The Moorish Wanderer

Pure Income Tax: a Rate for Everyone

Posted in Dismal Economics, Moroccan Politics & Economics, Morocco, Polfiction, Read & Heard by Zouhair ABH on March 23, 2012

I suspect lawyers got the better of economists when it comes to the proper rates that apply to Income Tax rates. income brackets are determined somewhat arbitrarily -I haven’t come across any MINEFI stating otherwise yet- and all exemptions, tax breaks, loopholes and other regulations are yet to prove their usefulness, both as a policy instrument and as an incentive to influence taxpayers’ behaviour.

As it stands now, Income tax represents 3.8% of total GNI; roughly speaking, that means every household in Morocco pays some 4.440 dirhams in taxes – which is quite absurd, since a lot of these do not pay it actually, and another bunch is getting away with it; while it is understood the poorer 10% do not pay income tax due to their very low average annual income – some 25,172 dirhams, the wealthiest 10% earn an average of 427,931 dirhams per annum. So in effect, the real average tax payment is closer to 3.97% or 5,000 dirhams per household. But even that amount of money is phony; how can one explain the high discrepancy in the 38% marginal rate, the average 3.97% and the real marginal rate of 1.16%?

The is simple: there is an incredible inequality in household income distribution, and the present tax system is intrinsically unfair, as it lays a heavier burden on the middle/median incomes relative to the higher ones, and finally, there are many wealthier individuals with Agricultural Business whose taxes are negative, i.e. subsidized in their income. Indeed, the present tax code presents (urban) taxpayers with the following rates:

<30,000 per annum: ……………exempted
[30,001 ; 50,000] per annum: ………..10%
[50,001 ; 60,000] per annum: ………..20%
[60,001 ; 80,000] per annum: ………..30%
[80,001 ; 180,000] per annum: ………34%
>180,000 per annum: ………………….38%

which does not compute with income distribution, since the actual IR rates tend to hit the middle class harder – and by middle class I mean the 75,500 dirhams these households earn annually, and many of these cannot get away with the various loopholes and breaks the tax code allows for, thus creating an actual tax break for the 38% marginal rate.

Is it possible to provide an alternative tax system then? Sure. It would have the advantage of being simple, progressive and easier to carry out, because rates would adjust themselves automatically. There is one little caveat though: the statistical evidence from income distribution has to be solid and significant. Since I do not have access to the detail, I would venture some results based on the public data HCP released regarding income distribution in 2009.

Let me first start with some doodling with some simple assumptions – just to get my point across. Let’s assume income distribution is normally distributed with the present mean 114,420 dirhams, and (sampled) deviation of 1,474. Computations are therefore easier to run with custom tax rates: depending on how far a household’s income falls from the average 114,420, they have to pay a commensurate tax rate computed with the same normal distribution; since the average income rate households in Morocco below the median threshold are supposed to pay is 7%, then we can match Normal income distribution N(114,420 ; 1,474) with an equivalent Normal income tax distribution N(7 ; 1) in this simple setting, the wealthier 1% with an income of 117,850 dirhams and above would pay at least 9.3% income tax, while the middles classes, those close to the average 114,420 dirhams would pay no more than 6.9%. Under this scheme, and following this income distribution, tax receipts would increase from existing 28.96 Bn dirhams to 46.82 Bn dirhams, with an overall income fiscal pressure of 6.3% of total Gross National Income. and we still get to exempt the poorest 651.600 households from income taxes. The windfall profit from the scheme is essentially motivated by the fact that income and tax distributions have been matched with the same random parameters, hence insuring perfect fairness in taxation, cutting red tape and making sure every individual has a clear understanding of the tax system.

Application: under this scheme, a household earning 111,000 dirhams would have to pay 4.68%  income tax, such:

w_{t}\pm \alpha_{t}\sigma=114,420

and thus using the level of confidence to compute the custom income rate:
t_{p}=7\%\pm\alpha_{t}

another household earning 117,000 would thus pay a 8.75% income tax rate. Simple, quick and easy to implement. In each case, households with comparative incomes would pay respectively 5,194 and 10,237 dirhams, which is still far below the respective taxes of 20,540 and 22,580 dirhams they would have to pay under the present tax code.

