# The Moorish Wanderer

## The Economic Chronicles of the Kingdom, 1955-2011 Part.2

Posted in Dismal Economics, Moroccan Politics & Economics, Morocco, Read & Heard by Zouhair ABH on July 17, 2012

I should thank Romain Ferrali for his comment/question on some figures I have used on my Capdema presentation (quite a successful gathering, I am told. the Capdema event, obviously) about Morocco’s “1%”.

A challenge indeed, given the scarce information about income distribution from both HCP and the World Bank.

My initial -and strongest- assumption about income distribution is its stability across time: incomes evolve overtime, but the differences between the median and most percentiles relative to their respective incomes are assumed (and tested) to remain constant, or so we shall observe.

A caveat the reader would do well to consider: these incomes are computed on the basis of Gross National Income (from the World Bank Opendata) divided up by the number of households, either provided by HCP census or estimated on the basis of past annual demographic growth. Such a crude method bears several shortcomings in terms of sources of income not accounted for, the heterogeneity of different sources of income, the transfert effects between household to name but three. On the other hand, the primary source of interest remains the dynamics of income distribution, and if indeed additional information arises, I would be glad to carry on and finesse it further. This method might explain why HCP and myself disagree on the definition of “middle classes”: mine is simply the statistical definition of the income halfway between the poor and the rich.

The computations are based essentially on a set of three assumptions:

1/ Income distribution is constant: the same exponential distribution (with different parameter $\lambda$ for each year)

2/ Parameter $\lambda$ i.e. the inverse of GNI per capita, has its own statistical distribution.

3/ the parameter is stationary, possibly with a normal distribution whose mean and variance are estimated on the basis of time series.

An earlier blogpost assumed income distribution was exponential; an educated guess, you might say, given the fact that the decile-based cumulative density function clearly indicates a strong level of inequality – not very scientific indeed, but given the information at hand, it was the best I could come up with. I was lucky enough to find a paper than vindicates partially my assumption.

On income distribution in the United States, Dragulescu & Yakovenko note:

“The exponential Boltzmann-Gibbs distribution naturally applies to the quantities that obey a conservation law, such as energy or money [10]. However, there is no fundamental reason why the sum of incomes (unlike the sum of money) must be conserved. Indeed, income is a term in the time derivative of one’s money balance (the other term is spending). Maybe incomes obey an approximate conservation law, or somehow the distribution of income is simply proportional to the distribution of money, which is exponential [10]. Another explanation involves hierarchy.Groups of people have leaders, which have leaders of a higher order, and so on. The number of people decreases geometrically (exponentially) with the hierarchical level. If individual income increases linearly with the hierarchical level, then the income distribution is exponential.”

The authors provide two possible explanation for that particular distribution: it is either linked to the amount of money at hand, i.e. the higher the income a household earns, the higher its cash-in-hand is going to be, and because money is conserved, income benefits from that effect too. The second explanation is more sociological: income is assumed to have an institutional link to hierarchy, the social and professional status of a particular household confers a certain level of income. Here again, conservation in hierarchical statuses confers on income the same distribution.

The exponential distribution is a very useful statistical device. Its density function needs only one parameter, and is defined such:

$f(x) = \lambda \exp^{-\lambda x}, x>0, \lambda>0$

the restrictions on x is useless in this particular case, since income is obviously a positive amount of money, and lambda is necessarily positive, since:

$\mathbb{E}(x) = \frac{1}{\lambda}$

and there lies the usefulness of the said distribution: all we need is a time series of GNI per Capita or per Household to generate yearly income distribution. The idea is to use these as random vectors to check the effects of inequality over a long period of time. Once this set of distribution is generated, we test the results against empirical data from 1985, 1991, 1999, 2001, 2007 and 2010.  (available on the World Bank data nomenclature) The data at hand is the decile/quantile distribution of concentrated income.

we test whether differences in both values for available years are not statistically significant. Don’t bother with seemingly larger differences for 2007 and 2010, the sample size puts it in perspective.

If the three assumptions turn out to be correct, we should observe generated results close enough to empirical percentages from these years, and thus conclude to the robustness of the estimated income distribution. The policy implications of these results are infinite: fiscal policy, among others, would gain a lot from addressing issues of truth-telling and other institutional dysfunctions. But for now, I am focused on trying to describe as explicitly as possible statistical properties of income households in Morocco since its independence.

A first test to check whether income distribution is exponential, is to compare synthetic and empirical median income per household. The exponential distribution has the following property:

$\int_{0}^{x}\left(\lambda \exp^{-\lambda t}\right)dt= 0.5 = median$

which means the difference (or ratio) between average and median income per household is a constant commensurate to $ln(2)$ the null hypothesis in this case is to check whether observed discrepancies between both datasets are statistically insignificant. At 95% confidence interval, we get most empirical values lay between the 45-52% percentiles, which, given the size of the selected samples, is a pretty robust evidence these differences amount to very little. We therefore retain at high levels of confidence the assumption of the exponential distribution.

