Keywords: Ecuador, Volcano, Agriculture, Labor, Natural disasters. JEL Codes Q15, D81, Q54

We study the behavior of farmers living under the threat of the Tungurahua Volcano in Ecuador. Recent eruptions have caused significant damage, including crop loss, death of livestock, and destruction of dwellings. We collected a unique data set after a major eruption in 2016. We interviewed 222 farmers in the area affected by the eruption and 260 in a nearby control zone to understand why they choose to remain in the risky zone despite the existence of public programs aimed at relocating them to safe zones. We examine land and labor, which are farmers' primary productive assets. Firstly, we investigate the capitalization of volcanic hazards in farmland values and find a negative price premium of 21% compared to the control zone. Secondly, we explore non-farm labor in response to volcanic risk. Finally, we argue that repeated ash fall events increase the illiquidity of farm household assets, such as farmland, and that agricultural human capital is difficult to convert into non-agricultural capital. Our results convey important information for public policies aimed at supporting adaptation and resilience of people living under the threat of volcanoes and other natural disasters.

Highlights

-Farm households remain in volcanic areas despite repeated loss of crops and livestock.

-We analyze the case of the Tungurahua Volcano in Ecuador using primary data.

-We investigate the role that productive assets, i.e., land and labor, play in the decision to remain in the risky zone. -We show the significance of integrated land and labor policies to address natural hazards.

Introduction

As natural disasters increasingly affect the livelihoods of vulnerable populations across the globe, significant research efforts and financial resources are being devoted to risk mitigation, adaptation and resilience policies. Among natural disasters, volcanic activity is classified as a geophysical natural disaster that is "a hazard originating from solid earth", with four potential outcomes, i.e., ash fall, pyroclastic flow and lahar flow. Between 1900 and 2017 there have been 242 volcanic events worldwide, causing 96,366 deaths and affecting more than 6.6 million people (Emergency Events Database -EM-DAT 1 ), and causing a wide range of economic, social, and psychological impacts [START_REF] Doocy | The Human Impact of Volcanoes: a Historical Review of Events 1900-2009 and Systematic Literature Review[END_REF][START_REF] Glaser | The Global Effects of Volcanic Eruptions on Human Health and Agriculture: A Review[END_REF][START_REF] Wilson | Impacts on agriculture following the 1991 eruption of Vulcan Hudson, Patagonia: lessons for recovery[END_REF]. Volcanic disasters also have dramatic impacts on agriculture, as eruptions and ash falls degrade farmland and vegetation and cause severe livestock and crop losses. Nevertheless, in the long-term, ashes can improve agricultural land quality, as they provide nutrients for the soil [START_REF] Cook | Impact on Agriculture of the Mount St. Helens Eruptions[END_REF][START_REF] Kelman | Living with volcanoes: the sustainable livelihoods approach for volcano-related opportunities[END_REF][START_REF] Wilson | Impacts on agriculture following the 1991 eruption of Vulcan Hudson, Patagonia: lessons for recovery[END_REF], which constitutes an incentive to farm under the threat of volcanoes.

Ecuador is strongly plagued by volcanic hazards. According to the EM-DAT, between 1975 and 2017, Ecuador had 12 episodes of volcanic activity, affecting a total of 1,479,426 people. 2 The Tungurahua, 5,023 m, located in the central Andean region in the Tungurahua province, is the most active volcano in the country. In 1999, after a nearly 80-year period of quiescence, the volcanic activity restarted, from violent explosions with pyroclastic flows and tephra falls to minor eruptions with ash emissions [START_REF] Le Pennec | Impact of tephra falls on Andean communities: The influences of eruption size and weather conditions during the 1999-2001 activity of Tungurahua volcano, Ecuador[END_REF]. These geological hazards have produced large private economic losses as well as severe damage to physical infrastructure, such as road, water systems and electricity, schools, health centers and official buildings, putting a repeated drain on public resources. As a result, disaster management policy has evolved from ad hoc solutions to a long term and nationwide disaster management policy [START_REF] Solberg | Natural disaster management and the road network in Ecuador: Policy issues and recommendations[END_REF]. Among the new policy instruments implemented by the Ecuadorian government are the assembling of a community-based network of volunteers known as vigías an early warning system for civil protection and evacuation [START_REF] Armijos | Adapting to changes in volcanic behaviour: Formal and informal interactions for enhanced risk management at Tungurahua Volcano, Ecuador[END_REF][START_REF] Stone | Risk reduction through community-based monitoring: the vigías of Tungurahua, Ecuador[END_REF], public awareness campaigns, and, almost importantly, the construction of houses in resettlement zones. Public authorities hoped that relocating households from exposed areas to safe areas would help mitigate volcanic risk.

However, despite the existence of relocation programs, recent research has stressed that some populations living under the threat of the Tungurahua do not want to be relocated to safe areas [START_REF] Armijos | Living with volcanic risk: Vulnerability, knowledge and adaptation in the slopes of Tungurahua, Ecuador[END_REF]. Some families have definitively resettled in safe zones while continuing to cultivate their land on the slopes of the volcano, whereas others have remained at their dwellings in communities affected by ash falls. This phenomenon is not specific to Ecuador and often occurs in other areas of the world threatened by volcanic hazards [START_REF] Gaillard | Alternative paradigms of volcanic risk perception: The case of Mt. Pinatubo in the Philippines[END_REF][START_REF] Lavigne | People's behaviour in the face of volcanic hazards: Perspectives from Javanese communities, Indonesia[END_REF][START_REF] Wilson | Impacts of the 2006 eruption of Merapi volcano, Indonesia, on agriculture and infrastructure[END_REF]. 1 Université catholique de Louvain (UCL) -CRED, D. Guha-Sapir -www.emdat.be, Brussels, Belgium 2 "In EM-DAT, this is the sum of those left injured, affected and homeless after a disaster". "Affected: People requiring immediate assistance during an emergency situation. The indicator "affected" is often reported and is widely used by different actors to convey the extent, impact, or severity of a disaster in non-spatial terms. The ambiguity in the definitions and the different criteria and methods of estimation produce vastly different numbers, which are rarely comparable" (http://www.emdat.be/guidelines).

The literature has looked into factors that shape the behavior of people who face volcanic hazard, i.e., cultural, social and economic factors and risk perception, which has attracted the widest range of studies. A good overview can be found in the special issue of Journal of Volcanology andGeothermal Research 2008 (See also Van Manen, 2014;Rodrigez-Vangort, 2015). Cultural beliefs and social values have been studied by sociologists, anthropologists and geographers [START_REF] Armijos | Adapting to changes in volcanic behaviour: Formal and informal interactions for enhanced risk management at Tungurahua Volcano, Ecuador[END_REF][START_REF] Few | Living with Volcan Tungurahua: The dynamics of vulnerability during prolonged volcanic activity[END_REF][START_REF] Tobin | and volcano hazard: the eruption of Tungurahua and evacuation of the faldas in Ecuador[END_REF]. Evidence from case studies suggests that populations tend to stay in volcanic areas for the following reasons: lack of knowledge of volcanic hazards, marginal status of populations living in risky zones, volcanoes as a vector of cultural identity [START_REF] Bachri | The calamity of eruptions, or an eruption of benefits? Mt. Bromo human-volcano system a case study of an open-risk perception[END_REF][START_REF] Gaillard | Alternative paradigms of volcanic risk perception: The case of Mt. Pinatubo in the Philippines[END_REF]. Economic studies usually focus on risk and time preferences (e.g. [START_REF] Bchir | Does the exposure to natural hazards affect risk and time preferences? Some insights from a field experiment in Perú[END_REF][START_REF] Willinger | Risk and time preferences under the threat of background risk: a case-study of lahars risk in central Java[END_REF].

This paper aims to contribute to the literature by investigating the extent to which productive assets, land and labor play a role in a farm household's decision to remain in the risky zone after an ash fall event. Despite their importance in households' coping strategies under shocks [START_REF] Dercon | Wealth, risk and activity choice: cattle in Western Tanzania[END_REF][START_REF] Ellis | Household strategies and rural livelihood diversification[END_REF][START_REF] Rose | Ex ante and ex post labor supply response to risk in a low-income area[END_REF], productive assets have received little attention in the literature on volcanic risk. After repeated ash fall events, a portfolio position in these productive assets becomes at least temporarily irreversible. The land may become hard to trade or lose its value and only be saleable at a discount price. Agricultural human capital and skills have a farm-specific component; knowledge is experientially obtained and may not be easily transferable to other places. In addition, occupational mobility is limited by a worker's abilities and by geographical mobility constraints. Farmers are, thus, effectively trapped in a portfolio they cannot exit. Meanwhile, land remains a strategic asset that provides the basis for rural livelihoods while labor skills match the needs required by agricultural tasks. This leaves little option other than to "rationally choose" to live with volcanic risk.

