Chapter 23 gives a textbook macro-economic model so that we better appreciate the point of reference of ‘existing economics’. Chapter 24 clarifies heterogeneity and nonlinear taxation. There is nothing new here yet either. The subsequent chapters then take up the same subject matter, and gradually add elements and interpretations that support the novel analysis.

Our textbook model is a very simple and unpretentious first year undergraduate model. It is not interesting for itself, but for our later discussion.

We follow Dornbusch & Fischer (1994), chapters 1 - 4. The basic macro-economic identity for annual real values is:

C + G + I + NX   YR   YD + (RTAX - TRF)   C + S + (RTAX - TRF)

We take G, TRF and NX as exogenous and known. We are now only interested in expectational equilibrium. Aggregate demand is YR* = C* + G + I* + NX.  With the rate of interest i and the marginal tax rate r, behavioural relations are:

C* = TRF + c (YD* - TRF) + C₀

I* = I₀ - b i*

RTAX* = r YR*

In equilibrium C = C* gives YR* = YR  - since C = C* iff YD = YD* iff  I* = S* = I = S. This can be represented by the IS curve:

YR = TRF + c (YD* - TRF) + C₀ + G + I₀ - b i + NX     

i = (C₀ + G + I₀ + NX + TRF - (1 - (1 - r) c) YR ) /  b       (IS)

For the money and bond market:

L + DB   WN / P   MX / P + SB

Liquidity demand is:

L = k  (1 + h / (i - i_min)) YR

Equilibrium on the money market L = MX / P  gives the LM curve:

                     (LM)

Intersection of the IS and LM curves gives equilibrium for YR and i, and from these the other variables can be solved, in particular the price level P = MX / L[YR, i].

For our purposes we can use a Cobb-Douglas function with employment LE and capital KE:

YR = Y₀  LE ^a  KE ^{1 - a}

Y P YR =  W LE +  i P_K KE,

We assume that firms maximise profits - and since we assume constant returns to scale, there is no surplus. If firms accept wage W, then the marginal productivity of labour equals the real wage W / P, and then this determines LE  which must be at most labour supply LS. Unemployment then follows as u = 1 - LE / LS. If companies also accept the rental price of capital, then the marginal productivity of capital must equal i P_K / P, and this determines the employed real capital stock KE, which must be at most total stock KS.

The additional equations from these marginal conditions are (and we assume expectational equilibrium on these too):

LE =  Y  / W

KE = (1 - ) Y  / (i P_K)

Let p be an arbitrary price.

Statics assumes a timeless dimension. With supply S[p] and demand D[p], equilibrium (in expectations) is given by S[p] = D[p] and it solves for the equilibrating price p^·.

Dynamics concerns developments in time. The price movement p’ = dp/dt is related to excess demand D[p] - S[p], so that p’ = dp/dt = f[D[p] - S[p]]. The solution of this differential equation gives the movement towards equilibrium. Dynamics causes different concepts of equilibrium: depending upon the specification of variables and function, the equilibrium can be market clearing (p°) or the fulfillment of expectations (p*). Economic agents generally have different speeds of reaction when expectations are not fulfilled. When there are surprises, there can be a ‘trade-off’ between prices and quantities.

The textbook relations are simple in themselves, but the interactions already can be rather complicated. Figure 18 presents some common macro-economic interactions.

Homogeneity assumes that S[p], D[p] and p are real variables, while heterogeneity assumes vectors or densities. This book takes the density approach. In fact, employment e[w] = Min[s[w], d[w]] also provides the earnings or income distribution, i.e. the function that gives the number of people earning a level of income w, for labour supply s[w] and labour demand d[w].

The proportional tax is r Y.  A linear but non-proportional tax is Bentham[w, x] = r (w - x), though proportionality comes back again by assuming x = 0. A nonlinear tax adds curvature (see chapter 29), and then interacts with heterogeneous labour.

The following references put the argument into perspective.

In his presentation of the IS-LM model, John Hicks (1937) could disregard differences in labour as being of secondary complication. For our purposes, however, the case of heterogeneous labour causes a crucial difference. Policy co-ordination then involves three distributions:

1.        the gross income distribution that corresponds to the productivity distribution,

2.        the net income distribution aspired by the policy maker (‘society’),

3.        the actual net income distribution, resulting from taxes imposed (including e.g. the social security ‘insurance’ payroll tax) and from expenditure.

