Using Propensity Score Matching to Estimate the Effect of Coastal Flooding Risk on the Willingness to Offset 𝑪𝑶𝟐Emissions.
Paulina Koenig 12234656
BSc Economics and Business Economics Thesis supervisor: Davide Pace
University of Amsterdam
Statement of Originality
This document is written by Paulina Koenig who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of the
completion of the work, not for the contents.
The purpose of this study was to investigate the relationship between the exposure to coastal flooding risk and people’s willingness to accept CO2 emissions. This was motivated by observing that climate change may receive less attention than desired due to people’s lack of personal connection.
However, this is starting to change – as natural disasters become more frequent worldwide, climate change is no longer an isolated issue but rather an issue affecting people’s local environments. In my analysis, I used the dataset of Imai et al. (2021) containing information about the willingness to accept (WTA) for different levels of externalities by Americans and a dataset from the Federal Emergency Management Agency (FEMA) (2020) containing information about coastal flooding risk in the United States (U.S.).
Using the Propensity Score Matching (PSM) method, I estimated the effect of coastal flooding risk on WTA. I found that people living in areas at risk of coastal flooding, on average, demand a higher payment to accept a given level of externality. Looking at different externality levels, I found this effect to not be significant at the low levels but very significant at high levels. The findings support the claim that the local environment influences people’s decision-making in this context, and this insight could help design efficient policies aimed at promoting pro-environmental behavior. Future studies could examine whether this effect would be strengthened by making the scenario more personalized or introducing cooperation.
Climate change is one of the most pressing global problems that humanity is facing nowadays. The scope of its effect is unprecedented as it will influence the social, economic and environmental spheres of life. The changes in Earth’s climate expand below the atmosphere and can affect several ecosystems.
According to a Special Report on Extreme Events and Disasters (SREX) (2012) from the Intergovernmental Panel on Climate Change (IPCC), the number of many forms of extreme weather events will increase throughout the 21st century. Droughts will become more frequent, the winds of tropical cyclones will become faster, and the higher precipitation levels will likely increase the frequency of landslides and floods (SREX, 2012).
The distribution of these extreme weather events is uneven, with some countries facing many disasters each year, while inhabitants of other countries know of disasters only from the news. However, with the global temperatures rising, extreme weather events will become a reality for a large share of the global population. Currently, a country that experiences the highest number of natural disasters is the U.S.
(Szmigiera, 2021), which in 2019 noted the fourth-highest total number of extreme weather events (tied with 2018) following the years 2017, 2011 and 2016 (Smith, 2020). Furthermore, the number and cost of natural disasters have been increasing over the past years due to increased exposure, vulnerability and the number of extreme weather events (Smith, 2020). All of this creates a reality where people increasingly suffer from disasters, and, more importantly, start to feel the effects of climate change directly.
It is an important observation that more people are exposed to these kinds of risks because one of the biggest obstacles in achieving collective action against climate change is the lack of personal connection (Ariely, 2011). For many years the destructive consequences of climate change were linked with beautiful
vision and many people do not like the idea of harming the young or even unborn generations, the delay of consequences causes a delay of action. The perspective is likely to be changed now that the consequences appear sooner than many have assumed.
The current behavioral studies are trying to understand which factors are essential in people’s motivation to offset the negative consequences of climate change. This is done by estimating people’s willingness to accept (WTA) externalities such as loss of forest cover or 𝐶𝑂2emissions. Studies have found an association of WTA with variables such as political affiliation, gender or geographical location (Carlsson et al., 2012; Brouwer et al., 2008; Löschel et al., 2013b). However, the connection between the experience of local weather events and the WTA negative externalities is not yet clear. It has been shown that people who have more experience of this kind exhibit more climate change beliefs, but it is uncertain how such beliefs translate to direct action (Carlsson et al., 2012). In another study, the link between the risk of flooding and saving energy has been drawn, but the study used perceived risk rather than the objective measure of danger (Spence & Butler, 2011). Although self-reported risk perceptions give a deeper insight into individual cases, they make it challenging to make interpersonal comparisons because people rate their attitudes differently. This can make it difficult to draw a clear conclusion about the relationship in question.
This study will aid the existing literature on the willingness to accept externalities by looking at the influence of the objective measure of extreme weather event risk. More specifically, I will look into the U.S., as it is a country with diverse exposure to different natural hazards. Moreover, I will focus on coastal flooding (CFR) because it potentially affects 40% of the American population living by the coast (NOAA, 2021). CFR is also less random than other disasters; it may create long-term changes in people’s attitudes.
Therefore, the research question that I will try to answer in this paper is: Are people living in areas more at risk of coastal flooding willing to pay a higher price to avoid 𝐶𝑂2emissions?
I will answer this question with the use of Imai et al. (2021)’s study in progress that, amongst other things, recorded the WTA for a diverse pool of participants. This data will be combined with other data on climate risks, and econometric analysis will be conducted to estimate the effect. The following section will describe the current empirical findings and relevant theories for the relation of interest. Then, I will explain
the datasets and econometric models that will be used in the analysis. After this, I will present the results of my analysis, which will be followed by a discussion of my findings. In the last section, I will summarize the results, and I will outline the limitations of my study and suggestions for further research.
To better understand people’s preferences for offsetting carbon emissions, a large body of literature focuses on eliciting people’s willingness to pay (WTP) for reducing emissions and fighting the consequences of climate change. These studies look at different potential determinants of WTP, such as gender, age, or political affiliation. They also look at different ways of motivating WTP, such as reducing 𝐶𝑂2emissions, compensating for air travel emissions or - as in the case of the data used in this study - offsetting 𝐶𝑂2emissions associated with car use. Although such variability may help understand which scenarios cause stronger reactions among participants and better inform policymakers, it also leads to low comparability between the studies. One of the attempts to address this issue is the “Meta-analyses of the determinants and outcomes of belief in climate change” conducted by Hornsey et al. (2016). Although the studies used focus on beliefs rather than the willingness to pay, the actions of participants are largely influenced by beliefs. This influence will be explained in the later paragraphs.