To address the research question, we conducted a field survey allowing us to collect detailed information on the livelihoods of farmers in volcanic areas of Ecuador. However, the relevance of our analysis goes beyond the specific context of Tungurahua and applies to a wide range of natural hazards. Our results also convey important information for public policies aimed at supporting adaptation and resilience of people living under the threat of natural disasters.

The rest of the paper is organized as follows. Section 2 discusses the literature on coping responses of farm households under shocks. Section 3 provides information on the study area. Section 4 explores the land and labor characteristics that can shed light on why farm households stay in the risky zone despite volcanic threat and policy that explicitly encourage migration out of this area, and Section 5 concludes with some policy recommendations.

Coping responses of farm housholds under shocks

Farm households are an emblematic case of the dilemmas faced by populations living under the threat of volcanoes: on the one hand, ash falls often destroy (or decrease) their productive capital, i.e. land and labor; and on the other hand, volcanic activity can increase farmland quality in the long run. The economic literature on consumption smoothing, asset accumulation and coping strategies of farm households under shocks is prolific [START_REF] Carter | The economics of poverty traps and persistent poverty: An assetbased approach[END_REF][START_REF] Dercon | Wealth, risk and activity choice: cattle in Western Tanzania[END_REF][START_REF] Ellis | Household strategies and rural livelihood diversification[END_REF][START_REF] Hoddinott | Shocks and their consequences across and within households in Rural Zimbabwe[END_REF][START_REF] Kochar | Smoothing Consumption by Smoothing Income: Hours-of-Work Responses to Idiosyncratic Agricultural Shocks in Rural India[END_REF][START_REF] Reardon | Links between rural poverty and the environment in developing countries: Asset categories and investment poverty[END_REF][START_REF] Rose | Ex ante and ex post labor supply response to risk in a low-income area[END_REF][START_REF] Rosenzweig | Credit Market Constraints, Consumption Smoothing, and the Accumulation of Durable Production Assets in Low-Income Countries: Investments in Bullocks in India[END_REF][START_REF] Rosenzweig | Wealth, Weather Risk and the Composition and Profitability of Agricultural Investments[END_REF][START_REF] Zimmerman | Asset smoothing, consumption smoothing and the reproduction of inequality under risk and subsistence constraints[END_REF]. It lays down the foundations on the behavior of farm households' in terms of consumption, production and risk-response strategies, with a focus on their accumulation and use of productive and non-productive assets and on labor allocation decisions between farm and non-farm labor.

Farm households put in place various self-insurance strategies to cope with risks to their livelihoods [START_REF] Corbett | Famine and household coping strategies[END_REF]. The imperfection or inexistence of credit and insurance markets affect household decision-making [START_REF] Rosenzweig | Credit Market Constraints, Consumption Smoothing, and the Accumulation of Durable Production Assets in Low-Income Countries: Investments in Bullocks in India[END_REF]. Income shocks can lead farm households to decrease their consumption, health and education expenses, which has an impact on their long-term welfare through lower nutrition, human capital and long term consumption [START_REF] Carter | The economics of poverty traps and persistent poverty: An assetbased approach[END_REF][START_REF] Corbett | Famine and household coping strategies[END_REF][START_REF] Jensen | Agricultural Volatility and Investments in Children[END_REF]. Savings may also be used to smooth consumption [START_REF] Udry | Risk and saving in Northern Nigeria[END_REF]. Likewise, management of assets is central, such as livestock used as buffer stock against income shocks [START_REF] Fafchamps | Drought and saving in West Africa: are livestock a buffer stock[END_REF][START_REF] Rosenzweig | Credit Market Constraints, Consumption Smoothing, and the Accumulation of Durable Production Assets in Low-Income Countries: Investments in Bullocks in India[END_REF]. Households also carry out trade-offs between productive and non-productive assets, as well as between liquid assets and illiquid asset accumulation [START_REF] Dercon | Wealth, risk and activity choice: cattle in Western Tanzania[END_REF]. Household members may also supply labor to the non-farm labor market in order to cope with risk in farm production [START_REF] Fafchamps | Sequential labor decisions under uncertainty: An estimable household model of West-African farmers[END_REF][START_REF] Kochar | Smoothing Consumption by Smoothing Income: Hours-of-Work Responses to Idiosyncratic Agricultural Shocks in Rural India[END_REF][START_REF] Rose | Ex ante and ex post labor supply response to risk in a low-income area[END_REF].

Response patterns to shocks will also depend on farmers' risk preferences. 3 Risk-neutral farmers will likely devote more time to activities that provide a higher expected marginal return [START_REF] Mishra | Farm income variability and the supply of off-farm labor[END_REF] while risk-averse farmers will tend to allocate fewer labor resources to a risky activity (i.e., farming in the risky zone) and devote more resources to labor in safe zones (non-farm).

Individual behaviors in the presence of natural hazards must thus be approached in the light of the concepts of vulnerability, resilience and risk assessment. There are various types of household vulnerability: vulnerability to the risk of not being able to meet basic needs, such as access to food, housing and health services; vulnerability to the risk of falling into poverty (nonpoor households who experience a shock and fall into poverty); and for already poor households vulnerability of becoming caught in a poverty trap (i.e. chronic poverty) with limited resilience. Whatever the type of vulnerability, these coping strategies overlap in three ways: the degree of risk (probability) for a household to be exposed to a volcanic shock; the magnitude of the shock; and the household's ability to respond to these shocks and return to its initial position (resilience). A household's level of resilience depends largely on its asset endowments and the liquidity of these assets.

Presentation of the study area and sample

Study area

The Tungurahua is one of the Ecuadorian volcanoes that entered an eruptive phase in 1999 (after nearly a century-long quiet period). Major eruptions occurred in 2006, 2008 and 2010 but ongoing volcanic activity has been observed since 1999. More than 30,000 people live under the direct threat of the Tungurahua, and more than 200,000 live under the threat of sporadic ash falls [START_REF] Armijos | Living with volcanic risk: Vulnerability, knowledge and adaptation in the slopes of Tungurahua, Ecuador[END_REF]. The primary economic damage and losses associated with Tungurahua eruptions, even minor, result from ash and tephra falls that destroy crops and natural pastures, impact the roofs and glazes of houses, kill livestock, cause respiratory diseases for both humans and animals. Since most people in the affected communities are heavily dependent on agriculture for their livelihood, eruptions translate into significant income loss, food vulnerability, and for the poorest, enormous difficulties to recover. Resilience to volcanic activity is thus key for the affected populations.

Our sample of households is located in three provinces of Ecuador, Tungurahua and Chimborazo, which surround the Tungurahua volcano for the affected zone and Morona Santiago for the control zone. The affected area was chosen using the map of eruptive deposits (see figure 1). The choice of the control zone was based on the similarity in agro-climatic conditions, using several sources of data capturing topography, climate and other geographical characteristics including altitude, slope, theoretical sunning, azimuth and distance from the village center to the nearest main road. 4 We began with the calculation of the mean value of each criterion for the two villages Puela and Bilbao, 5 within a one-kilometer radius. For each criterion, we designated a band with limits defined by the average +/-one standard deviation. We searched for similar zones throughout the country so that the average of each criterion in a circle of one kilometer falls into the band defined for the affected zone. Among all the possible areas that emerged from this exercise, we chose those zones which were the closest to the affected area, i.e., the parish Quimiag located in the province of Morona Santiago.

