Olivier Chanel
email: olivier.chanel@univ-amu.fr.

Stéphanie V Lyk-Jensen

Jean-Christophe Vergnaud
email: jean-christophe.vergnaud@univ-paris1.fr.

Does Affective Forecasting Error Induce Changes in Preferences? Lessons from Danish Soldiers Anticipating Combat in Afghanistan The Version of Record of this

Keywords: Risk Preferences, Time Preferences, Affective Forecasting Errors, P

This paper investigates how affective forecasting errors (A.F.E.s), the difference between anticipated emotion and the emotion actually experienced, may induce changes in preferences on time, risk and occupation after combat. Building on psychological theories incorporating the role of emotion in decision-making, we designed a before-and-after-mission survey for Danish soldiers deployed to Afghanistan in 2011. Our hypothesis of an effect from A.F.E.s is tested by controlling for other mechanisms that may also change preferences: immediate emotion, trauma effect -proxied by post-traumatic stress disorder (P.T.S.D.)and changes in wealth and risk perception. At the aggregate level, results show stable preferences before and after mission. We find positive A.F.E.s for all three emotions studied (fear, anxiety and excitement), with anticipated emotions stronger than those actually experienced. We provide evidence that positive A.F.E.s regarding fear significantly increase risk tolerance and impatience, while positive A.F.E.s regarding excitement strengthen the will to stay in the military. Trauma has no impact on these preferences.

Introduction

Combat experiences are known to produce trauma, but can they also change individual preferences on time, risk and occupation? Given that preferences, cognitive ability and personality traits are fundamental determinants of decision-making in economic theory, 1 and generally considered stable and exogenous in standard economic models (Friedman 1962;[START_REF] Stigler | De Gustibus Non Est Disputandum[END_REF], substantial changes in preferences should affect future decisions.

Although a number of studies have explored the stability of preferences or personality traits after life events, the results remain mixed. 2 Recent studies on the impact of extreme events (E.E.) suggest that the experience of such violent events could explain psychological changes. These studies cover large economic shocks [START_REF] Arrondel | Mesurer les préférences des épargnants: Comment et pourquoi (en temps de crise)?[END_REF][START_REF] Brunnermeier | Do Wealth Fluctuations Generate Time-Varying Risk Aversion? Micro-Evidence on Individuals' Asset Allocation[END_REF]Krupka and Stephens 2013;Malmendier and Nagel 2011), and also include natural disasters [START_REF] Akesaka | Change in Time Preferences: Evidence from the Great East Japan Earthquake[END_REF][START_REF] Bernile | What doesn't Kill you Will Only Make you More Risk-Loving: Early-Life Disasters and CEO Behaviour[END_REF][START_REF] Callen | Catastrophes and Time Preference: Evidence from the Indian Ocean Earthquake[END_REF][START_REF] Cameron | Risk-Taking Behaviour in the Wake of Natural Disasters[END_REF][START_REF] Cassar | Trust, Risk, and Time Preferences after a Natural Disaster: Experimental Evidence from Thailand[END_REF]de Blasio et al. 2021;Eckel, El-Gamal, and Wilson 2009;Hanaoka, Shigeoka, and Watanabe 2018;[START_REF] Van Den Berg | Natural Hazards and Risk Aversion: Experimental Evidence from Latin America[END_REF][START_REF] Willinger | Risk and Time Preferences under the Threat of Background Risk: A Case-Study of Lahars Risk in Central Java[END_REF] and violence [START_REF] Brown | Impact of Violent Crime on Risk Aversion: Evidence from the Mexican Drug War[END_REF][START_REF] Callen | Violence and Risk Preference: Experimental Evidence from Afghanistan[END_REF]Jakiela and Ozier 2019;Kim and Lee 2014;[START_REF] Moya | Violence, Psychological Trauma, and Risk Attitudes: Evidence from Victims of Violence in Colombia[END_REF][START_REF] Voors | Violent Conflict and Behavior: A Field Experiment in Burundi[END_REF]. Moreover, Hanaoka, Shigeoka and Watanabe (2018) and [START_REF] Akesaka | Change in Time Preferences: Evidence from the Great East Japan Earthquake[END_REF] find that changes in preferences persist even five years after an earthquake, and [START_REF] Bernile | What doesn't Kill you Will Only Make you More Risk-Loving: Early-Life Disasters and CEO Behaviour[END_REF] obtain similar results for chief executive officers who experienced extreme fatal disasters in early life. However, there is no consensus regarding the direction of change in risk-taking behaviour: risk-taking can either increase (Garyn-Tal and Shahrabani 2021; [START_REF] Strom | An Exploratory Examination of Risk-Taking Behavior and PTSD Symptom Severity in a Veteran Sample[END_REF], potentially explained by coping mechanisms [START_REF] Ben-Zur | Threat to Life and Risk-Taking Behaviors: A Review of Empirical Findings and Explanatory Models[END_REF], or decrease [START_REF] Bernile | What doesn't Kill you Will Only Make you More Risk-Loving: Early-Life Disasters and CEO Behaviour[END_REF]de Blasio et al. 2021), as might be expected after exposure to major risks.

Being in the military constitutes a way of life, and differences in risk preferences between military personnel and civilians have been observed (Haerem et al. 2011). Indeed, Lahav, Benzion, and Shavit (2011) find that young Israelis doing their military service show relatively higher subjective discount rates than their peers living in a more peaceful environment. The persistent impact on risk-taking behaviour makes understanding the potential consequences of military deployments on preferences critical, not only for society as a whole but also for individual soldiers before deployment and on return to civilian life.

Research in economics and psychology points to several potential mechanisms that may explain how E.E.s change behaviours. Changes in individuals' risk perception or health status following E.E.s [START_REF] Aubert | Does Flood Experience Modify Risk Preferences? Evidence from an Artefactual Field Experiment in Vietnam[END_REF][START_REF] Beaud | Are People Risk Vulnerable?[END_REF]Gollier and Pratt 1996) or wealth constraints induced by the resulting economic shocks [START_REF] Brunnermeier | Do Wealth Fluctuations Generate Time-Varying Risk Aversion? Micro-Evidence on Individuals' Asset Allocation[END_REF]) could be involved. Moreover, trauma following exposure to an E.E. can also induce behavioural changes [START_REF] Callen | Violence and Risk Preference: Experimental Evidence from Afghanistan[END_REF] or changes in emotional affect, for example from being neutral to becoming anxious (Lerner andKeltner 2000, 2001).

We propose a new mechanism explaining how the experience of an E.E. can change preferences. We hypothesise that affective forecasting error (A.F.E.), i.e. the difference between the emotion anticipated regarding an E.E. and the emotion actually felt during it, helps predict changes in individual preferences. 3 The rationale is as follows: in a decision problem such as a risky choice, anticipated emotions help people to evaluate consequences and hence guide their decision. In anticipation of an E.E., people apply affective forecasting and, after experiencing the E.E., can compare the emotions actually felt with those anticipated, thus learning about the accuracy of their forecasts. An A.F.E. may then make people change the way they predict their emotions and consequently modify their choices in a decision problem. Our hypothesis is based on theories such as the appraisal-tendency framework (Lerner andKeltner 2000, 2001), which links evaluation processes with specific emotions, thereby placing accurate affective forecasting -anticipating future emotions -at the heart of effective decision-making (Loewenstein 2007;Loewenstein et al. 2001;[START_REF] Wilson | Affective Forecasting[END_REF]. Several studies reveal systematic prediction errors in affective forecasting (Gilbert et al. 1998;Gilbert and Wilson 2009).

This paper investigates whether A.F.E.s affect soldiers' preferences after the E.E. of combat. We measure three types of preferences: (i) preferences in making rational choices over time (time preferences), (ii) preferences in making rational choices under uncertainty (risk preferences) and (iii) preferences in a career perspective (occupational preferences). Information on such preferences is of obvious value for policy, theory and empirical analysis when measuring the welfare impacts of deployment, as changes in preferences may lie behind a behavioural change that could substantially impact both individuals and society at large.

In addition, we contribute to the methodological and empirical literature on affective forecasting by specifically testing the impact of A.F.E.s on preferences in an E.E., while controlling for other mechanisms that may also explain changes in preferences. We exploit a before-and-after comprehensive survey conducted among Danish soldiers deployed to Afghanistan in spring 2011 and hence likely to experience the E.E. of combat situations. Of the 51 countries engaged in the North Atlantic Treaty Organization (N.A.T.O.) forces and participating in the International Security Assistance Force (I.S.A.F.) since 2001, Denmark has had the highest casualties per capita.

