire, ou post-secondaire). Le biais comportemental de l’inattention à la corrélation contribuerait également voire plus au report de la parentalité. Le troisième et dernier essai présente des évidences empiriques de discrimination à l’embauche liée à la parentalité dans la province de Québec (Canada) par le biais d’envoi de CVs fictifs. Il examine également dans quelle mesure les congés parentaux et le dévouement au travail réduisent ou renforcent la discrimination à l’embauche. Environ 1300 candidatures ont été envoyées en réponse à des offres d’emploi en ligne pour cinq catégories d’emplois. Les résultats suggèrent que les hommes bénéficient d’un bonus lorsqu’ils sont parent tandis que les femmes subissent un malus (une pénalité). En effet, les pères ont un taux de rappels supérieur de 18 points de pourcentage à celui de leurs homologues masculins, tandis que le taux de rappels des mères est inférieur de 14 points à celui de leur correspondant femmes sans enfant. Nous avons noté que les mères subissent une discrimination même lorsqu’elles montrent leur dévouement au travail. De l’autre côté, le taux de rappels des hommes augmenterait lorsqu’ils signalent leur engagement au travail. La mobilité professionnelle ouvrirait, elle aussi, des perspectives d’emploi ou en d’autres termes les employeurs ont donc tendance à valoriser la mobilité des
Abstract
Via experimental and empirical methods, this thesis consisted of three essays studies, on the one hand, the decision rules used in life-cycle decision-making with an emphasis on the correlation neglect and its consequences, and on other hand, hiring discrimination in relation to parenthood.
Rational forward looking behavior requires solving complex problems involving computation of the expected maximum future valuations across choice alternatives (Emax computations). In Chapter 1, we conduct an experiment to measure the share of subjects able to perform these computations as well as the share of subjects using two alternative (sub-optimal) rules of com-putation which ignore correlation between future valuations. The first alternative rule captures subjects who perform Emax computations ignoring correlation between unobservables in the information set. The second alternative rule captures subjects computing the maximum of the expected future valuations (maxE computations), akin to the option-value model of Stock and Wise (1990). Our experimental design exploits different correlation structures between future valuations to separate the share of subjects using each rule. The experiment was conducted with a large and heterogenous sample of subjects, allowing to relate the propensity to use a given rule to a rich set of socio-economic characteristics. Our results suggest that 28% of subjects are able to perform Emax computations exploiting the correlation structure, 20% of subjects perform Emax computations ignoring correlation, while 52% of subjects perform maxE computations. Moreover, we find that the propensity to use a given rule significantly varies across education levels – higher educated subjects are significantly more likely to per-form maxE computations.
Chapter 2 studies how the labour uncertainties and increased fertility risks associated with delayed motherhood interact in shaping fertility decisions (timing and number of children).
Having a child comes with more uncertainties, and agents strategically avoid uncertainties and conflict between parenthood and employment, particularly among women, by securing their employment before turning to parenthood. Consequently parenthood is being experienced on average later in life than ever. We develop a life-cycle model of labor supply and fertility choices decisions and we quantify how labor market uncertainties as well as correlation ne-glect contribute to fertility delaying. Our parameters estimated (preferences, wage equations, quality of children) are in line with the existing literature. Moreover, our results suggest that a reduction in the labour uncertainties affect differently fertility decisions according to the education attainment. Indeed, the reduction in labour uncertainties increases number of children and decreases the age at first childbirth for lower educated couples, however, it de-creases the number of children and inde-creases age at first childbirth of highly educated couples. The behavioural bias of correlation neglect has a heightened effect on fertility decisions and contributes to parenthood postponement.
Finally, Chapter 3 presents experimental evidence about hiring discrimination in relation to parenthood in the province of Québec (Canada) via a correspondence testing. It also investigates to what extent parental leave as well as signalling work commitment reduce or reinforce hiring discrimination. Around 1300 applications were sent in response to online job openings for five categories of jobs. The results suggest that men benefit from a bonus when they experience parenthood while women undergo a penalty. Indeed, fathers have a callback rate 18 percentage points larger than their analogue childless men candidates while mother’s callback is 14 percentage points lower than the corresponding childless women’s callback. However, mothers have a higher callback rate than childless women for the job category patient attendant. Signalling job commitment does not eliminate motherhood penalty whereas substantially increases father’s callback rate. Our results suggest that taking parental leave does not affect mother’s callback rate and surprisingly increases father’s callback rate. Job mobility opens up job opportunities meaning employers tend to value the employee’s mobility.
Contents
Résumé iii Abstract vi Contents viii List of Tables x List of Figures xi Acknowledgments xiv Foreword xvi Introduction 1 Bibliography . . . 41 Life-cycle Decisions, Dynamic Programming, and Correlation Neglect: Experimental Analysis of Alternative Decision Rules 5 Résumé . . . 5 Abstract . . . 6 1.1 Introduction. . . 7 1.2 Experimental Design . . . 9 1.3 Econometric Model . . . 12 1.4 Results. . . 15 1.5 Conclusion . . . 20 Bibliography . . . 21
2 Labour Market Uncertainties and Correlation Neglect: Effects on Fer-tility Postponement 30 Résumé . . . 30
Abstract . . . 30
2.1 Introduction. . . 32
2.2 Key Patterns in the Data . . . 35
2.3 A Structural Analysis of Fertility Decisions: The benchmark model . 37 2.4 Estimation Results and Simulation . . . 44
2.5 Conclusion . . . 49
3 Parenthood, Parental Leave and Job Search Discrimination: Evidence
from a Field Experiment 59
Résumé . . . 59
Abstract . . . 59
3.1 Introduction. . . 61
3.2 Québec Parental Insurance Plan (QPIP) . . . 63
3.3 Theoretical Models . . . 64 3.4 Experimental Design . . . 66 3.5 Results . . . 69 3.6 Conclusion . . . 76 Bibliography . . . 78 Conclusion 88
List of Tables
1.1 Joint distributions for options B and C payoffs . . . 9
1.2 Experimental parameters for all 9 rounds of the main part of the experiment. Predicted behavior for Emax, Emax neglecting correlation, and MaxE compu-tations. Value of 0 represents choice of Option A, value of 1 represents not choosing Option A . . . 27
1.3 Risk-preference-revealing experiment . . . 27
1.4 Heterogeneity in rule and risk aversion preferences . . . 28
1.5 Estimated marginal effects on schooling outcomes. . . 29
2.1 Externally determined parameters . . . 55
2.2 Regression table . . . 55
2.3 Model-generated moments vs. empirical moments . . . 56
2.4 Estimated behavioural parameters . . . 57
2.5 Change in fertility and employment. . . 58
3.1 Parental leave plans . . . 83
3.2 Callback by gender and parental status . . . 83
3.3 Parents: effects of signalling commitment and engagement . . . 83
3.4 Parents: effects of career interruption. . . 84
3.5 Response time . . . 84
3.6 Determinants of female applicants’ callback rates . . . 85
3.7 Determinants of male applicants’ callback rates . . . 86
List of Figures
1.1 Screenshot of decision screen: choosing between option A (Exit) and B/C
(Con-tinue) . . . 23
1.2 Screenshot of decision screen: choosing between option B and option C when previously choosing Continue . . . 24
1.3 Risk-preference-revealing experiment . . . 25
1.4 Number of times of selecting option A according to risk aversion preferences . . 26
1.5 Model classification performances . . . 26
2.1 Evolution of age at first childbirth . . . 53
2.2 Distribution of number of children . . . 53
2.3 Employment rate by educational attainment and parental status . . . 54
2.4 Labour uncertainties by age at first birth and number of children . . . 54
3.1 Employment insurance maternity/parental benefit status of new mothers, Que-bec and rest of Canada. . . 80
3.2 Example of cover letter translated from French to English . . . 81
"Wouldn’t economics make a lot more sense if it were based on how people actually behave, instead of how they should behave?"