We conducted a quantitative survey in both zones in August 2016, .four months after the eruption of March 2016. A total of 489 farm households were randomly selected by random walk. 222 who farm land in the risky zone (111 were living in the risky zone and 111 were living in a resettlement zone) and 260 who farm land in the control zone. 6 Data were collected from household heads. The objective was to establish a snapshot of inhabitants' responses to volcanic activity. Many issues, such as risk exposure and perception, risk coping, agricultural land values, and residential location choice were addressed. We collected a large amount of plot-specific 4 Theoretical sunning is calculated as a function of the orientation of the slopes. The azimuth is the angle between the direction of a place and the geographic North. The source of the altitude data is the Shuttle Radar Topography Mission (SRTM) with an accuracy of 90m in [START_REF] Jarvis | Hole-filled seamless SRTM data V4[END_REF] International Centre for Tropical Agriculture (CIAT), available from http://srtm.csi.cgiar.org. The slope, azimuth and the theoretical sunshine are derived from the altitude and calculated with ArcGIS10 (Spatial Analyst module). The main roads are extracted from the Open Street Map database: http://www.openstreetmap.org. 5 The values are: slope: 9.72 -25.66 %; altitude: 2396 -2845 m; sunning: 1 738 857 -1 794 563 W.m-2.s ; azimuth: 121 -274 ° ; distance to main road: 6573 -12859 m. 6 The target population has been defined as farm households, i.e., households that operate a holding regardless of the residential choice. According to the 2010 Census, a total of 854 households, including 2,670 members, were living in the three parishes located in the most affected zone. In the parish of the control zone, the census indicates 1,480 households and 5,257 individuals. information on soil quality, slope, location and accessibility, as well as on agricultural use. Finally, we collected socio-demographic characteristics of household members, as well as their employment status.

Household socio-economic characteristics

Land is the most important key asset in agriculture. Table 1 gives some information about land tenure, land size and type of activity. Most respondents in both the risky and control zones, own farmland: 75.4% and 78.6%, respectively, of the plots for which we have characteristics are owned by farmers that belong to our sample. As a result, the renting of land is not extensive: 16.4% of plots in the risky zone and 18.5% in the control zone. Contractual arrangements are divided into equal parts for cash rent and sharecropping. Land is often rented on a short-term basis. Approximately 50% of contracts last less than one year. However, nearly one third of contracts have an indefinite term. Formal property rights have been secured through titling for the vast majority of parcels (83%). The landholding size is very small in the areas considered: 47.9% of households cultivate less than one hectare and the mean landholding size is 1.5 hectares. In addition, farmland distribution is highly unequal: farms with less than one hectare cultivate only 6.8% of the total land whereas farms with more than 5 hectares, which represent 8.7% of farms, occupy 56.2% of total land.

The evidence is mixed as to the degree of specialization of farmers. Farmers in the risky zone allocate most of their plots to agriculture (74.7%) whereas farmers in the control zone choose a mixed farming system in which 58.6% of plots are allocated to crops and 24.6% to pasture and livestock, leaving the remaining land fallow. Maize is the main crop cultivated on agricultural land in both zones. In the control zone potatoes are the second largest crop whereas in the risky zone it is beans.

Family labor is the second largest key asset in agriculture. Since the family labor force depends on the personal characteristics of household members, the relevant parameters are family size, age and gender composition of the household labor force, and human capital accumulation. Table 1 gives an overview of the main household members' characteristics. Overall, households in risky, resettlement and control zones are relatively homogenous in terms of age and gender. There are slightly more men in the risky zone (51.8% of the risky zone population and 52.2% in the resettlement zone) than in the control zone, where men account for 47.3% of the population. The population is relatively younger in the control zone (where the average age is 34) than in the risky (34.6) and resettlement zones (37.6). This also holds true for the household head. As far as human capital is concerned, the level of schooling of members who are economically active is low. If we consider the whole sample, nearly 8.7% of workers never attended school or attended only kindergarten and 55.8% completed only primary school. Only 29.3% of the workers completed secondary school and 6.3% have completed a university cycle. In both the risky and resettlement zones, most workers have completed primary school whereas workers in the control zone tend to have completed more years of education. Since education is essential for improving individual employment prospects, this low educational attainment may prevent people from looking for distant jobs or engaging in local non-farm income generating activities.

Non-productive assets consist mainly of dwellings, durable (electronic) goods and vehicles. Because of the ongoing threat of destruction, households in the risky zone logically hold significantly fewer durable goods than households in the resettlement and control zones.

Exposure and responses to volcanic shocks

Among the 222 farmers farming land in the risky zone, 56% experienced damage to their dwelling following the eruption of March 2016, such as damaged roof, walls, windows, and interior furniture. 57% had a total loss of their crops and 32% a partial loss. 46% experienced loss of livestock. These farmers implemented several coping strategies, as shown in Table 2. When facing a shock, households are expected to implement insurance mechanisms, dispose of productive assets, borrow money from friends, relatives, a bank or cooperative, and reduce their consumption levels [START_REF] Corbett | Famine and household coping strategies[END_REF]. They tend first to protect income-generating assets, even to the detriment of current consumption, selling or abandoning productive assets as a last resort [START_REF] Ellis | Household strategies and rural livelihood diversification[END_REF]. In our study area, farmers behaved as expected 7 with two interesting features. Many farmers sold livestock, which can be explained by the fact that they did not have a place to shelter them; and worse, livestock owners were paid very low for the livestock as buyers took advantage of the situation [START_REF] Armijos | Living with volcanic risk: Vulnerability, knowledge and adaptation in the slopes of Tungurahua, Ecuador[END_REF]. Also, relatively few of them were able to obtain a loan. 8 Logically, 45% respondents report the Tungurahua volcano to be very dangerous, 39% dangerous, 13% somewhat dangerous and 3% not dangerous. Nevertheless, people living on the slopes of the volcano overwhelmingly decided to stay despite both the human and economic risks from eruptions and the government's program of household relocation to safe areas: 84% of the respondents in the risky zone sample reported that their main residence was in an exposed area although 50% of them also have a residence in a protected zone. When asked if they would still be living in the exposed area while the volcano remains active, more than 94% of household heads said yes. The main reason for their reluctance to move (55.9% of answers) was related to economic opportunities, either because family income sources exist in the home location through farming, or because employment opportunities in other places were lacking or inaccessible. In addition, most family members (women, children and elders) stay at night in the resettlement home and go back to farm their land during the day, whereas only males stay overnight in the risky villages. This might give household members a feeling that the family is safe from the volcano's threat. Other obstacles to relocation, such as old age, lack of education, difficulty renting houses, and a dependent family member, are also frequently mentioned (27% of answers). Finally, 11% said they had adapted to the ash fall so did not need to relocate. 7 Previous studies show evidence that farmers also cope with shocks through land rental markets [START_REF] Eskander | Adaptation to natural disasters through the agricultural land rental market: evidence from Bangladesh[END_REF][START_REF] Ward | Migration and Land Rental as Responses to Income Shocks in Rural China[END_REF]. However, we do not have such information in our data. 8 Berg and Schrader (2012) analyzed the effects of volcanic shocks on the demand and access to credit in the area of the Tungurahua. Using a natural experiment, they found that the number of loans demanded increased in response to volcanic activity and that the access to credit depended on the extent of the clientbank relationship, even in the agricultural sector most severely affected by volcanic shocks.

Why do farm households stay in the risky zone?

The literature has explored factors that could explain a household's decision to remain in volcanic areas (See Section 1). However, land illiquidity and labor immobility have received relatively little attention despite the potential insight that studying these factors might provide in understanding the behavior of farm households living on the slopes of volcanoes.

Does the proximity of the volcano depreciate land values?

In the risky zone, all households in our sample are farmers and their primary asset is land. Therefore, analyzing their behavior calls for an understanding of farmland values. To this end, we use a hedonic pricing framework. Land is composed, not only of characteristics relating to the productive quality itself, but also of characteristics determined by location. The latter includes a wide range of location-determined characteristics, such as the quality of the environment (including proximity to the volcano), and the distance to markets or main roads. The hedonic price model consists of the analysis of the price of differentiated goods based on their characteristics. [START_REF] Rosen | Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition[END_REF] formalized the model for real estate prices, which was further developed for agricultural land by [START_REF] Palmquist | Land as a Differentiated Factor of Production: A Hedonic Model and Its Implications for Welfare Measurement[END_REF] and [START_REF] Palmquist | A hedonic study of the effects of erosion control and drainage on farmland values[END_REF]. The hedonic model consists of revealing the implicit prices of various attributes of heterogeneous goods. It implies that farmland is a heterogeneous good consisting of a set of characteristics Z = (z1,…,zk ,…,zK) sold in bulk. Plots are distinguished from each other, both through their intrinsic and extrinsic characteristics. The hedonic model calculates the implicit marginal price of these different characteristics from the overall price (value) P(Z) of the plot. At equilibrium, each implicit marginal price pk is equal to the marginal willingness to pay for this characteristic and is calculated, in the case of quantitative variables, as the derivative of the aggregate price P(Z) with respect to the quantity zk. The empirical calculation of different marginal implicit prices thus requires the estimation of the hedonic price function by regressing prices of agricultural land on their various characteristics. Here, we focus on land that is owned and cultivated by farmers.