Correlations between climate change belief and demographic variables (from Hornsey et al. (2016))
Note. This graph represents the correlations of given variables with climate change beliefs. Error bars represent 95% confidence intervals.
The results of their analysis show that political affiliation is the most significant demographic correlate of climate change beliefs (Hornsey et al., 2016) (see Figure 1). The more liberal a person’s political affiliation is, the more likely they are to exhibit climate change beliefs. This effect is also strong for political ideology but to a lesser extent than for political affiliation, which may prove that climate change beliefs are determined more by the parties people identify with rather than their underlying political ideologies. The other variables that emerge in the study include sex, age, income, education and race, but their correlation with climate change beliefs is relatively low (Hornsey et al., 2016).
Another set of variables that Hornsey et al. (2016) have looked at are considered to be antecedents of climate change beliefs according to theory. Here emerge variables that are of particular importance for
people who have experienced flooding are more likely to believe in climate change (Spence & Butler, 2011). What is more, the experience of flooding makes people more confident that their actions affect the state of climate change, and consequently, they show a higher willingness to save energy to fight climate change (Spence & Butler, 2011).
Interestingly, the experience of extreme events has a negligible effect relative to the experience of local weather change, which may further support the proposition that people are more likely to believe in a problem when it affects their immediate environment. Another line of research points towards the relevance of environmental cues. In these studies, the participants were primed to think about the negative consequences of climate change, as researchers in these studies turned up the heating in the laboratory rooms or placed dead trees around the participants (Hornsey et al., 2016). Here it is important to point out that no priming has been used in the experiment of Imai et al. (2021), as the participants were only asked to provide their zip code without being directly asked about their experience of local extreme weather events.
It is also crucial to point out the difference between objective risk and perceived risk. Objective risk is determined by indices or statistics, while the perceived risk is determined by a participant’s subjective perception of risk driven by emotions or experience. This study will focus on the objective risk, as no information about the perceived risk can be inferred from the dataset of Imai et al. (2021).
Correlations between antecedent variables and climate change belief (from Hornsey et al. (2016))
Note. This table represents the correlations of given variables with climate change beliefs. Error bars represent 95% confidence intervals.
What can be seen from this meta-analysis is that many demographic and psychological variables can be linked to climate change beliefs. However, the question arises: to what extent is the willingness to pay to offset 𝐶𝑂2emissions (or other negative consequences of climate change) determined by climate change beliefs? There exists empirical evidence that such a relationship exists; for example, studies show that participants who are more certain about an increase in an average global temperature are willing to pay
Consequently, many studies focusing on the relationship between willingness to pay to avoid negative consequences of climate change and other variables use climate change beliefs as control variables.
One example of such study is the cross-country analysis on the willingness to pay to reduce 𝐶𝑂2emissions by 30%, 60% and 85% by 2050 (Carlsson et al., 2012). Focusing on the results for the US, the authors of this study found that as in the studies about climate change beliefs, the effect of political affiliation is significant. They also find significant results for age and income. Most importantly, the study highlights significant differences between the countries. The results show that Americans believe less in climate change and have a lower WTP relative to other countries in the study (Carlsson et al., 2012). This is interesting in conjunction with the fact that among all countries in the world, Americans are most at risk of climate-related weather events (Szmigiera, 2021).
Another study that is important to consider given its similar scenario to motivate WTP to the experiment of Imai et al. (2021) is the study looking at air travel passengers’ willingness to pay to offset their 𝐶𝑂2emissions (Brouwer et al., 2008). The authors found that the demand for counteracting emissions is high, but this tendency is lower among North Americans. In the aftermath of the study, many voluntary offsetting schemes have been introduced, but they did not prove to be effective. The reason for the intervention's ineffectiveness seems to be the fact that passengers are only willing to participate if the other passengers do so too (Brouwer et al., 2008). This issue has been addressed in another study which found that participants were more likely to participate in an offsetting scheme under collective actions (Löschel et al., 2013a)
Another distinction that is important to make is between the stated and revealed preferences about WTP. Stated preferences are collected responses of participants to hypothetical questions, whereas revealed preferences are collected by studying the actual decisions that participants need to make. As the disparity between the two types becomes apparent, more studies are turning to the revealed preferences. An excellent example of such a study is one by Löschel et al. (2013b). Their study allowed the participants to buy European Union Allowances from the EU Emissions Trading Scheme using their income. The dataset used
in this study also comes from a setting that elicited revealed preferences as the monetary reward for the participants depended on their choices, thus preferences.
After investigating the current empirical findings on WTP, it is helpful to consider why the experience of local extreme weather events affects participants’ decision-making. One way to think about it is by using three psychological factors that may influence a person’s altruistic behavior. The factors are derived from Peter Singer (1972)’s thought experiment, where a person is faced with the decision of whether to save a drowning child or not. The first factor that plays a role in the decision process is the closeness effect reflecting a person's proximity to the cause. The second factor is vividness, which describes the detail of the problem that a person can perceive, e.g. whether they see the problem first-hand, if not, what kind of images are used to portray it. The third factor is the 'drop-in-the-bucket’ effect, and it describes the extent of the belief that a person can wholly and individually solve a given problem (Singer, 1972).
The increased number of local extreme weather events can affect the vividness and closeness effects. The increased media and press coverage can contribute to a higher vividness effect (Boycoff &
Roberts, 2007) as people become more exposed to potentially detrimental consequences of climate change.
Especially considering the weather events happening in a person’s close area can make the danger more realistic and change the person’s decision-making. More importantly, as extreme weather events become a local problem, the closeness effect becomes robust. People no longer associate negative consequences of climate change with distant and unknown places but can observe how these consequences may affect their
2008). This is not surprising given System 1 and System 2’s evolutionary grounding (Kahneman, 2011), where System 1 first developed when humans formed close-knitted communities that shielded themselves from potential dangers. At the time, people did not have to think about large-scale problems or problems that were happening far away. Although possibilities for charitable behavior have greatly expanded over the years, the remnants of this thinking are still present what makes people react more readily to problems related to survival and the local community and problems which require immediate action (Epstein, 2006).
