Policy Research Working Paper 10504 Natural Disaster, Infrastructure, and Income Distribution Empirical Evidence from Global Data Ze Song Gal Hochman Govinda Timilsina Development Economics Development Research Group June 2023 Policy Research Working Paper 10504 Abstract Natural disasters—such as flooding, hurricanes, and earth- pooling data from 130 countries for 1990–2017. The study quakes—have, on average, affected 130 million people and employs the generalized synthetic control method, which caused more than 40,000 deaths annually worldwide over involves identifying the causal effects by comparing the the past three decades. The average annual value of property actual post-disaster Gini index for treated countries with a damage is estimated at more than 90 billion dollars globally. counterfactual. The data are from the EM-DAT database Corresponding relief and reconstruction packages measur- maintained by the Centre for Research on the Epidemiol- ing in billions of dollars over the past three decades have ogy of Disasters and covers 70 percent of natural disasters brought large new investments and the formation of new globally. The key finding of the study is that catastrophic capital assets. The literature has debated the distributional natural disasters have negative relationships with inequality, impacts of natural disasters across households by income as measured by the Gini index, in both the short and long group. Most studies focus on a specific country or region, run. The study also discusses potential mechanisms, such and the findings do not converge. Some find that natu- as physical infrastructure, disruptive creation, institutions, ral disasters reduce income inequality, while others report political revolution, and financial aid, to further explain the opposite. This study adds new empirical evidence on findings from the empirical analysis. the impacts of natural disasters on income inequality by This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at gtimilsina@worldbank.org. The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Produced by the Research Support Team Natural Disaster, Infrastructure, and Income Distribution: Empirical Evidence from Global Data 1 Ze Song, Gal Hochman, and Govinda Timilsina2 Key Words: Income inequality, Natural disasters, Infrastructure development, Empirical studies, Counterfactual estimation technique JEL Classification: H54 1 The authors would like to thank Roy Van der Weide, Prem Sangraula, and Carolyn Fischer for their valuable comments and suggestions. The views and interpretations are of the authors and should not be attributed to the World Bank Group and the organizations they are affiliated with. We acknowledge World Bank’s Research Support Grant (RSB) for financial support. 2 Ze Song (zs219@economics.rutgers.edu) was a Ph.D. candidate at Rutgers University, New Jersey, United States during this study. Gal Hochman (gal.hochman@rutgers.edu) is a Professor at Rutgers University, New Jersey, United States. Govinda Timilsina (gtimilsina@worldbank.org) is a Senior Economist at the Development Research Group, World Bank, Washington, DC. Natural Disaster, Infrastructure, and Income Distribution: Empirical Evidence from Global Data 1 Introduction Large-scale natural disasters affect an economy in all dimensions. The direct impact is clear, including the death of people and damage to assets and capital (Pelling et al., 2002). However, it takes time to realize its impacts on the overall economy and its distribution across households by income as the impacts pass, directly and indirectly, through various channels (Noy, 2009). Households with different income quintiles face impacts differently due to heterogeneous exposures and differential coping capacities to the disasters (Fothergill and Peek, 2004). Existing studies investigate the impacts of natural disasters on household income distribution using country-specific household survey data (Bui et al., 2014; Abdullah et al., 2016; Feng et al., 2016; Keerthiratne and Tol, 2018; Warr and Aung, 2019). However, the results vary across these studies, and no conclusion can be drawn. For example, while examining the effect of natural disasters on household income, expenditure, poverty, and inequality using Vietnam’s 2008 Household Living Standard Survey, Bui et al. (2014), find that natural disasters cause high economic costs and worsen poverty and inequality. On the contrary, Abdullah et al. (2016), Keerthiratne and Tol (2018), and Warr and Aung (2019) report that natural disasters significantly decrease household income inequality in Bangladesh, Sri Lanka, and Myanmar, respectively. In addition, historian Scheidel (2017) argues that substantial reductions in economic inequality over human history have generally resulted from natural disasters because disasters destroy productive assets indiscriminately and reduce the asset difference between better-off households and their poorer neighbors. The mixed empirical findings can be attributed to county-specific situations, such as natural endowment, institutional structure, and response measures offered by the governments and international development communities. The type of natural disaster may also be the reason for the difference. In addition, the identification strategy applied to deal with potential endogeneity can also explain the opposite results. This paper aims to investigate the issue with a global database for a relatively long period. It also employs an alternative approach where the treated countries can be com- pared with a constructed synthetic control by exploiting the cross-country panel structure of the data. Most existing studies do not investigate the effect of natural disasters on income inequality using a cross-country panel. One exception is Yamamura (2015), which applies fixed effect techniques to a cross-country panel of 86 2 countries from 1965 to 2004. Yamamura (2015) finds that natural disasters have increased income inequality in the short term but that the effect disappears over the long run. However, this and other related studies face two significant limitations. First, a panel that includes country and time-fixed effects can only control time-invariant country-specific characteristics and global time trends that are not country-specific. Failure to capture unobserved time-varying effects yields omitted variable biases. Second, this strand should control for reverse causality–countries with better institutions and lower inequality may be more resistant to natural disasters, leading to an upward bias. This study addresses these two limitations by employing the generalized synthetic control (GSC) method proposed by Xu (2017). This approach generalizes the classic synthetic control method (Abadie et al., 2010, 2015) by introducing the interactive linear fixed-effect (IFE) model of Bai (2009) and capturing most of the unobserved time-varying factors. The GSC method artificially builds the control by weighing the outcome variable of the control countries to artificially yield similar income inequality to that of the treated countries in the absence of a natural disaster. In addition, contrary to the classic synthetic control method, the GSC method allows for multiple treated units and treatment periods. This paper considers only large natural disasters, defined as events with significant direct damage or death. Previous literature has demonstrated that only large disasters impact GDP growth (Cavallo et al., 2013). This study also arrives at a similar conclusion when analyzing the effect of the disaster on income inequality measured by the Gini index. While using a panel of 130 countries over three decades, our results suggest that exposure to natural disasters reduces income inequality in the short and long run. To this end, only extreme disasters cause a significant decrease in the Gini Index. Specifically, the average treatment effect of catastrophic disasters is -2.09. Relative to the average Gini Index of treated countries at the time of disaster of 42.95, this is a 4.87% reduction. More interestingly, the negative ramifications of natural disasters do not affect people experiencing poverty as much as it does the general