Estimating Households Vulnerability to Idiosyncratic and Covariate Shocks: A Novel Method Applied in Madagascar

World Development Vol. 37, No. 7, pp. 1222–1234, 2009 Ó 2008 Elsevier Ltd. All rights reserved 0305-750X/$ - see front matter www.elsevier.com/locate/worlddev

doi:10.1016/j.worlddev.2008.11.006

Estimating Households Vulnerability to Idiosyncratic and Covariate Shocks: A Novel Method Applied in Madagascar ¨ NTHER ISABEL GU Harvard University, MA, USA

and KENNETH HARTTGEN * University of Go¨ttingen, Germany Summary. — Households in developing countries are frequently hit by severe idiosyncratic and covariate shocks leading to high consumption volatility. A household’s currently observed poverty status might therefore not be a good indicator of the household’s general vulnerability to poverty. In the recent years, there has been an emerging literature on the concept and empirical analysis of vulnerability. But because of strong data requirements for vulnerability analysis and limited availability of panel and shock data for developing countries, static poverty analysis still dominates empirical vulnerability studies. In this paper, we propose a simple method to empirically assess the impact of idiosyncratic and covariate shocks on households’ vulnerability, which can be applied in a wide context as it relies on more commonly available cross-sectional or short panel data. We empirically illustrate our approach for Madagascar. We show that covariate shocks have a relatively higher impact on rural households, whereas idiosyncratic shocks have a relatively higher impact on urban households’ vulnerability. Ó 2008 Elsevier Ltd. All rights reserved. Key words — vulnerability, idiosyncratic and covariate shocks, multilevel modeling, Madagascar

There has recently been a growing theoretical literature on vulnerability measurement (e.g., Calvo & Dercon, 2005; Gu¨nther & Maier, 2008; Ligon & Schechter, 2003; Pritchett, Suryahadi, & Sumarto, 2000). Empirical studies applying vulnerability measures are, however, still dominated by static poverty analysis. The problem is that vulnerability analysis is—to date—severely constrained by data limitations in the two most important dimensions of vulnerability. First, to appropriately examine the dynamic aspects of poverty, lengthy panel data on income and consumption would be needed. But for many developing countries, lengthy panel data do not exist and cross-sectional surveys (or panels with two or three waves), with either income or consumption data, are the only data available. Second, to assess the underlying causes of vulnerability, comprehensive data on shocks and coping strategies would be necessary. However, most household surveys were not designed to provide a full accounting of the impact of shocks on households’ income or consumption, and information on idiosyncratic and covariate shocks is in most data sets either completely missing or very limited. In the recent years, the rising availability of panel data as well as an increasing interest in the collection of information about households’ shocks has also lead to an increase in the body of empirical literature on vulnerability. But most empirical studies are still constrained either by missing lengthy panel

1. INTRODUCTION Households in developing countries are frequently hit by severe idiosyncratic and covariate shocks resulting in high income volatility. 1 Although households in risky environments have developed various ex-ante and ex-post risk-coping strategies to reduce income fluctuations or to insure consumption against these income fluctuations, the variance of households’ consumption over time remains generally high (see, e.g., Townsend, 1994; Udry, 1995). A household’s currently observed poverty status is, therefore, in many cases not a very good guide for a household’s vulnerability to poverty, that is, its poverty risk. Most established poverty measures (see, e.g., Foster, Greer, & Thorbecke, 1984) only assess the current poverty status of households, ignoring poverty dynamics over time. Results from such a static poverty analysis might be misleading if high consumption volatility persists within countries. Not only might poverty rates fluctuate from one year to another, but even if aggregate poverty rates are constant over time, the share of the population which is vulnerable to poverty, that is, which is poor ‘‘only” from time to time, might be much higher. Moreover, these poverty measures cannot assess whether high poverty rates are a cause of structural poverty (i.e., low endowments) or a cause of poverty risk (i.e., high uninsured income fluctuations), which is important to know from a policy perspective. To overcome the shortcomings of traditional poverty assessments, which can only present a static picture of households’ welfare, vulnerability measures take into account the dynamic dimension of poverty. To do this, vulnerability assessments estimate ex-ante both the expected mean and variance of consumption, with the latter being determined by idiosyncratic and covariate shocks.

* The authors would like to thank Michael Grimm, Stephan Klasen, Walter Zucchini, three anonymous referees as well as the participants of the Verein for Socialpolitik (VfS), the Poverty Reduction, Equality and Growth Network (PEGNet) and the United Nations WIDER conferences for helpful comments and discussions. Final revision accepted: November 3, 2008. 1222

ESTIMATING HOUSEHOLDS VULNERABILITY TO IDIOSYNCRATIC AND COVARIATE SHOCKS

data or by limited information on the full range of idiosyncratic or covariate shocks. Therefore, many studies focus on either measuring households’ vulnerability or the impact of selected shocks on consumption. The objective of this paper is to assess the relative impact of idiosyncratic and covariate shocks on households’ vulnerability to poverty. More precisely, we both estimate how much of households’ vulnerability is structural and risk induced, and estimate the share of risk induced vulnerability that is idiosyncratic and covariate. We propose a method that can be applied to commonly available living standard measurement surveys (LSMS) or short panel data without being hindered by the usual data limitations for vulnerability analysis. This means that the method allows estimating the impact of idiosyncratic and covariate shocks on households’ vulnerability without lengthy panel data and without information on a wide range of shocks. The suggested approach is an integration of multilevel analysis (e.g., Goldstein, 1999) into Chaudhuri’s (2002) method to estimate vulnerability from cross-sectional or short panel data resolving the problem of missing lengthy panel data (see, e.g., Chaudhuri, Jalan, & Suryahadi, 2002; Suryahadi & Sumarto, 2003; Tesliuc & Lindert, 2004, for applications). The remaining paper is structured as follows: Section 2 briefly discusses the empirical literature on vulnerability to poverty. Section 3 proposes a methodology that allows assessing the relative importance of idiosyncratic and covariate shocks for households’ vulnerability. Section 4 presents an empirical application to Madagascar and Section 5 concludes. 2. EMPIRICS OF VULNERABILITY As discussed in the introduction, a household’s currently observed poverty status might not be a reliable guide to a households’ longer-term wellbeing. Policy and research in development economics have, therefore, long emphasized that it is crucial to go beyond a static ex-post assessment of who is currently poor to a dynamic ex-ante assessment of who is vulnerable to poverty. In the recent years, there has been an emerging literature on the concept and the empirical analysis of vulnerability. The theoretical literature on vulnerability is still in a rather early stage of research with numerous definitions and measures and seemingly no consensus on how to conceptualize vulnerability. Several competing measures have been proposed (e.g., Calvo & Dercon, 2005; Glewwe & Hall, 1998; Ligon & Schechter, 2003; Pritchett et al., 2000; for an overview see Hoddinott and Quisumbing (2003)) but the literature has not yet settled on a preferred definition or measure. But independent of the definition of vulnerability, vulnerability measures are always a function of the expected mean and variance of households’ consumption. The mean of the expected consumption is determined by household and community characteristics, whereas the variance in households’ consumption is determined by the severity and frequency of idiosyncratic and covariate shocks as well as the strength of households’ coping mechanisms to insure consumption against these shocks. For a comprehensive understanding of vulnerability to poverty it is hence important to know both the magnitude of consumption volatility (i.e., the level of vulnerability) and the causes of volatility in consumption (i.e., the sources of vulnerability). Currently available data do, however, seldom allow for estimating the level and sources of vulnerability simultaneously. The existing empirical literature on vulnerability

