The Moorish Wanderer

Middle Class Tax Burden

Posted in Dismal Economics, Flash News, Moroccan Politics & Economics, Morocco by Zouhair ABH on December 6, 2012

Listening to the Head of Government from time to time is entertaining and instructive at once. Whether one likes him and his politics or not, this is representative democracy at work. But overall he started to make use of statistics to get his points across, which is a marked improvement in his argument, and he is better for it. But he is still light on policy-making however.

There is this specific claim about the middle classes, and his failure to address it -or should I say, the failure of opposition caucuses to confront him on the issue- the tax hike on higher income was a sensible move, but it was not matched with an equivalent tax cut for these middle classes. Which leads me to beg the question: was this government policy to achieve some level of fiscal equity, or was it just a move to increase fiscal receipts? These are the questions I would have liked members of parliament to ask the Head of Government.

I argue here the present tax system, with or without the tax hikes on the top income-earners, is structurally unfair to everyone with an annual income below 300.000 dirhams, and specifically to the middle class (middle class as defined mathematically to be the median income per household in a defined income distribution)

First, I use both Exponential and Log-Normal distributions to prove a couple of nice (and useful) properties; I referred earlier on to the exponential distribution as a possible way to model household income distribution. Yet it misses a particular aspect crucial to policy-making: though inter-decile ratios are not constant over time, they can be proven to be centred around the asymptotic value (notably the \ln(2) between the mathematical expectation and median) but there is little in the exponential distribution for the policy-maker to exercise their social preferences.

Log Normal vs Exponential sample distributions. The Log-normal allows for 'more' high income households.

Log Normal vs Exponential sample distributions. The Log-normal allows for ‘more’ high income households.

The Log-normal distribution is not that different, but it has the advantage (and from a computational point of view, an additional difficulty) of fielding two parameters in its probability density function. As indeed one can see in the following densities:

g(x)=\lambda e^{-\lambda x} the exponential, and

f(x)=\frac{1}{x{\sqrt{2\pi \sigma }}}e^{-\frac{(\ln x - \mu)^2}{2\sigma^2}} the log-normal

Both distributions are different in form, but not so much in sample representations. Indeed, the exponential distribution is reputed to be strictly decreasing. But it can be argued households with no income (i.e. with zero or close to zero annual income) need to be taken out of the population, perhaps because they can always rely on transferred income (or because those with no income do not form a household) in any case, the sample population used to generate the exponential distribution of income does not look like it.

second, let us consider a Taylor approximation around the median point of the proposed distribution, that is:


It computes the marginal income around the median. Marginal income is the key to understand the present taxation system – as it divides up a household income into brackets, each subjected to increasing tax rates. In essence, the derivative around the median gives a fair idea of any additional income for this population (our median class) and how it would be taxed. A ‘fair’ tax structure would minimize the marginal tax burden around the median -namely, the marginal increase in tax rate for these households. In fact, the optimal tax plan would be a flat tax rate for all the median class, because then additional gains around would not be excessively taxed. A numerical example would be that of a household with an annual taxable income of 78,000 dirhams – a relatively small 4% increase (or 3,000 dirhams) is best left taxed at the same rate (or infinitesimally the same) while the present system takes away 940 dirhams from the 3,000 increase. A marginal tax burden of 32% for a 4% increase in income is not exactly fair.

So, the derivative around the median provides a generalized result that can then be compared to the present tax system, and assuming a strictly positive marginal increase in their income, the median household would observe the following result:

f(x) = \dfrac{\partial(\left | \exp \mu \right |\sigma \sqrt{2\pi})^{-1}}{\partial \exp \mu}=\frac{\dot{\exp \mu}}{(\exp \mu) \sigma\sqrt{2\pi}}

once this is plugged back into the earlier Taylor series, the net benefit for a median household is such:

f(x) = \frac{\dot{\exp \mu}}{\sigma\sqrt{2\pi}}\times\frac{(x - \exp \mu)}{\exp \mu}

And this is a pretty neat result in many aspects: the term \frac{(x - \exp \mu)}{\exp \mu} refers to the gross benefit for a median household gaining a supplement of x dirhams. But this needs to be replaced into the perspective of the whole distribution, so it is ‘discounted’ with the impact on the median itself – that’s \dot{\exp \mu} and then weighted by the measure of inequality (or income dispersion) \sigma\sqrt{2\pi}

The impact on the general welfare can then be computed by integrating (i.e. generalizing the individual boost around all median household) around the additional x dirhams to the median:

\int_{0}^{x}(\frac{\dot{\exp \mu}}{\sigma\sqrt{2\pi}}\times\frac{(u - \exp \mu)}{\exp \mu})\mathrm{d}u with an expected welfare gain of \frac{\dot{\exp \mu}}{\sigma\sqrt{2\pi}}\left(\frac{u^2}{\exp \mu}-u \right) which can be verified for u>1 is a net gain (any additional dirham contributes to generate additional welfare, that is).

