Do expected income changes bias contingent valuation willingness to pay figures?

Transcription

1 Do expected income changes bias contingent valuation willingness to pay figures? Franz Hackl Gerald J. Pruckner 1 February both: Department of Economics, University of Linz, A-4040 Linz/Auhof, Austria, phone: or 213, FAX: , s: franz.hackl@jku.at or gerald.pruckner@jku.at

2 Abstract This paper shows that expectations about future income changes may bias respondents answers in Contingent Valuation (CV) studies. A practicable ex post approach to control for these biases is proposed: Based on the interviewees individual assessment of the personal future income situation expected income changes can be econometrically corrected for in CV. This is illustrated by CV-data on an Austrian national park the realization of which causes expected income losses and gains in the forestry and tourism sector. Key words: Contingent valuation, environmental cost benefit analysis, expected income changes, applied welfare measures Zusammenfassung Dieses Papier diskutiert die Auswirkungen von erwarteten Einkommensänderungen auf die im Rahmen des kontingenten Bewertungsansatzes erhobenen Zahlungsbereitschaften. Eine einfach anzuwendende Prozedur zur Korrektur möglicher Verzerrungen der Zahlungsbereitschaften aufgrund der Einkommenserwartungen wird vorgeschlagen: Basierend auf der individuellen Bewertung der zukünftigen Einkommenssituation durch den Befragten können mit Hilfe eines ökonometrischen Verfahrens potentielle Verzerrungen reduziert werden. Dieser Vorschlag wird anhand von Daten über eine Zahlungsbereitschaftsanalyse eines österreichischen Nationalparks, durch dessen Realisierung negative und positive Einkommensänderungen im Bereich des Tourismus und Forstwirtschaftssektors erwartet werden, illustriert. Key words: Kontingenter Bewertungsansatz, Kosten/-Nutzenanalyse, Zahlungsbereitschaft, Wohlfahrtsmaße JEL classification: D6, H4, Q2

3 1 Introduction The Contingent Valuation Method (CVM) has become a common tool in Cost Benefit Analysis (CBA) to assess the social profitability of single projects or policy measures associated with environmental change. However, objections to CVM have been raised questioning the method s validity and reliability to evaluate environmental change. Errors may occur whenever researchers incorrectly interpret the answers given by CVM participants. This paper shows that respondents expectations about future income or price changes caused by environmental change represent one important source of misinterpretation. Expected income and price variations associated with the implementation of environmental projects can bias CVM answers. The broad potential relevance of this problem can be illustrated by the following examples. (1) One can think of the implementation of a national park, which causes expected future income losses in the forestry sector. These losses may lead to downward biased CVM welfare measures for the national park. Moreover, an increase in tourism may raise expected future income of residents representing a reason for upward biased welfare measures. (2) CVM answers on the valuation of environmental degradation due to the construction of a power plant can be expected to be downward biased whenever respondents anticipate future energy price reductions as a result of the increase in energy supply. (3) The valuation of environmental damage by basic industries can be downward biased if respondents consider product price increases due to expected future regulations. This paper investigates the role of expected income changes in CVM studies and the resulting consequences for the use of CVM figures in empirical CBA. The bias treated in this paper can be interpreted as specification error due to omitted variables related to expected income changes. In Section 2 we derive a cost benefit rule for social profitability associated with environmental change. It will be shown that the total economic value of environmental change comprises the direct monetary value (=consumption value in form of use and non use values) and market transactions initiated by the environmental change (e. g. costs of the provision of the environmental good). Even though the general objective of CVM is the measurement of the direct monetary value we will show that in empirical applications the researcher is left unclear whether respondents (i) indeed state this direct monetary value of an environmental good, (ii) express the total economic value associated with a change in environmental quality 1

