Associate Professor, Francesca Marchetta
email: francesca.marchetta@uca.fr

Professor, David E Sahn
email: david.sahn@cornell.edu

Luca Tiberti
email: luca.tiberti@ecn.ulaval.ca

Grégoire Rota

Catherine Araujo Bonjean

Keywords: Climate shocks, Employment, Schooling, Africa. JEL Codes Q54, J43, I25

We examine the impact of rainfall variability and cyclones on schooling and work among a cohort of teens and young adults by estimating a bivariate probit model, using a panel survey conducted in 2004 and 2011 in Madagascar-a poor island nation that is frequently affected by extreme weather events. Our results show that negative rainfall deviations and cyclones reduce the current and lagged probability of attending school and encourage young men and, to a greater extent, women to enter the work force. Less wealthy households are most likely to experience this school-to-work transition in the face of rainfall shocks. The finding is consistent with poorer households having less savings and more limited access to credit and insurance, which reduces their ability to cope with negative weather shocks.

Introduction

Weather events can affect human capital formation and exert a long-lasting influence on individual well-being and on macroeconomic performance. This is of particular concern in developing countries, where high rates of poverty, a labor force primarily employed in rainfed agriculture, and limited credit and insurance markets can magnify the effects of negative weather shocks. In this article, we study the influence of rainfall variability and hurricanes on schooling and entry into the labor market in Madagascar, one of the 10 countries in the world with the highest Climate Risk Index [START_REF] Kreft | Who Suffers Most from Extreme Weather Events? Weather-related Loss Events in 2014 and 1995 to 2014[END_REF]. Hurricanes, floods, and droughts are serious threats for the Malagasy fragile ecology and agricultural sector, in which nearly three out of four workers are employed. 1 According to a recent report from the US Agency for International Development (USAID), 2 climate scientists expect flooding and erosion to increase in some regions of the country, as rainfall increases in intensity; in the south, rainfall will be less predictable, leading to greater extremes, including more frequent drought.

Our main goals are to explore (1) how normal rainfall variability affects schooling and working decisions; (2) the extent to which there is heterogeneity across households in these responses; and (3) the impact of acute weather shocks, particularly cyclones, on schooling and work choices.

We focus on a cohort of young men and women in Madagascar who were between 21 and 23 years old in 2011, and who were initially surveyed in 2004. We build a balanced annual panel data set from 2004 to 2011, with information on the school and working situation of each individual, derived from retrospective questions included in the questionnaire of the 2011 round of the survey. We match individual-level data with satellite-based, fine-grained information on rainfall, 3 and with data on hurricanes, using information on the time-varying place of residence of each individual.

Our empirical analysis, based on a non-separable agricultural household conceptual framework, involves estimating a bivariate probit model of schooling and work for the young adult cohort members (CMs) residing in rural areas of Madagascar. We do so using time and geographically fixed-effects. The identification strategy relies on the large temporal and spatial historical variations in rainfall between 2004 and 2011, across 210 rural communities. Results show that positive rainfall deviations from the long-term average increase the probability of school enrollment, while reducing the probability of being engaged in work. We observe both contemporaneous and lagged effects. Moreover, these effects are heterogeneous across households. Specifically, they are attenuated when individuals are from wealthier households. This suggests that assets help to mitigate the effect of transitory adverse weather conditions. Women are more likely than men to be pushed to the labor market following a negative weather event. Our results also show that cyclones reduce the probability of being enrolled in school. While we cannot empirically test the mechanisms through which cyclones impact schooling and work decisions, a plausible conjecture is that these rainfall events destroy roads, interrupt electricity, and damage schools, contributing to school dropout. This article contributes to a rapidly growing body of research, which examines how extreme weather events influence economic outcomes (Dell, Jones, and Alken 2014), and more specifically, human capital. Prior research has shown that weather events have a significant impact on human capital through several dimensions: income [START_REF] Levine | The Impact of Rainfall on Rice Output in Indonesia[END_REF]; wages [START_REF] Mahajan | Rainfall Shocks and the Gender Wage Gap: Evidence from Indian Agriculture[END_REF]; nutrition and health [START_REF] Maccini | Under the Weather: Health, Schooling, and Economic Consequences of Early-Life Rainfall[END_REF][START_REF] Tiwari | Monsoon Babies: Rainfall Shocks and Child Nutrition in Nepal[END_REF]; and consumption and calorie intake (Asfaw and Maggio 6 2017). More relevant to our specific interest in schooling and work, [START_REF] Villalobos | Effects of Weather on Daily School Attendance Decisions and Academic Performance in Rural Costa Rica[END_REF] found that daily meteorological variations (precipitation and temperature) had a deleterious impact on schooling outcomes in Costa Rica, and that students in more humid and warmer villages were at a higher risk of absenteeism and poor academic outcomes. [START_REF] Groppo | The Impact of Extreme Weather Events on Education[END_REF] showed that students living in Mongolian districts affected by severe winters were less likely to complete compulsory school. The impacts were significant only for students living in herding households. The authors concluded that the effects were not associated with increased child labor in herding or with the closure of school facilities, but rather the effects were related to the drop in household income due to the loss of livestock. [START_REF] Maccini | Under the Weather: Health, Schooling, and Economic Consequences of Early-Life Rainfall[END_REF] found that favorable rainfall conditions, occurring in the year of birth, had a positive effect on educational outcomes for adult Indonesian women. [START_REF] Jensen | Agricultural Volatility and Investments in Children[END_REF] estimated that adverse rainfall conditions in Côte d'Ivoire decreased school enrollment of children.

Regarding the effects on labor outcomes, [START_REF] Jessoe | Climate Change and Labour Allocation in Rural Mexico: Evidence from Annual Fluctuations in Weather[END_REF] and [START_REF] Jacoby | Risk, Financial Markets, and Human Capital in a Developing Country[END_REF] found that weather shocks caused negative income fluctuations, which led to households withdrawing their children from school in order to increase labor market engagement, with possibly long-lasting negative effects on poverty and development. By assuming that households respond to exogenously determined wages, [START_REF] Shah | Drought of Opportunities: Contemporaneous and Long-Term Impacts of Rainfall Shocks on Human Capital[END_REF] found that positive rainfall conditions increased average wages in the Indian rural sector. This encouraged parents to increase their children's on-farm labor supply and, as a consequence, schooling participation decreased. Rainfall shocks, in this context, act as a "productivity wage shifter." The authors found that such an effect outweighs the income effect on schooling, given that it is a normal good. In other words, households could be motivated to lower human capital investments in their children's education, when wages for low-paying, unskilled jobs increase. [START_REF] Shah | Drought of Opportunities: Contemporaneous and Long-Term Impacts of Rainfall Shocks on Human Capital[END_REF] also found that higher rainfall in early life (defined as the period spent in utero and up to the age of 2 years) had a positive impact on math and reading tests and reduced the probability of being behind in school or of having never been enrolled. Finally, Dumas (2015) showed that child labor increased with higher rainfall in Tanzania in the absence of efficient labor markets. This effect is explained by what she calls the "price effect": the increase in labor productivity pushed parents to make their children work on the family farm. 4 Overall, the existing literature suggests that a positive weather event and, more specifically, a positive deviation in rainfall can have ambiguous effects on schooling and labor, strongly dependent on the context. This ambiguity reflects the conflicting income and price effects associated with shocks. That is, we might observe an income effect whereby a positive shock increases agricultural production, so that parents are able to send children to school for longer periods, with their entry into the labor market postponed.

Conversely, we could also observe a price effect: the increase in labor productivity associated with better climatic conditions encourages parents to have their children work, thus increasing the probability of school dropout. However, the overall effect might be even more complex when households' consumption and production choices are interconnected and depend on endogenously determined shadow prices. The complexity is particularly important in contexts like Madagascar, where labor markets are heterogeneous and affected by large transactions costs. Within a non-separable agricultural household framework, we find that the indirect effect (through the change in the shadow price) is negative. Henceforth, the overall effect is positive only if the direct (income) effects dominate.

The remainder of the article is structured as follows: Section 2 introduces the conceptual framework that underpins our estimation approach. Section 3 provides a description of the context of our study, and it introduces the data employed in the econometric analysis, presenting the relevant descriptive statistics. The estimation strategy that we employ is discussed in Section 4, and Section 5 describes the results of the econometric analysis. Finally, Section 6 draws the main conclusions and discusses the policy implications of our work.

Conceptual Framework

Weather shocks can have immediate and lagged effects on school and work decisions. In this study we define negative weather shocks, which can contribute to drought conditions, as rainfall events that are below the historical local trend. Conversely, a positive weather shock occurs when the rainfall deviation from the historical local trend is above zero. 5 In considering these positive and negative deviations, the underlying assumption is that less rain will adversely affect productivity and yields; conversely, above normal rains are favorable (e.g., [START_REF] Dillon | Agricultural Production, Dietary Diversity and Climate Variability[END_REF], with the exception occurring when these positive deviations are large and associated with floods. In Madagascar, such acute rainfall events occur primarily as cyclones, which are differentiated from normal weather deviations in our models. Positive and negative shocks, in turn, can have contemporaneous and/or lagged effects on decisions to drop out of school and enter the labor market.

In our model we rely on the data that we collected containing information on the exact month the CM left school and/or entered the labor market. This data also allows us to distinguish between immediate (or contemporaneous) and lagged effects of rainfall deviations on schooling and working decisions. As for the contemporaneous effect, CMs may or may not complete their school year, depending on the current year's rainfall-a decision affected by the households' expected revenues in the current agricultural season.

In our models, these immediate effects may result in the CM leaving school before the beginning of the harvest season in June.

Concerning the lagged effects, households may decide to keep their children at school (e.g., to pursue a new schooling year in September) or send them to work (e.g., by around November, at the start of the next agricultural season), depending on the production of and revenues generated from the crops grown in the previous rainy season. The decision as to whether a child remains in school during the agricultural cycle that follows the agricultural season in which the shocks occurred represents the lagged effects, which are captured by the rainfall variable observed in year t-1 on school or work status in year t.

Figure 1 shows the definition of our school, work, and rainfall variables, with respect to the months of the year. For the purpose of our analysis, we considered an individual to be in school in year t, if she was attending and completed school in the schooling year that began in September of year t-1 (i.e., she did not drop out of school before June of year t). We considered an individual at work in year t, if she reported having been employed, including unpaid work in a family enterprise, on or before May in year t. Thus, we did not consider her to have worked in year t, if she started working after June in year t (for these individuals, we assigned a working status for the year t+1); but she was considered as working if she had worked between month 6 and month 12 of year t-1. Our rainfall variable in year t is defined over the period November (t-1) through April (t), which broadly corresponds to the rainy season throughout the country. Consistently, the historical means are estimated for the same period of the year (i.e., between November of year t-1 and April of year t). Since our research focuses on rural areas, we defined our outcomes in accordance with the agricultural season of rice, which is the main crop in Madagascar.

