Chapter 40 Showed the Technical Possibility of Full Employment for a

welfare state. Chapter 34 showed that social choice is feasible, in the sense that there are consistent and reasonable constitutions that society might deem attractive. In particular, there is the example of a constitution that uses the efficiency criterion (Pareto optimality, PO) to select its policy. There still remains one issue to settle. This is the issue of information. Society might have a consistent preference, and consistently prefer full employment above unemployment, but when people don’t know that it is possible, and instead even have theories that tell them that full employment is impossible, then society might still choose for unemployment as the best of all evils. The issue of information already featured in our discussion of Arrow’s Theorem, and now returns for our discussion of unemployment.

We again follow the procedure given by our methodology. We select stylized facts, develop our concepts, deduce results, and link back to reality. We will first construct a subsidiary lemma that is very general and concerns any suboptimality due to misinformation. Then we take our theorem on the possibility of full employment, recognise it as an item of information, insert it, and construct our theorem on the possibility of co-ordination.

Stylized facts

Recorded full employment situations may have been caused by ‘chance’. Policy makers in 1950-1970 may have thought that functional finance was effective, while it also was the tax exemption level. A re-evaluation of the history may however also show that leading economic advisers in the 1950s may have been wiser than those of the 1960s.

It remains a stylized fact that much of the subject matter on employment is well-known. For example in Holland, CPB economists Van Schaaijk (1983), Bakhoven (1988) and Colignatus (1990) pointed the way to full employment. The state of knowledge turns out to be part of the model.

There is a Pareto Optimizing Change (POC) iff some advance and none suffer. A change from unemployment to employment need not be strictly POC. Note that we already have resolved that we don’t need high unemployment to keep inflation in check. So the CWIRU is no argument against a POC. There are other clear reasons that pose a problem. First these two:

· Some bureaucrats have plush jobs administrating the unemployed, and would lose their job and sense of power.

· The unemployed would lose their leisure. For some, the combination of low benefit B and leisure might be preferable to work at a higher income.

We can overcome these barriers by going back to basics, i.e. to our definitions. First of all, the bureaucrats are reminded that they are there to serve the public cause (‘res publica’) - and thus they have signed a contract - before they got the job - that they will welcome full employment and raise no anti-POC objections. In the same way, the people on the dole have signed a contract - before they got the benefit - that they will accept a job at a living wage, and will not raise anti-POC objections either.

A final observation is that the power elite, those who determine the SWF, might enjoy unemployment of a section of the population for some strange other reason. They might not care about the increase of income, freedom and welfare from a change towards full employment, but they would prefer the idea of people in helpless positions and the warm gratitude they show for their benefits. A king needs subjects. We resolve this problem by proper formulation of the theorem.

Concepts

Note that we use the symbols of chapter 39 (that forms a unity with this chapter).

Above theorem on the technical possibility of full employment is essentially incomplete. It has not been specified how the tax regime comes about. The tax regime is an expression of the social choice already made, but it has not been explained how a particular choice has been caused. What is required is a power distribution on the b + h + l agents in the economy. In conventional terms the power distribution is expressed as a social welfare function SWF, and the tax regime is the result of the maximisation subject to the state of information I:

maximise SWF(h, H, N, l, L, K, b, B, t; I) (40.1)

Using a SWF serves expository purposes. When turning to practical application we could use the Drissen & Van Winden (1990) approach. But the logic of both approaches is the same.

The introduction of regime indicator t as a separate variable in the SWF means that it stands as a proxy. The economy is not simply a collection of individuals maximizing utility over consumption and labour. There are some institutional aspects too. An example of an institutional influence is that some social security officials might benefit from unemployment, since it keeps them in attractive jobs. All such (Public Choice) phenomena can be collected on their point of relevance: the employment regime t.

Secondly, there is information I. Ever since Keynes and Tinbergen, or even earlier, but for some economists more acutely since Muth and Lucas, economists have given attention to the information sets that guide the activity of agents. This concerns not just plain knowledge, but rather what people believe about the state of the world. The information sets may contain individual and social aspects, like own prices and the (announced) general price level.

