This chapter is a bridge between the standard macro model and the elaborations on heterogeneous labour and taxes. The concept of the ‘welfare state’ depends upon our concept of subsistence and the elements that go into its index , and on the decisions that we take on this at the national level.
In Book III we already regarded some indexation of subsistence and taxes. Here we will refine indexation of net subsistence. Gross subsistence will be T -1[B] as determined by the tax system. A way to understand this chapter is that it formulates conditions for the tax system.
We already saw two possible indexation schemes for subsistence: (i) on average net income or (ii) on gross average income. The latter presumes that taxes are an indication of welfare too. This current chapter will look an another way of indexation that takes an intermediate position that might be better but that might also be needlessly complex.
We will find that if we adopt certain indexations, then we must accept some divergence in development in other terms.
Subsistence labour forms a special group within heterogenous labour. The group only exists if we acknowledge heterogeneity. In the labour supply density we already hypothised a ‘dromedary shape’ that partly reflected the fact that a minimum income means longer hours when the wage drops. Let us now discuss subsistence more extensively.
With man a social animal, sociobiological and social psychological causes apply in general. Precisely what these causes are, and how they apply, is a subject of serious study, see for example Aronson (1992a&b) and Wilson (1993). A regularity for mankind seems to be, vide these studies, that in certain cases people show a certain amount of care for their fellows.
This care should not be overrated. Part of it may not be empathy, but simply be precaution and an insurance for the event of personal misfortune. Also, some care obviously reduces the chance of a violent reaction of the disadvantaged. There are clear examples of empathy breakdown. For example, archeologists found ancient mines with such small shafts that these mines could only have been worked by children. We need not have illusions about working conditions, especially since it were lead mines. Nevertheless, whatever these clauses and contrary cases, ‘normal conditions’ seem to provoke a distinct level of care.
A strong assumption is that people have views about the whole income distribution. A simpler assumption is that people recognise a level of subsistence - which for dynamics likely implies that they adjust that subsistence to developments.
The strong assumption might well be that the income distribution is lognormal for social - and not ‘economic’ - reasons, and that the economic process only is oriented at directing people to a fitting place in that distribution. Economic productivity is essentially a nominal concept. It is not just the technical amount of goods per hour that can be produced, but also multiplied by the price of the product, and the price is determined in a social situation where status considerations apply. The assumption that economic agents have views about the income distribution actually need not be overly strong. As Tobin (1972, p122) states:
“(...) This observation led Keynes to his central explanation: Workers, individually and in groups, are more concerned with relative than absolute real wages.”
However, for our discussion, we narrow down the problem to the subsistence or the net minimum wage, and disregard views on the whole income distribution.
Suppose that a group recognises some subsistence. A group even might be defined by its shared views on this. For example, members of a royal family receive a certain allowance that meets their standard of living, and their standard of living helps to show that they are members of that royal family. The view oriented at the inner group thus is linked to the exclusion of others. Others should have less, precisely to distinguish them from the inner group. Being a royal family does not amount to much, if you don’t have subjects. This process works all the way down, so that even people in minimum conditions flatten out differences among themselves, and seem to compare themselves to beings of assumed lesser stature. (So the simpler assumption could be used to build the strong assumption.) This discussion also clarifies that the size of the group matters. There is only room for a national subsistence floor if the simpler assumption allows for a large group. So the simpler assumption properly reads that groups not only define subsistence for the inner group, which is less controversial, but also, more controversial, subsistence for society as a whole.
Note that any assumption, simple or strong, is not sufficient by itself. Society also has the coordination problem of aggregating the individual preferences on national subsistence, particularly since not everyone who wants to raise the living standard of the poor has the personal means to do so. Sometimes there are legal rules. Often labour unions come in. For example in Holland collective bargaining results into industry minimum wages that are on average at least 10% higher than the legal minimum wage. More generally, subsistence is simply a social convention. A certain level of living is regarded as inacceptable, both by most employers and by the work floor in general.
One way to implement a welfare system would be to set social security at B, and leave it at that. There would be no need for a minimum wage, since employers would have to offer at least B. In practice government nevertheless create a minimum wage system too, and allow a gap between the working wage and the benefit. One of the reasons is better control, so that agents are less likely to both receive a benefit and work on the side. One of the other causes undoubtedly derives of the social forces that call for a decent minimum. [82]
Sometimes labour market regulators may be aware of the problem of the minimum wage, and may opt for a lower indexation of M even though it results into a lower B. But the effectiveness of such policies that reduce subsistence depends upon the strength of conventions in all factories and sectors.