4 or (iii) announce none of both. In Section 3 CVM data from a national park study in Austria are used to show that the stated willingness to pay figures depend on expected income changes and do not represent direct monetary values. Moreover, we provide a simple and practicable procedure how expected income changes can be controlled for in empirical CVM analysis which enables the ex post reevaluation of theoretically correct willingness to pay figures for the use in applied CBA for small environmental projects. 2 The total economic value of environmental change Suppose a decision on the realization of a national park is based on CBA. From a theoretical point of view this problem can be formulated in a general equilibrium framework for a small environmental project as follows: A representative household maximizes utility under a given budget constraint maxu ( x D T, x D F, z, L S x T, L S x F ) s.t. pt x D T p F x D F + wl S x T + wl S x F + Π T + Π F 0 (1) with x D T and xd F denoting two private goods, in our example tourism and forestry1. z, L S x T, L S x F represent a public good (the national park) and labor inputs needed to produce the private goods x T and x 2 F. p T, p F and Π T, Π F denote prices and profits in the private sectors whereas w indicates an identical wage rate in both production sectors. The utility function depends on consumption of both private and public goods and on the amount of labor provided. On the income side the household earns factor income for the supply of labor 3. Moreover, the firms are owned by the household who treats the firms profits Π T and Π F as lump sum income. As far as expenditures are concerned, the household spends money on tourism and forestry goods. 4 1 Tourism and forestry have been chosen since the realization of the national park has pecuniary effects on the first sector and technological consequences on the second one. 2 The superscripts D and S indicate demand and supply. 3 We have chosen a comprehensive model including the production factor labor to show possible effects of employment on the cost benefit rule. 4 For simplicity reasons we do not consider any provision costs for the national park apart from production restrictions in the forestry sector. 2

5 The Lagrangian L of the maximization problem for the indirect utility function V (p T, p F, w, z, Π T, Π F ) becomes L : V (p T, p F, w, z, Π T, Π F ) λ( p T x D T p F x D F + wl S x T + wl S x F + Π T + Π F ). Substituting the first order conditions of the Lagrangian into the total derivative of the indirect utility function yields dv = λx D T dp T λx D F dp F + λ(l S x T + L S x F )dw + V z dz + λdπ F + λdπ T. After rearranging terms we get the monetary total economic value of a marginal change in the provision of the public good: dv dz 1 λ = dp T xd T dz dp F xd F dz + (LS x T + L S x F ) dw dz + V z A representative firm in the tourism sector T produces 1 λ + dπ F dz + dπ T dz. (2) x S T = F x T (z, L D x T ) with F x T z = 0 and F x T L D x T > 0. We assume there is no production related interdependence between the provision of the national park and the supply of tourism services although the demand for tourism services may increase after the establishment of the national park 5. Furthermore, we suppose a positive marginal product of labor. The total derivative of the firm s profits Π T = p T F x T (z, L D x T ) wl D x T dπ T = x S T dp T + p T F x T reads as: z dz + (p T F x T L D x T w)dl D x T L D x T dw. The substitution of the first order conditions from profit maximization into the total derivative of profits yields the following equation: dπ T = x S T dp T L D x T dw. Contrary to industry T the production in forest industry F depends on the amount of the public good provided. This influence is the result of certain production constraints to be met due to the implementation of the national park. Therefore, the 5 The production functions are assumed to be at least twice differentiable, and costs for a fixed capital stock are ignored. 3

6 production in sector F is given as: x S F = F x F (z, L D x F ) with F x F z < 0 and F x F L D x F > 0. In analogy to industry T the total derivative of profits in sector F can be written as: dπ F = x S F x F F dp F + p F z dz LD x F dw. The substitution of dπ T and dπ F into equation (2) and the assumption of market clearance in both the private commodity markets and the labor market yields the following equation: dv dz 1 λ = V z 1 λ + p F x F F z Therefore, the total economic value due to a marginal change in the provision of the public good z consists of two components: the direct monetary value of the environmental good V 1 (benefits) and the profit change p z λ F F x F in industry F (costs) due z to legislative production constraints caused by the environmental quality change (implementation of the national park) 6. Whereas the former term comprises the consumption value of an environmental good the latter component refers to the environment as a factor of production. Equation 2 indicates that the environmental project should be implemented only in case of a positive total economic value (= cost benefit rule). (3) It becomes obvious from equation (3) that changing profits in industry F appear as part of the total economic value whereas no comparable profit term occurs for industry T. This is for the reason that one has to distinguish between technological and pecuniary effects of environmental change. Whereas the profit loss in forestry p F F x F z results from a change in the production possibilities profit change in tourism is pecuniary in the sense that all changes in demand and supply of tourism cancel out under perfect market conditions. In this context it should be noticed that the analysis of marginal changes in z allows us to evaluate the good in question at the given income and price levels. Therefore, we need not consider income and price changes for the calculation of the direct monetary value V 1. z λ 6 The same result can be obtained directly by employing the envelope theorem. We have chosen the explicit maximization of utility and profit functions to elucidate the existence of pecuniary effects in the cost benefit rule. 4