During the survey, farmers were asked to report the per-cuadra (1 cuadra = 84 square meters) value of each plot of land they cultivate. 9 Table 3 provides the description and summary statistics of several intrinsic and extrinsic characteristics that explain farmland values. Annex 1 provides the regression results and implicit prices. The model explains 58.2% of land value variations. Since we estimated a log-log model, for continuous variables a 10% increase in the variable leads to a 10*coeff % change in the value of the cuadra; and for binary variables the impact in % is measured by 100(e coeff -1). The results support several commonly-held hypotheses about farmland prices. We find that the larger the surface of the plot, the lower the value per cuadra is. In the model, we have three accessibility variables that play a significant role in the formation of agricultural land prices. We find that poor access to parcels in case of rain lowers their value and the closer a plot is to the main road, the higher its value. Construction is also an important variable that adds significant value to land. Among plots on which there is construction, 83% are dwellings and 17% 9 There are several convincing arguments that support the assumption that self-reported farmland values closely approximate their market value. First, since we focus here on farmers who own and cultivate their land, we can postulate that they are the best informed on the various attributes of the plots. In particular, the accumulated experience conveys information about the previously adverse conditions, i.e. ash falls that have a plot-specific component. Second, farmers interviewed did not have any incentive to misreport the value of their land. Farmers are, thus, expected to be well informed about land prices. are prefabricated house (mediagua). We introduced three variables that measure the productive potential of the plot, i.e., the reported quality of the soil, its slope and access to irrigation water. Flat land is positively valued compared to more sloping land and both are negatively valued compared to a mixed slope. Soil quality is not significant, but this may be related to the fact that 91% is of good quality.

The most interesting and relevant result is that farmland in the risky zone has a negative premium of 21% compared to land in the control zone, ceteris paribus. This depreciated value of land near volcanoes means that a farmland loses its value to serve as an insurance mechanism, despite it being a farm household's main productive asset. Households thus face several challenges. First, their land capital is degraded by the eruptions. Second, farmland is an illiquid asset. Third, even if households wanted to sell their land, they would suffer a loss of value estimated above, which would not allow them to acquire the same productive capital outside the risky area. Since this loss would increase the cost of moving, this may also reduce the attractiveness of relocating. In addition, acquiring information on the land market of a new location might be difficult and searching for new land could entail high opportunity costs, transaction costs and uncertainty and reinforce the option of staying at the current place of work.

4.2.

Geographical and occupational immobility

Labor immobility is an important issue in determining the response of farmers to a volcanic threat. The more immobile labor is, the more difficult a location change in both residence and occupation would be. There is a fairly large body of empirical work on both aspects of labor immobility in rural areas. Among all the factors that are known to attach people to a place and reduce mobility, the extent to which farming skills are transferable across space is a main concern that has recently received attention in the literature [START_REF] Autor | The" task approach" to labor markets: an overview[END_REF][START_REF] Bazzi | Skill Transferability, Migration, and Development: Evidence from Population Resettlement in Indonesia[END_REF][START_REF] Gathmann | How general is human capital? A task-based approach[END_REF][START_REF] Huffman | Migration, fixed costs, and location-specific amenities: A hazard analysis for a panel of males[END_REF]. Most crops are sensible to growing conditions, such as soil conditions, soil management techniques, soil nutrient disorder etc. [START_REF] Cox | Prospects for developing perennial grain crops[END_REF]. Farming technical knowledge is thus usually associated with specific location and specific crop. As a result, farmers may encounter difficulties in transferring their human capital to safe locations where growing conditions may be different. As a result, a large productivity loss may occur that causes significant foregone earnings. Barriers to skill transferability may thus imply an adjustment cost that is out of reach of most farmers [START_REF] Gollin | Agricultural productivity differences across countries[END_REF].

Labor immobility also refers to the difficulty in taking advantage of opportunities in other sectors in nearby or distant areas. Numerous studies have examined the extent to which rural workers engage in non-farm activities,10 as well as the rationale behind this behavior, well summarized by Ellis (1998). 11 It is now widely held that labor mobility depends on the availability of attractive non-farm opportunities arising from a dynamic local economy and the capacity of household members to exploit these opportunities, which, in turn, depends on the level of their human, social and financial capital.

In the sampled areas, on-farm activities are the main occupation of the majority of household members: nearly 90% of them declare working on their own farm, in whichever zone they live. However, in addition to working on their farm, household members engage in non-farm work: 20.2% of household members declare a non-farm occupation in the risky zone, 15.2% in the resettlement zone and 27.1% in the control zone. These figures tend to suggest a significantly lower degree of participation in the non-farm labor market in the resettlement and risky zones compared to that in the control zone. This result contradicts most findings in the literature that document a positive relationship between risk exposure and participation in non-farm activities. As we will see, this indicates strong barriers to the adjustment to risk exposure. The range of non-farm occupations appears rather limited: commerce is the primary subsector that attracts workers in all three zones (66.5% of occupations in the control zone, 48.8% in the resettlement zone and 45.1% in the risky zone). Manufacture, construction and transport represent together the second largest subsector of occupations, with 40% of occupations in the risky zone, 31.7% in the resettlement zone, and 25.7% in the control zone. The third largest subsector of occupations, but far behind the other two, includes all of the occupations ranging from managerial to medical and administrative occupations and constitutes no more than 13.3% of occupations.

Most occupations are performed quite close to dwellings: 41.2% of non-farm activities are exercised in the same parish where workers live, another 43.3% are undertaken in the same province and only 15.5% in another province.

Table 5 shows that the weight of agricultural-related occupations is much greater for landed than for landless households. Multi-activity as well as non-farm occupation declines with an increase in landholding size: households whose landholding size falls in the first quartile have a higher number of workers engaged in non-farm activities on average than those whose landholding size falls in the last quartile. Hence, non-farm activities appear to be an inferior good. Households that lack farmland, and thus farming income, are those that engage more in the labor market or develop non-farm enterprises. Although the information on incomes is not available from survey data, the inverse relationship between land size and non-farm labor tends to suggest that diversification away from farm labor is mainly driven by push rather than by pull factors. Overall, diversification of economic activities in our sample appears quite low, in particular in the risky and resettlement zones. In most empirical studies, the drivers of geographical mobility involve many factors, among which are the availability of jobs the capacity of rural workers to perform these jobs, and the cost of commuting or moving.

The spatial distribution of economic activities and the resulting local labor market dynamism in nearby areas is a primary issue in understanding involvement by rural workers in non-farm activities. Access to a wide range of jobs for rural people depends on the availability of these jobs. A diversified local economy is better able to offer many jobs, and some industries offer jobs that are more flexible, better adapted to agricultural seasonality, and better suited to a farmer's skill set.

The survey does not provide information on the local labor market, such as the conditions in nearby urban market centers or other prosperous villages. However, we have qualitative information on the main cities close to the survey areas. Baños, which is the nearest city to both the risky and resettlement zones, is a major tourist center of around 20,000 inhabitants, so most job opportunities are in the leisure, entertainment or hospitality industries and require skills (communication, computer know-how, interpersonal skills) that are far beyond the reach of workers with a farming background. Riobamba is the capital city of the province Chimborazo and has 250,000 inhabitants. It is close to the control zone and has a large market which supports the demand for both agricultural and non-agricultural products and services that farm households are able to produce or supply. It is also expected to have a wider range of production activities and greater opportunities for non-farm jobs. This partly explains why the participation in nonfarm activities is higher in the control zone.

A second main source of labor immobility of rural workers comes from the fixed costs they incur when they enter the labor market. Among these costs, the commuting or moving costs associated with the distance between the residential and workplace is key. People living far from cities bear higher transport costs and have less information about employment opportunities, either directly or through social networks. These costs clearly reduce the probability of wage employment. Individuals living in rural environments also remain constrained in their selfemployment opportunities. Distance to a large urban center restrains the demand for nonagricultural products and services that farms are able to offer.

At first glance, the differences between the risky, resettlement and control zones in terms of distance (by road) to main urban centers cannot be considered as a significant impediment to non-farm work. The communities of the risky zone are on average 45 km away from the closest city Baños, whereas resettlement zones are a little bit closer (23.3 km). The closest city to the control zone communities is Riobamba, which is only 12 km away. Both zones have access to relatively good paved roads.