Our paper is the first to elicit both soldiers' before-mission anticipated emotions in the event of combat (the E.E.) and -seven months later -the after-mission emotions experienced by those who were actually involved in combat. Unlike other types of E.E., soldiers' potential exposure to combat is expected, making it possible to measure emotions both beforehand and afterwards and to analyse soldiers' subsequent behavioural change. Since the literature on the behavioural consequences of E.E.s focuses mainly on victims of violence or natural disasters, where A.F.E.s are not involved, our findings contribute new insights into behavioural changes. Given that inaccurate forecasts of emotional consequences can affect decision-making, we exploit this before-after framework to study the impact of A.F.E.s on future decision-making through a change in preferences. Examining the reactions of this group of soldiers deployed to Afghanistan in spring 2011 on experiencing stronger or weaker emotions than they anticipated may shed light on whether this learning changes their risk, time and occupational preferences in general.

We build our analysis on how different variables may affect the soldiers' preferences and control for possible traumatic experience, risk perception and change in wealth. For each soldier, we have detailed background information, measures of degree of exposure to combat from validated survey questions, information on preferences and on the emotions of fear, anxiety and excitement before and after the military mission.

First, we check the between-soldier validity and within-soldier consistency of the answers. Then we explore both within-and between-soldier stability in preferences and emotions before and after combat. Second, we empirically test whether A.F.E.s in a combat setting predict changes in individual preferences and control for other potential mechanisms.

We find aggregate stable risk tolerance, time and occupational preferences before and after the mission. Moreover, we find significant positive A.F.E.s: stronger emotions were anticipated than those actually experienced. Testing for individual forecasting error adjustment with econometric models, we show that positive A.F.E. regarding fear increases risk tolerance and impatience, while positive A.F.E. regarding excitement strengthens the will to stay in the military. In our study, a direct effect of trauma on soldiers' changes in preferences can be ruled out.

In the remainder of the paper, we briefly review the literature relevant to our hypothesis, describe the data, explain our empirical strategy and present the results. We conclude with both research and policy implications.

Literature and hypothesis

In a decision problem, emotions intervene in several ways (see [START_REF] Rick | The Role of Emotion in Economic Behavior[END_REF] for a synthetic presentation). First, when choosing between different options, evaluating future consequences is important, and psychological theories [START_REF] Caplin | Psychological Expected Utility Theory and Anticipatory Feelings[END_REF]Lerner andKeltner 2000, 2001;Loewenstein et al. 2001) suggest that emotions play a crucial role in this assessment. Rational individuals try to obtain outcomes that will make them happy and to prevent outcomes that will make them miserable. The higher the intensity of anticipated emotions, the more effort individuals invest in feeling or suppressing the emotion [START_REF] Mellers | Anticipated Emotions as Guides to Choice[END_REF]. Indeed, an individual who feels anxious about a potential outcome of a risky choice may choose a sure option (Hartley and Phelps 2012;[START_REF] Maner | Dispositional Anxiety and Risk-Avoidant Decision-Making[END_REF]. This central role of anticipated emotions in decision making is nicely highlighted by [START_REF] Charpentier | Models of Affective Decision Making: How do Feelings Predict Choice?[END_REF], who show that computational models that use anticipated feelings about monetary gains and losses better predict choices in a gambling task than standard value-based models.

In addition to the anticipated emotions, several types of immediate emotions can affect decision-making. First, the very process of previewing anticipated emotions can instantly create an emotional state and have a priming effect. These anticipatory emotions, such as anxiety induced by having to make a risky choice, are known to influence choices. Second, emotions may be induced by factors external to the decision problem. For example, we expect the beforemission phase (i.e. before leaving for Afghanistan) to be a stressful period filled with negative emotions (anxiety, fear), especially for first-timers. Many studies report that when individuals are primed for a particular situation, those sensitive to fear become more risk-averse, while those sensitive to anger become less risk-averse [START_REF] Callen | Violence and Risk Preference: Experimental Evidence from Afghanistan[END_REF]Kugler, Connolly, and Ordóñez 2012;Lerner andKeltner 2000, 2001;[START_REF] Meier | Emotions and Risk Attitudes[END_REF]. Similarly, the psychological state of the soldiers after the mission may be affected by the potentially traumatic combat experience, thereby inducing immediate emotions. Indeed, [START_REF] Callen | Violence and Risk Preference: Experimental Evidence from Afghanistan[END_REF] observed that, when primed to recall fear, Afghan civilians exposed to violence exhibited an increased preference for certainty.

Our A.F.E. hypothesis is rooted in the crucial role of anticipated emotions in decisionmaking and the questionable accuracy of these predictions. Empirical evidence indicates that people predict their future emotions poorly (Gilbert et al. 1998), with both positive and negative emotions systematically overestimated [START_REF] Wilson | Affective Forecasting[END_REF]. This overestimation may have consequences on preferences: Kermer et al. (2006) suggest that loss aversion could result from such A.F.E., as individuals anticipate that stronger negative emotions will arise from a loss, whereas the emotions actually felt are far weaker. Hence, when considering emotions as an informational system that guides decision-making, researchers need to investigate how accuracy in affective forecasting affects choices and whether persistent A.F.E. might be a factor in detrimental decision-making [START_REF] Miloyan | Feelings of the Future[END_REF].

In contrast to natural disasters, or other violent situations where the event comes (almost) as a surprise, soldiers anticipate their military mission and forecast their feelings under combat, which enables them to observe their A.F.E.s. Our hypothesis is that A.F.E.s may induce changes in preferences in the specific case of an expected E.E., through a learning process. The effect of A.F.E. on behaviour could be similar to that in standard reinforcement learning, with prediction errors viewed as the main driver of adaptation [START_REF] Sutton | Introduction to Reinforcement Learning[END_REF].

One possible mechanism supporting our hypothesis is a learning effect on how anticipated emotions are formed. Gilbert and Wilson (2009) propose several mechanisms explaining prediction errors, suggesting that forecasting errors come from individuals' previewing their emotions based on an inaccurate representation of the future event. In our case, soldiers may discover that combat is not what they imagined. This learning will make them change the way they predict their emotions, both for future combat and for other events involving similar affective forecasting. Indeed, by observing their A.F.E.s regarding combat, they may identify the sources of forecasting errors that are common to their anticipated emotions in general.

Another learning mechanism may be revising the perception of emotional sensitivity. In predicting an emotion, people try to guess their future reaction (feeling) to a stimulus, and their affective forecasting will depend on how they perceive their own emotional sensitivity. However, people's perceptions of their own sensitivity may differ from the real sensitivity that determines true emotions. Hence, A.F.E. can serve to revise individuals' beliefs about their own sensitivity; and because they use affective forecasting for decision-making, this revision (the learning effect) may induce changes in preferences. We would expect soldiers to learn that they are not as sensitive to fear as they thought and thus to become more risk-tolerant regarding any decisions involving anticipated fear, either hypothetically or in real life.

Figure 1 summarises our framework and the different mechanisms that can influence choices. We assume that both affective forecasting and psychological state influence the decision process. Psychological state is determined by sociodemographic characteristics, wealth, risk perception, anticipatory emotions and trauma. Some of these determinants differ before and after the mission: anticipatory emotions generated by combat expectations before the mission, intensity of combat, trauma and changes in risk perception and wealth after the mission. Affective forecasting generates anticipated emotions both when evaluating the future consequences of the decision process and in combat. Our hypothesis is that A.F.E. changes subsequent affective forecasting. Our data allow us to test (i) whether A.F.E.s change soldiers' choices, while accounting for changes in psychological state; and (ii) whether there is a direct effect from trauma.

[Figure 1 about here]

Materials and Methods

Materials

The data come from a before-and-after survey combined with records from the Danish Ministry of Defence. The respondents were Danish soldiers deployed to Afghanistan in spring 2011 within the N.A.T.O.-led International Security Assistance Force (I.S.A.F.) 11 mission. To facilitate data collection and increase the response rate, we asked the soldiers to fill out a paper and pencil survey questionnaire during both before-mission preparation (January 2011) and after-mission debriefing (August 2011). In all, 487 soldiers (465 male and 22 female) completed the before-mission questionnaire and 371 (355 men and 16 women) completed both questionnaires. 4 The method chosen for data collection explains the high average before-after response rate (almost 95%). 5

The data was collected at different military forts, the first being Fort Oksbøl in January 2011, a few days before the mission started. Then, after the mission, between 17 and 25 August 2011, we collected data at the following forts: Aalborg, Fredericia, Holstebro, Skive, Slagelse, Oksbøl/Varde and Vordingborg. The soldiers were not allowed to communicate with one another during data collection, and the questionnaires were collected immediately after completion. Answering the questionnaire took an average of 25 minutes. Identical questions on time, risk, occupational preferences and (anticipated and experienced) emotions were used in both questionnaires.

To ensure that potential differences were not due to differences in populations, we only considered responses from soldiers who answered both before-and after-mission questionnaires and provided a valid employee identifier. 6 The questionnaire covered beforeand after-mission variables (largely inspired by the literature), the latter with the suffix '_after'.