More than two-thirds of our sampled individuals reported rice as the main cultivated crop.

While maize is an important secondary crop, its agricultural calendar closely resembles that of rice. 6 A large majority of rural households are primarily engaged in agricultural activities, either working their own land or as hired laborers on someone else's land. 7 Also, as found in Tanzania [START_REF] Tiberti | Rural Policies, Price Change and Poverty in Tanzania: An Agricultural Household Model-Based Assessment[END_REF] and several other countries in sub-Saharan Africa, because of high transaction costs and heterogeneity across workers and households, the labor market is imperfect or absent (e.g., see the examples reported in de Janvry and [START_REF] De Janvry | Progress in the Modeling of Rural Households' Behavior under Market Failures[END_REF]). In such a context, engagement in the selling or purchasing of a good in an imperfect market might be unprofitable for households and for this reason, production and consumption decisions are interconnected. Hence, we believe that the non-separable agricultural household model (AHM) (see, e.g., [START_REF] Singh | Agricultural Household Models: Extensions, Applications, and Policy[END_REF]) is an appropriate framework for our empirical strategy. [START_REF] Jessoe | Climate Change and Labour Allocation in Rural Mexico: Evidence from Annual Fluctuations in Weather[END_REF] proposed a similar framework to study the effects of weather changes on employment and migration patterns in Mexico. More precisely, consistent with the non-separable model, we assume that consumption, production, and labor market decisions are interrelated, and consequently, exogenous shocks such as rainfall deviations affect the endogenously determined shadow wages of labor and family members' time allocation. As a consequence, the effect of the rainfall shock on the CM's decision is not simply given by the direct income (or production) effects (with the endogenous price held constant), but also by an indirect effect through the shock's impact on the endogenous prices. Typical for this type of approach, a useful tool to understand the expected sign of the impact of an exogenous shock on a farm household's behavior is comparative statics analysis.

Starting with standard setting (see, for example, [START_REF] Henning | Modeling Farm Households' Price Responses in the Presence of Transaction Costs and Heterogeneity in Labor Markets[END_REF]), we assume that farm households maximize their utility function, 𝑈, which depends on the vector, 𝑪, of consumption of purchased and own-produced commodities, and of leisure, and on some household characteristics 𝑠 𝑐 . Utility maximization, 𝑚𝑎𝑥 𝑈(𝑪, 𝑠 𝑐 ), is subject to the production technology constraint 𝐺(𝑿, 𝑅, 𝑧) = 0, the time constraint [START_REF] Henning | Modeling Farm Households' Price Responses in the Presence of Transaction Costs and Heterogeneity in Labor Markets[END_REF], under non-separability, the marginal cost of hiring labor and the marginal revenue from off-farm work correspond to the shadow wage.

Let us consider a change in an exogenous input 𝑧, such as rainfall. By assuming that farm households demand on-farm labor and supply off-farm labor simultaneously, the impact on the CM's decision of whether to be in school or to be working 𝑄, our endogenous variables of interest) is the following (de Janvry, Fafchamps, and Sadoulet 1991):

(1) where 𝜕𝐶 𝑙 𝜕𝑦 ⁄ × 𝜕𝑦 𝜕𝑧 ⁄ is the rainfall-induced income effect on the demand for leisure.

The sign of the numerator is expected to be positive. In fact, 𝜕𝑋 𝑙 𝜕𝑧 ⁄ , the effect of the overall on-farm labor supply (family and hired labor), with respect to a change in rainfall, is expected to be positive because positive rainfall deviations (excluding floods) increase agricultural production and thus the demand for on-farm labor. A supporting result for this assumption is reported in Sadoulet and de Janvry (1995, p. 74) and in [START_REF] Jessoe | Climate Change and Labour Allocation in Rural Mexico: Evidence from Annual Fluctuations in Weather[END_REF]. The second term of the numerator is the product between the change in income resulting from positive rainfall deviations (𝜕𝑦 𝜕𝑧 ⁄ ) (see, for example, [START_REF] Bengtsson | How Responsive Is Body Weight to Transitory Income Changes? Evidence from Rural Tanzania[END_REF]), and the consequent income effect of the demand for leisure (𝜕𝐶 𝑙 𝜕𝑦 ⁄ ).

The effect of rainfall deviations on income, 𝜕𝑦 𝜕𝑧 ⁄ , is expected to be positive and relatively high, especially in Madagascar where rainfed agricultural production is prevalent. Since leisure is normally assumed to be a non-inferior good, the second term is also positive.

The sign of the denominator is expected to be positive as well. The first term, 𝜕𝑋 𝑙 𝜕𝑃 𝑙 * ⁄ (the own price effect of on-farm labor), is expected to be negative. As shown in [START_REF] Henning | Modeling Farm Households' Price Responses in the Presence of Transaction Costs and Heterogeneity in Labor Markets[END_REF], with labor market imperfections caused by nonproportional variable transaction costs and labor heterogeneity, the function cost of hiring on-farm workers is convex and the income function from off-farm economic activities is concave. If such hypotheses hold (as is plausible in our context), it follows that

(𝜕𝑋 𝑙 ℎ 𝜕𝑃 𝑙 * ⁄ -𝜕𝑋 𝑙 𝑠 𝜕𝑃 𝑙 * ⁄
) ranges between zero (autarky case) and infinity (if labor market works perfectly). Finally, the own-price effect to Hicksian demand of leisure (𝜕𝐶 𝑙 𝐻 𝜕𝑃 𝑙 * ⁄ ) is negative. It follows that the better the functioning of the agricultural labor market (and so, the greater the integration to the labor market), the lower the indirect effect (tending toward zero).

If we return to our utility function 𝑈(𝑪, 𝑠 𝑐 ), the direct (income) effect, given that schooling is a normal good, is expected to increase the likelihood of staying in school and reduce the likelihood of entering the labor market, especially since there will be less need to pull children out of school to help cope with the decline in agricultural output and earnings. On the opposite, the likelihood of schooling decreases with positive changes in the shadow wage (as its opportunity cost increases) and, so, the indirect effect of positive rainfall deviations is expected to be negative. Hence, the overall effect is positive if the direct effect dominates, and negative in the case when the indirect effect prevails. 9

In addition to the direct and indirect effects discussed earlier, the CM's decision might be affected by infrastructure effects-such as cyclones destroying schools, roads, electric grids and causing damage to other physical structures-which could prevent school attendance.

In the empirical analysis below, we are not able to disentangle the relative importance of the direct and indirect effects as they impact schooling and work decisions, but only the overall effect. In addition, our analysis tests for the existence of contemporaneous and lagged effects. For example, in the case of a negative weather shock from a lower rainfall leading to drought, we examine whether this effect is felt immediately, as evidenced by CMs dropping out of school during the agricultural season in which the rainfall shock occurs, or instead, choosing not to enroll in school and to work in the academic year subsequent to the shock. In the case of positive deviations in rainfall, we also examine contemporaneous and lagged effects. Better rains lead to higher family income, which may increase both the likelihood that CMs remain in school during the current agricultural calendar, as well as encourage parents to enroll CMs in school the following academic year, rather than having them entering the labor market. In the case of cyclones, we only look at contemporaneous impacts of the destruction of infrastructure. 10

Finally, we test for the existence of heterogeneity to vulnerability. Pre-shock assets can help households to mitigate the effects of the shocks, as they can be used as buffer stocks and as collateral for credit loans, especially in the case of transitory shocks. Such capacities can differ, however, by the size of the households' assets holdings. Therefore, we expect that weather shocks impact CMs differently, depending on their households' abilities to buffer shocks, which in this article, is proxied by a household wealth index in the initial period.

Context, Data, and Descriptive Statistics

Context

Madagascar's geography, located between the Indian Ocean and the Mozambique Channel, often makes the island the terminus of tropical cyclones and storms that originate on the western coasts of Australia. Most of the regions of the country are classified as high risk for cyclones, with the Eastern Coast being the most affected. The frequency of tropical cyclones is expected to decline in the next decades, but their intensity will increase [START_REF] Mavume | Climatology and Landfall of Tropical Cyclones in the South-West Indian Ocean[END_REF][START_REF] Hervieu | Madagascar, terminus des cyclones[END_REF]. The country is particularly vulnerable to tropical cyclones due to the lack of good disaster warning strategies [START_REF] Fitchett | A 66-Year Tropical Cyclone Record for South-East Africa: Temporal Trends in a Global Context[END_REF].

Between 2000 and 2012, a number of tropical cyclones have hit Madagascar, with the 2004 cyclones, Elita and Gafilo, the most devastating storms, killing about 380 people, leaving 200,000 homeless, and destroying about 1,400 schools throughout the country [START_REF] Rajaon | Les écoles résistantes aux cyclones: Etude de cas[END_REF]. More recently, Enawo-the most devastating cyclone in more than a decade-struck in 2017, affecting nearly a half million people.

Although rainfall is expected to intensify in some regions of Madagascar, especially those vulnerable to cyclones, lower rainfall is projected in the south of the country. In addition to strong winds, tropical storms are often accompanied by heavy rains and increasingly, widespread flooding. This is due in part to climate change and in part to environmental degradation. It is not only Madagascar's extreme vulnerability to weather events, but also the fact that its agricultural sector represents around one-quarter of the country's GDP, employing about 75 percent of the population and that most landholdings are small-scale, rainfed farms-which makes the country an interesting case to study, in terms of the impact of weather events on schooling and work decisions.

Individual Data and Descriptive Statistics

In this article, we use individual data from two surveys: the Madagascar Life Course Both the 2004 and 2011-12 surveys collected comprehensive information on cohort members and their family members. The questionnaire included modules on education, labor, migration, entrepreneurship, agriculture, family enterprises, health and fertility, and cognitive abilities, as well as household assets and housing conditions. The cohort-based sample also collected considerable retrospective data using recall techniques; for example, we know the exact month and year that a cohort member left school, the precise timing of entry into the labor force, and the type of work performed. The cohort-based sample was complemented by community surveys of social and economic infrastructure, as well as general information on the key historical developments in the villages where the CMs were living in 2004. We have information on 1,119 cohort members living in rural areas (roughly half of them are women) and aged 21 to 23 at the time of the 2011-12 survey, compared to the average age in 2004 of 14.9 (Table A.1). Among them, 316 rural CMs left their community of origin between 2004 and 2012 to move to another Malagasy area; we defined them as (internal) migrants. of school returned at a later date. A negative shock, such as a rainfall deficit, during the teenage and young adult years will induce people to leave school and, therefore, have permanent effects, including lower human capital accumulation.

