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.

Concepts

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].

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

= [-1]

uf = ERU

CWIRU = ERU = ERU

Maybe temporarily, but impossible in the long run

Other

CWIRU = ERU

Maybe temporarily, but impossible in the long run

Non-CWIRU

uf = ERU

° = h[uf, u[-1]] + … if expected …

° = h[uf, u[-1]] + …

Other

ERU

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. 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 unemployment may be far from uf_ = ERU. 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.

A homogeneous Phillipscurve

A linear format

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.

- [-1] = ( - [-1]) + f[u] (28.1)

= _ + (1 - ) [-1] + f[u_] (28.2)

Equilibria

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. Hence:

= [-1] + f[E[u]] / (1 - )

E[u] = f -1[ (1 - ) ( - [-1]) ] = u

In this specification, the CWIRU can be ERU, and ERU can be CWIRU. Namely, when * = [-1], or when expectational equilibrium is associated with constant wage inflation. Some ERU 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 for each separate year, then might still have an erratic development over the years. Similarly, the CWIRU can be an ERU, 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 = uf = f -1[ (1 - ) ( - [-1]) ] (28.4)

This equation has the same format as ERU. 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.

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.

Selection of f[u]

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.

On expectations

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.

Heterogeneous Phillipscurves

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.

More factors that cause a shift

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 + __]

Crowding out

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.

Unemployment among the higher skilled is not large. The analysis here is that this is caused by crowding out on the labour market. When potentially higher productive people face the choice between unemployment and a comparatively lower paid job, they choose the latter (noteably when they are tired of waiting or when the benefit runs out). They thereby “take the places” of others - who repeat the process to others below. The initial set-back in pay level tends to translate into demand for pay rises. Who crowds out, has a stake in trying for pay rises. A lot of crowding out will cause a mood for inflation. Who have been crowded out towards unemployment, have some incentive not to inflate, but have little countervaling power against the general mood for inflation.

Figure 23 already presented the stylized fact for labour demand and supply, i.e. that vacancies tend to occur at higher income and unemployment at lower income.

There is a meaningful aggregation of vacancies and unemployment by subcategory of low and high productivity workers, giving Vl, Vh, Ul and Uh. When vacancies are asymmetrically relevant only for the higher incomes (V ~ Vh, Vl ~ 0), and when there are always vacancies for higher incomes due to crowding out (Vh >> 0), then V is not that important. However, V may become important again when Vl is made nonzero by proper tax policies. If low productivity labour has a stronger position in the labour market, then the risk of unemployment is spread more evenly, and trend-setting high productivity labour will be cautious about wage claims. High values of Vl and Uh, i.e. vacancies for the low productivity group and unemployment for the highly productive group, have the largest wage checking effect. High Vl and Uh make it difficult for the trend setting higher productive workers to shift the risk of unemployment to the lesser productive workers. We will not formally develop this point.

Crowding out on the labour market typically refocusses the policy co-ordination problem to the lower end of the market. This phenomenon tends to reduce the problem and our vocabulary in these pages to social subsistence, tax exemption and (legal) minimum wage.

Poverty

A crucial difference between the United States and Europe is that the US accept more poverty (e.g. by low controls on its minimum wage laws), while Europe chooses high minimum wages and benefits to raise standards of living. The shift of the Phillipscurve thus is more obvious and stronger in Europe than in the US. In the US the working poor still work, so unemployment is lower, and the shift of the Phillipscurve is less strong. Sometimes the argument stops here. It remains a topic of consideration though whether more than just this can be said about poverty.

Poverty affects productivity directly. A clear case is medical care. With less medical care, there are longer periods of illness, and more chances for complications of a less well attended illness. Employers are less likely to hire less healthy persons.

Poverty affects personal appearance. A shabbily dressed and badly groomed individual has less chance of employment than a person of average appearance.

Poverty affects social attitudes. Social seggregation and cultural differences reduce the chances of employment.

Poverty affects capacities. Rich people need not study much, need not read many papers, and may only watch soap operas. They are rich, and can enjoy themselves. But those of the rich who would like to study, read, watch serious tv programs, and drive out to educational events, have the means to do so. Those who are not that rich, and those who have to study to maintain a higher living standard, may work and still earn enough to enable them to study. Those of the poor section that might want to do the same, do not have those means.

One aspect of US poverty is crime. Poverty does not actually force people to crime, as some people demonstrate, but for many it in fact appears to be very seductive. Jacobs (1996:573), referring to Freeman (1996:25-42), explains that about 2% of US males is in prison, about the same rate as long term unemployment in Germany. Taking account of women, the overall US imprisonment rate is about 1.2%. The highest rate of European imprisonment is for the UK, with 0.3%. So for the US we might add 0.9% to the unemployment rate.

Also, additional 5% of US males is on conditional leave etcetera from the prison system. More have a criminal record. Those points reduce the chance for employment.

Some of these points, like imprisonment, work directly as a minimum wage. Some other points rather affect the employment or earnings distribution, and cause a structural rise of Ul.

The submarket Phillipscurves

Here, for simplicity, we take the wage level w instead of wage inflation. The rates of change can be found by comparing to w[-1].

