Summary of the solution to the current mass unemployment in the OECD area
An analysis using example data on Holland 1950-1998
September 3 1997
This review summarises key aspects, such as:
A summary remains a summary. The last sections link to more extensive discussions
on the world wide web.
heterogeneous labour, and the use of an earnings distribution
the minimum wage and unemployment
decomposition of the minimum wage in subsistence and tax burden
analysis of the Tax Void
differential indexation and its consequences
dynamic marginal tax rates
The earnings distribution
The following graph gives an earnings distribution of a standard shape.
With each level of earnings (income) there is a number of persons who earn
that level. The density is best measured in '(million) personyears'. The
graph approximates the situation in Holland 1997, though without parttimers.
The horizontal axis gives earnings in Dfl thousands; and a 1997 guilder
is about $0.5.
Graph 1: Earnings distribution
The earnings distribution can be used to compute how large unemployment
will be below the minimum wage. Graph 2 gives the situation for the Dutch
minimum wage of about Dfl 36 thousand. Conforming to the facts, Dutch unemployment
is about 25% of a potential labour force of 8 million people. Note 1: not
all unemployment is caused by the minimum wage. Note 2: Dutch official
statistics grossly underestimate unemployment, and reduce the labour force.
Graph 2: Unemployment below the minimum wage
Analysing the minimum wage
We wonder how the minimum wage comes about. We see two terms in the minimum
M = B + Tax[M]
Tax[w] = r (w - x)
NetIncome[w] = w - Tax[w]
M = minimum wage
Graph 3 gives the net income plot. The horizontal axis gives income, the
vertical axis net income. The tax is given by the difference between net
income and the 45-degrees line. The graph is drawn for Holland, where the
tax includes social premiums. Basic net income in Holland is about Dfl
21 thousand per annum.
B = basic net income
w = an arbitrary wage
r = marginal rate
x = exemption
The basic net income requirement is included in the graph by a horizontal
line at B. The intersection of the B-line and the net income line gives
the minimum wage M. You must earn at least M to satisfy the minimum net
income requirement B.
Graph 3: Net income plot
Graph 4 gives the same result, but then as a tax plot. The horizontal
axis gives income, the vertical axis the tax. Net income is now given by
the difference between the tax and the 45-degrees line.
The minimum net income requirement now gives a B-line parallel to the
45-degrees line. You can see that it takes a part of net income that can
be found above the tax line. Now it is the intersection of the B-line and
the tax line that gives the minimum wage M. You must earn at least M to
satisfy the minimum net income requirement B.
Graph 4: Tax plot
The Tax Void
Let us now combine the earnings distribution and the tax plot.
Note that the tax graphs have coloured areas only above the minimum
wage. Though taxes are defined below the minimum wage, there are no taxes
collected, since people are unemployed below the minimum wage. The colourless
area from exemption till the minimum wage can be called the Tax Void.
In the Tax Void the tax code has only a paper function. The tax
code helps to drive up the minimum wage, but it does not collect any revenue.
Abolishing taxes in this area, therefor, does not cost anything too. Note
that abolishing the tax void would mean that exemption would be chosen
at the value of basic net minimum.
Within the unemployment below the minimum wage, we find a section that
is still above the basic net minimum. This section has the property that
if taxes would be abolished, then people could still earn a living wage,
and need no income support. This kind of unemployment can be called the
Tax Void Unemployment. Graph 5 gives a plot of that section for Holland.
Graph 5: Tax Void Unemployment
For the record: the Dutch minimum wage only holds for fulltimers, and
not for parttimers. Holland has a lot of parttime work (for that reason).
We have eliminated parttimers from the present analysis.
Cause of the Tax Void
How has the tax void come about ? Since abolishing the tax void does not
cost anything, and would generate a lot of employment, why don't we abolish
it ? Why do we continue the present absurd situation of mass unemployment
It appears that the situation has come about gradually, by a mechanism
that is difficult to observe directly. It involves the co-ordination of
tax policy with social policy, specifically the indexation of taxes and
As is common in OECD countries, tax parameters are indexed on inflation
only. This is important for exemption x:
x = S pi
Tax[w, x] = r (w - x)
Tax[w, S pi] = r (w - S pi)
r = marginal rate
pi = price index
S = subsistence at the base year, when pi = 1, so that exemption =
The indexation of subsistence differs from other incomes. When incomes
follow an index wi, subsistence commonly follows net average income, i.e.
income after taxes.
