Top expenditure distribution in Arab countries and the inequality puzzle 1

2.1 Available data

Most Arab countries conduct household income and expenditure surveys (HHIES) periodically to collect evidence regarding the distribution and components of incomes and expenditures of their population. However, not all countries make the survey micro-data publically available in their entirety or at all. This study relies on a set of HHIESs harmonized and released to the public by Economic Research Forum (ERF) in collaboration with national statistical agencies: the Egyptian Household Expenditure, Income and Consumption Survey; the Jordanian Household Expenditure and Income Survey; the Palestinian Expenditure and Consumption Survey; the Sudanese National Baseline Household Survey; and the Tunisian National Survey on Household Budget, Consumption and Standard of Living. These are high quality, well-documented surveys that have been validated and used successfully in a number of existing studies [8, 28, 37]. All HHIES surveys are nationally representative, and thus comparable across countries and years, but individual households cannot be tracked over time.

All recent HHIESs available at the time of writing are used, including the surveys for Egypt 2008, 2010 and 2012; Jordan 2006 and 2010; Palestine 2007, 2010 and 2011; Sudan 2009; and Tunisia 2005 and 2010. The Egyptian surveys were administered during April ‘08–March ‘09, July ‘10–June ‘11, and July ‘12–June ‘13, that is two years before the uprising, in its midst, and during the flux one year after the uprising when the Muslim Brotherhood was promoting a new national constitution. The Jordanian surveys were collected in the 12 months following April ‘06, and those following April ‘10 – for the most part before public protests in the country became widespread in the spring of 2011 and led to constitutional reforms. In Palestine, the surveys were collected throughout the years 2007, 2010 and 2011, at the time of relaxation of the Israeli security regime and prior to the September 2012 surge of major protests against domestic economic policy. In Sudan, the survey took place in the summer of 2009, three years prior to the start of Arab-Spring inspired protests against the government’s austerity plans. Finally, the Tunisian surveys were administered during May ‘05–May ‘06, and June ‘10–May ‘11. Fieldwork for the second survey was thus at its height in January 2011 when major public protests erupted, motivated by people’s economic and democratic concerns, and led to the toppling of the country’s president.

In the following analysis, the surveys are used one by one as cross-sectional samples. We are able to use multiple survey waves for four of the five included countries. This allows us to follow the evolution of expenditures and of inequality over time, and in the case of Egypt before and after the popular uprising. While the five countries do not represent the entire Arab region, they show a mosaic of the economic conditions and survey practices across the region. The surveys differ in their sampling rate from the population, and cover a heterogeneous block of countries in terms of their economic development, demography and labor force composition, inequality, and political climate at the time of survey fieldwork. Table 1 presents the essential information on survey sources and data distribution. Additional information is provided in the supplementary materials.

Before any analysis with the available sample, it is useful to check whether extreme expenditure observations are simply errors such as data-entry errors or are true values incidentally very distant from the central moments of the expenditure distribution. The eleven surveys differ significantly in the level and the dispersion of the highest several expenditures. The Egyptian data exhibit modest dispersion. The single highest expenditure exceeds the one ranked twentieth by merely 190 percent in 2008, 210 percent in 2010, and 120 percent in 2012.3 The Jordanian data show more substantial dispersion, and include an influential observation in the 2010 wave. In the 2006 wave, the highest observed expenditure per capita exceeds the second highest one by 64 percent, and the twentieth highest one by 354 percent. In the 2010 wave, on the other hand, the highest expenditure per capita is more than seven times as high as the one in the second place, and more than twelve times as high as the one ranked twentieth.4

In Palestine 2010, similarly, the highest one or two expenditures appear extreme. In the 2007 and 2011 waves, the single highest expenditure is 29–43 percent higher than the second highest expenditure, and 189–262 percent higher than the one ranked twentieth. In 2010, however, an outlying top expenditure is 134 percent higher than the second highest one, and more than seven times as high as the twentieth highest one. It is likely that the small sample sizes in Jordan ‘10 and Palestine ‘10 are partially responsible for the presence of outliers.

In Sudan, the highest observed expenditure per capita exceeds the second highest one by 29 percent, and the twentieth by 189 percent, a medium degree of top expenditure gaps. In both waves of the Tunisian survey, the household with the highest expenditure per capita surpasses the expenditure of the second richest household by a mere 17–23 percent. Similarly, it surpasses the expenditure of the twentieth household by only 211–213 percent. Rather than having a single outlier, the Sudanese and Tunisian surveys have 3–4 outlying households – their expenditures are clustered nearby each other, while they exceed the following values by 50 percent. On the other hand, no further clustering of observations is found lower down the expenditure distribution.

