Variation in risk seeking behavior in a natural experiment following a large negative wealth shock induced by a natural disaster

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1 Variation in risk seeking behavior in a natural experiment following a large negative wealth shock induced by a natural disaster Lionel Page David Savage Benno Torgler Queensland University of Technology March 13, 2012 Abstract An ongoing challenge in behavioral economics is to understand the variations observed in risk attitudes as a function of their environmental context. Of particular interest is the effect of wealth on risk attitudes. The research in this area has however faced two constraints: the difficulty to study the causal effects of large changes in wealth, and the causal effects of losses on risk behavior. The present paper address this double limitation by providing evidence of the variation of risk attitude after large losses using a natural disaster (Brisbane floods) as the setting for a natural experiment. Most models relying on Expected Utility Theory assume that the utility function is DARA (ref), implying that the view that risk aversion decrease with wealth is predominant among economists. Over the recent years economists have more and more used Prospect Theory (Kahneman and Tversky 1979), the most successful of non Expected Utility models. In this framework, it is the changes in wealth which are the carrier of utility, instead of the wealth itself. A key hypothesis of PT is that people tend to become risk averse after a gain and risk seeking after a loss (at least during the time where the recent changes in wealth are still subjectively perceived as gains and losses ). Experimental economists have developed many techniques to elicit risk attitudes in the laboratory and in the field. However, by design, economic experiments have limitations (Levitt and List 2009). This is particularly true in the case of the study of the effect of wealth on risk attitudes. First, due to budget constraints, stakes are usually small, so no significant change in wealth can be produced in the laboratory. Second, due to ethical constraints, it is not almost impossible to We thank Richard Ebsteing for his very useful comments. 1

2 induce real losses for experimental participants. In practice, most of the experimental literature aiming at measuring risk attitude does not investigate wealth effects. Most often wealth effects within the experiment, when the participant can accumulate rewards, are considered as possible noise in the analysis. This has lead to the adoption of the random lottery incentive where participants, who make several choices during the experiment, are only paid for one of them, at the end (Harrison and Rutström 2008). Kahneman and Tversky suggested in their seminal paper the possible ability of PT to explain changes in behavior after changes in wealth level: A person who has not made peace with his losses is likely to accept gambles that would be unacceptable to him otherwise (Kahneman and Tversky 1979). This suggestion, supported by the notion than gamblers take too much risk to chase their losses is difficult to study in the context of laboratory experiment where ethical rules prevent participants to face real losses. Interestingly, this explanation relies on a lack of adaption of the reference point. The difficult question of the location of the reference point and adaptation to changes in wealth is also something which makes the study of the effect of changes in wealth. Theoretical progress have been made recently to model how a reference point can adapt slowly after a change in wealth (Rayo and Becker 2007), creating the possibility for Kahneman and Tversky suggested behavior. In the present paper, we provide new evidence on the effect of changes in wealth on risk behavior. Specifically, we look at the effect of large losses on risk attitude, shortly after the loss incurred. Relative to the existing literature, our study present two interests: it provides evidence on behavior after losses and it provides evidence on behavior after a large shock in wealth. To do so, We use a natural disaster as the setting of a natural experiment where random shocks in wealth can be observed in a population. Specifically, we explore individual risk attitudes after the 2011 Australian floods (Brisbane). We use the a priori random limit of the flood as a strategy to compare the reaction of very similar populations of home owners around the flood limit where a large difference in wealth shock can be observed between the home owners just affected and those just not affected. Our methodology is close in spirit from a regression over discontinuity, although we do not observe in our case the treatment, ie the feeling of a large loss. We sampled 229 residential home owners in the Brisbane flooded areas following the January 2011 floods. Participants were offered the opportunity to chose between a fixed sum, $10 and a risky gamble, a lottery scratch card potentially worth $500,000. The participants were selected from earthier side of the margin of the flood peak from seventeen suburbs spread across the city and completed a raft of survey questions including several questions on risk, for which they were paid. The survey s were administered in the subjects own homes and only if they were at home on the day the suburb was canvassed. Additionally, the survey collected a range of demographic and personal background information on the home owners and their families. The survey also asked home owners their belief about the value of the house (before and after the flood). Our main finding is that after a large negative wealth shock, those 2

