# Top Incomes, inequality and the Egyptian case

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Income inequality has been a hotly debated topic in Egypt since the 2011 revolution. However, researchers remain divided over the “true” level of inequality in this country. A blog posted on Vox in August argued that inequality in Egypt was underestimated and could be better represented by using house price data to estimate the top end of the income distribution. This blog is a response to that article and seeks to clarify issues relevant to the measurement of inequality in Egypt and elsewhere.

A central problem is the mismeasurement of top incomes and how it skews the measurement of inequality. Income or expenditure inequality is generally measured using household budget surveys in a sample representative of a national population. If the survey sample is properly designed and all individuals respond to all income and expenditure questions accurately, these surveys are ideal to measure inequality. However, some respondents choose not to respond to surveys and others do not respond to income or expenditure questions, resulting in mismeasurement of inequality.

There have been at least three different approaches to addressing this problem. Atkinson, Piketty and Saez (2011) used tax records to estimate and correct top incomes. Cowell and Victoria-Feser (1996a and 1996b) replaced top income observations with parametric shapes observed on distributions of reliable incomes. Under both methods, Gini coefficients are estimated combining artificial or external data for top incomes and real survey data for the rest of the distribution. Mistiaen and Ravallion (2003) and Korinek, Mistiaen and Ravallion (2006 and 2007) inferred the probability of non-response based on regional non-response rates and re-weighted the sample to correct for top income bias.

Three papers have recently provided different estimations of inequality in Egypt using different methodologies. Hlasny and Verme (2016) used the 2009 Egyptian Household Income, Expenditure and Consumption Survey data and compared the second and third methods described above to correct for top incomes biases for both income and expenditure. They found very similar results between the two methods – an upward correction for inequality comprised between 1.1 and 4.1 percentage points. Alvaredo and Piketty (2014) used a purely parametric method relying on Hlasny and Verme’s estimates of inequality for the bottom of the distribution and parameters derived from tax records for the top. They found upward corrections for inequality of between 1 and 14 percentage points depending on the choice of parameters. Van der Weide et al. (2016) used Egyptian HIECS data for the bottom 95 percent and data from house prices for the top 5 percent. They found an upward correction of inequality of 11 percentage points for urban areas.

These studies do not disagree on *relative* inequality, the fact that Egypt shows low inequality relative to other countries. Studies on inequality in Egypt since the 1960s have consistently found low inequality in Egypt by world standards and this is confirmed by the recent studies by Hlasny and Verme (2016) and Alvaredo and Piketty (2014) whereas van der Weide et al. (2016) do not provide cross-country evidence. It seems fair to conclude that inequality in Egypt is low by world standards whether comparisons are made before or after corrections for top incomes.

These studies seem to differ in the measurement of *absolute* inequality, the question of what is the “true” level of inequality in Egypt. However, this difference may be explained, at least in part, by the underlying assumptions of the different papers. Alvaredo and Piketty (2014) rely on a baseline Gini for the bottom of the distribution taken from Hlasny and Verme (2016). This is already corrected for top income biases and therefore overestimates inequality in the bottom of the distribution. The top income parameters are arbitrarily selected within a range derived from mostly rich countries, which are expected to lead to higher Gini estimates. These two considerations suggest that the resulting Ginis may be overestimates. The median upward correction in this paper is 4.5 percentage points, not far from the upper bound in Hlasny and Verme (2016).

Corrections of inequality by van der Weide et al. (2016) relied on survey data for bottom incomes, and on a single parameter based on house prices data for top incomes. The key parameters of the paper rest on assumptions that can lead to overestimation. Top house prices appear to be distributed more widely than Pareto distribution would predict, particularly in Cairo. House listing prices are assumed to be representative of and proportional to household imputed rents but there is no evidence of that in the paper. Household rents are assumed to follow a constant-elasticity relationship with incomes per capita but they do not – van der Weide et al.’s indexes of top-tail distribution indicate a markedly narrower distribution for incomes than for house prices, regardless of the top-tail cutoff. To the extent that imputed rent appears to rise as a share of income among the richest households, inferring incomes from rent will overestimate inequality. It is unlikely that house prices in Egypt remained distributed the same way between 2009 and 2013. If the distribution widened, then using the 2013 distribution to correct the measure of income inequality in 2009 will overestimate the true Gini. Overall, estimating incomes with wealth indicators (or imputed rents based on them) is bound to overestimate inequality given that the dispersion of wealth is typically higher than the dispersion of income.

No one can claim to know the exact degree of inequality in Egypt. Regarding *relative* inequality, fifty years of research on Egypt have shown inequality to be low compared to other countries. The latest research confirms this. On inequality in *absolute* terms, most scholars would agree that it is underestimated in Egypt due to top incomes biases, but would disagree on the scale of the underestimation. Part of the difference may be explained by assumptions and parameters that rest on weak foundations. While parametric functions are very helpful in filling data gaps, they are not a substitute for real data.

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