Dan Ariely, Predictably Irrational: The Hidden Forces That Shape Our Decisions
Acknowledgements
Undertaking this PhD has been a truly life-changing experience for me, and it would not have been possible to do without the help, support and guidance that I received from many people. First of all, I would like to offer my special thanks to my supervisors Prof. Charles Bellemare and Prof. Sabine Erika Kroger for the patient guidance, encouragement and advice they have provided throughout my time as their student. I have been extremely lucky to have supervisors who cared so much about my work, and who responded to my questions and queries so promptly. I would like to express my very great appreciation to my supervisors for their valuable and constructive suggestions during the development of this research work. Their willingness to give their time so generously has been very much appreciated. Without their guidance and constant feedback this PhD would not have been achievable. A very special gratitude goes out to all down at them for providing scholarship and travel financing with their research grants.
I would like to thank the committee members, Markus Herrmann, Marion Goussé, Bertrand Achou for their interest in my research. I am grateful to Lanny Zrill for acting as external reviewer. My special thanks are extended to the whole faculty and staff of Département d’Économique of Université Laval for their support during my doctoral studies.
Thank you to my classmates and friends Bago and Koffi Akakpo for their support throughout these years. I thank other fellow colleagues in the PhD program in economics, especially Marius, Steve, Antoine, Rolande, Morvan, Guy Morel, Jean-Louis Bago, Elysee Aristide, Mélissa Huguet, Thomas, Aly Yedan, and Blanchard for creating a positive atmosphere in the department. My heartfelt thanks to big brother and friend, Marius and my former classmate and associate Yaya Diallo.
During my PhD, I had the great privilege and opportunity to visit the Interdisciplinary Center for Economic Science (ICES) of the Georges Mason University chaired by Dr Daniel Houser. I would like to thank Prof. Daniel Houser for the invitation, the kind introduction to different people during the stay and thank the faculty and students of ICES for their incredible warmth and hospitality. I was truly honoured to have spent three months in ICES.
I express my sincere thanks to my dear friends Aminata Diagne that I had the great chance to meet in the research center Isra-Bame/Sénégal. Some special words of gratitude go to my friends who have always been a major source of support when things would get a bit discouraging: Blanchard, Lacina Diarra, Thierno Diop, Abdou Sambe, his wife Marie-André, and their children Khadija and Ismael. Thanks to Sidi Ndiaye, Serigne Mbaye Sarr, Mbagnick Ndiaye, Omar, Tidiane, Idrissa Diagne, Kandé Cissé, Khadim Sourang, Mambodj. A special thank to my dear friend Florence.
I would also like to say a heartfelt thanks to my deceased Mum and Dad for always believing in me and encouraging me to follow studies, for their great role in my life and their numerous sacrifices. A special thanks to my wife, Seynabou who has been extremely supportive of me throughout this process. Thanks to my brothers and sisters for helping in whatever way they could during this challenging period. A very special thank you to my brother Momodou who convinced me during our many discussions that I should pursue a doctoral degree and who made it possible for me by supporting, advising, and helping during the first steps. Thanks to Lamine, Ablaye, Coumba, Bana, Diatou, Sofie, Yande. Thanks for all your encouragement!
Foreword
This thesis is consisted of three chapters. Chapter 1 and Chapter 2 are coauthored with my supervisors, Charles Bellemare and Sabine Kroger.
Introduction
In a diverse context, agents make decisions affecting their current as well as their future wellbeing. For instance, having a child is a risky project and comes with more uncertainty in terms of future income, health, and utility. Indeed, having children is believed to be one of the explanations of women poor employment prospects as the costs of children for women’s careers and lifetime earnings are substantial (Adda et al.,2017). Past behaviours and current status could also limit, even prevent from better livelihood opportunities. For example, leaving work for parenting can be perceived as a move away from the ideal worker norms stating that ideal employees are always flexible and available to perform work (Sallee,2012). As a consequence, applicants with a past parental leave might be seen less committed and less engaged, and employers could tend to rely less on them.
Forward looking economic models implement this idea of making decisions affecting current as well as future wellbeing by assuming agents maximize the expected present value of utility in each period of the future. However, future utility often depends on the realized values of several variables (e.g., income, health, marital status, infertility risks, age) which are often correlated. As a result, evaluating future expected maximal utility will typically require that agents take into account the correlation structure between the relevant variables affecting their future well-being. Bellman et al. (1954) recognize that agents can make an optimal decision in this multi-period problem by solving a recursive sequence of two-period problems. This is known as the dynamic programming approach (henceforth Emax computations). The Emax computations approach is central to the empirical analysis of policy interventions on life-cycle decisions and has been used to analyze many life-cycle decisions including labor force par-ticipation (Eckstein and Wolpin, 1989), schooling (Keane and Wolpin, 1997), and retirement (Gustman and Steinmeier, 1986). Although theoretically optimal, the Emax computations
approach imposes that agents solve arbitrarily complex problems, in particular, evaluating future expected maximal utility. However, decision makers do not often consider the likeli-hoods of events which are correlated and mostly use some heuristics that lead to biases. The heuristic of correlation neglect occurs when individuals ignore correlation between relevant variables when making decisions (Kallir and Sonsino,2009).
Studies on the impact of correlation neglect on decision making in economics is limited, in particular in dynamic setting. Moreover, few empirical studies proposed reliable ways of disentangling alternative hypotheses or identifying causal effects of past behaviours by taking into account endogeneity problem and its implications for inference and proposing solutions to overcome them. There is a long tradition in economic science of collecting original data to test specific hypotheses. Over the last years, laboratory experiments and field experiments had been extensively used to provide innovative research designs in economics with combination of other methods including theoretical economics and structural microeconometrics. This thesis uses these innovative methods to study the effect of the behavioural bias of correlation neglect on a dynamic setting. It also focuses on the question of discrimination in relation to parenthood and explores a possible mechanism of the discrimination through behavioural bias.
In reality, the capacity of agents to perform the rational forward-looking behaviour-related complex calculations is limited, and agents consequently use simpler decision rules that might neglect correlation between relevant variables. In Chapter 1, I design and implement an innovative experiment that allow to measure the share of subjects able to perform Emax computations as well as the share of subjects using two alternative (sub-optimal) rules of computation which ignore correlation between future evaluations. The first simpler decision rule is given by the option value model (henceforth maxE computations) proposed by Stock and Wise(1990) that do not take into account the correlation between future outcomes of each variable. The second sub-optimal is similar to Emax computations rule, but agents neglect correlation between variables. Our experimental design exploits different correlation structures of future valuations to separate the share of subjects using each rule and the experiment was conducted with a large and heterogeneous sample of subjects. We combine this innovative experimental design and structural econometrics to estimate the probability of using each rule and to relate the propensity to use a given rule to a rich set of socio-economic characteristics.