Socio-Demographics and Military Variables

Appendix Table 1 shows respondents' reported socio-demographic characteristics, and military variables (see also supplementary appendix Table S.3 for the subsamples of those exposed or not exposed to combat, and sample comparison tests). 7 Also included are some military background characteristics: respondents' length of employment in the Army (Seniority), previously deployed or first-timers (FirstTimer), and previous deployment (or not) of other family members (FamDeployed).

In the before-mission questionnaire, we asked the soldiers to give their subjective evaluation of the probability of experiencing combat during the mission, recorded in the variable ProbSub ranging from 0 to 100. The military administrative records indicated whether soldiers had returned before the end of any previous mission for any reasons, e.g. being wounded or having psychological problems (Returnee_previous), and their average monthly gross earnings during the mission (Earnings). The intensity of combat exposure was measured via the Deployment Risk and Resilience Inventory (D.R.R.I.) (King et al. 2006), whose combat items were scored and summed, so that a higher score reflects higher intensity during any previous missions (Intensity_previous).

Finally, in the 'after' questionnaire, the D.R.R.I. is used to measure the Intensity of combat exposure for the current mission and to define the variable Combat if soldiers positively 5 The before-mission response rate is approximately 82-86% and the after-mission rate is 99%. Danish soldiers' average mission lasts six months. However, differing deployment periods mean that some soldiers may be absent at mission preparation, debriefing, or both -e.g. while most soldiers are deployed for six months, mechanics return after only four months. Furthermore, some of our soldiers returned earlier for medical or personal reasons, and one was killed in action (K.I.A.). Most returned to Denmark less than one month before responding. 6 Although experiencing combat could have prevented soldiers from answering both questionnaires, 75% of the wounded answered them. In Tables S.1 and S.2 in Supplementary Appendix A, we test for the bias in nonanswering the 'after' questionnaire (attrition) and find no differences in the central variables of our analysis. While t-tests show that the variables age, seniority in the army and having children are significant, the F-test for joint significance cannot reject the null hypothesis that attrition is random. Furthermore, an attrition probit model test (Fitzgerald, Gottschalk, and Moffit 1998) cannot reject the null hypothesis that attrition is random for the variables in Tables S1 (p-value=.331) and S2 (p-value=.2147). Finally, the pooling tests (according to Becketti et al. 1988) similarly show that we cannot reject the null hypothesis that attrition is random (with respective p-values of .41 and .21). Thus we do not expect attrition to constitute a major threat for our findings. 7 As expected, the equality tests between average characteristics of exposed and non-exposed soldiers show very significant differences, ruling out the exogeneity of combat exposure. As Table S.4 in Supplementary Appendix A shows, soldiers can predict the probability of combat but not its intensity.

answer one of its combat items. We measured P.T.S.D. symptom severity by using the P.T.S.D. checklist (P.C.L. 4, [START_REF] Weathers | Psychometric Review of PTSD Checklist (PCL-C[END_REF] of 17 items directly adapted from the Diagnostic and Statistical Manual of Mental Disorders IV, P.T.S.D. Criteria B-D (see Supplementary Appendix B). On a 5-point scale with anchors ranging from 1 ('not at all') to 5 ('extremely'), respondents are asked to rate how severely the problem has affected them in the last month. We summed all 17 items for a total P.T.S.D. severity score ranging from 17 to 85.

Appendix Table 1 shows that respondents are about 29 years old on average; 60% have a partner but only 21% have children; less than one-third have completed basic education (9th grade U.S. or first cycle secondary school); and almost 40% come from a family with divorced parents. The soldiers have been in the armed forces for six years on average, 27% have previously deployed family members, 1.4% are previous returnees, 33% are first-timers and their before-mission subjective evaluation of the probability of combat involvement is 74%. The soldiers declare an average P.T.S.D. of 26 for this mission, 56% have experienced combat and the average anticipated combat intensity for this mission is lower than the intensity of previous combat experienced (2.094 vs. 2.552). Figure S.1 in Supplementary Appendix A shows that the number of dead or wounded soldiers from missions in Afghanistan since 2002 far exceeds the number from the I.S.A.F. 11 mission.

Before-and-After Control Variables

We also applied before-and-after measurements to two personality traits from the Big Five Inventory (John, Donahue, and Kentle 1991;John, Naumann, and Soto 2008): neuroticism, a tendency to worry excessively (Neuroticism, on a 1-5 scale), and conscientiousness, a tendency to plan and think carefully before acting and to be self-disciplined, punctual, reliable and competent (Conscientiousness, on a 1-5 scale). We also included a variable indicating degree of control over life events (Control, on a 0-4 scale) [START_REF] Rotter | Generalized Expectancies for Internal versus External Control of Reinforcement[END_REF]. Appendix Table 2 shows that the personality trait variables are on average relatively stable.

Finally, we collected data on the self-reported risk attitude and Wealth variables beforeand-after-mission. We asked the soldiers whether, compared to the general Danish population, they saw themselves as more or less exposed to five different types of risk in their daily lives in Denmark: traffic accidents, physical assault, disease, unemployment and natural disasters [START_REF] Chanel | Approche socio-anthropologique et économique de la pollution atmosphérique: Une application au département des Bouches-du-Rhône[END_REF]. Each risk assessment ranges from 'much less exposed' to 'much more exposed' (on a 1-5 scale), and the variable RiskExposure sums up these 5 scores (on a 5-25 scale). The variable PhysicalRiskExposure is a sub-variable only for the risk of physical assault (on a 1-5 scale). Appendix Table 2 shows an increase in both the Wealth and the risk attitude variables on average.

Risk, Time and Occupational Preferences

We collected risk, time and occupational preference variables (see Table 1 for summary statistics). Given the self-completed paper and pencil questionnaire, overly complex or interactive elicitation designs were not feasible. In the spirit of Falk et al. (2018), we employed both quantitative choice questions and qualitative self-assessment.

[Table 1 about here] Risk aversion is measured in two ways. First, with a certainty equivalent task in the following lottery (see Etchart-Vincent and l'Haridon 2011; or Kachelmeier and Shehata 1992):

"You get the opportunity to buy a ticket in a lottery. There are 10 people in the lottery. The prize is worth DKK 20,000 (EUR 2,667) and the winner of the lottery is found by drawing lots, i.e. everyone has an equal chance of winning. What price are you willing to pay for a ticket in this lottery?"

The variable RiskAver categorises the soldiers according to their willingness to pay (W.T.P.) for a ticket compared to the expected gain (EUR 266.7), from 1 (low risk-aversion, W.T.P. higher than expected gain) to 4 (high risk-aversion, W.T.P. lower than 2.5% of the expected gain).

Second, we also asked soldiers whether they perceived themselves more as someone who wants to avoid risks or as someone who does not mind taking risks to achieve something in life (see [START_REF] Arrondel | Le questionnaire de l'enquête Insee-Delta: Comportements face au risque et à l'avenir[END_REF] or the qualitative assessment of Falk et al. 2018). The variable RiskLover ranks answers from 1 ('I'd rather avoid risks') to 10 ('I do not mind taking risks'). Falk et al. (2018) reported that this measure is a valid predictor of risktaking behaviour in the field and in experiments.

To measure the soldiers' attitude towards risk tolerance, we used the following gainsand-losses question (see Grable and Lytton 1999):

"Given the best and worst case returns on the four investment choices below, which would you prefer?"

Check one box only The variable RiskTolerance ranks answers on a scale from 1 to 4, with 1 meaning low risk tolerance and 4 meaning high risk tolerance.

A
To measure time preferences, we used an intertemporal ascending choice sequence with 7 levels, simpler than the staircase method used in Falk et al. ( 2018) but very similar to the questions used in [START_REF] Barsky | Preference Parameters and Behavioural Heterogeneity: An Experimental Approach in the Health and Retirement Study[END_REF]), Dohmen et al. (2010) and Fuchs (1982):

"Imagine that when you come back from your mission, you receive a tax-free bonus, DKK100,000 (EUR 13,333) The variable Impatience is ranked from 0 to 7, 0 being a low preference for the present (patience, option B always checked) and 7 being a high preference for the present (high impatience, option A always checked).

Finally, we measure preferences for future career in the military by asking the following in both questionnaires: "As for the future, where will you be in your working life in 5 years?"

The variable CareerPerspective ranks answers as do not know or other (coded 0), return to civilian life (education or job, coded 1), short-term contract in the army (coded 2), military education (coded 3), and long-term contract in the army (coded 4), and indicates the will to stay in the military. We ranked a military education higher than a short-term contract because seeking longer military training presumably reflects greater commitment to the military.

