Daymamics of Multidimensional Food Security Measurement in Rural Ethiopia

Most studies measuring food security have used one or two of the dimensions of food security, with snapshot data at a particular point in time. Policies derived from such measurement might be misleading because of the dynamic nature of food security or insecurity in vulnerable populations. This paper presents a composite food security measure that captures the four dimensions of food security i.e., availability, accessibility, utilization, and stability over time. Principal Component Analysis (PCA) is used to reduce the four dimensions into a single index. Data from three rounds of household-level panel data, collected by the Central Statistical Agency (CSA) of Ethiopia in collaboration with the World Bank are used to demonstrate this measurement. The aggregate food security indices result revealed that 44, 57, and 45 percent of households were food secured in 2011, 2013, and 2015 respectively. On the other hand, only 20 percent of households were food secured all the time while 67 percent of households termed as transitory food insecure since they remained food insecure at least in one of the survey periods. The rest 13 percent of households were also termed chronically food insecure since they fall short of food all the time of the study. The finding confirmed a high prevalence of multidimensionally food-insecure households in rural Ethiopia. Therefore, various food security intervention programs that enhance the four dimensions should be introduced.


Introduction
Food insecurity is at the top of the agenda of politics around the globe, as about 825 million people most of who live in Africa and Asia are threatened by hunger (Diouf & Sheeran, 2010;FAO, 2017). Food insecurity is a difficult problem both in the urban and rural parts of Ethiopia although the extent and severity of the problem vary from the moisture scarce northeast highland plateaus to some pastoral areas of the country. CSA and WFP (2014) report that 29 percent of the rural and 21 percent of urban populations were food insecure. FAO and IFAD (2016) have also reported that the percentage of undernourished people in the country declined from 74 percent in 1990 to 32 percent in 2015. To address this situation in chronically foodinsecure areas, the government has designed comprehensive interventions including, soil and water management, plant nutrient generation and recycling, drought and pest-resistant crop varieties, improved post-harvest management, and diversification of livelihood in farming areas located in the moisture deficit parts of the country (FAO, 2012).
Food security is a complex concept that is influenced by multiple economic, social, political, and environmental factors. This vast-complexity makes food security an extensive and flexible concept with numerous intimately linked definitions as reflected in many research and policy papers. S. Maxwell and Smith (1992) identified about 200 definitions and 450 indicators of food security in various published writings from 1943-1992. The literature on food security measurements is heterogeneous, in terms of the unit of analysis, methodology, and dimensions involved. These make capturing all the dimensions of food security using one indicator very challenging; therefore, combining more than one indicator has been strongly recommended by several scholars (Headey & Ecker, 2012;D. Maxwell & Coates, 2012;Nathalie, 2012). Consistent with this suggestion, composite indicators (the use of two or more indicators) have been developed to improve the measurement of food security.
Composite measures enable a group of indicators that capture various dimensions of food security to be combined into a solo measure or index. Hitherto, some researchers developed composite food security measurements: Napoli, De Muro, and Mazziotta (2011), introduced the composite food insecurity multidimensional index; Rose and Charlton (2002), developed a composite measure of food security for South Africa; others are the IFPRI Global Hunger Index (von Grebmer et al., 2013) and the nutrition index (Wiesmann, Von Braun, & Feldbrügge, 2000). These measurements emphasize national-level indicators such as income, poverty, undernourishment, food production, and macro-level data.
However, to date, most food security measurement studies use partial measures (i.e., take into account one or two dimensions). So, this paper aims to fill the gaps unexplored by previous research works (Abafita & Kim, 2013;Demeke, Keil, & Zeller, 2011) by developing a multidimensional measure of food (in)security in Ethiopia.