AverageEarnings = a = A wi = A rwi pi
Subsistence = B = S rsi pi
wi = wage index
It turns out that rsi = rsi[rwi, r, S / A].
rwi = real wage index = wi / pi
rsi = real net average income index
A = average income in the base year
S = subsistence in the base year
Deduction of the real subsistence index
Let A be the average gross wage in the base year, and let h = S / A be
the ratio with subsistence. In the following definitions, we take defaults
r = 50% and h = .5.
Note that we better write the tax function as Tax[w, x] and net income
as NetIncome[w, x]. Then the index of the real net average wage is:
NetIncome[a, x] / pi
rsi = ----------------------------
(a - Tax[a, x]) / pi
rsi = ----------------------------
(A - Tax[A, S])
rwi A - r (pi rwi A - S pi) / pi
rsi = -------------------------------------
(A - r (A - S))
with S -> A h:
rwi A - r ( rwi A - A h )
rsi = ---------------------------------
(A - r (A - A h))
rwi - r ( rwi - h )
rsi[rwi, r, h] = ----------------------------
1 - r (1 - h)
By consequence, we only need data on rwi, r and h to proceed. As said,
we will take r = h = .5. Then we need data on rwi. For this, we again turn
to our example Holland.
Data on the Dutch economy
Year % change index 1950=100
pi, wi pi, wi
1950 8.7 - 100 100
1951 11.1 10.4 111 110
1952 0.3 5.4 111 116
1953 -0.7 4.2 111 121
1954 4. 9.2 115 132
1955 1.7 8.9 117 144
1956 2.1 8.6 119 157
1957 5.5 10.8 126 174
1958 1.6 4.4 128 181
1959 1.2 2.4 130 185
1960 2.3 8.2 133 201
1961 2.1 7.2 135 215
1962 2.6 5.9 139 228
1963 3.8 9. 144 248
1964 6.5 14.9 154 285
1965 3.6 11.1 159 317
1966 5.3 11. 168 352
1967 2.9 8.8 172 383
1968 2.5 8.9 177 417
1969 6.2 13.4 187 473
1970 4.4 12.8 196 533
1971 7.9 13.6 211 605
1972 8.3 12.6 229 682
1973 8.5 15.8 248 789
1974 9.5 15.6 272 912
1975 10.1 12.8 299 1029
1976 9. 10.9 326 1142
1977 6.1 8.7 346 1241
1978 4.5 7.2 362 1331
1979 4.3 6.1 377 1412
1980 6.9 6.1 403 1498
1981 6.3 4.2 429 1560
1982 5.3 6.3 452 1659
1983 2.8 3.8 464 1722
1984 2.1 0.5 474 1731
1985 2.2 1.8 484 1763
1986 0.2 2.1 486 1799
1987 -0.2 1.4 485 1825
1988 0.6 1.1 488 1846
1989 1.6 0.8 495 1860
1990 2.5 3. 508 1916
1991 3.1 4.4 523 2000
1992 3.2 4.1 540 2082
1993 2.6 2.9 554 2142
1994 2.7 2.4 569 2194
1995 2. 1.3 580 2222
1996 2.1 0.5 593 2233
1997 2.8 2.5 609 2289
1998 2. 3. 621 2358
Graphical presentation of the Dutch data
Before we use the Dutch data for our analysis, let us first see what they
mean. We note:
In the last period inflation continues while real wages stagnate (causing
the Dutch export surplus).
1950-1970: low inflation and high real growth
1970-1982: high inflation and turbulent real growth
1983-now: reduced inflation and stagnating growth
Graph 6: Continued inflation, stagnating real wage
1950 = 1
Graph 7 gives the same data, but in a different format.