This chapter shows how huge agents tend to ignore correlation between relevant variables when making decisions over time. It has been shown that the maxE computations and Emax computations rules can generate very different behaviour (Stern, 1997). Understanding the relevance of maxE computations and Emax computations rules in practice is essential to produce more accurate predictions of the effects of policy interventions.
Chapter 2 highlights how the behavioural bias of correlation neglect shapes individuals’ deci-sions in real life. To extend the first one, this chapter focuses on how correlation neglect can shape fertility decisions and whether it is as important as standard driving factors documented in the literature including labour market uncertainties. To do so, a dynamic structural model is built, estimated, and simulated to evaluate how couples’ labor supply and fertility (timing and number) respond to labor market uncertainties and increased infertility associated with postponement. Our results shed light on the importance of labor uncertainties and infertility risk associated with postponement on fertility decisions. This chapter shows how labor market insecurities, measured by income volatility, affect differently fertility decision according to the educational attainment. This chapter also provides evidence of the heightened importance of the correlation neglect on fertility postponement.
The focus of the third chapter is on the question of hiring discrimination in relation to par-enthood in the labour market of the province of Quebec. It also investigates to what extent parental leave, time elapsed since the parental leave as well as self-professed commitment or en-gagement to work reduce or reinforce hiring discrimination. It explores a mechanism through which discrimination can occur. The field experiment was designed and implemented, in which fictitious job applications were sent to real job vacancies to directly investigate whether mothers and fathers are subject to discrimination. Each job application consisted of a cover letter and résumé. The experiment took place between February and July 2018 in the two metropolitan areas of Quebec and Montreal, and targeted five types of jobs including re-ceptionist, secretary, accountant clerk, patient attendant and computer programmer. This chapter provides evidence of the discrimination of parents and shows how men benefit from parenthood with a bonus in terms of employment prospects and how women undergo a penalty when they become parents. This chapter also shows that the discrimination that mothers are facing might due to normative discrimination.
Bibliography
Adda, J., C. Dustmann, and K. Stevens (2017): “The career costs of children,” Journal of Political Economy, 125, 293–337.
Bellman, R. et al. (1954): “The theory of dynamic programming,” Bulletin of the American Math-ematical Society, 60, 503–515.
Eckstein, Z. and K. I. Wolpin (1989): “The specification and estimation of dynamic stochastic discrete choice models: A survey,” The Journal of Human Resources, 24, 562–598.
Gustman, A. L. and T. L. Steinmeier (1986): “Pensions, unions and implicit contracts,” . Kallir, I. and D. Sonsino (2009): “The neglect of correlation in allocation decisions,” Southern
Economic Journal, 1045–1066.
Keane, M. P. and K. I. Wolpin (1997): “The career decisions of young men,” Journal of political Economy, 105, 473–522.
Sallee, M. W. (2012): “The ideal worker or the ideal father: Organizational structures and culture in the gendered university,” Research in Higher Education, 53, 782–802.
Stern, S. (1997): “Approximate solutions to stochastic dynamic programs,” Econometric Theory, 13, 392–405.
Stock, J. H. and D. A. Wise (1990): “The pension inducement to retire: An option value analysis,” in Issues in the Economics of Aging, University of Chicago Press, 1990, 205–230.
Chapter 1
Life-cycle Decisions, Dynamic
Programming, and Correlation
Neglect: Experimental Analysis of
Alternative Decision Rules
Résumé
Un comportement prospectif rationnel nécessite l’habilité de résoudre des problèmes complexes incluant la capacité de calculer la valeur maximale des valeurs futures d’options de choix (calculs Emax). Nous avons mené une expérience pour mesurer la proportion de participants capables d’effectuer ces calculs complexes ainsi que la proportion de sujets utilisant deux règles de calcul alternatives qui sont toutes deux sous-optimales et qui ignorent la corrélation entre les évaluations futures. La première règle alternative capture les sujets qui effectuent des calculs Emax en ignorant la corrélation entre les variables de l’ensemble d’informations. La seconde règle alternative capture les participants calculant le maximum des évaluations futures attendues (calculs maxE), similaires au modèle option value deStock and Wise(1990). C’est pourquoi notre conception expérimentale exploite différentes structures de corrélation entre les évaluations futures pour séparer la part des sujets utilisant chaque règle. L’expérience a été menée sur un échantillon important et hétérogène de participants, ce qui a permis de relier la propension à utiliser une règle donnée à un ensemble de caractéristiques socio-économiques. En somme, les résultats que nous avons obtenus suggèrent que 28% des participants sont capables d’effectuer des calculs Emax en exploitant la structure de corrélation, 20% des sujets effectuent des calculs Emax en ignorant la corrélation, tandis que 52% des participants utilisent la règle
de calcul maxE . De plus, nos résultats laissent entrevoir que la propension à utiliser une règle donnée varie de manière significative avec les niveaux d’éducation - les participants les plus instruits sont beaucoup plus susceptibles d’utiliser la règle de calcul maxE
Abstract
Rational forward-looking behavior requires solving complex problems involving computation of the expected maximum future valuations across choice alternatives (Emax computations). We conduct an experiment to measure the share of subjects able to perform these computations as well as the share of subjects using two alternative (sub-optimal) rules of computation which ignore correlation between future valuations. The first alternative rule captures subjects who perform Emax computations ignoring correlation between unobservables in the information set. The second alternative rule captures subjects computing the maximum of the expected future valuations (maxE computations), akin to the option-value model of Stock and Wise
(1990). Our experimental design exploits different correlation structures between future val-uations to separate the share of subjects using each rule. The experiment was conducted with a large and heterogenous sample of subjects, allowing to relate the propensity to use a given rule to a rich set of socio-economic characteristics. Our results suggest that 28 percent of subjects are able to perform Emax computations exploiting the correlation structure, 20 percent of subjects perform Emax computations ignoring correlation, while 52 percent of sub-jects perform maxE computations. Moreover, we find that the propensity to use a given rule significantly varies across education levels – higher educated subjects are significantly more likely to perform maxE computations.