population. In particular, while focusing on countries with more than 50% of the population living below the poverty line, 2% of the most extreme catastrophic disasters yield a 4% increase in the Gini index. Although the subsample result is not statistically significant, it suggests the ramifications are less profound in the extremely poor countries. The study also tries to explain some channels through which natural disasters affect income inequality. For example, natural disasters like floods and hurricanes destroy crops and livestock, reducing farmer income sources. Meanwhile, floods can damage road infrastructures that disrupt the transport of goods and services needed for production processes. It could result in temporary 3 unemployment for laborers working in the damaged supply chains. Foreign aid provided by international organizations may help remedy the loss caused by natural disasters, but the money may not be equally distributed. Not trying to capture all possible channels, we investigate several essential mechanisms. They are physical infrastructure, institutions, political revolution, financial aid, and disruptive creation. Previous studies (Abdullah et al., 2016; Scheidel, 2017; Keerthiratne and Tol, 2018; Warr and Aung, 2019), along with our analysis, reveal that natural disasters destroy infrastructures and capital assets, which are generally owned by the rich. Some other factors like institutional quality, financial aid, and political revolutions are useful in understanding the distributional effect of natural disasters. In addition, disasters may stimulate a revolution that updates the economic structure from within. The idea of disruptive creation (Schumpeter, 1950) is frequently employed to explain the impact of natural disasters on long-run growth, especially in developing countries. It is also helpful in understanding the declining income inequality. The paper is organized as follows. Section 2 describes the empirical model used, followed by descriptions of data sources and underlying assumptions in Section 3. Section 4 and Section 5 present the results and discuss potential mechanisms, respectively. Finally, conclusions and policy implications are drawn in Section 6. 2 Methodology 2.1 The Generalized Synthetic Control (GSC) Method This paper builds on the work of Xu (2017), which generalizes the Synthetic Control method via integrating the interactive fixed effects (IFE) model with the classic Synthetic Control (SC) estimator. The IFE model aligns with the factor models used in quantitative finance, including the unit-specific intercepts (factor loading) that interact with the time-varying coefficients (factors). Formally, Xu (2017) proposed the following three steps: First, we estimate an IFE model using the control countries (i.e., countries not exposed to natural disasters) over the entire sample period. Technically, let = 1, 2, … , denote countries and t = 1, 2, ...0 , ..., T denote periods (years) where 0 is the year of the disaster. Then, following Bai (2009)’s notation, = + ′ + ′ + (1) is the measure of income inequality in country at time . is the treatment indicator 4 that equals one if a country has been exposed to a natural disaster at time t and zero otherwise (i.e., = 1 when ∈ and ≥ 0 and = 0 otherwise). Thus, that measures the heterogeneous treatment effect on country at time is of particular interest. is a × 1 vector of observable regressors, and is a × 1 vector of unknown coefficients, which is estimated at this step. In addition, is an × 1 vector of unknown factor loadings, is an × 1 vector of common factors so that ′ = 1 1 + ⋯ + . The factor component takes a linear, additive form by assumption, where are idiosyncratic errors, and and are unobserved. 3 ̂ , The control countries are used to estimate � � , and using an iterative principal component estimator (Bai, 2009). This approach consists of iterating between estimating and using principal components while holding constant and estimating in the linear model using the most influential factors of and until reaching convergence. 4 We explain the estimation of the IFE Model at length in the Appendix A.3. ̂ and Assuming � are the same for both the treated and the control countries, the outcome � ′ ̂ ′ � = + . This leads us to the values for each treated country can be predicted using second step of this estimation procedure. In the second step, the factor loadings are estimated for each treated country (recall that step one estimated for all control countries). Specifically, the predicted treated country’s mean � and squared error (MSE) during the period that preceded the disaster is minimized. Given � , the distance between the observed outcome and the predicted outcome for each given treated country is � minimized while focusing on the period before the natural disaster occurred, giving rise to . Last, we reintroduce the control countries into the original model to estimate the distributional impacts of the natural disaster on income inequality. Formally, the treated country is assumed to experience the natural disaster at time 0 . It allows the estimation of the effect of the event (i.e., ) on country for ≥ 0: � = − (2) � Where the treated counterfactual is calculated as ′ ̂ � ′ � = + , and the estimated treatment effect is calculated using Equation (2). 3 This model captures a wide range of unobserved time-variant heterogeneity. Notably, the conventional difference-in- difference model with two-way fixed effects is one special case of this generalized model specification. 4 For the moment, the number of factors R is assumed to be known. But in practice, the exact number of factors R can be selected through a cross-validation procedure described in Xu (2017). 5 The GSC method aligns with the classic SC method and reweights the control countries to track the treated countries. The difference between the two methods stems from the reweighting procedure. Once generating the control countries, the two methods proceed similarly. To this end, the generalizing of synthetic control provides two main advantages in studying the causal impact of natural disasters on income inequality. First, as noted above, it allows for multiple treated countries and variable treatment periods; there is no need to find one-by-one matches of control countries for each treated country. The reason is that the IFE model is estimated once while focusing on the period before the natural disaster. Second, when the model is correctly specified, the GSC method discards no observations from the control group and thus is more efficient than the original SC matching method. However, the GSC method also has limitations. First, it requires a sufficient number of pre- treatment periods, at least equal to the number of fixed effects estimators, to lead to unbiased estimates. Second, the method assumes that treated and control units share common support in factor loadings. 2.2 Modeling Natural Disasters Since identification requires that only some countries are affected by natural disasters, we start by creating a binary indicator–i.e., in Equation (1). Previous studies on natural disasters demonstrate that only catastrophic natural disasters yield significant economic impacts (Cavallo et al., 2013). Thus, this paper focuses only on large natural disasters, not on recurrent events that happen frequently and affect multiple nations at any given time. We follow Cavallo et al. (2013) and define large natural disasters by considering the magnitude of the natural disasters from a worldwide perspective. Unlike Cavallo et al. (2013), which focuses on economic growth, this paper studies the impact of large natural disasters on income inequality. More importantly, the study uses the GSC method to study multiple events simultaneously. In other words, instead of focusing on a single event, we use the full information about the world’s natural disasters and study their impact on income inequality. This exercise not only adds statistical power to the results but also provides the external validity of the distribution effect of natural disasters. To compare the magnitude of events and study the impact of natural disasters across countries, we standardize