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analysis can, therefore, be divided into two strands of literature: the first concentrating on the measurement of vulnerability within a population and the latter analyzing the impact of selected shocks on households’ consumption. (a) Estimates of vulnerability The first strand of the literature, which intends to estimate the vulnerability of households, has been pioneered by Townsend (1994, 1995) and Udry (1995) who were some of the first using panel data to analyze whether households are able to insure consumption against idiosyncratic income fluctuations. In this spirit, several studies followed, analyzing consumption fluctuations over time (e.g., Christiaensen & Boisvert, 2000; Dercon, 2003; Dercon & Krishnan, 2000; Glewwe & Hall, 1998; Jalan & Ravallion, 1999; Morduch, 2005; Skoufias & Quisumbing, 2004). All these studies have in common that they rely on panel data, which are very limited for developing countries. Moreover, the existing studies and drawn conclusions are often based on very few rounds (often not more than two waves) of rural panel data. The specific dynamics of urban households are in most studies ignored (Morduch, 2005). An exception here is Skoufias and Quisumbing (2004). Moreover, in many developing countries even short panel data for rural households are completely missing, and one has to rely on cross-section surveys to estimate vulnerability. To date, only few studies have tried to estimate vulnerability based on cross-sectional data. The cross-sectional studies that exist are either based on some interpretation of the error term of cross-sectional data (e.g., Chaudhuri et al., 2002) or construct a pseudo panel based on repeated cross-sections (e.g., Christiaensen & Subbarao, 2004). The second strand of the empirical literature on vulnerability, which focuses on the impact of selected shocks on households’ consumption, has also large data-driven limitations. Information on idiosyncratic and covariate shocks is very limited in most household surveys and sometimes even completely missing (see, e.g., Table A.1 in Appendix for limited list of shocks available for Madagascar). As a consequence, most authors have focused on the impact of the selected shocks on consumption (e.g., Alderman, Hoddinott, & Kinsey, 2006; Christiaensen & Subbarao, 2004; Grimm, 2006; Gertler & Gruber, 2002; Gertler, Levine, & Moretti, 2006; Glewwe & Hall, 1998; Kochar, 1995; Ligon & Schechter, 2003; Paxson, 1992; Rosenzweig & Binswanger, 1993; Skoufias & Quisumbing, 2004; Woolard & Klasen, 2005). Concentrating on certain shocks does not allow for an analysis of the relative importance of various shocks on households’ consumption, which would be needed to assess, if certain shocks should be given first priority in ‘‘poverty-prevention” programs. In addition, there are severe econometric problems related to work, which mostly relies on standard regression analysis (ordinary least squares, OLS) to study the impact of shocks on households’ consumption. First, focusing on certain shocks introduces a considerable omitted variable bias as various shocks are often highly correlated (see Table A.2 in Appendix for Madagascar). The impact of selected shocks on households’ consumption is therefore likely to be overestimated. Second, it is often assumed that the impact of shocks on consumption is the same across all households, which is a rather strong assumption to make. We should, for example, expect that the marginal effect of shocks on households’ consumption is lower for households at the upper end of the income distribution where households should possess better insurance mechanisms (Gubert & Robil-

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liard, 2007; Skoufias & Quisumbing, 2004). Third, the problem of reverse causality might be severe as households’ wellbeing often has an impact on the likelihood of certain shocks; for example, poor households normally face higher mortality risks. Most important, several studies that have analyzed the impact of covariate community shocks might be biased because they disregard the hierarchical (or multilevel) data structure underlying these estimates (Goldstein, 1997, 1999). 2 If covariate community shocks are simply assigned to each household within a community, ‘‘blowing up” data values from a small number of communities to many more households, the assumption of independent observations is violated, leading to estimates that are in reality statistically insignificant leading to an overestimation of the impact of covariate shocks on households’ consumption (for a more detailed discussion see Section 3).

faced the discussed econometric problems of concentrating on some selected covariate shocks without taking into account hierarchical data structure. Moreover, they classified ex-ante shocks into covariate and idiosyncratic shocks, which is problematic as several shocks have a covariate and idiosyncratic component. 3 It is difficult to evaluate the exact impact of these estimation problems, but from the discussion above it is likely that most issues rather overestimate the impact of covariate shocks on households’ consumption. Only recently, Heltberg and Lund (forthcoming)—using panel data with an extended list of covariate and idiosyncratic shocks—found that idiosyncratic health shocks have the greatest impact on household’s vulnerability. We think that our suggested approach, which addresses some of the problems discussed above, might contribute to a better understanding of the relative importance of idiosyncratic and covariate shocks on households’ vulnerability.

(b) Idiosyncratic and covariate shocks 3. METHODOLOGY We cannot bridge the data gaps that exist with regard to the missing panel data and missing comprehensive information on shocks in developing countries. What we propose is an estimation method that allows us to study the relative impact of idiosyncratic and covariate shocks on households’ vulnerability without lengthy panel data and without facing the discussed econometric problems that usually occur when estimating the impact of certain selected shocks on households’ consumption. Although we cannot distinguish between the effects of various shocks, a disaggregation of covariate community versus idiosyncratic household-specific shocks is already interesting. Micro-economic theory claims that households can insure consumption against idiosyncratic shocks better than against covariate shocks. Covariate (community) shocks are correlated across households and hence mutual insurance mechanisms within communities can easily break down during covariate ‘‘crisis” (see, e.g., Ray, 1998). On the other hand, mutual insurance across communities, which would mitigate the problem of correlated shocks within communities, is hypothesized to break down because of information asymmetries and enforcement limitations (Ray, 1998). Idiosyncratic shocks are by definition not correlated and therefore can be mutually insured within communities where information asymmetries and enforcement limitations are assumed to be smaller than across communities. We can test this hypothesis with our method. In addition, an assessment of the relative importance of idiosyncratic and covariate shocks might help policy makers to set up insurance priorities. Insurance mechanisms for idiosyncratic on the one hand and covariate shocks on the other hand differ significantly. Whereas higher information asymmetries persist for mutual insurance mechanisms across communities, the contrary is the case for external or formal insurance mechanisms where higher information asymmetries prevail for consumption volatility within communities. Moreover, in contrast to idiosyncratic shocks, covariate shocks are easier to target because are geographically clustered. Several studies (e.g., Carter, 1997; Ligon, & Schechter, 2003; Dercon & Krishnan, 2000; Harrower & Hoddinott, 2004; Christiaensen & Subbarao, 2004) have attempted to estimate the relative importance of covariate and idiosyncratic shocks on households’ consumption. Their estimation results indicate that covariate shocks have a more significant impact on households’ consumption than idiosyncratic shocks. However, these studies have in most cases analyzed rural households, and

(a) Mean and variance of consumption Our proposed method is an extension of the methodology proposed by Chaudhuri (2002), which allows estimating expected mean and variance in consumption using cross-sectional data or short panel data. Such an estimation procedure is very valuable because lengthy panel data are practically non-existing for developing countries. In the following, we only present the estimation procedure for cross-sectional data although the same method can be applied to short panel data. 4 Whenever panel data are at hand these should be preferred to cross-sectional data. We show the application for cross-sectional data as these are by far the most available data for developing countries. The main hypothesis made is that the error term in a consumption regression, or the unexplained variance in the consumption of otherwise equal households, captures the impact of both household-specific and community-specific shocks on households’ consumption. Furthermore, the assumption is made that this variance is correlated, that is, can be explained, with observable household and community characteristics. Suppose that the consumption of household i (i = 1, ... , n) in period t is determined by a set of variables Xi. We can hence write down the following equation: ln ci ¼ b0 þ b1 X i þ ei ;

ð1Þ

where ln ci is per capita household (log) consumption; Xi, a set of household as well as community characteristics; and ei, the unexplained part of households’ consumption, which captures the impact of shocks on households’ consumption. As we further assume that the impact of shocks on households’ consumption is correlated with observable household and community characteristics, we can define the variance of the unexplained part of households’ consumption ei as r2ei ¼ h0 þ h1 X i þ gi :

ð2Þ

Standard ordinary least squares (OLS) regression techniques assume homoscedasticity, that is, the same variance V ðei Þ ¼ r2 across all households. In contrast, we assumed that the variance of the error term is not equal across households but depends on Xi 5 –and reflects the impact of shocks on households’ consumption. Since we assume heteroscedasticity, using OLS for an estimation of b and h would lead to unbiased but inefficient coefficients. To overcome this problem, Eqns.