JEL codes: D03, D84, C50
1.1
Introduction
Forward looking behavior is a core element of life-cycle models. Dynamic programming models relying on Bellman’s principle of optimally remain the workhorse of life-cycle analysis and are extensively used to perform welfare analysis and compute optimal policies (Wolpin,2013). The credibility of policy recommendations derived using these models hinge on the validity of the model’s underlying assumptions. The assumptions maintained to conduct life-cycle analyses are very salient. These models notably assume that rational forward-looking agents are able to solve arbitrarily complex choice problems over their life-cycle. Doing so requires amongst other things forming "correct" (often rational) expectations of future outcomes, keeping track of the law of motion of state variables, and being able to compute the expected maximum future discounted utility across choice alternatives, referred to below as the Emax computation. The assumption that agents act rationally in these choice settings is at odds with experimen-tal evidence where a significant share of high educated subjects have difficulties solving these complex problems in laboratory settings. Disentangling the reasons for these difficulties is important to better predict behavior and policies, but also to inform practitioners of possible elements of model misspecification that require consideration. Recent laboratory experiments have started shedding light on potential difficulties. Houser et al. (2004) conduct controlled laboratory experiments and find that close to 66% of subjects fail to solve the dynamic op-timization problem near-perfectly. Their design allows to attribute these failures to agents having difficulties using the law of motion to forecast future values of state variables. The capacity of agents to perform the Emax computation on the other hand has not to our knowl-edge been directly tested. What is more, behaviourally validated alternative decision rules to Emax computations remain unknown.1
The main focus of this paper is to measure the share of subjects able to perform Emax computations and to characterize alternative computation rules used by subjects. Our main analysis focuses on two alternative rules which have in common that correlation between future valuations is neglected. Recent research suggests that correlation neglect may be a prominent bias in many different settings including portfolio decisions (Kroll et al.,1988) , voting behavior (Levy and Razin, 2015) , and belief formation (Enke and Zimmermann, 2017). Although
1Their setup also involved their experiment such that the joint probability distribution of unobservable
less explored, correlation neglect can have important implications in life-cycle choice settings including savings and retirement behavior, schooling decisions, and timing of childbearing.2
The first alternative rule we consider captures subjects able to perform Emax computations but do so ignoring possible correlation between the unobservable variables affecting next period outcomes. Our second alternative decision rule captures subjects computing the maximum of the expected values of the different choices available in the next period (the maxE operator), akin to the option-value model (see Stock and Wise,1990). The later has mostly been viewed as a way to approximate the Emax function in life-cycle models without having to compute multiple integrals, although the quality of the approximations performed using this rule has been seriously questioned (see Stern, 1997). The option value model has been applied to the analysis of retirement (Lumsdaine et al., 1992), transitions from work to other status (Burkhauser et al.,2004), and job/sector changes (Ausink and Wise,1996).
Our analysis exploits data from an online experiment conducted using a representative sample of the Dutch population. Subjects in our experiment go through a sequence of rounds. In each round, they first have to decide whether to exit the round and earn a known amount, or go to the next period and choose between two options. Importantly, subjects do know the exact payoffs of both options before deciding to exit or not the round. Rather, they are informed of the joint probability distribution of these payoffs. A rational agent will exploit the joint probability distribution to compute the expected value of the next period payoff maximizing choices when deciding whether to exit or not the round. The experiment varies the correlation structure and payoff levels of both options across the different rounds. We show that those variations induce different choice sequences depending on the computation rule considered and a subject’s level of risk aversion. We identify the later by exploiting choices that each subject made in a separate lottery task. Our econometric model has the structure of a finite mixture model where each subject uses one of the three computation rules outlined above. We estimate the model combining decisions in all rounds with choices in the lottery task to estimate the shares of subjects using each rule, controlling for risk aversion and possible errors in decision making.
Our preferred specification suggests that 52% of subjects perform maxE computations, con-sistent with the option-value model. We further find that 20% of subjects are predicted to
2
Ignoring the increased fertility risks associated with delayed motherhood may for example induce couples to postpone child-bearing longer than would otherwise be justified.
perform Emax computations ignoring correlation between the stochastic outcomes, while 28% of subjects are predicted to compute Emax exactly. Together, we find that close to 72% of subjects use a rule ignoring correlation between future valuations. Our analysis also reveals a significant link between education and the rule used.
The organization of our paper is as follows. In Section1.2we present our experimental design and procedures. Section1.3 presents our econometric model. Section1.4presents our results and Section 1.5concludes.
1.2
Experimental Design
The experiment was conducted using the LISS panel of Tilburg University. 1494 panel mem-bers were invited to participate in our experiment. 1156 of the invited panel memmem-bers partici-pated in the experiment, 1111 of which (96.1%) completed the whole experiment. Participants were informed that they can earn real money depending on their choices in the experiment as well as chance. 10% of participants are randomly selected and one of their ten decisions (described below) was randomly selected and the amount earned in that particular round was paid out and later deposited into their bank accounts.
The experiment had two separate parts played sequentially. The first (main) part focused on choices to identify the distribution of decision rules. The second part aimed attention at measuring risk aversion for each subject. We discuss in turn the design of each part.
The first part of the experiment consisted of 9 independent rounds. In each round, subjects were presented possible payoffs for three options, labeled A, B, and C. Option A always paid a specified amount with certainty. Options B and C each paid one of two possible payoffs. Table 1.1presents the structure of the joint distributions of payoffs for options B and C.
Option C xc xmin
Option B xb π1 π2 0.5
xmin π2 π1 0.5
0.5 0.5 1
Table 1.1: Joint distributions for options B and C payoffs
same low payoff (xmin ) or a high payoff (xc), such that xb > xc for all rounds. Low or high
payoffs were equally likely for both options and for all rounds. The joint distribution of payoffs for both options depended on two parameters π1and π2 whose values were varied across round
to induce either positive (π1 > π2), negative (π1 < π2), or no correlation (π1 = π2 = 0.25)
between the payoffs of both options. Table 1.2 presents the payoffs and joint distributions for all 9 rounds. The table also presents the φ correlation coefficient between the payoffs of options B and C.
Subjects were first asked to choose between options. First, they have to decide whether they go for Option A or whether they want to continue and choose in a second stage between Option B and Option C (see figure 1.1). If the participant chooses Option A, he will receive the corresponding payoff and the round ends here. If he chooses to continue, the computer will draw randomly one of the two outcomes for each Option B and Option C. Agents are informed about the payoffs that were drawn for Option B and Option C before they are asked to choose between the two options (see figure 1.2 ). He receives the payoff corresponding to the option he has chosen and this ends the round. Agents are asked to make those decisions over 9 rounds, each round possibly with another set of options payoffs and chances. The order of tasks was randomly presented.
Future utilities under uncertainty are assumed to be evaluated throughout three possible decisions rules. All nine rounds impose the sequence of restrictions (xb > xc> xmin) in order
to separate the three main decision rules of interest.
We first consider Emax computations or Dynamic Programming (DP) rule that fully exploits all available information . Evaluation of the value of not choosing Option A is given by
E [max (U (B), U (C))] = π1U (xb) + π2U (xb) + π2U (xc) + π1U (xmin) (1.1)
where (1.1) exploits the specific restrictions (xb > xc> xmin) that our design imposes on the
possible payoffs of the three options.
Emax computations neglecting correlation (DPNC) assume subjects set correlation between the payoffs of both options to zero. In terms of 1.1, this implies setting π1 = π2, yielding
E [max (U (B), U (C))] = 1 4U (xb) + 1 4U (xb) + 1 4U (xc) + 1 4U (xmin) (1.2) Finally, we consider MaxE computations in line with the option-value model (OV). These computations imply subjects evaluation the value of not choosing Option A using
max (E [U (B)] , E [U (C)]) = max U (xb) 2 + U (xmin) 2 , U (xc) 2 + U (xmin) 2 (1.3)
The experimental parameters (xa, xb, xc, xmin, π1, π2) have been chosen such that any agent
using the MaxE computations (OV) rule always chooses the option A whereas subjects using the Emax computation (DP) rule and those using the Emax computations but neglecting correlation (DPNC) can choose the option A (leave) or option B-C (continue) according to the correlation between option B and option C. The left-hand side of the table1.2presents the values of the experimental parameters. For example, in decision task 1, option A pays e95 while option B (C) pays a high payoff e115 (e105) and a low payoff e60 (e60). π1 and π2
are equal to 0.4 and 0.1, respectively. These values of π1 and π2 induce a positive correlation
between options B and C (Φcor = 0.6 3). The parameters π1 and π2 have been chosen across
the tasks in the way to have positive, negative or absence of correlation between options B et C (1-3:positive correlation, 4-6:negative correlation, 7-9: absence of correlation).