the magnitude of catastrophes by the size of the economy. Specifically, we divide the number of lives lost by the country’s population and the total estimated damages by a country’s GDP. Figure 1 shows the distribution of two measurements of disasters: death ratio and damage rate. The distribution of these measurements is highly skewed to the left, suggesting most disasters are small and 6 recurrent. A few disasters are catastrophic and cause severe damage, such as Myanmar’s 2008 cyclone Nargis and Haiti’s 2010 earthquake. Disasters events are categorized using percentiles while considering the 80th, 90th, 93rd, and 98th percentiles of the world distribution of magnitude. Countries whose measurements fall above the cutoff percentile are the treated countries, whereas the rest are the control units. In other words, equals one for countries following a natural disaster event that yielded an impact larger than the cutoff percentile of global events and equals zero otherwise. Assuming a cutoff of the 98th percentile, countries to the left of the red lines drawn in Figure 1 met the definition of a natural disaster. Table 1 depicts countries and years experiencing natural disasters that cause damage or death whose magnitude is more significant than 98 percent of events in the sample. Panel (A) is associated with the death rates. Among the 130 countries, 20 countries witnessed large natural disasters 25 times. Regarding the damage rate measure in Panel (B), 22 countries experienced large natural disasters 25 times. We observe differences in the treated countries when changing from one measurement to another. Nonetheless, some catastrophic disasters are counted under both definitions, suggesting they caused significant damage and death. Some early events with insufficient pre-treatment periods will not be considered the treated countries and will be automatically dropped from the data while running the estimation program. Given the definition of significant natural disasters, we can categorize countries into treated and control countries and use this information to estimate the average treatment effect of substantial natural disasters on income inequality. This methodology estimates the average treatment effect and determines events’ overall causal impact on income inequality, including direct and indirect effects. 3 Data and Sample Next, we survey the data and its sources, starting with the dependent variable, income inequality. 3.1 Income Inequality, the Dependent Variable A country’s income inequality ( in Equation (1)) is from the poverty and inequality data from the World Bank’s Poverty and Inequality Platform (PIP). PIP is managed jointly by the Data and Research Groups in the World Bank’s Development Economics Division. It reports both poverty measures and inequality measures, including the Gini Index for 168 countries from 1968 to 2022. The Gini index is based on primary household survey data obtained from government statistical agencies and World Bank country departments. Data for high-income economies are mostly from the Luxembourg 7 Income Study database. In addition to the gold standard of the PIP dataset, we check the robustness of results using an alternative dataset that provides inequality measures. Specifically, we use the Standardized World Income Inequality Database (SWIID). 5 The SWIID maximizes the comparability of available income inequality data for the broadest possible sample of countries and years (Solt, 2020), with the Gini index available from 1960 to 2019 for 169 countries. Results based on the alternative measure are available in Appendix A.1. 3.2 The Independent Variables 3.2.1 Natural Disaster Data on natural disasters is from the EM-DAT database maintained by the Centre for Research on the Epidemiology of Disasters. This dataset covers more than 200 countries where the tragedy occurred between 1970 and 2019. Disaster events must fulfill at least one of the following criteria to enter into the database: • death of 10 or more people, • 100 or more people affected/injured/homeless, or • declaration by the country of a state of emergency and an appeal for international assistance. The classification used follows the IRDR Peril Classification and Hazard Glossary. This classification covers multiple disaster types, including geophysical, meteorological, hydrological, climatological, and biological. Following Cavallo et al. (2013), this study focuses on earthquakes, floods, and storms, the three most common types of disasters, accounting for more than 70% of the total occurrence in the raw data. The information we use includes the number of people who lost their lives because of the event, total estimated damages (in thousands of US$ at the value during the period of occurrence), and the year when the disaster started and ended. We only consider the year when the event occurred and aggregate it to country-year levels because the outcome variable of interest, the Gini Index, is calculated yearly. In addition, for country- year observations, we can observe the number of occurrences, total deaths, and total damage caused by the three disaster types. 5 SWIID takes a Bayesian approach to standardize observations collected from the OECD Income Distribution Database, the Socio-Economic Database for Latin America and the Caribbean generated by CEDLAS and the World Bank, Eurostat, the World Bank’s PovcalNet, the UN Economic Commission for Latin America and the Caribbean, national statistical offices around the world, and many other sources (Solt, 2020). 8 3.2.2 Control Variables We use the following covariates (′ in Equation (1)) real GDP per capita, population, and a composite measure for human capital. We extract real GDP and human capital data from Penn World Table 10 (Feenstra et al., 2015), using the “rgdpna” series, which measures real GDP in constant 2017 US PPP dollars. We quantify the human capital stock via the “hc” series, an index based on years of schooling and returns to education (Inklaar and Timmer, 2013). We extract the population from World Development Indicators (WDI). 3.3 Sample Construction A country panel dataset of 130 countries from 1990 to 2017 is constructed, which includes developed and developing countries. We use the most recent year to impute missing observations when building the data. For example, if one nation had missing Gini Index data for 2017, we extrapolate the missing 2017 data by keeping the same value as stated in 2016. When the data missing is for the first year, like 1990, we use the same value as 1991. However, if a country has no observation for any control or dependent variables, we drop that country. This methodology generates a panel of 130 countries. Table 2 depicts the summary statistics. The table shows the country-year mean value of the Gini Index (from both PIP and SWIID datasets), human capital index, real GDP, population, total death, and disaster damage. Column (1) indicates the mean values for 130 countries over the two decades. Column (2) is associated with the countries exposed to large disasters belonging to the top 99 percent. Column (3) is related to the rest of the countries, representing a reservoir of the control group. The difference between the two groups of countries justifies using the GSC method to construct a synthetic control group. 4 Model Results and Interpretations To better understand if natural disasters indirectly impact income distribution, we study the average treatment effect of natural disasters on the Gini index. With the help of the GSC method, we estimate the average treatment effect by comparing the post-intervention average to the counterfactual Gini Index for the treated countries when the constructed counterfactual is specified in Equation (2). Below, we investigate the effect of the natural disaster on the Gini coefficient using two alternative definitions: death rate (section 4.1) and damage rate (section 4.2). 