There is early recognition in the literature of the need for heterogeneous labour in discussing dynamics. For example, 20 years ago, Solow (1976:152), occasionally but not consistently using the more accurate term ‘surface’:

“George Perry, who was one of the earliest quantifiers of the Phillips surface, has recently produced an alternative explanation of great interest [reference]. Perry’s basic insight is that the aggregate unemployment rate may be an ambiguous measure of pressure in the labor market when the composition of the labor force and of the group of unemployed is changing. (...) In other words, the Phillips curve would have shifted upward. (...) Perry quantifies this observation by making the plausible assumption that an unemployed body generates downward pressure on the wage level proportional to the amount of “unemployed labor” he or she represents. In turn, the amount of unemployed labor can be measured by the number of dollars of wages it represents.”

No economist working in the field and worth his salt will have neglected Solow’s paper. Issues of the substitutionability of one kind of labour for another, and of dispersion measures for the differences in responses, can found even earlier in the literature.

Van Praag & Halberstadt (1980) present a continuous productivity distribution.

Bruno & Sachs (1985) give a standard reference for stagflation. Their formal analysis uses homogeneous labour and proportional taxes, though some of their statements allow for an interpretation of heterogeneity and nonproportionality.

The need for modelling heterogeneous labour and nonproportional taxation is clearly recognized in the literature, see e.g. Beenstock et al. (1987) and Minford & Ashton (1993). Layard, Nickell & Jackman (1991), another standard, allow for heterogeneous labour, yet tend towards proportionality in taxation.

In addition, these references use dynamics but do not explicitly discuss the consequences of changes in tax parameters. Auerbach & Kotlikoff (1987) give a wealth of information on fiscal dynamics but do not specifically tackle stagflation.

Other references which put the Phillipscurve in perspective are Okun (1981), Blanchard & Fischer (1989), Friedman (1991), The Economist (1994) and Phelps (1994). Extensive theoretical and empirical work has been done by the Central Planning Bureau (1992a&b), Gelauff (1992) and Colignatus (1992b).

It is useful to recognise some current views on the labour market and the influence of taxes. This allows us to better see the impact of our new analysis.

There exists a simple popular view that makes two errors:

·         it is static and not dynamic

·         it assumes homogeneity and not heterogeneity.

This model is the comparative statics model with homogeneous supply and demand for labour. Borjas (1996:159), Mankiw (1998:125) and The Economist of February 26 1994 present that model. As a model it of course is consistent and it can help us to get our thoughts started, but as a representation of real markets it is erroneous.

Figure 19 gives the wage W on the vertical axis and supply and demand quantities on the horizontal axis. (Note the causal order.) It must be mentioned that marginal tax rates have played a role in the deduction of the supply and demand curves.

In this Marshallian model, the original equilibrium is attained at the intersection of the LS and LD curves, at wage W°  and employment LE°. An income tax causes workers to demand a higher wage, and supply shifts up, to LS1. Premiums that raise wage costs for employers cause these employers to offer a lower direct wage, and demand shifts down, to LD1. The new equilibrium of LS1 and LD1 is LE < LE°  where employers pay direct wage W1 > W°  and where workers receive net W2 < W°.

For this model, with supply and demand schedules derived with marginal analysis of utility and profits, there is an important role for statutory marginal tax rates. First best here are lump sum taxes and zero marginal rates.

There are clear objections to this model:

·         It is comparative statics, with homogeneous and flexible labour.

·         It concerns any kind of tax, while some taxes are socially desired and generate employment. The model doesn’t distinguish between optimal and suboptimal taxes.

·         Empirical research shows that labour supply elasticities are low. Elasticities are higher for partners, but that is less relevant here. People are very much in the position that they have to work for a living, and taxes generally pose no restraint on the availability for the labour market. This means that LS ~ LS1 ~ vertical. (Borjas (1996) shows this graph too.)

·         The model does not really allow for unemployment. We might define U = LE° -LE, but LE° is an unobserved variable. Firms and workers react to observed variables, and in those terms there is full employment. Even if labour would be inflexible in this model, then there still would be no involuntary idleness at the net wage earned.

The use of this model thus is limited. Mankiw (1996) correctly presents the model as a ‘tax incidence’ model, and we should be hesitant of other conclusions.

The Simple View however regards this model as a real description of real labour markets, and it thus makes the category mistake of using arguments concerning the income distribution for issues of growth and employment.

The reader is advised to read again Chapter 2 of Keynes’s 1936 General Theory. The General Theory is in my perception an effort to seriously develop dynamics. Keynes’s precursors did discuss dynamic developments, but always ended up in static modelling. See also Patinkin (1976:140 footnote 4).

In the following quote, Keynes discusses a real wage reduction caused by prices. For our purposes, we might substitute a real wage reduction caused by taxes.