Therefore, increased local weather events have a potential of higher activation of System 1 thinking, meaning that climate change is no longer a disconnected large-scale problem, but a problem that is happening in the present tense to one’s environment and close ones. Following this reasoning, I would expect that people living in areas characterized by higher risk related to weather events will be willing to contribute more to combat the negative consequences of climate change. Therefore the hypothesis that I will test in this study is:
𝐻0: Coastal flooding risk does not influence WTA.
𝐻1: Coastal flooding risk increases WTA.
In the following section, I will describe the data that will be used to test this hypothesis.
The data used in this research comes from a study in progress by Imai et al. (2021), a collaboration between the University of Amsterdam and Ludwig-Maximilians-Universitat Munchen. In this experiment, the participants answered questions about climate change and 𝐶𝑂2emissions, for which they received a monetary reward. The study took place in December 2020 on the Prolific platform and was divided into seven parts, where part four focused on the willingness to accept 𝐶𝑂2emissions.
In part four, the participants were asked how much money they would have to be offered to accept a specific size of emissions. The price had to be between 0 and 100 pounds, and this question was asked for 1, 5, 20, 50, 100, 200, 450 and 700 miles worth of emissions. After picking the minimum price, the computer randomly chose a number between 0 and 100. If the number was higher than the participant’s minimum price, the participant would receive the monetary value of the number chosen by the computer, and the emissions would be incurred. If the number was below the minimum price, the emissions would not have occurred, and the participant would not receive a monetary reward. In this experimental setting, the default state was where the researchers would pay a donation to offset given emissions. If the participant received a monetary reward, the donation would be cancelled. This is equivalent to a state of creating emissions. If the participant gave the maximum price equal to 100, she would proceed to the next stage, where she was asked about her unbounded price. If no price would satisfy the participant, she could indicate that no monetary reward would compensate her for the emissions.
The important variables from this dataset include the externality, which represents the number of miles for which emissions are created and switch, which is the minimum price stated by the participant. In addition, this dataset included other demographic variables which were used as control variables. Among
hazards. This index is based on three considerations: Expected Annual Loss, Social Vulnerability and Community Resilience. A score in NRI indicates a county’s position relative to other counties in the US for a given natural hazard. A range of 0 to 100 constrains the scores. Every score also has a corresponding categorical value, such as “Very Low” or “Relatively Moderate” risk (FEMA, 2020). The critical variables in this dataset include cfld_risks, which gives the numerical rating of the coastal flooding risk in a county, and cfld_riskr, which gives a categorical rating of a county’s coastal flooding risk.
As the data from Imai et al. (2021) gave the geographical location in terms of zip codes and the data from FEMA was represented for counties, it was necessary to attach the zip codes to their corresponding counties to be able to merge the data skillfully. To do that, I have found a dataset from the United States Zip Codes (2021) website, which contains a list of all zip codes in the U.S. and the counties in which they are situated. This dataset was merged with the dataset from Imai et al. (2021), so it was known from which county a participant is. This could next be used to attach the coastal flooding risk for the area where the participant lives.
The last element of creating a dataset included finding a list of counties that lay by the coast, as this is one of the control variables used in my study. This dataset came from the U.S. Census Bureau, Population Division (2018). It was used to create a dummy variable coastal_county which indicated whether a county a participant lives in is a coastal county or not.
In its final shape, the dataset contains demographic information about 811 participants, their willingness to accept 𝐶𝑂' emissions for different sizes of the externality, the coastal flooding risk of their county and whether their county lies by the coast. Some participants had to be dropped from the sample for various reasons. If the participants did not have complete information included in the control variables, their answers were not used. In some cases, the dataset with coastal flooding risk did not contain the counties of some participants, then the participants’ answers were also not used. The number of participants equal to 811 is the one I arrived at after making these adjustments. It was the highest number possible to conduct the analysis comprehensively. More detailed information about the variables used in this study can be found in Appendix 1.
To capture the effect of having coastal risk in one’s residential area, it is useful to consider using the OLS regression. This method estimates the relationship between the dependent variable and one or more control variables. One of its main elements is minimizing the squared residuals between the predicted values and the actual values (Angrist & Pischke, 2014). An important concept next to OLS is the average treatment effect (ATE), which can help estimate the effect of the independent variable of interest (Angrist & Pischke, 2014). ATE is estimated using the following formula:
Average Treatment Effect
Note. 𝑌1 represents the outcome variable under treatment, 𝑌0 represents the outcome variable without the treatment, X represents the binary variable for whether a participant was treated or not (1 for treatment, 0 for control), i represents an individual observation.
Given that my research is an observational study rather than an experimental study, the use of ATE may lead to biased results as the treated participants may differ from the control participants significantly.
Therefore it may be helpful to turn to the average treatment effect on the treated, which measures the difference in the outcome variable between the treated participants and the treated participants had they not been treated (Angrist & Pischke, 2014). The formula for ATET is given below:
Average Treatment Effect on the Treated.
Note. T is a binary variable taking the value of 1 under treatment and 0 otherwise.
As can be seen in the formula, the last term cannot be observed and to address that, I will use the Propensity Score Matching (PSM) method. This method involves creating a group of control participants with similar observable characteristics to the treatment group but who did not receive the treatment (Dehejia
& Wahba, 2001). This method has an advantage over OLS because it creates a balanced dataset for selected covariates resulting in an unbiased estimate of the treatment effect (Littnerova et al., 2013).
To implement this method, the first step that needs to be undertaken is estimating the propensity score. Propensity score estimates the probability of receiving treatment conditional on chosen covariates;
this involves creating a logistic model with coastal flooding risk as a dependent variable (necessarily a binary variable) and other covariates such as age or gender as independent variables. This allows us to create a score, based on which we can compare individuals who are very similar on several traits but who differ in terms of the treatment variable (Dehejia & Wahba, 2001).