Variable I is an aggregate. It represents the state of knowledge of those in power, where ‘having some power’ is a state of nature given by an array or by a distribution. The latter is not further developed here. A basic point however is that if some economist would know how to solve unemployment, but those in power don’t, then the budget set is IB, while I < IB - and those in power apparently prefer not to know.

The use of variable I could complicate the analysis in various ways. R&D could be an economic activity affecting social welfare itself, amending (40.1) etcetera. But the present formulation suffices for our purposes. Note, the maximisation process itself finds its operational implementation in the actual work of some agents in the economy. Such work might be implicit and thus not explicitly remunerated. More conventionally there are some administrators (e.g. a “Council of Economic Advisers“) who are explicitly paid for their information handling activities (often: whatever outcome on t).

Piore (1987) reminds us that unemployment is not a natural disaster like an earthquake, but derives its cause, nature and significance from the social system as a whole. In this line, when unemployment arises, we would find the solution by studying the whole system. This includes information. And Piore’s reminder, being a reminder, is a piece of information. Indeed, one important social type of information concerns theory itself, and economic models in particular. The development of the theory of Rational Expectations (or model-consistency) implies this too. Economic theories about unemployment are themselves part of the information sets in society. An adequate description of unemployment not only requires a statement of taxes, social security and e.g. legal minimum wage, and their technical interaction, but also a statement of people’s perceptions, of the theories in the journals, and of what journalists and politicians make of these.

When unemployment arises, it may be caused by the power distribution, but the cause can also be plain lack of knowlegde. It may very well be that Piore’s proposition has not gotten sufficient attention from policy makers and advisers. And this lack of attention, if it were true, would be a prime example of the influence of the information set on economic activity.

There are two relevant states of information: I = 1 meaning that those in power perceive of a (sound, compact) solution of unemployment, and I = 0 meaning that this is not the case. Note that knowledge about the theorem on co-ordination, that is to be formulated next, might but need not be included itself in I = 1.

The Dissipation of Knowledge I by science, education and media need not be detriment to those in power, but it might be. In the latter case I would not be POC in the ordinary sense. However, many would hold that I morally dominates POC - and if these people are in power, then this conviction is reflected in the SWF. Note also that I need not be positive, e.g. when a wise king dies or a wise government party loses the elections. Note that when I coincides with a shift in power, the prime cause can be both personal properties involved or the information; but here everything is aggregated into the latter.

We conclude this section by a short abstract discussion of the concept and properties of information, and Lemma III.

Regard a controlable dichotomous system with states s = 0 or s = 1. Two consecutive states are of the form {0, 0} and {1, 1} where the regimes are maintained, and {0, 1} and {1, 0} where there is a switch. If policy is conscious, then the movement from one state to the other (or the same) depends on information - and thus there are four lists of basic information. With 4 such items, an agent’ mind can possess any combination. There are 15 of such combinations: namely 1 case where all 4 are known, 4 cases of only 3 items, 6 of 2 items, and 4 cases when only 1 is known. It will be useful to compress this abundance.

The following definitions are useful:

Definition: Basic information is a list of “what one does” to have one state in one moment and another state in the next moment. An example list is: {“Provide oxygen and a dry place”, “Light the match”, “Let it burn till it is all cinders.”}. Other examples are recipes, film scripts, computer programs (“Click on a button”). We can denote basic information as BI(s1, s2). Note: In this version of the proof we allow basic information to be true or false.

Definition: A state s is said to be controlable iff there exists - in principle - true basic information on both s and 1-s, and the agents have the resources to use this information. Note that this information need not be known by the agents (need not be available), and it need not even be known to the agents that the matter is not unknowable.

Definition: Information is available when at least one agent in the economy has it. (This is stronger than the ‘existence in principle’ of controlability.)

Definition: Sound information J(s) is a list of both what one does to maintain s and what one might do to change s into 1 - s, using true cause and effect relations. Thus J(s) = BI(s, s) BI(s, 1-s) | truth. Denote an arbritrary belief as J’(s) - that however will not be sound since it would not be necessarily true.