For instance, median income in synthetic data for 1985 was 23,293 dirhams, vs empirical median income of 24,210 dirhams, which falls within the 51%-52% percentile (which is more than enough to test at 95% confidence). It is worth pointing out however that these discrepancies, for all their statistical irrelevance, are systematically in favour of empirical data, which points out to an income distribution marginally more unequal than the exponential distribution suggests. However, because the fit is robust enough, we shall settle for the synthetic model. A final caveat perhaps: the test was carried on 6 particular dates, which still does not preclude significantly different results for the 51 remaining years. The likelihood of such event nonetheless is very low in view of the levels of confidence used earlier.

The fact the distribution has been the same (with its parameter $\lambda$ evolving with GNI per household) since 1955 might lead to think that income inequality has remained constant since 1955 (recall the ratio Median/Mean is $\log(2)$) and for some inter-quartile ratios,  results are stationary, which means inter-quartile income inequality has not change significantly over the past half a century.

large discrepancies between the top 1% and the median incomes starting from the 1970s

The picture is not all that clear, though: first off, the upper bound evolves frequently, a properties that has to do with the elusive nature of high income households (the 1% more affluent) the synthetic income distribution. If anything, there seem to be no particular link that growth since 1955 has contributed to influence income inequality one way or the other. What looks to be painfully clear however, is that the richest 1% have enjoyed a distribution of income growth whose trend is undoubtedly in their favour: between 1955 and 2010, the richest 1% have improved their income relative to all percentiles below the median by 6%, even as GNI per Household grew an average 6.91% over the same period of time. It might look like jumping to conclusions, but unequal distribution of income growth seem to contribute a lot, if indeed 86% of it goes to the top 1%.

I would say the graph and these computations understate the discrepancies between top and ‘regular’ earners: the sample size goes only as far as list maximum values of an annual income of 1,077,000 dirhams per annum, even as rarefied incomes are larger by far. If anything, these computations would instead minimize the reality of income inequality, because extreme values on the right hand-side tail are bounded.

So there it is: a quick look at the relationship between growth and inequality indices point to the lack of correlation: growth in Morocco does not necessarily bring about better quality of life to households below the median line. If anything (but the statistics gets blurry there) income inequality abated during the 1990s (a period of recession as well as structural reforms) and increased with the early 2000s (an economic expansion by many measures)

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

Posted in Dismal Economics, Moroccan Politics & Economics, Morocco by Zouhair ABH on December 11, 2011

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.

Though Gross Domestic Income grew at a higher pace starting from early 2000s, FDIs and MRE remittances made significant differences between GNI and GDI

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.

+80% of top 10% and +50% for the average - over 12 years.

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:

the wealthiest 10% households would represent no more than 131,000 - less than two variances away from the mean

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.

Generated Pareto distribution vs Empiricial distribution per deciles

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 20
Distribution_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

## Policy Proposals on Taxation, Part.2

Posted in Dismal Economics, Moroccan Politics & Economics, Morocco, Read & Heard, The Wanderer by Zouhair ABH on March 6, 2011

As it is, the bulk of government receipts is made of indirect taxes, like the VAT. And on the other hand, the subsidy expenses (that might amount to MAD 21 billion) are growing rapidly, and they too, represent a sizeable chunk of government expenses. It does look  like the government is taking away with one hand (the right one) what it has just given with the other (the left one, obviously).

Such accounting flaws are not necessarily wasteful; however, it does amount to a transfer subsidy from the less well-off to the richest. This is due to the fact that VAT and subsidy are respectively ‘egalitarian’ taxes and expenses, but when compared to their income, it is clear it benefits mainly to the well-off.

Since the 1980s, consumption share remained stable (compared to the previous 30 years)

The numbers I lay before the readers are roughly patched up, and that is mainly, if not solely, due to a lack of data: I have to reconcile data circa 2001 on consumption propensity, with Gross National Income data and Budget law circa 2009. To do so, there remains a strong assumption about stable consumption patter, which can be seen from the graph.Let us consider two types of consumers in Morocco: the lower 10% bracket, with a an average annual income of MAD 48,067.33, has a annual overall consumption of MAD 21,790 roughly 45.3% of immediate income. The upper 10% bracket, on the other hand, has an average annual income of MAD 817,144.7 (that’s about 3 Million Moroccans, with large discrepancies within this population) with an annual consumption of MAD 266,150 i.e. 32.5% of income.