Table A.1 reports some descriptive statistics of all the control variables used in our econometric estimation, in addition to rain-related variables. As reported in Table A. In our models, we also rely on data from the community questionnaire, especially for a question on the topography of the village where individuals live. More specifically, we create a classification with the following categories: hills (where 47 percent of CMs live), coastal plains (10.5 percent), interior plains (11.3 percent), plateau (16 percent), valleys (13 percent), and others. The community questionnaire also provides information on the presence of the middle and high schools, as well as information about their year of construction, which we use in our models.

In terms of our focus on the impact of climate and weather data on schooling and work, we use the Köppen-Geiger climate classification system in order to identify the climatic zones of the country. This system first classifies geographical areas into five main In this study, we employ several rainfall-based indicators. First, we estimate the standardized rainfall deviations over the period November-April (rainy season), 16 by taking the variation between the total amount of rain precipitation over these months in year t in community c and the 1991-2011 average, normalized by its 1991-2011 standard deviation (SD). 17 This indicator captures (positive or negative) rainfall deviations with respect to the local, long-term average. Also, given that the measure is standardized to the community's average, differences in the yearly deviations across rainy and dry zones are comparable. Based on the standardized rainfall indicator, we identified exclusive categories to capture, in particular, extreme rainfall shocks. 18 We also defined a variable drought, that takes the value 1 if rainfall deviation is lower than 1 at time t. Finally, we used a relative seasonality index to capture the degree of variability of rainfall through the period November-April for each year.

It is not only the quantity of rain that falls in a year that matters, but also its distribution, or timing, during the year. If it all occurs in a few months of the year, the same quantity of rain can have different (sometimes detrimental) effects on agricultural production and the integrity of infrastructure than if it falls more evenly throughout the year. Following Walsh and Lawler (1981, p. 202), we defined the seasonality index as "the sum of the absolute deviations of mean monthly rainfalls from the overall monthly mean, divided by the mean […] rainfall" over November-April. This index ranges between 0 (if rainfall is distributed equally across months) and 1.20 or higher (if all the yearly rain falls in one or two months). According to the literature (see, for example, FAO [2016]), for values between 0.4 and 1, the index indicates areas with seasonal rainfall. As shown in

Estimation Strategy

We assume that schooling and work decisions are interdependent. A cohort member can choose to be only at school, only at work, sharing her time between school and work, or neither at school or at work. To allow interdependency of the different alternatives, we adopted a bivariate probit model, where we define 𝑆 * and 𝑊 * as the latent variables of attending school (S) and participating in work activities (W), respectively, 19 as shown in the basic specification:

(3) (5)

𝑆 𝑖𝑡 * =
𝑆 𝑖𝑡 = { 1 𝑖𝑓 𝑆 𝑖𝑡 * > 0 0 𝑖𝑓 𝑆 𝑖𝑡 * ≤ 0 } (6) 𝑊 𝑖𝑡 = { 1 𝑖𝑓 𝑊 𝑖𝑡 * > 0 0 𝑖𝑓 𝑊 𝑖𝑡 * ≤ 0 }
In this model, 𝑆 𝑖𝑡 takes the value of 1 if the cohort member i was enrolled in school during year t, and 𝑊 𝑖𝑡 equals 1 if the cohort member was engaged in economic activities.

The definition of the school and work variables have been detailed in Section 2 (also refer to Figure 1). 𝑿 𝑖𝑡 is a set of explanatory variables that includes characteristics of the cohort member, of her parents, and of the community in which she resided in 2004, as illustrated in Section 3. In particular, consistent with the theoretical framework discussed previously in the article, we control for the transaction costs (the presence of a paved road in the village and the quality of land are proxies for these costs) and introduce factors influencing the shadow price of schooling (such as the father's and mother's education levels and health and working statuses, as well as the number of brothers and sisters) and labor (such as land endowment in 2004 and the value of assets other than land). The variable 𝑟𝑎𝑖𝑛 𝑐𝑡 is one of the rainfall variables described in the previous section, as observed in community 𝑐, where the CM lived in the year t. By introducing the interaction of the rainfall variable with a household wealth index in 2004, which is the initial year of the analysis, we allow for heterogeneous effects across households. 20 More specifically, we can control for households' resilience to climatic shocks, which is hypothesized to vary according to the CM's initial wealth. We control for the CM's age (denoted by dummies 𝜃 𝑖𝑡 ), climatic zones z (𝜇 𝑧 ), and the year (𝜃 𝑡 ). The inclusion of these fixed effects ensures that our results are not biased by systematic differences related to these variables. In a separate specification, we include a dummy that is equal to 1 if a hurricane (of at least strength 1) hit the community where the CM lived during year t. This is done in order to test whether experiencing a cyclone has an impact on the probability of attending school and/or being engaged in work. We also estimate a specification in which we introduce the rainfall variable at time t-1. This allows us to test for the existence of a lagged effect of rainfall deviation on schooling and working decisions.

One concern is that economic and social development or, more generally, differences in a given community can be systematically correlated with rainfall levels. If this is the case, rainfall might be associated with some unobserved determinants of school and work decisions. We employ two strategies to overcome such a possibility. First, we used rainfall levels normalized to local historical levels, so that high or low rainfall communities in year t are defined only with respect to their historical trends and not with respect to other communities (which might be comparatively more rainy). Second, we run a separate estimation in which we control for communities' fixed effects to test the robustness of our results and to make sure that rainfall deviations are not systematically associated with local development or other differences across communities, which may be indirectly related to school and work status (see specification 8 in Table 4).

Finally, we acknowledge the concern that individual, unobserved heterogeneity may be correlated with our main explanatory variable, rainfall. This would be the case if past rainfall patterns were both correlated with current rainfall patterns and with unobserved individual characteristics. For instance, past unfavorable rainfall patterns could have reduced households' assets or increased their resilience to shocks. If this was the case, what we would observe is not only the effect of current rainfall deviation, but also the possible effect of the long-term pattern of rainfall. We are confident that it is not the case, because we do not use absolute values, but rather a standardized deviation from the longterm mean as the main explanatory variable for rainfall. Furthermore, we control for the wealth of the CM's family in 2004. Moreover, when we regress rainfall deviation on its lagged value, the lagged value is not significant. To further address this concern, as shown in Table A.6, we checked whether rainfall deviation was correlated with a past rainfall pattern, over the eight-year period of analysis. Through a simple regression analysis, we verified that our variable is not explained by the long-term mean of a range of other variables that measure precipitation, including the mean of the same variable, not normalized, and the mean of the variable measuring total precipitation from station data (normalized and not normalized) during the agricultural season or during the entire year.

Results

The first set of results for key parameters is reported in Table 1, while Table A.4 provides the results for the full specification. The correlation coefficient athrho between 𝜺 𝑖𝑡 𝑆 and 𝜺 𝑖𝑡 𝑊 is significantly different from zero and is negative, meaning that the schooling and working choices are jointly determined and that unobserved factors, which increase the probability of attending school, also decrease the probability of working. Table 1 shows the effect of the continuous standardized rainfall deviation on school and work decisions. Rainfall deviations positively affect the probability of attending school while they reduce the probability of being engaged in a work activity (column 1). This finding is consistent with the expected positive effect of good rains on incomes. Unfortunately, our data do not allow us to test the impact on rainfall deviations on agricultural production. However, various earlier studies (e.g., [START_REF] Bengtsson | How Responsive Is Body Weight to Transitory Income Changes? Evidence from Rural Tanzania[END_REF] for Tanzania, in addition to other studies cited in the introduction) found a positive effect. Also, we cannot disentangle the income from any price effect, which may be affecting the magnitude of the overall effect.

We also note that the effects are heterogeneous across households, which can be seen when we include the interaction of household wealth, measured at the time the CMs were 14 to 16 years of age, with rainfall (column 2). This interaction is negative and significant for schooling and positive for work, suggesting that the effect of rainfall deviation on the decision to attend school or work is attenuated when CMs are from wealthier households. This finding is consistent with our expectations and points to wealth-and related factors, such as greater access to savings, credit, and insurancehelping to buffer the impact of adverse weather events. This result is also consistent with the findings of Beegle, Dehejia, and Gatti (2006), who found that asset holdings mitigated the (increasing) effects of transitory income shocks on child labor.

Specification 3 further adds the occurrence of cyclones into the model. Like rainfall shocks, cyclones reduce the probability of attending school and appear to push the cohort members into the workplace. We can safely assume that in the case of cyclones, the CMs enter the workplace and drop out of school as a result of economic hardship, possibly exacerbated by damage to schools and related infrastructure that impede access to educational opportunities.

Specification 4 in Table 1 adds the lagged rainfall and the interaction of the lagged rainfall with 2004 assets. The rainfall and interaction terms are not statistically significant at conventional levels in the schooling model. What is interesting is that the addition of the lagged rainfall variable and the interaction with the asset index do not affect the significance or magnitude of the contemporaneous effect. This corroborates the observation that the impacts of current and lagged rainfall events on schooling operate independently of one another. The probability of working is strongly affected by both current and lagged rainfall episodes. The sign, significance, and magnitude of the contemporaneous and lagged effects are very similar, and this is also applied to the interaction between lagged rainfall and assets. 21 Source: Authors' elaboration from the Madagascar Young Adult Survey and EPSPAM. Notes: Specification (1) includes all variables shown in Table A.4 except for the interaction between rainfall and assets; (2) corresponds to the specification in Table A.4 (this is our base specification); and (3) as in (2) plus dummy variable for cyclones; (4) as in (3) plus lagged (t-1) rainfall variable.

In Table 2 we present the marginal effects, based on the specification in the last column in Table 1, to gain insight into the magnitude of the impacts of cyclones and lagged and current rainfall shocks. The occurrence of a cyclone or hurricane decreases the probability of being enrolled in school by 15.2 percentage points and increases the probability of being engaged in a work activity by 10.5 percentage points at mean asset levels. In terms of rainfall, looking at the last column of Table 2, we find that a unit of z-score 22 increase in the standardized rainfall increases the probability of being enrolled in school by 2.5 percentage points (baseline probability 49%) and decreases the probability of being engaged in work by 4.1 percentage points (baseline probability 52%), calculated at the samples' mean asset levels. Similarly, we find that lagged rainfall increases the probability of work by 5.0 percentage points, slightly higher than contemporaneous rainfall, although the impact on school enrollment is only 1.4 percentage points (which is not, in any case, statistically significant). We also calculate the marginal effects at different levels of assets to determine the extent to which wealth buffers the impact of rainfall fluctuations. Table 2 shows the point estimates for the 25th, 50th, and 75th percentiles of the asset distributions, and Figure 4 plots the curves from the 10th to the 90th percentiles. At the 25th percentile, the impact of a change in one unit of our rainfall measure is a 3.6 percentage point increase in the probability of school, as contrasted with only a 1.7 percentage point increase for CMs from households at the 75th percentile (for the latter, the effect is not statistically significant).