“To sum up: there are two objections to the second postulate of the classical theory. The first relates to the actual behaviour of labour. A fall in real wages due to a rise in prices, with money-wages unaltered, does not, as a rule, cause the supply of available labour on offer at the current wage to fall below the amount acually employed prior to the rise of prices. To suppose that it does is to suppose that all those who are now unemployed though willing to work at the current wage will withdraw the offer of their labour in the event of a small rise in the cost of living. Yet this strange supposition apparently underlies Professor Pigou’s Theory of Unemployment [voetnoot] and it is what all members of the orthodox school are tacitly assuming.” (Keynes (1936:12-13)).

Note, by the way, that the format of Figure 19 can always be used in terms of the average wage W. So the format of Figure 19 may be inviting to our intuition, in that we think that we indeed can draw a diagram like that, but we then should be aware that our true model is heterogeneous labour and not homogeneous labour.

An alternative view is more empirical, thus inherently more dynamic, and builds on Keynes’ observation. Empirical research, see e.g. Ashenfelter & Layard (1986), Theeuwes (1988), Hum & Simpson (1991) and Gelauff (1992) shows that marginal tax rates have ‘surprisingly’ low elasticities. The reason for a lesser importance of marginal rates is that labour supply is not flexible, but rather fixed. That labour supply is primairily given by demographic factors, is for example a well known assumption of practical models developed at the Dutch Central Planning Bureau. In Western economies people will have to become active on the labour market in order to earn a living, and taxes hardly form a barrier. People are still very much like Marx’s proletariat, and they have little else to fall back on but to supply their labour. There is some choice for partners and for people on benefits, but this does not have a major impact. For the majority, if anything, the average wedge is more important than the marginal one, see Den Broeder (1989). Recently Minford & Ashton (1993) see scope for a larger effect of marginal rates, but, their study is still far from explaining stagflation, partly for the reason that it is not fully dynamic.

By consequence, the major equilibrating forces exert themselves on the wage and the related employment. Here arises the dynamic situation of (wage) inflation and unemployment, and thus the issue of the Phillipscurve. Thus, conceptually, tax rates have their major impact not on labour supply but on the Phillipscurve.

The next question then is whether their effects are positive or negative. The common argument is that a higher marginal rate fuels inflation. Whether this is the case then becomes the next issue.

Before we can continue the discussion, a note on the ‘efficiency wage theory’ is required. The idea is here that, though people are forced to work to earn a living, they still can choose whether they shirk or not. They take account of a probability of getting caught and getting fired, but supervision would be expensive, and, if fired, one eventually could find another job. Unemployment then is required to discipline the workers. Borjas (1996:459) provides an introductory discussion, and the graphs are quite similar to the supply and demand schedules of old.

I tend to regard this approach as an example of academic excess. This may be an error on my side, but let us look at some of the arguments: 10% of the European labour force is unemployed, hence Europeans apparently shirk a lot ! And employers are so dumb that they cannot think of cheap ways to determine productivity, like setting standards and such. Agreed, shirking is undoubtedly a phenomenon, and eventually the superior economic model will include a subtle relationship between wage, effort and productivity to determine the last digits, but all this is less relevant for the Great Stagflation and the need for an Economic Supreme Court.

Given more than one view, there is scope for confusion. This has in fact occurred.

·         The OECD policies referred to above, directed at lowering statutory marginal rates, have been advocated using the rhetoric of the Simple View even though economic advisers often are aware of the Complex View.

·         If one would really think that high marginal rates reduce work effort and supply, then a situation of high unemployment would call for higher rates - that would reduce unemployment. Policy however has been to reduce rates. 

Secondly, when these views are confronted with the effects of the policy of rate reduction, there again is ample scope for confusion.

When unemployment has been reduced, then this is being seen as corroboration of the Simple View. For example the data on the US now show the combination of a reduction of taxes on higher incomes and some reduction of unemployment, and it will now be difficult for policy makers to accept other lines of arguments. Actually, in so far as there has been some success in practice, it is because the policies have also lowered average rates. Higher budget deficits have been relied on to pay for additional benefits and average rate reductions for higher incomes. The reduction of marginal rates actually had a negative impact.

In most cases unemployment has remained high. In this case one should expect that policy makers would reconsider their views. They don’t seem to do this, and rather look at the few cases where there seems to have been success along the expected pattern.