9 4.1 Death Rate We start with large natural disasters defined through death rates. Figure 2 shows the average treatment effect of large disasters on the Gini index for the four cutoffs: 80th, 90th, 93rd, and 98th percentiles. Each panel represents a separate regression and is associated with a different cutoff. Panel (a) defines large natural disasters as events above 80 percent of the world’s death rate distribution. Similarly, panels (b) to (d) adopt the 90th, 93rd, and 98th percentiles, respectively. The higher the cutoff value, the fewer events are considered large disasters. In each panel, the X-axis represents the year relative to the large natural disaster, truncated at 15 years before and 15 years after the disaster. The solid black line represents the average treatment effect of large natural disasters on the Gini index. The grey area is the 90% confidence interval of the estimates. The bar plot at the bottom of the figure shows each period’s treated countries. As we lift the cutoff on the distribution, the number of treated countries reduces. For example, when we define the disaster with an 80th percentile cutoff, 40 countries experience a disaster (see panel (a)), while the number of treated countries decreases to 19 when the cutoff is raised to the 98th percentile (see panel (d)). In addition, some events that happened in the early years may not have enough pre-intervention years. In contrast, other recent events may lack enough post-intervention years, reducing the number of treated countries as we move away from the event year. As shown in Figure 2, large natural disasters reduce income inequality when the events are defined using the death rate regardless of the cutoffs. However, the magnitude and statistical significance of the treatment effects do vary with the cutoffs. Specifically, when we define large natural disasters to be those above the 80th percentile of the world death rate distribution, as shown in panel (a), the treatment effects on the Gini index are minimal in the first few years and gradually tend to be negative. Nonetheless, the effects are not significant. So is the effect using the 90th or 93rd percentile as the cutoff (see panels (b) and panel (c)), suggesting that many natural disaster events under this definition are recurrent. On the contrary, when we define large natural disasters as those above the 98th percentile of the world death rate distribution, as shown in panel (d), the Gini index decreases significantly in response to the events, and the effects last for years. The results align with Cavallo et al. (2013), which suggests that only extremely large disasters have a significant economic impact in the short and long run. In addition, our findings support Keerthiratne and Tol (2018) and Warr and Aung (2019) that find natural disasters reduce income inequality and generalize their results to the global level. Next, we supplement the figure by quantifying the estimates of average treatment effects in 10 Table 3. We estimate the magnitude of reduction in the Gini Index for treated countries after major natural disaster events and calculate how large the impact is compared to the worldwide average Gini Index. Panel (A) of Table 3 is associated with the average causal effect of a large disaster on the Gini index, defining large disasters with death rates. Each row represents a separate cutoff, from the 80th percentile to the 98th. Column (1) indicates the average treatment effect after the intervention, which pools all the treated units and time together. Column (2) shows the total number of post-intervene treated units. In other words, it equals the sum of the bar plot at the bottom of Figure 2 after time 0. Columns (3) to (6) are related to the statistical inference, indicating the standard deviations of the GSC estimates, confidence intervals, and P-values, respectively. The last column shows the number of factors in the IFE model chosen by the cross-validation algorithm. The best-fitted model is the classic two-way fixed- effect model when the factor equals zero. In line with Figure 2, Table 3 indicates that large disasters negatively impact the Gini Index (reduce income inequality) regardless of the cutoff selection. However, as we raise the cutoff, the magnitude of the treatment gets larger, from -.79 for the 80th percentile to -2.09 for the 98th percentile. Relative to the average Gini Index for treated countries at the time of disaster of 42.95, this is a 4.87% reduction. Given the rising global income inequality, measured by the absolute Gini coefficient, in the past three decades, the decline in Gini Index caused by natural disasters is significant. The results also pass the equivalence test (Figure 3) and the placebo test (Figure 4). The equivalence test directly tests whether the error term is orthogonal to the timing of the treatment in the pre-treatment periods. The test searches for evidence to reject the hypothesis of inequivalence. We complement the equivalence test with the placebo test, where the event is assumed to happen two periods earlier. Then, using the same counterfactual estimators, the Placebo test checks if the estimated average treatment effects in the placebo periods are statistically different from zero (Liu et al., 2022). The counterfactuals pass both tests. We also assess the absence of time-varying confounders by comparing the results with those of a model following a fixed-effect approach. Finally, we also compare the IFE to a Matrix Completion (MC) method, a generalization of the factor-augmented models. The results of the IFE are very similar to those of the matrix completion, which are shown in Appendix A.2. Yet, both models result in very different outcomes from the fixed-effect model, thus supporting the IFE approach. As suggested by previous literature (Keerthiratne and Tol, 2018), the reduction in income inequality in response to large natural disasters might be explained by the fact that rich people bear the disproportionately higher cost of the damage of natural disasters. This is because rich people are more 11 likely to derive income from capital assets. At the same time, the poor usually have a high share of agricultural or unskilled labor income. Natural disasters destroy capital assets and lead to profit loss for the rich. Although poor people are vulnerable to disasters, they own fewer capital assets, so the absolute level of the loss might be less for the poor than for the rich. 4.1.1 Countries in Poverty To better understand the effect of natural disasters on people experiencing poverty, we repeat the analysis while focusing on countries where more than 50% of the population is below the poverty line. The output of these runs is summarized in Figure 5, showing that the effect of natural disasters on the Gini index is less profound or even positive in extremely poor countries. The average treatment effect using the IFE estimator (Panel (a)) while focusing on the 98th percentile is 1.89—a 4% increase relative to the average Gini Index in the treated countries. Poor communities are often disproportionately affected by natural disasters. The combination of limited resources, inadequate infrastructure, and lack of access to critical support systems can exacerbate the impact of natural disasters on these vulnerable populations. Nevertheless, the negative ramifications of the effect of natural disasters on embodied assets skew the impact of these disasters disproportionately toward the wealthier parts of the population. Because natural disasters consume capital, they have a more significant negative impact on the more affluent parts of the population, resulting in income inequality declining. Natural disasters can cause significant death and damage, impacting both human lives and infrastructure. Natural disasters can cause extensive damage to critical infrastructure, including roads, bridges, buildings, power grids, and communication systems. This damage can disrupt essential services, such as transportation, electricity, water supply, and telecommunications, hindering rescue and recovery efforts and prolonging the impact of the disaster. The destruction of infrastructure, loss of businesses, and disruption to agricultural activities can lead to economic downturns in affected regions. The cost of rebuilding and recovery can be substantial, straining government budgets and resources. When measuring the effect of natural disasters on countries, however, the event’s severity depends on whether it is measured by the number of deaths or through direct and indirect damages. While the event’s severity is skewed toward poorer countries when measuring the severity of the event using deaths, when using damages, more developed and more affluent countries make the dubious list of extreme events. Even though the number of fatalities among wealthy OECD countries is relatively small compared to others, when using total damages, it surpasses any other group by a significant amount. 