7 3 The empirical measurement of unbiased environmental benefits In contrast to the welfare theoretic analysis with only the consumption value V 1 z λ F and the technologically induced profit loss in forestry p x F F to be considered for z the representative houshold s total economic value, pecuniary effects can play an important influence for the total economic value of a single respondent in a CV-survey. The cost benefit rule in Section 2 (equation (2)) implies that in total the pecuniary effects cancel out in equilibrium even though a single respondent may face pecuniary income profits (losses) which represent negative (positive) welfare effects for another agent. The purpose of CVM is the elicitation of people s direct monetary values for environmental change. This would require that respondents neglect income effects resulting from market transactions. However, in empirical CVM surveys it remains a priori unclear whether respondents correctly state their consumption value V 1 or z λ express their total economic value dv 1. This uncertainty about the measured value dz λ results from the great cognitive demand that CVM makes on the respondents even in the absence of any income changes. In this already difficult valuation process the provision of infomation on the treatment of income effects could create more confusion on the respondents than it would reduce the uncertainty for the researcher. Therefore, we argue it is unrealistic that all all respondents can be explicitly requested to announce their direct monetary value of the national park neglecting all income effects. Moreover, even if we knew that people had tried to announce their total economic values we would need to assume that respondents (i) correctly anticipate the true scale of income effects and (ii) include all relevant forest- and tourism-related income changes such that the pecuniary effects will cancel out in the subsequent aggregation of respondents total economic values. Since - in contrast to the requirements of a welfare economic perspective - people may not consider all relevant income effects in CVM surveys, it remains open which components from equations (2) and (3) are taken into account. The expectation that the interviewees are able to process adequately all the necessary information in a relatively short time period of CVM interviews seems too ambitious. 5

8 From that follows that the problem whether respondents state the direct economic value, the total economic value or a mixture of both cannot be solved by providing ex ante information. Therefore, we propose the following ex post approach: Apart from questions on the respondents personal background (age, income,... ) CVM questionnaires should ask whether interviewees expect changes in their personal income situation caused by environmental change. The answers to these questions can then be used to check potential influences of income changes on willingness to pay in retrospect. This has been done in the following empirical analysis. The data we refer to have been collected in a CVM study on the Austrian Kalkalpen national park which is situated on the north rim of the Alps 7. The realization of this national park represents a small environmental change since neither a significant increase or decrease in prices nor in income can be expected. In personal interviews 301 local residents were asked closed-ended double-bounded dichotomous choice questions to express their willingness to pay for the proposed national park project 8. After providing general information on the consequences of the realization of the national park we have confronted the respondents with the following willingness to pay questions: Even though the subsequent questions cannot be answered easily, I kindly ask you to answer honestly and well-conceived. Realize that the Kalkalpen National Park is associated with financial cost. The following questions try to highlight how residents voted on this project if they had to pay a specific amount of money for it. Those who vote for say this environmental project is worth the money to them. Some say that they want rather spend the money for other commodities that are more important to them. And some say the money they would have to pay for the Kalkalpen National Park is more than they can afford. Of course whether you would vote for or against this project depends on how much the National Park will cost your household. Cost estimations say that the Kalkalpen National Park will cost your household AC 3.6/10.9/25.4/50.9 a year to be paid in an earmarked National Park fund. If this project cost your household AC 3.6/10.9/25.4/50.9 a year would you vote for 7 For details on this study, see Hackl and Pruckner From these 301 questionnaires 23 repondents have been excluded from our sample because the interviewees answered on both WTP questions either with do not know or do not answer questions like this in general. 6