So there is good evidence that suggests the total income distribution is improved when median income increases. The impact on the average household income is not as high as one would expect (up to a \sigma^2 term) but the general welfare of all individuals close enough to the median definitely improves, and those below the median can expect over time to catch up to it. Obviously, a tax rate that does not take this effect into account might indeed stifle the described effect. And this is what we are set out to demonstrate.

My third and last step involves using logged income to emphasise the effect of tax burden on middle class. This means we are back to the useful bell-shaped curve Gauss-Laplace. The log here does not denote of any particular distribution, but indeed could depict the social preferences a policy-maker needs to display in view of the results computed earlier on: since welfare gains are highest for median households, the policy-maker needs to place a larger emphasis upon them – and the Normal distribution serves this purpose pretty well – in mathematical terms, the tangent is almost flat around the median.

Plotting the densities of tax rates and income provides no particular explanation as to the transfer effect, nor the tax burden per income. For instance, there is no particular correlation between income and their theoretical tax brackets, a strange result given the progressive tax structure in place. Additionally, a supposed preference for median income household (captured by a Normal distribution centred around the median income) contradicts the present tax structure: the average tax rate is 27%, whose corresponding income coincides with income between 60,000 and 180,000 annual income. But since there is not such rate, it has to be a convex combination of the 30% and 34% rates, with the 30% rate falling on income between 60,000 and 80,000 – our median class. The convex combination puts the weight on these households at 57%. In fact, those with income between 74,313 and 77,330 dirhams per annum pay 7% more in taxes than the immediate tax bracket (those with income marginally above 80,000 a year) just because of the present tax system. In aggregate terms, this is almost 4 Bn dirhams in deadweight loss due to the present system.

The main problem with the present tax system is its ‘jumping function’ which results in disproportionately larger tax burden for those at the margins. Unfortunately for the middle class, many of them are on the margin, the closer to 80,000 a year, the higher the tax burden. A good example can be provided for the figures mentioned before: incomes of 74,313 and 77,330 dirhams pay respectively 8,293.87 and 9,198.36. And although the difference in income is merely 4%, the richer household will pay 10% more than their immediate neighbour. In fact, this fiscal injustice reaches its peak around the median.

A 5-year Austerity Package The Government Wouldn’t Dare Think About

Posted in Dismal Economics, Flash News, Moroccan Politics & Economics, Morocco, Read & Heard by Zouhair ABH on August 14, 2012

It is plain clear now we are headed toward the end of an expansionary cycle that dates back to late 1990s. Government stimulus cannot do much about it, and we have to bite the bullet. Not only that, but the “if it ain’t broken don’t fix it” policy about Morocco’s structural problems has taken us down the dark path of debt. Austerity, as I have mentioned before several times, is necessary to pre-empt any draconian conditions if we ever fall short.

From BKAM annual report, 2011. The Compensation Fund has reached historical levels, and threatens more than just budget balances.

The austerity package, like all austerity packages -but unlike the present course of action down here- involves both sides of the balance sheet: revenue enhancement as well as expenditure. The single biggest budget problem, I would argue, has a lot to do with the subsidies: in the name of stabilising prices (and preventing social unrest) the Compensation Fund exploded in absolute and relative terms, to threatening levels to the budget and foreign trade.

Taxes: Close Loopholes, Simplify the Tax Code, Broaden the Tax Base

In effect, these principles call for a radical re-alignment of tax sources: the treasury relies too much in indirect taxes, stamp duties and other discretionary revenues, which either denotes of an institutional weakness to extract taxes where it needs to, or chooses to pick easy targets (read: the middle class) rather than confront powerful special interests. From a personal point of view, I can hardly find economic (and quantitative) argument behind allowing farmers and real-estate developers generous tax breaks, and even subsidies even as their profits are going sky-high.