Remark: True information is sound when the information concerning {1, 1} and {1, 0} is joined, or if the information on {0, 0} and {0, 1} is joined. One may e.g. know how to burn or not to burn a match, but not how to restore cinders into a match again (except for restarting the universe, but that is not likely controlable). Let 1 stand for match, and 0 for cinders. Then J(1) exists, but J(0) doesn’t (only partly, to maintain cinders as they are). Using sound information rather than basic information has analytical advantage. A Roman emperor may think that he maintains his good fortune by sacrificing to the gods. We rather discuss cases where governments deliberately abstain from wrong policies.

Remark: Consider the list {“If you happen to flip back to 0, use BI(0, 1) to go back to 1”}. Can we classify this as BI(1, 1) ? We could allow this if the cost of the temporary flip is low. For example, riding a bicycle requires continual readjustment of equilibrium. We can define BI(s, s) = {chance(s, 1-s)} BI(1-s, s) | truth, as implied control information. But since this does not give BI(s,1-s), the implied control information does not give sound information. Stated differently, we are interested in durable states s, and not in flipping states. If we observe s then we want this to be caused by deliberate rejection of the use of BI(s, 1-s). We also regard cases in which implied control would be costly.

Definition: The tuple (J(1), J(0), s) is the state of a sound system. Note: Though the information is denoted as a function of s, information in a controlable state is the prime cause and s the prime effect.

Definition: Information is called compact iff J(0) J(1). Note: Compactness means that one knows the explanation of one state, iff one knows the explanation for the other state. Then we can use a single variable J or J’.

Definition: A state s is said to be caused by chance iff a situation of s and unsound belief J’(s) are stable. It is said then that there is a hidden cause linking J(s) to s.

Definition: If the sound information concerns a model then we can denote J in binary values, with 1 = ‘the model is known’ and 0 = ‘the model isn’t known’, rather than use the whole list of statements. With binary information, compactness J(0) J(1) becomes J(0) = J(1).

Remark: Consider the example of the Roman emperor. His model is ‘sacrifice fortune’ (and if fortune slips after a sacrifice, then apparently more sacrifices are required). One of his basic informations is BI(~fortune, fortune) = {‘sacrifice fortune’, ‘In this case sacrifice’}. Since J’(1) J’(0) this is a compact belief.

Remark: If s is the case, and one doesn’t believe J(s), so that J(s) = 0, then one believes some alternative J’(s). Someone unfamiliar with matches would have the unsound (perhaps only basic) information ‘this is just a piece of wood’. More complex situations need thorough analysis. E.g. someone may know the text of a theorem and benefit from that, but may not know its proof.

Lemma III: If there is sound information (J(1), J(0)) on a controlable dichotomous state s, then: (i) if the information is not compact then there are 8 states of the system, with 4 states implying a hidden cause, (ii) if the information is compact, these numbers are halved.

Proof:

We tabulate the possible states of the system (J(1), J(0), s) in Table 16.

In cases (rows) (3), (4), (6) and (7), the agent doesn’t possess sound information and believes some J(s) (e.g. ‘the world is as it is’), but he chances at s nevertheless. This implies that there is a hidden cause. (For example, the state of the system was inherited, and the agent wishes to keep things as they are. In that case (J’(1), J’(0), s) has causality within a more complex model, describing in more detail how people act on their beliefs.)

If the information is compact, we only consider states (1) to (4). Q.E.D.

Discussion: To understand the proof, look for example at row 6: There is a true model for sequential states {1, 1} and {1, 0}, or to maintain 1 or change to 0. But nothing is truly known about maintaining 0 or changing back from 0 to 1 (though beliefs can exist). Observed is s = 0. Perhaps it once was a conscious choice to go from 1 to 0, and perhaps one uses the implied control {chance(0, 1)} BI(1, 0) | truth. But we are concerned with durable cases for which implied control would be costly. We want to see deliberate rejection of the use of BI(0, 1). But this information is not present. Hence the endurance of 0 is caused by chance.

Table 16: States of the system

J(1)

J(0)

meaning

(1)

given J = 1

one chooses

s = 1

(2)

given J = 1

one chooses

s = 0

(3)

given J = 0

one chances at

s = 1

(4)

given J = 0

one chances at

s = 0

(5)

given J(1) = 1

one chooses

s = 1

(6)

given J(0) = 0

one chances at

s = 0

(7)

given J(1) = 0

one chances at

s = 1

(8)

given J(0) = 1

one chooses

s = 0

Note that a conscious choice is made when one does not use the information to switch to the other state.