ESTIMATING HOUSEHOLDS VULNERABILITY TO IDIOSYNCRATIC AND COVARIATE SHOCKS

(1) and (2) have to be estimated with an estimation method that allows for heteroscedastic standard errors. 6 For each household, we can then estimate the expected mean (Eqn. (3)) and variance (Eqn. (4)) of consumption using consistent ^ and ^ and asymptotically efficient estimators b h: ^0 þ b ^1 X i ; ^ ci jX  ¼ b E½ln 2 ^ ¼ ^h0 þ ^ V^ ½ln ci jX  ¼ r h1 X i : ei

ð3Þ ð4Þ

We expand the proposed method by Chaudhuri (2002) with multilevel analysis (Goldstein, 1999). This allows us to differentiate between unexplained variance at the household level (i.e., the impact of idiosyncratic household-specific shocks) and unexplained variance at the community level (i.e., the impact of covariate community-specific shocks). Second, multilevel analysis corrects for inefficient estimators, which might occur whenever the proposed method by Chaudhuri (2002) is applied to hierarchical data structures, that is, whenever household and community variables are used simultaneously.

Multilevel models are designed to analyze the relationship between variables that are measured at different hierarchical levels (for an introduction see, e.g., Bryk & Raudenbush, 1992; Goldstein, 1999; Hox, 2002). We speak of ‘‘hierarchical” or ‘‘multilevel” data structure whenever variables are collected at different hierarchical levels with lower-levels (e.g., households) nested within higher-levels (e.g., communities). Using a multilevel model allows using both individual observations and groups of observations simultaneously in the same model without violating the assumption of independent observations, providing correct standard errors and significance tests (Goldstein, 1999). If this data structure were ignored, for example, if certain community characteristics were simply assigned to each household living within this community, the assumption of independent observations would be ignored, leading to downward biased standard errors and overestimated t-values. As a result, the precision of estimates would be overstated. 7 Moreover, multilevel models do not only account for dependencies between individual observations but also explicitly analyze dependencies at each level and across levels. In a multilevel model, each level is formally represented by its own sub-model, which expresses not only the relationships among variables within the given level but also across different levels. For example, multilevel models assume that community characteristics and covariate shocks do not only have a direct impact on households’ consumption, but might also have an indirect impact through the returns to household-specific characteristics. Last—and most important for our case—multilevel models decompose the unexplained variance of the dependent variable (e.g., consumption) into a lower-level (e.g., household) and a higher-level (e.g., community) component. We use this decomposition for an assessment of the impact of idiosyncratic households-specific versus covariate community-specific shocks on households’ consumption. To formally illustrate the basic idea of multilevel modeling suppose i = 1, . . . , I units (e.g., households) at level one and j = 1, . . . , J units (e.g., communities) at level two and that household i is nested within community j. If ln cij is per capita household (log) consumption and Xij a set of household characteristics of household i in community j we can set up the following regression equation: ln cij ¼ b0j þ b1j X ij þ eij ;

where the error term eij reflects the unexplained variance in households’ consumption. Note that in contrast to standard regression models and Eqn. (1), the variables in Eqn. (5) are denoted by two subscripts: one referring to the household i and another to the community j, and that coefficients are denoted by a subscript referring to the community j. This means that it is assumed that b0j and b1j vary across communities. Various community characteristics Zj can then be introduced to estimate the variance of coefficients across communities b0j ¼ c00 þ c01 Z j þ u0j ;

ð6Þ

b1j ¼ c10 þ c11 Z j þ u1j :

ð7Þ

The error terms u0j and u1j represent level two residuals, that is, the unexplained variance in consumption across communities. Eqns. (6) and (7) hence reflect the impact of community characteristics Zj on households’ consumption, which differs across communities but which is the same for all households within the same community j. Substituting Eqns. (6) and (7) into Eqn. (5) provides the full model, which can be written as ln cij ¼ c00 þ c01 Z j þ ðc10 þ c11 Z j ÞX ij þ u0j þ u1j X ij þ eij

(b) Multilevel analysis

ð5Þ

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ð8Þ

and estimated via maximum likelihood (Bryk & Raudenbush, 1992; Goldstein, 1999; Mason, Wong, & Entwistle, 1983). The first part of Eqn. (8) reflects the deterministic part of the equation, including the interaction term XijZj, which analyzes cross-level interactions between variables at the household and community level. The second part captures the stochastic part of the model. In contrast to standard OLS regressions the error term in (8) contains not only an individual or household component eij but also a group or community component u0j þ u1j X ij . The error term u0j represents the unexplained variance across communities of the intercept b0j . The error term u1j X ij reflects the unexplained variance across communities of the slope b1j . The error term eij captures the remaining unexplained variance in households’ consumption within communities. 8 The stochastic part in Eqn. (8) demonstrates the problem of dependent errors in multilevel analysis. Whereas the household error component eij is independent across all households, the community level errors u0j and u1j are independent between communities but dependent, that is equal, for every household i within community j. This already leads to heteroscedastic error terms. For the case that the household- and community-specific error terms eij, u0j , and u1j are themselves heteroscedastic—an assumption we make and test—multilevel modeling also allows to specify heteroscedasticity at the community and household level. 9 (c) Idiosyncratic and covariate variance To assess the relative impact of idiosyncratic and covariate shocks on households’ vulnerability using cross-sectional data we incorporate multilevel modeling—described in Section 3(b)—into the method proposed by Chaudhuri (2002)—described in Section 3(a). In a first step, using a basic multilevel model, we regress per capita household (log) consumption of household i in community j on a set of household X ij and community covariates Zj, which can be denoted: ln cij ¼ c00 þ c01 Z j þ ðc10 þ c11 Z j ÞX ij þ u0j þ u1j X ij þ eij :

ð9Þ

Only those cross-level interactions Z j X ij were included in Eqn. (9), where the estimated coefficient c11 on the interaction term was significant (see Table 2). Otherwise the interaction term (as well as the corresponding error term) was set to zero. Inter-

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action terms should only be incorporated in multilevel models if they show significant results (Hox, 2002). Eqn. (9) hence estimates three error terms, one at the household level eij and two at the community level u0j and u1j . It is assumed that the error term eij at the household level captures the impact of idiosyncratic shocks. The error terms u0j and u1j X ij at the community level capture the impact of covariate shocks on households’ consumption. Note that the error term u1j X ij at the community level includes an idiosyncratic part X ij . The model specified in Eqn. (9) can therefore also capture indirect effects of covariate shocks, which have an impact on the returns to household characteristics. In the final specification we do, however, not analyze u0j and u1j separately because the focus of this paper is to distinguish between covariate and idiosyncratic variance. An analysis of the channels through which covariate shocks have an impact on households’ consumption is left for further interesting research. Again, following Chaudhuri (2002), we assume that the variance of consumption at the household and at the community level, that is, the impact of idiosyncratic and covariate shocks, depends on a set of household and community characteristics. In the second step, we therefore regress the squared residuals of Eqn. (9) on a set of household X ij and community Zj, characteristics: e2ij ¼ h0 þ h1 X ij þ h2 Z j þ h3 X ij Z j ; ð10Þ u20j ¼ s0 þ s1 Z j ;

ð11Þ

2

ðu0j þ eij Þ ¼ h0 þ h1 X ij þ h2 Z j þ h3 X ij Z j :

ð12Þ

In the final step, we estimate the expected mean as well as the expected idiosyncratic r2eij , covariate r2u0j , and total r2eij þu0j variance of households’ consumption 10 with the estimated coefficients of Eqns. (9)–(12). These estimates can be used to assess the impact of idiosyncratic and covariate shocks on households’ vulnerability, applying any measure of vulnerability. (d) Critical discussion Obviously, in the absence of any time-variant information on consumption, two rather strong assumptions have to be made when using cross-sectional surveys to estimate expected mean and variance in consumption. First, the most critical assumption is that it has to be assumed that present cross-sectional variance can be used to estimate future inter-temporal variance in consumption. This implicitly assumes that the variance in consumption of a particular household is constant over time, i.e., that Varðeijt Þ ¼ r2ij for t = 1, . . . , n. Moreover, although cross-sectional variance might explain inter-temporal variance due to idiosyncratic or covariate community-specific shocks, the model will miss the impact of inter-temporal shocks on the national level. The argument for justifying this assumption is the non-existence of lengthy panel data in developing countries. Only lengthy panel data would allow us to draw precise conclusions about inter-temporal variance in consumption, since it includes information on changes in consumption over some extended time period. Second, the existence of measurement error is a major concern for the estimation of variance in consumption. Large measurement error as well as unobserved but deterministic heterogeneity in households’ characteristics could lead to an overestimation of variance in consumption, especially to an overestimation of the impact of idiosyncratic shocks on households’ consumption.