12 4.2 Damage Rate Do the effects of natural disasters on income inequality depend on how we measure extreme events? To compare the impact of natural disasters quantified via death rates with that of damages, we define large disasters using the damage rate in this section to evaluate the robustness of the above conclusions. Figure 6 shows the average causal effect of a large disaster on the Gini index over time. Again, Panels (a) to (d) adopt the 80th, 90th, 93rd, and 98th percentiles, respectively. The X-axis represents the year relative to the large natural disaster. Generally, large natural disasters under the definition of damage rate reduce income inequality. As shown in Panel (b) of Table 3, the magnitude and statistical significance of the treatment effects also increase as we lift the cutoffs, from -1.05 for the 80th percentile to -2.66 for the 98th percentile. Relative to the average Gini Index for treated countries at the time of disaster of 42.4, this is a 6.27% reduction. In addition, the results pass both the equivalence test (Figure 7) and the placebo test (Figure 8). These results suggest that although natural disasters measured via damages affect the affluent population of a country, poor communities in those countries often lack the financial means to prepare for or recover from natural disasters adequately. And the lack of resources makes it difficult for people that lack financial resources to recover and rebuild after a disaster. In addition, because land value is relatively expensive in affluent areas, many poor communities live in areas prone to natural disasters. These areas usually have lower land costs or lack affordable housing options, yielding disasters with a higher risk of severe damage or displacement. Post-disaster, these communities likely face significant challenges in recovering. Moreover, the lack of social support systems further hinders their recovery and makes them more susceptible to long-term poverty. We suspect that the catastrophic loss inflicted by the natural disaster led the government and support system to compensate for the loss and try to recover as much of the wealth lost as possible, thus preserving the income distribution among the population and alleviating the effect of the natural disaster on income inequality. Overall the analysis leads to similar trends as recent literature (Keerthiratne and Tol, 2018; Warr and Aung, 2019) that large natural disasters reduce income inequality. Besides, our study also suggests that the findings are not country-specific and generalized globally. 5 Qualitative Discussion of Potential Mechanisms The GSC is a robust methodology that enables us to establish causal claims empirically. 13 However, it is a black box and provides only the average treatment effect of natural disasters. Moreover, GSC does not allow the identification of the mechanisms yielding the estimated causal effect. Instead of empirically identifying the paths, this section provides a qualitative discussion based on the literature to help understand the empirical results. The potential channels discussed here are physical infrastructure, disruptive creation, institutions, political revolution, and financial aid. 5.1 Physical Infrastructure Extreme natural disasters directly impact physical infrastructures like roads, rails, power plants, and telecommunication networks. These ramifications will disproportionately affect capital assets (Skidmore and Toya, 2002; Crespo Cuaresma et al., 2008; Kadri et al., 2014; Willis et al., 2016). Moreover, the potential loss of physical assets, such as buildings and factories, alters income distribution since it disproportionately affects the people who own capital (Abdullah et al., 2016; Scheidel, 2017; Keerthiratne and Tol, 2018; Warr and Aung, 2019). Keerthiratne and Tol (2018) study the impact of natural disasters on income inequality in Sri Lanka using household income data and decompose the income sources to understand better the potential mechanisms that can explain the effect of natural disasters on income. They found that natural disasters decrease non-agricultural income inequality but increase seasonal agricultural income inequality. Wealthier households have a higher share of non-agricultural income, such as manufacturing, while poorer families rely more on agricultural activities. Even in the case of agriculture, poor households are mostly small- holders and large-size farms are owned by the rich. Damages to agriculture can also fall on the rich households with farming businesses. Therefore, natural disasters disproportionately affect the rich people in the country who own the capital or production capacities. Scheidel (2017) also supports this hypothesis by finding a reduction in income inequality due to natural disasters. It argues that natural disasters indiscriminately destroy productive assets and reduce the asset differences between better-off households and poorer neighbors. Our data also support the claims made above. First, we empirically assess the impact of natural disasters on three categories of physical infrastructure: energy, transportation, and communications. 6 6 Electricity infrastructures are represented by the percentage of urban and rural access to electricity and electricity generating capacity in megawatts (MW). The communication infrastructure is measured with the portion of the population using the internet. Road density and the number of registered carrier departures from domestic air transport per 100 people are used for transportation. The road density measurement refers to the ratio of road length in km to the country’s area in squared km. Registered carriers’ departures worldwide include domestic takeoffs and takeoffs abroad of air carriers registered in the country. 14 The effect of substantial natural disasters 7 on the physical infrastructure stock over time is presented in Figure 9, where each panel represents a separate regression that corresponds to a different infrastructure measure: • Electricity: Panel (a) and panel (b) represent the access to electricity in rural and urban areas: rising to large natural disasters, households in rural areas do not lose access to electricity compared to non-affected countries. However, the percentage of electricity access in the urban area reduced significantly in response to large natural disasters. The disproportionate ramifications on the power system in the urban, and the income disparity across rural and urban areas, can explain our findings of lowering income inequality after major natural disasters. In addition, panel (c) represents the capacity of electricity generation, where power generation capacity significantly decreased after major natural disasters, and the effect persisted for several years. • Transportation: Panel (d) and panel (e) depict air carriers and road density. The analysis suggests road density decreases in countries exposed to major natural disasters compared to non- affected countries. • Communication: Finally, the communication infrastructure represented by internet access in panel (f) decreases after significant disasters. Significant natural disasters are directly causing damage to physical infrastructure stock. Therefore, the loss of physical assets due to natural disasters will likely reduce income to affluent, urban households. While people having fewer capital assets suffer fewer income losses over the long run. 5.2 Institutional Capacity and Political Revolutions Institutional capacity is an essential factor explaining the link between disasters and the heterogeneous distributional impact of disasters. Several studies highlight this factor. For example, Banerjee et al. (2020) find divergent results of two earthquakes in two Italian regions in 1976 and 1980. Compared with the simulated GDP that would have been observed, they find the long-term impact of natural disasters on GDP per capita is positive in one case and negative in the other. The lower pre-quake institutional quality is the critical reason for explaining the case with bad outcomes. Similarly, Breckner et al. (2016) find that market forces and public institutional infrastructure are essential in bolstering resilience against natural disasters. In addition to institutional capacity, political revolutions stimulated by natural disasters may 7 Substantial natural disasters are events that cause a death rate greater than the 97th percentile of all the natural disasters in the sample. 