# Summary of the solution to the current mass unemployment in the OECD area

September 3 1997

## Introduction

This review summarises key aspects, such as:
• 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
A summary remains a summary. The last sections link to more extensive discussions on the world wide web.

## 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.

## Analysing the minimum wage

We wonder how the minimum wage comes about. We see two terms in the minimum wage:
M = B + Tax[M]
Tax[w] = r (w - x)
NetIncome[w] = w - Tax[w]
M = minimum wage
B = basic net income
w = an arbitrary wage
r = marginal rate
x = exemption
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.

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.

## 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 subsistence.

### Taxes

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 = subsistence

### Subsistence

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
Where:
wi = wage index
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
It turns out that rsi = rsi[rwi, r, S / A].

### 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 = ----------------------------

NetIncome[A, S]```

```             (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:
• 1950-1970: low inflation and high real growth
• 1970-1982: high inflation and turbulent real growth
• 1983-now: reduced inflation and stagnating growth
In the last period inflation continues while real wages stagnate (causing the Dutch export surplus).

### Graph 6: Continued inflation, stagnating real wage

#### 1950 = 1

Graph 7 gives the same data, but in a different format.

## 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
rsi = real subsistence index = real net minimum index
B = base net income = nominal net minimum
M = minimum wage = nominal gross minimum
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.

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.

## 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.

## 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 rates.

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 / 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:
```      h x

r (1 - -----)

g w```
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 thoughts.

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 Wide Web:
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'.

## Research agenda

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:
• 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.
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.

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 spend.

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 solve unemployment.

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:

• 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.
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.

See my new book "Definition & reality in the General theory of Political economy" on the internet.

(C) Thomas Cool
http://thomascool.eu