Leaving aside that MMT and New Keynesian Economics (NKE) define full employment differently, this claim obscures a fundamental difference between the two theories. In NKE, as with neoclassical approaches more generally, there would be an automatic tendency to full employment in the long run if there were no imperfections or rigidities to impede the supposed adjustment process (including, in the case of NKE, no impediment to appropriate interest-setting monetary policy). For example, the favored justification for a fiscal response to unemployment in the wake of the global financial crisis was that the economy was in a liquidity trap, taken to mean that the real rate of interest was stuck above its so-called ‘natural’ rate due to monetary authorities confronting the zero lower bound. Absent this rigidity and any other rigidity (sticky wages, sluggish revision of expectations, etc), NKE implies that there will be full employment in the long run.

MMT is not neoclassical. It comes out of a different, broad theoretical tradition (which includes Post Keynesian economics and related Kalecki and Keynes influenced approaches) in which there is no general tendency for the economy to tend toward full employment even in the absence of imperfections and rigidities. In these theories, complete wage, price and interest-rate flexibility would not imply spontaneous adjustment to full employment over any time frame. Nor could policy administered interest-rate adjustments be relied upon to generate full employment, even when the economy was not at the zero lower bound, in contrast to the conclusion of NKE. The notion of a natural rate actually makes no sense in MMT or in the theoretical tradition from which it emerged.

The rejection of natural rate reasoning, and by extension appeals to a liquidity trap in the sense this term has been used since the global financial crisis, is theoretically informed by the capital debates (Matias Vernengo provides an informative introduction) and various arguments of Keynes (Bill Mitchell has a long series of posts entitled ‘Keynes and the classics’ beginning here). It is also consistent with the paucity of empirical support for a significant inverse relationship between the rate of interest and private investment upon which neoclassical spontaneous adjustment to full employment depends (see, for example, papers by Robert Chirinko, Jamus Lim and Steve Sharp and Gustavo Suarez).

Why is this relevant to the present comparisons between MMT and NKE?

It is relevant because it means the policy implications of MMT are in fact different to NKE over any time frame. In MMT there is no presumption that the economy will be at full employment in the long run. (This is so unless a job guarantee is in place, in which case there will be what MMTers refer to as ‘loose full employment’ at all times. This will be full employment in the sense that anyone who is willing and able to take a job at the job-guarantee wage will be employed.) In the absence of a job guarantee, there is no presumption in MMT that the economy tends toward full employment. An implication is that larger government deficits now do not necessarily imply smaller deficits or higher taxes in the future. It may be that full employment requires deficits in the future just as it does now. True, if it turns out in the future that full employment can be achieved with a smaller deficit, MMT will call for a smaller deficit. But it could go the other way.

If, as MMT prescribes, a job guarantee is put in place, full employment will not even be the relevant benchmark. With a job guarantee implemented, loose full employment will be achieved at all times irrespective of the overall level of demand. The relevant benchmark will then be the “non-acceleraiting buffer employment ratio” (NAIBER), meaning the smallest fraction of total employment that can be located in the job guarantee sector while still maintaining low, stable inflation. On the basis of MMT, there would be no spontaneous tendency for the economy to move toward the NAIBER, just as there is no tendency in the absence of a job guarantee for the economy to move toward full employment.

The premises and logic of MMT lead to the job guarantee as the means of simultaneously achieving and maintaining both full employment and price stability. Unless this is also the conclusion of NKE, based on its premises and logic, it can hardly be said that MMT “has nothing new to say at full employment”. Clearly it is not the obvious conclusion of NKE. If it were, New Keynesians would have drawn the conclusion long ago. Within the framework of NKE there need to be rigidities (e.g. a liquidity trap) to justify fiscal demand management. Even under conditions of unemployment, there is no place for fiscal demand management in NKE unless a rigidity can be identified.

It is perhaps also worth noting that a related claim – that MMT can be reduced to NKE with the policy tools switched (with fiscal rather than monetary policy assigned to demand management and monetary rather than fiscal policy geared toward controlling the level of interest on public debt) – is similarly unfounded. The observation so far as it distinguishes MMT’s preferred assignment of policy tools from NKE’s preferred assignment is a good one in my view (discussed previously here). However, the notion that MMT can be characterized simply by assuming within the New Keynesian framework that the interest rate can be geared solely toward keeping interest rates on public debt low relies on monetary authorities being able to choose the interest rate without regard to the so-called natural rate of interest and to do so indefinitely. This notion is unproblematic in MMT since within this framework there is no valid reason for supposing the existence of a natural rate of interest. The interest rate, in the MMT framework, is a policy variable, including in the long run. But in NKE, the existence of a natural rate follows from its neoclassical premises (including its marginalist microfoundations). So to impose, within the New Keynesian framework, the arbitrary restriction that the interest rate must be set according to public debt considerations is not only *ad hoc* but violates the constraint on policymakers that is implied by the existence of a natural rate, an existence that follows from the premises of the theory.