This is an opportunity to assert an economic-oriented fiscal policy, instead of the daunting pile of bureaucratic regulations, with no economic justification whatsoever: why would we make individuals pays VAT on some of their subsidized consumption? And why would we keep the arcane progressive 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 evidence is overwhelmingly in favour of keeping the overall fiscal pressure constant over time, and it clearly isn’t.

a little more than 40% of total major taxes come from consumption. Guess why the Government cannot commit to a serious subsidies reform?

Let us look like at the numbers: the total fiscal receipts for the 2012 Budget is expected to be 170.67Bn MAD: that’s the total amount of taxes expected to be collected from VAT, Corporate Tax, Income Tax, Customs and miscellaneous stamp duties. To give you an idea of how much that broad measure of fiscal pressure, think of it as the Government’s share in every good and service produced in this country, and that is GDP: 21.2% of it goes into the pockets of government – and that is not enough. They borrow money too, but that’s another question. Incidentally, you can find the best evidence explaining why the past governments and the current one cannot commit to a serious reform on the subsidies system: about 40% of the main taxes come from consumption, that is a third of total fiscal receipts. this mainly VAT-funded receipt has a perverse link to the subsidies: the higher consumers buy subsidized goods, the higher VAT receipts are going to be, and the better the treasury will feel about its primary balance. A defiant reform  of the Compensation Fund would mean the instant denial of a lucrative resource to the budget.

Obviously, there is nothing wrong with the existence of a government funding itself through taxation – for those interested in the theoretical argument behind it, there are some papers worth looking into (don’t get sidetracked by the Maths, the conclusions are rocking) but, the present structure is flawed: 14.35% of these fiscal receipts are coming from discretionary taxes. So the main course is the so-called distortionary taxes, i.e. those who affect the behaviour of all agents, consumers or businesses: VAT, Corporate and Income Taxes. The optimal fiscal policy is actually far simpler than the arcane tax code we currently have: we first look at the contributions of each aggregate component to GDP, then produce at a long-term rate the respective average rates for labour, taxes and consumption; We know for instance that Capital relative contribution to wealth creation (that is, GDP) ranges between 33.5% and 32.7%, while that of Labour captures the remaining to 67% to 66.5% (the odd discrepancies, around 0.16% is left to technological progress) – assuming a long-term average maximum fiscal pressure of 19.2%, total primary fiscal receipts should be around 151Bn dirhams (against the current 123Bn for the 2012 Budget) with Consumption and Income Tax accounting for 96Bn and Corporate/Capital tax for the remaining 54Bn. These are moderate tax increases considering the present levels, but then again, the effective tax rate on the capital stock is less than 2.6%, and total taxes on the labour force around 11% (consumption and production). Why so? First, these discrepancies belie the unequal distribution in both income and consumption, and second, Morocco is a developing country, so the effect of taxation on low capital stock per capita (181,759dhs) can hamper growth. Note that I referred to the capital stock, and not its distributed dividend. Taxes on labour and consumption are further split into respective 48Bn – an effective tax rate per household of 7% (recall the pure income tax from an earlier post) and 11% per household consumption (that new consumption rate I might post something about).

Based on a pessimistic 4.3% annual growth (average growth since 1999) all the way up to 2022, this should be the expected level of fiscal receipts from the proposed tax system.

All in all, without boring you with the details, this fiscal revamping should be a net tax cut of 12Bn, down from 171Bn to 159Bn(we make room for various discretionary taxes worth 1% of GDP) what is more, the broader definition of fiscal pressure is brought down below 20% of GDP, the closest I can get to the Hauser ceiling.

These computations are based on the aggregate number of households, including the agricultural sector – this reform effectively ends the subsidy where fewer than 15% wealthy farmers benefit from a tax break on potentially as much as 90Bn worth of agricultural products. In the process, fiscal equality rewards other sectors and agents by cutting their taxes and/or simplifying them. Finally, I would like to point out these figures are computed on the basis of a 4.3% annual GDP growth with historical volatility, which means the uncertainty factor has already been taken into account.

Expenditure: Freeze, Cuts and Postponements

This is always the least popular item in the austerity package (as if austerity wasn’t already a killjoy), especially when there are talks of cuts to public service pay-wage and related items. And if any serious fiscal consolidation were to take place, it will do something about the 94Bn expenditure on human resources, especially the higher echelon.