It is useful to note that conventions are sensitive to various considerations. For example, the Dutch legal minimum wage holds for fulltimers, but does not hold for parttimers. Holland now has a lot of parttime work. [83] It is also interesting to observe that tax exemption x is established within the bureaucratic realm where there is no direct confrontation with the standard of living. For its own historical reasons, exemption is generally indexed on inflation. These matters, while also being evidence that human care for other people should not be overrated, again clarify that our subject matter is not simple in itself. Subsistence itself is very simple, especially to those who are subject to it, but it can be made complex, especially by those who govern.
Economic theory has long been aware of notions of empathy, vide Adam Smith (1759, 1984) on moral sentiments.
Some tax theorists suggest that the social subsistence level should be exempt from taxation. Hofstra (1975) recalls the Cohen Stuart 1889 analogy, that a bridge must hold its own weight before it can be used.
In his 1980 presidential address to the American Economic Association, Solow (1980) discussed his reading of Pigou’ work, and writes:
“The last comment of Pigou’s that I want to cite is especially intriguing because it is so unlike the sort of thing that his present day successors keep saying. Already in the 1933 Theory of unemployment he wrote: “... public opinion in a modern civilized State builds up for itself a rough estimate of what constitutes a reasonable living wage. This is derived half-consciously from a knowlegde of the actual standards enjoyed by more or less ‘average’ workers ... Public opinion then enforces its view, failing success through social pressure, by the machinery of .. legislation” (p.255). A similar remark appears in Lapses [Pigou 1944 Lapses from Full Employment]. Such feelings about equity and fairness are obviously relevant to the setting of statutory minimum wages, and Pigou uses them that way.” (p5)
Solow in the next sentences also emphasises the power of social pressure, and shows himself aware that the minimum wage need not be a special application since social pressure is abundant:
“... it is even more surprising ... that employers so rarely try to elicit wage cutting on the part of their laid-off employees, even in a buyer’s market for labor. Several forces can be at work, but I think Occam’s razor and common observation both suggest that a code of good behavior enforced by social pressure is one of them.”
We already have encountered these indexes of subsistence:
· The graphs in Book III are based on indexation on the net average wage Net[W] = W - T[W]. This presentation has been chosen since its approach is more conservative.
· Another indexation is on W itself, which thus considers taxes a part of well-being. Property (13.3e) however shows this equivalent to the first, for the Bentham tax, provided that exemption is properly indexed too.
Indexation on gross income (i.e. on W) agrees better with economic intuition, since taxes need not be a real burden, when they generate goods that enter the utility function. However, some taxes can be wasteful or can be discarded for other reasons. In the following we will take a middle position, adding and substracting income elements. In particular:
· some public goods Q are provided by nature: breathing air and the berries in the field
· taxes go into public goods Gp, that subsistence workers get for free too (as licensed free riders)
· some government expenditure Gs may benefit only special interest groups (wastefully)
· some government expenditures Gn actually benefit the average tax payer, and should be considered part of ‘net income’
· some taxes go to the support of the unemployed - B U - which the unemployed cannot provide for themselves
· there is the possibility of different consumption baskets (different deflators)
· it is recognised that people at subsistence tend to have more sweat and less leisure
· tax revenue can change disproportionally with income.
Considering these element, it seems that the adoption of a detailed index would likely cause little difference with gross income indexation. Many of the additions compensate for many of the substractions. Also, if subsistence were to lag behind average income, then it might well happen that subsistence is increased at some point anyway.
It nevertheless remains useful to develop the detailed index formally. If your interest in the subject is not very strong, you are advised to skip the remainder of this chapter. The reader who studies this section will notice that we do not achieve very much. Some of the formulas look complex, but on close inspection only say the obvious.
We assume a ‘basic insurance’ setup for social security. The unemployed get a benefit of B. At higher earning levels they may have additional insurance, and be paid on top of B. But this is of no concern for our issue. Also, who is on benefit but gets a job offer, accepts this, on the penalty of losing the benefit anyhow. This means that nominal transfer payments are NTRF = B U. We also take b = NTRF / LE = B u (redefining the symbol b - no longer the IS curve). Similarly q = Q / LE.