We will first discuss heterogeneous labour supply, and forward a hypothesis on its distribution. Note that supply is difficult to observe, since generally we only observe actual employment, which is the minimum of supply and demand. However, data on actual earnings do allow the encouraging conclusion that the earnings distribution can be approximated by a lognormal distribution. For an indication we look at Dutch data on the distribution of income in 1950 and 1988. We complete this chapter by a more thorough sets of definitions for earnings, cost and income accounting, and we construct integrals that are relevant for the minimum wage.

Let us first regard labour supply.

At a Dutch economists “Masterclass” session in Fall 1991, Orley Ashenfelter explained that labour supply was unresolved and actually some kind of a researcher’s nightmare. In a break I put my suggestion on the blackboard, and my ‘quiggly’ line (see below) at least drew the compliment of an amused smile. I almost put this suggestion into Colignatus (1994a), but backed away from that since it was not essential for that paper (and I used only the normal right hand side of the supply graph). However, to my surprise and pleasure I saw that same quiggly line in De Groot & Keuzenkamp (1995) who discuss results of Quah (1993).

De Groot & Keuzenkamp have another subject than labour supply. Their problem is whether international economic growth results into convergence, as Adam Smith’s “The Wealth of Nations” seems to imply. De Groot & Keuzenkamp refer to the results of Quah (1993) who has compiled the distribution of output per labourer per country, which turns out to be that quiggly line.

To understand the point, let me first explain my reasoning on labour supply. At low productivity, one has to work 24 hours around the clock in order to survive. For example, if subsistence is at B and productivity is y, then the hours are B / y. Hours thus quickly rise when y drops (the working poor). When productivity increases, one quickly starts working less hours, particularly since the kind of work at that level often concerns hard labour. At higher levels of productivity again, the kind of work is less exacting and pay is better, and one may work longer hours again. However, at the highest levels of productivity, labour again becomes a relative disutility. In summary, when plotted in a graph, the figure looks like a dromedary, starting high at the left, having a dip in the neck, then the bump, and sliding away towards the tail.

If labour supply is like this, then it likely affects the productivity distribution across nations. While every individual has his or her own parameters, aggregation may average things out, and as a result one nation then may stand for a certain income group. Thus Quah’s finding is consistent with my intuition and indirectly confirms it.

Figure 20 plots the quiggly line, for imaginary income y in thousands of dollars and subsequent working hours per week, for both long and short ranges of income so that the curvature can better be appreciated.

Note: These are not observations, just give an hypothesis on shape

I’m still working on a correct form of the complete utility function. Barro & Sala-i-Martin (1995) give a recent discussion of the trade-off of work and leisure in the context of growth, and that might be a fruitful framework. However, for the present purposes, our development may stop here.

In the 1988 plot, the estimation has been done with the 1988 ‘parttimers’ dropped, but they are included again in the income-frequency plot so that we can better appreciate that their inclusion would confuse a discussion on fulltimers. But it is nice to see the dromedary shape returning.

There are some useful definitions and formulas for heterogeneous labour markets. These hold for any distribution, not just the lognormal distribution. Let y and w be micro values that have a certain density. First of all, there are the following accounting definitions, for annual and nominal values:

·           = the profit rate, expressed as a markup on labour costs

·         y = labour costs + profit = w (1 + ) = product revenue = productivity

·         labour cost quote = LCQ = w / y = 1 /  (1 + )

·         labour costs = w = (direct) wage + nonwage (but labour related) costs

·         w = net labour income + (direct + indirect) taxes + premia + other nonwage costs

·         tax = T[w] = (direct + indirect) taxes + premia

·         gross labour income = labour costs - other nonwage costs = net labour income + tax

·         Neglecting the “other nonwage costs” gives w = labour costs = gross labour income. (Thus the w are labour earnings only if the other nonwage costs are zero.)

Observed labour costs have a density fw[w]. Since the product is y = w  (1 + ), equalisation of profit rates with respect to labour would give the labour cost density fw[w] as a shift of the productivity density fy[y]. Normally, though, the profit rates are equalised in terms of capital, which for example causes different Labour Cost Quotes (LCQ) per sector of industry, and then the relation between fw[w] and fy[y] is a more complicated affair.

The proper labour supply density sp[.] depends on net labour income (w - T[w]). But supply can, with the neglect of “other wage costs”, be regarded as a function of labour cost w, as:

s[w] = sp[w - T[w]]

Labour demand is a density d[w]. Total supply follows from the integral:

            &          

The employment density is the minimum of supply and demand, and equals the observed labour cost density:

e[w]  =  Min[s[w], d[w]]  =  fw[w]

For total employment we take account of a minimum wage M.

For the discussion below it is also useful to compute aggregate labour costs and its (nominal) tax revenue:

Important are the average wage W = WT / LE  and the average tax rate ATXR = TAX / WT (when we can neglect other nonwage costs).