15 also help understand the distributional impact. Cavallo et al. (2013) find that extremely large disasters harm output in the short and long run. They also show that radical political revolutions following the disasters are the true reason for seeing decreasing outputs. Once they control these political changes, even extremely large disasters do not significantly affect economic growth. In contrast, the political revolution has historically been associated with the inequality decline (Muller, 1985; Justman and Gradstein, 1999). 5.3 Financial Aid Humanitarian aid and financial support by the international community after a natural disaster also help explain the reduction in income inequality. International organizations or domestic governments distribute humanitarian assistance directly to affected communities to speed up recovery. The size of the aids could be huge. For example, the catastrophic earthquake in Haiti in 2010 unleashed a 13.5- billion-dollar humanitarian aid. According to a report by the Inter-American Development Bank, the number of goods and services the country produced in 2008 was only $7 billion. Suppose the aids are appropriately delivered and distributed to people according to their needs. In that case, the money in the short run will turn into income and, in the long run, help increase technical efficiency (Barone and Mocetti, 2014), reducing inequality. Several studies also discuss the potential moral hazard in aid delivery (Andor et al., 2020; Amarasiri de Silva, 2009). For example, Andor et al. (2020) use survey data from German homeowners to test the theory of charity hazard—individuals anticipate it and forgo private precaution measures. They analyze different private flood precaution strategies and floods in exposed vs. non- exposed areas, finding a substantial charity hazard in the insurance market for individuals in flood- prone areas. In addition, Amarasiri de Silva (2009) studies the post-tsunami humanitarian aid delivery in Ampara District, Sri Lanka, finding that delivering aid without considering local networks and diverse ethnicities leads to increased ethnic division, inequality, and disorder. 5.4 Disruptive Creation Disruptive creation is related to the economist Joseph Schumpeter in the 1950s, de- scribing the “process of industrial mutation that continuously revolutionizes the economic structure from within, incessantly destroying the old one, incessantly creating a new one” Schumpeter (1950). Several studies employ this concept to explain the impact of natural disasters on long-run growth, especially in developing countries. For example, while examining the long- run relationships 16 among disasters, capital accumulation, and economic growth using cross-country data, Skidmore and Toya (2002) find that higher frequencies of climatic disasters are related to a substitution from physical capital investment towards human capital investment. Expanding human capital investment can reduce educational inequality and, thus, income inequality (Glomm and Ravikumar, 1992; Lee and Lee, 2018). In addition, Skidmore and Toya (2002) find that a country whose capital stock is reduced by natural disasters has the incentive to adopt new technologies, thereby improving total factor productivity. Crespo Cuaresma et al. (2008) study the impact of catastrophic risk on technology transfer and find that richer countries eventually experience creative destruction after a disaster. Barone and Mocetti (2014) examine the impact of two large- scale earthquakes in two Italian regions on GDP per capita. Those authors found that increased technical efficiency via disruptive creation can explain the positive effect on income. Forces that enhance creative destruction or raise the rate at which high-growth individuals lose that status can decrease inequality (Jones and Kim, 2018). Put differently, when the economic growth triggered by natural disasters brings relatively more opportunities to low-income households, we can expect a reduction in income inequality in the long run. 6 Conclusion How natural disasters affect income inequality is an essential empirical question in development economics. Existing studies on this question are sparse (Bui et al., 2014; Keerthiratne and Tol, 2018; Warr and Aung, 2019). The findings from these studies contradict each other. Moreover, the existing studies suffer from methodological limitations. This study brings up some empirical evidence on the relationship between natural disasters and income inequality using panel data covering 130 countries for almost 30 years (1990-2017) and one of the latest techniques in econometrics, the generalized synthetic control method developed by Xu (2017). The method employed in our study is built on Abadie et al. (2010) and Bai (2009), which involves identifying the causal effects by comparing the actual post- disaster Gini index for treated countries with a counterfactual. The data on natural disasters include the most common disasters, earthquakes, floods, and storms, which cover more than 70% of disasters globally. Contrary to previous work focusing on a single country, we use a country panel covering most major events worldwide using the newly developed identification strategy. This excise allows us to use all the information about natural disasters and study their impact synthetically. We find the negative 17 correlations between natural disasters and income inequality from short- and long-run perspectives. The intuition behind our findings is that affluent households generate disproportionately higher income from assets prone to natural disasters like earthquakes and floods. On the other hand, poor households usually have a high share of agricultural or unskilled labor income. They are the ones who have to supply unskilled labor during post-disaster activities, such as the repair and reconstruction of roads and buildings damaged by natural disasters. Although poor people are vulnerable to disasters, natural disasters are more likely to cost them social welfare (losing homes and lives) than their income sources. Some existing studies also report similar findings (e.g., Keerthiratne and Tol, 2018, for Sri Lanka and Warr and Aung, 2019, for Myanmar). Other factors might have also contributed to reducing income inequality after natural disasters. For example, financial aid from humanitarian agencies and international development partners that often target the poor might have contributed. Existing literature also suggests that natural disasters can cause disruptive creation that could help to reduce income inequality in the long run. Natural disasters are undesired, but they occur as they are beyond the control of human beings. However, response activities can be designed to help reduce social problems. For example, the COVID recovery packages in many countries have environmental and social objectives as they are focused on people with low incomes and the needy. The stimulus packages in response to the financial crisis also help low-income households. Similarly, relief and reconstruction packages after natural disasters could help the poor more than the rich, contributing to lower income inequality in the short run. In future studies, a quantitative analysis of potential mechanisms is needed. 