Though cutting expenditure is not on the table, it would be interesting to see how a freeze on half the civil service – and a 2% annual increase for the lower echelon. Let us not forget that for the last couple of years, the average annual salary was 192.000dhs per annum, i.e. 65% more than the average annual income per household, and about 3 times more than the median income per household. If anything, the average income where at least one breadwinner is working with the civil service could be earning more than 83% of all the households in Morocco. Fairness dictates some of these civil servants need to see their taxpayer-funded salaries trimmed a bit.

The other juggernaut is the Compensation Fund: never, since the early 1980s, has household consumption been so heavily subsidized, and yet the large gap in consumption and standard of living creeps in, stronger than ever. A complete overhaul of the fund will have an initial negative effect on household consumption, but then again, it should not last no less than 10 quarters (based on domestic exogenous shocks) or 15 quarters if exogenous effects from foreign trade are taken into account; this means any unpopular reform needs to be undertaken at the very first year, until the negative effects eventually die away before election season. My plan subsidizes about 20% of the median consumption basket to the benefit of 60% Moroccan households, costs in 2012 about 25Bn and is indexed to household consumption growth. The poorest 10% receive an annual cash relief between 7,200 and 9,500 dirhams. Incidentally, it cuts subsidies twice its current budget and insures strategy-proof allocation of subsidies to those who genuinely need it, and does not harm middle class standards of living.

The Debt, Rates and PSBR

This whole austerity problem is not out there to serve a sinister right-wing dogma: our fiscal house was quite in order for the past decade, and yet we did not bother to push for continuous reforms; instead, the past government chose an unnecessary large tax cut (from 4 to 7Bn in 2007-2008) to the wealthiest while nothing was done to close loopholes and tax breaks for the privileged few. Obviously, these tax cuts and preferential treatment were funded by increasing public service borrowings: it went from 51Bn in 2007, to 65.7Bn in 2012, and that number can be expected to increase even further.

What the government fails to understand -and so would Paleo-Keynesians in the process- is that public borrowings are crowding out small businesses and individuals; this is even more perverse as these small companies in business with public service procurements are punished twice: the budget pays at later terms, and takes away the existing liquidities from M3. Big business is secured in its day-to-day financing; it is the small guy who takes the fall for the growing public debt.

Accordingly, there is a need to introduce a ‘debt ceiling’ mechanism, where over-borrowing is subject to a floor vote in Parliament, and conditioned by commitment on behalf of ministerial departments to cut or freeze spending over the same period of time the newly issued debt matures; for instance, a 5-year treasury bond has to be matched with spending cuts/freezes whose effect is likely to last 5 years as well. In this particular example, The expected borrowings cannot go beyond 5% of M3, or 47Bn in 2012.

Bottom Line: What Will You Bring Us, Mr Moorish?

Blood, Toil, Tears and Sweat. Well, almost. Unfortunately, making the deficit disappear while fighting government debt is mission impossible; if anything, there will be a large deficit in 2012 (about 7% of GDP) but that gradually disappears, with the first surplus reached by 2020. If anything, the effects of this 5-year austerity plan show around 2018, too late for the 2016 general elections. On the other hand the size of government relative to GDP would have shrunk from the current 44% to 25% by 2021, with all public services and welfare mechanisms in place. The deficit for 2012, projected to be 55Bn, would gradually go down until it reaches 20Bn surplus – or 12Bn if 8Bn dividends are not taken into account. We would however left by then the danger debt zone, with projected overall public debt ratio of 50% by mid 2014 to 2015, not to mention a robust 3% growth in public investment.

“The path Of Prosperity” vs “The Light at the End of the Tunnel”

If anything, the Moroccan economy would look at lot healthier by 2018: lighter, better and fairer government touch, lower tax burdens, lower rates and sustainable deficits and public debt. As always, any of these reform proposals assumes incredible courage among our elected officials, and a sheer willingness to take on special interest, lobbies and established rents. And most of all, an unwavering sense of social justice, because fiscal consolidation, whatever its initial motive, tends to fall harder on the weak, and treat harshly the middle class.

Only a keen interest in keeping suffering at the lowest possible level can bring about the broadest consensus around austerity; for this like so many other policies, a sense of purpose is needed, and carried by committed responsible politicians.

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:

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
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
#Sample as previous: 1/1000 of total number of Households
I_Exp<-rexp(n, rate = 1/114420)
quantile(I_Exp, probs = c(0.01,0.99,0.90, 0.25,0.5, 0.1, 0.05))
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.