Finally, many empirical studies show that labor mobility of agricultural workers is low because they usually lack the skills to work in non-farm jobs (ILO, 2011). The noticeable differences in the time-allocation pattern between the three zones are consistent with the level of education of the rural labor force. Unskilled workers make up the vast majority of the workforce in the risky and resettlement areas where most workers have acquired only a primary education and thus retraining would be difficult and/or costly. In comparison, educational attainment in the control zone is so the capacity of household members to take non-farm opportunities is better.

Discussion and conclusion

Natural disasters, such as volcanic eruptions, impose severe non-productive and asset loss to affected populations. Dwellings, land, crops and livestock are damaged with every natural hazard. Despite this regular destruction, some populations choose to live under the threat of volcanoes. In this paper, we use primary data collected from farmers living under the threat of the Tungurahua volcano in Ecuador from farmers living in a nearby control zone to examine farm household behavior, with the specific intention of proposing natural hazard-response economic policies. Our attention is particularly directed to the examination of the household's main productive assets, i.e., farmland and labor.

Farm households living near active volcanoes face hard choices since the maintenance of livelihoods depends on the return on economic activities. Their decision to stay should be understood as the result of asset illiquidity and labor immobility. We have shown that farmers tend to own location-specific assets and would thus incur significant costs in relocating. Assets, such as farmland that are not easily marketable (or at a low value) clearly restrict a farmer's ability to relocate. Farmers may also lack resources to move or change occupations. Such barriers suggest that adjustment to volcanic shocks through the diversification of economic activities may be extremely difficult for some workers. Our paper thus complements anthropological, social and geographical approaches such as [START_REF] Armijos | Living with volcanic risk: Vulnerability, knowledge and adaptation in the slopes of Tungurahua, Ecuador[END_REF], [START_REF] Armijos | Adapting to changes in volcanic behaviour: Formal and informal interactions for enhanced risk management at Tungurahua Volcano, Ecuador[END_REF][START_REF] Few | Living with Volcan Tungurahua: The dynamics of vulnerability during prolonged volcanic activity[END_REF].

Nonetheless, there are many reasons for living near the Tungurahua. First, land on the slopes of the Tungurahua volcano is highly productive, with soils fertilized by ashes and a favorable climate. Second, efforts by Ecuadorian authorities to inform the population through the community-based network of vigias have helped people to return to their original homes in the volcanically threatened area around the Tungurahua with less risk [START_REF] Stone | Risk reduction through community-based monitoring: the vigías of Tungurahua, Ecuador[END_REF]. As a result, people tend to perceive the risk as acceptable. All of this has thwarted the government's efforts to induce risk area residents to evacuate and relocate to safe areas.

However, current public policies in Ecuador are not sufficient because they adopt a disaster risk management approach that consists of aid provided during emergency periods [START_REF] Armijos | Living with volcanic risk: Vulnerability, knowledge and adaptation in the slopes of Tungurahua, Ecuador[END_REF]. Considering the impact of ash fall on productive assets and constraints faced by farm households with respect to their occupational attributes, we argue that relocation policies should be complemented by interventions on land and labor markets to address natural hazards. There is a need for more integrated policies that account for land and labor specificities.

Ash falls compromise the agricultural production of farmers already burdened by poverty. Increasing agricultural productivity should greatly help to manage the inherent risks of agricultural production in areas threatened by volcanic eruptions. Enhanced agricultural productivity should also be passed on in land prices and compensate, at least partly, for the discount in land prices linked to eruptions. As there are so many aspects that determine agricultural productivity, there is a large scope for policy intervention. The uptake of new technologies, such as use of improved seed varieties, expansion of irrigation and the adoption of higher value crops depend foremost on the availability of technologies appropriate to local conditions. Scientists have the responsibility to provide information on suitable options. Agricultural extension services, broad access to credit services and potentially the creation of crop and livestock insurance against volcanic shocks are also vital means to ensure widespread adoption of productivity-enhancing technologies.

However, the poorest farmers might not have sufficient land or access to strategic inputs to escape poverty. Diversification of household income sources is another common means of managing the risks associated with eruptions. The principal policy challenge is how to unlock employment opportunities and ensure that farmers can access alternative jobs. Policies should therefore facilitate development of opportunities in neighboring areas in tourism, small shops, transport cooperatives, and small-scale mining. Common means of supporting enterprise development include improved access to credit services, markets, and technology, as well as entrepreneurship training. Integrating rural workers into non-agricultural labor jobs would require entire households to transform their assets and skills. Public authorities should thus consider implementing a training policy in non-agricultural activities that would ease occupational mobility.

Policymakers who have implemented resettlement strategies in the past must acknowledge the lack of realism of expecting households to resettle away from dangerous zones without taking into account the livelihood opportunities (or lack thereof) elsewhere. A balance must be found between volcanic risk and livelihood transferability when designing resettlement schemes. Our findings are certainly relevant for other natural disasters, especially in areas under repeated shocks as landslides, floods and drought.

Figure 1 :

 1 Figure 1 : Location of communities

Table 1 . Household socio-demographic characteristics

 1 * p<0.1 indicate if the difference between the risky/resettlement zones and the control zone are statistically significant. Stars in brackets refer to the difference between the risky and resettlement zones.

	Description

Table 2 . Responses to the March 2016 eruption %

 2

	Provided mutual assistance in the form of labor exchange	72.07
	Reduced food expenses	67.57
	Spent savings	63.06
	Received assistance from the government	60.36
	Sold livestock	50.00
	Reduced health and education expenses	49.10
	Received assistance from a church or NGO	24.77
	Worked on other farmland (outside of family)	24.32
	Changed crops	15.77
	Obtained a loan from friends or relatives	12.61
	Obtained a loan from a bank or cooperative	12.16
	Received money from friends or relatives living in Ecuador	7.66
	Received remittances	4.05
	Sold farmland or land	1.35
	N = 222

Table 3 . Summary statistics for the hedonic model Owned and cultivated plots in both zones Control Risky

 3

	Variable

*** p<0.01, ** p<0.05, * p<0.1 indicate if the difference between the control zone and the red zone is statistically significant. Note: To allow the logarithmic transformation of ln_road and ln_canton_time, we added 0.0001 to all observations.

Table 4 . Characteristics of non-farm occupations

 4 ** p<0.01, ** p<0.05, * p<0.1 indicate if the difference between the risky/resettlement zones and the control are statistically significant. Stars in bracket refer to the difference between the risky and resettlement zone.

	Risky	Resettlement	Control	All
	zone	zone	zone	sample

*

Table 5 . Average number of members working non-farm per household

 5

				All
		Landholding size	sizes
	<= 0.2	0.2 -0.74	0.74 -1.48	> 1.48
	ha	ha	ha	ha

See Binswanger (1980),[START_REF] Brunette | A Meta-analysis of the Risk Aversion Coefficients of Natural Resource Managers Evaluated by Stated Preference Methods[END_REF], and[START_REF] Holt | Risk Aversion and Incentive Effects[END_REF] for discussions on farmers' risk preferences measured through revealed and stated preference methods.

Non-farm activities include non-agricultural wage work and self-employment activities which generate income. Note that some activities linked to agriculture, such as agro-processing, sales of agricultural products, or agricultural wage jobs are often undertaken by households. Since this analysis focuses on the occupational mobility out of agriculture, they have been excluded from the calculations.

For a comprehensive survey of the determinants of labor mobility in rural areas in Latin America, see also the special issue of World Development "Rural Non-farm Employment and Incomes in Latin America", published in March 2001.

Acknowledgments

This research has been made possible in part thanks to funding from LABEX CLERVOLC. In addition, we would like to thank the FERDI (Fondation pour les Etudes et Recherches sur le Développement International) and the ANR (Agence Nationale de la Recherche, France) for their financial support through the program ''Investissements d'avenir'' and the LABEX IDGM+ (ANR-10-LABX-14-01) mechanism. Thanks also to Emily Wilkinson (Overseas Development Institute) and Teresa Armijos Burneo (University of East Anglia) for useful discussions and to Olivier Santoni (FERDI) and Jean-Luc Le Pennec (IRD) for their help in the field survey and control area choice. The usual disclaimers apply.