Emotion-related and A.F.E. Variables

The before-and-after survey data also yielded information on anticipated, and -for those exposed to combat -experienced emotions relative to combat (see Table 2 for summary statistics). We collected data for three emotions known to be related to risk aversion and valuable in the military context: Fear, Anxiety and Excitement. All three are measured on a 0-4 scale ranging from 0 ('not at all') to 4 ('certainly'). Excitement may capture a form of arousal similar to that of anger but more pertinent to the combat situation [START_REF] Braender | Adrenalin Junkies: Why Soldiers Return from War Wanting More[END_REF]. Hence, according to psychological classifications, we have two unpleasant emotions and one pleasant emotion [START_REF] Russell | A Circumplex Model of Affect[END_REF]. For each of them, the A.F.E. is computed as the difference between anticipated emotion and emotion actually experienced. On average, we find positive A.F.E. regarding the three emotions, the highest for Fear and the lowest for Excitement.

[Table 2 about here] Figure 2 indicates that tiny aggregate before-and-after changes can hide noticeable individual changes in preference as well as emotion variables. However, the modal category is 0 (i.e. no change), except for AFE_Fear with a modal category of 2 (i.e. a small overestimation).

[Figure 2 about here]

Soldier-level Validity, Consistency and Correlations

We now investigate the soldier-level validity of the between-soldier responses (see Appendix A), the consistency of the within-soldier responses (see Appendix B) and the correlations in A.F.E.s and changes in preferences (see Appendix C). We find pairwise correlation coefficients consistent with expectations among the four variables related to time and risk preferences as well as among the personality trait variables, both before-and after-mission (see Tables A.3 and A.4 in Appendix). To assess the consistency of the answers over the seven-month period (January to August 2011), we investigate individual changes at soldier level for preferences (see Table B.5 in Appendix). We find positive and significant correlations for risk preference variables (between .46 and .49) and Impatience (.35) -in the same range as those found in the literature -and for CareerPerspective (.65). Beforeand after-mission equality tests consistently show non-significant changes in RiskTolerance, Impatience and CareerPerspective, an increase in RiskAver and mixed results for RiskLover.

The three emotion variables show positive A.F.E., with lower correlation (around .21) for Fear and Excitement than for Anxiety (.35) (lower part of Table B.5 in Appendix B). These values, of the same order of magnitude as those reported by Coteţ and David (2016), provide evidence that after-mission emotions are both imperfectly predicted and largely overestimated. The magnitude of the values suggests that the I.S.A.F. 11 mission apparently went better than the soldiers expected, producing fewer negative emotions.

Finally, we provide results based on the pairwise correlation matrix between the A.F.E.s and the changes in preferences (Appendix C). As expected, we find some significant correlations among the A.F.E.s, as well as among the changes in preferences. For example, changes in RiskTolerance and RiskAver are significantly negatively correlated. The correlation between A.F.E. and changes in preferences is significantly negative between AFE_Excitement and RiskAver_dif (p-value=.0415), and positive between AFE_Fear and RiskAver_dif (p-value=.0715) and RiskTolerance_dif (p-value=.0967).

Overall, in line with the literature, the soldiers' answers are found to be consistent with expectations, their preferences are stable over the seven-month period and sufficient beforeand-after changes appear for the A.F.E. hypothesis to be tested.

Methods

We test our hypothesis that A.F.E.s predict changes in individual preferences by investigating the stability of preferences under an E.E: combat exposure. We use a within-subject design in which preferences are elicited for the same individual before and after the mission.

Since A.F.E.s are defined as differences, we explore their relationship with changes in preferences as: Because X may simultaneously affect DP and AFE_E with potential endogenous issues, we test the A.F.E. hypothesis in a three-step procedure inspired by [START_REF] Robinson | Root-N-consistent Semiparametric Regression[END_REF]'s partially linear regression. 8 In the first two steps of this residual-on-residual approach, the effect of X is successively removed ('partialled out') from DP and AFE_E. The third step explores the relation between DP and AFE_E based on the residuals computed from the first two step regressions, which are by construction uncorrelated with X. 9Based on the emotional process (see Figure 1), a first step explains preferences before and preferences after by factors likely to influence preferences, in a simultaneous equation model. These factors include individual characteristics and personality traits (which come into both equations), a covariance term to account for correlation between the two dependent variables and equation-specific controls. First, as immediate emotions (e.g. anticipatory emotions) influencing preferences before and after a mission may be different due to a change in the soldiers' psychological state, we use expectations of exposure to combat (ProbSub) and anticipated emotions (E) about combat as proxies for the psychological state before the mission, while we use the P.T.S.D. score (PTSD) and a dummy for having been exposed to combat (Combat) as measures of the psychological state after the mission. Second, changes in wealth and risk perception may affect preferences. We thus add Wealth and PhysicalRiskExposure to the equation explaining preferences before and add the after-before change in these variables to the equation explaining preferences after. The following system corresponding to the first step is estimated for the full sample at soldier level:

DP=fAFE_E + dX + e with E[
Step 1 𝑃 = 𝑎 ! + 𝑎 " 𝑃𝑟𝑜𝑏𝑆𝑢𝑏 + 𝑎 # 𝐸 + 𝑎 $ 𝑃ℎ𝑦𝑠𝑖𝑐𝑎𝑙𝑅𝑖𝑠𝑘𝐸𝑥𝑝𝑜𝑠𝑢𝑟𝑒 + 𝑎 % 𝑊 & + 𝑎 ' 𝑋 + 𝜀 " (1a) 𝑃_𝑎𝑓𝑡𝑒𝑟 = 𝑏 ! + 𝑏 " 𝑃𝑇𝑆𝐷 + 𝑏 # 𝐶𝑜𝑚𝑏𝑎𝑡 + 𝑏 $ ∆𝑃ℎ𝑦𝑠𝑖𝑐𝑎𝑙𝑅𝑖𝑠𝑘𝐸𝑥𝑝𝑜𝑠𝑢𝑟𝑒 + 𝑏 % ∆𝑊 & +𝑏 ' 𝑋 + 𝜀 # (1b)
where P is the preference, E is the emotion, X controls for soldiers' characteristics measured before the mission, and ɛ1 and ɛ2 are error terms with covariance 𝜎 ( ! ( " .

We then compute the residuals of the change in preferences e D(∆P) ≡ (𝜀 # I -𝜀 " I ) from (1a)-(1b) for the whole sample, for use as dependent variable in the third step. The second step regresses AFE_E on actual intensity of combat exposure and soldiers' characteristics X. 10 Indeed, the change in emotion is based on i) E_after, which depends on the intensity of the combat exposure, and ii) the anticipated emotion E, which was based on expected intensity of combat exposure rather than actual intensity. Consequently, we estimate the following equation for those soldiers involved in combat (because E_after is unknown for non-combatants).

Step 2: 𝐴𝐹𝐸_𝐸 = 𝑐 ! + 𝑐 " 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 + 𝑐 # 𝑋 + 𝜂 (2) We then compute the residuals of the change in emotions for combatants, e D(𝐴𝐹𝐸_𝐸) ≡ 𝜂̂ and set residuals to zero for non-combatants (because their A.F.E. is null). 11 The third step uses the residuals estimated in steps 1 and 2 to account for endogeneity by estimating the following residual-on-residual regression for the entire sample:

Step 3: e D(∆𝑃) = 𝑑 ! + 𝑑 " e D(𝐴𝐹𝐸_𝐸) + 𝑑 # 𝐶𝑜𝑚𝑏𝑎𝑡 + 𝜉 (3) with the variables as previously defined and where 𝜉 is the error term. The parameter of interest is 𝑑 S " , whose sign and significance represent A.F.E.'s impact on the change in preferences. Figure 3 summarises the empirical approach.

[Figure 3 about here] To account for the additional variances of the first-and second-step estimates, which feed the third step with estimated rather than measured variables, we need to correct the standard errors of the third-step estimates (see details in Supplementary Appendix C).

Finally, we consider the possibility that the change in preferences is due to a direct effect of trauma for which we use the P.T.S.D. score as a proxy. Because PTSD could result from selection, an Instrumental Variable (I.V.) approach in which combat intensity would only affect changes in preferences through PTSD is conceivable (Intensity and PTSD are indeed significantly and positively correlated, with p-value=.0002). However, we cannot rule out the possibility that Intensity affects preferences in ways other than via PTSD (exclusion restriction). We therefore favour a reduced form model of an effect of trauma on the change in preferences and use Intensity, to test a direct effect of PTSD.

We first test whether combat intensity is exogenously distributed in the sample. According to high-ranking Danish officers, forecasting the probability of the soldiers' being involved in an exchange of shots or a rocket attack, along with the intensity of this exposure, is 10 As the post-emotions (E_after) are known only for combatants, we cannot estimate a system of equations on the entire sample, with instrumental variables to account for the endogeneity issues. Excluding X from Eq.