After estimating the propensity score, the next step is to pick a suitable matching method, which connects the treated individuals with the untreated ones and will later allow for estimating the average treatment effect, and the average treatment effect on the treated. Regarding matching, three considerations that will prove crucial are: whether or not to match with replacement, how many comparison units should be used for each treated unit and which matching method to choose (Dehejia & Wahba, 2001). In this study, I have decided to use nearest-neighbor matching with replacement. The benefit of matching with replacement is that it minimizes the propensity-score distance between the treated, and comparison units, and it is helpful in bias reduction. With the nearest-neighbor matching, I will use only a single comparison unit, as it will also allow for the reduction of the propensity-score distance and reduced bias. Another strong method is caliper matching that uses all matched units within a given propensity-score radius, the so-called
‘caliper’. The benefit of this method is that it only uses as many comparison units as are available within a caliper, which works in favor of the precision of the estimates (Dehejia & Wahba, 2001). Nevertheless, it is not significantly more effective than the nearest-neighbor matching (Dehejia & Wahba, 2001). In the last step, I will estimate the ATE and ATET using the matched units from the previous steps.
All in all, in my analysis, I will first estimate the OLS regression. This regression will be repeated using a Tobit specification as the participants were bounded in their choices (0 was the lowest and 100 was the highest) for the willingness to pay. The Tobit regression allows for adjusting for this bias. Then, I will estimate the propensity scores, match the units using the nearest-neighbor matching method and estimate the ATE and ATET. On top of that, I will also conduct tests for heterogeneity and multicollinearity to exclude the possibility of bias in my results. The following section will outline the results of my analysis.
Before introducing any regressions that will test the effects of different variables, it is essential to look at the simple relationship between the value of the willingness to pay to avoid 𝐶𝑂2 emissions (switch) and the externality value (externality). As the focus of this paper is the influence of coastal flooding risk, this relationship will be measured for participants who live in areas prone to coastal flooding risk and participants living in areas where such risk is not present. To do that, I have computed the mean values of switch for each externality level for both groups and displayed the relationship in Figure 3. The y-axis shows the mean value of switch, and the x-axis shows the level of the externality.
The Relationship between the Mean Value of switch and the Level of externality
Note. The table represents the relationship between the level of externality (independent variable) and the mean value of the willingness to accept 𝐶𝑂2 emissions (dependent variable) for two groups of subjects:
those with and without coastal flooding risk.
Both functions display an increasing tendency meaning that the higher the externality value is, the more the participants are willing to pay to avoid 𝐶𝑂2emissions. It can also be observed that for every level of externality, participants from areas with coastal flooding risk are willing to pay more than their counterparts. The difference between the two groups becomes more pronounced at higher levels of the externality, which can be observed in Table 1. The difference is as small as 0.5 pounds for the externality of 1 mile and grows to 5.0 pounds for the externality of 500 miles. Even though the graph shows a clear difference between the groups, it cannot yet be treated as a causal result, as no control variables were used to estimate the relationship. Other control variables such as income, political orientation or gender drive the observed results. Therefore it is necessary to conduct a more thorough analysis to isolate the effect of the variable of interest. I have also conducted a Wilcoxon rank-sum test for each externality level to see whether the two groups derive from the same population (see Appendix 4). These results do not support the hypothesis that they come from different populations, which further reinforces the suggestion of a more thorough analysis.
The Difference in the Mean Value of switch
Externality (in miles) Mean switch for participants living in
areas with CFR (in pounds)
Mean switch for participants living in areas without CFR (in
The difference in the mean value of switch
between the two groups (in pounds)
1 30.9 30.4 0.5
5 34.6 33.8 0.8
20 39.9 38.5 1.4
50 44.1 42.8 1.3
100 48.2 46.4 1.8
200 53.0 49.6 3.4
450 56.2 52.1 4.1
700 60.6 55.6 5.0
Note. The table shows the mean values of the willingness to accept 𝐶𝑂2 emissions for different levels of externality for subjects with and without CFR. The last column shows the monetary difference between the two groups.
Another important observation that can be drawn both from Figure 3 and Table 1 is that both of the functions increase at a decreasing rate, in other words, both functions display a concave shape. This observation has also been made in a study by Pace and van der Weele (2021). This suggests that participants make significant changes to their willingness to pay for low levels of externality. At higher levels of externality, this willingness to accept seems to be smoothed out. Although many explanations can be drawn as to why such a trend is observed, what can be indeed noted is that the participants do not make a simple linear calculation on how much to expend per unit of externality; their decision-making is instead subject to more complicated rules and heuristics. The explanations of participants’ behavior as described above will not be a topic discussed in this paper.
Returning to the concave shape of the two functions, it is crucial to test statistically if this is indeed the case. To do that, I have conducted a concavity test, where I constructed an OLS regression, where the independent variables are the externality variable and the square root of the externality variable (externality_sqrt). The dependent variable in this regression is switch, and several control variables were included and can be observed in Table 2.
The Concavity Test
switch Coefficient Standard error
t P> | t | 95% Confidence Interval
externality -0.04 0.01 -5.71 0.00 -0.05 -0.03
externality_sqrt 2.02 0.20 10.10 0.00 1.63 2.41
interaction 0.18 0.13 1.34 0.18 -0.08 0.44
coastal _county 2.25 1.21 1.85 0.06 -0.13 4.63
age 0.12 0.03 4.80 0.00 0.08 0.20
gender -3.78 0.78 -4.88 0.00 -5.30 -2.26
avgincome 9.02e-06 0.00 0.88 0.38 -0.00 0.00
liberal 7.02 1.38 5.10 0.00 4.32 9.72
white -1.57 1.00 -1.57 0.12 -3.54 0.40
university 2.27 1.35 1.68 0.09 -0.38 4.93
democrat -0.91 1.21 -0.76 0.45 -3.28 1.45
republican -6.52 1.51 -4.31 0.00 -9.49 -3.55
cfr -1.60 1.97 -0.81 0.418 -5.46 2.27
The table that can be observed above clearly shows that the coefficients for externality and externality_sqrt are highly significant with a p-value of less than 0.001. These results support the claim that switch is an increasing and concave function of externality. This observation will prove to be relevant when estimating later OLS and Tobit regressions. Given the focus of this paper, I have also checked for the significance of the interaction term (interaction) between externality_sqrt and cfr to see whether the observed concavity is driven by differing coastal flooding risks. The above results show that the coefficient for this term is not significant.