Appendix Annex 1. Hedonic pricing results and marginal effects

Regression results

Variation of the value per cuadra due to a 10%


E Jacques

L Maillé

Y Le Petitcorps

C Lorrette

C Sauder

PRELIMINAR RESULTS ON JOINING OF THIN SiC f /SiC m COMPOSITES BY SILICIDES COMPOUNDS AND LOCAL HEATING

Keywords: Brazing, Silicides, Composite Materials, Diffusion Bonding, Nuclear applications

The present work describes the methodology and the results for joining SiC substrates in the solid state by reactive and non reactive metallic silicides in order to use these materials as container for the Gas Fast Reactor. The operation temperatures are in the range of 1000°C but short time incursions at 1600 or 2000°C have to be anticipated. As joining material, we have chosen to study four titanium and niobium silicides: TiSi 2 and NbSi 2 (non reactive with SiC) and Ti 5 Si 3 and Nb 5 Si 3 (reactive with SiC) in order to modify the joint /substrate bonding. The joining between these silicides and the silicon carbide substrate was prepared by Spark Plasma Sintering in order to limit the contact time during the sintering. Post thermal treatments in the solid state performed under a control atmosphere have been performed in order to study the thermal stability of the assembly. Polished cross sections were prepared to study the interface composition, the cracking path in the vicinity of the joint/ substrate interface. In order to decrease the residual stresses within the joint, SiC particles were mixed with the silicide ones. In the case of the non reactive silicides, the SiC particles effectively reduce the cracks whereas for the reactive silicides, the SiC particles reacts with the joint leading to a thermally stable composition and the bonding to the substrate is improved. In order to prepare the joining technology, few trials of local heating have been investigated with a Laser beam. The advantage of local heating is the possibility to heat at high temperature (around 1800°C) for short time without damaging the composite structure : a CO 2 laser source has been used for this purpose. Thermal cartographies have been measured from one side to the other of the silicon carbide plate.

1-INTRODUCTION

For forty years, the energy production never stopped growing to respond the demographic and industrial growth. Today, controversies concerning the use of fossil energies and the poor yield of renewable energies have made nuclear power essential. It represents 80% of the energy production in France. The ageing of nuclear power plants encourages countries all over the world to devote a part of their research programs to the Generation IV reactors. Such reactors have to meet technology goals: improve nuclear safety, minimize waste and natural resource utilization, and to decrease the cost to build and run such plants. The French institution CEA focuses its efforts on different concepts of reactors and in particular on the Gas Fast Cooled Reactor (GFR). This reactor is helium-cooled, with an outlet temperature in the range of about 500°C to 1000°C in standard situation. Several fuel forms are being considered for their potential to operate at very high temperatures and to ensure an excellent retention of fission products, examples given for ceramic matrix composite (CMC) tubes or honeycombs, advanced fuel particles, or ceramic clad elements of actinide compounds. In this study, we focused on a tube concept made of thin CMC: SiC f /SiC m composites. Silicon carbide ceramic matrix composites have been developed at first for applications in aeronautic such as rockets, jet engines or turbines. The temperature requirements for Generation IV reactors make them attractive also for nuclear applications. In actual nuclear reactors, metallic alloy tubes are used as fuel container but such alloys have too poor properties above 500°C. Silicon carbide (SiC) has sufficient thermal and mechanical properties : a low Coefficient of Thermal Expansion (4.10 -6 K -1 ), a good thermal conductivity (300W??.m -1 .K -1 , a high stiffness (400GPa) and a high melting, more over, SiC is neutron transparent in order to allow good performances of the nuclear core. The structural materials are also submitted to different thermomechanical strains: thermal gradients, helium pressured at 70 bars in the reactor…) and then need to have good damage tolerance, thermal shock resistance and a limited brittleness. Mechanical properties of unreinforced silicon carbide are noticeable with a Young' modulus twice as much as steel at room temperature but its brittleness is important. Using SiC fiber reinforcement in a SiC matrix permits to increase the damage tolerance (typically 0.6% of tensile deformation before break at room temperature) thanks to a damage mechanism. SiC f /SiC m ceramic composites are then good candidates to answer all these specifications. Nevertheless, there are some technological issues to overcome such as the difficulty to accomplish complex geometries. Then, a suitable method of joining SiC f /SiC m components is required. Riveting and bolting are not considered for ceramics and the key issue seems to reside in joining pieces by brazing, soldering (but not possible on very refractive materials such as silicon carbide) or solid state diffusion bonding. The joining material should have the same thermomechanical properties as the composite and have to keep these properties at very high temperature. Several other joining methods have been developed for the assembly of ceramics such as mechanical fastening, plasma spray or physical and chemical vapor deposition. Brazing is used extensively due to its simplicity, low cost investment and potential to be a mass production process. In recent years, joining SiC with Ag-Cu or Cu-based braze has been reported but their utilization is restricted to 500°C. Other authors have developed eutectic brazes from metals but the presence of free silicon doesn't enable their use beyond 1400°C. Many studies have been carried out on Ti-Si-C and Cr-Si-C systems on eutectic compositions: Si-22%wtTi (TiSi 2 and Si), Si-18%atCr (CrSi 2 and Si) and Si-44%atCr (CrSi and CrSi 2 ). The aim of this study is to find relevant compositions and processing routes for joining SiC f /SiC m tube composite. The requirements for the brazing composition can be describe as follow : The brazing has to be adherent to the silicon carbide substrate with a limited reaction zone in order to avoid the damaging of the SiC, the brazing must not be cracked in order to avoid any leaks, the assembly must withstand for short durations temperatures around 1600°C. Taking into account these requirements, 4 silicides have been selected ( TiSi 2 , Ti 5 Si 3 , NbSi 2 , Nb 5 Si 3 ), these silicides have a higher CTE and a lower Young's modulus than SiC. These silicides are available in a powder shape. In order to reduce the strain mistmatch, few amount of SiC powders have been had to the brazing composition. More over, M 5 Si 3 silicides are reactive to SiC, in order to limit the reaction with the silicon carbide substrate, few amount of SiC powders or metallic disilisides powders (MSi 2 ) have also been had to the brazing composition. The joining of two the silicon carbide substrates was prepared by Spark Plasma Sintering in order to limit the contact time during the sintering. Post thermal treatments in the solid state performed under a control atmosphere have been performed in order to study the thermal stability of the assembly. Polished cross sections were prepared to study the interface composition, the cracking path in the vicinity of the joint/ substrate interface.

2-MATERIALS AND METHOD :

2-1 : Selection of the constituents :

The study of ternary phase diagrams (M, Si, C) shows a chemical stability of some metal-based silicides or carbides with silicon carbide, whereas other silicides of the same metal are unstable and forms a metallic carbide (Figures1a-c). By considering the matches of the properties between SiC and the joining material, MSi 2 , M 5 Si 3 and MC ( M=Ti or Nb) can be considered as potential joining compounds (Table1).

Table 1. Physical properties of compounds of interest

The ternary phase diagrams of Ti-Si-C and Nb-Si-C show the thermodynamic stability of disilicides with the silicon carbide. On the contrary, with silicides such as Ti 5 Si 3 or Nb 5 Si 3 , a reaction zone should be observed due to the absence of equilibrium. Different diffusion paths can be considered :

Ti 5 Si 3 -> TiC -> SiC Ti 5 Si 3 -> TiC -> T1 -> SiC Nb 5 Si 3 -> NbC -> NbSi 2 -> SiC Nb 5 Si 3 -> NbC -> SiC
The main advantage of using chemically stable silicides as joining material is the chemical stability in time of the assembly. But with this lack a chemical reaction, a weak bonding between the elements can be expected. On the other hand, a strong bonding can be expected with the M 5 Si 3 silicides but to the prejudice of a chemical damage of the SiC substrate. A compromise has to be found among adhesion, mechanical behavior against cracks and chemical reactivity with silicon carbide. By considering the thermomechanical behavior, the mistmatch between the physical properties of SiC and the silicides shows that after cooling, the SiC is in a compression state, whereas the silicides are in tension. Due to the lack of room temperature ductility of the silicides, the brazing will be cracked. In order to decrease the CTE and to increase the stiffness of the brazing, 0 to 30% in Vo. of SiC were added to the all silicides. In the case of the M 5 Si 3 silicides, the chemical reaction with SiC will transform the joint composition into a more stable one as described before. Détailler la taille des poudres, les épaisseurs des joints, la nature des différents mélanges, la preparation des mélanges de poudres, les conditions de frittage SPS, les moyens de caractérisation, les différents traitements thermiques…Schéma des échantillons oui All the samples have been prepared with a Spark Plasma Sintering equipment. This device permits the sintering of ceramics in a very short time. Limiting thus the grain growth or the reaction zone with the substrate. The singularity of this technique is the application of a uniaxial pression on the sample during the process combined with an alternative or DC current. The samples are pressed within a graphite die and the pressure in the chamber is around 5Pa. The sintering temperature is always 200°C below the melting temperature of the compound in order to maintain a solid state reaction. The temperature rising rate is 100°C/min and a pressure of 50MPa is applied since the sintering temperature is reached.