Similarly, the change in the probability of working associated with a one unit decline in rainfall is to raise the probability of work by 5.5 percentage points for those belonging to the 25th percentile, while for CMs from households at the 75th percentile, the increase in work probability is almost half that, 3.1 percentage points. As we get further toward the lower bounds of the asset distribution, we can see that the impact of rainfall shocks on work and school choices is much greater than that for households with greater wealth, and conversely, the probabilities of going to school or working is less affected by climate shocks among CMs from wealthier families (Figure 4). Source: Authors' elaboration based on specification (4) in Table 1. Notes: Dashed grey curves identify the confidence intervals.

We next consider several extensions and robustness checks, reported in Table 3.

First, we include an interaction with gender (column 5). The negative and significant interaction in the work equation suggests that young women in our cohort are even more percentiles on assets susceptible to being pushed into the labor market with negative rainfall deviations than male CMs. When the rains are particularly favorable, however, young women experience a stronger reduction in the probability of being engaged in a work activity.

In another specification (column 6), we exclude from the sample those individuals who migrated from the community where they lived in 2004. 23 The reason for this exclusion is that the community variables that we introduced in the model-the presence of schools and the type of land-are from the community where the individual lived in 2004. When migrants are excluded from the sample, the coefficients are little changed and are of the same magnitude. Also, with such a specification, we test whether our results are biased because of the endogeneity of migration decisions, which are also possibly related to rainfalls. According to our results, this does not seem the case, as our estimates are fairly robust, irrespective of the sample (with or without migrants) that we include.

We also ran a model that excluded from the sample those CMs coming from households who were not engaged in the agricultural sector, which we define as households where none of the members cultivated any land between 2004 and 2011 and where neither the CMs nor their fathers have reported that their primary sector of work is agriculture.

This allows us to check whether the rainfall effect is higher for "agricultural" households.

Results, reported in column 7 of Table 3, are stable to the exclusion of non-agricultural households. We can infer from this model that the impact of weather shocks operates at least, in part, indirectly on schooling and work choices-for example, affecting food prices and availability, and more generally, labor market and economic conditions in the rural communities in which the CMs reside. Finally, in specification (8), we estimate the model using community fixed effects. Of course, for those CMs who migrated during our period, communities are not constant over time. Both rainfall coefficients are still significant and of a similar magnitude.

In Table 4 we run a series of other robustness checks, by employing different definitions of the rainfall variable. We first show, in specification ( 9), the results of a model using rainfall measures based on the full year, not just the rainy season, to define the standardized rainfall deviation. As can be seen, this change does not qualitatively change the results. Specification (10) then reports the results based on a categorical definition of the rainfall deviation: the coefficients are higher as rainfall deviation increases, both for schooling and work. In specification (11), we introduce a dummy variable, instead of the rainfall deviation, to analyze more directly the specific effect of drought. 24 Results show that drought would generate a reduction in the probability of school attendance and an increase in the probability of being engaged in work activities, especially for the poorest CMs. Finally, specification (12) introduces a seasonality index to assess whether a less even distribution of rainfall over the agricultural season affects the CMs' school and work decisions. While schooling is not affected by the intraseasonal distribution of rainfall, a higher concentration of rainfall increases the probability of working, even though, again, assets holdings help households mitigate such a negative effect. A higher concentration of rainfall throughout the year is expected to negatively affect agricultural land productivity and so the revenue of agricultural households. For this reason, according to our results, young adults may enter the workforce to contribute to household income, even without having a large effect on schooling participation. 2) plus a seasonality index and the interaction between the seasonality index and the assets.

Conclusion

In this article we explore the impact of weather events on school and work decisions of a cohort of young adults in Madagascar. This is a particularly important issue, given the evidence that human activity is contributing to rapid climate change, which may lead to more severe cyclones, more frequent droughts and floods, and a higher concentration of rainfall in certain periods within a given year. Further exacerbating the potential deleterious impacts of climate variability in poor countries, such as Madagascar, is the lack of wellestablished credit and insurance markets as well as poverty that limits the ability of households to buffer the impact of negative climate shocks.

Our focus on the impact of weather events on schooling and work is especially pertinent to the cohort of teens and young adults we study, who are transitioning from school to work. The concern is that deleterious shocks will cause young people to drop out of school earlier than might be expected and enter the labor market to mitigate the impact of drought, floods, and cyclones. A priori, the sign of the impact of rainfall deviations on school and work is undetermined. According to the non-separable agricultural household conceptual framework we use, while a positive increase in rainfall deviation is expected to increase school through an income (direct) effect, the sign of the indirect (through the rainfall-induced change in the shadow wage) effect is likely to be negative and its magnitude depends on the degree of imperfection of markets. The higher the market imperfections, the more reduced the positive income effect. To address this question empirically, we estimate a bivariate probit model for a cohort of 1,119 young men and women from 2004 to 2011, who are transitioning from their teenage years to young adulthood during that period.

The results of our work provide compelling evidence that negative rainfall deviations and cyclones reduce the probability of attending school and push young men and women into working. Most affected by these weather events are the less wealthy households, as one would expect, given their more limited savings, less access to credit and insurance, and generally more limited ability to cope with negative shocks. We also find that there are both contemporaneous and lagged effects of the weather shocks, and that they are of a similar magnitude. Another source of particular concern is our finding that poor young women are even more susceptible to being pushed into the labor market when negative rainfall deviations are experienced.

Our results are robust to a range of rainfall definitions. We also conduct numerous robustness checks, including using community fixed effects and conducting individuallevel heterogeneity tests that address possible correlations between the characteristics of the CMs and rainfall variability.

It is important to recall here that we analyze the effect of normal rainfall variability-our period of interest is not characterized by exceptional rainfall events. The effects we observe could be more pronounced in case of prolonged negative seasons.

The findings in our article add to a rapidly growing literature on the role of weather shocks on a range of outcomes, including schooling and work. Although climate scientists will continue to address the causes of weather shocks and work to prevent human activity that contributes to climate change, our research also highlights the importance of mitigation efforts. These are especially important for the poor in ecologically fragile countries like Madagascar, which lack economic and social institutions that can help protect the vulnerable from climate shocks. Notes: If not specified differently, variables are expressed in percentages. The questionnaire asks CMs the following question: "Did your father (your mother) have any illness or disability, or an injury during the last seven years (since 2004), which prevented him (her) from working or carrying on business for a month or more?" Also, we were not able to observe changes in parents' working activities over time. In order to build this variable, we used the answers collected in 2011-12. Working status refers to 2011-12 for those parents who are still economically active, while it refers to the time of retirement for the inactive ones, and to the time of death for those no longer alive.

Appendix: Figures and Tables

Figure 1 .

 1 Figure 1. Definition of school, work, and rainfall variables

  11 The past three years have been characterized by a prolonged drought, which has been exacerbated by an exceptionally strong El Niño in 2015-16. According to the Food and Agriculture Organization of the United Nations (FAO 2016), El Niño has resulted in the lowest precipitation in 35 years. Drought has, in turn, contributed to crop failures, disease, and malnutrition. According to the United Nations Children's Fund (UNICEF), at the beginning of the academic year 2015-16, parents started to take children out of school, when teachers' and students' absenteeism increased as a result of drought conditions (UNICEF 2016).

Figure 2 .

 2 Figure 2. School-to-work transition between 14 and 23 years old (in 2004-2011), rural cohort members

  1, about 46 percent of CMs left their original households between 2004 and 2011-12 and are now living in newly formed households. Twenty-eight percent of the CMs migrated out of their community during this time period. Almost half of them migrated within the same district of origin, 36 percent moved to another district of the same province, and only 17 percent moved to another province. TableA.1 also reports the percentage of households cultivating land in 2004 and the household asset index in the same year.13

  climate groups: tropical, dry, temperate, continental, and polar. Then, it classifies each group by the seasonal precipitation type and the level of heat. According to this classification, Madagascar is divided into eight climatic zones, as shown in Figure A.1.

Figure A. 2

 2 Figure A.2 shows how the communities where our cohort members live have been

Figure A. 3

 3 Figure A.3 shows the trend of the standardized rainfall deviation between 2004 and

Figure 3 .

 3 Figure 3. Distribution of rainfall deviations (left panel) and distribution of the mean of rainfall deviation by community (right panel)

Figure

  Figure A.3, most of the climatic zones in Madagascar experienced one or more years in

Figure 4 .

 4 Figure 4. Marginal effects of rainfall deviations on the likelihood of schooling (left panel) and working (right panel)

Figure A. 1 .

 1 Figure A.1. Climatic zones, Köppen-Geiger climate classification system

Figure A. 2 .

 2 Figure A.2. Cyclones having hit sample communities over the period 2004 to 2012

Figure A. 3 .

 3 Figure A.3. Rainfall deviation from the long-term, national mean, and by climatic zones (2004-2011)

  schools, defined as having classrooms with less than 20 students. In these new clusters, we also did a complete enumeration of all the children in the cohorts' age range and randomly selected 15 children of the same age as those of the original PASEC sample. In addition, in each of the original PASEC clusters, we did a complete enumeration and selected 15 children who were not in the original PASEC sample. This was to make sure that we did not exclude those who never attended school, or enrolled very late, which is not an uncommon occurrence in Madagascar. Thus, the 2004 and 2011-12 samples include cohort members who would not have been selected by the original school-

Transition of Young Adults

Survey (2011Survey ( -2012) )

and the Progression through

School and Academic Performance in Madagascar Survey (EPSPAM 2004)

. These are the two latest rounds of a survey that follows a cohort of young adults born in the late 1980s. The sample in the cohort was based on a survey, Programme d'Analyse des Systèmes Educatifs de la CONFEMEN (PASEC), conducted in 1998 with second-grade students, who were from randomly selected schools throughout the country. This school-based sample, however, was not representative of young children in that age range, because many children were not enrolled in school; schools that were very small and had few students per grade were excluded. To partially address this issue, the 2004 survey supplemented the 48 PASEC clusters with an additional 12 clusters, randomly selected from remote rural communities with small primary based survey, because they dropped out of school early or never attended. This sampling approach was designed to make the cohort nationally representative. Comparisons of descriptive statistics of the cohort with other nationally representative surveys indicate that we were able to achieve this objective

[START_REF] Herrera | The Impact of Early Childbearing on Schooling and Cognitive Skills among Young Women in Madagascar[END_REF][START_REF] Aubery | Cognitive Achievement Production in Madagascar: A Value-Added Approach[END_REF]

.

12

Table A .