I will use four models in my analysis, where the dependent variable switch will remain the same in every model. Every model will also use the following control variables: externality, externality_sqrt, age, gender, avgincome, liberal, white, university, democrat, republican. Model 1 will also control whether a person lives in a county with coastal flooding risk (cfr) and whether a county lies by the coast (coastal_county). Model 2 will use cfr but not the coastal_county variable. Model 3 will use coastal county and a variable giving a rating of the severity of coastal flooding risk in an area (cfld_risks). Model 4 will use cfld_risks but not the coastal_county variable. The difference between Model 1-2 and Model 3-4 is the coastal flooding risk variable. In Model 1-2, I will be using cfr, a binary variable that takes the value of 1 for moderate to high coastal flooding risk and 0 for low or no coastal flooding risk. Model 3-4 uses cfld_risks, a continuous value of the coastal flooding risk, a rating from FEMA described in the Data section. I wanted to use these two measures to see whether the value of switch increases proportionally with risk or whether the response is triggered instead by a cutoff; people either recognize that the risk is relatively high and act on it or do not notice the risk and have a weaker reaction. Model 1 and 3 builds on Model 2 and 4, respectively, by adding the coastal_county variable reflecting whether a person lives by the coast or not. These specifications can be interesting because the comparisons between models can infer whether the potential effect can be attributed to the apparent risk or simply the fact that someone lives close to the coast, which somehow affects their decision-making.
Before running the regressions, it is also essential to take a closer look at the distribution of the standard errors in the data to rule out heteroskedasticity or to adjust the method for its presence. I used the
Breusch-Pagan / Cook-Weisberg test to test for heteroskedasticity, which takes the null hypothesis of constant variance. This test was run for all models, and the results of it can be seen below in Table 3.
Breusch - Pagan / Cook - Weisberg Test for Models 1-4
Model 1 Model 2 Model 3 Model 4
chi2(1) 63.0 60.4 35.4 33.9
Prob > chi2 0.00 0.00 0.00 0.00
Note. The table shows the results of the Breusch - Pagan / Cook - Weisberg Test for Models 1-4, where the first row gives the values from the Chi-squared test, and the second row gives the significance at which the hypothesis about homoscedasticity can be rejected.
Table 3 displays the value of the Chi-squared test in the second row and the corresponding p-value in the third row. The test shows that for every model, the null hypothesis is rejected, meaning that the assumption of homoscedasticity is unwarranted. A graphical representation of the problem for Model 1 can be seen in Figure 4. The residuals should be evenly distributed between the line where residuals are equal to 0. Nevertheless, it can be seen that the residuals take positive values more often in the first part of the fitted values and negative values more often in the second part of the fitted values. Therefore it is necessary to run the subsequent regressions using robust standard errors. To be more specific, in the following parts, I will use the clustered standard errors, which are a special kind of robust standard errors. As the dataset contains WTA for different externality levels answered by each participant, clustered standard errors will reduce heteroskedasticity across clusters of observations so individual participants.
The regressions that will be used next will test the significance of the cfr and the cfld_risks variables. I will first use the OLS regression to see the effect of different variables on the dependent variable
Heteroskedasticity in Model 1
Note. The graph shows the values of the residuals on the y-axis for given fitted values on the x-axis for the specification of Model 1.
OLS Regression for Models 1 - 4
switch Model 1 Model 2 Model 3 Model 4
(0.00) externality_sqrt 2.05***
* p < 0.10, ** p < 0.05, *** p <0.01
Note. The table shows the OLS regressions for Models 1-4, where the dependent variable is switch and several control variables are included. The top number in a given cell represents the coefficient of a variable, and the bottom number represents the standard error of a variable.
What can be seen in Table 4 is that the variables describing externalities have significant coefficients with a p-value of less than 1%. The marginal effect of externality on switch is not constant, and an additional unit of externality will initially increase switch but eventually lead to a negative effect. The variable of age is also significant for all models but only on a marginal level. In all models, its coefficient shows that being older by one year increases switch by around 0.14 pounds, ceteris paribus. The coefficient of gender is also marginally significant for all models and shows that, on average, male participants paid 3.78, 3.66, 3.82 and 3.67 pounds less (respectively) than their female counterparts. The coefficient of avgincome proved to be insignificant in all four regressions, while the dummy liberal is significant at 5%
for all models. The coefficients in these models show that being a liberal increases the willingness to pay by 7.02, 7.06, 6.99 and 7.10 pounds, respectively, ceteris paribus. Variables white, university and democrat, did not prove to be significant in any of the regressions. Lastly, the republican variable is highly significant among all models and displays a negative coefficient.
Turning to the variables of interest, Table 4 shows that the coefficients for both cfr and cfld_risks are not significant. When taking a closer look at the interval for cfr, for Model 1, it can be said that with 95% confidence, the cfr parameter is between -7.81 and 7.41; for Model 2, it is between -5.11 and 7.91.
Turning to cfld_risks, for Model 3, it can be said with 95% confidence that the cfld_risks parameter lies - 0.21 and 0.14; for Model 4, it is between -0.12 and 0.15. The confidence intervals do not give a clear answer about the magnitude or direction of the potential effect, but they show that potentially the effect could be pretty strong. Moreover, these intervals may prove to be important in the analysis of other methods used in my study. One factor that may distort the estimation of these variables is their correlation with the coastal_county variable.
To address the issue of potential multicollinearity between the coastal_county variable and the cfr variable, I first measured the correlation between them and found it to be 0.5371. However, in itself, the correlation does not prove the problem’s existence; it already shows a pretty high degree of correlation. To get a clearer picture of multicollinearity among used variables, I used the Variance Inflation Factor (VIF), where the value above 10 shows that multicollinearity may be an issue. Table 5 and Table 6 give the values of VIF for all variables, and it can be observed that the values range from 1 to slightly above 2, meaning that multicollinearity is not an issue in these regressions. This means that the lack of significant effects for the variables of interest most likely is not caused by the correlation between different variables in the regression.