Wage w, a continuous vector for each market, depends upon the power position of employers and employees, which is determined, amongst others, by the relative situation of unemployment versus vacancies. Since unemployment and vacancies have been expressed above as functions of w we solve w as a fixed point. We also add the equilibrating w* (or expectations E[w]) that are a function of product y, the tax burden for forward shifting, the labour cost quote, macro variables and the history of the variables. The submarkets Phillipscurves can include influences of other submarkets and general developments pertaining to all markets. A macro-economic hypothesis is that the development within markets is not merely influenced but even dominated by general events. The relationships are clearly dynamic, and we thus read all variables as time dependent.

w[y, T, Macro] = w[ w*[y], ud[w], vd[w], T[w] / w, w / y, Macro, History ]

Note that modern large models depend upon convergence techniques, and that the computation of fixed points can be included into convergence in general (though it would be computationally burdensome).

Shifting back

The stylized facts can be summarized as:

· In the 1950-1970 period, welfare states generally had a high tax exemption level and full employment.

· In the 1970-2005 period welfare states generally had a low tax exemption level. To ensure a decent stardard of living, required gross income then rose and exceeded productivity in the low end of the market, generating unemployment, while shifting the Phillips curve and reducing its sensitivity.

· Even when the statutory tax system has a low exemption level, then subsidies for the lowly productive keep them in work. And subsidies can be at the firm or state level. This is crucial for the Japanese and Swedish experiences, see e.g. Aoki (1990) and Standing (1990). Note that, in a reduced form, subsidies turn up as ‘system-wide exemption’. A subsidy is no ‘real’ subsidy if it compensates for wrong taxes.

Measures to block crowding out boil down to giving the low productivity group some guarantee for work at decent income. Such guarantees can be collective/semi-private arrangements of the Swedish/Japanese type. For the more common mixed economies, the guarantee is market-conforming, and notably consists of tax exemption.

29. Tax basics

Taxes are relevant for the discussion of stagflation at least for the following reasons:

(1) Taxes divert income and thus affect aggregate demand, especially when tax revenues go to benefits and consumption instead of saving and investments.

(2) Taxes are thought to cause forward shifting, i.e. that taxes are shifted into wage costs, which then may cause inflation.

(3) Taxes reduce net wages, and might affect the supply of labour. Statutory marginal rates are thought to have disincentive effects.

(4) If exemption is lower than subsistence, then a higher minimum wage is required. Differential indexation widens the gap.

In the following we will first discuss the relation of social insurance premiums to the economic concept of a tax. Then we regard the common tax structure of OECD countries, where the structure concerns both a statute and the dynamic adjustment policy. We introduce a nonlinear tax function and rules on indexation that captures this structure. We then show the effects of differential indexation, and present our new analysis on marginal rates.

Tax dynamics can be split into two components: the dynamics of the short run - where a local temporal equilibrium is attained using the calculations on the marginals - and the dynamics of the long run - where the locus of possible equilibrium points is shifted by long run effects on the levels of the variables. Both components appear to be equally important for our understanding of the subject. The observations on the long run can be usefully discussed in conjunction with the theoretical developments.

Taxes and premiums

In our discussion we will take premiums as part of taxes in so far as it is economically relevant to do so. This may need some clarification.

Premiums for old age, sickness, disability, unemployment and the like are often regarded as insurances, and studied separately. In the practical situation of empirical economies these provisions are often indeed administered by separate institutions called ‘insurance companies’. And there indeed exists the possibility to apply the mathematics and economics of insurance to these topics. However, that these provisions are called ‘insurance’ should not cause us to regard them as only such. Part of these so-called insurances are provisions for the efficiency of the labour market.

To understand this, let us take the case of a low wage labourer. Suppose that he would have to pay such an amount of premiums, for only a limited package of insurance, that his net wage would make him eligible for benefits, or his gross wage would make him unemployed so that he also gets a benefit. Once he relies on benefits, the mentioned insurances are provided for him for free.

This thus shows the structural identity of the problem of exemption in ‘insurance’ with the problem of exemption in taxation. Hence, on economic grounds, insurances here are lumped together with taxes, in so far as they are provisions for the well functioning of the labour market.

Note too that governments would be wise to follow a ‘basic insurance policy’ which holds that workers can be insured up to a basic level but without payment of premiums. This reminds of the ‘basic income argument’, but only applies to the mentioned premiums. Similarly poor people exempt from taxation receive public goods, without paying for them.

Common structure

Most developed nations have nonproportional taxes, i.e. tax codes with an exemption at the threshold and then a (rising) statutory marginal rate. The latter parameters in fact concern the intercept and the slope of the tax function. There is also a remarkable similarity in the policy regarding these two parameters (or sets of parameters), see OECD (1986):

· The policy feature concerning the intercept or exemption. Exemption generally is low, also with respect to social insurance. Tax parameters, and notably exemption, are generally indexed on inflation. Since incomes tend to grow faster than inflation, exemption lags behind incomes. There is a deliberate tax creep - measured by the ‘macroeconomic progression factor’.

· The policy feature concerning the slope or the statutory marginal rate. Both in theory and public discussion there is a consideration that high marginal rates have disincentive effects. This has resulted in the policy objective to reduce marginal rates. One way to reduce marginal rates has been the switch from income tax to VAT.

Given the common notion of budget neutrality, these two features in policy tend to complement each other. Budget neutrality requires that the revenue loss due to slope reduction is compensated for by other proceeds. These other proceeds will often come from the tax creep and the reduction of exemption. At least, it is often thought that the reduction of exemption generates additional revenue. This, however, turns out to be a wrong assumption.

Nonlinear tax function