 A 2 shows the distribution of the CMs, corresponding to the climatic zones in which they lived in 2004 and in 2011. Data on cyclones are taken from the Tropical Cyclones Windspeed Buffers 1970-2015,provided by the Global Risk Data Platform.14 We have information on the number and strength of cyclones that hit sample communities. The strength of a cyclone is measured through the Saffir-Simpson hurricane wind scale (SSHWS). This scale classifies cyclones into five categories on the basis of the wind speed, from 1 (minimal strength, between 119

	Weather Data and Indicators

to 153 km/h) to 5 (maximal strength, more than 252 km/h). We also have information on tropical storms, which are approximately 63-118 km/h in wind speed.

Table 1 . Effects of Rainfall on School and Work Decisions, Main Specifications

 1

		(1)	(2)	(3)	(4)
	Equation: School
	Rainfall (6 months)	0.057*	0.098**	0.108***	0.110***
		(0.031)	(0.040)	(0.039)	(0.041)
	Assets	0.009***	0.010***	0.010***	0.010***
		(0.003)	(0.003)	(0.003)	(0.003)
	Rainfall x Assets		-0.002*	-0.002*	-0.002*
			(0.001)	(0.001)	(0.001)
	Cyclones			-0.237*** -0.388***
				0.096	(0.097)
	Lagged rainfall				0.053
					(0.044)
	Lagged rainfall x Assets				-0.001
					(0.001)
	Equation: Work	(1)	(2)	(3)	(4)
	Rainfall (6 months)	-0.101**	-0.146*** -0.153*** -0.163***
		(0.040)	(0.047)	(0.047)	(0.045)
	Assets	-0.010*** -0.010*** -0.010*** -0.010***
		(0.003)	(0.003)	(0.003)	(0.003)
	Rainfall x Assets		0.002*	0.002*	0.003**
			(0.001)	(0.001)	(0.001)
	Cyclones			0.237*	0.269**
				(-0.130)	(0.132)
	Lagged rainfall				-0.175***
					(0.046)
	Lagged rainfall x Assets				0.002**
					(0.001)
	Observations	8,600	8,600	8,600	8,600

Table 2 . Marginal Effects of Cyclones, Rainfall, and Lagged Rainfall on School and Work Decisions, at Different Assets Levels

 2

		School	Work	School	Work	School	Work	School	Work
		Assets p25		Assets p50		Assets p75		Assets mean
	Lagged rainfall	-0.018	-0.061***	0.015	-0.052** *	0.011	-0.041* *	0.014	-0.050* *
		(0.015)	(0.017)	(0.013)	(0.017)	(0.014)	(0.018) (0.013)	(0.017)
	Rainfall	0.036***	-0.055***	0.027**	-0.044** *	0.017	-0.031*	0.025**	-0.041* *
		(0.012)	(0.016)	(0.012)	(0.016)	(0.13)	(0.017) (0.127)	(0.016)
	Cyclones	-0.148***	-0.102***	-0.152** *	0.105**	-0.153** *	0.106* *	-0.152** *	0.105* *
		(0.035)	(0.048)	(0.036)	(0.049)	(0.037)	(0.051) (0.036)	(0.050)

Source: Authors' elaboration from the Madagascar Young Adult Survey and EPSPAM.

Table 3 . Effects of Rainfall on School and Work Decisions, Robustness Checks (Sub-population and Fixed Effects)

 3

		(2)	(5)	(6)	(7)	(8)
	Equation: School
	Rainfall (6 months)	0.098**	0.093**	0.082*	0.100**	0.086**
		(0.040)	(0.043)	(0.045)	(0.042)	(0.041)
	Assets	0.010***	0.010***	0.008**	0.009**	0.010**
		(0.003)	(0.003)	(0.004)	(0.004)	(0.004)
	Rainfall x Assets	-0.002*	-0.002*	-0.000	-0.003*	-0.002*
		(0.001)	(0.001)	(0.001)	(0.001)	(0.001)
	Woman (dummy)	-0.218*** -0.219*** -0.177**	-0.184***
		(0.065)	(0.065)	(0.073)	(.069)
	Rainfall x Woman		0.008
			(0.039)
	Community fixed effects no	no	no	no	yes
	Equation: Work	(2)	(5)	(6)	(7)	(8)
	Rainfall (6 months)	-0.146*** -0.111**	-0.136*** -0.133*** -0.085*
		(0.047)	(0.047)	(0.051)	(0.050)	(0.046)
	Assets	-0.010*** -0.010*** -0.009*** -0.006*	-0.007***
		(0.003)	(0.003)	(0.003)	(0.003)	(0.003)
	Rainfall x Assets	0.002*	0.002*	0.001	0.002	0.002
		(0.001)	(0.001)	(0.002)	(0.001)	(0.001)
	Woman (dummy)	0.015	0.025	0.035	0.026
		(0.064)	(0.057)	(0.064)	(0.063)
	Rainfall x Woman		-0.066**
			(0.034)
	Community fixed effects no	no	no	no	yes
	Observations	8,600	8,600	7,355	7,720	8,600
	Source: Authors' elaboration from the Madagascar Young Adult Survey and EPSPAM.
	Notes: For specification (2), see the notes to Table 1; (5) as in (2) plus interaction between rainfall and
	woman; (6) as in (2) but by excluding migrants (see text for definition); (7) as in (2) but by excluding non-
	agricultural households (see text for definition); (8) as in (2) plus community fixed effects.

Table 4 . Effects of Rainfall on School and Working Decisions, with Different Definitions and Measures of Rainfall

 4

	Equation	School

Table A .1. Descriptive Statistics

 A

	Time-varying characteristics	Mean (2004)	SD (2004)	Mean (2011)	SD (2011)
	Age (years)	14.87 0.81 21.87 0.81
	Father's shock	7.86 0.27 18.77 0.39
	Mother's shock	5.81 0.23 12.69 0.33
	Father works	91.25 0.28 81.33 0.39
	Mother works	90.19 0.30 86.14 0.35
	CM lives in a new household	1.34 0.16 46.47 0.50
	Brothers less than 18 years old (number) 0.60 1.04 0.42	0.85
	Sisters less than 18 years old (number)	0.53 0.94 0.39	0.82
	Migrant	3.57 0.19 28.24 0.45
	Middle school in village	71.49 0.45 77.93 0.41
	High school in village	20.73 0.41 45.31 0.50
	Time-invariant characteristics	Mean		SD
	Female	51.12		0.50
	Age at school entry (years)	6.95		1.82
	Father has no education	50.04		0.50
	Father has completed primary	17.42		0.38
	Father has completed college	32.53		0.47
	Mother has no education	60.50		0.49
	Mother has completed primary	23.32		0.43
	Mother has completed college	16.18		0.37
	Household assets in 2004 (0 to 100)	20.23		16.65
	Household cultivates land in 2004	40.93		0.49
	Land type, coastal plain	10.44		0.30
	Land type, interior plain	11.28		0.33
	Land type, hill	46.97		0.49
	Land type, plateau	16.03		0.36
	Land type, valley	12.86		0.33
	Land type, others	2.42		0.15
	Paved road in village	12.69		0.33
	Number of observations		1,119

Source: Authors' elaboration from the Madagascar Young Adult Survey and EPSPAM.

Table A .2. Climatic Zones

 A Authors' elaboration from the Madagascar Young Adult Survey.

	Climatic zones	2004 (percentage)	2011 (percentage)
	1. Equatorial rainforest, fully humid	15.64	16.53
	2. Equatorial monsoon	19.48	17.16
	3. Equatorial savannah with dry winter	13.05	14.39
	4. Steppe climate (hot steppe)	4.02	4.02
	5. Warm temperate, fully humid (hot summer)	7.33	7.69
	6. Warm temperate, fully humid (warm summer)	20.64	18.86
	7. Warm temperate, dry winter (hot summer)	11.35	10.72
	8. Cwb. Warm temperate, dry winter (warm summer) 8.49	10.63
	Source:

Table A .3. Cohort Members Hit by Cyclones, in %

 A Authors' elaboration from the Global Risk Data Platform and Madagascar Young Adult Survey.

	Year	% CM hit by at least a tropical storm or	% CM hit by at least a tropical cyclone
		a tropical cyclone	strength ≥ 1
	2004	64.34	14.75
	2005	10.99	0.09
	2006	28.95	0.09
	2007	27.17	2.06
	2008	37.27	0.00
	2009	26.18	2.23
	2010	2.06	0.00
	2011	4.20	0.00
	Source:

Table A .4. Full Specification of the Base Model

 A

	Equations	School	Work
	If CM is a girl	-0.218***	0.015
		(0.065)	(0.057)
	Age at school entry	-0.027	0.023
			(0.020)
	If CM lives in a new household	-0.289***	0.089
		(0.096)	(0.075)
	Number of child siblings, boys	0.002	-0.011
		(0.028)	(0.039)
	Number of child siblings, girls	0.010	0.088**
		(0.035)	(0.037)
	If father experienced any illness or death	-0.184*	0.104
		(0.103)	(0.123)
	If mother experienced any illness or death	-0.125	0.294**
		(0.126)	(0.145)
	If father works	-0.129	0.046
		(0.105)	(0.114)
	If mother works	-0.026	0.293**
		(0.121)	(0.120)
	Number of secondary schools (cycle 1) in the community	0.181**	0.011
		(0.083)	(0.102)
	Number of secondary schools (cycle 2) in the community	0.099	-0.216*
		(0.083)	(0.131)
	If community has access to a paved road	0.101	0.130
		(0.109)	(0.131)
	If the hh had a land in 2004	0.149**	0.125*
		(0.072)	(0.068)
	Rainfall deviation (6 months)	0.098**	-0.146***
		(0.040)	(0.047)
	Assets in 2004	0.010***	-0.010***
		(0.003)	(0.003)
	Rainfall deviation x Assets	-0.002*	0.002*
		(0.001)	(0.001)
	Control for (dummies):
	Age of CMs	Yes	Yes
	Father's education	Yes	Yes
	Mother's education	Yes	Yes
	Year (2004 to 2011)	Yes	Yes
	Climatic zone	yes	yes
	Land type	yes	yes
	Athrho	-0.579***
		(0.058)
	Observations	8,600
	Source: Authors' estimation.

Table A .5. Average Precipitation (in mm) and Precipitation around 1 z-score of Rainfall between November and April, National and by Climatic Zones

 A

	Zone	Average	1 z-score	0 z-score
	1	1175.389	2166.787	994.8435
	2	1070.435	1783.585	964.6864
	3	842.5096	1227.292	725.5471
	4	510.2336	574.7544	390.2637
	5	1113.622	1225.844	979.7858
	6	1065.659	1312.056	925.751
	7	1321.616	1618.008	1219.17
	8	1210.272	1496.411	1074.956
	National	1077.534	1423.665	946.4648
	Source: Authors' estimation.
	A.6.