3-RESULTS AND DISCUSSION

3-1 : Non reactive silicides (MSi 2 or MSi 2 +SiC)

We have first studied the sintering of the chemically stable silicides TiSi 2 and NbSi 2 . The good adhesion of the two is relevant but cracks are observed in both cases (Figure 2a). Those cracks are very harmful while they are crossing grains and even within the SiC substrate. To minimize this effect, we introduced a certain amount of SiC fine powders. For TiSi 2 , the SEM images confirm the hypothesis while the higher the amount of SiC fine powders is the smaller density of cracks is observed (Figures 2a-c). No thermal treatment has been carried out on TiSi 2 as its melting temperature is below 1600°C. A good adhesion is observed for NbSi 2 +10%SiC but a worsening is noted after 3hours at 1600°C ( Figure 3). To conclude on these compositions, MSi 2 + 20%SiC particles are interesting materials on a physicochemical point of view even after thermal treatments ( 1500°C for TiSi 2 or 1600°C for NbSi 2 ). In order to improve the joint morphology, it would be better to use smaller silicides powders (similar to SiC ones), this would permits also to reduce the joint thickness. The assembly was done under pressure, it would be interesting to study the bonding without any pressure during the sintering.

3-2 : Reactive silicides (MSi 2 or MSi 2 +SiC)

The same experiments have been carried out with the reactive silicides Ti 5 Si 3 and Nb 5 Si 3 (Figure 4). The presence of a reaction zone between the joint and the SiC substrate is observed when the joint contains less than 10% of SiC p (Figure 4a,b). As expected, there is a chemical reaction at the interface with the silicon carbide substrate. For higher content of SiC p (20 or 30%), the reaction occurs at the interface but also within the joint itself (Figure 4c). The chemical transformation of the joint seems to be correlated to the amount of SiC powder incorporated. With 0 to 10% of SiC, less than 5% of the joint thickness has reacted, 20% are transformed with 20% of SiC p and nearly 35% are transformed with 30% of SiC p . ( Pour faire ce calcul, j'ai considéré que la zone de reaction faisait le double de ce qui est indiqué dans le tableau cad des 2 côtés du substrat et que l'épaisseur totale du joint faisait 500m.). The EDS analysis of this reacted zone reveals the presence of titanium carbide (TiC x ) against the SiC substrate where as no TiSi 2 is observed. The presence of TiC x is interesting for at less two reasons, TiC has a Young's modulus and a CTE close to SiC and TiC x is in equilibrium with SiC and Ti 5 Si 3 (Figure 1, Table 1). After thermal treatment, a large debonding and a strong reaction with the SiC substrate is noticeable ( Figure 5 a-b) for the low content of SiC p . These results emphasize the role played by the SiC powders mixed to the silicide (Figure 5c). An EDS analysis has revealed that the thermal treatment leads to the formation of the Ti 3 SiC 2 , TiC within a Ti 5 Si 3 matrix and is coherent with the ternary phase diagram (Figure 1a). The presence of the pseudo-ductile Ti 3 SiC 2 is interesting for mechanical purpose of the assembly. After 3h hours of diffusion time, the joint is still composed 65% of unreacted Ti 5 Si 3 in the middle of the joint thickness. The TiC formed at the joint/ silicon carbide interface plays the role of a diffusion barrier.

In the case of Nb 5 Si 3 with a large amount of SiC p , a good behavior is also observed before and after a thermal treatment (Figure 6a-b). Within the joint, The thickness of the reaction zone is limited by comparison with Ti 5 Si 3 whereas the substrate is strongly chemically attacked (Figure 6a-b). The EDS analysis leads to the formation of niobium carbide (NbC x ). The chemical composition of Nb 5 Si 3 after thermal treatment remains the same with the presence of the NbC x interface between SiC and Nb 5 Si 3 . Whereas NbC x and TiC x are very similar with a vacancy in carbon, the difference of chemical reaction between the two silicides with SiC can be explain by the presence of the T1 compound (in the Si,C, Ti) phase diagram which can play the role of a diffusion barrier. As a consequence even that Nb 5 Si 3 has a higher melting point than Ti 5 Si 3 , it is less interesting for this application. After the thermal treatment at 1600°C, some un-reacted Ti 5 Si 3 is still present in the joint and the composition of the blend (SiC+Ti 5 Si 3 ) has to be tuned. In order to get rid of the drawbacks of reactive and non reactive silicides and above all to minimize the presence of the reaction zone, we have blended them in a certain quantity and observed the behavior of the joints (Figure 7). For TiSi 2 +Ti 5 Si 3 +SiC composition, a lack of reaction zone is relevant even after a severe heat treatment, few cracks are however present and are crossing the joint from the SiC substrate showing a good bonding. The stability of the joint even after a thermal treatment is of interest. The ternary phase diagram of the Ti-Si-C system shows that TiSi 2 and Ti 5 Si 3 are not stable and should form TiSi (Figure 1). We don't observe the formation of this phase but the presence of TiC at the interface of Ti 5 Si 3 grains and the presence of a dominant phase of TiSi 2 is noted. Then, we assume that Ti 5 Si 3 reacts with the SiC fine powder more easily than with the disilicides to form TiC x and probably Ti 3 SiC 2 . The initial powder sizes of TiSi 2 and Ti 5 Si 3 have to be decreased in order to have a thinner joint. Moreover, by decreasing the size of the powders, will make easy the sintering.

For NbSi 2 +Nb 5 Si 3 +SiC composition, we observe the formation of a reaction zone between the joint and the substrate but it is considerably thinner than in the case Nb 5 Si 3 alone 25µm against 5µm in that case ( Figures 6a and7b). However, the thermal treatment leads very large and damageable cracks in the joint and at the interface between the substrate and the joint where the NbC x is present (Figure 7c).

3-4 : Local heating with a CO 2 Laser beam

4-CONCLUSION

What ever the composition of the silicide is, it is necessary to blend with the silicide powder with fine SiC particles (1m). The amount of SiC has not been adjusted but at least 20% in volume are necessary. A compromise has to be find, in order to minimize the residual stresses a maximum of SiC is required but with a high amount of SiC p , the sintering and the solid state diffusion to the substrate will be more difficult. For all the composition, in order to facilitate the sintering and to decrease the thickness of the joint, the initial powder sizes of the silicides have to be decrease. Three types of composition were found to be of interest : (1) The first one is a TiSi 2 +SiC, the stability is limited to the melting temperature of the disilicide (1540°C) but this composition can be sintered at a low temperature, (2) the second one Ti 5 Si 3 +SiC is unstable, TiC x and Ti 3 SiC 2 are formed at the substrate interface allowing the bonding without damaging the substrate, the amount of the Ti 5 Si 3 has to be tuned in order to have a stable joint in time, (3) Finally, the 3 rd composition TiSi 2 +Ti 5 Si 3 +SiC is of interest because the presence of TiSi 2 limits the quantity of Ti 5 Si 3 which can react with the silicon carbide substrate. The operating temperature is however limited to the melting temperature of the disilicide.(j'ai suppose que sur la photo 7a, il n' y a pas eu de traitement thermique) The adhesion of these composition has now to be tested by a mechanical test.

5-REFERENCES

Figure

  Figure 1. : Ternary diagram of the systems M-Si-C (a) Ti-Si-C at 1227°C, (b) Ti-Si-C at 1727°C, (c) Nb-Si-C at 1727°C SiC TiC NbC Ti 3 SiC 2 (T1) TiSi 2 Ti 5 Si 3 NbSi 2 Nb 5 Si 3 Tf (°C) 2700 3140 1540 2120 1930 2480 α (10 -6 K -1 ) 4.5 7.6 10.4 11 8.4 7.3

  Figure 2. SEM micrographes of as-pressed materials : (a) TiSi 2 , (b)TiSi 2 + 10% (vol) SiC, (c) TiSi 2 + 20% (vol) SiC, with the joint, the silicon particles are the grey spots

Figure 3 .