It has hence to be assumed that the error term in Eqn. (1) mainly captures some ‘‘economic” variance and only to a lesser extent measurement error in consumption. 11 Using only one cross-sectional data, there is little we can do to distinguish real consumption from measurement error (Luttmer, 2000; Woolard & Klasen, 2005) as has been done by other studies on vulnerability (e.g., Ligon & Schechter, 2003; Skoufias & Quisumbing, 2004). Carter (1997) faces a similar problem and makes the—arbitrary—ad hoc assumption that half of the residual variance in consumption is due to measurement error. Following Carter (1997), we hence undertake a robustness check of our results for several assumptions with respect to the share of measurement error in the estimated individual variance in consumption. Our main results persist (for more details see Section 4 and Table A.3 in Appendix). Moreover, Ligon and Schechter (2004) do not recommend estimating vulnerability from one single cross-section because of the strong assumption of low unobservable household-specific effects that have to be made. Hence, whenever we assume high unobserved deterministic heterogeneity, short panel data should be preferred to cross-sectional data—to control for household-specific fixed effects. The proposed extension of Chaudhuri (2002) in Sections 3(b) and (c) can, however, easily be applied to short panel data. The proposed method has the advantage that it overcomes the problem of the missing lengthy panel data in developing countries. In addition, Chaudhuri (2003) demonstrates the robustness of the above described approach using a two-year panel of Indonesia and the Philippines, comparing estimated expected poverty rates from the vulnerability estimates in the first year with the actual incidence of poverty in the second year. 12 Furthermore, conducting Monte Carlo experiments Ligon and Schechter (2004) show that the proposed approach of Chaudhuri (2002) is the ‘‘best” so far proposed estimator of households’ mean and variance in consumption whenever expenditure is measured with low error and whenever only short panel data are at hand. Keeping the critical assumptions in mind, the proposed approach should be understood as an illustrative attempt of assessing the vulnerability of households, when—as it is the case for most developing countries—only cross-sectional or short panel data is at hand. As already discussed, there is no doubt that lengthy panel data are in any case preferable for the estimation of households’ vulnerability. However, the extension of the concept of Chaudhuri (2002) with multilevel modeling might give interesting insights in the relative impact of idiosyncratic and covariate shocks on households’ vulnerability whenever only cross-sectional data (or a short panel) without any information about shocks is available.

4. EMPIRICAL APPLICATION (a) Data description We empirically illustrate our proposed approach for Madagascar. Madagascar is one of the poorest countries in sub-Saharan Africa with a GDP per capita of 923 US$ PPP and— according to the international poverty line of 1 US$ PPP a day—an estimated headcount poverty rate of 61.0% (UNDP, 2007). Its poor economic performance is also reflected in very low indicators of human wellbeing: Life expectancy at birth is 58.4 years, under-five mortality rate is 119 in 1000, and child undernutrition (measured in weight for age for children below the age of 5) amounts up to 42% (UNDP, 2007). In addition, households in Madagascar are frequently hit by covariate

ESTIMATING HOUSEHOLDS VULNERABILITY TO IDIOSYNCRATIC AND COVARIATE SHOCKS

shocks (see Table A.1 for a limited list of shocks), which have an additional severe down-side impact on households’ wellbeing. Mills, Ninno, and Rajemison (2003) further report that households are most often hit by shocks that show a quite strong temporal and spatial correlation (Tables A.1 and A.2). We use Madagascar as a case study because of three reasons: first, frequent occurring (climatic) shocks have been identified as an important phenomenon in Madagascar by other authors (Gubert & Robilliard, 2007; Mills et al., 2003). Second, these shocks might have a severe welfare impact as Madagascar is one of the poorest countries in the world (UNDP, 2007). Third, Madagascar faces the same data limitations as most other developing countries. But in principle any other country with a living standard measurement survey could have been chosen. Data on household characteristics are taken from the national representative household survey of 2001 (Enqueˆte Aupre`s Des Me´nages), covering 5,080 households (1,778 urban and 3,302 rural households) in 186 communities. The community census is the 2001 ILO/Cornell Commune Level census which covers 1,385 of the 1,395 communities in Madagascar. Both surveys do not have any time dimension. The community survey provides information on community characteristics such as social and economic infrastructure as well as data on the occurrence of some limited number of covariate shocks. More precisely, for each community and for the three years preceding the survey (2001, 2000, 1999) it is reported whether the community was exposed to any of 16 covariate shocks (most of these are reported in Tables A.1 and A.2 in Appendix). In many studies, the village has been used as the ‘‘natural” covariate level, but there is no necessity to do so (Genicot & Ray, 2003; Morduch, 2005), and using communities instead, as we do in this analysis, does not seem less useful.

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To estimate households’ expected mean and variance in consumption, we first use the household characteristics in Table 1. In addition, we consider an agricultural asset index (composed of eight productive assets) estimated via principal component analysis (Filmer & Pritchett, 2001). At the community level, we include population density, mean educational level, the percentage of households working in the formal sector and the percentage of households possessing an enterprise within the community. Moreover, we construct an infrastructure index, again based on principal component analysis, using fourteen characteristics reflecting the infrastructure of the community (see Table A.4 in Appendix). Using an aggregate index for agricultural assets and community infrastructure instead of individual variables has three main reasons. First, the two chosen indices provide a proxy of the overall agricultural productivity of households and of the infrastructure within communities. Second, as households’ (communities’) endowment with different agricultural assets (with different infrastructure facilities) is highly correlated, the coefficients of individual agricultural equipments (infrastructure facilities) would often not show any significant effects if they were included separately into the regression. Third, multilevel models require extensive computational power. It is, therefore, recommended to limit parameters if possible (Hox, 2002). 13 (b) Estimation results As described in Section 3, we estimate the expected mean and variance per capita household (log) consumption using multilevel modeling. We also decompose the unexplained consumption variance into an idiosyncratic (household-level) and a covariate (community-level) component. The regression results of the multilevel model for the estimated mean of (log) consumption are presented in Table 2.

Table 1. Summary statistics for households and communities Urban

Rural

National

Household characteristics Age of HH head (years) Number of children Female headed households (%) Household size Residence (%) Years of schooling of HH head Works in agriculture (HH head) (%) Works in informal sector (HH head) (%) Works in formal sector (HH head) (%) Works in public sector (HH head) (%) Enterprise owner (%) Land owner (%) Number of cattle

42.60 1.70 23.30 4.42 35.00 7.80 41.00 22.88 21.47 14.36 30.22 31.51 0.93

41.71 2.16 21.93 4.78 65.00 4.15 83.00 7.04 5.80 4.16 20.24 86.82 4.88

42.25 1.88 22.40 4.56 100.00 6.35 57.66 16.59 15.41 10.31 26.26 53.40 2.50

Community characteristics Bus stop (%) Save water (%) Electricity (%) Hospital (%) Market (%) Bank (%) Fertilizer (%) Community road (%) Provincial road (%) National road (%) Secondary education facility (%) Tertiary education facility (%)

95.25 98.43 98.43 93.01 97.88 82.06 82.06 94.66 87.86 93.67 100.00 97.89

45.54 50.00 42.00 7.14 47.32 6.25 22.32 90.99 54.46 53.75 67.86 10.71

75.40 79.21 76.06 58.53 77.69 51.78 58.20 93.20 74.52 77.65 87.16 63.07

Source: 2001 Enqueˆte Aupre`s Des Me´nages (EPM) and 2001 ILO/Cornell Commune Levels; own calculations. Notes: Children are defined as individuals between the age of 0 and 14.