VIF for Model 1 and Model 2 Variables
VIF for Model 3 and Model 4 Variables
Note. The table shows the values of VIF for all control variables in Model 3 and 4. A value of VIF above 10 may indicate the presence of multicollinearity.
As already expressed in the Method section, it might be worthwhile to consider using the Tobit regression to get more precise results in this survey setup. As the participants were asked to give a price between 0 and 100, 100 will constitute the higher bound in the regression. The regressions will be run for the same four models, and the clustered standard errors will be used. The results of this regression can be observed in Table 7. Regarding the significance levels of different variables, the Tobit specification did not lead to many changes in the results. The variables representing the externality level remain highly significant. Significant or marginally significant coefficients can still be observed for variables: age, liberal and republican. One of the differences between the specifications is that the gender variable was marginally significant for all models in OLS, while for Tobit, it is only valid for Model 1 and 2. Despite scarce changes
in the significance levels, the Tobit regression produced more precise values of the coefficients. What can also be noted is that there is no change in the signs of the coefficients, so the positive significant coefficients remain positive and negative significant coefficients remain negative. The variables of interest cfr and cfld_risks are still not significant, so the null hypothesis stating that these variables do not affect switch cannot be rejected using the Tobit model.
Tobit Regression for Model 1 - 4
switch Model 1 Model 2 Model 3 Model 4
(0.00) externality_sqrt 2.087***
-0.70 (3.66) republican -7.44*
1.40 (3.32) coastal_county 2.72
* p < 0.10, ** p < 0.05, *** p <0.01
Note. The table shows the Tobit regressions for Models 1-4, where the dependent variable is switch, and several control variables are included. The top number in a given cell represents the coefficient of a variable, and the bottom number represents the standard error of a variable.
The following method that will be used to quantify the relationship between the willingness to pay for 𝐶𝑂2emissions and the coastal flooding risk is the Propensity Score Matching, which was explained theoretically in the Method section. This method will be used for two externality levels: 1 and 700 (although I will also briefly comment in the Discussion section on the results from other levels of externality). The first step in this method is to estimate the propensity score for all observations. Initial statistics, as shown in Table 8, show that the pool of the untreated is quite large, which is favorable for many matching techniques.
The Distribution of the Treatment Variable (cfr) among Participants.
cfr Frequency Percentage Cumulative percentage
0 673 83.0 82.3
1 138 17.0 100
Total 811 100
Note. The table shows the distribution of the two groups in the entire sample: their frequency, percentage and cumulative percentage.
A set of control variables serve as regressors for the treatment variable cfr, and the results of this regression can be observed in Table 9. The results help establish the propensity score for each observation, which essentially shows how likely a participant is to be treated based on the given characteristics. The next step involves matching the participants who were treated with those not based on the closeness of the
correctly. After this step, it is possible to estimate the ATET and ATE for the two levels of externalities.
To recall the difference between the two, ATET estimates the treatment effect only for the treated subjects, while ATE gives the treatment effect for the entire sample of subjects.
Estimation of the Propensity Score
cfr Coefficient Standard
z P > | z | 95% Confidence Interval
age -0.01 0.01 -1.41 0.16 -0.03 0.00
gender -0.17 0.21 -0.81 0.42 -0.57 0.24
avgincome 0.00 0.00 1.01 0.311 0.00 0.00
coastal_county 2.89 0.23 12.59 0.00 2.44 3.34
liberal 0.18 0.38 0.48 0.63 -0.56 0.93
white -0.19 0.26 -0.74 0.46 -0.69 0.31
university 0.77 0.41 1.86 0.06 -0.04 1.57
democrat 0.60 0.32 1.85 0.06 -0.03 1.23
republican 0.31 0.44 0.70 0.49 -0.56 1.18
constant -3.50 0.64 -5.45 0.00 -4.76 -2.24
Note. The table shows the logistic regression where cfr is the dependent variable, and several control variables are used. The columns give information about their coefficient, standard error, z-value, p-value and the 95% confidence interval for every control variable.
Assessment of the Matching Quality (for Nearest-Neighbour Matching Method)
Treated Control %bias t p > | t |
age 39.9 41.8 -12.9 -1.12 0.26
gender 0.54 0.54 1.3 0.12 0.91
avgincome 77355 84293 -15.9 -1.34 0.18
coastal_county 0.72 0.76 -1.6 -0.14 0.89
liberal 0.75 0.76 -1.6 -0.14 0.89
white 0.65 0.59 12.6 0.99 0.32
university 0.93 0.91 7.1 0.65 0.52
democrat 0.67 0.67 0.0 0.00 1.00
republican 0.17 0.19 -3.6 -0.31 0.76
Note. The table compares the values of different variables for the treated and control group to assess the matching quality. In addition, it displays information about the percentage value of the bias, the t value and the p-value.
Starting with the externality = 1, the estimation of ATET and ATE can be seen in Tables 11 and 12, respectively. It can be observed that both ATE and ATET take negative values, which is an observation at odds with the hypothesis. Nevertheless, both are not significant, meaning that cfr has no significant effect on switch at an externality level of 1, and the null hypothesis cannot be rejected.
The Estimation of ATET for externality = 1
AI Robust Standard
z P > | z | 95% Confidence Interval
ATET cfr (1 vs 0)
-6.81 6.42 -1.06 0.289 -19.4 5.79
Note. The table gives the value of ATET for the externality level of 1. In addition, it displays information about its coefficient, AI robust standard error, z-value, p-value and the 95% confidence interval.
The Estimation of ATE for externality = 1
AI Robust Standard Error
z P > | z | 95% Confidence Interval
ATE cfr (1 vs 0)
-5.04 4.42 -1.14 0.25 -13.7 3.61
Note. The table gives the value of ATE for the externality level of 1. In addition, it displays information about its coefficient, AI robust standard error, z-value, p-value and the 95% confidence interval.