Effects of the Long-term Mean of Variables Measuring Precipitation on Normalized Rainfall Deviation

  Means are calculated over the period 1992-2012.

	Long-term mean of rainfall variables	Coefficient
		(SD)
	Mean of annual precipitation, station data, normalized	-0.0217
		(0.225)
	Mean of annual precipitation, station data	-0.000
		(0.000)
	Mean of annual precipitation, satellite data	0.000
		(0.000)
	Mean of November to April precipitation, station data	0.000
		(0.000)
	Mean of November to April precipitation, satellite data -0.000
		(0.000)
	Constant	-0.025
		(-1.118)
	Observations	1,533
	Notes:

This work was supported by the LABEX IDGM+ (ANR-10-LABX-14-01) within the program "Investissements d'Avenir" operated by the French National Research Agency (ANR). Simone Bertoli for useful suggestions, as well as the participants to seminar presentations at LAMETA, Montpellier and at NOVAFRICA, Lisbon, to the 3rd IZA/DFID GLM-LIC Research Conference in Washington, and to the Labor and Development Workshop, Paris. Luca Tiberti acknowledges the financial support from the Partnership for Economic Policy (PEP), with funding from the Department for International Development (DFID) of the United Kingdom (or UK Aid), and the Government of Canada through the International Development Research Center (IDRC). Francesca Marchetta acknowledges the support received from the Agence Nationale de la Recherche of the French government through the program "Investissements d'avenir" (ANR-10-LABX-14-01); the usual disclaimers apply.

Notes

1 World Development Indicators (the data refer to 2015).

2 See https://www.usaid.gov/madagascar/environment, accessed January 2018. 3 Satellite-based data are preferred to those from the CRU (Climatic Research Unit), because of the poor quality of the latter from 2006 to 2009 (see Footnote 18). 4 The literature also explores the impact of weather events on the diversification choice.

For example, [START_REF] Skoufias | Occupational Diversification as an Adaptation to Rainfall Variability in Rural India[END_REF] showed that ex ante rainfall variability in India was associated with more diversification of rural households from agricultural to off-farm sectors. Similarly, [START_REF] Bandyopadhyay | Rainfall Variability, Occupational Choice, and Welfare in Rural Bangladesh[END_REF] found that ex ante rainfall variability risks in Bangladesh pushed adult members that were not the heads of their households away from the agricultural sectors, also at a cost of a lower total household welfare. 5 Other papers adopt measures of rainfall based on deviation from historical trend (e.g., [START_REF] Björkman-Nyqvist | Income Shocks and Gender Gaps in Education: Evidence from Uganda[END_REF][START_REF] Dumas | Shocks and Child Labor: The Role of Markets[END_REF][START_REF] Shah | Drought of Opportunities: Contemporaneous and Long-Term Impacts of Rainfall Shocks on Human Capital[END_REF][START_REF] Sesmero | How Do African Farm Households Respond to Changes in Current and Past Weather Patterns? A Structural Panel Data Analysis from Malawi[END_REF]. 6 See http://www.fao.org/agriculture/seed/cropcalendar/welcome.do 7 Data used in the empirical analysis show that only 27% of sample households did not cultivate any land between 2004 and 2012, while only 10% of them did not engage in agricultural activities over the period. We consider a household engaged in agricultural activities if it cultivates land or if the CM or her father is engaged in the agricultural sector. See Section 5 for the definition of "non-agricultural household." 8 In accordance with [START_REF] Rosenzweig | Fertility, Schooling, and the Economic Contribution of Children of Rural India: An Econometric Analysis[END_REF], child schooling and leisure can be considered as similar goods with respect, for example, to their respective shadow price.

For this reason, for simplicity, we assume that child schooling is included in 𝐶 𝑙 . For example, the shadow prices of child schooling and leisure are both "positively correlated with the number of children and the opportunity cost of school attendance and child leisure" [START_REF] Rosenzweig | Fertility, Schooling, and the Economic Contribution of Children of Rural India: An Econometric Analysis[END_REF]Evenson 1977, p. 1067). 9 The change in the shadow prices of child education and working can also be affected by rainfall-induced changes in the price of commodities, complementary (to labor) inputs and substitutes. 10 In the case of inefficient government infrastructure, cyclones could have an extended lagged effect as well, because the physical infrastructure may not be rebuilt for several time periods. We have tried to include the lagged cyclone effect in our model, but it turns out not to be significant.

11 See https://www.usaid.gov/madagascar/environment (accessed January 2018). 12 The reality is that no survey in Madagascar conducted in the past decade can really be considered nationally representative, since the most recent census, upon which sampling frames have been built, was conducted in 1993. 13 We computed this measure of wealth (based on non-land assets), using factor analysis on data observed in 2004, following the procedure used by [START_REF] Filmer | Estimating Wealth Effects without Expenditure Data-or Tears: An Application Educational Enrollments in States of India[END_REF].

14 Data available at: http://preview.grid.unep.ch/index.php?preview=data&events=cyclones&evcat=1&lang=e ng 15 We also tried to use CRU 3.24 data, gridded data that interpolate between the ground stations with a resolution of 0.5 x 0.5 degrees, but these data present a large number of observations with a zero anomaly between 2006 and 2009. This is due to the lack of weather stations available within the radius that is used for rainfall and temperature observations. We thus decided not to use CRU data due to their poor quality for our case study. We also wanted to use the Standardized Precipitation Evapotranspiration Index (SPEI) to take into account the effect of evapotranspiration, but, unfortunately, the SPEI database is based on CRU data for rainfall. 16 Although there are some differences with respect to the beginning and end of the rainy season within the country, in most of the areas, this season goes from November to April, with a few others experiencing a slightly shorter rainy season (see http://www.fao.org/agriculture/seed/cropcalendar/welcome.do, accessed January, 2018). 17 Satellite rainfall data are reported for grid cells of about 10 km 2 . They do not exactly correspond to our sample communities (i.e., survey clusters) in terms of surface, but there is no more than one community in a grid cell. Therefore, we would use the term community to designate both survey clusters and grid cells as the two coincide perfectly for our scope. 18 These are defined as follows: Category 1 if rainfall deviation is lower than -1; Category 2 if rainfall deviation ranges between -1 and 0; Category 3 if rainfall deviation ranges between 0 and 1; Category 4 if rainfall deviation ranges between 1 and 2; Category 5 if rainfall deviation is higher than 2. 19 As to why we did not use a probit with fixed individual effects, most of the variables used in our estimations are binary; controlling for fixed individual effects requires enough variability within each observation, which is not the case with our data. Also, see the threads discussed by [START_REF] Greene | The Behaviour of the Maximum Likelihood Estimator of Limited Dependent Variable Models in the Presence of Fixed Effects[END_REF]. 20 While we also have wealth information for 2012, we choose to use the lagged wealth to avoid possible reverse causality and limit the impact of unobservable heterogeneity on current school and work decisions. 54 21 We also estimated a specification, including a quadratic term for the rainfall variable, in order to capture the effect of excessive rain and floods. This term is not significant.

Results are available from the authors upon request. 22 Table A.4 provides information on how one unit of z-score translates into absolute mm of rainfall, by climatic zone and nationally. 23 We also estimated the baseline model on the sample of 803 individuals who never changed their residence between 2004 and 2011. Results are stable and are available from the authors upon request. 24 The variable drought takes the value 1 when rainfall deviation is below the 20th percentile.


Franz-Philipp Schmidt

Arthur Losquin

Ferdinand Hofer

Andreas Hohenau

Joachim R Krenn

Mathieu Kociak

How Dark Are Radial Breathing Modes in Plasmonic Nanodisks?

Keywords: plasmonics, electron energy loss spectroscopy, cathodoluminescence, transmission electron microscopy, nanoparticles

Due to a vanishing dipole moment, radial breathing modes in small flat plasmonic nanoparticles do not couple to light and have to be probed with a near field source, as in electron energy loss spectroscopy (EELS). With increasing particle size, retardation gives rise to light coupling, enabling probing breathing modes optically or by cathodoluminescence (CL). Here, we investigate single silver nanodisks with diameters of 150-500 nm by EELS and CL in an electron microscope and quantify the EELS/CL ratio, which corre sponds to the ratio of full to radiative damping of the breathing mode. For the investigated diameter range, we find the CL signal to increase by about 1 order of magnitude, in agreement with numerical simulations. Due to reciprocity, our findings corroborate former optical experiments and enable a quantitative understanding of the light coupling of dark plasmonic modes.

