## Some Metrics on Income Distribution – More Details and Methodology

The argument about the nefarious effect of too concentrated an income in a particular country can always be made to gainsay any potential benefits to the trickle-down -or supply side- economics: while it is almost impossible -and probably counterproductive to enforce or allow for perfect, egalitarian distribution of income and wealth, evidence can buttress the case for a wide median/middle class, empowered with a large income share, and comforted in a steady and balanced growth in its wealth.

From a policy point of view, I believe the wages and income issues are perhaps the only thing that can bring together large scores of Moroccan populations whose cultural and political loyalties are too polarized, but eventually find solace in pledges to improve their standards of living, and would even go as far as support that political organization credible enough to reduce inequalities and guarantee steady income growth for all.

So, let us consider other metrics to income instead of GNI – a raw measure indeed, but one that does not provide precise information on generated income; fortunately, national accounting can provide us with a bit of help to devise some custom-made aggregate for National Domestic Income. World Bank data defines the Gross National Income aggregate (code NY.GNY.TOTL.KN [xls]) it provides as:

Gross national income is derived as the sum of GNP and the terms of trade adjustment. Data are in constant local currency.

Clearly there are some components one isn’t very interested in; the figure of interest should be purely domestic – we are, after all, interested in domestic income. Because GNI is basically the sum of domestic income and primary income from abroad, we can therefore compute it with net foreign income from FDIs, Workers’ remittances and portfolio inflows.

There is always the delicate question of remittances: for only too many households, remittances from relatives working abroad are the only source of income, and in a sense, it distorts somehow the big picture one is keen on painting; but there goes the limitations of data availability – the local Morccan office for national statistics (Haut Commissariat au Plan – HCP) does not provide adequate format for data processing, if it ever does; I am grateful for many of their documents, but there is no comprehensive plan to upload relevant data, say in xls or csv format; as for the World Bank, they can only put online what the Moroccan authorities are giving them – any additional information needs to be paid for, and I don’t think I have the money for it 🙂

But still, even with these rule-of-thumb, back-of-the-envelope computations, final results are not as bad as one may make out; quite the opposite, they seem to be quite close to whatever comes up in official reports. Still and all, it is always good exercise to investigate whatever figures of interest.

Now, rearranged figures show that domestic income distribution per deciles and quantiles are on the low side when compared to GNI breakdown – which is only logical, given the computed differences in FDI and remittances – nonetheless, one finds out that upper 20% and 10% within still benefit from a high annual income: for the wealthiest 10%, it was MAD 222,000 per annum in 1999, it neared 400,000 in 2010 – while average domestic income was MAD 71,000 in 1999, it increased to MAD 106,000 in 2010.

It is clear that the average annual increase was higher for the richest 10% (+5.47%) than the observed average (3.7%) and that applies only to domestic income. As for median income, an annual increase of 2.5% was recorded over the considered 12-years time period, growing from 53,000 to 70,000 per annum, and in constant terms; the conjugated effects of a base 1999 inflation (CPI) and the downgrade in income distribution to the expenses of median households vindicates the claim made in an earlier post that median households have lost purchasing power to monetary illusion.

during the considered 12 years, CPI inflation (base year 1999 instead of HCP’s ICV base year 2006) was at annual average of 3.4%, in addition to the annual 1.14% dent in median income share, this means a real discount of 4.54% on any nominal income increase; it stems from the number computed earlier on (2.5%) that there was significant loss to real purchasing power to this class of households – relatively higher, when compared to a GNI-based computations, and this only makes sense: foreign currency inflows are not subject to the same inflationary distortions, and so, tend to make up partially for the purchasing power downgrade, across the board.

But the bottom line of the argument made earlier is vindicated by these findings: middle class are hurt in their income, and this comes to a blow, because a balanced society with low risks for social unrest needs a strong and wide middle class base – if this is observable in a host of country, there is good reason to believe that it would apply equally to Morocco as well.

But let is now consider something different, less dynamic – the present distribution of income as it were. In statistics, probability distribution are quite useful to assess, in this case, wealth distribution across households – we start from the purest egalitarian distribution of all, the uniform distribution.

**Uniform/Egalitarian:** very easy a computation, just take every household, number them from 1 to 6.5156.000 (approximately) and then allocate them with the same income, namely GNI per household. Median, Average and Variance are clearly defined and everything is fine. This how an egalitarian society would look like: all households deciles would have the same income, i.e. 106,000 per annum with uniform growth per household from 1999 and 2010. The only snag is that it is utopian and almost impossible to enforce. Plus there are no immediate economic benefits to such a distribution: can we expect growth if everyone is insured to have the same income as the others regardless of their contribution to society?

**Normal (or Laplace-Gauss) distribution:** a little more complicated a distribution, but one that remains within the realm of acceptable inequality: the bell curve distribution concentrates quite a lot around the mean (which coincides with the median too) as a matter of fact about 66% of all relevant information lies very close to the mean. Now, considering the distribution at hand with a GDI per household capita of 106,000, and say 36,000 as a variance, we get a pretty decent income equability, as the graph below would show:

But then again, that would be too good to be true – though it is realistically more achievable, and the case for a strong and wide middle class can then be made more forcefully.

**Pareto Distribution:**and this is the last distribution one should have a look at, because as far as available empirical data goes, this is the closest we can get to the real income distribution in Morocco. And it all adds up: as we observe average income per households is 106,000, there are 30% households above that line capturing 60% of total Domestic Income.

We compare and confirm that incomes in Morocco follow very closely a Pareto-like distribution, which denotes of its unequal distribution indeed.

Finally, it is enough to look at the Gini index to understand why the Pareto-shaped distribution in Morocco is so unequal: HCP’s own computations put the Gini Index at 0.46, certainly one of the highest in the world. According to the United States 2008 Census, their 2009 income Gini Index was around 0.469 – very close to Morocco’s. What does this tell about our own economy?

I would suggest that we have achieved the same level of income concentration as the United States’, but ultimately failed to raise standards of living for the middle and median classes, not even commensurate to the selected benchmark’s own growth over 1999-2010.

Generated Data (computed on R open-source software) shows:

#data computed for a normal distribution, #with average 106 and standard deviation of 20Distribution_Income <- rnorm(6516, mean=106, sd=20) Income_Norm<-dnorm(6000, mean=106,sd=36) plot(density(Distribution_Income, bw=4),col="Black", lwd=4) hist(Distribution_Income, col="tomato4", main="Generated Normal Income Distribution", xlab= "Income Per Household (thousands dirhams)", ylab= "Number Of Households in Thousands") #Monte Carlo-like simulation to test mean and median convergence Distribution_Income_MC<-rep(Distribution_Income, each=1000) vector_generated<-c(summary(Distribution_Income_MC)) summary(vector_generated) # Min. 1st Qu. Median Mean 3rd Qu. Max. #34.48 95.76 106.10 105.80 116.10 176.10 #compute the income share held by the 10% wealthiest (quintile above 90%) qnorm(0.90, mean = 106, sd = 20, lower.tail = TRUE, log.p = FALSE) #[1] 131.631 #----------------------------------------------------------------------- #Pareto Distribution #need to setup "VGAM" Package library(VGAM) Distribution_Income_Pareto<-rpareto(6516, 106, 100) summary(Distribution_Income_Pareto) hist(Distribution_Income_Pareto, probability=TRUE, col="wheat4", main="Income Distribution Per Pareto", xlab="Income per Household in Thousands") #minimum value 100 selected gets the closest to empirical distribution

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