Even though one might argue that richer households do not buy cheaper good (They might buy their bread from Paul bakery than the nearest l’picri) but when numbers are crunched together, the discrepancies in terms of consumption pattern differ very little. Furthermore, 2001 HCP survey of household pattern of consumption shows that food consumption is the main discriminating factor: “ni le sexe du chef de ménage ni son état matrimonial ne pourraient constituer des facteurs de différenciation quant à la part des dépenses consacrées aux dépenses alimentaires puisque ces coefficients restent, toutes modalités confondues, au voisinage de la moyenne nationale.” […] “Les dépenses d’habitation et d’énergie constituent la seconde composante du budget du ménage. Le coefficient budgétaire de ce poste n’a pas sensiblement changé en passant de 20,1% en 1985 à 21,4% en 1998 pour se situer à 22,1% en 2001.” In fact, if anything, bread and crop consumption is mainly in favour of the better off: […] Par ailleurs, la dépense [de consommation de pain] qui lui est réservée augmente en valeur avec le niveau de vie : les 20% les plus favorisés dépensent en pain acheté 11 fois plus que les 20% les moins favorisés […]au niveau national, les 20% les plus aisés réalisent une dépense par tête en pâtes alimentaires équivalents à quatre fois et demi celle des 20% les moins aisés” and these are the very products targeted for subsidy, alongside other strategic products like flour, sugar, whose consumption is either at par, or more stressed in the 10 to 20% well-off.

In addition, VAT receipts do also target blindly the less well-off, and quite effectively, all households pay indifferently between 7% and 14% of their food consumption. According to the 2009 budget, VAT and other indirect taxes receipts amounted to MAD 62.6 Billion, which exacts some 8.7% of GNI. More precisely, net VAT receipts amount to MAD 26.4 Billion, (with 94% VAT imports) this, however, is more or less squandered in subsidies, as indeed the total amount for subsidies was about 26 Billion in 2009. It does show that, not only this policy has a neutral fiscal effect on the budget, but it actual transfers purchasing power from poor to rich households.

An almost logarithmic progression of effective productivity per worker (U.Penn figures)

Can we therefore seriously discuss a subsidy lift? For the time being, it is rather a risky move, and the effects would be worse on Moroccan households. Without much details, it has to do with the relatively low productivity per worker (that partly explains why an increase in commodity prices cannot be offset with high productivity) or indeed a very low rate of effective productivity (in real terms, productivity only doubled over 50 years)

On the other hand, there is a way to allocate VAT and subsidies alike so as to support the less fortunate of Moroccan citizens. Though the proposed policy is complex (and to that matter, with no particular proven record of success). Basically, the idea is to use the income tax brackets as determinants for a consumption tax or tax credit. Since the data at hand is very crude, We shall stand by the use of averages (not to be confused with mean-testing) but if more detailed datasets were available, advanced statistical models could be of great use to determine the best way to partition household populations, and thus apply the optimal rate of consumption tax and tax breaks. Just like the proposal on introducing wealth tax, the purpose is to rebalance contributions commensurate to each individual’s wealth.

We shall us the decile partition to allocate progressive rates, so as to reduce the burden on the 10 to 20% less well-off. Under the assumption that consumption tax follows closely income distribution, not only the effective impact of taxation on the 10% less well-off will be reduced from 8.7% tp 3.2%, but it actually allows to double the VAT receipts to MAD 42.93 Billion (in case of more sophisticated statistical methods, the windfall income would be lower, but certainly larger than the initial 26 Billion receipts). The result is not only fiscally positive, but on the whole, it does not hurt overall consumption very much (save perhaps for the richest households, but their proven low marginal propensity of consumption can offset their -supposed- loss of purchasing power) and in fact provides additional revenues to sustain the Caisse de Compensation -and thus gives time to devise a new policy in targeting vulnerable populations.

An almost pure distribution of consumption tax

On the other hand, there is also the need to introduce tax breaks (and for the 5% worse-off, a food-stamps program) for the ‘squeezed middle’, i.e. those aspiring middle classes, or those on the marginal borders of taxation that wouldn’t benefit from these measures. These households remain relatively in low numbers (no more than 1.66 million individuals, about 500.000 households, when considering the lower brackets) and any total or partial tax breaks would cost less than  MAD 2 Billion. Obviously, because level of detailed figures stops at the decile level, I could not delineate precise measures for these population, but the crude figures do show a marginal cost for these tax breaks.

At the end of the day, one can conclude that, given appropriate steps and a strong political will for the policy, it is not only possible to purely suppress VAT (and, over the long run, reform the CdC) and introduce a progressive taxation system that would preserve the purchasing power of the lower classes, while not endangering public finances; Far from it, the policy brings money that could be used for productive schemes.