(2) does not change our results (not shown). 11 To check the robustness of our results to this assumption of null A.F.E. for non-combatants, we will also estimate step 3 on combatants alone (see results in Table 3).

very difficult for those assigning soldiers to daily missions. The random aspect of high combat intensity exposure is explained mainly by the unpredictability of the war against the Taliban: combat exposure in the form of ambush, improvised explosive devices, or an exchange of shots is as good as randomly distributed within and between units. Moreover, soldiers are not on duty every day, and both daily missions and leave schedules are rotated among the troops. All these factors make the risk of exposure to intense combat -resulting in being K.I.A., wounded or a returnee -exogenous. We estimate a linear probability model explaining the intensity of combat (Intensity) with several explanatory variables, including military variables: 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 = 𝛼 ! + 𝛼 " 𝑃𝑟𝑜𝑏𝑆𝑢𝑏 + 𝛼 $ 𝑋 + ω (4a) Second, we test whether trauma (proxied by after-mission soldiers' P.T.S.D. score or Intensity of combat score) affects preferences for the full sample: Δ𝑃 = 𝛽 ! + 𝛽 " 𝑃𝑇𝑆𝐷 + 𝛽 # 𝑋 + 𝑢 (4b) ∆𝑃 = 𝛾 ! + 𝛾 " 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 + 𝛾 # 𝑋 + 𝑣 (4c) where u and v are error terms.

Results

Testing the A.F.E. Hypothesis

To test how A.F.E.s impact changes in preferences, we apply the three-step strategy for each of the 15 pairs of emotions and preferences, for two sets of soldiers' characteristics X (including or not including personality traits) and for two samples (combatants only or all soldiers with A.F.E. set to zero for non-combatants).

Table 3 shows the results for the pairs for which the A.F.E. hypothesis was verified. We find a significant and positive effect of A.F.E. regarding Fear on RiskTolerance (p-value between .0084 and .0315): the more a soldier has over-estimated being afraid, the more his RiskTolerance increases after the mission. We find a significant and positive effect of A.F.E. regarding Fear on Impatience (p-value between .0373 and .0689): over-estimating Fear increases Impatience after the mission. Finally, we find a significant and positive effect of A.F.E. regarding Excitement on CareerPerspective (p-value between .0211 and .0408): overestimating Excitement increases CareerPerspective after the mission, i.e. the will to stay in the military. To test whether first-timers react differently to A.F.E.s, we also apply the three-step strategy separately to first-timers and non-first-timers. As expected, compared to soldiers previously deployed, first-timers' RiskTolerance and Impatience are consistently impacted more by A.F.E.s in absolute terms. However, the results are never significant, likely because the smaller sample sizes (n= 72 to 75 observations in step 3) yield lower precision. Nevertheless, this finding suggests a greater impact of A.F.E. for the first-timers, unable to take advantage of a learning effect. Overall, we consistently find that A.F.E. plays a significant role in explaining changes in preferences: A.F.E.s regarding fear affect risk tolerance and impatience while A.F.E.s regarding excitement affect career perspectives.

[Table 3 about here] Our estimates in Table 3 fulfil the standard OLS requirements (exogeneity by construction, use of robust variance estimates in the presence of heteroscedasticity and verified normality of the residuals). Their consistency and asymptotic normality rely on accurate estimates in equations ( 1) and (2) (see formal condition in Wager 2021). Estimates in Table 3 are coherent with the signs of the pairwise correlations in Appendix C.12

Testing a Direct Effect of Trauma on Preferences

The changes in preferences could be due to the relief of experiencing less intense combat and no trauma. We therefore test the direct effect of trauma, proxied by the post-mission intensity of combat / P.T.S.D. score, on the changes in preferences.

The exogeneity of combat intensity (Intensity) among soldiers' characteristics is shown in Table S.4 in the supplementary Appendix: the F-statistics for combat intensity are small and the p-value>.2, thereby confirming that before-mission soldiers' characteristics cannot predict the intensity of combat.

Table 4 then presents regression coefficients for the relations among combat intensity, PTSD and changes in preferences. OLS regressions (Panel A) and reduced-form regressions (Panel B) show no significant effect on preferences. The absence of a direct effect of trauma on the changes in preferences is likely due to the low scores for P.T.S.D. 13 As previously mentioned, combat exposure and number of casualties for the I.S.A.F. 11 mission were relatively lower than in earlier and later missions. We therefore estimated equation (4b) replacing the P.T.S.D. score by binary variables based on different thresholds for PTSD (e.g. greater than 30, corresponding to 28% of the sample). The effect remains insignificant.

[Table 4 about here]

Discussion

Using a sample of combat soldiers deployed to Afghanistan in 2011, we test the hypothesis that A.F.E. affects time, risk and occupational preferences under E.E.s. We find very significant positive before-and-after mission correlations for preferences and emotions. These results confirm the stability of these variables at the individual level, at least in the short term. We observe significant positive A.F.E., suggesting that soldiers learn that they are not as sensitive to emotion as they thought. As a result, they become more risk-tolerant and impatient, and are more likely to plan to stay in the military. A.F.E. regarding combat apparently affects behaviour with respect not only to the military, but also to risk and time preferences. Moreover, we do not find evidence supporting a direct impact of trauma on changes in preferences.

While empirical findings on preference stability after an E.E. (natural disasters or violent conflicts) are mixed (Golsteyn and Schildberg-Hörisch 2017; Schildberg-Hörisch 2018), our paper exploits an elicitation of emotions before and after an E.E. to shed light on the emotional origin of changes in preference: A.F.E. Our findings enhance scholarly understanding of preference changes due to exposure to other E.E.s, whether naturally caused (e.g. by flood or earthquake) or human-caused (e.g. by auto accidents or terrorist attacks). However, we acknowledge that a combat mission is undertaken voluntarily, while most other E.E.s do not usually involve choice.

In many countries, however, an increasing number of soldiers and private security forces are participating in international security operations. Hence information on preferences is of obvious value for policy, theory and empirical analysis when measuring the welfare impacts of such operations. Policy applications including cost-benefit analysis of military deployments often involve making welfare calculations over life paths, with uncertain impacts spread over time. The impact of military experience may change the daily behaviours and preferences of recruits, and explain differences in veterans' and non-veterans' later achievements. Moreover, a number of other studies have found long-lasting effects on decision-making after exposure to combat (Elder and Clipp 1989;Malmendier, Tate, and Yan 2011), violence [START_REF] Bucciol | The Shadow of the Past: Financial Risk Taking and Negative Life Events[END_REF]Kim and Lee 2014) or natural fatal disasters [START_REF] Bernile | What doesn't Kill you Will Only Make you More Risk-Loving: Early-Life Disasters and CEO Behaviour[END_REF]de Blasio et al. 2021). Such changes may lie behind a behavioural change that could substantially impact both individuals and society at large.

Our analysis has several limitations. First, in addition to anticipation errors and potential adjustments, soldiers may also be subject to a recall bias about their emotions during combat. Particular episodes during the mission, e.g. peaks or end-of-mission events, may dominate the memory of the emotion experienced (Fredrickson and Kahneman 1993;[START_REF] Ochsner | Are Affective Events Richly Recollected or Simply Familiar? The Experience and Process of Recognizing Feelings Past[END_REF][START_REF] Redelmeier | Memories of Colonoscopy: A Randomized Trial[END_REF]. 14 Second, as soldiers are not necessarily representative of the general population, the results may not be generalisable to other groups, or our findings could be specific to I.S.A.F.11 soldiers, whose P.T.S.D. scores were not high. Nevertheless, soldiers constitute a useful sample for studying stability in preferences, because the stakes (particularly where combat is involved) are much higher than for participants in laboratory experiments, where stimuli do not necessarily mimic real life (Al-Ubaydli, List, and Suskind 2017). Moreover, despite the absence of incentives, our survey should yield reliable answers because it was conducted in a formal setting (military fort) in the presence of high-ranking officers, thereby imparting a certain solemnity and commitment to the task. Furthermore, given that the survey forms were anonymized, the soldiers had no motivation to lie about their own emotions and decisions. The consistency of our results with those of previous studies also confirms this reliability. A third limitation is that these soldiers were clearly expecting the E.E., which raises the question of whether the A.F.E. hypothesis is generalisable to an unexpected E.E. In other words, can people also anticipate the emotions they would feel in an unexpected E.E., and can these emotions be compared with those they actually feel when it occurs?

A valuable future step would be to identify the mechanism underlying the A.F.E. effect. We have suggested two possible learning effects. First, soldiers may have discovered that they were mistaken when predicting future events and that they had forecast their emotions on inaccurate stimuli. Second, soldiers may have discovered that their emotional response to an E.E was not what they expected, leading them to revise their self-perception of emotional sensitivity. Another possibility is that A.F.E may change the evaluation criteria. This explanation is in line with Braender (2020)'s observation that, while the thrill of the danger appeared the most important motivating factor before the mission, the experience of actual combat became the most important on return. Thus, after discovering that combat did not produce the anticipated level of excitement, soldiers may have reduced the importance of this excitement criterion and perhaps increased the value of other criteria motivating them to remain in the army. However, we cannot exclude a non-A.F.E. mechanism: since soldiers recall their most recent emotions when they forecast their emotions, changes in preference might depend directly on the emotions experienced rather than on A.F.E.s. Unfortunately, our data do not permit us to disentangle all these mechanisms.