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We standardize the magnitude of catastrophe by the size of the economy by dividing the number of lives lost by the country’s population and the total estimated damages by a country’s real GD 22 Figure 2: Treatment Effect of Disasters on Gini Index–Death Rate (a) Disasters above 80% death rate (b) Disasters above 90% death rate (c) Disasters above 93% death rate (d) Disasters above 98% death rate Note: This Figure shows the average causal effect of a large disaster on the Gini index. Each Panel represents a separate regression. Large natural disasters are constructed for each regression with different cutoffs from the 80th to 98th percentile of the world distribution of death rate. In each Panel, the X-axis represents the year relative to the large natural disaster, truncated at 15 years before and 15 years after the events. The solid black line represents the average treatment effect of large natural disasters on the Gini index. The grey area is the 90% confidence interval of the generalized synthetic control estimates. The bar plot at the bottom of the figure shows each period’s treated units. 23 Figure 3: Treatment Effect of Disasters on Gini Index–Equivalence Test (a) Disasters above 80% death rate (b) Disasters above 90% death rate (c) Disasters above 93% death rate (d) Disasters above 98% death rate Note: This Figure shows the average causal effect of a large disaster on the Gini index. Each panel represents a separate regression. Large natural disasters are constructed for each regression with different cutoffs from the 80th to 98th percentile of the world distribution of damage rate. In each Panel, the X- axis represents the year relative to the large natural disaster, truncated at 15 years before and 0 years after the events. The equivalence test passes if the lines stay within the dashed lines. 24 Figure 4: Treatment Effect of Disasters on Gini Index–Placebo Test (a) Disasters above 80% death rate (b) Disasters above 90% death rate (c) Disasters above 93% death rate (d) Disasters above 98% death rate Note: This Figure shows the average causal effect of a large disaster on the Gini index. Each panel represents a separate regression. Large natural disasters are constructed for each regression with different cutoffs from the 80th to 98th percentile of the world distribution of damage rate. In each Panel, the X- axis represents the year relative to the large natural disaster, truncated at 15 years before and 15 years after the events. The solid black line represents the average treatment effect of large natural disasters on the Gini index. The bar plot at the bottom of the figure shows each period’s treated units. And the Placebo Test value is also reported in the figure. 25 Figure 5: Treatment Effect of Disasters on Gini Index–Extreme Poor Countries (a) Integrated Fixed-Effect: Countries with more than 50% Poverty Population (b) Matrix Completion: Countries with more than 50% Poverty Population Note: This Figure shows the average causal effect of a large disaster on the poor. Each Panel represents a separate regression corresponding to different levels of impact. Large natural disasters are constructed for each regression 98th percentile of the world distribution of death rate. In each Panel, the X-axis represents the year relative to the large natural disaster, truncated at 15 years before and 15 years after the events. The solid black line represents the average treatment effect of large natural disasters on infrastructure measures. The grey area is the 90% confidence interval of the generalized synthetic control estimates. The bar plot at the bottom of the Figure shows each period’s treated units. 26 Figure 6: Treatment Effect of Disasters on Gini Index–Damage Rate (a) Disasters above 80% damage rate (b) Disasters above 90% damage rate (c) Disasters above 93% damage rate (d) Disasters above 98% damage rate Note: This Figure shows the average causal effect of a large disaster on the Gini index. Each panel represents a separate regression. Large natural disasters are constructed for each regression with different cutoffs from the 80th to 98th percentile of the world distribution of damage rate. In each Panel, the X- axis represents the year relative to the large natural disaster, truncated at 15 years before and 15 years after the events. The solid black line represents the average treatment effect of large natural disasters on the Gini index. The grey area is the 90% confidence interval of the generalized synthetic control estimates. The bar plot at the bottom of the figure shows each period’s treated units. 27 Figure 7: Treatment Effect of Disasters on Gini Index–The Equivalence Test (a) Disasters above 80% damage rate (b) Disasters above 90% damage rate (c) Disasters above 93% damage rate (d) Disasters above 98% damage rate Note: This Figure shows the average causal effect of a large disaster on the Gini index. Each panel represents a separate regression. Large natural disasters are constructed for each regression with different cutoffs from the 80th to 98th percentile of the world distribution of damage rate. In each Panel, the X- axis represents the year relative to the large natural disaster, truncated at 15 years before and 0 years after the events. The equivalence test passes if the lines stay within the dashed lines. 28 Figure 8: Treatment Effect of Disasters on Gini Index–The Placebo Test (a) Disasters above 80% damage rate (b) Disasters above 90% damage rate (c) Disasters above 93% damage rate (d) Disasters above 98% damage rate Note: This Figure shows the average causal effect of a large disaster on the Gini index. Each panel represents a separate regression. Large natural disasters are constructed for each regression with different cutoffs from the 80th to 98th percentile of the world distribution of damage rate. In each Panel, the X- axis represents the year relative to the large natural disaster, truncated at 15 years before and 15 years after the events. The solid black line represents the average treatment effect of large natural disasters on the Gini index. The bar plot at the bottom of the figure shows each period’s treated units. And the Placebo Test value is also reported in the figure. 29 Figure 9: Treatment Effect of Disasters on Infrastructure–Death Rate (a) Rural access to electricity (b) Urban access to electricity (c) Electricity generation (d) Air transport (e) Road density (f) Internet Note: This Figure shows the average causal effect of a large disaster on physical infrastructure. Each Panel represents a separate regression corresponding to different infrastructure measures. Large natural disasters are constructed for each regression with 97th percentile of the world distribution of death rate. In each Panel, the X-axis represents the year relative to the large natural disaster, truncated at 10 years before and ten years after the events. The solid black line represents the average treatment effect of large natural disasters on infrastructure measures. The grey area is the 95% confidence interval of the generalized synthetic control estimates. The bar plot at the bottom of the Figure shows each period’s treated units. 