Let g = NG / LE be average nominal government expenditure per worker, with g = gn + gp + gs. We will assume Ricardian equivalence, so that government budget deficits are regarded as part of taxes, so that there effectively is no deficit. [84] Hence TAX = NG + NTRF.
Then the average wage tax rate AWTR TAX / WT = (TAX/LE) / (WT/LE) = (g + b) / W.
For the special interests we distinguish two kinds of situations.
· When average income itself is the special interest, then gs can also be regarded as net income, part of gn, and then this case is equivalent to gs = 0. Note that we could include gn in Net[W] mathematically anyhow (but don’t do this for clarity).
· Alternatively gs 0. In particular, the average income group could be a victim of a coalition of the poor and the rich, the first getting a high B and the second a large gs. [85] In a democracy with voting population LS, a majority of LS/2 + 1 indeed can levy high taxes on the other LS/2 -1. In that case it would not be fair to regard the tax on the average wage as beneficial to the common good. (Note that this analysis for gs 0 is weak, since not all possible redistributive schemes are considered.)
Price indices for the average and subsistence workers are P and Pb. Real positions thus are W / P and B / Pb. Government prices are Pgn, Pgp and Pgs, giving gnr and gpr and gsr. Similarly Pq and qr.
The difference in leisure and sweat will be compensated here by choosing a suitable Real Income Ratio RIR.
All together, we have:
· Net position of the average worker Net[W] + gn + gp + q
· Net position of the subsistence worker B + gp + q
· The real income ratio RIR (B/Pb + gpr + qr) / (Net[W]/P + gnr + gpr + qr)
The government would set RIR at a specific value, and then determine B from the other values:
B = Pb { RIR (Net[W] / P + gnr) - (1 - RIR) (gpr + qr) } (27.1)
One thing to show is that B has a small multiplier on itself because of b. We can use the average tax rate difference Z between national and private average:
Z TAX / WT - T[W] / W
Z = (g + b) / W - T[W] / W
T[W] = g + b - Z W
Net[W] = W - T[W] = W + Z W - g - b = (1 + Z) W - g - b
Using this for the RIR:
· Net position of the average worker (1 + Z) W - gs - b + q
· Then RIR (B/Pb + gpr + qr) / ((1+Z) W/P - gsr - B/Pb u + qr)
(27.2)
The first term of (27.2) contains a small (negative) multiplier of B on itself. In full employment, u 0.02, and with RIR 0.30 the multiplier might easily be neglected. That is, neglected in (27.2) but not for the determination of the RIR in the base year - since B u cannot be neglected for the base of the RIR. Since (27.1) and (27.2) are mathematically the same, using (27.1) makes that the question of neglecting that small multiplier does not arise.
Another point is that the index becomes simpler if all price indices are the same. Taking P = Pi gives RIR (B + gp + q) / ((1+Z) W - gs - B u + q).
Let us consider a numerical example. Suppose that gn = gs = q = 0 and that prices are equal. Suppose also that AWTR = TAX/WT = 0.30. We also take the Bentham tax T[y] = Bentham[y] = 0.5 (y - B). Let us consider the path that subsistence is half of average income, i.e. B/W = ½, and then compute the various ratios. Then:
· Indexation on gross average income gives B / W = 0.5.
· Indexation on net average income gives B / Net[W] = B / (2B - 0.5 B) = 0.66.
· Then T[W] / W = 0.5 (W - ½ W) / W = 0.25, and Z 0.30 - 0.25 = 0.05.
· Since gn = gs = 0, g = gp, and AWTR = (gp + b) / W = gp/W + ½ u = 0.30. If we assume full employment u = 0.02, then gp/W = 0.29.
· Then RIR = (B / W + gp /W) / ((1 + Z) - 0.01) = (½ + 0.29) / 1.04 = 0.76.
Note that the ratio numbers 0.50, 0.66 and 0.76 by themselves mean little. In both cases B is set at half W, so the value of B is not affected. The only point is that the bases are different each time, and apparently smaller. These bases of course change again for other assumptions on the various variables and functions. Where there is no difference at a particular moment (base year), there however arise differences over time. The following tries to find out more about this.