Principal Component Analysis
Principal Component Analysis (PCA) is used to generate a composite index using selected indicator variables under each dimension of food security. PCA can transform selected multiple indicators into fewer components that capture most of the information in the original indicators. Vyas and Kumaranayake (2006) have outlined steps to construct composite socioeconomic indices using PCA; Qureshi (2007) and Demeke et al. (2011) have also applied it to generate a composite food security index.
Index construction can be highly subjective, particularly in the determination of weights assigned to each element of the index. PCA can extract a linear combination of indicator variables that gives maximum variance and converts them into fewer or a single index (Zeller, Sharma, Henry, & Lapenu, 2006). The derived index denotes a summary of the best linear relationship among the original variables (Conte, 2005). Suppose that there is a set of n correlated indicator variables for each food security dimension (x1, x2, x3, . . ., xn); PCA allows for the generation of different uncorrelated components whereby each component is a linear weighted sum of the original variables. Mathematically, PCA is specified as follows: 11 = 11 1 + 12 2 + … … … … … + 1 .
(1) = 1 1 + 2 2 + … … … … … + Where represents the weight for variable in the i th (i= 1, 2, …, n and j = 1, 2, …, m) principal component. Estimated principal components are sorted in descending order thus the first principal component explains the largest amount of variance in a data set conditional on the constraint that the sum of the squared weights is equal to one ( 1 2 + 2 2 + 3 2 + … … + 2 = 1). Each subsequent component explains an extra but less proportion of the variation of indicator variables. Fewer components are required to capture the common information if a higher degree of correlation exists between the original variables (Vyas & Kumaranayake, 2006).
After identifying the components, the households' food security score/index can be derived as follows: Where represents household i's food security index that is assumed to follow a normal distribution with a mean of 0 and a standard deviation of 1; is the weight of variable j in the PCA model, ij X is a value of the j th variable for the i th household, j  and j  are mean and standard deviation respectively of the j th variable for all farm households. Since the analysis uses panel data, it is important to derive an index that can be used to make comparisons over time. Following Cavatassi, Davis, and Lipper (2004), the study pooled the three waves of survey data and conducted PCA over the combined three-period data set. Then, the derived weights were applied to the value of indicator variables for each survey round using equation (2) that computes an index that is comparable over time. Thus, the food security index of farm households in each period is the sum of the weighted z-scores of each period multiplied by the actual value of variables.
Two main aggregation methods exist in the literature for generating a combined index and each method has its advantages and disadvantages. Additive aggregation is the simplest method; it entails the calculation of the ranking of households by each indicator and summation of the resulting ranking (Fagerberg, 2001). However, this method is undesirable due to the full compensable nature of aggregation such that the low performance of some indicators can be compensated for by the high performance of other indicators. On the other hand, geometric aggregation addresses the problem of full compensable even though the computation is a little harder than the simple aggregation. For this paper, the score of each dimension was aggregated using the geometric mean to create overall food security indices. Anand and Sen (1997) have stated that power means of order greater than one are very useful in building composite indices of food security measures that place equal weight on the four dimensions. The method has been used to measure Human Development Index (HDI) and Human poverty index (HPI) by the United Nation Development Program (UNDP) and other scholars (Antony & Rao, 2007;Napoli et al., 2011). Hence, this study aggregates the four dimensions of food security using Sen's suggestion (Anand & Sen, 1997) of power three, which is the aggregate food security index specified as follows: = Availability; = Associability; =Utilization; and = Stability The necessary indicator variables intimately related to each food security dimension have been selected through exploring a rich set of food security literature (Abafita & Kim, 2013;Bashir, Schilizzi, & Pandit, 2012;Demeke et al., 2011;Magrini & Vigani, 2016;Napoli et al., 2011).
The number of indicator variables that are included in PCA analysis should be greater than two and sometimes only two variables can be used to do PCA analysis if a correlation greater than 0.70 exists between variables (Tabachnik & Fidell, 2007;Yong & Pearce, 2013). In general, the minimum requirements of indicator variables depend on the study design and the data sets.
Based on the previous empirical works, economic theories, and dataset in hand, the study chose four indicators for each of the four dimensions of food security i.e availability, access, stability, and utilization. A total of sixteen variables were used to generate the overall food security indices of farm households (see Table 1).
7 Value of physical farm and household assets Birr 1 Quantity of cereal production in teff equivalent of wheat, barley, sorghum, maize and millet 2 Name of Ethiopian Currency (Currently 1USD=27.6 Eth Birr) 3 CPI-deflated real prices are used in computing the value of crop output 4 DDS: Dietary Diversity Score is often used as a proxy measure of the nutritional quality of household's diet. An adult household member can have a food group of 0-12 while a child may have 0-8 food group. Each food group contains more than one food items. Hence when a household lays on more food groups that implies a household consumes more variety of foods.

Data Source
The measurement is based on household-plot level agricultural production panel data collected in 2010/2011, 2012/2013, and 2014/2015. The data was collected by the Central Statistics Agency of Ethiopia in collaboration with the World Bank Living Standards Measurement Study-Integrated Surveys on Agriculture (LSMS-ISA). The Survey covers all nine regions of the country but, this research included only four regions (Amhara, Oromia, SNNP, and Tigray) because the other regions were not included in the first survey period, and are also not engaged in cereal production because the agroecology in the regions is not conducive for cereal production. The number of households interviewed were 3,969 (2011), 5,262 (2013), and 4594 (2015). In this study, a total of 1,412 farm households were selected in each wave which forms a panel data of 4,236 observations. Specifically, the sample encompasses farming households who cultivated five major food crops (teff, wheat, barley, maize, and sorghum) that account for about three-fourths of total cultivated land. Table 2 shows the sample size used in the study by region and year.

Descriptive Statistics
Descriptive statistics including measures of central tendencies, dispersions, and tables are used to summarize variables under each food security dimension and a mean difference test is performed to analyze yearly changes over the study period.