30 Table 1: Large Natural Disasters Panel (A) Death Rate Panel (B) Damage Rate Country Year Death Rate Percentile Country Year Damage Rate Percentile Iran, Islamic 1990 0.071 % 100 Maldives 1991 12.27 % 99 Rep. Bangladesh 1991 0.128 % 100 Tajikistan 1992 15.71 % 100 Philippines 1991 0.01 % 99 Lao PDR 1993 22.76 % 100 Tajikistan 1992 0.024 % 99 Moldova 1994 17.11 % 100 Haiti 1994 0.015 % 99 Yemen, Rep. 1996 20.91 % 100 Honduras 1998 0.236 % 100 Bangladesh 1998 8.6 % 99 Nicaragua 1998 0.068 % 100 Dominican 1998 9.14 % 99 Republic El Salvador 1998 0.008 % 99 Honduras 1998 59.59 % 100 Türkiye 1999 0.029 % 99 Nicaragua 1998 21.31 % 100 Venezuela, 1999 0.125 % 100 Türkiye 1999 8.19 % 99 RB Belize 2001 0.012 % 99 Belize 2000 33.35 % 100 El Salvador 2001 0.02 % 99 Mongolia 2000 7.04 % 99 Iran, Islamic 2003 0.039 % 100 Mozambique 2000 7.43 % 99 Rep. Haiti 2004 0.03 % 99 Belize 2001 28.79 % 100 Indonesia 2004 0.074 % 100 El Salvador 2001 15.05 % 100 Sri Lanka 2004 0.183 % 100 Algeria 2003 7.37 % 99 Maldives 2004 0.033 % 100 Jamaica 2004 8.8 % 99 Thailand 2004 0.013 % 99 Maldives 2004 38.32 % 100 Guatemala 2005 0.012 % 99 Myanmar 2008 12.55 % 99 Pakistan 2005 0.048 % 100 Chile 2010 13.73 % 99 Myanmar 2008 0.28 % 100 Haiti 2010 68.6 % 100 Haiti 2010 2.226 % 100 Thailand 2011 10.87 % 99 Japan 2011 0.016 % 99 Nepal 2015 24.17 % 100 Philippines 2013 0.008 % 99 Fiji 2016 12.17 % 99 Nepal 2015 0.031 % 99 Haiti 2016 14.59 % 99 Note: This table depicts countries and years experiencing natural disasters that cause damage or death whose magnitude is more significant than the 98 percent of events in the sample. The left panel is associated with the death rates, and the right is related to the damage rate. 31 Table 2: Summary Statistics (1) (2) (3) (4) All Treated (>98 Percent) Control Reservoir Diff mean sd mean sd mean sd b t Gini Index (PIP) 39.7 9.5 42.8 8.8 39.4 9.5 -3.41∗∗∗ (-6.42) Gini Index (SWIID) 39.1 8.8 42.7 5.9 38.8 9.0 -3.91∗∗∗ (-7.96) Total Death 1070.1 10339.8 4927.1 24257.6 306.8 2924.9 -4620.30∗∗∗ (-5.97) Total Damage (000’US$ unadjusted) 2011769.9 10978145.4 2177953.3 15123128.8 1978881.1 9964895.6 -199072.25 (-0.24) Human capital index 2.4 0.7 2.2 0.5 2.4 0.7 0.16∗∗∗ (4.04) Nonimal GDP (mil. current US$) 356264.1 1341285.7 250425.3 750502.6 367487.9 1388883.0 117062.64 (1.55) Real GDP (mil. 2011 US$) 547915.1 1650810.1 513297.2 830700.5 551586.2 1714971.0 38289.05 (0.41) Rural access to electricity (% of rural population) 66.1 39.1 72.0 28.8 65.5 40.0 -6.54∗∗ (-2.97) 41 Urban access to electricity (% of urban population) 86.6 22.3 94.2 8.9 85.8 23.2 -8.36∗∗∗ (-6.69) Electricity generation (MW per mil. people) 822.2 1101.4 380.6 414.3 869.4 1140.8 488.82∗∗∗ (7.95) Individuals using the Internet (% of population) 19.9 26.9 16.4 18.9 20.3 27.6 3.85∗ (2.54) Air carrier departures (per mil. people) 7999.6 19639.8 9960.2 40805.5 7791.7 15813.4 -2168.46∗ (-1.96) Road Density 0.6 1.0 0.4 0.5 0.6 1.0 0.18∗∗ (3.29) Observations 3640 349 3291 3640 Note: This table shows the summary statistics of all variables for 130 countries from 1990 to 2017, including the Gini index, total death and damage caused by natural disasters, and control variables like the human capital index, GDP, and population. Column (1) indicates the mean values for 130 countries over the two decades. Column (2) is associated with the countries exposed to large disasters that caused the top 98 percentile death rate. Column (3) is related to the rest of the nations, representing the control group. Table 3: Average Treatment Effect of Large Disasters on Gini Index Panel (A) Death Rate (1) (2) (3) (4) (5) (6) (7) ATT N SD Lower Bound Upper Bound Pvalue #Factor 80pct -0.79 675 1.06 -2.62 0.85 0.46 3 90pct -2.88 545 2.71 -5.65 2.95 0.29 1 93pct -1.65 454 0.89 -3.07 -0.15 0.06 3 98pct -2.09 268 1.19 -3.97 -0.28 0.08 2 Panel (B) Damage Rate (1) (2) (3) (4) (5) (6) (7) ATT N SD Lower Bound Upper Bound Pvalue #Factor 80pct -1.05 783 1.11 -2.77 1.02 0.35 3 90pct -1.18 466 1.50 -3.28 1.25 0.43 2 93pct -1.54 448 1.02 -3.03 0.19 0.13 3 98pct -2.66 259 1.25 -5.06 -0.81 0.03 2 Note: This Table shows the average causal effect of a large disaster on the Gini index. Each row represents a separate regression. Large natural disasters are constructed for each regression with different cutoffs from the 80th to 98th percentile of the world distribution of disaster magnitude. Column (1) indicates the average treatment effect after the intervention, which pools all the treated units and time together. Column (2) shows the total number of post-interventions treated units. Columns (3) to (6) are related to the statistical inference, indicating the standard deviations of the GSC estimates, confidence intervals, and P-values, respectively. The last column shows the number of factors in the IFE model chosen by the cross-validation algorithm. 42 A Appendices A.1 Average Treatment Effect of Large Disasters on the Gini Index, Alternate Dataset We test the effect of large disasters on income inequality using the SWIID income inequality database, which provides an inequality measure. The SWIID income inequality database imputes missing data and offers complete coverage. In line with Table 3, Table A1 shows the average treatment effect of large natural disasters based on different cutoffs on the Gini index, suggesting an overall negative impact. The magnitude and significance of the treatment effect increase when we raise the cutoffs. In other words, more significant natural disasters yield a larger reduction in income inequality. A.2 Average Treatment Effect of Large Disasters on the Gini Index, Alternate Estimator We test the effect of large disasters on income inequality using a matrix completion (MC) estimator instead of an iterative fixed effect (IFE) estimator. The results of the IFE (see Table 3) are very similar to those of the matrix completion shown in Table A2. A.3 Estimating an Interactive Fixed-Effect Model Let = 1, 2, . . . , + 1, . . . , denote countries and = 1, 2, . . . 0 , . . . , denote years where 0 is the year of disaster. The control and treated units are subscripted from 1 to and from + 1 to N, respectively. Suppose control units follow an interactive fixed effect model: = + Λ′ + 43 The least square objective function is: (, , Λ ) = Σ=1 ( − − )′( − − ) To identify , , and , more constraints are needed on the factors and factor loadings: (1) all factors are normalized, and (2) they are orthogonal to each other. More specifically, we estimate , , and Λ by minimizing the SSR subject to the following constraints: ′ = Λ′ Λ = Bai (2009) proposed an iteration scheme that can lead to a unique solution starting from some initial value of or . In each iteration, given and Λ , the algorithm computes is: −1 ̂ (, Λ) = �Σ ′ � Σ ′ ( − ) (3) =1 =1 and given , it computes and from a pure factor model ( − ) = _ + _ 44 Table A1: Average Treatment Effect of Large Disasters on Gini Index Panel (A) Death Rate (1) (2) (3) (4) (5) (6) (7) ATT N SD Lower Bound Upper Bound Pvalue #Factor 80pct -.312 675 .521 -1.299 .904 .549 3 90pct -.807 517 .468 -1.691 .017 .085 3 94pct -.581 464 .522 -1.687 .466 .265 3 98pct -1.318 217 .681 -2.528 -.035 .053 3 Panel (B) Damage Rate (1) (2) (3) (4) (5) (6) (7) ATT N SD Lower Bound Upper Bound Pvalue #Factor 80pct 0.100 772 0.352 -0.574 0.845 0.776 3 90pct 0.095 466 0.442 -0.856 0.924 0.830 3 94pct -.282 480 .533 -1.218 .563 .597 3 98pct -.939 259 .524 -1.803 -.111 .073 3 Note: This Table shows the average causal effect of a large disaster on the Gini index. Each row represents a separate regression. Large natural disasters are constructed for each regression with different cutoffs from the 80th to 98th percentile of the world distribution of disaster magnitude. Column (1) indicates the average treatment effect after the intervention, which pools all the treated units and time together. Column (2) shows the total number of post-intervention treated units. Columns (3) to (6) are related to the statistical inference, indicating the standard deviations of the GSC estimates, confidence intervals, and P-values, respectively. The last column shows the number of factors in the IFE model chosen by the cross-validation algorithm. 45 Table A2: Average Treatment Effect of Large Disasters on Gini Index, MC Estimator Panel (A) Death Rate (1) (2) (3) (4) (5) (6) ATT N SD Lower Bound Upper Bound Pvalue 80pct 0.22 675 0.89 -1.45 1.50 0.80 90pct -0.82 545 0.81 -2.25 0.41 0.31 93pct -1.02 454 0.85 -2.51 0.22 0.23 97pct -1.39 268 1.01 -2.94 0.55 0.17 Panel (B) Damage Rate (1) (2) (3) (4) (5) (6) ATT N SD Lower Bound Upper Bound Pvalue 80pct 0.50 783 0.60 -0.66 1.32 0.40 90pct 0.81 466 0.67 -0.36 1.86 0.23 93pct -0.13 448 0.79 -1.52 1.09 0.87 98pct -1.11 259 0.95 -2.90 0.37 0.25 Note: This Table shows the average causal effect of a large disaster on the Gini index. Each row represents a separate regression. Large natural disasters are constructed for each regression with different cutoffs from the 80th to 98th percentile of the world distribution of disaster magnitude. Column (1) indicates the average treatment effect after the intervention, which pools all the treated units and time together. Column (2) shows the total number of post-intervention treated units. Columns (3) to (5) are related to the statistical inference, indicating the standard deviations of the GSC estimates, confidence intervals, and P-values, respectively. 46