It would also be interesting to directly test change in affective forecasting after an A.F.E., as the learning mechanism we propose should go hand in hand with reduced A.F.E. due to experience. This suggestion is borne out by the higher A.F.E.s for our subsample of firsttimers, although not significant because of a lack of statistical power. Previous results suggest the persistence of A.F.E.s, as people are unable to remember their forecasts; however, those findings concerned events far less extreme than combat [START_REF] Meyvis | Why don't we Learn to Accurately Forecast Feelings? How Misremembering our Predictions Blinds us to Past Forecasting Errors[END_REF].

Finally, soldiers may not be the only people whose preferences are affected by inaccurate affective forecasting. Since learning through E.E is costly, finding less extreme ways to make people better at forecasting their emotions would be a valuable subject for future research. .544 Note: a P-value of bilateral equality test with unequal variance, * p < 0.1, ** p < 0.05, *** p < 0.01. We estimated an OLS with all the variables and a dummy for 'answering only "before"' as the dependent variable and we obtain an F-test for joint nullity of 1.16 (p-value =.30). We estimate an attrition probit model (Fitzgerald, Gottschalk, and Moffit 1998) explaining the attrition variable (only answering 'before') with all the variables from Table S1. The Wald test of joint nullity of all coefficients Chi-squared (15)=16.80 (p-value=.3310) cannot reject the randomness of attrition. The pooling test due to Becketti et al. (1988) also confirms that we cannot reject the null hypothesis of attrition being random (p-value=.41). .204 Note: a P-value of bilateral equality test with unequal variance, * p < 0.1, ** p < 0.05, *** p < 0.01. We estimated an OLS with all the variables and a dummy for 'answering only "before"' as the dependent variable and we obtain an F-test for joint nullity of 1.32 (p-value= .21). We estimate an attrition probit model (Fitzgerald, Gottschalk, and Moffit 1998) explaining the attrition variable (answering only 'before') with all the variables from Table S2. The Wald test of joint nullity of all coefficients Chi-squared (11) =14.34 (p-value=.2147) cannot reject the randomness of attrition, as does the pooling test due to Becketti et al. (1988) (p-value=.214). The F-statistics test the hypothesis that all explanatory variables are jointly non-significant. P-values of the F-statistics are reported. The columns contain coefficients and robust standard errors (in parentheses) from OLS regressions. Similar results are obtained with a logistic regression for Combat (details upon request). All the variables are before-mission and the regressions also control for the soldier's unit. * p < 0.05, ** p < 0.01, *** p < 0.001.

  e |X, AFE_E]=0 where P denotes preferences (Impatience, RiskAver, RiskTolerance, RiskLover and CareerPerspective), AFE_E denotes A.F.E. regarding emotions E (Fear, Anxiety and Excitement), X controls for soldiers' characteristics, D is the after-and-before mission difference and E[.|.] the conditional expectation operator. However, if AFE_E is not exogeneous conditional on X, E[AFE_E |X] ¹0 which makes E[e|X] ¹0 and standard estimates of f are biased.

Note:

  Rectangles represent events, mental states and decisions, while ovals represent psychological processes. The continuous lines indicate relationship and the dotted lines show how the A.F.E. is formed.

Figure 1 Figure 2

 12 Figure 1 Summary of the Different Emotional Processes Considered

Figure S. 1

 1 Figure S.1 Number of dead, wounded, returnees from Danish participation in ISAF missions

  50% chance of winning DKK 1,500 and a 50% chance of winning nothing.……

	4

1

A 50% chance of winning DKK 6,000 and a 50% chance of losing DKK 1,500 .… 2 A 50% chance of winning DKK 19,500 and a 50% chance of losing DKK 6,000…..

3

A 50% chance of winning DKK 36,000 and a 50% chance of losing DKK 18,000.…

Table 1

 1 Time and Risk Preference Characteristics of the Sample (n=355)

	Variables

Note: Obs.: Observations, St. Dev.: Standard deviation.

Table 2

 2 Emotion Characteristics of the Sample (n=355) Obs.: Observations, St. Dev.: Standard deviation.

	Variables

Table 3

 3 Testing Affective Forecasting Error Effect on Changes in Risk, Time and Occupational Preference Variables

			RiskTolerance and AFE_Fear	Impatience and AFE_Fear	CareerPerspective and AFE_Excitement
	AFE (d1)	.1402 **	.1850 ***	.1413 **	.1823 **	.3553	.4118 **	.3548	.4130 **	.1772 **	.2021 **	.1752 **
		(.0292)	(.0084)	(.0315)	(.0121)	(.0574)	(.0373)	(.0689)	(.0481)	(.0334)	(.0211)
	Combat (d2)	.0960	.0807	-	-	.01157	.0571	-	-	.0758	.0560
		(.5341)	(.6210)	-	-	(.9769)	(.8892)	-	-	(.6957)	(.7747)

  Note: P-values in parentheses: *** p<.01, ** p<.05, * p<.10. Soldiers' characteristics X are: earnings, age, age square, couple, parent divorced, children, education (3 modalities), first-timer, family deployed member, seniority and unit level (8 modalities). Personality traits are conscientiousness, neuroticism and control. Robust standard errors in parentheses have been corrected for both 2-step estimations and predicted dependent variable (see Supplementary Appendix C for details).

		**	2.179	5.705 ***	8.074 ***	4.423 **	2.767 *	4.203 **	5.326 ***	2.751 *	3.171 ***	5.053 ***	6.011 ***
		(.0482)	(.116)	(.0043)	(.0005)	(.0133)	(.0655)	(.0173)	(.0062)	(.0664)	(.0044)	(.0079)	(.0033)
	Adjusted-R2	.01695	.0157	.0268	.0461	.0307	.0244	.0377	.0509	.0139	.0173	.0283	.0345
	Observations	191	182	118	113	191	182	116	111	190	183	116	111

Table 4

 4 Combat Intensity. P.T.S.D. and change in Time, Risk and Occupational Preferences Note: p-value in parentheses: *** p<.01. Soldiers' characteristics are: earnings, age, age square, couple, parent divorced, children, education (3 modalities), first-timer, family deployed member, seniority, changes in wealth and risk perception, conscientiousness, neuroticism, control, and unit level (8 modalities). An I.V. model instrumenting PTSD with Intensity leads to similar conclusions (details available upon request).

	Preferences	RiskAver RiskToleran	Impatienc	RiskLover CareerPerspe
			ce	e		ctive
	A. O.L.S. Regressions: Dependent is change in preferences
	P.T.S.D. score (17-85)	-0.0031	-0.0025	0.0030	-0.0172	-0.0167
		(.769)	(.779)	(.872)	(.210)	(.110)
	Adjusted R2	0.0554	0.0292	-0.0108	0.0062	-0.0519
	B. Reduced-Form regressions: Dependent is change in preferences
	Intensity	0.0169	-0.0228	-0.0265	0.1643	0.0027
		(.694)	(.617)	(.850)	(.191)	(.961)
	Adjusted R2	0.0254	0.0349	-0.0303	-0.0001	-0.0684

Table A .

 A 3 Before-mission Pairwise Correlations among Risk and Time Behavioural Variables Note: P-values in parentheses, number of observations in italics. *** p<.01, ** p<.05, * p<.10.Table A.4 After-mission Pairwise Correlations among Risk and Time Behavioural Variables Note: P-values in parentheses, number of observations in italics. *** p<.01, ** p<.05, * p<.10. In each cell, the result of the test is given along with p-values in parentheses (bilateral for correlation and equality tests when equality is not rejected, unilateral otherwise). KS for Kolmogorov-Smirnov. Non Rej. for non-rejection of equality test. *** p<.01, ** p<.05, * p<.10. a Controls in regressions explaining the after-mission variable by the corresponding before-mission variable include earnings, age, age square, couple, parent divorced, children, education (3 modalities), first-timer, family deployed member, seniority and unit level (8 modalities). Regressions are estimated with robust standard errors. Table C.6 Pairwise Correlations among Changes in Emotion and Risk and Time Behavioural Variables Table S.1 Socio-demographic (all Before-mission) and Military Characteristics of the Database

