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How much of the inequality in emotional and physical abuse can be explained?The analysis of the preceding section, encapsulated in Table 4.5, highlighted several factors which affected the likelihood of wives facing emotional and physical abuse from their husbands. Of these, three in particular stood out: the number of controls imposed on women by their husbands, the wealth of the wives’ households, and the frequency with which the husbands were drunk. The issue that is analysed in this section, using the tools of inequality decomposition, is the relative contribution of these three factors to inequality between wives in the predicted likelihood of being emotionally and physically abused. The estimated bivariate probit equations for emotional and physical abuse predicted, for each of the 16,127 women in the estimation sample, the probability of her being emotionally and physically abused, conditional on the relevant values of the determining variables for that woman. Armed with a knowledge of these individual probabilities, it is possible to estimate how much of the overall inequality in these 16,127 probabilities of emotional abuse, and the 16,127 probabilities of physical abuse, can be explained by a particular factor. To this end, this section uses the methodology of inequality decomposition. This decomposes overall inequality into “betweengroup” and “withingroup” inequality. When the decomposition is additive, overall inequality can be written as the sum of withingroup and betweengroup inequality:
When inequality is additively decomposed then one can say that the basis on which the individuals were subdivided (say, household wealth) contributed [(B/I) x 100]% to overall inequality, the remaining inequality, [(AH) x 100]%, being due to inequality within the groups. So, inequality decomposition provides a way of analysing the extent to which interpersonal inequality (in this case, in the probabilities of emotional and of physical abuse) is “explained” by a factor or a set of factors. If, indeed, inequality can be “additively decomposed” then, as Cowell and Jenkins (1995) have shown, the proportionate contribution of the betweengroup component (В) to over all inequality is the income inequality literature’s analogue of the R^{2} statistic used in regression analysis: the size of this contribution is a measure of the amount of inequality that can be “explained” by the factor (or factors) used to subdivide the sample. In order to decompose inequality additively, however, it has to be measured in a very specific way. Only inequality indices which belong to the family of Generalised Entropy Indices are additively decomposable (Shor rocks, 1980), and one of these indices is Theil’s (1967) Mean Logarithmic Deviation (MLD) Index which is used in this section’s analysis. The MLD ^{N} index is defined over N persons as ^log(p, Ip) IN, where p_{;} is the prob l ; 1 ability of person i (i = 1, ..., N) being abused, either emotionally or physically, by her husband and p = Y^p,/N is the mean probability. Table 4.6 shows that, for tne 16,127 wives in the estimation sample, inequality in the distribution of the predicted probabilities of being abused by their husbands was considerably greater for emotional abuse than for physical abuse: the MLD values for emotional and physical abuse were, respectively, 0.358 and 0.198 with associated Gini coefficients of 0.438 and 0.278. Thus, inequality in the distribution of the PPs of physical abuse was, in terms of the MLD, only 55% of inequality in the distribution of the PPs of emotional abuse. When the 16,127 wives were grouped by the number of controls imposed on them by their husbands (0, 1, 2, or 3+), inequality between the four groups (i.e., wives with no controls, one control, two controls, three or more controls) contributed 54% to overall inequality in emotional abuse and 30% to overall inequality in physical abuse. When the 16,127 wives were grouped according to the number of controls imposed on them and the frequency with which their husbands were drunk (never, sometimes, often), inequality between the 12 groups contributed 72% to overall inequality in Table 4.6 Percentage contributions to inequality in the distribution of predicted probabilities of wives being emotionally and physically abused
Source: Own calculations from the National Family Health Survey4. Note: MLD = Theil’s Mean Logarithmic Deviation, as defined in the text. emotional abuse and 38% to overall inequality in physical abuse. Finally, when the 16,127 wives were grouped according to the number of controls imposed on them and the frequency with which their husbands were drunk and their households’ wealth (poorest, poor, middle, rich, richest), inequality between the 60 groups contributed 74% to overall inequality in emotional abuse and 49% to overall inequality in physical abuse. So, nearly threefourths of overall inequality in the predicted likelihood of emotional abuse, and nearly half of overall inequality in the predicted likelihood of physical abuse could be explained by just three factors. (1) the number of controls that husbands imposed on their wives, (2) the drunkenness of husbands, and (3) household wealth. In order to assess the separate contributions of wealth and drunkenness to inequality in the distribution of the probabilities of emotional and of physical abuse, the calculations are as follows. When the division was only by the number of controls imposed, the betweengroup contribution, for emotional abuse, was 0.193 to an overall inequality of 0.358, and for physical abuse, it was 0.059 to an overall inequality of 0.198. When the division of the sample was by wealth and drunkenness, the betweengroup contribution for emotional abuse rose to 0.257, and for physical abuse, it rose to 0.075. Finally, when the division of the sample was by wealth and drunkenness and household wealth, the betweengroup contribution for emotional abuse rose to 0.266, and for physical abuse, it rose to 0.097. Thus, of the overall 0.266 betweengroup contribution to emotional abuse, the number of controls contributed 73% (0.193/0.266), husbands’ drunkenness contributed 24% ([0.257  0.193]/0.266), and household wealth contributed the remaining 3%. On the other hand, of the overall 0.097 betweengroup contribution to physical abuse, the number of controls contributed 61% (0.059/0.097), husbands’ drunkenness contributed 17% ([0.075  0.059]/0.097), and household wealth contributed the remaining 22%. 
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