I decided to then look at the highest value of the externality equal to 700. Table 13 presents the value of ATET, which is significant and positive. It shows that for the group of treated subjects, living in an area at risk of coastal flooding increased switch by 10.87 pounds, ceteris paribus. A significant value can also be observed for ATE in Table 14. It shows that for the entire sample of subjects, living in areas at risk of coastal flooding increased switch by 9.34 pounds, ceteris paribus. These two results support the alternative hypothesis I presented stating that coastal flooding risk increases subjects’ WTA. It is also interesting to see that between levels 1 and 700, the sign of the treatment effects changes from negative to positive – this will be discussed in the next section.
The Estimation of ATET for externality = 700
AI Robust Standard
z P > | z | 95% Confidence Interval
ATET cfr (1 vs 0)
10.9 5.10 2.13 0.03 0.88 20.9
Note. The table gives the value of ATET for the externality level of 700. In addition, it displays information about its coefficient, AI robust standard error, z-value, p-value and the 95% confidence interval.
The Estimation of ATE for externality = 700
AI Robust Standard Error
z P > | z | 95% Confidence Interval
ATE cfr (1 vs 0)
9.34 4.73 1.98 0.05 0.08 18.6
Note. The table gives the value of ATE for the externality level of 700. In addition, it displays information about its coefficient, AI robust standard error, z-value, p-value and the 95% confidence interval.
Lastly, it would be interesting to look at the results of the PSM when controlling for the level of externality. The advantage of this approach is that it takes all observations for which data is present, meaning that a more general conclusion can be drawn about the effect of climate risk on WTA, and the effect can be measured more precisely. Table 15 shows that ATET is highly significant with a p-value below 0.1%. This shows that having coastal flooding risk in one’s area increases the WTA by 6.58 pounds
The Estimation of ATET for the PSM
AI Robust Standard
z P > | z | 95% Confidence Interval
ATET cfr (1 vs 0)
6.54 1.77 3.69 0.00 3.07 10.0
Note. The table shows the value of ATET when the externality level is included as a control variable. In addition, the table displays information about its coefficient, AI robust standard error, z-value, p-value and the 95% confidence interval.
The Estimation of ATE for the PSM
AI Robust Standard
z P > | z | 95% Confidence Interval
ATE cfr (1 vs 0)
-0.80 1.06 -0.75 0.45 -2.88 1.29
Note. The table shows the value of ATE when the externality level is included as a control variable. In addition, the table displays information about its coefficient, AI robust standard error, z-value, p-value and the 95% confidence interval.
Starting with the results from the Tobit specification, it can be observed that variables associated with gender, age and political affiliation proved to be significant. Political affiliation has been identified as an essential variable explaining people’s willingness to pay to offset 𝐶𝑂2 emissions, and this study further enforces this observation. Other studies also note the role of gender in WTA, with females paying on average more than males, and a similar effect can also be observed in my results. Contrary to other studies, these results also highlight the role of age in the opposite direction than it was previously found. The results of the Tobit regression show that WTA increases with age controlling for other important variables such as income or education.
It is also interesting to note that the average income was not found to be significant. One of the reasons for that could be the existence of potential bias in this variable. The experiment was run using the platform Prolific, and although the platform is offering many pre-screening checks to make sure that the information provided by the participants is reliable and the pool of participants is diverse, there could be an incentive for participants to alter their data in the case of income. Presumably, people in the higher income brackets would not be as interested in these studies relative to participants with low earnings because they have a higher opportunity cost, and this may create a higher demand for the high-earning participants. For this reason, participants with lower earnings may have an incentive to provide false information about their income to have more opportunities to participate in different studies, and this may distort the actual effect of income. Although this hypothesis cannot be verified, it is crucial to consider generally with platforms similar to Prolific.
Turning to the effect of coastal flooding risk, the Tobit regressions show no significant effect for
risk of flooding showed that people who reported flooding experience expressed more concern about climate change. More importantly, their concerns directly translated into a higher willingness to pay to save energy (Spence & Butler, 2011). It is doubtful, though, to what extent this higher willingness to pay is a long-term phenomenon affected by previous flooding experience and to what extent it could have been temporarily induced by priming.
Another concern that may emerge when looking at the Tobit regression results is whether the coastal flooding risk is salient enough on its own compared to other weather events risks. For example, even though a county may have low or no coastal flooding risk, it may be subject to many other climate change risks, affecting the willingness to pay. This seems to suggest that taking the general risk rating would be more valuable than focusing on a single type of extreme weather event. I tested this hypothesis by rerunning the Tobit regressions, including the general risk rating (risk_score) as a control variable and running the Tobit regressions without cfld_risks, cfr and coastal_county but with risk_score. In both cases, the risk_score coefficient was insignificant, and the coefficients that were significant before for the other variables remained significant. A similar analysis was also conducted for PSM, where instead of using the cfr variable as the treatment variable, I used a treatment describing general risk. To do that, I created a new binary variable risk_score_bi which takes the value of 1 for high or moderate levels of general risk and the value of 0 for low levels of risk. Again, as in the Tobit regression, no significant results have been observed.
The results of both of the methods can be found in Appendix 2.
The effect of coastal flooding risk was also tested using the PSM method for externality levels of 1 and 700. For the externality level of 1, both ATE and ATET did not prove to be significant. Interestingly, the effect was negative for both of them, showing that coastal flooding risk decreased rather than increased WTA. Considering Figure 3, it is reasonable to think that the difference between the treatment and control groups is not that pronounced at this level of externality. Therefore, the treatment effect may be distorted.
Perhaps at low levels of externality, the preferences are not clearly developed.
On top of that, the externality of 1 mile driven by car is probably incurred by participants daily, and as they never put a price on this choice, it might lead to the high variability of choices. I have also
estimated ATE and ATET for higher levels of externality, and the precise results can be found in Appendix 3. I found no significant results until the level of 450, where ATET was marginally significant. Finally, at the level of 700, both ATE and ATET were significant at 5%, showing that for the entire sample and the narrowly defined treated sample, coastal flooding risk decreased WTA. This allows me to reject the null hypothesis for the externality level of 700. What can be inferred from these findings is that the relationship between cfr and switch only becomes pronounced at higher levels of externality. One of the reasons for that could be that people may not feel obliged to pay the costs for externalities at low levels because these externalities are at the level of everyday activities. People may feel more responsible at higher levels, and the reaction is more substantial for people at risk because they may be more familiar with the potential consequences.