Assessing the aggregate-expenditure shares of the richest households, we find that they are higher in Jordan, Palestine and Sudan and lower in Egypt and Tunisia (last row in Table A1). Since it is unclear whether the dispersion of top expenditures in one survey (Jordan, or Palestine) is too wide due to measurement issues, or the dispersion in another survey (Tunisia) is too narrow due to underreporting, we take an agnostic view of the validity of each observation, and let parametric estimation on the entire distribution of top expenditures tell us which observations step out of line relative to the predicted pattern.5

Table 2 provides additional information on the actual distribution of top expenditures: the share of aggregate expenditures accounted for by the top 0.1 percent of observations (or 7–11 households across surveys) to as many as 20 percent of observations (or 780–2,662 households) are shown in brackets. These results confirm a disproportionate concentration of wealth among the super-wealthy 0.2 percent of households (19–21 units) in Jordan ‘10 and in Sudan, where they command over 2.9–3.0 percent of aggregate expenditures. Tunisia ‘05 is nearly at that level of concentration among the uppermost expenditure households. Regarding expenditure shares among the following 20 percent of households, Sudan and Tunisia ‘05 exhibit disproportionate concentrations. The richest 1 percent (10%, or 20%) of households control 7.6–7.8 percent (30.8–32.4 or 46.3–48.0%, respectively) of aggregate expenditures.

The observations in the uppermost tail of expenditure distributions may reflect true values of expenditures in the population, and may be appropriate to include for the sake of measuring inequality in the population. Alternatively, extreme observations may arise due to various errors and, if included, should be corrected for the identified errors. In either case, the uppermost observations may introduce spurious volatility of inequality across survey waves.

It is well known that the inclusion of extreme observations tends to influence commonly used measures of inequality [40]. Some measures such as the Theil index and other Generalized Entropy indices are very sensitive to exact values of top observations, but even the Gini coefficient is not robust to them [41]. To evaluate how sensitive inequality measurement is to extreme expenditure observations, without judgment on their authenticity, we would want to identify which observations are outliers and estimate our measures of inequality with and without them. Neri et al. [42], for example, define outliers in the EU Surveys on Income and Living Conditions (SILC) as observations exceeding the median 4–5 times, and find that this comprises 0.1–0.2% of households.

In HHIESs measurement errors may arise for several reasons, including intentional misreporting, errors in recollection, or data entry errors. Across survey waves, expenditure distributions may also exhibit different upper tails on account of sampling variability. Top expenditures may generally also be deliberately obscured by national statistical agencies to comply with privacy norms or correct for measurement problems, but this is not the case with the survey samples at hand. Due to the potential measurement problems and sampling differences across survey waves in our set of Arab household surveys, our estimation of inequality levels and trends may be biased. We thus turn to a recently promulgated correction method that can address these issues.

2.3 Replacement using values from a Pareto distribution

To compare the actual distributions of top expenditures to distributions that may be predicted in the given countries, and study the presence of extreme values in our data, we follow an approach applied by Atkinson, Cowell, Jenkins, Piketty and others to summarize the dispersion of economic outcomes by a parametric distribution, report properties of the estimated distribution, and use the estimates to correct the observed top tail for suspected statistical problems [38, 43].

Inequality estimates imputed from parametric distributions can be less sensitive to extreme observations and sampling variations than non-parametric observations from actual survey data. Parametric estimates for the top tail could be combined with non-parametric statistics for the rest of the distribution to obtain estimates with better empirical properties [32, 41]. Burkhauser et al. [44] compared four methods for dealing with under-representation or top-coding in the survey data – essentially replacing top-coded values using four alternative parametric estimators and combining the estimates with non-topcoded observations.

The following estimation approach is motivated by an empirical regularity that top observations across countries and years follow a particular pattern represented well by the Pareto distribution. Arnold [45] reviews the properties of the Pareto distribution as well as of the broader family of Pareto distributions. The Pareto distribution is highly skewed and heavy-tailed, and is thought to be suitable to model upper incomes, expenditures, wealth or other welfare aggregates [46, 47, 48]. As expenditures grow larger, the number of observations declines following a law dictated by a constant Pareto coefficient θ . The Pareto distribution can be described by its probability density function as follows:

f ⁢ ( x ) = θ x θ + 1 , 1 ⩽ x ⩽ ∞ .(1)

Here x is the variable of interest, which in our case will be expenditure per capita in international purchasing-power parity dollars. The Pareto coefficient θ can be estimated by maximum likelihood methods [39, 49] as

θ = 1 log ⁡ x ( n - k + 1 ) - k - 1 ⁢ ∑ i = 0 k - 1 ( log ⁡ x ( n - i ) ) ,(2)

where x ( j ) is the j th order statistic in the sample of expenditures n , and k is the delineation of top expenditures such as the top 10% of observations [50].