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WORLD DEVELOPMENT

All coefficients show the expected signs, which are, however, not of interest for this study. The variance in consumption that is explained at each level is shown by R21 and R22 , where R21 = 0.38 refers to the explained variance at the household level within communities and R21 = 0.66 refers to the explained variance at the community level. The R2 s did not improve when additional household and community characteristics were added. We then applied a White-test to verify that the variance of both the error terms eij and uj is indeed heteroscedastic and checked if the two error terms are uncorrelated 14 which allows us a decomposition of the total error term into idiosyncratic and covariate variance. Last, we regressed the squared error terms on several household and community characteristics to estimate the total, idiosyncratic, and covariate variance in consumption for each household in our sample. The estimated average mean and variance in consumption for the whole sample are presented in Table 3, also separately for rural and urban households. The expected per capita (log) consumption of rural households is below the (log) poverty line, whereas the expected per capita (log) consumption of urban households lies above the (log) poverty line.

With regard to the estimated standard deviation in consumption, we show that the estimated standard deviation is slightly higher for rural households than for urban households, with a standard deviation of 0.58 compared to 0.54 (Table 3). Idiosyncratic variance is much higher than covariate variance for urban and only slightly higher for rural households. Hence, the relative importance of idiosyncratic variance is much higher for urban than for rural households. More precisely, whereas among urban households the estimated idiosyncratic standard deviation of consumption is 3.25 times as high as covariate standard deviation, the respective rate is only 1.57 for rural households. As a robustness check, we assume that half of the estimated idiosyncratic variance is measurement error. The idiosyncratic standard deviation is still 2.13 as high as covariate standard deviation for urban households and 1.14 as high for rural households (see Table A.3). Table 3 presents both the expected mean and variance of households’ consumption but aggregated over all households. To obtain a full assessment of the level and sources of vulnerability we have to assess expected mean and variance of households’ consumption jointly but separately for each household. This will be done in the next section.

Table 2. Regression results of per capita consumption (two-level model) Coefficient

Standard error

0.003** 0.000 0.092** 0.084** 0.033** ref. 0.142** 0.138** 0.218** 0.054* 0.006** 0.004** 0.055**

(0.000) (0.000) (0.012) (0.007) (0.004)

0.035 0.151* 0.066** 0.562** 0.254*

(0.026) (0.081) (0.014) (0.229) (0.114)

0.008** 0.001** 0.091** 0.007* 0.146**

(0.003) (0.000) (0.038) (0.003) (0.053)

r2eij (household)

0.250

(0.010)

R20 Obs. level 1 r2uj (community)

0.379 4694 0.094

(0.011)

R21 Obs. level 2

0.657 180

Household level characteristics Age (head) Age 2/100 (head) Number of children Household size Years of schooling (HH head) Works in agriculture (HH head) Works in informal sector (HH head) Works in formal sector (HH head) Works in public sector (HH head) Enterprize owner Land owner Number of cattles Agricultural asset indexa Community level characteristics Infrastructure indexa Population densityb Average schooling % Working in formal sector % Enterprize owner Community  household interaction Infrastructure index  years of schooling Population density  enterprise owner Population density  informal sector Average schooling  land owner % Enterprise owner  agricultural asset index

(0.033) (0.026) (0.049) (0.027) (0.019) (0.001) (0.018)

Source: 2001 Enqueˆte Aupre`s Des Me´nages (EPM) and 2001 ILO/Cornell Commune Levels census; own calculations. Notes: Values are household weighted. Per capita consumption is measured in Madagascar Franc (CFA) per anno. r2e refers to the unexplained variance at the household level and r2u to the unexplained variance at the community level. R20 and R21 are imputed R2s for the two levels, respectively. * P-value < 0.1. ** P-value < 0.01. a The agricultural asset index and the infrastructure index are based on a principle component analysis. The scoring coefficients of the indices are presented in Table A.3. b Population density is a city dummy.

ESTIMATING HOUSEHOLDS VULNERABILITY TO IDIOSYNCRATIC AND COVARIATE SHOCKS

1229

Table 3. Mean and standard deviation of p.c. log consumption Urban

Rural

National

Poverty line Mean (estimated)

13.81 14.38

13.81 13.53

13.81 13.80

Standard deviation (estimated) Total Idiosyncratic Covariate Idiosyncratic/covariate

0.54 0.52 0.16 3.25

0.58 0.47 0.30 1.57

0.57 0.49 0.25 1.96

Source: 2001 Enqueˆte Aupre`s Des Me´nages (EPM) and 2001 ILO/Cornell Commune Levels census; own calculations. Notes: Estimates are household weighted. Per capita consumption is measured in Madagascar Franc (CFA) per anno. National poverty line: 990,404 CFA.

(c) Vulnerability to poverty All proposed vulnerability measures could be applied to analyze households’ vulnerability given the estimated mean and variance in consumption of the previous section. We opt for the measure proposed by Pritchett et al. (2000), defining vulnerability as the probability of a household to fall below the poverty line in the near future. The focus of this paper is the estimation of vulnerability parameters (the mean and variance in consumption), so the applied measure of vulnerability only serves for illustrative purposes. We hence chose a measure that has in contrast to most other vulnerability measures an intuitive interpretation even though it might have some undesirable axiomatic properties (Calvo & Dercon, 2005). Assuming that consumption is log-normally distributed, we can estimate the probability of a household i in community j to fall below the poverty line using the estimated expected mean and variance of consumption of the last section: 0 1 Bln z  ln ^cij C ^tij ¼ P^ ðln cij < ln zjX ; ZÞ ¼ /@ qffiffiffiffiffi A; ^2ij r

ð13Þ

where /ðÞ denotes the cumulative density of the standard normal distribution function; z, the poverty line; ln ^cij the ex^2ij the pected mean of per capita (log) consumption and r estimated variance of per capita (log) consumption. tij is the estimated vulnerability or probability to fall below the poverty line. The estimation is conducted separately for the estimated ^2eij and covariate variance r ^2uj in conidiosyncratic variance r ^2eij þuj for the overall variance in sumption as well as jointly r consumption. Last, we have to define a vulnerability threshold t above which we consider households as vulnerable to poverty as well as a time horizon which we consider as the ‘‘near” future. In the empirical literature, a common vulnerability threshold is 50% and a time horizon of t + 2 years (see, e.g., Chaudhuri et al., 2002; Tesliuc & Lindert, 2004). This means households are considered as vulnerable if they have a 50% or higher probability to fall below the poverty line (at least once) in the next two years, that is, tij;tþ2 P 0:5. This is equivalent to a 29% or higher probability P to fall below the poverty line in any given year. 15 However, taking into account the critical assumptions that have to be made to draw conclusions about future variance in consumption with only cross-sectional data at hand, we constrain our analysis to a time horizon of t + 1, but keep the probability P and vulnerability threshold tij;tþ1 equal to 29%. 16 Utilizing the stated vulnerability threshold and time horizon we estimate that 66.32% of households in Madagascar are vulnerable to poverty, that is, 66.32% of households have a 29% or higher probability to fall below the poverty line in the next year (Table 4). The figures for urban and rural households are 23.91% and

85.69%, respectively, indicating that rural households are much more vulnerable to poverty than urban households. Besides the vulnerability rate, we also calculate the mean vulnerability, that is, the average probability to fall below the poverty line. 17 The estimated average probability to fall below the poverty line should approximately be equal to the observed poverty rate and can therefore serve to test whether the vulnerability estimates are feasible (Chaudhuri et al., 2002). Poverty rates and average probabilities to fall below the poverty line are almost identical (Table 4). (d) Sources of vulnerability Last, we decompose vulnerability estimates into the sources of vulnerability. We first analyze whether vulnerability is mainly driven by permanent low consumption prospects (i.e., structural or poverty induced vulnerability) or by high consumption volatility (i.e., transitory or risk induced vulnerability). 18 In other words, if the (estimated) expected mean consumption ln ^cij of a household already lies below the poverty line ln z, then the household is referred to as structural or poverty induced vulnerable (Figure 1). If the (estimated) expected consumption ln ^cij lies above the poverty line ln z, but a high estimated variance in consumption r ^2ij leads to an estimated vulnerability that is greater than the set vulnerability threshold of 0.29, then the household is said to face risk induced vulnerability (Figure 1). In Table 4, we see that rural vulnerability is mainly a cause of low expected mean in consumption whereas urban vulnerability is mainly driven by high consumption volatility. More precisely, 67.56% of rural households have an expected per capita consumption that already lies below the poverty line, and ‘‘only” 18.13% of rural households are vulnerable because of high consumption volatility. In contrast, only 7.32% of urban households face structural induced vulnerability, whereas 16.58% face risk induced vulnerability (because of high consumption fluctuations). Structural induced poverty is hence 3.78 times higher than risk induced poverty across rural households. In contrast, urban households face more often risk induced than structural induced poverty (the ratio of structural to risk induced poverty is smaller one). We further analyze the impact of idiosyncratic and covariate shocks on vulnerability to poverty. Table 4 indicates that idiosyncratic shocks have almost the same influence as covariate shocks on rural households’ vulnerability but a much higher impact than covariate shocks on urban households. 83.17% of rural and 22.89% of urban households are vulnerable to idiosyncratic shocks. In contrast 78.33% of rural and only 11.62% of urban households are vulnerable to covariate shocks. The ratio of idiosyncratic to covariate vulnerability is thus 1.06 in rural areas but 1.92 among urban households. 19