3 directly affected display very different risk behaviors to those who just escaped a direct effect by being much more willing to adopt riskier options in their decision-making process. Individuals whose properties were directly affected by the flood waters were much more likely to accept a risky gamble, the scratch card, than their immediate unaffected neighbors, who were in many cases only meters away from themselves being affected. Our finding clearly supports the predictions of prospect theory with the adoption of risk seeking behavior after a large wealth shock. We contribute to the literature on decision making under risk by providing for the first time experimental evidence on the change in risk attitude induce by a large negative shock in wealth. Our study provides supporting empirical evidence that individuals who have incurred a negative wealth shock are much more likely to accept a risky gamble. The remainder of this paper is organized as follows. Section I presents the literature on the study of risk attitudes in particular when individual face losses. Section II presents the experimental design and the empirical methodology. Section III displays the results and finally Section IV concludes. 1 Background In his 2002 Nobel Laureate lecture, Daniel Kahnman explains how one of the key principle behind Prospect Theory is the rejection of what he calls the Bernouilli s error (Kahneman 2002). Kahneman was referring to the widely used hypothesis in applied economics stating that the carrier of utility is the total level of wealth. Although this hypothesis is not part of the EU theory framework as such. It has been for a long time embraced by economists as a natural assumption. In their 1979 paper, Kahneman and Tversky presented another hypothesis namely the fact that the carrier of utility are the changes in wealth (or more generally in outcomes), relative to a reference point (typically, but not necessarily the status quo). In this framework Kahneman and Tversky posit that people are likely to adopt a more risk adverse behavior when faced with choices involving gains and they become more risk seeking when faced with choices involving losses This pattern, called the reflection effect, is modeled with a utility function that exhibits differing curvature for gains (concave - risk aversion) and for losses (convex - risk seeking). While the empirical literature on PT has grown rapidly over the recent period, the study of individual behavior after losses has faced specific practical and ethical difficulties which have hindered research progress in this area. Studying risk behavior after losses is difficult in a laboratory setting, as individuals are paid to participate and not to face the possibility of losing their own money which affects their willingness to take risks. Thus far, experimentalists have either studied individual behaviors, when faced with small losses following an initial gain (endowment) or have relied on hypothetical losses. These two strategies face important limitations. On one hand, the framing of a situation 3

4 as a loss relative to an initial endowment requires to assume that participants consider separately the endowment and the loss. Given the short duration of most experiment, this is a questionable assumption. The gambling literature shows in particular that recently earned money, like the endowment, may lead to take more risk, a phenomenon called the house money effect. An explanation of the house money effect is that the newly acquired sum does not feel yet as a personal property but as the money of the house, which can therefore be gambled without fear of a loss. On the other hand, the use of hypothetical losses raise the question of validity of the preference elicited. The lack of incentives may lead to a hypothetical bias whose importance has clearly been established (Harrison and Ruthstrom, 2008). Outside the laboratory, we find a limited but growing literature testing PT in the field investigating topics such as: finance, the labor market, savings and consumption, insurance, and betting (Camerer 2004). A large number of studies have confirmed many predictions of PT (Tom, Fox, Trepel, and Poldrack 2007). However, only few studies have looked at changes in risky behavior after a change in wealth. The only notable strand of research looking at changes in behavior after a change in wealth level is the literature on the disposition effect in finance which indicates that shareholders are more likely to hold on losing shares after a drop in price (Terrance Odean, 1998). The disposition effect is compatible with an increase in risk behavior after a loss predicted by PT. However, the non-experimental design of these studies does not allow the elimination of other confounding explanations (Barberis and Xiong 2009, Odean 1998). In the domain of gains, research on the effect of large monetary windfalls after lottery gains (Gardner and Oswald 2007) has provided evidence of habituation over time and provided indirect support for PT, but without providing evidence on changes in risk behavior. 2 Experimental Design In the present paper we find a solution to the limitations of laboratory and non-experimental field studies by using the peak of an unexpected urban flood in Brisbane (the capital and most populous city of Queensland, Australia) as a natural experimental setting (Campbell, Stanley, and Gage 1963). We investigate whether people may be more prone to take risky gambles shortly after experiencing a large loss in an attempt to return themselves to their initial reference point. This experiment provides the first evidence of a change in risk behavior following a large negative shock in wealth. The 2011 flood was an extreme event, with approximately 78% of the state flooded (an area larger than that of France and Germany combined) affecting over 2.5 million people (Queensland Floods Commission of Inquiry, 2011) with an estimated cost of $5 billion in flood damages. A critical identification assumption of our study is that the population of home owner is comparable around both sides of the flood limit. This hypothesis is reasonable given that the flood limit was a priori unpredictable. The last 4