The right-hand side of the table 1.2 presents the prediction of choice of agents according to their decision rule and their attitudes toward risk. For example, in Decision task 1, an individual will choose option A (leave) if he is using the Emax computation (DP) rule, option B-C (continue) in the case of Emax computation rule but neglecting correlation (DPNC), and option A (leave) if he is using the MaxE computations rule (OV).
However, this design cannot classify all individuals according to these attitudes toward risks. Indeed, this design permits to classify only agents whose relative risk aversion is between -0.5 and 0.75 (0.25 ≤ θ ≤ 1.5). Thus, the reason behind the implementation of second experiment (part two) aimed to measure individual’s risk aversion.
In the part two, participants are asked to make tasks a bit different from the previous ones. Each participant is shown a table of sixteen pairs of lotteries such as the ones presented in
3
Φcor= π(π1−(π1π2)
Figure1.3. There are again three options. Option A pays a certain amount which varies from e10 to e95 as one moves down the screen. Option B pays always e15 and Option C pays always e90. Participants are asked to choose the line from which they would like to switch from option A to option B-C. If a participant makes the latter choice, the computer will choose one of the two options with equal chances, i.e., chances are 50 out of 100 to get the amount of Option B and 50 out of 100 to get the amount of Option C. Participant who maximizes his utility switches at some point from option A to option B-C or chooses option A throughout the screen (see figure 1.3). The column 3 of Table 1.3 gives the range of the relative risk aversion corresponding to each switching line between 1 and 17. As shown in Figure 1.4, the number of times participants select the option A depends on risk aversion preferences. As we can see, the experimental design can classify only agents who switch between the line 4 and the line 12. In the subsequent analysis, participants who don’t switch between 4 and 12 will be pulled out to the sample.
Participants were informed that they can earn real money depending on their choices in the experiment as well as chance. One of the ten rounds will be randomly selected and the amount earned in that particular round will be paid out.
1.3
Econometric Model
We use the expected utility theory with a power utility of the form:
U (x, θ) = xθ (1.4)
where x is outcome and 1 − θ = r is relative risk aversion. This is the most widely parametric family used in literature (Wakker,2008) which fits better than other families (Camerer and Ho,
1994). It has been used in many domains including psychology (Luce and Krumhansl,1988), economics (Holt and Laury, 2002; Palacios-Huerta and Serrano, 2006) and health domain (Bleichrodt and Pinto,2000).
Assume that individual i ∈ {1, ..., N} faces j ∈ {1, ..., 9} dichotomous choices between option A and option B-C, meaning Continuing and choosing between option B and C later. Agents choose the alternative in each choice situation that maximizes their utility. In the first experi-ment, let Yit= 1 if the individual opts for option B-C that means Continuing and choosing
between option B and C later, and Yit = 0 if the individual opts for option A . Let collect
the individual’s sequence of decisions, so that Yi = (Yi1, ..., Yi9).
Let Ai be the variable of our second experiment determining the line where the agent switches
in the second experiment.
We assume that each individual i uses a decision rule c ∈ nOV, DP N C, DPo with a given probability. The probability of using a decision rule c is scand
3
P
c=1
sc= 1.
Conditional on the decision rule c, let CEc
it(A) the certainty equivalent of option A and
CEitc(B − C)the certainty equivalent of continuing and choosing later between options B and C. We define ∆CE as the difference between the certainty equivalent of option continuing (option B-C) and the certainty equivalent of option A:
∆CEitc(π1, π2, ri, xa, xb, xc, xmin) = CEitc(B − C) − CEitc(A) (1.5)
For a given choice situation t, an individual will opt for option B-C (to go to the next period) if CEc
it(π1, π2, ri, xa, xb, xc, xmin) ≥ 0. We admit stochastic decision by adding a so
called Fechner error in line with the existing literature (Loomes,2005;Von Gaudecker et al.,
2011): Yit= 1 n ∆CEitc(π1, π2, ri, xa, xb, xc, xmin) + λεit≥ 0 o (1.6)
On the other hand, the probability that an agent i switches at line k in the part two is defined as follows: P (Ai= k) = P ri ∈ [rinfk , rksup[ (1.7) = Φ(rksup) − Φ(rkinf) (1.8)
where Table 1.3provides the corresponding interval of the relative risk aversion based on the individual’s switching line. Φ is the normal cumulative distribution function.
Conditional on the individual’s decision rule and the level of risk aversion, the probability an individual i chooses Y for choice situation t is :
P (Yit= Y | ri∈ rkinf, rksup) = Λ 2Yit− 1 1 λ∆CE c it π1, π2, ri, xa, xb, xc, xmin ! (1.9)
where Λ(x) = (1 + e−x)−1 stands for the cumulative standard logistic distribution function and ∆CEc it defines as follows ∆CEitc = (π1+ π2)x1−rb i+ (π1+ π2)x1−rmini ! 1 1−ri − xa if decision rule c is OV 1 4 x1−ri b + x 1−ri b + x 1−ri c + x 1−ri min ! 1 1−ri − xaif decision rule c is DPNC π1x1−rb i+ π2x1−rb i+ π2x1−rc i+ π1x1−rmini ! 1 1−ri − xaif decision rule c is DP (1.10)
Conditional on the type of individual i, the probability of choosing to switch at line k and choosing Y for choice situation t is :
Lcit π1, π2, ri, xa, xb, xc, xmin,Yit
!
= P (Ai= k, Yit= Y ) (1.11)
= P (Ai = k) ∗ P (Yit = Y | Ai = k) (1.12)
= P (Ai = k) ∗ P (Yit= Y | ri ∈ rkinf, rksup) (1.13)
Conditional on the decision rule c and the level of risk aversion, the probability that an individual i chooses Y is:
9 Y t Lcit π1, π2, ri, xa, xb, xc, xmin, Yit ! (1.14)
The unconditional probability will be the average across types :
3 X c=1 sc 9 Y t Lcit π1, π2, ri, xa, xb, xc, xmin, Yit ! (1.15)
The contribution of the individual i in the likelihood is :
`i= 3 X c=1 sc Z rksup rk inf 9 Y t Lcit π1, π2, ri, xa, xb, xc, xmin,Yit ! f (ri)dri ! (1.16)
The likelihood of the population is :
` = n X i=1 Log 3 X c=1 sc Z rksup rk inf 9 Y t Lcit π1, π2, ri, xa, xb, xc, xmin,Yit ! f (ri)dri !! (1.17) ri ∼ N (µi, σ2) (1.18)
Where µi = κ + Xiβ
Xi is a matrix of individual characteristics.