I have also conducted another analysis using PSM, where I controlled for the level of externality.
The findings of this part showed a highly significant value of ATET, showing that for the treated sample, the risk of coastal flooding increased WTA. No such effect was found for ATE. It is helpful to combine these findings with the findings of PSM for specific externality levels because it helps understand the connection between the investigated relationship with the externality level. It seems that the effect is strong for the treated, but probably it is mainly driven by the discrepancies in choices at higher levels of externality.
It can be speculated that at higher levels, people already at risk have higher activation of System 1 thinking and react more strongly, whereas, at the low levels, no sense of urgency is ignited in any of the groups.
It could be interesting to consider what factors could contribute to a higher sense of urgency at the lower levels of the externality. One of the aspects that might be important is the specification of the cause towards which the participants are donating money by withdrawing their monetary reward. In this experiment, the researchers focused on decreasing 𝐶𝑂2emissions, but perhaps if the cause was more
It can be speculated that with a cause more specific to the coastal flooding risk, the sense of urgency would be more robust which would translate to a higher WTA for subjects living in risky areas. I believe that, on average, no such effect would be observed for subjects from non-risky areas, as this specific cause would not be closely related to their environment.
The next interesting consideration is related to one of the previously mentioned studies that looked at WTP for air travel passengers. Due to the high demand for offsetting emissions, many schemes were created, but they were not effective because they did not facilitate collective action. In general, climate change is a global problem that can only be tackled through united effort; it can be said that climate change suffers from the drop-in-the-bucket effect. However, the set-up of this experiment only allowed for individual action, so the participants were not informed about the choices of others, and no collective schemes were implemented. This lack of collective element could be critical especially considering System 1 and, more precisely, participants’ association with the local community. It can be argued that the collective element, together with a more personalized cause, could lead to even higher activation of System 1 for participants from risky areas, and the difference between participants from risky and non-risky areas would be more significant.
Nevertheless, it is still debatable whether personal or collective responsibility should be emphasized with these kinds of issues. On the one hand, personal responsibility should be highlighted as collective responsibility can diffuse a person’s incentive for individual problems and create a free-riding problem (Ostrom, 1990). On the other hand, it can be argued that collective responsibility should be emphasized as people may not believe that they can change anything as individuals. Regarding climate change, it has been shown that emphasizing collective responsibility amplifies mitigation behaviors (Obradovich & Guenther, 2016). Even though this is still up for debate, it is vital to notice that the results could be different if collective action was implemented.
All things considered, the null hypothesis can be rejected for high levels of externality, and more research should be devoted to capturing the effect at the low levels of externality. It seems that there is a connection between coastal flooding risk and WTA. One of the causes for this could be a higher sense of
urgency among the participants from risky areas, yet many other causes can be debated. It can also be argued that some survey modifications could have led to a more pronounced effect, and the observations made could be helpful in further research and future policies.
The purpose of this study was to investigate the relationship between coastal flooding risk and people’s willingness to accept 𝐶𝑂2emissions. This was motivated by the observation that climate change seems to be an issue that receives insufficient attention due to people’s lack of personal connection. This is starting to change as natural hazards become more common worldwide; climate change is no longer associated with distant places but more often with people’s local environments. Therefore, this study looked at coastal flooding risk as it affects a large part of the American population, and it can be easily associated with global warming and has the potential to make long-term changes in people’s attitudes.
I used the OLS and Tobit regressions and the Propensity Score Matching method to study the previously mentioned relationship. Both OLS and Tobit regressions found a significant influence of variables such as political affiliation or gender, which replicates the findings of previous studies. The two methods did not find a significant effect of coastal flooding risk on the willingness to accept. Since the dataset I used came from an observational rather than experimental study, it is reasonable to assume that the treated subjects differ significantly from the untreated subject making the comparison not entirely feasible.
I used the Propensity Score Matching method to address this issue, and I obtained a highly significant effect of coastal flooding risk. This showed that, on average, people living in areas with coastal flooding risk require a higher price for a given level of externality than do participants living in areas without such risk. The analysis was also conducted for each externality level individually, and it was shown that the effect is significant only for the high levels of externality. This means that the null hypothesis can be rejected for high levels of externality but not for the low levels.
Nevertheless, some aspects of the study need to be considered when assessing the validity of these findings. One limitation that can be named for this study is that the dataset from Imai et al.(2021) did not contain more information about participants’ geographical location than their zip codes, and no information was available on participants’ previous experience with natural hazards. This could affect the findings
because the current geographical location of participants may not precisely capture how the geographical location affects people’s perceptions.
One of the reasons for that could be that the participants may not have lived in a given area for a long time, and the potential change in attitude has not yet crystallized. This could lead to differences between long-term and short-term residents. Moreover, people can also be influenced by information about the areas where their close ones live or lived. This may lead to a similar activation of System 1 as to when the local environment of a person is in question. Finally, the influence of media also has to be accounted for, as people are not only influenced by the easily perceived changes to their local environment, but they can also be as strongly influenced by changes in environments other than their own.
These factors could be diminished by collecting more information from participants about the named issues and conducting the analysis controlling for these factors. Future research could also focus on creating an experimental setting testing where the experimenters would impose the treatment, and the outside influences could be more easily controlled.
Considering the themes covered in the Discussion section, future research could also examine whether personalizing the cause towards which the participants contribute will widen the gap between the treated and the untreated participants. Another approach would be to compare the collective and individual actions. I believe that emphasizing cooperation could lead to even higher activation of System 1. A follow- up question to this would be whether cooperation is practical only between participants from the same or similar counties or whether cooperation in itself is enough to create unity in the fight against climate change.
The answers to these questions could prove to be important in further understanding how the local environment influences people’s decisions and how these insights can be used to inform future policymaking. Furthermore, considering the continued increase in the frequency of natural disasters, it