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WORLD DEVELOPMENT Table 4. Vulnerability decomposition Urban

Rural

National

Poverty rate Mean vulnerability Vulnerability rate

0.21 0.20 0.24

0.64 0.64 0.86

0.49 0.50 0.66

Poverty induced vulnerability Risk induced vulnerability Poverty induced/risk induced

0.07 0.17 0.41

0.68 0.18 3.78

0.47 0.20 2.35

Idiosyncratic vulnerability Covariate vulnerability Idiosyncratic/covariate

0.23 0.12 1.92

0.83 0.78 1.06

0.64 0.57 1.12

Source: 2001 Enqueˆte Aupre`s Des Me´nages (EPM) and 2001 ILO/Cornell Commune Levels census; own calculations. Notes: Estimates are household weighted. Per capita consumption is measured in Madagascar Franc (CFA) per anno. National poverty line: 990,404 CFA.

We also checked the robustness of our results to the chosen vulnerability threshold (keeping the poverty line of ln 990,404 Madagascar Franc constant) and to the chosen poverty line (keeping the vulnerability threshold of 0.29 constant). 20 As expected, the overall vulnerability rate increases with lower vulnerability thresholds and higher poverty lines and decreases with higher vulnerability thresholds and lower poverty lines. Irrespective of the probability threshold and poverty line, vulnerability to poverty is always higher in rural than in urban areas and covariate shocks are comparatively always more important for rural households than for urban households.

5. CONCLUSION

Figure 1. Poverty and risk induced vulnerability. Source: illustration by the authors.

Note that in Section 3 we stated that in Chaudhuri’s approach measurement error might lead to an overall overestimation of the impact of idiosyncratic shocks. As in the previous section, we undertake a robustness check and assume ad hoc that a substantial share of individual variance is due to measurement error. But even if we assume that 50–75% of the estimated individual variance is due to measurement error, our major result holds (see Table A.3). Idiosyncratic vulnerability is relatively more important in urban areas and covariate shocks have a relatively higher impact on rural households’ consumption. Further, idiosyncratic vulnerability seems to be much more prevalent especially among urban households than indicated by some previous studies.

We propose a method, which is able to analyze the level and sources of vulnerability using currently available standard cross-sectional or short panel household surveys without any information on idiosyncratic and/or covariate shocks. For an empirical illustration, we apply the proposed method to cross-sectional data from Madagascar. Defining vulnerability as the probability of a household to fall below the poverty line, we stated that both covariate and idiosyncratic shocks have a considerable impact on both urban and rural households’ vulnerability. Furthermore, our results indicate that idiosyncratic shocks have a relatively higher impact on urban households’ and covariate shocks a relatively higher impact on rural households’ vulnerability. It is difficult to assess whether a higher impact of certain types of shocks on rural or urban households’ consumption is the result of a more severe impact of these shocks on households’ income or the result of worse insurance mechanisms of households against these shocks. In other words, with the proposed method we can only assess the net (and not gross) impact of shocks on households’ consumption. With these cautionary remarks in mind, we still provide some possible explanations for our results. The suggested higher impact of idiosyncratic shocks on consumption volatility of urban households and almost equal importance of idiosyncratic shocks (in comparison with covariate shocks) for rural households might first imply that insurance mechanisms within communities do not function any better than insurance mechanisms across communities. This would, however, be contradictory to micro-economic theory. Or, and this fact has rarely been tested in the literature yet, idiosyncratic shocks have a much higher impact on households’ income than covariate shocks and even if mutual (but imperfect) insurance mechanisms are in place, might still lead to higher consumption fluctuations than covariate shocks.

ESTIMATING HOUSEHOLDS VULNERABILITY TO IDIOSYNCRATIC AND COVARIATE SHOCKS

Another alternative explanation could be that at least some covariate shocks are more anticipated than idiosyncratic shocks—because of a high frequency and a high correlation across years (see also Table A.1 in Appendix)—so that ex-ante coping strategies take place. Both theories might be worthwhile to be tested empirically in further research. In the past, several studies have found covariate shocks to be more important than idiosyncratic shocks. The reason might be that the majority of these studies only analyzed rural households and faced the discussed econometric problems of concentrating on some selected shocks without taking into account hierarchical data, (see Sections 2 and 3(b)). Moreover, assessing the relative impact of idiosyncratic and covariate shocks based on a classification of shocks into covariate and idiosyncratic shocks is problematic as several shocks have an idiosyncratic and a covariate component. We do not make such an a priori distinction in our approach. A drawback of our approach is that high measurement error could lead to a general overestimation of the impact of idiosyncratic shocks. We provide a robustness check that shows that even in the presence of very high measurement error, our main results still hold. The relatively higher impact of covariate shocks on rural households’ consumption relative to urban households might be explained by the fact that there are several covariate shocks—such as climatic shocks—which might have a higher impact on rural (agricultural) areas than on urban (non-agricultural) areas. It is further possible that urban households face high information and enforcement limitations even within communities. Informal insurance mechanisms against idiosyn-

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cratic shocks might, therefore, work better among rural than among urban households. Our results also indicate that consumption fluctuations are higher for rural households but that the relative importance of consumption fluctuations (vs. low mean consumption) is higher for urban households’ vulnerability. Urban households should hence more often be included into vulnerability studies that have so far focused on rural villages and households— somewhat ignoring the increasing urban population in developing countries. We are aware of the fact that some rather stringent assumptions have to be made to estimate future variations in consumption based on data of only one single year (or short panel data). Therefore, the proposed approach should not be seen as an alternative to estimate vulnerability with lengthy panel data. But as long as lengthy panel data with comprehensive information on idiosyncratic and covariate shocks are missing, the suggested approach can provide quite interesting insights into the relative impact of idiosyncratic and covariate shocks on households’ vulnerability. We further recommend that—independent of the data available—any study analyzing the influence of covariate shocks on households’ consumption should apply multilevel modeling as it appropriately takes into account the hierarchical structure of the data that are used for such analysis. Last, given the discussed data limitations current living standard measurement surveys have to be improved to include a (better) time dimension as well as comprehensive data on shocks and coping mechanisms.

NOTES 1. Here, and in the following, idiosyncratic shocks refer to householdspecific shocks (e.g., injury, birth, death, or job loss of a household member) that are only weakly correlated across households within a community. Covariate shocks refer to shocks that are correlated across households within communities but only weakly correlated across communities (e.g., natural disasters or epidemics).

in clustered survey samples (Deaton, 1997) and in principle these correction procedures could also be applied to hierarchical data structure. But in contrast to multilevel models, the proposed procedures for cluster sampling assume intra-class correlations between observations within clusters that are equal for all variables. This is usually not the case for variables of different hierarchical levels (Hox, 2002).

2. We speak of hierarchical data structure or multilevel data whenever variables are collected at different hierarchical levels with lower hierarchical levels nested within higher hierarchical levels. For a detailed discussion of multilevel data structure see Section 3(b).

8. The residuals eij, u0j , and u1j are assumed to have a mean of zero. The residuals uj are assumed to be independent of eij. The covariance between u0j and u1j is assumed to be different from zero.