Steps of Multidimensional Food Security Index Estimation
To compute farm households' food security index, the study follows several steps of PCA. One percent of the total observations had missing values in at least one covariate. In literature, there are various possible options to manage the problem of missing values. For example, Cortinovis, Vella, and Ndiku (1993) have suggested dropping observations with at least one missing value; however, this way of elimination might lower the sample size and reduce the validity of the results particularly if the original sample size is small (Nakagawa & Freckleton, 2008 were standardized to a zero mean and standard deviation of one before the PCA estimation was carried out.
The results of the PCA estimation were examined with an intermediate step that

Descriptive Statistics Food Security Indicator Variables
The descriptive statistics of food security indicators used to derive each dimension of the food security index presented in Table 3.  7 On average, how many times the sample household heads faced health shock in each year 8 The proportion of household heads who faced health problem

Result of Principal Component Analysis of Each Food Security Dimension
The Kaiser-Meyer-Olkin (KMO) test of sample adequacy is used to assess the suitability of the data for PCA. The values in Table 4 for each food security dimension shows the data set of the study is suitable for principal component analysis. KMO takes a value between 0 and 1. A smaller value indicates that variables have little in common to do PCA estimation while values greater than 0.5 are considered satisfactory to apply PCA (Kaiser, 1974). In other words, a high KMO value indicates that a relatively larger proportion of the variance can be explained by the principal components. All four food security dimensions have KMO values greater than 0.5 hence attesting to the existence of a medium pattern of correlation among selected indicators in each dimension.
Therefore, applying PCA estimation to derive farm households' food security index is appropriate.  crop producers so they depended on production rather than buying food crops for consumption.
Sometimes smallholder farmers take food crops to the market for sale. In such a context, when there are many net food crop sellers or producers, the effect of increasing food prices on food security tends to be positive (Dimova, 2015) through the income. Finally, the stability dimension indicators such as shock frequency and the number of months households are without enough food has negative component loadings while the number of income sources and real asset value variables has positive component loadings.  (2011, 2013 & 2015) Finally, the household food security index is computed using the component loading coefficients of each indicator variable as a weight. The computed household food security index ranges from negative to positive value. The indices have a mean value of zero and standard deviation of one and higher index values denote a higher level of food security (McKenzie, 2005). The normalization 9 was necessary to limit the index values between 0 and 1. Table 5 presents households' average food security indices of each dimension and the average indices of farm households for availability, accessibility, utilization, and stability dimension were 0.57, 0.48, 0.70, and 0.54 respectively. The minimum and maximum index values of each food security dimension are also presented below.

Classification of Households' Food Security Status
The main challenge of examining households' food security status overtime is the arbitrariness of selecting a threshold point. Defining a cut-off point implies dividing the sample into two distinct groups, namely "food secure" and "food insecure". This can be excessively restrictive because of the multidimensional nature of food security. The literature on PCA indicates both data-driven and arbitrary (based on the assumption that indices are uniformly distributed) segregation mechanisms, that break indices into different groups. Commonly used arbitrary cut-off points have the lowest 40 percent of households being treated as 'food insecure', the highest 20 percent as 'food secure', and the remaining 40 percent as of the households being treated as 'vulnerable to food insecurity' (Filmer & Pritchett, 2001;Vyas & Kumaranayake, 2006). On the other hand, Abafita and Kim (2013); Demeke et al. (2011) applied the data-driven segregation mechanism to classify households into relative food secure and food insecure groups using the mean values of the index as a cut-off point. The research for this paper follows the latter approach to group the samples into relative food secure and food insecure classes. Hence, households with an index below the mean were grouped as relatively food insecure whereas households with an index above the mean were grouped into relative food secure. This relative classification enables analysis of the changes in households' food security status over time.

Dynamics of Households' Food Security Status
To look at the percentage of households that move from one cluster into another cluster within the survey periods the study built an economic transition matrix. The transition matrix, which is

Source: Own Computation from ESS 2011-2015
The earlier transition matrix depicts only the movement of households between the first and the last panel year that explains an overall movement among the five groups. So, it has not given attention to the movements of households in-between and it didn't explicate the transition between food secure and food insecure category. The subsequent tables summarize the movement of households between food secure and food insecure category in each of the panel years: Source: Own Computation from ESS 2011-2015 As

Conclusion
A composite multidimensional food security measurement index was estimated in the study. The advantage of a composite multi-dimensional food security measurement is to captures more than one food security indicator in the food security measurement. Principal Component Analysis (PCA) was employed to derive the food security index of farm households. For each dimension of food security, four indicator variables were used to derive the household food security index.
More than half of the households were food secured in each dimension and the percentage of food secure households increased in terms of availability, accessibility, and utilization over the study period. In terms of the stability dimension, the proportion of food secure households declined On the other hand, most farm households were transitory food insecure implying that farm households fell into the state of food insecurity at least in one period and a few proportions of households were chronically food insecure.

Competing interests
The author declares that no competing financial interests. There were no funders that had a role in this study, analysis, decision to publish, or preparation of the manuscript.

Author's contributions
Mohammed Adem designed the study and conducted the analysis of the data. He also wrote the manuscript.

Availiablity of Data and Mataerials
The datasets and analysed during the current study are not publically available due to confidentiality of personal data but are available in a restricted from the corresponding authors on reasonable request.

Funding
This study had not been financially supported by anybody.

Acknowledgment
The author would like to acknowledge Central Statistics Agency of Ethiopia and World Bank for the data access.