9 the project or against it? (FOR, AGAINST, DO NOT KNOW, DO NOT ANSWER QUESTIONS LIKE THIS IN GENERAL) What if the cost estimates showed that the project would cost your household AC 10.9/25.4/50.9/79.9 (AC 1.8/3.6/10.9/25.4) a year? Would you vote for or against the Kalkalpen National Park project? (FOR, AGAINST, DO NOT KNOW) At the end of the questionnaire - among questions on respondents personal background - we asked the local residents about their individual income changes they would expect if the national park project was realized. The wording of the question was as follows: Which kind of income changes do you expect from the economic consequences of implementing the Kalkalpen National Park project? Do you think your household income will increase, decrease or remain the same? (HOUSEHOLD INCOME WILL INCREASE, HOUSEHOLD INCOME WILL DECREASE, HOUSEHOLD INCOME WILL REMAIN UNCHANGED) Thus we have measured expected income changes on an ordinal scale 9. In the first part of the following empirical analysis the influence of positive and negative income change expectations is tested. The second part shows a simple procedure to eliminate undesired income effects in WTP answers. Since the effects of positive and negative expectations about future income on the individual WTP may outweigh by calculating mean WTP the whole sample of respondents was split into three subsamples. Analyzing the statistical influence of positive income expectations on WTP figures we tested the mean WTP of people without income change expectations (= Subsample 1, 245 observations) against a sample of respondents including people with no or positive expected income changes (= Subsample 2, 256 observations) 10. To illustrate the statistical influence of negative expectations we compared the mean of Subsample 1 with the mean of people 9 From 278 remaining interviewees 245 reported no, 11 indicated positive, and 22 stated negative income expectations. 10 It is not possible to test the WTP of people without income changes directly against the WTP of people with positive income change expectations because unbiased maximum likelihood estimators require a sufficient number of observations which is not guaranteed for a sample only including respondents with positive income expectations. Moreover, our approach provides information about the size of the error that would occur if income expectations were not controlled for. 7

10 with no or negative income expectations (= Subsample 3, 267 observations). The maximum likelihood estimation of the distribution function of WTP figures was based on the closed-ended double-bounded dichotomous choice CVM model (see Hanemann 1984 and Hanemann et al 1991) with the following specification for the utility difference v between the status quo and the realization of the national park v = a 0 + a 1 ln (B) + a 2 ln (Y ) + a 3 D + a 5 educ + a 6 age + a 7 club. The probability that a respondent pays a specified amount of money for the national park depends on the logarithm of the bid B, the logarithm of per capita net income of the household Y, a regional dummy 11 D, the last grade of formal education educ, the respondent s age age and the membership to a wildlife club club. The estimated coefficients for Subsamples one to three can be seen in Table 1. Since the maximum likelihood procedure provides only one WTP point estimate the jackknife simulation technique (see Cooper 1994) has been applied to obtain a distribution for WTP 12. The welfare measures of the different Subsamples and Jackknife simulation results are given in Table 2. The first two tailed test of the equality of means in Subsample 1 and 2 (AC in Subsample 1 against AC in Subsample 2) shows a significant difference even at the 99.9 percent level 13. The same is true for negative expectations about future income changes. The mean WTP figure in Subsample 3 (AC 17.41) differs significantly from its counterpart in Subsample 1 (AC 18.04) as well. Figure 1 shows a graphical representation of the distribution of WTP in the different Subsamples. Therefore, we found evidence that positive and negative income expectations significantly influence people s reported WTP figures in our CVM study We have included a regional dummy to account for differences in tourism infrastructure simulated data sets have been used in the jackknife procedure. 13 (n 1)S1 The pooled sample standard deviation S p can be calculated by S p = 2+(m 1)S2 2 m+n 2 = 2.35 with the sample standard deviations S 1 = 2.4 and S 2 = 2.31, and the sample sizes n = 245 and m = 256. In order to compare the two sample means we calculate the test statistic t = X 1 X 2 = 6.8 with the sample means X 1 = and X 2 = Since the tabulated value S p 1/n+1/m t 499 (0, 005) = < 6.8 the null hypothesis of identical means can be rejected. 14 The observed difference cannot be attributed to different statistical properties of respondents with positive, negative and no income expectations. Tests of identical means across these three groups have not shown any significant differences for all explanatory variables that have been used 8