3. For example, it is difficult to say whether the death of a household member is an idiosyncratic or a covariate shock, as the death might have occurred because of age—in this case the death was an idiosyncratic shock—or because of an epidemic—in this case the death constituted a covariate shock. 4. For a discussion of implementing the proposed method using panel data with a two wave panel see Chaudhuri (2002) or Ligon and Schechter (2004). 5. It is still assumed that the conditional distribution of ei has a mean of zero. 6. One often used method is weighted least squares (for a detailed discussion, see Maddala, 1977). Chaudhuri (2002) applies three-step feasible generalized least squares. 7. A related problem of dependent individual observations, leading to biased standard errors, also occurs in surveys with cluster sampling. Several methods have been proposed to estimate unbiased standard errors

9. For the estimation of the multilevel model, the GLAMM package for STATA is used. To provide consistent and asymptotically efficient estimators, the Huber/White sandwich estimator is used (Maas & Hox, 2004). ^2uj do not necessarily have to be 10. In this model, estimates of r ^2eij and r positive. We did not face this problem. An alternative way to estimate the variance of consumption, which guarantees positive values, is to use the log of variance in consumption. 11. This assumption is, however, also made in other strands of literature (e.g., the error term in wage equations capturing unmeasured skill diversity, see Lemieux (2006)). 12. In the first round, given the estimated expected mean and variance in consumption of households, households were grouped into 10 deciles based on their estimated probability to fall below the poverty line. The predicted poverty rates within each group—which must be equal to the estimated mean probability to fall below the poverty line—matched almost exactly the actual poverty rates in the second cross-sectional round.

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WORLD DEVELOPMENT

13. The estimated expected mean and variance in consumption do, however, not change significantly if we include the assets and infrastructure facilities separately into the regression. 14. The correlation between eij and uj is 0.063. 15. Formally, this can be derived from tij;tþk ¼ 1  ½P ðln cij > ln zÞk , where tij;tþk is the vulnerability threshold in t to fall below the poverty line (at least once) in the next k years. P ðln cij > ln zÞ is the probability to have consumption above the poverty line in any given year. 16. If we take a time horizon of t + 1 the probability to fall below the poverty line in any given year is equal to the vulnerability threshold.

17. Note that the estimated mean vulnerability is in contrast to the vulnerability rate independent of any vulnerability threshold and/or time horizon. 18. We implicitly assume that low expected mean consumption only reflects structural poverty and is not risk induced, although this does not necessarily have to be the case. Low consumption prospects can also be risk-induced through behavioral responses of households, for example, engaging in low risk but also low return activities (Elbers, Gunning, & Kinsey, 2003; Morduch, 1994). 19. In Table A.5 in Appendix we provide the same decomposition of vulnerability for various other household groups. 20. Tables are not presented here. Estimates can be obtained from the authors.

REFERENCES Alderman, H., Hoddinott, J., & Kinsey, B. (2006). Long term consequences of early childhood malnutrition. Oxford Economic Papers, 58(3), 450–474. Bryk, A. S., & Raudenbush, S. W. (1992). Hierarchical linear models: Applications and data analysis. Newbury Park: Sage Publications. Carter, M. R. (1997). Environment, technology, and the social articulation of risk in West African agriculture. Economic Development and Cultural Change, 45(3), 557–590. Calvo, C., & Dercon, S. (2005). Measuring individual vulnerability. Discussion paper no. 229. Oxford: University of Oxford. Chaudhuri, S. (2002). Empirical methods for assessing household vulnerability to poverty. New York: Mimeo, Department of Economics, Columbia University. Chaudhuri, S. (2003). Assessing vulnerability to poverty: Concepts, empirical methods and illustrative examples. New York: Mimeo, Department of Economics, Columbia University. Chaudhuri, S., Jalan, J., & Suryahadi, A. (2002). Assessing household vulnerability to poverty from cross-sectional data: A methodology and estimates from Indonesia. Discussion paper no. 0102-52. New York: Columbia University. Christiaensen, L. J., & Boisvert, R. N. (2000). On measuring household food vulnerability: Case evidence from Northern Mali. Mimeo, World Bank. Christiaensen, L. J., & Subbarao, K. (2004). Toward an understanding of household vulnerability in rural Kenya. World Bank policy research paper no. 3326. World Bank. Deaton, A. (1997). The analysis of household surveys. Baltimore: John Hopkins University Press. Dercon, S. (2003). Growth and shocks: Evidence from rural Ethiopia, CSAE. Working paper no. WPS/2003-12. Oxford: Department of Economics and Jesus College. Dercon, S., & Krishnan, P. (2000). Vulnerability, seasonality and poverty in Ethiopia. Journal of Development Studies, 36(6), 25–53. Elbers, C., Gunning, J. W., & Kinsey, B. (2003). Growth and risk: Methodology and micro evidence. Tinbergen Institute discussion paper TI 2003-068/2. Filmer, D., & Pritchett, L. H. (2001). Estimating wealth effects without expenditure data – or tears: An application to educational enrollments in states of India. Demography, 38(1), 115–132. Foster, J., Greer, J., & Thorbecke, E. (1984). A class of decomposable poverty measures. Econometrica, 52, 761–765. Genicot, G., & Ray, D. (2003). Endogenous group formation in risk-sharing arrangements. Review of Economic Studies, 70(1), 87–113. Gertler, P., Levine, D., & Moretti, E. (2006). Do microfinance programs help families insure consumption against illness? Working paper series 1045. UC Berkeley: Center for International and Development Economics Research. Gertler, P., & Gruber, J. (2002). Insuring consumption against illness. American Economic Review, 92(1), 55–70. Glewwe, P., & Hall, G. (1998). Are some groups more vulnerable to macroeconomic shocks than others. Hypothesis tests based on panel data from Peru. Journal of Development Economics, 56(1), 181–206. Goldstein, H. (1999). Multilevel statistical models. London: Arnold.

Goldstein, H. (1997). Multilevel models in educational and social research. London: Griffin. Gubert, F., & Robilliard, A. S. (2007). Risk and schooling decisions in rural Madagascar: A panel data-analysis. Journal of African Economies, July 14. Gu¨nther, I., & Maier, J. (2008). Individual vulnerability and loss aversion. Zuerich: Swiss Federal Institute of Technology (ETH). Grimm, M. (2006). Mortality and survivors’ consumption. DIW discussion paper no. 611. Berlin: German Institute for Economic Research. Harrower, S., & Hoddinott, J. (2004). Consumption smoothing and vulnerability in the zone Lacustre, Mali. FCND discussion paper no. 175. Washington: IFPRI. Heltberg, R., & Lund, N. (forthcoming). Shocks, coping, and outcomes for Pakistan’s poor: Health risks predominate. Journal of Development Studies. Hoddinott, J., & Quisumbing, A. (2003). Methods for Microeconometric risk and vulnerability assessments. Social protection discussion paper, no. 0324. Washington: World Bank. Hox, J. (2002). Multilevel analysis – Techniques and Applications. Mahwah: Lawrence Erlbaum Associates. Jalan, J., & Ravallion, M. (1999). Are the poor less well insured? Evidence on vulnerability to income risk in rural China. Journal of Development Economics, 58(1), 61–81. Kochar, A. (1995). Explaining household vulnerability to idiosyncratic income shocks. The American Economic Review, 85(2), 159–164. Lemieux, T. (2006). Increasing residual wage inequality. Composition effects, noisy data, or rising demand for skill?. American Economic Review, 96(3), 461–498. Ligon, E., & Schechter, L. (2003). Measuring vulnerability. Economic Journal, 113(486), C95–C102. Ligon, E., & Schechter, L. (2004). Evaluating different approaches to estimating vulnerability. Social protection discussion paper series no. 0410. Washington: World Bank. Luttmer, E. F. P. (2000). Inequality and poverty dynamics in transition economies: Disentangling real events from noisy data. Washington, DC: Mimeo, World Bank. Maas, C. J. M., & Hox, J. (2004). Robustness issues in multilevel regression analysis. Statistica Neerlandica, 58(2), 127–137. Maddala, G. S. (1977). Econometrics. Tokyo: McGraw-Hill. Mason, W. M., Wong, G. M., & Entwistle, B. (1983). Contextual analysis through the multilevel linear model. In S. Leinhardt (Ed.), Sociological methodology. San Francisco: Jossey-Bass. Mills, B., Ninno, C., & Rajemison, H. (2003). Commune shocks, household assets and economic well-being in Madagascar. Washington: Mimeo, World Bank. Morduch, J. (1994). Poverty and vulnerability. The American Economic Review, 84(2), 221–225. Morduch, J. (2005). Consumption smoothing across space: Testing theories of risk sharing in the ICRISAT study region of South India. In S. Dercon (Ed.), Insurance against poverty. Oxford: Oxford University Press. Paxson, C. H. (1992). Using weather variability to estimate the response of savings to transitory income in Thailand. The American Economic Review, 82(1), 15–33.