One way to trace developments over time is to make plots as we did in Book III. Another approach is more formally, and a commonly used route here is the assumption of a constant macro-economic progression factor. This factor is the elasticity of tax revenue with respect to income (Koopmans (1975:103)), thus mepf = (Y / TAX) ( TAX / Y). The factor is determined by tax parameters, their indexation, the income distribution and its change. In this case, without a deficit, the progression factor applies to expenditure too, which may be taken to mean, effectively, that taxes are indexed such that tax revenue follows expenditure.
We shall take the progression factor for the average wage, which is exclusive of profits and the growth of employment. Thus our = (W / g) ( g / W). We assume a nominal position, thus include price developments in government expenditure relative to the average wage. We set gn = 0 now, since it can be included mathematically with gp. We also assume that is equal for gs and gp, so that gs = gs[0] W / W[0] = gs0 W and gp = gp[0] W / W[0] = gp0 W . Thus g = g[0] W / W[0] with properly g[0] = gp[0] + gs[0].
Then g / W g / W = NG / WT. This has the specific property that = 1 implies that the quote g / W = g[0] / W[0] is constant, and thus NG /WT is constant too. We will use this property below.
Taking W separate:
and hence
(27.3)
Inclusion of the progression factor does not cause special observations yet. If < 1 then in the limit of W the indexation can be rather simple, especially if Pb qr / W goes to zero too. If > 1, then there could be a point where the markup on W is zero, or subsistence would have to be zero - which would suggest an unrealistic tax function. The progression factor becomes more useful if we regard special cases.
Definition: A (democratic) state is “Madisonian”, iff gs = 0. James Madison remarked that a proper democracy with a majority rule actually safeguards the interests of the minorities.
Definition: A “real welfare state” aspires at a constant RIR and takes q = 0. The idea on the latter is that breathing air is prerequisite to utility and no source of it. The berries in the field are owned by someone, and no longer free. (If they were free, then Coase’s Theorem shows that they could be counted as part of income, and hence they would no longer be free for all practical purposes.)
Definition: A “pragmatic” real welfare state sets u = 0 in the determination of the benefit level and RIR. The factor B u really does not amount to much.
Definition: “Uniform prices” means P = Pb = Pgs = Pgb = Pgn = Pq. If this happens then one price index P suffices.
Theorem B1: In a pragmatic Madisonian real welfare state with Ricardian equivalence and uniform prices, (i)
RIR = (B + g) / ((1 + Z) W) (base year)
and
B = W ((1 + Z) RIR - NG/WT) (henceforth)
(ii) If RIR is constant, then: (1) A constant quote for government layouts (or progression factor = 1) only allows for some variation in B/W by variation in the average tax rate difference Z. (2) If Z is constant, then B is fully indexed on W.
Proof:
(i) For the base year: substitute the results of the definitions in the RIR (vide (27.2)), note that the prices cancel and that g = gp. Then find the base year result as stated, and then use (NG /WT) W = g to get the annual expression.
(ii) For (1), we use = 1 NG /WT = g[0] / W[0] from above. Then simply rework the equation for a constant.
For (2), if NG/WT and Z are constant, write B = c W. Then B / W = c = B / W. Hence Log[B] = Log[W].
Q.E.D.
Theorem B2: In a pragmatic Madisonian real welfare state with Ricardian equivalence and uniform prices, net income indexation is only feasible for special tax functions.
Proof: To see what happens if B is indexed on Net[W], write n = Net[W] / W. Note that 1- n is the marginal tax rate for W, and that B / W = B / Net[W] n.