11 Given this result one needs to ask which economic value has been elicited from the respondents. One may presume from the theoretical section that respondents have reported their direct monetary values. However, this is in clear contradiction to our finding that the reported WTP figures differ between people with and without income change expectations. The presupposition that direct monetary values have been reported would require identical WTP figures across our Subsamples one to three. We know from theory that income changes do not matter in valuations of small environmental projects and that the direct monetary values are determined by the present and constant income level. An alternative interpretation of our results is that respondents have stated total economic values. This interpretation is compatible with our finding that respondents with negative (positive) income expectations stated lower (higher) WTP figures. However, we have argued above that CVM questions for the total economic value seem too demanding. Therefore, we doubt that all respondents have announced their total economic value including all relevant technological and pecuniary effects. That is why we conclude that the individual answers to our questionnaire do represent either direct consumption values, total economic values or values which consider pecuniary or technological effects only partially. A priori it is impossible to determine which components the stated WTP amount comprises. Therefore, the question arises how these problems can be overcome or by which means the expected income changes can be controlled for in empirical CVM studies. Obviously, respondents who state positive or negative income change expectations could be eliminated from the original sample. The remaining respondents with no income change expectations then guarantee the measurement of direct monetary values. However, this may lead to a drastic drop in the sample size. In our CVM study the number of observations would go down by approximately 12 percent. To avoid this drawback we propose the following ex post approach: Instead of creating a subsample we use the original sample and include both positive and negative income expectations as explanatory variables in the equation for the utility difference v. The dummy variable Y pos is equal to one if the rein the econometric analysis. 9

12 spondent has stated an increase in expected income and zero otherwise. Likewise is Y neg equal to one in case that the person has expected a decrease in future income. The following two models have been estimated: Model 1 : v = a 0 + a 1 ln (B) + a 2 ln (Y ) + a 3 D + a 5 educ + a 6 age + a 7 club +a 8 Y pos + a 9 Y neg Model 2 : v = a 0 + a 1 ln (B) + a 2 ln (Y ) + a 3 D + a 5 educ + a 6 age + a 7 club +a 8 Y pos + a 9 Y neg + a 10 Y pos educ + a 11 Y neg educ +a 12 Y pos age + a 13 Y neg age + a 14 Y pos ln(y ) +a 15 Y neg ln(y ) + a 16 Y pos club + a 17 Y neg club +a 18 Y pos D + a 19 Y neg D + a 20 Y pos ln(b) + a 21 Y neg ln(b) As compared to our basic estimation Model 1 adds both Y pos and Y neg as shift variables. Compared with this Model 2 allows both for shifts and changing slope parameters due to expected income changes. It is based on the assumption that income expectations influence WTP figures differently depending on the value of other independent variables. Whereas the former model represents a minimal specification of income expectations the latter model is the most comprehensive in the sense that it accounts for all possible combinations of income expectations and other explanatory variables. Table 3 shows the estimated coefficients for Models 1 and 2, and the respective WTP measures can be seen in Table 4. Based on this approach it is possible to calculate the direct monetary values without any reduction in the sample size. Given the estimated parameters and the means of explanatory variables income expectations can be controlled for by simply taking zeros for Y pos and Y neg. Thereby any WTP bias that may have been introduced through expectations about future income changes can be corrected. Whereas the mean of Model 1 (AC 18.59) still overestimates the mean of Subsample 1 (AC 18.04) the more comprehensive Model 2 (AC 18.01) statistically coincides with the WTP of Subsample 1 (compare Table 4). Moreover, the proposed approach allows the calculation of WTP measures for people either expecting positive or negative income changes in the future. This 10

13 can be easily done by selecting the appropriate values for the dummies Y pos and Y neg. The welfare measures and their distributions are given in Table 4 as well. Apparently the welfare measures of the two models differ significantly (AC versus AC in case of positive income expectations and AC 7.33 versus AC 1.83 for negative expected income changes). This spread, which is also illustrated by the distribution of Jackknife simulations in Figures 3 and 4, can be explained by the relatively small number of respondents with positive and negative income expectations. A second argument against the use of these welfare figures in CBA refers to the uncertainty for these groups of respondents which theoretical components the calculated WTP figures include. 4 Concluding Remarks Summarizing this paper we found evidence that expected income changes significantly influence people s WTP for a small environmental project. Based on our findings it is too optimistic to expect that the respondents state their direct monetary values for environmental change. The cognitive demands that a CVM survey makes on interviewees are very high. To account for resulting expected income change biases we propose an econometric ex post correction. CVM questionnaires should be extended by questions controlling for respondents future income expectations. These expectations can be used to calculate unbiased direct economic values for environmental change. However, this paper represents only a first step towards the correction of biased welfare measures caused by the respondents expectations about their future personal economic situation. Further research efforts should be invested in the following areas: First, the field of applications, where this problem appears to be relevant, must be identified. We suppose that apart from national park realizations similar problems may arise whenever a change in environmental quality interacts strongly with economic variables such as prices or income. Second, this analysis is restricted to income expectations as a reason for biased CVM welfare measures. From a theoretical point of view expectations about future price changes can bias WTP figures as well. The third field of research is probably the most challenging one. We have presented an analysis for small environmental projects. The approach is 11