ESTIMATING HOUSEHOLDS VULNERABILITY TO IDIOSYNCRATIC AND COVARIATE SHOCKS Pritchett, L., Suryahadi, A., & Sumarto, S. (2000). Quantifying vulnerability to poverty: A proposed measure, with application to Indonesia. SMERU working paper, Social Monitoring and Early Response Unit (SMERU). Washington: World Bank. Ray, D. (1998). Development economics. Princeton: Princeton University Press. Rosenzweig, M. R., & Binswanger, H. P. (1993). Wealth, weather risk and the composition and profitability of agricultural investments. Economic Journal, 103(416), 56–78. Skoufias, E., & Quisumbing, A. R. (2004). Consumption insurance and vulnerability to poverty: A synthesis of the evidence from Bangladesh, Ethiopia, Mali, Mexico and Russia. European Journal of Development Research, 17(1), 24–58. Suryahadi, A., & Sumarto, S. (2003). Poverty and vulnerability in Indonesia before and after the economic crisis. Asian Economic Journal, 17(1), 45–64.

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Tesliuc, E., & Lindert, K., 2004. Risk and vulnerability in Guatemala: A quantitative and qualitative assessment. Social protection discussion paper 0404. Washington: World Bank. Townsend, R. M. (1994). Risk and insurance in village India. Econometrica, 62(3), 539–591. Townsend, R. M. (1995). Consumption insurance: An evaluation of risk bearing systems in low-income economics. Journal of Economic Perspectives, 9(3), 83–102. Udry, C. (1995). Risk and saving in Northern Nigeria. The American Economic Review, 85(5), 1287–1300. UNDP (2007). Human development report 2007. New York: Palgrave Macmillan. Woolard, I., & Klasen, S. (2005). Income mobility and household poverty dynamics in South Africa. Journal of Development Studies, 41, 865– 897.

APPENDIX A See Tables A.1–A.5. Table A.1. Households with exposure to shocks Households in communities with exposure (in%)

Correlation of shocks across years (1999–2000)a

73.93 54.19 32.53 33.64 22.72 39.46 75.91 24.69 21.00 17.97 7.37

0.88 0.81 0.81 0.44 0.84 0.63 0.85 0.52 0.70 0.57 0.25

Malaria Tuberculosis Typhoid Cholera Rice pest Swineflu Newcastle Flooding Impassible bridge or road Drought Cyclones

Source: 2001 Enqueˆte Aupre`s Des Me´nages (EPM) and 2001 ILO/Cornell Commune Levels census; own calculations. Note: Shock exposure is equal to shock occurrence. a Mills et al. (2003). Table A.2. Correlation of shocks

Malaria Tubera Typhoid Cholera Swineflu Newcastle Flooding Roada Drought Cyclones

a

Malaria

Tuber

Typhoid

Cholera

Newcastle

Flood

Roada

Drought

Cyclones

1 0.60 0.40 0.39 0.35 0.63 0.15 0.29 0.26 0.07

1 0.44 0.36 0.25 0.49 0.15 0.18 0.24 0.14

1 0.34 0.07 0.29 0.24 0.26 0.28 0.15

1 0.21 0.34 0.17 0.15 0.06 0.11

1 0.20 0.19 0.18 0.03

1 0.36 0.09 0.43

1 0.02 0.34

1 0.09

1

Source: ILO/Cornell Commune Level census 2001. a Tuber: tuberculosis and road: impassible road or bridge. Table A.3. Robustness check of vulnerability measures Urban

Rural

National

No

25%

50%

75%

No

25%

50%

75%

No

25%

50%

75%

Total standard deviation (est.) Idiosyncratic Covariate Idiosyncratic/covariate

0.54 0.52 0.16 3.25

0.48 0.45 0.16 2.81

0.40 0.37 0.16 2.31

0.31 0.26 0.16 1.63

0.58 0.47 0.30 1.57

0.51 0.41 0.30 1.36

0.45 0.33 0.30 1.14

0.38 0.24 0.30 0.80

0.57 0.49 0.25 1.96

0.50 0.42 0.25 1.68

0.43 0.35 0.25 1.40

0.35 0.25 0.25 1.00

Total vulnerability Idiosyncratic vulnerability Covariate vulnerability Idiosyncratic/covariate

0.24 0.23 0.12 1.92

0.22 0.20 0.12 1.67

0.18 0.17 0.12 1.42

0.15 0.14 0.12 1.17

0.86 0.83 0.78 1.06

0.84 0.82 0.78 1.05

0.80 0.80 0.78 1.03

0.78 0.78 0.78 1.00

0.64 0.64 0.57 1.12

0.62 0.62 0.57 1.09

0.60 0.60 0.57 1.05

0.58 0.58 0.57 1.02

Source: 2001 Enqueˆte Aupre`s Des Me´nages (EPM) and 2001 ILO/Cornell Commune Levels census; own calculations. Notes: no = no measurement error is assumed; 25% = 25 % of the estimated variance is measurement error; 50% = 50 % of the estimated variance is measurement error; and 75% = 75 % of the estimated variance is measurement error. Estimates are household weighted. Per capita consumption is measured in Madagascar Franc (CFA) per anno. National poverty line: 990,404 CFA.

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WORLD DEVELOPMENT Table A.4. Scoring coefficients for the agricultural and infrastructure index

Agricultural index

Infrastrcture index

Shed Tractor Plow Cart Harrow Other equip. for animals Other equip. for tractor Manual agricultural equip.

0.177 0.052 0.344 0.302 0.337 0.120 0.073 0.197

Mean Standard deviation

0.000 1.000

Bus stop Community road Provincal road National road Secondary school Tertiary school Hospital Clean water Electricity Veterany Agricultural services Fertilizer Market Bank

0.121 0.032 0.081 0.106 0.119 0.152 0.148 0.117 0.121 0.149 0.123 0.131 0.117 0.118 0.000 1.000

Source: 2001 Enqueˆte Aupre`s Des Me´nages (EPM) and 2001 ILO/Cornell Commune Levels census; own calculations. Notes: Estimated with principle component analysis.

Table A.5. Vulnerability decomposition

Poverty rate Mean vulnerability Vulnerability rate Poverty induced vulnerability Risk induced vulnerability Poverty induced/risk induced Idiosyncratic vulnerability Covariate vulnerability Idiosyncratic/covariate

Poverty rate Mean vulnerability Vulnerability rate Poverty induced vulnerability Risk induced vulnerability Poverty induced/risk induced Idiosyncratic vulnerability Covariate vulnerability Idiosyncratic/covariate

Poverty rate Mean vulnerability Vulnerability rate Poverty induced vulnerability Risk induced vulnerability Poverty induced/risk induced Idiosyncratic vulnerability Covariate vulnerability Idiosyncratic/covariate

Small households (63)

Large households (>3)

0.33 0.37 0.53 0.32 0.21 1.52 0.51 0.45 1.13

0.58 0.57 0.73 0.54 0.19 2.84 0.72 0.64 1.13

Lower education (64 years)

Higher education (>4 years)

0.72 0.73 0.94 0.79 0.15 5.27 0.93 0.87 1.07

0.35 0.36 0.49 0.27 0.22. 1.22 0.46 0.38 1.21

First quarter of infra index

Fourth quarter of infra index

0.76 0.75 0.97 0.87 0.10 8.70 0.96 0.94 1.02

0.26 0.26 0.34 0.15 0.19 0.79 0.32 0.20 1.60

Source: 2001 Enqueˆte Aupre`s Des Me´nages (EPM) and 2001 ILO/Cornell Commune Levels census; own calculations. Notes: Estimates are household weighted. Per capita consumption is measured in Madagascar Franc (CFA) per year. National poverty line: 990,404 CFA.

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