With B = W (1 + Z) RIR - g (theorem B1) use W (1 + Z) = (Net[W] + g + b) and get:
B = RIR Net[W] - (1 - RIR) g + RIR b
Note that b 0, since we have set u = 0 only in the determination of the RIR. Then:
B / W = (RIR Net[W] - (1 - RIR) g + RIR b) / W
= RIR n - (1 - RIR) g / W + RIR u B / W
B / W= (RIR n - (1 - RIR) g / W) / (1 - RIR u)
We again find a small multiplier. Dividing by n gives the transform to Net[W]:
B / Net[W] = (RIR - (1 - RIR) NG / WT / n) / (1 - RIR u)
LogB / Log[Net[W]] = Net[W] / B (RIR - (1 - RIR) g / W / n) / (1 - RIR u)
Indexation on Net[W] means that the left hand side is 1, and that Net[W] / B is some constant. Setting net income ratio B / Net[W] = NIR[0]:
NIR[0] = (RIR - (1 - RIR) g / W / n) / (1 - RIR u)
We want to find the conditions under which RIR is a constant (for the ‘real welfare state’). Solving above expression for RIR gives:
A special case has = 1 and thus NG/WT = g / W constant, and n constant, i.e. for the Bentham tax function n = 1 - r. This is only feasible if u is constant too. There is a more general class when g / W / n is some constant, but u must be constant here too. In other cases the RIR is implicitly adjusted to make B / Net[W] constant. But nonconstancy of the RIR conflicts with above definition of the welfare state (that must have constant RIR).
Q.E.D.
This chapter deals with the confrontation of labour supply with labour demand, and the equilibrating dynamics. With high unemployment, wage growth may be reduced. With low unemployment there may be ample room for wage demands, and wage inflation can rise.
Chapter 25 already provided a background discussion on the Phillipscurve, and for example pointed to Graaflands c.s. derivation from a Nash maximising framework. In this chapter we take that possible development for granted, and concentrate on concepts: what variables are relevant for a Phillipscurve, and how do we characterise equilibrium.
It appears to be useful to first develop some concepts of dynamics.
The Phillipscurve reflects the hypothesis that (wage) inflation is influenced by unemployment. Of course other factors are important too, such as (price, wage) expectations and forward shifting of taxes. Whatever other influences, the key notion of the Phillipscurve remains the influence of the employment situation. Wage adjustment now is considered to be the dependent variable while normally the price would be the independent variable. Wage adjustment will consist of a shift along a curve and a shift of the curve, and for both we still use the term ‘Phillipscurve’.
As remarked, labour supply is relatively fixed. Utility maximisation and rational calculation will primairily be directed at finding a competitive wage (competition not necessarily meaning full competition - as we e.g. referred to a Nash equilibrium). An individual who sets his wages too high will become unemployed. Even the probability of becoming unemployed will have a sobering effect. Given this framework, the model must concern a dynamic process of unemployment (threats) and wage adjustment.
First consider a homogeneous market with price level P. Price adjustment towards the market clearing equilibrium price P° depends upon excess demand, and since excess demand is determined by the price level, we get a differential equation:
P’ = dP / dt = f[ D[P] - S[P] ] = f ° [ P° - P ]
Note that the choice of ‘excess demand’ as the explanatory variable is arbitrary. We might as well take excess supply, or allow demand and supply to react differently, or have a different sensitivity to prices and quantities. Similarly, we can also take the quantity as the explained variable. And we can also formulate the equation in expectational variables.
Some authors hold that above relationship for price dynamics is an hypothesis that needs further clarification. I think that this is too cautious. Admittedly, it might be too simple to only presume that agents know that they are involved in a market ‘tatonnement’ process, and further explanations can be helpful. Agents have various tools available, and the choice of offering and accepting prices and quantities can be described, using an optimising framework. The speed of adjustment in markets depends upon characteristics like the size of the market, the historical relationships between agents, ‘menu costs’, and the like. It is also useful to distinguish ‘normal’ periods and ‘shocks’. However, the level of detail depends upon the use of the model, and above relationship suffices our goal.
Inflation is the rate of growth of prices, i.e. p = dLog[P] / dt = P’ / P. The change in inflation is dp / dt = P”/ P - (P’)2 / P2 in terms of the original price level. Acceleration of inflation would be d2 p / dt2.
We need to clarify a term. The economic literature uses the term “Non-Accelerating-Inflation Rate of Unemployment” (NAIRU) for that rate of unemployment that causes dp / dt = 0.
This term thus should be “non-accelerating prices” or “non-changing, or constant, inflation”.
Secondly, it appears that the formulation in terms of differentials is less useful for practical economics than the formulation in differences. So we will use differences instead. Inflation then is p = (P /P[-1] - 1) (often expressed as a percentage).