Densities for unemployment ud and vacancies vd follow from the difference between supply and demand and actual employment:

ud[w]  =  s[w] - e[w]            &           vd[w]  =  d[w] - e[w]

The aggregate unemployment and vacancy are U and V, and their rates are:

u  =  (LS - LE) / LS  =  u[M]          &           v  =  (LD - LE) / LS  =  v[M]

Figure 23 gives the stylized fact that vacancies tend to occur at higher income brackets and unemployment at lower ones. The figure is quite stylized, since it is a difficult issue to construct plausible s[w] and d[w].

If labour supply LS was homogeneous, we would have difficulty explaining that u LS  would be unemployed, since these persons are similar by assumption. Basically then u is a probability.

For heterogeneous labour we could use characteristics and a mechanism that explains why some are employed and others not. This mechanism could be related to the shift of the densities over time due to aggregate demand, inflation, technology, job changes and the like. In fact, we would use such methods to determine ud[w] and vd[w] in practice - and perhaps we would not start with w as the defining characteristic, but start with other characteristics and work towards the wage. However, we will not look into this deeply. We will use heterogeneity mainly to explain the effect of the minimum wage. For a level of income above the minimum wage we again assume some probability, quite analoguous to the homogeneous case. Basically, an agent has offers for various kinds of jobs and incomes, and associated probabilities (and one for unemployment). The s[w] and d[w] thus have a stochastic base.

Minimum wage unemployment differs from the ‘normal’ unemployment above the minimum. Thus:

u  =  um + un

Only part of um can be gainfully employed when the minimum wage would be abolished.

Only un will exert a meaningful pressure on wages. A major dynamic process is that um rises over time, contributing to the phenomenon of hysteresis. Labour market processes and wage settlements might stay stable in terms of un, i.e. the “normal” unemployment rate, but they shift in terms of u, the overall unemployment rate.

One may wonder why M is nonzero, when its abolition would create employment ume. The apparent reason for governments is that labour markets are not fully competitive and require some regulation. This issue is taken up again in the next chapter on subsistence.

There are some notable effects:

(a)    On the supply side, if ms < M, then would-be earners of ms < w < M become eligible for benefits. When they accept these benefits voluntarily or from social pressure, they, in a sense, form no real supply. Yet they are supply, otherwise they would not be eligible for a benefit.

(b)    On the demand side, if md < M, then there would be a real demand for md < w < M if government would reduce M. But this demand is not relevant when M exists.

A crucial point to see is that, as we here are concerned with productivity, that we can use subsidies to manipulate the densities, for example by subsidising a particular industry or profession. Doing this of course causes an accounting problem: does the w on the horizontal axis measure productivity before or after such subsidy ? The most practical approach is to use w inclusive of subsidies - because market measurements are always inclusive. Subsidising firms would allow them to hire at higher wages: this would shift d to the right. Subsidising workers would allow them to work for lower wages: this would shift s to the left. What happens to employment is not a priori obvious.

It turns out that the minimum wage is important in practice. Our analysis will strongly rely on minimum wage unemployment. In this we differ a bit from the original position taken by Keynes. As Tobin (1972: 122) states:

“But why is the money wage so stubborn if more labor is willingly available at the same or lower real wage ? Consider first some answers that Keynes did not give. He did not appeal to trade union monopolies or minimum wage laws. He was anxious, perhaps over-anxious, to meet his putative classical opponents on their home field, the competitive economy.”

In my view, Keynes’s argument (as further explained by Tobin) is to the point, and aggregate demand, sticky wages and the co-ordination failures on these are established concepts in macro-economics. However, the record of the Great Stagflation is very much influenced by the minimum wage problem, and thus it is that kind of analysis that merits our attention here.

With respect to the textbook macro-economic model in chapter 23, we can introduce a minimum wage component in unemployment u_M that can rise gradually over the long run due to taxation. With u = u_M + u_R  (R from ‘remainder’) a possible Phillipscurve with less dampening effect of u_R is:

dLog[P] = dLog[P]* - Log[ (u_M + u_R) / u* ]

Alternatively, the two submarkets have their own curves. In both cases, it must be determined how the two submarkets develop and how they interact. The most obvious hypothesis is that high productivity labour sets the trend for the development of wages. When minimum wage unemployment rises stronger than general unemployment, then the higher educated have more scope for wage demands, and then there is an upward effect on wages and prices, even stronger so when price expectations come into play. This would show an unfavourable (upward or rightward) shift of the (aggregate) Phillipscurve.