Graph 7: Inflation plotted against the real wage
1950 = 1
Using the data for our analysis
We now use the data for our analysis. We had deduced above: rwi -> rsi
-> B -> M, where:
rwi = real wage index
For Holland, 1950 exemption can be taken as 1950 subsistence. Also, exemption
in Holland in 1950 was about Dfl 1000, so the indices relate easily to
Dfl thousand values.
rsi = real subsistence index = real net minimum index
B = base net income = nominal net minimum
M = minimum wage = nominal gross minimum
We find that real subsistence has risen about 3-fold since 1950, and
the nominal gross minimum about 30-fold. The computed nominal gross minimum
of '30' relates well to the factual 1997 minimum wage of about Dfl 36 thousand.
Not only inflation accounts for the rise, but also an increased tax burden
(that encouters inflation again).
Graph 8: Different indices for the minimum wage
1950 = 1
It was the slow rise of subsistence B and the lagging of exemption x
in the 1950-1975 period that caused a multiplied rise of M, creating the
Tax Void. Also, since the Earnings distribution is nonlinear, there was
a nonlinear increase in unemployment.
Graph 8 shows that the real values stagnate since about 1980, and that
the development since then is determined by inflation. Since inflation
does not occur in the rsi index, the real situation is stable. For example,
the gross to net ratio at the minimum since 1980 is quite constant. Note
too that this in a sense presents a difficulty. The problem with the minimum
wage was caused before 1980, and policy makers wanting a solution in 1997
will rather look at the last decennium rather than to the 1950-1975 period.
A provoking question
To better grasp the analysis, we might as well ask a provoking question.
If this differential indexation continues (taxes adjusted for inflation,
real net minimum adjusted for net average income), when will your current
income become the new minimum wage ? Let us assume the 1997 subsistence
of Dfl 21 thousand, a real growth of 2% per annum and stable prices (to
compare real values). When your income is Dfl 100 thousand, then it will
take only till 2060 before your income becomes the new minimum wage. In
real terms, indeed. Graph 9 gives results for more income levels.
Graph 9: In what year is my income the minimum wage ?
Marginal tax rate & VAT
The analysis can be extended with an analysis on marginal tax rates. For
clarity: in above tax function, r is the (static) marginal tax rate.
Many economists hold that a high marginal tax rate is a disincentive
for labour effort. They frequently propose a change from the income tax
to the Value Added Tax (VAT). The VAT has no exemption, and, assuming the
same total tax revenue, thus might allow for a lower marginal tax rate.
Above analysis already exposes one flaw to that argument. Having no
exemption means a higher gross minimum wage ! So, those tax theorists who
propose a shift from income tax to VAT actually neglect labour market economics,
as they have been doing for the last 40 years. Graph 10 shows the development
of the relative revenue shares of Dutch income tax and VAT for the years
1975, 1980, 1985, 1990 and 1997. The minimum wage problem has worsened
also by this development.
Graph 10: Revenue shares of income tax and VAT
Marginal tax rate & dynamics
I do agree with the basic idea about the disincentive effects of marginal
tax rates. For, economic theory assumes maximising agents, and a maximum
can normally be expressed in terms of marginals. However, the marginal
must be computed correctly. Above marginal rate r is only a static rate,
that applies to a specific regime. However, tax rates are adjusted from
year to year. This needs an analysis on the dynamic marginal tax
Let /\ stand for the delta sign, so that /\w
= w - w(-1). Then the proper (dynamic) marginal tax rate is /\Tax
/ /\w. For above tax function:
Tax[w, x] - Tax[w(-1), x(-1)]
Dynamic Marginal = --------------------------------------
w - w(-1)
Generally the dynamic marginal is lower than the static marginal. In fact,
when tax parameters are indexed in a certain way, then the tax can have
the same growth rate as income, and then the dynamic marginal rate equals
the average tax rate:
balanced growth rate = /\Tax / Tax = /\w
/\Tax / /\w = Tax / w
In general, when personal income is expected to grow by rate g, so that
w(+1) = (1 + g) w, and when exemption is expected to be adjusted by rate
h, so that x(+1) = (1 + h) x, then we find:
Tax[(g + 1) w, (h + 1) x] - Tax[w, x]
ExpectedDynMarg[w, g, x, h] = ---------------------------------------
(g + 1) w - w
Which for our tax function simplifies to:
r (1 - -----)