The special theorem

When we apply Lemma III, which is about information handling in general, to our subject matter of employment, we get what for this area amounts to a theorem. The first theorem is special since it assumes the BHL property.

Definition: There is wrong co-ordination if a SWF optimal change is blocked only by ‘lack of knowledge’ of the power elite while the information actually is available. (Co-ordination can go wrong on other counts too.)

Theorem BHL.2: Given theorem BHL.1: (i) full employment results from conscious choice or chance (ii) unemployment results from conscious choice or from wrong co-ordination

Proof:

Theorem BHL.1 shows that full employment for the BHL welfare state is a controlable dichotomous state. The theorem is sound and compact. Thus Lemma III applies.

Possible states of sound compact knowledge and employment (I, t) are:

(1) (1, 1): having the knowledge, full employment results;

(2) (0, 1): lacking the knowledge, full employment results; thus there is a hidden cause; thus it is by chance;

(3) (1, 0): having the knowledge, unemployment results; thus, the explanation comes from the power distribution, so that full employment is not to the advantage of those in power, and the choice for unemployment is conscious;

(4) (0, 0): lacking the knowledge, unemployment results. Note that theorem BHL.1 is available knowledge (e.g. it was published by Colignatus (1992b, 1995a, or this book)). Where we currently speak about ‘lack of knowledge’ then we mean the knowledge of the power elite, who do not fully use the knowledge budget set. Introduction of theorem BHL.1 into the knowledge bank of the power elite unveils two subcases:

(4.1) There is a switch to (1): optimal change was blocked only by lack of knowledge, while the information actually is available: hence wrong co-ordination; (4.2.) There is a switch to (3): information doesn’t matter.

Q.E.D.

Remark: In both employment regimes we have ‘conscious maximizing behaviour subject to the state of information’, but the regimes cause different conditions. There is little use in subdividing case (2). If more information is introduced, then the power distribution may cause unemployment. This effect however has already been covered in (3). See the note “more on chance”.

Remark: Cases (3) and (4.2) give the situation where the possibility of full employment merely is logical but not empirical. It is conceivable that power parameters and political reaction patterns are such that the economy remains in a state of unemployment forever.

Remark: In case (4.1), and when there are subpopulations of theorists (‘those who know’) and policy makers (‘those who can do’) then there is the Van Schaaijk Corollary: “Those who know, cannot do anything about it; those who can, don’t know.” The addendum here is that ‘not-knowing’ is no excuse for a policy maker who should know.

There remains the interesting point of the potential difference between Pareto Optimality and SWF optimality, when information is the active variable. One may remember the bureaucrats in their plush jobs and the benefit recipients who enjoy their leisure. Here Lemma IV applies.

Definition: A situation is Properly Pareto Optimal (PPO) compared to an alternative iff it would be PO when some conditions are properly defined and interpreted - while it seems non-PO when these conditions are ill-defined and wrongly interpreted.

Lemma IV: For a BHL economy, regime 1

(i) has the highest level of national income,

(ii) is PPO compared to regime 0.

Proof:

(i) Equation (3-t) immediately implies Y(1) Y(0).

(ii) Regard the change from 0 to 1:

(B) permanent benefit recipients are not affected by a regime switch,

(H) N(1) N(0),

(L) K(1) B.

Hence all agents improve in a material sense. Thus regime 1 is PO compared to regime 0, if we restrict attention to these income aspects. The actual choice is made by the SWF, and this choice includes power effects of the bureaucrats (who may want to maintain unemployment) and the unemployed (who enjoy leisure while on benefit). This contorted SWF can be cleaned up by proper contracts and execution of those contracts. Then PO is restored.

Q.E.D.

Remark: It stands to reason that if a change to full employment occurs, it is mainly because it is POC. This highlights the problem of wrong co-ordination.

Remark: In normal work-ethic conditions, the income-leisure utility considerations of the l low productivity workers improve too, when they move from forced leisure to a decent job. It is conceivable though, that the advance in net income does not compensate for the loss of leisure. Therefor, the concept of PPO is useful. In another respect, the voting power of l may be small, and when society decides that unemployment was a silly affair, the l may be said to have had an unintended bonus while it lasted. (Society might even try to recover that bonus.)