				SUPPLEMENTARY APPENDIX
	RiskTolerance Impatience 0.0745 (0.1796) 326 -0.2229 *** (0.0000) 327 -0.0866 (0.1146) 333 0.2386 *** (0.0000) 0.0953 * (0.0805) RiskTolerance Impatience RiskAver RiskLover Conscientiousnes RiskAver RiskLover Conscientious ness Neuroticism -0.0925 * (0.0881) s Neuroticism 0.1066 * (0.0561) 322 -0.2155 *** (0.0001) 321 -0.0574 (0.3019) 326 0.2060 *** (0.0002) 324 0.1165 ** (0.0344) 330 -0.0385 (0.4830) 334 Conscientiousne Impatience RiskAver RiskLover Impatience RiskAver RiskLover ss 0.0069 (0.9023) 323 -0.1006 * (0.0687) 328 -0.0648 (0.2396) 331 0.0813 (0.1313) 346 Neuroticism -0.0461 (0.4107) 321 0.0731 (0.1874) 327 0.0528 (0.3380) 331 -0.1488 *** (0.0057) 344 -0.4408 *** (0.0000) 342 Control 0.0626 (0.2659) 318 -0.1198 ** (0.0316) 322 -0.1033 * (0.0632) 324 -0.0557 (0.3106) 333 0.1892 *** (0.0005) 331 -0.3040 *** (0.0000) 329 Table B.5 Stability Between Before-and-After Mission Variables Before-and-after mission correlation Before-and-after mission equality tests of … Variables Pairwise Corre lation Regression coeffi cient a Mean (paired data) Median Mean rank (Wilc oxon) KS test Risk, Time and Occupational Preferences RiskTolerance n=316 .4647 *** (<.0001) .4649 *** (<.0001) Non Rej. (1.000) Non Rej. (.5152) Non Rej. (.5078) Non Rej. (.937) Impatience n=324 .3544 *** (<.0001) .3579 *** (<.0001) Non Rej. (. 9285) Non Rej. (.9999) Non Rej. (.9405) Non Rej. (.813) RiskAver n=330 .4732 *** (<.0001) .4715 *** (<.0001) Higher ** (.0490) Higher ** (.0168) Higher ** (.0335) Non Rej. (.275) RiskLover n=347 .4912 *** (<.0001) .4645 *** (<.0001) Non Rej. (.1028) Higher** (.0305) Higher* (.0801) Non Rej. (.435) CareerPerspectiv e n=333 .6489 *** (<.0001) .4627 *** (<.0001) Non Rej. (.2388) Non Rej. (.5856) Non Rej. (.4115) Non Rej. (.581) Emotions Fear n=189 .2193 *** (.0024) .2705 *** (.003) Lower *** (<.0001) Lower *** (<.0001) Lower *** (<.0001) Lower *** (<.0001) Anxiety n=186 .3549 *** (<.0001) .3093 *** (<.0001) Lower *** (<.0001) Lower *** (<.0001) Lower *** (<.0001) Lower *** (<.0001) Excitement n=189 .2085 *** (.0040) .0945 (.288) Lower *** (.0016) Lower *** (.0009) Lower *** (.0016) Lower ** (.012) AFE_Anxiety AFE_Excitem ent RiskTolerance_ dif Impatience_dif RiskAver_dif AFE_Anxiety 0.1833 ** (0.0123) 186 AFE_Excitement -0.1770 ** (0.0148) 189 -0.0693 (0.3472) 186 RiskTolerance_dif 0.1267 * (0.0967) 173 0.0475 (0.5382) 170 0.0094 (0.9022) 173 Impatience_dif 0.0627 (0.4073) 177 0.1069 (0.1604) 174 0.0738 (0.3287) 177 0.1679 ** (0.0255) 177 RiskAver_dif 0.1370 * (0.0715) 174 0.0607 (0.4301) 171 -0.1547 ** (0.0415) 174 -0.1686 ** (0.0262) 174 -0.1072 (0.1557) 177 RiskLover_dif 0.0721 (0.3268) 187 0.0013 (0.9863) 184 -0.0246 (0.7379) 187 -0.0029 (0.9697) 178 -0.0819 (0.2702) 183 0.0725 (0.3318) 181 CareerPerspective_dif 0.0708 (0.3452) 180 0.0735 (0.3295) 178 0.0690 (0.3573) 180 0.0349 (0.6473) 174 -0.0226 (0.7654) 177 0.0325 (0.6696) 175 Appendix A All soldiers (n=465) (1) Answer only before (n=110) (2) Answer before and after (n=355) (3) Mean St. Dev. Mean St. Dev. Mean St. Dev. Age (years) 29.166 7.727 30.936 8.744 28.617 7.310 Couple (share: in a relationship) 0.611 0.488 0.636 0.483 0.603 0.490 Children (share: has a child) 0.230 0.421 0.309 0.464 0.206 0.405 EducBasic (share: basic education) 0.280 0.449 0.255 0.438 0.287 0.453 EducYouth (share: youth education) 0.344 0.476 0.345 0.478 0.344 0.476 EducVocat (share: vocational education) 0.234 0.424 0.236 0.427 0.234 0.424 EducFurther (share: further education) 0.129 0.336 0.145 0.354 0.124 0.330 ParentDiv (share: parents divorced) 0.378 0.486 0.391 0.490 0.375 0.485 Seniority (years: seniority in the armed forces) 6.993 6.865 9.041 8.287 6.392 6.277 FamDeployed (share: having previously deployed family members) 0.282 0.450 0.318 0.468 0.270 0.445 FirstTimer (share: not previously deployed) 0.323 0.468 0.309 0.464 0.327 0.470 Returnee_previous (share: has been returnee before this mission) 0.034 0.182 0.073 0.261 0.023 0.149 Earnings (Euros: monthly gross earnings) 6,879 1,964 7,081 2,013 6,816 1,947 Wealth (Euros, before the mission) 13,890 27,360 11,484 14,610 14,636 30,219 Note: AFE_Fear Wounded or killed in combat 0.019 0.138 0.027 0.164 0.017 0.129	RiskLover_dif 0.1393 * (0.0586) 185 Equality test (3) vs. (2 ) a .013 ** .527 .037 ** .497 .973 .956 .572 .761 .004 *** .345 .728 .057 * .226 .156
		329	337	341
	Conscientiou	0.0250	-0.0381	0.0238	0.0672
	sness	(0.6529) 325	(0.4895) 332	(0.6639) 336	(0.2139) 344
	Neuroticism	-0.0580	0.0992 *	-0.0916 *	-0.1308 **	-0.3823 ***
		(0.2991)	(0.0714)	(0.0941)	(0.0152)	(0.0000)
		323	331	335	344	340
	Control	-0.0243	-0.0423	0.0600	0.0127	0.2784 ***	-0.2879 ***
		(0.6637)	(0.4431)	(0.2718)	(0.8154)	(0.0000)	(0.0000)
		323	331	337	342	337	339

Note: P-values in parentheses, number of observations in italics. *** p<.01, ** p<.05, * p<.10.

Table S .

 S 2 Other variables (all Before-mission) of the Database

		All soldiers	Answer only before	Answer before and	Equality
		(n=465) (1)	(n=110) (2)	after (n=355) (3)	test (3)
		Mean	St. Dev.	Mean	St. Dev.	Mean	St. Dev.	vs. (2) a
	ProbSub (%: Subjective probability of combat involvement)	74.731	34.591	76.231	34.178	74.270	34.762	.634
	RiskTolerance (1-4: low-high risk tolerance)	1.991	0.998	1.990	1.005	1.991	0.997	.997
	RiskAver (1-4: low-high risk aversion)	2.927	1.028	2.852	1.040	2.951	1.025	.389
	Impatience (0-7: patient-impatient)	3.285	2.249	3.557	2.277	3.200	2.237	.159
	RiskLover (1-10: feel less-more risk lover)	7.126	1.924	7.255	1.874	7.085	1.940	.414
	CareerPerspective (0-4: low-high will to stay in the military)	2.570	1.332	2.748	1.325	2.516	1.331	.116
	RiskExposure (5-25: less-more exposed to risks in daily life)	11.990	3.313	12.020	3.200	11.981	3.352	.917
	PhysicalRiskExposure (1-5: less-more exposed to risk of physical	2.389	1.009	2.472	1.009	2.364	1.010	.331
	assault)
	Neuroticism (1-5)	2.273	0.536	2.276	0.535	2.272	0.537	.944
	Conscientiousness (1-5)	3.832	0.378	3.838	0.383	3.831	0.377	.875
	Control (0-4)	3.106	0.991	3.000	0.986	3.139	0.992

Table S .

 S 3 Socio-demographic (all Before-mission) and Military Characteristics of the Sample Note: a This score is computed for 190 previously deployed soldiers. b P-value of bilateral equality test with unequal variance, * p < 0.1, ** p < 0.05, *** p < 0.01.