Let us regard the dynamic marginal under a regime of sound economics. In
the ideal case, exemption in the base year is put at subsistence, in this
case Dfl 21 thousand. Ideally, subsistence rises with national income,
and not just real net average incomes. This ideal implies that exemption
is adjusted not just for inflation, but for the nominal growth of national
income. Let us assume this ideal, and let us assume that nominal growth
is 4%, consisting of 2% inflation and 2% real growth. Let us then regard
the situation of a single economic agent. He knows that next year exemption
will be adjusted with 4%. He has to judge whether it is worthwhile to him
to invest or to increase labour effort, so that his income will rise. If
his income rises with 4%, then his dynamic marginal will be equal to his
present average tax rate. If his income rises by 8%, then his dynamic marginal
will depend upon his actual income level, but anyway will be less than
the statutory marginal rate of 50%. Graph 11 gives the plot of the dynamic
marginal for those two rates, for various levels of income
Graph 11: The dynamic marginal rate
Individual income grows at 4% or 8%, while national income grows at 4%
and the statutory marginal rate is 50%
Empirical analysis often shows marginal rates to be less relevant -
and average tax rates to be more important - than 'common theory' claims.
This analysis on the dynamic marginal explains this.
Spillover and domino effects
Above analysis concerns a specific type of unemployment, i.e. minimum wage
unemployment. The next question is how this relates to other kinds of unemployment.
It is useful to observe that the analysis in these pages is new. Concepts
like the tax void, differential indexation and dynamic marginal tax rates,
and the insights on their interaction, are really new, and have been concocted
by me in a search for new scientific results. That means that governments
have not incorporated these concepts in their policy making. Policy making
up to now has been based upon a different analysis, and, alas, by being
different from the right analysis, the governmental analysis is a wrong
one. This is not without consequence. By analogy, when a patient gets a
medicine based on a wrong diagnosis then the illness may get worse rather
than diminish. In the present case, the tax void unemployment has important
spillover or domino effects on unemployment above the minimum wage, and
the channel of transmission is the misguided policy reaction up to now.
For example, in the 1970s governments tried to stimulate the economy
by incurring big deficits, but they ended up with inflation. In the 1980s
and 1990s governments opt for low inflation, and they end up with high
real rates of interests and mass unemployment in Europe and poverty in
the United States. (Note that poverty reduces real employment chances,
in a way not all too dissimilar from a minimum wage floor.)
For example, Dutch economic policy is based on a general restraint on
wages. This policy has fueled Dutch exports and reduced Dutch imports,
witness above data and the graphs on real Dutch income. The general restraint
in fact subsidises exports, and Holland runs an external surplus for quite
some years now. The proper policy reaction however would be a wage cost
policy targetted at heterogeneous labour.
Governments currently regard minimum wage unemployment as just one type
of unemployment, and not even the most important type. It is often conjectured
that globalisation is more important, which is a cause external to the
economy. The policy reaction is to reduce taxes for higher incomes, so
that they are encouraged to work and spend more, and so that labour market
flexibility can be increased. The reduction of taxes for the higher incomes
obviously is financed by a reduction of provisions for the lower incomes,
aggravating the minimum wage and poverty problems.
Note, though, that 'globalisation' is an overrated, misunderstood and
abused concept. Paul Krugman has already explained this eloquently.
Secondly, you do not need to reduce taxes on the higher incomes. If
you reduce the tax void, then many low income jobs will be generated, and
the higher incomes will benefit from the services provided. Higher incomes
will see an increased purchasing power of their incomes.
So there are important spillover and domino effects from the current
policy mismatch. Governments presently have a wrong diagnosis on unemployment,
and have a policy reaction that actually worsens the situation.
Diagnosis and Therapy
Please note that the present discussion only gives a diagnosis, and that
it is a different affair to find the proper therapy.