In short, MMT is not merely a policy position on government deficits that can be faithfully and fully represented by placing arbitrary restrictions on New Keynesian models. It is a theory built upon non-neoclassical foundations in which even under complete wage, price and interest-rate flexibility there would be no tendency for output to move to any particular level independently of fiscal policy, over any time frame. One implication of this – but only one implication – is that there is no reason to suppose that the fiscal stance called for today is in any particular relationship to the fiscal stance called for in the future. Fiscal surpluses today will not necessarily call for tax cuts in the future and fiscal deficits today will not necessarily call for higher tax rates in the future.

The foregoing argument is not intended to deny that there has been considerable common ground between MMT and NKE when it comes to the appropriateness of fiscal deficits in the aftermath of the global financial crisis. Economists of both persuasions have quite rightly been supportive of expansionary fiscal policy. The argument concerns the theoretical justification for this policy stance in the short term and the implications of this policy stance in the long term.

**Related Posts**

Balancing the Budget Over the Cycle

Institutions, Monetary Operations and a Demand-Led Global Economy

Vernengo on Keynes vs Neoclassical Synthesis

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1. the arbitrariness of exempting the wealthy from any expectation that income of the able-bodied be conditional on labor-force participation;

2. the range of options that would be available to all individuals under some kind of ‘job and/or income guarantee’;

3. the unfairness of work outside the labor force (most notably home parenting and housework) being performed without receipt of income simply because it is not codified within a waged or salaried occupation;

4. the relatively small ecological footprint of low-income individuals and the benefit that accrues to all when some people voluntarily eschew consumerism beyond the minimal level necessary for survival.

Here I mainly have in mind a combined ‘job or income guarantee’, which could be implemented in various ways. In lean form, the policy would give individuals without a job the option of either a job guarantee position or smaller basic income payment. In expansive form, universal basic income would be implemented alongside a job guarantee.

Although much the same arguments would apply to standalone basic income, a combined policy offers certain benefits that a standalone policy would not. In particular, it would ensure both that: (i) anybody wanting a job could obtain one; and (ii) survival would not depend on labor-force participation. In combination, the two policies would have inbuilt safeguards: the existence of basic income would make it difficult for enemies of the job guarantee to reduce it to workfare; the operation of the job guarantee would limit the possibility of basic income simply acting as a wage subsidy for employers.

To elaborate on the points listed above:

**1.** There are already able-bodied individuals who receive interest, dividends or other forms of profit income without being required to participate in the labor force. If it is unfair for income to be received without a labor-time commitment, then this should apply as a general rule. Either everyone should be given a right to minimal income without a labor-time commitment or nobody should. The fairness critique of basic income would hold more weight if the requirement for able-bodied individuals to participate in the labor force was made general, as might occur in a socialist society.

**2.** If everyone had the choice of opting out of the labor force, those who chose not to would be doing so voluntarily. If a particular person felt that the lot of a basic income recipient without employment was so desirable, they would need only take that option themselves. If, in the view of policymakers and the community at large, too many were choosing to do that, then: (i) the job guarantee provider and other employers would have to lift their game by either paying more or mechanizing roles, or (ii) the basic income payment would need to be reduced relative to the job guarantee wage to modify the relative appeal of the various options open to individuals.

**3.** The notion that basic income would be unfair due to individuals outside the workforce receiving an income “for nothing” does not take into account that: (i) much socially beneficial activity occurs outside the workforce (most obviously, home parenting and housework, but also other roles); and (ii) much unproductive or outright destructive activity occurs in jobs. A home parent or community volunteer receiving basic income while a factory worker earned a wage in preference to or as well as basic income would not represent an obviously more outlandish injustice than, say, an economist receiving a salary that is a multiple of the factory worker’s wage.

It can be countered that a better way to broaden society’s conception of productiveness is through a collective method such as a job guarantee rather than an individualistic one such as basic income or some combination of the two approaches. Certainly a job guarantee offers a vehicle for broadening social conceptions of productiveness and I would strongly support a development of the program in that direction.

But in terms of any debate that pits a job guarantee against basic income, taking this position raises its own issues. On the one hand, the more a job guarantee caters to individuals (such as home parents) who may have no intention of taking a job outside the program, the less it can be claimed that a job guarantee would be superior in its macro-stabilizing effects to a combined job or income guarantee. On the other hand, if roles such as home parenting are to be excluded from a job guarantee, then the fairness of denying income to people engaged in such obviously socially useful activities can be questioned.