β is the vector of parameters
κ is the bias of the relative risk aversion. This bias can be viewed as the fact the relative risk aversion that an agent reveals by the means of the experiment eliciting attitudes toward risk (the second experiment) can be slightly different to the level of risk aversion he uses to make his decision in the first experiment devoted to identify type of agents.
The integral in equation1.17does not have an analytical solution and we approximate it using standard simulation techniques. We employ the BFGS algorithm with numerical derivatives to maximize the likelihood function.
1.4
Results
Table 1.4shows the results of our structural model where we sequentially add covariates and bias in order to see possible differences across models. In order to allow possible comparison and to evaluate the quality of predictions, five different models (Model 1, 2, 4, and 5) are considered, or a set of 5 estimations overall. Model 1 which is the most parsimonious and includes only unobserved heterogeneity in the aversion preferences. Model 2 adds to Model 1 observed heterogeneity in risk aversion. Model 3 adds to Model 1 a common bias across individuals in the measure of risk aversion while Model 4 adds to Model 3 observed hetero-geneity in risk aversion. Model 5 is the most comprehensive model and allows observed and unobserved heterogeneity in the risk aversion and observed heterogeneity in the probability of using a given decision rule.
1.4.1 Shares of decision rules with heterogeneity in risk preferences
Model 1 presents the results of the model with only unobserved heterogeneity in the aver-sion preferences. The results suggest that share of participants using option value or MaxE computations rule, meaning subjects computing the maximum of the expected values of the different choices available in the next period, is 60%. The share of subjects who are able to perform Emax computations but do ignore possible correlation between the unobservable vari-ables affecting next period outcomes represents 16%. Overall, the proportion of participants who neglect correlation when making decision that are those who use MaxE decision rule and
Emax computations rule but neglecting correlation is 76%. Only 23% of participants use the DP decision rule by performing Emax computations . On average, the agents are risk averse and the chance that a typical agent is risk averse is 56%(Φ(0.07/0.4)).
Model 2 allows both observed and unobserved heterogeneity in risk aversion. The observed heterogeneity will permit to investigate how risk aversion varies with some sociodemographic variables such as gender, education, self-employment, age and income. The share of each type remains approximatively the same as in Model 1. Self-employment significantly affects the level of one’s risk aversion. Indeed, the self-employed are less risk averse and the result is in line with other studies such asHalek and Eisenhauer(2001) andColombier and Masclet(2008). Regarding the age, the results suggest that relative risk aversion increases significantly after age 65. These results are similar to Halek and Eisenhauer (2001). Our results also suggest that risk aversion increases with education as in Hersch (1996) and Halek and Eisenhauer
(2001). The higher the education level of someone, the greater is the risk aversion. In other words, a higher level of education may lead to a greater awareness of cost of risk. However, other papers (Hartog et al.,2002) find a negative relation between risk aversion and education. Income has a significant effect on risk preferences. The richer the agent, the less risk averse he will be. Agents with income greater than e1000 are less risk averse than agents who earn less than e1000. There is a slight difference between Model 1 and Model 2 in terms of standard deviation of the risk preferences.
In Model 3, a common bias across individuals in the measure of risk aversion is allowed. More precisely, it is assumed that agents can overestimate or underestimate their level of risk aversion when they make their choice in the first part of the experiment. The results suggest that there is a decrease of the share of subjects performing the MaxE computations rule (51% vs 61%) and a slightly increase of the share of subjects using the Emax computations as well as those doing so but who do ignore possible correlation between the unobservable variables. The bias is estimated to be positive and equal to 0.48. When we allow observed heterogeneity in the risk aversion (Model 4), the distribution of decision rules and determinants of risk aversion are very similar to Model 3 and Model 2, respectively. It is worth noting that the results are robust to different specifications, even when taking account into the task duration, and other estimations. Tables are available upon request.
1.4.2 Can some observed factors account for decision rule used?
In this stage, we would like to investigate whether the propensity to use a given type is related to observed factors. Instead of assuming the individual heterogeneity is uncorrelated with the regressors in a random effects or random parameters specification, we opt here for a more general approach. We will model the propensity to use a given decision rule via a multinomial logit:
sc = Pexp(Z3 iγc)
cexp(Ziγc)
(1.19) Model 5 of Table 1.4 shows results of the estimation and the MaxE computations or OV decision rule is taken as the reference class. Columns 5, 6, and 7 respectively display the effects of the set of regressors on risk aversion, the propensity to use the Emax computations rule and Emax computations but ignoring correlation. Education plays a central role on the propensity to use the Emax computations rule relative to MaxE computations rule. Education decreases the probability of using the Emax computations rule. The higher one’s education level, the greater is the chance to perform the MaxE relative to Emax rule. Regarding risk aversion, the results are similar to previously. Self-employed and richer are less risk averse while the more educated people are more risk averse.
1.4.3 Effect of the decision rule on education investment
Classification
An important step in latent class is the use of the results in order to classify agents into appropriate class. In our case, it consists of classifying participants into MaxE computations rule, Emax computations rule, and Emax computations rule but ignoring correlation. The Bayes rule is used to calculate the posteriori probability. Given the estimates, the posteriori probability that an individual uses the decision rule c, conditional on the observed choice, is according to Bayes rule:
ˆ P (c | Yi) = ˆ scfˆc(Yc) 3 P c=1 ˆ scfˆc(Yc) (1.20)
Subjects are classified according to the highest posteriori probability across the latent classes. For example, a participant is Emax type if his posteriori probability of using Emax compu-tations rule is the highest. Figure 1.5shows whether our model is distinctly able to classify participants into one class or group. As shown, our model attributes to each participant a high
probability (one) or low probability (zero) of using a given decision rule, providing evidence of the good classification performance of our preferred model. According to this posteriori classification, the proportion of participants who are using MaxE computations rule is 71.58% while the one of those using Emax computations rule is 24.77%. The subjects who are using Emax computation but neglecting correlation represent only 3.65%.
Theoretical model of pursuing education
The enrolment for college is viewed as an investment project. We follow in Becker (1975) and Catsiapis (1987). Using the theory of human capital, the decision to pursue college is modelled with a simple model in terms of the expected Net Present Value (NPV) of educational investment.
The choice of pursuing college depends on the comparison between the expected present value of pursuing college and the expected present value of exiting and engaging in labor market. As known, education plays a central role on unemployment incidence. The literature has documented that less well-educated have higher unemployment rate and individuals with higher qualifications have higher probability of regaining employment (Riddell and Song,2011;
Wolbers,2000). In economic downturn, they are less vulnerable to layoffs. Higher education will be seen as an insurance for future income. Therefore, a higher education would insure about uncertainty and would allow a more stable employment prospect and income in the future. For these reasons, we assume that a higher education will insure a certain amount, wm while the exit will imply a more uncertain future income:
Net Present Value = wm
1−r if agent pursue education
Sc if agent stop and goes in the labor market
(1.21)
Sc is the expected present value of exiting and opting for the labor market based on the
decision rule (OV or MaxE, Emax computation but neglecting correlation or DPNC, Emax computation or DP). For example if the individual is using MaxE computatiosn rule , Sc =
max E(U (Ω)) while it is Sc= E(max U (Ω)) in the case of Emax computation rule where Ω is the set of state variables.