Thirdly, we regard wage inflation rather than product price inflation, thus = (W /W[-1] - 1). Please note that we use the different letter font for wage inflation, since we use w for the level variable in densities like e[w]. Properly we should substract productivity growth, but for our purposes we may now assume that productivity is constant. Note that wage inflation can be different from price inflation, since productivity is determined in terms of the output price, and output will not be only consumer goods but also exports, investments and intermediates.
We will use the term “Constant Inflation Rate of Unemployment” (CIRU) for that rate of unemployment that causes p = p[-1]. Similarly, the Constant Wage Inflation Rate of Unemployment (CWIRU) gives that rate of unemployment that causes = [-1]. [86]
We use the term “Equilibrium Rate of Unemployment” (ERU) for that rate of unemployment that causes wages to adjust to their equilibrating or market clearing level ° = (W° /W[-1] - 1). The CWIRU might be a special kind of ERU. The idea is that once inflation has been constant for a long while, you start expecting it. Table 8 contains an overview of the concepts.
Table 8: Concepts for wage inflation
|
|
|
REH: white noise surprise = * + |
Non-REH: other surprises |
|
CWIRU
|
uf = ERU[FE] |
CWIRU = ERU[REH] = ERU[FE] |
Maybe temporarily, but impossible in the long run |
|
Other |
CWIRU = ERU[REH] |
Maybe temporarily, but impossible in the long run |
|
|
Non-CWIRU
|
uf = ERU[FE] |
° = h[uf, u[-1]] + … if expected … |
° = h[uf, u[-1]] + … |
|
Other |
ERU[REH] |
No equilibrium in any of these senses |
Note: We use ° to indicate market clearing equilibrium, and * or E[.] for expectations
and expectational equilibrium. We use · when we allow for either.
We can recognise at least two equilibria:
· FE: full employment, when all labour resources are used except for friction unemployment uf = ERU[FE]. Normally ° is a direct function of uf, for example ° = h[uf, u[-1]] + dLog[Money]. It may be that people’s expectations on nominal wages are not fulfulled, so that ° E[] . A FE policy is only successful if = ° and u = uf.
· REH: the rational expectations equilibrium, when expectations are fulfilled except for random error. Thus * = E[], it so develops that = * + , and this optimality is only in terms of expectations. In ERU[REH] unemployment may be far from uf = ERU[FE]. The situation can be stable if people only regard the price signals (and whatever else is in the specification), and are satisfied as long as their expectations are fulfilled.
Let the change in wage inflation be sensitive to wages with degree and sensitive to quantities with a function f[u], with u the rate of unemployment. The following gives a rich (wage) Phillipscurve that contains not only the rate of unemployment but also past and (forward looking) equilibrating wage inflation. [87]
- [-1] = ( - [-1]) + f[u] (28.1)
= + (1 - ) [-1] + f[u] (28.2)
Generally for the CWIRU from (28.1):
0 = ( - [-1]) + f[CWIRU]
CWIRU = f -1[ - ( - [-1]) ]
According to the Rational Expectations Hypothesis (REH): * = E[] = . Then from (28.2) - interpreting REH as ‘model consistency’:
* = E[] = * + (1 - ) [-1] + f[E[u]]
* = [-1] + f[E[u]] / (1 - ) (28.3)
We can also prove that u = E[u] and then define E[u] = ERU[REH]. [88] Hence: [89]
= [-1] + f[E[u]] / (1 - )
E[u] = f -1[ (1 - ) ( - [-1]) ] = u
In this specification, the CWIRU can be ERU[REH], and ERU[REH] can be CWIRU. Namely, when * = [-1], or when expectational equilibrium is associated with constant wage inflation. Some ERU[REH] however can exist with nonconstant inflation that is not CWIRU. Since equilibrium wage inflation * is determined also by other factors such as money, the ERU need not be constant. Even when u = ERU[REH] for each separate year, then might still have an erratic development over the years. Similarly, the CWIRU can be an ERU[REH], but need not be. It can even be that = E[] but expectations are not REH - since the error is not white noise.