In the course of some years I have experienced that discussing therapy
is useless when people do not even understand the diagnosis. For example,
mr. Wim Kok, the recent leader of the European Union and Dutch Prime Minister,
laughed loudly when I suggested to raise Dutch tax exemption from the current
Dfl 7 thousand to Dfl 21 thousand. He must have thought of staggering costs,
and it didn't help when I said that it need not cost anything. Similarly,
the Dutch Finance Secretary mr. Willem Vermeend has his eyes fixed on a
change from the income tax to the VAT, and his mind is not open to contrary
So my exposition stops here, and I'll wait for signs of understanding.
But let me remark about therapy that, to undo the damage of the last
four decades, it is not necessary to take four new decades. Return to optimality
can be much and much faster.
The extensive analysis on the Internet
Of course, the tax-wage-inflation-unemployment relationships are more complex
than stated in this summary. But the nutshell analysis given here remains
convincing, especially when confronted with those other complexities. For
the extensive analysis, you can find the following elements on the World
For the record: Most of these papers (a) have been accepted for presentation
at Dutch research conferences, (b) have some counterpart in a publication
in Dutch, (c) but have been rejected for publication, with quite silly
reasons, by the journals 'Economics Letters', 'De Economist', the 'European
Economic Review' and 'Public Choice'.
Solved ! A breakthrough in economics, ewp-get/9604002:
My renewed short announcement to the economic community and a larger
audience that the current mass unemployment has been solved analytically.
Solved: An answer to Krugman, Phelps, Ormerod and Heilbroner, ewp-get/9704002:
This shows how the present analysis answers questions posed by the
structure, inflation and unemployment, ewp-mac/9508002 (or html
This paper gives a structural analysis. It shows how the Phillipscurve
shifts as a consequence of a rising minimum wage. Reduced competition on
the labour market causes rising wage claims. Policy makers have reacted
within the Keynes-to-Friedman framework, with homogeneous labour and either
low or high rates of interest, and have neglected the problems caused by
impact of the minimum wage on exposed and sheltered sectors, ewp-get/9608001:
This shows how the present analysis on the internal imbalance can be
extended to explain external imbalance. Actually, the whole analysis started
a dead wrong OECD tax policy causes mass unemployment, ewp-mac/9508003:
This is an exposition using Mathematica. It overlaps for 50%
with this current HTML exposition. Not included are the density graphs;
but included is an estimation and counterfactual analysis (How rich we
could have been!) not shown here.
the political economy of employment in the welfare state, ewp-mac/9509001:
This is mathematical economics. The paper gives a general theorem and
proof for the reduced form of any model containing key macro-economic variables.
A second theorem and proof explains why the co-ordination problem can cause
labour supply: A suggestion, ewp-lab/9509001:
This elaborates on the earnings distribution.
institutional explanation of stuctural unemployment of low income labour,
Presentation for the 7th Research Day of the Social Sciences, Amsterdam,
April 11 & 12 1996, ewp-oth/9605001:
This tries to develop an empirically warranted theory of stagnation
in policy co-ordination, using results of social psychology. (Thus the
structural form, and not the reduced form.)
curvature of the tax wedge, ewp-pe/9604001:
This extends on the effects of differential indexation. One of the
points not discussed above is the squeezing of income differences.
constitutional amendment for an Economic Supreme Court, ewp-get/9604003:
The stagnation in economic co-ordination can be traced to a weakness
in the Trias Politica constitutions of Western democracies. This paper
identifies the problem and advances a suggestion for solving it.
Russia to help itself, ewp-get/9604004:
Well, Russia suffers serious economic problems, and there is a way
out, not costing the West any money.
the nature and significance of a free lunch, ewp-get/9607003:
Many economists argue that there are no free lunches. But above analysis
gives a solution to unemployment that does not cost anything. So, some
explanation might be needed.
solution to Arrow's difficulty in social welfare, ewp-get/9707001:
One of the reasons why co-ordination may stagnate, is that many economists
misunderstand Kenneth Arrow's result.
programs written in Mathematica, ewp-prog/9508001:
Discusses my Mathematica programs, many of which were used to
develop this analysis. See also my home
dynamic marginal tax rate, ewp-get/9708002:
Explains in more depth that in order to compute marginal tax rates
correctly, you have to include changes in the tax parameters over time.