#Income Distribution 
#Phase 1: assume Income follows Normal Distribution
#Sample 1/1000 of total number of Households - HCP Census
n<-6516
I_M<-rnorm(n, mean=114420, sd= 1474)
hist(I_M, prob=TRUE)
quantile(I_M, probs = c(0.01,0.99,0.95, 0.25,0.5, 0.1, 0.05))
Tax_Norm<-rnorm(n, mean=0.07, sd=0.01)
quantile(Tax_Norm, probs = c(0.01,0.99,0.95, 0.25,0.5, 0.1, 0.05))

But we do not live in a Gauss-Laplace world; there are such high income inequalities that mean and median household income in Morocco are at a 2:1 ratio, yet another indicator of the disparities. As a matter of fact, I did point out -in a rather hurried manner- that the best estimate for income distribution across Moroccan households is the well-known Pareto distribution. I will try to provide a correct estimator this time, and from then on apply the proposed tax policy instrument;

Cumulative share of decile households (HCP)

How do we know income distribution in Morocco is indeed a Pareto distribution? Well, the first item to look at is the cumulative distribution function built from the published data; the graph gives compelling evidence that indeed income distribution is Pareto – which is not great news since it means high discrepancies in income across households, and subsequently unfair tax brackets embedded in the tax code.

The object of interest here is indeed income share per decile, and the basic idea is to match it up continuously with custom tax rates, hence eliminating tax brackets and all loopholes to the benefits of all: government receipts increase, and a pure tax rate ‘discrimination’ (discrimination in the sense that every individual has only to pay its own, intrinsic tax rate) allows for a lower tax burden compared to the present tax system. Everybody gains from it. Luckily enough, there is little to estimate; what is more, the properties of the Exponential distribution allow for some computations to run smoothly;

since we are considering a 1/1000 sample, the maximum income in this case is 1.18 Million dirhams – the richest household in this sample, so to speak. We check easily that the minimum income earned at the 1% level is 520,600 dirhams, while the median sample is 79,500 dirhams – which in line with the real-life data (75,500 dirhams)

The next batch of computations is pretty straightforward, we need income tax rates to match income distribution with its own Exponential distribution, and so:

#Phase 2: generation Exponential Income distribution
n<-6516
#Sample as previous: 1/1000 of total number of Households
I_Exp<-rexp(n, rate = 1/114420)
summary(I_Exp)
quantile(I_Exp, probs = c(0.01,0.99,0.90, 0.25,0.5, 0.1, 0.05))
Tax_Exp<-rexp(n,rate=1/7)
summary(Tax_Exp)
quantile(Tax_Exp, probs = c(0.01,0.99,0.90, 0.25,0.5, 0.1, 0.05))

And so we end up with interesting results: the richest 1% have to pay some 31.47% income tax – which is still below the nominal existing rate, and the median rate 4.73% for those earning around 79,500 per annum. The same computations apply equally to different incomes: for a household earning 86,000 dirhams, the custom rate would be 5.72%. All you have to do is look at the probability value at which household income wt lies, then match it up with the corresponding rate – with perhaps an exemption for the bottom 10%. Households below 420,000 dhs income would benefit from this scheme: median income households of 75,500 dirhams would pay about 4,873 dirhams compared to the 10,325 dirhams they would pay under the present tax system. As a matter of fact, even households earning 173,918 dirhams would pay 10.91%, i.e. 18,978 dhs which is still below 41,900dhs they would pay under the existing tax code.

Again, receipts from the new tax system under this scheme would top the existing receipts to 46.4Bn dirhams, way more than the, again, existing 28.96Bn, with no prejudice to the overall fiscal pressure relative to GDP or GNI.

the boost in fiscal receipts is mainly due to the tax discrimination effect described above – and the elimination of a host of loopholes and tax breaks do contribute as well.

4 Responses

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  1. […] Since the idea of fairness is very subjective, and finds ideological interpretations in the field of policy-making, I would argue the most obvious quantitative implication of my idea of fairness is based on the statistical distribution of the considered aggregate: for instance, if you income falls close to the median or the average, you should pay an income tax with a commensurate rate; same goes for consumption or property value. Ideally, you would pay specific rates on specific items according to a pre-established, economically-justified rule. That means, in essence, that VAT should be scrapped, income tax has to be reformed, and no one has to pay stamp duties – the ideal system would be to increase fiscal receipts and at the same time cut the effective tax burden by spreading the tax base, and there is evidence it can be achieved. […]

  2. […] 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. […]

  3. […] taxation system (designed some 150 years ago when Teddy Roosevelt was President) when we have much more sophisticated (and simpler) taxation systems? Not to mention the chaotic fiscal structure: the academic body of […]

  4. […] the size and cost of the civil service payroll. They would cheer the introduction of a de facto wealth tax on the rich, yet express scepticism to the idea of tax cuts to corporations. Strangely enough, the voices of […]


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