For full employment, policy is successful, if and only if u = uf and = *, so that:
ERU[FE] = uf = f -1[ (1 - ) ( - [-1]) ] (28.4)
This equation has the same format as ERU[REH]. It follows that uf can be REH, and REH could be uf. However, they need not be, since, though we have used the same symbol f, in practice there can be different functions and also additional variables depending upon the FE or REH assumption. [90]
Similarly, with this specification there might be constancy, and of course there might be not. And as said, constancy might not be the real issue, as small fluctuations in a stable range might be acceptable too. [91]
In the selection of f[u] we have to take account of the fact that u can shift as a result of the minimum wage. Workers below the minimum wage are not relevant for the labour market, and do not exert a downward pressure on wage inflation. Above we saw that u = un + um. Let fu[un] give the fundamental nonshifted relationship for that part of unemployment that still affects the development of wages. Conforming to empirical regularity:
fu[un] = - Log[un + ]
Here is a parameter for horizontal adjustment, gives the slope, and is a constant shift in u. Note that fu[un] may be very sensitive to low values of un and , since the logarithm from 0 till 1 is very steep, and un commonly is measured in percentages and thus covers that range. Now, for f[u], an endogenous shift in u then can be included by:
f[u] = f[un + um] = fu[un] = fu[u - um] = - Log[u - um + ]
Note that f[u] here is also acceleration, since 1/(1-) disappears in and . Figure 24 gives two regimes, plotted for both the f[u] in the left part and the Phillipscurve in the right part. Parameters are = = 5, = 0, and um = 0 [case (a)] respectively um = 6 [case (b)]. It is assumed that * = [-1] = 2 respectively 5, so that the minimum wage unemployment of 0 associates with an equilibrium wage inflation path of 2, while the high minimum wage unemployment of 6 associates with a high wage inflation path of 5. Since * = [-1] the CWIRU’s can be found when f[u] = 0, and these result in values of 2.7 and 8.7 (= 2.7 + 6).
Figure 24: Dynamics: unemployment and inflation
Given the assumption of * = [-1] it also follows that the Phillipscurves are just horizontal translations of the f[u], and one can see the values of 2, respectively 5, for the assumed wage inflations at the CWIRU’s.
The cases (a) and (b) in Figure 24 reflect the developments in the OECD in the 1950-2005 period. Case (a) gives the situation somewhat like the 1950s. The trade-off of inflation and unemployment then took place at low rates along the long drawn line. The trade-off of wage (price) acceleration and unemployment gives the CWIRU. At that point price acceleration is zero, and inflation remains at a low and constant value. Case (b) gives the situation of stagflation, where both the CWIRU and the trade-off-process around it have worsened. The move from (a) to (b) can be called ‘stagflationary’. In the 1960s and 1970s authorities targetted for low unemployment at the cost of rising and eventually high inflation. In the 1980s and 1990s the authorities targetted against inflation and accepted high unemployment.
The short term Phillipscurve concerns the direct trade-off of unemployment and (wage) inflation and is given by the long drawn curves. This trade-off has only limited explanatory value. Nowadays unemployment is concentrated at the low income section of the income distribution, and it is not likely that this can be battled with high wage inflation. This phenomenon is rather explained by the shift of the CWIRU or the long run relationships between equilibrium unemployment and wage acceleration, which are given in the left diagram.
It is useful to note:
· The CWIRU need not be constant. It could be if e.g. the relation indeed is linear and if the coefficients are fixed. But neither need be the case. The CWIRU in all likelihood is itself a variable that traces out a path. (Which is another reason why the name ‘natural rate’ is unfortunate.)
· There is a movement of the curve and a movement along the curve.
· The movement of the curve is not determined by the labour market alone. Policy makers may neglect labour market measures, and may opt for high inflation (1970s) or for high interest rates (1980/90s) to fight minimum wage unemployment that is not affected by these.