Since agents expect such changes, their proper marginal tax rate is lower
than the statutory rate(s).
Though the former section shows that I have done a lot of work already,
my time is limited, and much can still be done. Some points are:
You might do wise to buy stock in companies that would specifically benefit
from the new low wage employment. But stock in general would be a safe
bet anyhow, provided that governments get to understand the analysis.
use factual exemptions and minimum wages instead of above computed values
extend the analysis to other countries. Note that I asked the OECD for
information, and that they said, a bit to my surprise but fitting with
my observation on the policy neglect, that they didn't have the data. Note
that my analysis uses differential indexation only, and that this is warranted
by the literature that does exist
test the aspects of the dynamic marginal, not only in time series but also
in experimental situations
check on what employment could be generated
adapt current macro-economic models, and investigate the effects on the
whole economy, and, of course, the world economy
revitalise the economics of full employment. Develop the repercussions
on economics and politics, e.g. on the stability of EMU, on exchange rates,
developing countries, etcetera.
I explain since the end of 1989 that the current mass unemployment in the
OECD area has been solved analytically. For the record: I have informed
all Dutch political parties of my analysis, and also have sent a letter
and paper to the European parliament. There was no reaction. I am a bit
amazed by the little response that I receive. Of course, an important component
of my analysis concerns the explanation of stagnation in macro-economic
policy co-ordination, so I am just a bit and not very surprised.
I still would enjoy serious attention. On the human side: many people
needlessly suffer from unemployment. On the personal side: I do not have
the time and resources to spend on economics as much as I would enjoy to
The following is a sad complication. Above date of 1989 didn't come
about by coincidence. Note that I've worked at the Dutch Central Planning
Bureau (CPB) in the 1982-1991 period. (The CPB is the Dutch counterpart
to the US Council of Economic Advisors.) Some fundamental insights had
been developed at that bureau, notably by colleagues Van Schaaijk and Bakhoven,
but these notions had no consequences on official publications. In 1989
I was involved in the CPB study "Netherlands in triplo" and "Scanning the
future" (published in 1992), and in 1989 the Berlin Wall fell. It was obvious
that continued unemployment in Western Europe would be detrimental to economic
recovery in the East, and this suddenly made unemployment much more important
than it had been before. So in November 1989 I wrote an internal memo proposing
various economic reforms that might be considered as research projects
not only for the final version of the long run study but also for the medium
run. Since then the CPB directorate has actively blocked internal discussion
and eventual publication of the analysis. Since this is a breach of the
scientific code, I have advised Dutch parliament to investigate the situation.
A small commission of Dutch scientists already concluded that there seems
to have been too little room for discussion. Since nobody further seems
to care about it, it seems, paradoxically, that only parliament can make
a real difference.
Curiously, my 1989-1991 CPB director, mr. Gerrit Zalm, who blocked discussion
on my analysis, now is one of the European finance ministers trying to
But note that the neglect is not total. The Dutch party of the Greens
(De Groenen), of which I am no member though, recently have taken an interest
in the analysis. They have asked the Dutch CPB to officially comment on
some scenarios based on the analysis. Note that the CPB provides the service
to parties in Dutch parliament of analysing the economic consequences of
election programmes. In line of that service for the Dutch 1998 elections,
the CPB has been at work, and has presented a 4 page public report, No
97/22 June 26 1997. The findings are:
So we can see, again, the effect of dogma. The CPB analyses unemployment
as a supply side problem and continues to 'blame the victims', and chooses
not to have time for alternative approaches that regard unemployment as
a demand problem. But we are making some progress here, compared to 1989.
The CPB acknowledges the existence of the Tax Void, but doesn't think that
exploiting it will generate much employment.
The CPB acknowledges the phenomenon of the 'dynamic marginal rate', i.e.
the defining formula above, but does not acknowledge that expectations
about it matter, and the CPB still maintains that high marginal rates are
bad for the economy.
The CPB has not run the computer yet. The researchers are busy adjusting
the model for effects of marginal rates on schooling and the informal economy,
and the new model should be finished in November, just in time for the
election model runs.
See my new book "Definition &
reality in the General theory of Political economy" on the internet.
(C) Thomas Cool