5 serious flood was over 35 years earlier (1974) and Queensland had undergone a drought over a 10 year period before the flood. It was generally believed the construction of the Wivenhoe dam after the 1974 floods would prevent future disasters of this sort (David Humphries, 2011). The limits of the 1974 flood were known by residents (though not perfectly as there is no regulation for it to be revealed by estate agents). But the limits of the 2011 flood different due the different height of the floods and to the man made changes in hydrology and topography over the intermediate period. Home owners could not anticipate the 2011 flood line at the time they purchased their homes. On average the marginal home owners had the same type of information regarding the ex-ante risk of flood, whether they were eventually affected or not. The risk assessment performed by the Brisbane City Council (Brisbane City Council, 2011), which is available to residents online, showed no statistically significant difference (p=0.91) in the risk of flood over a 20 year time frame between the properties of participants. It is reasonable to assume that home owners could not have sort themselves ex ante around the 2011 flood limit as a function of their risk preference and other demographics. For this hypothesis to be as valid as possible we focus our analysis on a sample of residents very close from the flood limits. We provide evidence below supporting that the identification hypothesis of similarity of home owners around the flood line is supported by looking at observable characteristics. The experimental design uses the fact that around the flood limits home owners experience very different fates regarding the evolution of their wealth. First, home owners directly affected face costly damages caused by the flood waters to houses and their contents. Second, house values change markedly around the new flood limit with house affected incurring a large negative risk premium (at least for some time after the flood). This experimental design also relies on the fact that the participants answers were collected four weeks after the devastating flood, which ensured that the impact of the event was presumably still fresh and still very real in the minds of the participants (lack of habituation). 2.1 Flood Data The data in this study consists of the choices and responses of the two hundred and twenty-nine individual home-owners who were surveyed across the weekends of the 12th-13th and 19th-20th of March, Participants answered a survey questionnaire and chose to be rewarded for their participation either with a fixed sum of $10 (all amounts are in Australian dollars) or with a lottery scratch card worth $10 in news agents and with a maximum prize of $500,000. Three screening questions were used to exclude non home-owners from the experiment. Participants were not randomly selected but were taken from specifically targeted houses and street sections from across sixteen suburbs. Every property was selected through an identical process: Visual analysis of aerial/satellite (Nearmap, 2011) photos taken after the flood peak (January 14th) selecting streets on the margin of the peak. To limit variation in in- 5

6 come/wealth and property value, the target areas were limited to single streets, such that one side of a street was flood affected while the other was not. This was expanded to include flooding across rather than along the street. However, to localize and maintain the marginal nature of cross flooding, a limited number of houses were selected on each side of the flood line. After comparing topological maps (PDOnline Interactive Mapping, 2011) and satellite photos, houses were sorted into control and treatment groups from which houses were selected. Some randomness was introduced into the sample through the collection process; surveys were filled out only if the resident was home on the day and chose to enter into the study. Given the relatively small height of the flood reached in the houses at the margin, affected home owners where in most cases still residing in their house. As a consequence the response rate was quite high, and very similar on both sides of the margin: 22% for non-affected houses and 20% for affected houses (difference: p=0.38%). We estimated the distance to the flood limit using the lowest habitable level of the house. This is due to the fact that the same flood level may affect differently houses with their doorstep on the street level and houses on stilts (very common in Brisbane). To do this estimation, we first relied on the Brisbane City Council contour plot map to estimate the height of the lowest part of the house and compare it to the height of the flood in the area, estimated by the Brisbane City Council. We also asked home owners to give an estimation of the vertical height of the flood relative to the house. When the flood reached the house, we used the home owners estimate of the height of the flood in the house (this is often very precise as the measurement is often done by the insurance company). When the flood did not reach the house, we mostly used the map information. However, when the flood peak was very close from the house we also looked at the home owners s answer as they often revealed that the house was on stilts when a significant difference existed with the map estimate. In the case of discrepancies between the map estimate and the home owner answer we checked the architectural disposition of the house using the street view tool from Google Map and we kept the home owner s estimate when the house was on stilts. In an explicit effort to avoid researcher bias, none of the survey questionnaires were administered by the researchers, as such. A team of research assistants (RA s) were employed. All RA s underwent a training session prior to being placed into the field and were at no time told the objectives or purpose of the survey and were provided with a script so that all questionnaires could be administered in as close a fashion as possible, creating a consistent approach across all surveys, reducing extraneous noise. 2.2 Methodology Around the limits of the flood peak, home owners experienced very different fates. On the flood side, the water reached their house damaging their good and decreasing the value of their property. On the other side of the flood edge, home owners goods were safe and the impact on the property values of the closeness 6