Replacing observed expenditures with fitted values from the Pareto distribution yields measures of expenditure distribution and inequality that do not account for parameter-estimation error and sampling error in the available dataset. This problem is on top of the issue of combining standard errors of the parametric Gini among top expenditures and the nonparametric Gini among lower expenditures. An and Little [51], and Jenkins et al. [52] account for sampling error by drawing random values from the estimated distribution for all potentially imprecise top observations, combining them with actual lower-level values, and calculating a quasi-nonparametric inequality measure (that is, inequality measure estimated non-parametrically on partially synthetic data) with its bootstrap standard error. Repeating the exercise multiple times, we can note variability in the obtained inequality measure. Following Reiter [53], the expected measure of inequality in such partially synthetic data can be computed as a simple mean of inequality measures from individual random draws, 𝐺𝑖𝑛𝑖 𝑞𝑢𝑎𝑠𝑖 :

𝐺𝑖𝑛𝑖 𝑞𝑢𝑎𝑠𝑖 ^ = ∑ i = 1 m 𝐺𝑖𝑛𝑖 quasi i / m(3)

Its sampling variance can be computed as:

var ^ = ∑ i = 1 m ( 𝐺𝑖𝑛𝑖 quasi i - 𝐺𝑖𝑛𝑖 𝑞𝑢𝑎𝑠𝑖 ^ ) 2 / ( m - 1 ) m + ∑ i = 1 m var quasi i / m .(4)

The first term here is the sampling variance across different draws from the Pareto distribution, and the second term is the mean sampling variance within an individual draw. m is the number of repetitions and var quasi i is the variance of the quasi-nonparametric Gini coefficient from an individual draw i . This methodology still ignores standard error from the estimation of parameters in the Pareto distribution. However, this is expected to be quite small compared to the sampling error, and can be ignored in large datasets where parameters have been estimated precisely [52].

The quasi-nonparametric Gini coefficient can be compared to an uncorrected nonparametric estimate. As long as it was correct to assume that top expenditures in the population are distributed as Pareto, a difference between the quasi non-parametric and non-parametric estimates would indicate that some observed high expenditures may have been generated by a statistical process other than Pareto, and that our inequality measure is sensitive to this. Quasi non-parametric Ginis that are lower than non-parametric Ginis can be interpreted as evidence that some top expenditures in the national samples are extreme compared to those generated under the Pareto distributions. A higher quasi non-parametric Gini would indicate that the observed top expenditures are lower than what would be generated under the Pareto distribution, potentially implying under-representation of rich units or underreporting of top expenditures in the sample.

In the following empirical analysis top expenditures are replaced by random draws from the Pareto distributions estimated on them. The reason for estimating the distributions on the same observations as those that will be replaced (rather than, say, estimating right-truncated Pareto distributions only on lower expenditure values deemed reliable) is that this approach allows us to remain agnostic regarding the validity of any individual observation. The approach does not require us to decide a priori which observations to use for estimation, and which observations to replace. Consequently, this approach can be viewed as addressing the problem when some expenditures are randomly under- or over-reported, or rank-proximity swapped. To the extent that different survey waves manage to cover different top-expenditure households through random sampling, this approach also mitigates the problem of overestimation of the variation in inequality across survey waves due to sampling errors. However, this approach cannot address problems of stand-alone systematic underreporting or top-coding of expenditures [54].

For the choice of an inequality index, this study uses the Gini coefficient as the primary measure, for its properties of being well understood and easily estimable under both parametric and nonparametric distributions, widely reported, and less sensitive to extreme observations than other indices. The results of inequality corrections in this study can thus be viewed as conservative estimates for the true effects of extreme observations on inequality measurement in general, under the baseline hypothesis that top-income issues do not affect inequality measurement in the Arab region. To the extent that the estimated Gini is affected by measurement issues, we may safely conclude that the consequences for other inequality measures would be as large or larger. For comparison, Table A4 reports the top expenditure shares in the actual and corrected distributions.

Finally worth noting, the statistical analyses undertaken in this study were implemented using algorithms [49, 55, 56] for Stata version 13, on an Intel Core i5 CPU laptop running at 2.50 GHz with 8 GB of memory, running Windows 10 64-bit Professional operating system.