We may recall the 1995 Nobel Prize for Robert Lucas. The Swedish Academy put the following text on the internet:
“The change in our understanding of the so-called Phillips curve is an excellent example of Lucas’s contributions. The Phillips curve displays a positive relation between inflation and employment. In the late 1960s, there was considerable empirical support for the Phillips curve; it was regarded as one of the more stable relations in economics. It was interpreted as an option for government authorities to increase employment by pursuing an expansionary policy which raises inflation. Milton Friedman and Edmund Phelps criticized this interpretation and claimed that the expectations of the general public would adjust to higher inflation and preclude a lasting increase in employment: Only the short-run Phillips curve is sloping, whereas the long-run curve is vertical. This criticism was not quite convincing, however, because Friedman and Phelps assumed adaptive expectations. Such expectations do in fact imply a permanent rise in employment if inflation is allowed to increase over time. In a study published in 1972, Lucas used the rational expectations hypothesis to provide the first theoretically satisfactory explanation for why the Phillips curve could be sloping in the short run but vertical in the long run. In other words, regardless of how it is pursued, stabilization policy cannot systematically affect long-run employment. Lucas formulated an ingenious theoretical model which generates time series such that inflation and employment indeed seem to be positively correlated. A statistician who studies these time series might easily conclude that employment could be increased by implementing an expansionary economic policy. Nevertheless, Lucas demonstrated that any endeavor, based on such policy, to exploit the Phillips curve and permanently increase employment would be futile and only give rise to higher inflation. This is because agents in the model adjust their expectations and hence price and wage formation to the new, expected policy. Experience during the 1970s and 1980s has shown that higher inflation does not appear to bring about a permanent increase in employment. This insight into the long-run effects of stabilization policy has become a commonly accepted view; it is now the foundation for monetary policy in a number of countries in their efforts to achieve and maintain a low and stable inflation rate.”
The Academy is a bit too assertive. The Phillipscurve need not be vertical in the long run. It may well be that there is no fixed solution, and that the long run gives a non-converging movement. Also Phelps (1994) has reminded us that the CWIRU (in his words the NAIRU or ‘natural rate’) need not be constant.
Secondly, there can be other causes than expectations, and these might be more important for understanding the present situation. One important cause is the mechanism of the minimum wage. Hence the models used by Lucas and his predecessors need not be the relevant models for explaining the empirical shifts in the Phillipscurves and their CWIRU’s.
If labour is heterogeneous, then utility maximisation and rational calculation are not only directed at demanding a competitive wage, but they are also directed at selecting the kind of submarket (and its associated wage). This complicates the situation. Can we say that a dentist is ‘unemployed’ in the market for farmers ? Or closer linked, that an assistant professor is ‘unemployed’ in the market for professors ? However, we may note that an individual who sets his wages too high will become unemployed in any submarket. This causes an intuition that the selection of submarkets can still be represented by wage schedules. There will be more equilibrating forces than wages only, e.g. education or migration, but it can be reasonable to concentrate on wages.
With heterogeneity, the unemployment that is relevant for a submarket will have effects on the evolution of the wage in that submarket. Aggregating, however, we get an effect of macro unemployment on the average wage. Hence above simple relationship can be retained, but its interpretation changes from homogeneity to aggregation of heterogeneous submarkets.
Above we used um to show how the Phillipscurve can shift. Note that this in fact has only been a didactic procedure. I wanted you to understand the formulas, and it appeared very instructive to draw graphs of shifting Phillipscurves. However, when there are LS homogeneous labourers, we have some difficulty explaining why (1 - u) LS could work and u LS could not, even though they essentially are the same. Hence minimum wage unemployment and the shift of the Phillipscurve due to it, properly belong to the world of heterogeneous labour.
We here can extend the list of factors that can cause a shift in the aggregate Phillipscurve:
· The match of demand and supply above the minimum wage may cause separate problems. We will discuss the issue of crowding out on the labour market below.
· Vacancies will strengthen the position of employees and their unions. Employers may nevertheless wait with filling vacancies in order to find better opportunities later.
· There is ‘forward shifting’ of the tax burden T[w] / w from employees to employers (and then into product prices).
· The Labour Cost Quotes w / y may not just affect the equilibrating wage (or expectations) but may as well cause a shift.
· Poverty - see below.
We would basically model all submarkets - with minimum wage unemployment of course only occurring at the bottom. However, let us first look at the macro level only. Let us be the summary shift variable inclusive of all factors including um. Let usr be the summary shift variable exclusive of um. Let v the rate of vacancies, TAX/WT the tax burden. Let History be the history of all variables. Then redefine f[u]:
us = us[u, v, TAX/WT, WT/Y History] = um + usr[u, v, TAX/WT, WT/Y, History]
f[u] = fu[u - us] = - Log[u - us + ]
A crucial topic is crowding out on the labour market. Highly productive labour can replace lowly productive labour more easily than conversely, and this has effect on wage claims. This might be something like a continuous version of the insider-outsider theory.