 3 Figure 3. NbSi 2 +10%SiC (a) as pressed and (b) after 3h at 1600°C

Figure

  Figure 4. SEM micrographes of as-pressed materials : (a) Ti 5 Si 3 , (b)Ti 5 Si 3 + 10% (vol) SiC, (c) Ti 5 Si 3 + 20% (vol) SiC

Figure

  Figure 5. SEM micrographes after 3h at 1600°C heat treatment : (a) Ti 5 Si 3 , (b)Ti 5 Si 3 + 10% (vol) SiC, (c) Ti 5 Si 3 + 20% (vol) SiC

Figure 6 .

 6 Figure 6. SEM micrographes of Nb 5 Si 3 +20%SiC joint composition (a) as-pressed, (b) after 3h at 1600°C heat treatment

Figure 7 .

 7 Figure 7. SEM micrographes of 40MSi 2 40M 5 Si 3 -20SiC(% Vo.) (M= Ti or Nb)/ SiC interfaces (a) TiSi 2 + Ti 5 Si 3 + SiC after 3h at 1600°C heat treatment ( je ne comprends pas TiSi2 aurait du fondre ou alors c'est le matériau avant traitement thermique?), (b) as-pressed NbSi 2 +Nb 5 Si 3 +SiC, (c) NbSi 2 +Nb 5 Si 3 +SiC after 3h at 1600°C heat treatment

Table 2 : Compositions of interest for the joint (M=Ti or

 2 The different compositions of the joint are recapped in table 2.

	(a)	(b)	(c)


Alexandra Kirsch
email: alexandra.kirsch@uni-tuebingen.de

Explain to whom? Putting the User in the Center of Explainable AI

The ability to explain actions and decisions is often regarded as a basic ingredient of cognitive systems. But when researchers propose methods for making AI systems understandable, users are usually not involved or even mentioned. However, the purpose is to make people willing to accept the decision of a machine or to be better able to interact with it. Therefore, I argue that the evaluation of explanations must involve some form of user testing.

Reasons for Explanations

I regularly present the following definition by Brachman [START_REF] Brachman | Systems that know what they're doing[END_REF] in my AI lecture: A truly cognitive system would be able to learn from its experienceas well as by being instructed -and perform better on day two than it did on day one. It would be able to explain what it was doing and why it was doing it. It would be reflective enough to know when it was heading down a blind alley or when it needed to ask for information that it simply couldn't get to by further reasoning. [. . . ] Once a student raised his hand and asked whether the ability to explain one's own actions is a necessary feature of cognition. After all, he cannot explain all his actions (and if he does, it is doubtful whether such an explanation reflects the psychological processes that really led to the action) and still would be considered as a cognitive system.

The ability of an agent to explain its own decisions is often regarded as a necessary feature without a clear understanding of why agents should have this ability. Connected to this is the question of what an explanation is. With the current hype of statistical machine learning, the general feeling is that these methods need some way to make their decisions plausible to people (like the DARPA initiative Explainable Artificial Intelligence1 ). But when researchers talk about explanations, they hardly ever consider the end user. In this paper I argue that comprehensibility and explainability must always be regarded in the context of a specific use case and that its adequacy can only be determined by interaction with users.

Usability Principles

The idea to build comprehensible technical devices is much older than the current trend in AI. Many usability guidelines from the fields of design and humancomputer interaction include implicit or explicit explanation to users. Norman [START_REF] Norman | The Design of Everyday Things[END_REF] proposes four basic design principles, all of them contain elements of explainability: conceptual model: users should understand the underlying mechanisms of the system; visibility: all functionality should be visible, a kind of explanation of what the system is capable of; mapping: the visible elements should intuitively map to functionality; feedback: the user should always be informed about the system's state. Thus, any device should be designed in a way that users are aware of the system's capabilities and current state. This can be interpreted as a kind of explanation, one can also say that such a system does not need any additional explanation. For AI researchers this means that 1) comprehensible systems can often be built by adhering to well-known usability principles, 2) the design and usability of the overall system is often more important than AI features to result in an overall positive user experience.

Legibility

Embodied and virtual agents differ from typical human-computer interaction in that they can perform more pronounced actions and often have additional sensing capabilities. What is an explanation in this context? Of course, such agents could generate explanations of their actions, possibly in natural language. But in many cases a constant stream of explanations may annoy users and its effectiveness is questionable. When we look at human-human interaction, we hardly ever need to explain our actions to others. So why should a machine do so?

A more natural way of interaction could be to implicitly communicate goals and the necessity of actions. Lichtenthäler and Kirsch [START_REF] Lichtenthäler | Legibility of Robot Behavior : A Literature Review[END_REF] define the term legibility as follows:

Robot behavior is legible if: (Factor 1) a human observer or interactor is able to understand its intentions, and (Factor 2) the behavior met the expectations of the human observer or interactor. This definition centers on the human observer, implying that legibility can only be determined by experiments involving users. Such tests can again be inspired by standard usability testing, but the quality criteria and setup must often be adapted to the task and embodied situation of the agent. In addition, if physical robots are involved, there are additional questions of how to ensure the safety of participants.

As an example, consider the task of legible robot navigation [START_REF] Kruse | Human-aware robot navigation: A survey[END_REF]. Robot navigation has traditionally been treated as a purely technical problem, but with humans sharing the space of the robot or directly interacting with it, legibility becomes an issue. But then, the quality of a navigation act cannot just be characterized by its success and possibly the time needed to reach the goal point, one must also determine whether human observers can indeed infer the goal point and that the human expectations are met [START_REF] Lichtenthäler | Increasing perceived value between human and robots -measuring legibility in human aware navigation[END_REF].

Performing user tests is time-consuming. Therefore, it would be nice to have a general set of measures that determine legibility, but that can be measured without direct user involvement. An experiment of Papenmeier et al. [START_REF] Papenmeier | Human understanding of robot motion: The role of velocity and orientation[END_REF] identifies two factors that influence the legibility of robot navigation: 1) the movement direction: a robot looking towards the direction it is moving to (or towards the goal point, both were identical in the experiment) is perceived as more autonomous than one with a different orientation while moving; 2) the velocity profile: deceleration of the robot causes surprise in human observers (as measured by a viewing time paradigm), while acceleration and constant velocities do not.

Explainability and Interaction

Legibility as used above is a criterion for passive interaction: even though a person has no direct contact with the agent, the behavior should be legible. But it is also a prerequisite for direct interaction, for example a person trying to initiate an interaction would have to be able to predict the robot's movements. But direct interaction may require more than just a basic, implicit understanding of the other's intentions, it may at times require a more explicit explanation.

Decision methods can be designed in a way that resembles human decision making. The Heuristic Problem Solver [START_REF] Kirsch | Heuristic decision-making for human-aware navigation in domestic environments[END_REF] and the FORR architecture [START_REF] Epstein | Navigation with learned spatial affordances[END_REF] follow closely the way that humans make decisions: they explicitly generate alternatives and evaluate them. In this way, an explanation is generated along with the solution: the alternatives that were considered as well as the reasons for choosing one can directly be communicated to users [START_REF] Korpan | WHY: Natural explanations from a robot navigator[END_REF].

In addition, such an explicit decision-making paragidm enables an interactive process of humans and machines jointly determining a solution. It is practically impossible to model all the knowledge a person has with respect to a task. But if people can interact with the decision process of the machine, they can use this additional knowledge without having to formalize all of it. Thus, a person could propose or delete alternatives, or change the evaluations of alternatives.

Here again, the question is whether the explanation is adequate. Ideally, the machine should provide enough information for a person to be satisfied with or even be willing to take responsibility for the decision. Or in the case of interaction, a possible measurement is whether the joint decision-making is more efficient and effective than a purely computational or purely human one.

The ability to explain one's decisions and actions is often unquestioningly required from cognitive systems. But the frequency, form and implementation of explanations depend on the specific application and context. In many cases, standard feedback mechanisms known from human-computer interaction are all that is needed. Other applications may demand that users are able to identify the source of errors. Even others may need an explicit dialogue between human and machine that allows the machine to request help if necessary. Explanations can take different forms, from standard interaction methods of flashing lights, sounds and graphical displays, to language or the display of actions. In the last section I have mentioned systems that generate an explanation along with the solution. An alternative is the post-hoc generation of explanations for black box algorithms, which is currently popular with the rise of statistical machine learning.

In all respects, the users are the leveling rule. An explanation is not a mathematical construct, an explanation is good if people find it helpful in the specific context. Therefore, the AI community should expand its evaluation metrics beyond optimization criteria to user-centered measures and evaluation procedures.

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https://www.darpa.mil/program/explainable-artificial-intelligence