In recent years, focused electron probes have opened new avenues toward the spectral analysis of nanostructures with broadband optical sensitivity. Electron energy loss spectrosco py (EELS) in a scanning transmission electron microscope (STEM) (see Figure 1a) provides information with nanometer spatial resolution and sub eV spectral resolution. The EELS signal is proportional to the photonic local density of states (LDOS), projected along the electron beam direction. [START_REF] García De Abajo | Probing the photonic local density of states with electron energy loss spectroscopy[END_REF][START_REF] Hohenester | Electron energy loss spectra of plasmonic nanoparticles[END_REF] EELS thus provides access to all linear optical properties of nano objects and has been applied to probe highly localized fields, in particular plasmon eigenmodes in nanostructures. [START_REF] Nelayah | Mapping surface plasmons on a single metallic nanoparticle[END_REF][START_REF] Schaffer | High resolution surface plasmon imaging of gold nanoparticles by energy 5 filtered transmission electron microscopy[END_REF] Thanks to the unprecedented spatial resolution of STEM EELS, the classification of plasmon modes on flat nanoparticles into edge and film modes could be derived [START_REF] Schmidt | Dark plasmonic breathing modes in silver nanodisks[END_REF] and their correspondence to the dispersion relations of straight edges and extended films, respectively, was found. [START_REF] Schmidt | Universal dispersion of surface plasmons in flat nanostructures[END_REF][START_REF] Campos | Plasmonic Breathing and Edge Modes in Aluminum Nanotriangles[END_REF] The introduction of 3D EELS imaging based on tomographic reconstruction has further enriched the field. [START_REF] Nicoletti | Three dimensional imaging of localized surface plasmon resonances of metal nanoparticles[END_REF][START_REF] Collins | Eigenmode Tomography of Surface Charge Oscillations of Plasmonic Nanoparticles by Electron Energy Loss Spectroscopy[END_REF][START_REF] Horl | Tomographic imaging of the photonic environment of plasmonic nanoparticles[END_REF] A related technique is cathodolumi nescence (CL), [START_REF] Kociak | Cathodoluminescence in the scanning transmission electron microscope[END_REF] relying on photon emission upon electron excitation (Figure 1a). In a STEM, CL probes plasmon eigenmodes with the same high spatial resolution as EELS and even better energy resolution that is not limited by the exciting electron beam. [START_REF] Yamamoto | Photon emission from silver particles induced by a high energy electron beam[END_REF] CL is related to the radiative part of the LDOS. [START_REF] Kociak | Cathodoluminescence in the scanning transmission electron microscope[END_REF][START_REF] Losquin | Link between Cathodoluminescence and Electron Energy Loss Spectroscopy and the Radiative and Full Electromagnetic Local Density of States[END_REF] Therefore, the comparison of EELS and CL provides complementary information on the optical properties of plasmonic systems [START_REF] Losquin | Link between Cathodoluminescence and Electron Energy Loss Spectroscopy and the Radiative and Full Electromagnetic Local Density of States[END_REF][START_REF] Kociak | Mapping plasmons at the nanometer scale in an electron microscope[END_REF][START_REF] Coenen | Nanoscale Spatial Coherent Control over the Modal Excitation of a Coupled Plasmonic Resonator System[END_REF] that can be related to extinction and scattering cross sections, respectively. [START_REF] Losquin | Unveiling nanometer scale extinction and scattering phenomena through combined electron energy loss spectroscopy and cathodolumines cence measurements[END_REF][START_REF] Kawasaki | Extinction and Scattering Properties of High Order Surface Plasmon Modes in Silver Nanoparticles Probed by Combined Spatially Resolved Electron Energy Loss Spectroscopy and Cathodoluminescence[END_REF] This, in turn, is closely related to the respective contributions to damping in the system in terms of radiation damping and full damping, i.e., the sum of the radiation and ohmic contribution. [START_REF] Bosman | Surface plasmon damping quantified with an electron nanoprobe[END_REF][START_REF] Martin | High resolution imaging and spectroscopy of multipolar plasmonic resonances in aluminum nanoantennas[END_REF] In this Article, we discuss a combined EELS/CL study to characterize light coupling of radial breathing modes (RBMs) in silver nanodisks. RBMs have zero net dipole moment. In disks much smaller than the light wavelength, they are thus dark modes that do not couple to light. However, increasing size gives rise to retardation, thus making the RBM bright. [START_REF] Fung | Electron photon scattering mediated by localized plasmons: A quantitative analysis by eigen response theory[END_REF][START_REF] Miao | Electron beam excited photon emission from monopole modes of a plasmonic nano disc[END_REF] We find that with increasing size (150-500 nm) the EELS signal does not change significantly, but the CL signal increases by about 1 order of magnitude, corresponding to increased scattering [START_REF] Langhammer | Absorption and scattering of light by Pt, Pd, Ag, and Au nanodisks: absolute cross sections and branching ratios[END_REF] and thus radiation damping. To quantify the light coupling properties of RBMs, we introduce EELS/CL ratios that we obtain from different disk sizes and support the experimental results with numerical simulations. The direct measurement of the bright vs dark properties of plasmonic modes will benefit not only their fundamental understanding but also their use in processes such as surface enhanced fluorescence or surface enhanced Raman scattering and in applications such as biosensing.

EXPERIMENTAL SECTION

The nanodisks were fabricated by electron beam lithography on a 15 nm thick Si 3 N 4 substrate. The disk height was fixed at 30 nm, and the diameter was varied between 150 and 500 nm. We performed EELS and CL experiments on a VG STEM machine at 100 kV acceleration voltage. All the data shown hereafter have been synthesized from EELS and CL spectral images taken on the same disks but at different times. For numerical simulations, we used the MNPBEM toolbox, [START_REF] Hohenester | MNPBEM A Matlab toolbox for the simulation of plasmonic nanoparticles[END_REF] which relies on the boundary element method. Details are given in the Methods section.

RESULTS AND DISCUSSION

Nanodisks possess high symmetry and are thus ideal geometries to investigate canonical plasmonic behavior. RBMs have a zero net dipole moment and are therefore dark modes (i.e., they do not couple to light) in disks much smaller than the light wavelength. Optical spectroscopy data have shown that for disks with a 200 nm diameter and inclined light incidence with respect to the disk surface, retardation allows RBM excitations by light, [START_REF] Krug | Probing plasmonic breathing modes optically[END_REF] while no excitation was achieved for smaller disks. Considering the reciprocity principle, RBMs excited locally, e.g., by a fast electron beam, should therefore radiate light into the same inclined direction from where it could be excited optically, as long as a minimum nanodisk size (where retardation becomes relevant) is considered. We thus compare EELS and CL on single nanodisks with varying diameters to quantify the size dependent retardation effect and thus the light coupling properties of RBMs.

We start with a direct comparison of the RBM maps in Figure 1, for nanodisk diameters of 150-500 nm (high angle annular dark field, HAADF, images in Figure 1b). The EELS maps in Figure 1c show the RBM intensities (highest within the orange circle) that roughly remain the same for all disk sizes. We note that signals from neighboring plasmon modes contribute within the spectral window of the maps. These are higher order edge modes for the larger disks (i.e., periodically varying intensity along the circumference). For the smaller disks the surface plasmon SP 1 (ref 6 and compare Figure 2) causes an additional signal homogeneously distributed over the disk surface, so that the RBM signal at the disk center is poorly visible. The orange circles delineate the RBM area to clearly separate it from other mode contributions. The behavior of the CL signal is markedly different: being virtually absent for the smallest disk, it strongly increases with increasing disk diameter (Figure 1d). The slight oval shape as well as the noncentric emission maximum for the 400 and 500 nm disks comes from a small sample drift. We discuss a more detailed interpretation of the RBM maps in the next to last two paragraphs of this Article.

To understand this finding, we first include the full experimental spectral range in our analysis. For an example of a single silver nanodisk, 500 nm in diameter, the EELS (a) and CL (b) data are depicted in Figure 2. We observe that, first, EELS and CL maps at three different mode energies (A-C) give similar mode patterns, as shown in the top row of Figure 2. While map A has the highest intensity along the disk circumference, mode B shows an additional feature in the center, and mode C exhibits a ring shaped intensity distribution at half radial distance (R/2). Second, EELS and CL spectra obtained from specific regions on the particle are quite similar. The green spectra correspond to the edge, the red spectra to the region at R/2, and the blue spectra to the disk center, as indicated in the inset. Nonradiating modes are evidently missing in the CL data, which include the surface plasmons SP 1 at 2.9 eV (antisymmetric mode) and SP 2 at 3.35 eV (symmetric mode) and the bulk plasmon BP at 3.75 eV. [START_REF] Schmidt | Universal dispersion of surface plasmons in flat nanostructures[END_REF] Energies below 1.4 eV could not be detected by the CL setup.

In accordance with former work [START_REF] Schmidt | Dark plasmonic breathing modes in silver nanodisks[END_REF] we assign mode A to an edge mode of third order (hexapole). The first and second order edge modes (dipole and quadrupole) are well resolved in the EELS data (green spectrum, D and Q) but are outside the CL detection range. Mode B is the RBM (a film mode of first order), and mode C is a mixed edge/film mode, also referred to as (0, 1) and (1, 1) modes, respectively. [START_REF] Schmidt | Dark plasmonic breathing modes in silver nanodisks[END_REF] For both data sets, mode patterns and spectral signatures are thus mostly identical, in accordance with previous work on EELS and CL. [START_REF] Losquin | Unveiling nanometer scale extinction and scattering phenomena through combined electron energy loss spectroscopy and cathodolumines cence measurements[END_REF] Importantly, however, the RBM CL signal is quite strong (B, blue spectrum in Figure 2b), which can readily be assigned to retardation induced light coupling, given the disk diameter of 500 nm.

Aiming at a quantization of the light coupling size dependence, we now trace the signal intensity of the RBM as a function of the disk diameters for EELS and CL. EELS and CL spectra for all nanodisk diameters 150-500 nm are shown in Figure 3. Experimental data, again from three different disk regions, i.e., disk center (blue), along the circumference at R/2 (red), and the edge region (green), are displayed in Figure 3a.

For a detailed description of the spectrum normalization for the EELS and CL data see the Supporting Information ("Normalization" section). On one hand, the peak positions of the RBM shift in a similar manner for both EELS and CL, as indicated by the blue arrows. On the other hand, the different RBM peak intensities in EELS and CL are evident from the spectra. In particular, the CL RBM peak intensity strongly increases with increasing disk size, while EELS shows an almost constant RBM intensity for all disk diameters. We note that all plasmon eigenmodes discussed in this work are below 3 eV, and therefore damping due to interband transitions is not to be expected. The simulations plotted in Figure 3b reproduce the measured trend. While for a disk diameter of 400 nm an intense RBM peak is found in the simulated CL spectrum, the peak maximum is reduced by over 90% for the disk diameter of 150 nm (see Figure S1b in the Supporting Information). In addition, in the simulations the spectra originating from the disk edge (green spectra) clearly resolve the dipolar edge mode for EELS and CL (lowest energy peak in each spectrum), while the higher order edge modes are less pronounced in the case of CL. This is valid in particular for the smaller disk diameters, indicating the weakly radiating character for these modes. In accordance with the experimental setup, light detection is considered in the simulations in the half space above the sample, excluding the hole at the topmost position where the electron beam passes (see Methods). The agreement between experiment and theory but also the mismatch in particular for the CL edge spectra are further discussed in the Supporting Information (see "Agreement between simulation and experi ment" section and Figure S4). This includes spatial averaging, defects within the sample, and the lack of knowledge on the exact angular detection range as possible reasons for the mismatch in the CL edge spectra.

To further analyze the size dependent light coupling proper ties of RBMs, we plot the CL to EELS ratio of the RBM signal in Figure 4 for both simulated (dashed) and experimental (solid) data. The signals used for the ratio values are summarized in Figure S1. We apply for the experimental CL to EELS ratio values a modified EELS signal I center -I R/2 (instead of I center only), which we obtain by subtracting the R/2 spectrum from the center spectrum. This removes the contribution of the neighboring surface plasmon SP 1 (compare red and blue EEL spectra in Figure 3a). Thereby, we extract an EELS signal for each disk diameter that originates from the RBM only. The experimental CL to EELS ratio values are renormalized to the simulated value of the 400 nm diameter disk, using the same normalization factor for all experimental ratio values. With the normalization, the experimental and the simulated data agree very well. We note that an alternative way to analyze the data is via the center to edge signal ratio, leading basically to the same results (Supporting Information, "Center to edge ratio", Figure S2). In any case, the CL to EELS ratio increases with disk diameter, showing a concurrent increase in scattering strength and radiation damping of the RBM. Increasing the nanodisk diameter from 150 to 500 nm this ratio increases by roughly 1 order of magnitude, in agreement with recent theoretical work on nanodisk RBMs. [START_REF] Miao | Electron beam excited photon emission from monopole modes of a plasmonic nano disc[END_REF] This clearly demonstrates that RBMs that are dark in small nanodisks can efficiently couple to light for larger disk sizes.