Capital market is supposed be perfect and labor market offers fixed. This implies that the choice does not depend on preferences and the Net Present Value (NPV) can be used as the individual decision rule for choosing education investment.
If the Net Present Value of continuing college is greater than the Net Present Value of leaving, the individual would choose to pursue. Otherwise, the individual would decide to leave and go for the labor market. We can recall that:
max E(U (Ω) ≤ E(max U (Ω)) (1.22)
In other words, valuation of future utilities when using MaxE computations is always smaller than those of the Emax computations rule, meaning the option value rule underestimates the value of exiting and opting for the labour market and consequently overestimates the probability of pursuing school. As a result, individuals using MaxE computations are more likely to continue school or invest in school than those using Emax computations rule. The next section aims at verifying this theoretical prediction.
Empiral Results
In order to test the theoretical prediction above, we propose the following equation :
Ci = Xiβ + γDPi+ δDP N Ci+ εi (1.23)
Where Ci is college attainment; Xi is a matrix of individuals characteristics which include
age, gender, family income, place of residence; DPi is a binary variable indicating that the
individual is using Emax computations rule ; DP NCi is a binary variable indicating that the
individual is using the Emax computations rule, but ignoring correlation.
The literature has focused on the effect of uncertainty on the demand of education (Kodde,
1986;Fitzsimons,2007). Table 1.5reports the estimation results where in column 2, we add some control variables. The empirical results are in line with the theoretical predictions. Agents that are using the Emax computations rule as well as those using the Emax com-putations rule but ignoring correlation are less likely to pursue education than those using MaxE computation rule. The propensity of pursuing college for participants using the Emax computations rule is 16% less than the probability of those using the MaxE computations rule whereas the probability of pursing college for those using the Emax computations rule but
neglecting correlation is 9% less. These results tend to confirm the external validity which is one of the challenges of experimental economics. The other results are similar to previous studies (see Lauer,2002;Byun et al.,2012). The older the participant, the less the likelihood of pursing college will be. The female are less likely to pursue education. The male’s proba-bility of pursuing college would be 5 percentage points higher. As far as the family income is concerned, all coefficients are positive and significant. These results might be the consequences of financial constraints. The effect of the place of residence is not significant.
1.5
Conclusion
Understanding how agents make complex life-cycle decisions is essential to develop better policy interventions. The dynamic programming framework has dominated empirical work on life-cycle decision making, maintaining strong assumptions about the rationality of agents and their ability to solve complex problems. This paper focuses on computation rules used by agents to evaluate their future well-being, conditional on a specific action in their choice set. We found that 62% of subjects in our experiment use decision rules neglecting correlation between future outcomes. Amongst these subjects, the option-value decision rule clearly dominates. Starting with Stock and Wise (1990), the option-value model has been used to approximate decision rules of perfectly rational economic agents and simplify numerical computations, rather than because researchers had a genuine belief that agents performed MaxE computations. Our analysis is to our knowledge the first to validate in a controlled experiment the option-value model as a behaviorally relevant framework for many subjects. It remains that a significant share of subjects appear to ignore correlation in life-cycle decision settings. Houser et al.(2004) reported that a similar share of subjects in their experiment had difficulties solving dynamic programming type problems. There, difficulties are attributable to the law of motion of deterministic state variables and understanding how it operates. Together, these results suggest that many core elements of the dynamic programming approach may be misspecified for a sizeable share of agents. Misspecification does not necessarily translate into significant biases if optimal policies are robust to these departures from rational decision making. Future work should try to analyze robustness of optimal policies to misspecification of these core elements.
Bibliography
Ausink, J. and D. A. Wise (1996): “The military pension, compensation, and retirement of US Air Force pilots,” in Advances in the Economics of Aging, University of Chicago Press, 83–114. Becker, G. S. (1975): “Front matter, human capital: a theoretical and empirical analysis, with
special reference to education,” in Human Capital: A Theoretical and Empirical Analysis, with Special Reference to Education, Second Edition, NBER, 22–0.
Bleichrodt, H. and J. L. Pinto (2000): “A parameter-free elicitation of the probability weighting function in medical decision analysis,” Management science, 46, 1485–1496.
Burkhauser, R. V., J. S. Butler, and G. Gumus (2004): “Dynamic programming model estimates of Social Security Disability Insurance application timing,” Journal of Applied Econometrics, 19, 671–685.
Byun, S.-y., J. L. Meece, and M. J. Irvin (2012): “Rural-nonrural disparities in postsecondary educational attainment revisited,” American educational research journal, 49, 412–437.
Camerer, C. F. and T.-H. Ho (1994): “Violations of the betweenness axiom and nonlinearity in probability,” Journal of risk and uncertainty, 8, 167–196.
Catsiapis, G. (1987): “A model of educational investment decisions,” The Review of Economics and Statistics, 33–41.
Colombier, N. and D. Masclet (2008): “Intergenerational correlation in self employment: some further evidence from French ECHP data,” Small Business Economics, 30, 423–437.
Enke, B. and F. Zimmermann (2017): “Correlation neglect in belief formation,” The Review of Economic Studies, 86, 313–332.
Fitzsimons, E. (2007): “The effects of risk on education in Indonesia,” Economic Development and Cultural Change, 56, 1–25.
Halek, M. and J. G. Eisenhauer (2001): “Demography of risk aversion,” Journal of Risk and Insurance, 1–24.
Hartog, J., A. Ferrer-i Carbonell, and N. Jonker (2002): “Linking measured risk aversion to individual characteristics,” Kyklos, 55, 3–26.
Hersch, J. (1996): “Smoking, seat belts, and other risky consumer decisions: Differences by gender and race,” Managerial and decision economics, 17, 471–481.
Holt, C. A. and S. K. Laury (2002): “Risk aversion and incentive effects,” American economic review, 92, 1644–1655.
Houser, D., M. Keane, and K. McCabe (2004): “Behavior in a dynamic decision problem: An analysis of experimental evidence using a Bayesian type classification algorithm,” Econometrica, 72, 781–822.
Kodde, D. A. (1986): “Uncertainty and the Demand for Education,” The review of economics and statistics, 460–467.
Kroll, Y., H. Levy, and A. Rapoport (1988): “Experimental tests of the mean-variance model for portfolio selection,” Organizational Behavior and Human Decision Processes, 42, 388–410. Lauer, C. (2002): “A Model of Educational Attainment Application to the German Case,” .
Levy, G. and R. Razin (2015): “Correlation neglect, voting behavior, and information aggregation,” American Economic Review, 105, 1634–45.
Loomes, G. (2005): “Modelling the stochastic component of behaviour in experiments: Some issues for the interpretation of data,” Experimental Economics, 8, 301–323.
Luce, R. and C. Krumhansl (1988): “Measurement, scaling, and psychophysics,” Stevensys hand-book of experimental psychology, 3–74.
Lumsdaine, R. L., J. H. Stock, and D. A. Wise (1992): “Three models of retirement: Compu-tational complexity versus predictive validity,” in Topics in the Economics of Aging, University of Chicago Press, 21–60.
Palacios-Huerta, I. and R. Serrano (2006): “Rejecting small gambles under expected utility,” Economics Letters, 91, 250–259.