Remark: There is scope to define and judge PO from some fundamental rights rather than from the actual bureaucratic flux.

Remark: In an applied general equilibrium context we would have to deal with complexer aspects, like people fearing to lose their jobs, and the loss of income resulting from crowding out. Adding ‘approximately’ would help Lemma IV surviving.

The general theorem

Definition: There is wrong co-ordination if a SWF optimal change is blocked only by ‘lack of knowledge’ of the power elite while the information, though not yet available, still could be found rather quickly by not much effort. (Co-ordination can go wrong on other counts too.)

Theorem G.1: If full employment is a controlable dichotomous state for which sound compact information exists in principle, that also can become available rather quickly by not much effort, then: (i) full employment results from conscious choice or chance (ii) unemployment results from conscious choice or from wrong co-ordination

Proof:

Work along the proof of theorem BHL.2. Note that BHL.2 fills in the properties that are now provided by hypothesis: controlability, soundness, compactness, and availability. Note that controlability means that the information exists in principle, while it need not be available yet.

Q.E.D.

Remark: Theorem BHL.2 thus gives an existence proof for this general theorem, i.e. shows that it is not vacuous.

Remark: The value of the theorem is that it focusses our attention on the perceptions that we have to deal with when judging the arguments in this book. Some questions to be answered are: (1) Do we still believe in full employment (only friction unemployment), or do we think that there are serious bottlenecks - or do we even think that we live in a probabilistic universe ? (2) Do we seriously believe that governments have done their best, or at least a reasonable effort, for (a) using available information, (b) finding additional solutions ? (3) Do we really think that the BHL-concept is useless, and that governments have been right to neglect the papers on them ? (4) Do we seriously believe that the PO-changes that seem so likely, are not POC ?

On the interaction of the reduced form theorems

Our analysis has not provided complete statistics on existing welfare states, and it can neither replace the need for more study, especially with the cornucopia of applied general equilibrium modelling. The analysis here does however fit in with the stylized facts. It is good strategy to apply logic to circumvent the uncertainty of parameter estimates. There is sufficient reason as well to accept that the two propositions forwarded here give main results in a nutshell.

The first proposition is that both unemployment and full employment are possible for the (BHL) welfare state. The second proposition is that unemployment follows from either conscious choice or wrong co-ordination caused by (deliberate) lack of knowledge, and full employment from choice or chance.

It may be emphasized that the logical force of the argument derives from the undeniables both that one can take subgroup averages and that two points share a line. That line finds its translation, in economic vocabulary, of a social welfare function with a power interpretation.

Above discussion on information is a small step in formalising rather well-known insights. Formalisation, how small the step may be, can be crucial to get the statistics going, and in helping to establish what the state of the world actually is. Apparently we need statistics on what economic advisers and policy makers believe.

Above discussion provides a foundation for a policy conclusion, that it would be good for many welfare states with declared objectives on full employment to improve on informational procedures.

More on chance

The mentioning of ‘chance’ in the lemma and theorems induces a short discussion on randomness.

Let Queen Q fall in love with Prince Random PR. Q especially adores PR when he goes about the court with an attractive air of responsibility. To this end she gives him the job of Treasurer. However, PR does not know much about taxes, and true to his name he chooses tax exemption at random. Hence, any regime is ‘subject to approval by official royal authority’, and in this sense there is a SWF and maximisation. And only economists think that the economy or economic theory are relevant. On the other hand, this is an incomplete sense of optimality. If PR happened to choose regime 0, then teaching PR about taxes would have Pareto Optimizing effects. In this sense, only one case is really optimal. This example shows that we can discuss cases with random elements, and that we can maintain our classification of cases. In fact, Y(1) - Y(0) would be the ex post implicit price paid, in regime 0, by the Queen for decentralizing decisions to a nitwit. If PR has ex ante probability p of choosing regime 0, the ex ante expected loss is (1 - p).(Y(1) - Y(1)) + p.(Y(1) - Y(0)). It is not very useful, however, to indulge in the notion of randomness, when considering the theorem. The stylized fact is that it is the (deliberate) lack of knowledge that is crucial here.