14 not applicable to large (non marginal) environmental change since in that case the direct monetary value itself depends on changes in income which complicates the empirical econometric analysis considerably. 5 Literature Cooper J. C., 1994, A comparison of approaches to calculating confidence intervals for benefit measures from dichotomous choice contingent valuation surveys, Land Economics 70(1), Hanemann W. M., 1984, Welfare evaluations in Contingent Valuation experiments with discrete responses, American Journal of Agricultural Economics 66, Hanemann W. M., J. Loomis, B. Kanninen, 1991, Statistical efficiency of doublebounded dichotomous choice Contingent Valuation, American Journal of Agricultural Economics 73, Hackl, F., Pruckner, G. J., 1999, Notes on the gap between payment card and closed-ended cvm-questions, Applied Economics

15 Variables Intercept Ln offer Ln income Regional Dummy Education Age Club Membership Subsample 1 (No income change) 5.31 a Subsample 2 (No and positive income changes) (5.97) b (6.15) ( 8.66) ( 9.02) (1.45) (1.10) ( 3.63) ( 3.84) (1.76) (2.24) ( 3.95) ( 3.92) (4.05) (4.24) Subsample 3 (No and negative income changes) 5.13 (6.02) 8.70 ( 8.88) 0.37 (1.56) 0.97 ( 3.53) 0.23 (1.58) 3.33 ( 3.89) 1.35 (4.38) AIC c N a Single asterisk indicates significance at 5 % level, double asterisks indicate significance at 1 % level. b t-values in parentheses. c Akaike s information criterion. Table 1: Estimated coefficients for dichotomous choice contingent valuation models 13

16 Sample 1 (No income change) Sample 2 (No and positive income changes) Sample 3 (No and negative income changes) Median Mean Standard Deviation Confidence Interval (95 %) [ ] [ ] [ ] Table 2: Welfare measures in AC for dichotomous choice contingent valuation models 14

17 Variables Model 1 Model 2 Intercept Ln offer Ln income Regional Dummy Education Age Club Membership Ypos Yneg Ypos*Education Yneg*Education Ypos*Age Yneg*Age Ypos*(Ln Income) Yneg*(Ln Income) Ypos*(Club Membership) Yneg*(Club Membership) Ypos*(Regional Dummy) Yneg*(Regional Dummy) Ypos*(Ln Offer) Yneg*(Ln Offer) 5.23 a 5.34 (6.12) b (6.00) ( 9.15) ( 8.67) (1.17) (1.44) (3.49) ( 3.63) (1.74) (1.75) ( 3.56) ( 3.94) (4.42) (4.07) (2.07) (0.23) ( 2.01) ( 0.26) 5.74 (0.19) 0.69 (0.17) (0.27) (0.59) 7.92 ( 0.44) 3.01 ( 0.84) (0.49) 1.30 (0.27) ( 0.26) 6.39 (1.04) ( 0.65) 1.60 ( 0.10 AIC c N a Single asterisk indicates significance at 5 % level, double asterisks indicate significance at 1 % level. b t-values in parentheses. c Akaike s information criterion. Table 3: changes Estimated coefficients for different specifications of expected income 15

18 Income Expectation Welfare Measure Subsample 1 (No income change) Model 1 Model 2 No Median Mean Standard Deviation Confidence Interval (95 %) [ ] [ ] [ ] Positive Median Mean Standard Deviation Confidence Interval (95 %) [ ] [ ] Negative Median Mean Standard Deviation Confidence Interval (95 %) [ ] [0 5.74] Table 4: changes Welfare measures in AC for different specifications of expected income 16

19 Figure 1: Mean WTP-distribution of Jackknife simulations (in ATS) Figure 2: Distribution of Jackknife simulations for no expected income changes (in ATS) 17

20 Figure 3: Distribution of Jackknife simulations for positive expected income changes (in ATS) Figure 4: Distribution of Jackknife simulations for negative expected income changes (in ATS) 18