Finally, we discuss the direction of light emission from the nanodisk plasmon modes excited by fast electrons. Figure 5a shows two simulated CL spectra from the edge (green) and center (blue) regions of a silver nanodisk (30 nm thick, 200 nm in diameter, on a 15 nm thin Si 3 N 4 substrate modeled as another disk, 700 nm in diameter), where the light signal emitted in all directions (4π sr) was considered (for simulations of other disk sizes see Figure S3 in the Supporting Information). To assign the plasmon modes to the peaks ( 1)-(3), we plot in Figure 5b the corresponding charge distribution. From that we attribute the dipolar, quadrupolar, and RBM mode to the peaks (1)-(3), respectively. Heuristically, EELS and CL probe the absolute value of the eigencharge distribution. [START_REF] Kociak | Mapping plasmons at the nanometer scale in an electron microscope[END_REF] For the RBM mode, the eigen charge density is much weaker on the edge than in the center, leading to an expected much stronger contrast in the center than on the edge, as confirmed by simulations in Figure 5b (3). Figure 5c illustrates the emission patterns of the modes by plotting the energy flux density of the electromagnetic field. We find that the dipole mode emission is fairly symmetric, while the quadrupolar mode shows two higher intensity lobes in the direction opposing the beam position, in accordance with recently observed directional emission on gold nano disks. [START_REF] Coenen | Directional emission from a single plasmonic scatterer[END_REF] Similar to the RBM, the quadrupolar mode is of dark character for small particles, corresponding to smaller CL intensity for decreasing disk size (Figure S3). The RBM emits mostly into the substrate, with a maximum at a polar angle θ of 135°and a weaker emission into the upper direction with an emission maximum at θ = 45°. The RBM emission into the upper direction is strongly reduced for smaller disks, virtually disappearing for a disk diameter of 100 nm (see Figure S3 in the Supporting Information), in accordance with the small CL intensity measured for small disks. At θ = 0°, i.e., in the direction perpendicular to the surface, there is no emission even for larger disk diameters, as expected from the RBM charge symmetry. It is thus evident that an RBM cannot be excited by a plane wave under perpendicular incidence for all disk sizes, while it can be excited by a plane wave with tilted incidence for large disks. In general, these results emphasize the reciprocity of data from CL and optical spectroscopy. [START_REF] Krug | Probing plasmonic breathing modes optically[END_REF] It seems counterintuitive that the RBM, which for obvious symmetry reasons does not have a dipolar moment, can radiate. Indeed, as is the case for the edge modes, the most intense modes are usually dipolar in nature, and often, when the particle is small with respect to the light wavelength, only the dipolar radiation is detectable. This is because the multipolar decomposition in the far field corresponds to a polynomial series of terms with increasing power of products of k and R, with k = ω/c and R being the radius of the disk. For small R, only the dipolar component prevails so that in the case of the small disks, indeed, the RBM mode is very dark due to the missing dipolar contribution. As the size of the disk increases, the higher order components quickly increase, making the mode quite bright.

CONCLUSIONS

In summary, we have shown by a combined EELS/CL study how the dark mode character of plasmonic nanodisks is relieved with increasing disk diameter. Expressed as a CL/ EELS signal ratio, RBM light coupling increases for almost 1 order of magnitude when increasing the disk diameter from 150 nm to 500 nm. Correspondingly, scattering and radiation damping of the disk increases, which are important aspects in the design of plasmonic nanostructures and their application in, for example, surface enhanced spectroscopies. Generally, combining EELS and CL with optical scattering and extinction spectroscopy provides a conceptual toolbox, relying on reciprocity to assess the full breadth of the properties of plasmonic modes.

METHODS

Silver nanodisks (30 nm thick) with diameters ranging from 150 to 500 nm were prepared by electron beam lithography in a RAITH eLINE+ system, using a poly(methyl methacrylate) resist on a 15 nm thick silicon nitride (Si 3 N 4 ) membrane and a standard silver evaporation and lift off procedure. [START_REF] Hohenau | Electron beam lithography, a helpful tool for nanooptics[END_REF] Silver was evaporated at a vacuum pressure of approximately 5 × 10 -6 mbar with an evaporation rate of 10 Å/s and no sample cooling.

The samples were studied in a VG HB 501 STEM, equipped with a cold field emission gun (energy full width at half maximum <300 meV) at 100 keV electron beam energy. Both, EELS and CL systems are homemade and fitted to the same microscope. [START_REF] Losquin | Unveiling nanometer scale extinction and scattering phenomena through combined electron energy loss spectroscopy and cathodolumines cence measurements[END_REF][START_REF] Myroshnychenko | Plasmon spectroscopy and imaging of individual gold nanodecahedra: a combined optical microscopy, cathodolumines cence, and electron energy loss spectroscopy study[END_REF] The EELS system is based on a 666 Gatan spectrometer, fitted with custom made filter and multipole power supply and a direct, optical fiber free, optical coupling to a CCD camera. The CL system 28 consists of a parabolic mirror that can be put into optical focus through a three axis high precision stage. Light reflected by the mirror is sent onto one end of an optical fiber bundle. The other end of the optical fiber is fitted to an optical spectrometer that is not fixed on the STEM column. All experiments on the same disks have been performed on the same day. As the acquisition parameters were very different, EELS and CL experiments have been made in sequences. All data presented in this work stem from spectral images. EELS spectra have been spectrally realigned and deconvoluted from the zero loss peak, using a Richardson-Lucy deconvolution algorithm (see Figure S5 in the Supporting Information). 29 CL spectra have been converted from nm to eV units by applying a λ 2 prefactor (see Supporting Information, "Normalization" section).

The EELS and CL experiments were modeled by calculating numerically the electric field induced by a fast electron source moving perpendicular to single silver nanodisks lying on a Si 3 N 4 membrane. EELS spectra were obtained from the work done by the Lorentz force on the fast electron source (eq 8 from ref 30); CL spectra, from the radiant energy crossing the portion of a sphere surface located at infinity (eq 50 from ref 30). A fraction of the sphere surface (1.2π sr of the upper half sphere, excluding the hole at the topmost position where the electron beam passes) was taken to mimic the actual detection angular spread used in the experiment (schematically shown in Figure 1a). The calculations were performed using the Boundary Element Method Maxwell equation solver [START_REF] García De Abajo | Retarded field calculation of electron energy loss in inhomogeneous dielectrics[END_REF] available in the MNPBEM toolbox. [START_REF] Hohenester | Simulating electron energy loss spectroscopy with the MNPBEM toolbox[END_REF] The Si 3 N 4 membrane was modeled as a disk of relative permittivity ε = 4 whose top facet is in contact with the bottom facet of the silver nanodisk. The relative permittivity of silver was taken from ref 33. The nanodisk and substrate boundaries were meshed nonuniformly, with the smallest mesh elements around the nanodisk edges. Particles with different sizes were modeled by changing the nanodisk and substrate sizes while keeping the same mesh. Convergent simulations were obtained by taking the radius of the substrate disk 500 nm larger than the nanodisk radius and by using mesh elements with areas of 3 nm 2 . As an example, for a 200 nm large nanodisk, the nanodisk and substrate were discretized respectively by about 6000 and (excluding the boundary in contact with the nanodisk) 4500 elements. The edge spectra were calculated for an electron position within the disk located 5 nm away from the edge. The influence of the electron beam position, the damping, and the angular detection range on the simulated CL spectra is discussed in the Supporting Information (see "Agreement between simulation and experiment" section and Figure S4).

Figure 1 .

 1 Figure 1. Experimental methods and spectroscopic maps of 30 nm thick silver disks with diameters of 150-500 nm. (a) Sketches of experimental EELS and CL setups: In EELS, the energy lost by the electrons transmitted through the sample is analyzed by an electron spectrometer. In CL, the energy of light emitted from the sample is analyzed. The light is collected from above the sample within a limited detection range, which excludes the propagation direction of the electrons. (b) HAADF images, (c) EELS, and (d) CL maps of the RBM. The EELS and CL maps are integrated over an energy window of ±0.25 eV around the RBM peak energy, and the contrast range is normalized on the corresponding RBM peak areas (for details on the normalization see Figure S1a in the Supporting Information). The inner area of the orange circles indicates the region with the highest RBM signal.

Figure 2 .

 2 Figure 2. EELS vs CL measurements on a 500 nm diameter silver disk on a Si 3 N 4 membrane: (a) EELS and (b) CL maps and spectra. Maps A-C (top) extracted at energies given by the black arrows in the spectra (bottom) and integrated over a constant energy width (colored area below the spectra) correspond to an edge (A), film (B), and mixed edge/film (C) mode with distinct mode pattern. The spectra originate from regions as indicated in the inset, i.e., edge (green), half radial distance (red), and center (blue) of the disk. D, Q, SP 1 , SP 2 , and BP correspond to the dipolar, quadrupolar, antisymmetric surface, symmetric surface, and bulk plasmon mode, respectively.

Figure 3 .

 3 Figure 3. Size dependent EELS and CL spectra. (a) Experimental EELS and CL spectra of Ag disks with diameters as indicated. The spectra correspond to the center (blue), R/2 (red), and edge (green) region of the disks. (b) Corresponding simulated EELS and CL spectra. The blue arrows are guides to the eye.

Figure 4 .

 4 Figure 4. Ratio of CL to EELS signal of the RBM as a function of disk size for the experimental (solid) and simulated (dashed) data.Experimental ratios have been normalized so that the value for the disk diameter of 400 nm coincides with the simulated result.

Figure 5 .

 5 Figure 5. Light emission profiles from nanodisks. (a) Simulated CL spectra of a 30 nm thick Ag disk, 200 nm in diameter, from the edge (green) and the center (blue) region as indicated in (b). (b) Surface charge distribution of the dipolar (1), quadrupolar (2), and breathing mode (3), corresponding to the three peak energies in (a); the dashed arrows indicate position and direction of the exciting electron beam. (c) Emission patterns of the plasmon modes (1)-(3), with the color reflecting the absolute value of the energy flux density, each normalized to its maximum (red color). The relative intensity scale is given by the factors as depicted, indicating the lowest overall emission for the RBM (3).

ACKNOWLEDGMENTS

This work was supported by the FWF SFB NextLite (F4905 N23), ESTEEM2 (FP7 project, no. 312483), NAWI Graz, and the Graz Centre for Electron Microscopy (ZFE). We thank Markus Krug and Gernot Schaffernak for fruitful discussions on optical spectroscopy of metallic nanoparticles.

AUTHOR INFORMATION

Corresponding Author *E mail: franz.schmidt@uni graz.at.

Notes

The authors declare no competing financial interest.