7 to the flood limit is likely to be much smaller. In spirit our methodology is close to a regression over discontinuity design. However it differs from it in some aspects. First, the treatment is not observable. This stems from the fact that the treatment we are interested in is the feeling of loss from home owners, following the floods. Second, this treatment will differ among home owners for a given distance to the flood limit. This is not only due to the fact that for a given distance, home owners may update their beliefs differently, it is also due to the fact that architectural differences will have critical impact on the monetary effect of floods for home owners. In flooded areas, many ground based houses are next to houses on stilts where habitable rooms are 3m above ground. The amount of valuable located in flooded part of the house may also vary, as well as the propensity of the insurance company to reimburse the flood damage (in the 2011 Brisbane floods, some companies decided to reimburse all cases while other dismissed some cases as not covered by the insurance policy). These characteristics of the data observed does not allows us to precisely estimate a regression discontinuity model. However the careful selection of the sample around the limits of the floods, allows us to study whether a significant variation in risk behavior can be observed on both sides of the flood limits. We place each observation one dimension representing the vertical distance between the estimated height of the doorsteps of the house and the flood height in the area estimated by the Brisbane Council (Brisbane City Council, 2011).. We then use a non parametric local linear regression estimator to estimate the proportion of risk takers in our sample as a function of their location relative to the flood line (in vertical distance). Given the concentration of our observations around small positive and negative distances from 0, we opt for a nearest neighbor estimator which adapts the smoothing window to the local density of observations. This choice allow our estimator to be more precise around the flood limit 0, and to have less variance away from the flood limit where our observations are more scarced. The dependent variable in our analysis is the dummy indicating whether an individual chose to accept the risky gamble or not (accepted = 1). Our analysis relies on the identification assumption that home owners located near the flood limits are similar in characteristics. For this identification assumption to be credible, we only keep observations from home owners whose house was located within 2.5m vertically of the flood linie. Given that in the field experiment few observations were collected for houses outside this boundary, we are left with 200 observations. 3 Results The left panel of Figure 1 represents the result of the local estimation of the proportion of risk takers as a function of their distance to the flood lines. Our results show a marked increase in risk taking around the point where the flood limits reach the habitable part of the house. Notably, most of the change in risk 7

8 Figure 1: Proportion of risk takers (left) and subjective loss in property values (right) around the flood line. On the x-axis, the level of the flood in the house is estimated relative to the lowest habitable level. The confidence interval of the estimation is displayed with dotted lines. taking happens within a range of 1.5 meters around the height of the house. Risk taking increases by 50% between homes where the flood was 0.75m below the house level and the homes where the flood was 0.75m above. Our hypothesis is that this change is induced by the loss provoked by the flood. The right panel of Figure 1 displays the declared change in house value expected by home owners. The expected loss of property value as a function of the distance to the flood line mirrors the evolution of risk taking. This suggest that most of the subjective loss experienced by the home owners occurs around this area. On average, we observe a estimated drop of $80,000 between -0.75m and +0.75m where most of the variation in risk attitude is observed. This subjective estimate does not include the losses from personal property which is also likely to jump around the flood limit. In order to check whether our assumption that samples of home owners on both sides of the flood limits do not systematically differ in characteristics, we use answers to our questionnaires to test for differences across the two groups. We do not find any significant in observable characteristics using t-tests: income (p=0.76), house value before the flood (p=0.27), proportion having content insurance (p=0.80), age of the respondent (p=0.73). This supports our assumption that the margins of the floods provide a natural experiment setting allowing us to study the effect of the floods on risky behavior, in a population where the treated and the control groups present identical characteristics. The confidence interval displayed on Figure 1 suggests clearly a statistically significant shift around the flood line in terms of risk attitude. We run a probit model of the impact of the flood level on the propensity to take the risky gamble around the flood limits. To ensure the robustness of our estimates we vary the window of observations around the estimated flood limit between 1m and 2.5m each side. Table 1 displays the results. The shift in risk attitude is clearly significant around the flood line and is still very significant when the window is only 1m each side, in spite of the smaller sample of observation. This robustness of the effect on a smaller window supports the idea that this effect is causal given 8