		Full Sample (n=355)	Not exposed to	Exposed to combat	Equality test
				combat (n=156)	(n=199)	Exposed vs. Not
	Variables	Mean	St. Dev.	Mean	St. Dev.	Mean	St. Dev.	exposed b
	Age (years)	28.617	7.310	26.633	5.558	31.147	8.432	<.0001 ***
	Couple (share: in a relationship)	0.603	0.490	0.533	0.500	0.692	0.463	.002 ***
	Children (share: has a child)	0.206	0.405	0.111	0.314	0.327	0.471	<.0001 ***
	EducBasic (share: basic education)	0.287	0.453	0.307	0.462	0.263	0.442	.365
	EducYouth (share: youth education)	0.344	0.476	0.362	0.482	0.321	0.468	.416
	EducVocat (share: vocational education)	0.234	0.424	0.216	0.413	0.256	0.438	.378
	EducFurther (share: further education)	0.124	0.330	0.101	0.301	0.154	0.362	.140
	ParentDiv (share: parents divorced)	0.375	0.485	0.372	0.485	0.378	0.487	.903
	Seniority (years: seniority in the armed forces)	6.309	6.212	4.729	4.240	8.318	7.606	<.0001 ***
	FamDeployed (share: having previously deployed family members)	0.270	0.445	0.312	0.464	0.218	0.414	.046 **
	FirstTimer (share: not previously deployed)	0.327	0.470	0.397	0.491	0.237	0.427	.001 ***
	Returnee_previous (share: has been returnee before this mission)	0.014	0.118	0.015	0.122	0.013	0.113	.857
	Earnings (Euros: monthly gross earnings)	6,816	1,947	7,209	2,294	6,403	1,387	.0018 ***
	Wealth (Euros, before the mission)	14,636	30,219	19,170	37,475	9,814	18,739	.0043 ***
	Wealth_after (Euros, after the mission)	55,785	34,609	62,648	42,174	48,488	21,989	.013 **
	Intensity (0-10: Severity score of this mission)	1.539	1.924	0.839	1.028	3.125	1.462	<.0001 ***
	Intensity_previous (0-10: Severity score of the previous mission) a	2.552	2.540	1.679	2.068	3.501	2.672	<.0001 ***

  Table S.4 Regression Results for Combat Exposure and Intensity of Combat

		(0.0046)	(0.0051)	(0.0009)	(0.0010)
		Intensity of combat exposure	Exposure to Combat (0/1)
	Neuroticism	Coefficient	Coefficient -0.3481	Coefficient	Coefficient 0.0779
		(Standard error)	(Standard error) (0.2553)	(Standard error)	(Standard error) (0.0534)
	Age	0.3162	0.3444	0.0239	0.0070
	Conscientiousness	(0.2032)	(0.2085) -0.4551	(0.0287)	(0.0289) 0.0372
			(0.3577)		(0.0781)
	Age*Age	-0.0069 *	-0.0075 *	-0.0004	-0.0002
	Control	(0.0034)	(0.0034) 0.1697	(0.0004)	(0.0004) 0.0434
			(0.1283)		(0.0283)
	ParentDiv F-statistic	0.0790 1.3378	0.0300 1.1207	0.0110 4.6478	0.0147 4.1538
	F-Stat p-value	(0.2594) 0.2046	(0.2652) 0.3451	(0.0532) 0.0000	(0.0549) 0.0000
	Partial-R2	0.1077	0.1202	0.1824	0.2117
	Couple Observations	0.0255 159	0.0710 152	0.0337 284	0.0385 267
	Note:	(0.2445)	(0.2628)	(0.0555)	(0.0582)
	Children	0.2277	0.2545	-0.0993	-0.0776
		(0.4495)	(0.4532)	(0.0999)	(0.1018)
	EducBasic	0.1797	0.1984	0.0283	0.0220
		(0.3871)	(0.4078)	(0.1058)	(0.1121)
	EducYouth	0.0898	0.1250	-0.0513	-0.0937
		(0.3884)	(0.3967)	(0.1001)	(0.1049)
	EducVocat	-0.0707	-0.0203	-0.0796	-0.0754
		(0.3960)	(0.4122)	(0.0980)	(0.1029)
	FirstTimer	0.0603	0.1003	0.0333	0.0293
		(0.3139)	(0.3065)	(0.0675)	(0.0687)
	Seniority	0.1118	0.1168	0.0081	0.0087
		(0.0614)	(0.0623)	(0.0110)	(0.0119)
	FamDeployed	0.5563 *	0.5615 *	0.0870	0.0987
		(0.2421)	(0.2431)	(0.0528)	(0.0539)
	ProbSub	0.0116 *	0.0099	0.0064 ***	0.0066 ***

As the number of women is too small for reliable statistical inference, we focus on the 355 male soldiers deployed to Afghanistan in combat and logistics units.

This residual-on-residual approach has since been applied in several causal inference analyses to tackle nonlinearity[START_REF] Banerjee | Inequality and Growth: What Can the Data Say?[END_REF], simultaneity (Graham 1999) and endogeneity issues in parametric models(Gallegati et al. 2014), or more recently as double/debiased machine learning in non-parametric models accounting for high dimensional settings[START_REF] Chernozhukov | Double/debiased machine learning for treatment and structural parameters[END_REF]).

 9 This approach is also in the spirit of[START_REF] Wooldridge | Control Function Methods in Applied Econometrics[END_REF]'s interpretation of the control function approach to make endogenous explanatory variables appropriately exogeneous.

The differences between pairwise correlations and estimates in Table3may be driven by two factors. First, pairwise correlations could not properly account for the complex empirical strategy presented in Figure3(particularly the endogeneity problem and the learning effect on the anticipatory emotions). Second, estimates in equation (3) may suffer from a lack of accuracy in equations (1) and (2) as pointed out in Wagner (2021).

A total score of at least 50 is considered to be P.T.S.D.-positive in military populations (44 in the general population).

For example, a soldier was K.I.A. less than one month before the end of the I.S.A.F. 11.

Acknowledgements

This work was supported by the Agence Nationale de la Recherche [grants RISKEMOTION, ANR-2008RISKNAT00701 and ANR-17-EURE-0020] and by the Excellence Initiative of Aix-Marseille University -A*MIDEX; Soldaterlegatet with financial support from Tryg [grant ID119562], Lundbeck, Novo Nordisk, and Aase and Ejnar Danielsen's funds. We thank Dean Lillard and Vincent de Gardelle and an anonymous reviewer for their numerous and valuable comments and suggestions, which helped improve the paper. We also thank participants in the SFI Advisory Research Board Conference, the 2014 Annual Meeting of the Association of Southern European Economic Theorists (ASSET), the 6th Conference of the French Experimental Economics Association (ASFEE) and participants in the CEEM seminar in Montpellier for suggestions on an earlier version, and Marjorie Sweetko and Natalie Reid for their thorough re-reading of the English. We are grateful to the Danish Armed Forces for facilitating data collection.

Declaration of interest statement

No potential conflict of interest was reported by the authors.

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Note. Rectangles represent variables, while ovals represent psychological processes.

Figure 3 Summary of the Empirical Strategy

1.

Repeated, disturbing memories, thoughts, or images of a stressful military experience? 1 2 3 4 5

2.

Repeated, disturbing dreams of a stressful military experience? 1 2 3 4 5

3.

Suddenly acting or feeling as if a stressful military experience were happening again (as if you were reliving it)?

4.

Feeling very upset when something reminded you of a stressful military experience? 1 2 3 4 5

5.

Having physical reactions (e.g., heart pounding, trouble breathing, sweating) when something reminded you of a stressful military experience? 1 2 3 4 5

6.

Avoiding thinking about or talking about a stressful military experience or avoiding having feelings related to it? 1 2 3 4 5

7.

Avoiding activities or situations because they reminded you of a stressful military experience? 1 2 3 4 5

8.

Trouble remembering important parts of a stressful military experience? 1 2 3 4 5

9.

Loss of interest in activities that you used to enjoy? 1 2 3 4 5 10.

Appendix C Standard error correction procedure

Corrections related to a predicted regressor are standard practice [START_REF] Murphy | Estimation and Inference in Two Step Econometric Models[END_REF][START_REF] Greene | Econometric Analysis[END_REF], and those related to a predicted dependent variable have been proposed by, for example, [START_REF] Dumont | Correcting Standard Errors in Two-stage Estimation Procedures with Generated Regressands[END_REF] or [START_REF] Chen | Incorrect Inferences When Using Residuals as Dependent Variables[END_REF]. However, our three-step modelling makes corrections tricky, especially because of the simultaneous equation system in step 1 and the need for both corrections in step 3. To obtain the corrected standard errors, we, thus proceed in two phases. , by drawing 1000 i.i.d. samples in the respective normal distribution N(.). As each observation is only represented once in each of the 1,000 generated samples (no replacement), this sampling method is different from bootstrapping. Second, to provide mean estimates accounting for the additional variance of the dependent variable, we estimate equation (3) on the 1000 generated samples with e D `(∆P ) ≡ (𝜀 2 I \ -𝜀 1 I \ ) as the dependent variable.

The second phase consists in a correction of the standard error of the regressors implemented in step 3, based on their variance-covariance matrix [START_REF] Greene | Econometric Analysis[END_REF]).