Riddell, W. C. and X. Song (2011): “The impact of education on unemployment incidence and re-employment success: Evidence from the US labour market,” Labour Economics, 18, 453–463. Stern, S. (1997): “Approximate solutions to stochastic dynamic programs,” Econometric Theory, 13,
392–405.
Stock, J. H. and D. A. Wise (1990): “The pension inducement to retire: An option value analysis,” in Issues in the Economics of Aging, University of Chicago Press, 1990, 205–230.
Von Gaudecker, H.-M., A. Van Soest, and E. Wengstrom (2011): “Heterogeneity in risky choice behavior in a broad population,” American Economic Review, 101, 664–94.
Wakker, P. P. (2008): “Explaining the characteristics of the power (CRRA) utility family,” Health economics, 17, 1329–1344.
Wolbers, M. H. (2000): “The effects of level of education on mobility between employment and unemployment in the Netherlands,” European Sociological Review, 16, 185–200.
Figures
Figure 1.1: Screenshot of decision screen: choosing between option A (Exit) and B/C (Con-tinue)
Figure 1.2: Screenshot of decision screen: choosing between option B and option C when previously choosing Continue
Figure 1.4: Number of times of selecting option A according to risk aversion preferences
Tables
Experimental parameters Predicted behavior
xa xb xc xmin π1 π2 Φcor θ ∈ (0.25, 1.5) θ < 0.25 D1 95 115 105 60 0.4 0.1 0.6 0 1 0 0 0 0 D2 65 90 80 25 0.45 0.05 0.8 0 1 0 0 0 0 D3 100 130 110 50 0.45 0.05 0.8 0 1 0 0 0 0 D4 85 105 90 30 0.05 0.45 -0.8 1 0 0 0 0 0 D5 75 90 80 30 0.1 0.4 -0.6 1 0 0 0 0 0 D6 100 115 105 50 0.15 0.35 -0.5 1 0 0 0 0 0 D7 45 65 55 25 0.25 0.25 0 1 1 0 0 0 0 D8 70 100 90 25 0.25 0.25 0 1 1 0 0 0 0 D9 90 115 105 60 0.25 0.25 0 1 1 0 0 0 0
Table 1.2: Experimental parameters for all 9 rounds of the main part of the experiment. Predicted behavior for Emax, Emax neglecting correlation, and MaxE computations. Value of 0 represents choice of Option A, value of 1 represents not choosing Option A
Switching Line Percent RRA if switch after (*) to BC
1 r < −11.120 2 3.81 −11.120 < r < −4.88 3 3.00 −4.88 < r < −2.8 4 2.77 −2.8 < r < −1.74 5 2.65 −1.74 < r < −1.09 6 3.46 −1.09 < r < −0.64 7 7.5 −0.64 < r < −0.29 8 7.61 −0.29 < r < 0.01 9 18.45 0.01 < r < 0.26 10 18.57 0.26 < r < 0.51 11 10.61 0.51 < r < 0.75 12 6.34 0.75 < r < 1.01 13 6.00 1.01 < r < 1.31 14 3.00 1.31 < r < 1.75 15 2.19 1.75 < r < 2.65 16 4.04 2.65 < r
M1 M2 M3 M4 M5
Aversion Aversion Aversion Aversion Aversion DPNC DP
Const 0.07 0.12∗ 0.06∗∗ 0.09 0.10 -0.21 0.61 Female 0.01 0.001 0.00 -0.21 0.13 Self Empl. -0.22∗∗∗ -0.22∗∗∗ -0.22∗ -15. -0.24 34 and younger 0.07 -0.05 -0.05 -0.10 0.08 35-44 0.08 0.08 0.08 0.11 -0.04 45-54 -0.01 -0.02 -0.02 -0.10 0.16 54-64 -0.12∗∗∗ -0.13∗∗ 0.13∗∗∗ -0.65 -0.41
Hi Sec / Int Voc T 0.03 0.06 0.06 -0.22 -1.13∗∗∗
Hi Voc Tra 0.21∗∗∗ 0.28∗∗∗ 0.28∗∗∗ -0.89 -1.03∗∗∗ University 0.32∗∗∗ 0.39∗∗ 0.39∗∗ -0.50 -1.85∗∗∗ Income 1000-2499 -0.30∗∗∗ -0.29∗∗∗ -0.29∗∗∗ -0.53 -0.11 Income 2500+ -0.23∗∗∗ -0.22∗∗∗ -0.22∗∗∗ 0.14 -0.18 σr 0.40∗∗∗ 0.37∗∗∗ 0.40∗∗∗ 0.61∗∗∗ 0.38∗∗∗ biais 0.48∗∗∗ 0.48∗∗∗ 0.49∗∗∗ Parameters Share OV 0.60∗∗∗ 0.61∗∗∗ 0.52∗∗∗ 0.52∗∗∗ Share DPNC 0.16∗∗∗ 0.16∗∗∗ 0.19∗∗∗ 0.19∗∗∗ Share DP 0.24∗∗∗ 0.23∗∗∗ 0.28∗∗∗ 0.28∗∗∗ λ 8.94 8.94∗∗∗ 10.18∗∗∗ 10.18∗∗∗ 10.28∗∗∗ ∗p < 0.05,∗∗p < 0.01,∗∗∗p < 0.001
VARIABLE Model 1 Model 2 DPNC -0.13*** -0.16*** DP -0.10*** -0.09*** Female 0.05* Age 35-54 -0.09*** Age 55-65 -0.23*** Age 65+ -0.36***
Family Income e1000-e2500 0.15***
Family Income e2500+ 0.39***
Urban 0.03
Chapter 2
Labour Market Uncertainties and
Correlation Neglect: Effects on
Fertility Postponement
Résumé
L’arrivée d’un enfant engendre plus d’incertitudes et les agents évitent stratégiquement les incertitudes et les conflits entre la parentalité et l’emploi, en particulier chez les femmes, en sécurisant leur emploi avant de se tourner vers la parentalité. Conséquemment, le report de la première naissance est plus que jamais perceptible dans les sociétés. L’objectif principal de cet article est d’explorer la manière dont les incertitudes liées au travail et les risques accrus d’infertilité, associés au retard de maternité, interagissent dans la formulation des décisions en matière de parentalité (timing et nombre d’enfants). Nous avons développé un modèle de cycle de vie des décisions en matière d’offre de travail et de choix de parentalité et nous avons également cherché à quantifier les effets de l’incertitude sur le marché du travail ainsi que l’inattention à la corrélation sur le report de la première maternité. Nos paramètres estimés (préférences, équations salariales, qualité des enfants) sont conformes à la littérature existante (Hwang et al.,2018;Eckstein et al.,2019). De plus, nos résultats suggèrent qu’une réduction des incertitudes sur le travail affecte différemment les décisions de fécondité selon le niveau d’éducation. En effet, la réduction des incertitudes sur le marché du travail augmente le nombre d’enfants et diminue l’âge à la première maternité pour les couples peu scolarisés, et diminue le nombre d’enfants et augmente l’âge à la première naissance des couples plus scolarisés. Le biais comportemental de l’inattention à la corrélation contribuerait également voire plus au report de la parentalité.