9 that on the smaller the window, the more compelling is the assumption that the populations of home owners are similar on both sides of the flood line. To estimate the link between loss in property and the tendency to choose the risky gamble, we estimate an IV probit using the flood height around the flood limit as a instrumental variable for the loss in property value incurred. Arguably, the answers to our survey questions about the value of the owner s property before and after the flood are likely to be characterised by some significant measurement error likely to drive bias downward direct estimations. We ran simple probit to explain the effect of loss in property values on risky decisions and although the coefficient is positive, it is not significant. The instrumentation by the flood level will correct for this downward bias, under the assumptions that the flood level is not correlated with observed and unobserved characteristics in our population of participants and that the effect of the flood goes only via its impact on property losses. This should not be entirely the case as owners also incurred direct loss in their valuables due to the floods. To interpret our results, we can just assume that the two types of losses are correlated (more expensive houses contains more expensive valuables). So one dollar lost in property value would signal that the owner is likely to have lost even more in valuables. In any case, the loss in property value can be interpreted as a proxy for the total loss incurred by the flood. Table 1 displays the results of the IV estimations. Overall, the effects are strongly significant and suggest that the loss of $10,000 in property value around a loss of $100,000 increase the likelihood to take the risky gamble by 6 to 8 %. Probit 1m 1.5m 2m 2.5m Flood level ( 0.07) ( 0.05) ( 0.03) ( 0.03) Nb of observations IV Probit 1m 1.5m 2m 2.5m Loss in property value (AU$10,000s) ( 0.02) ( 0.01) ( 0.01) ( 0.02) Nb of observations Marginal effects displayed. Estimated in flood level=0 and loss=$100,000. Standard errors in brackets. denotes significance at the level. Table 1: Effect of the wealth loss on risk attitude. 4 Conclusions While rare, choices made in situations where large variations in wealth are at stake can have critical and long lasting consequence in an individual s life. Although interesting, the effect of large variations in wealth are almost impossible to study with experimental techniques. Using a natural disaster as the setting for a natural experiment, our study provides support to the prediction from PT that individual will become more risk seeking after a loss. Our results demon- 9

10 strate that individuals who have suffered the large wealth shock of flood waters in their house are approximately 50% more likely to accept a gamble than their immediate neighbors who remained unaffected. As the flood transition point (around the zero) is approached, we observe a distinct increase in the proportion of homeowners willing to accept a gamble. This is reflected in homeowners belief about the loss of wealth (house value) caused by the flood, where the average cost of being affected in the floods resulted in a loss of approximately $80,000. No significant differences in observable characteristics is observed between home owners across the flood line, supporting our identification hypothesis that home owners did not sort themselves ex anted around the realized 2011 flood limits when they bought their houses. Given the constraints laboratory and field experiments face in the study of risk attitude after large variations in wealth, our study suggests that natural experiments where random or quasi-random large variations of wealth are generated can be used to study this question. References Barberis, N., and W. Xiong (2009): What Drives the Disposition Effect? An Analysis of a Long-Standing Preference-Based Explanation, the Journal of Finance, 64(2), Camerer, C. (2004): Prospect theory in the wild: Evidence from the field, Colin F. Camerer, George Loewenstein, and Matthew. Rabin, eds., Advances in Behavioral Economics, pp Campbell, D., J. Stanley, and N. Gage (1963): Experimental and quasiexperimental designs for research. Houghton Mifflin Boston. Gardner, J., and A. Oswald (2007): Money and mental wellbeing: A longitudinal study of medium-sized lottery wins, Journal of Health Economics, 26(1), Harrison, G., and E. Rutström (2008): Risk aversion in the laboratory, in Research in Experimental Economics, Volume 12, ed. by J. Cox, and G. Harrison, pp Emerald, UK. Kahneman, D. (2002): Maps of bounded rationality: A perspective on intuitive judgment and choice, Nobel prize lecture, 8(December), Kahneman, D., and A. Tversky (1979): Prospect theory: An analysis of decision under risk, Econometrica: Journal of the Econometric Society, pp Levitt, S., and J. List (2009): Field experiments in economics: the past, the present, and the future, European Economic Review, 53(1),

11 Odean, T. (1998): Are investors reluctant to realize their losses?, The Journal of Finance, 53(5), Rayo, L., and G. Becker (2007): Evolutionary efficiency and happiness, Journal of Political Economy, 115(2), Tom, S., C. Fox, C. Trepel, and R. Poldrack (2007): The neural basis of loss aversion in decision-making under risk, Science, 315(5811),