**4.** In a world in which environmental limits are increasingly pressing, a person who voluntarily opts out of consumerism to the extent possible is doing the rest of us a favor. Even if it is felt that people in jobs are more “deserving”, and even in cases where workers are working in environmentally neutral or even positive roles, the higher income they receive compared with basic income recipients outside the labor force gives them more capacity to consume. Other factors remaining equal, higher income individuals will place more stress on the environment through their consumption than somebody getting by on a smaller income. The point is simply that work (even when of a socially useful kind) is not the only form of positive social contribution, especially at this particular juncture in history.

**Related Post**

—–

Casting a wary eye outside the window, it’s a dire environmental and geopolitical predicament that we have brought upon ourselves. Having waited our whole lives to grow old, it now seems many of us never will. At least there’s an upside then.

—–

The following transcript of a panel TV show, ‘A Game in Crisis’, was uncovered while looking for excuses not to post on economics.

**A:** (*to B*) This terrible school shooting. Two players dead and another subbed off before half time.

**B:** (*nods*)

**A:** Is there a risk that parents will come to regard footy as simply too dangerous for their kids to play?

**B:** Well I don’t think anyone should blame footy. It’s obvious that brandishing a gun is against the spirit of the game.

**A:** It also violates the official rules of play, and has for a long time now.

**B:**: Evidently some players are slow learners.

**A:** The situation might really have got out of hand had officials not acted swiftly and appropriately.

**B:** They handled it beautifully. You don’t like shootings to occur during play, but when they happen it’s good to know that the offenders will be sanctioned and their opponents given a chance to hit back on the scoreboard.

**A:** Yes, a kick at goal was awarded, though from a rather acute angle. It missed and the home team went on to lose the game.

**B:** It’s unfortunate. But there’s not a lot officials can do about that. Players still have to take their opportunities.

**A:** The goal kicker might have shown more composure had she not been shot.

**B:** Shoulda coulda woulda. The coach made a similar point, but at the end of the day footy’s not about making excuses.

—–

You know gun laws are lax when hand weapons are the preferred mode of irony for otherwise peace-loving artists and musicians.

—–

Happy holidays.

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**Summary of the Model**

Readers of the earlier post could be forgiven for thinking that the modified income-expenditure model introduces lots of new variables. Although it does involve some variables that are not explicitly included in the base model, there are actually very few new variables introduced. Those that are introduced are there because: (i) we are considering the composition of income in addition to its total level; and (ii) we are explicitly considering the level and composition of employment, whereas the level of employment is only implicit in the base model.

Basically, we have income variables, employment variables and demand variables. The income variables are total income Y, sector b income Y_{b} and sector j income Y_{j}. The corresponding employment variables are L, L_{b} and L_{j}. Partly compensating for the inclusion of sectoral income and employment variables, we have simplified the treatment of demand such that there are only autonomous demand A, induced household consumption net of endogenous imports C_{I} and job guarantee spending G_{j}.

At this stage, only the income measures, sectoral employment levels, induced household consumption and job guarantee spending are endogenous variables. Autonomous demand and total employment are exogenous.

Anything else in the model is either a parameter (and so exogenously given) or a summary term involving the parameters. The parameters are the marginal propensity to leak α (equal to one minus the net marginal propensity to consume c), sector b productivity ρ_{b}, the job guarantee wage w_{j} and the fraction of job guarantee spending going to wages ϕ (equal to one minus the fraction of job guarantee spending going to materials m). The summary terms are k, M, v and q. The first three of these relate to the dynamics about to be illustrated. The last summary term is job guarantee spending expressed as a fraction of the income gap.

**Overview of the Dynamics**

When income is fully adjusted to demand, the system is in a steady state. An exogenous change in demand disturbs the steady state. (The same is true of an exogenous change in total employment). On the basis of the suggested dynamics, the exogenous change in demand sets off an adjustment process that brings the system back to a steady state. This is true under all plausible values of the parameters.

The dynamics followed by the system are dictated by very simple recursive (difference) equations. In the initial time step, income and sector b income are assumed to respond by the amount of the exogenous change in demand. In the subsequent time step, consumption responds to the change in income in accordance with the net marginal propensity to consume and job guarantee spending adjusts by a fraction of the change in sector b income. These adjustments alter income and its composition in the same time step. This causes further adjustment in induced consumption and job guarantee spending at the next time step with immediate effects once again on income and its composition. The process continues until a steady state is restored.

This is certainly not the only way the dynamics could have been depicted. (I have experimented with a number of alternatives.) The choice was made mainly for a couple of reasons. First, the dynamics are analogous to the way the base model’s dynamics are typically interpreted, with endogenous spending adjusting to changing income with a lag. Second, even under present assumptions in which sector b productivity and the labor force participation rate are taken as given, there is likely to be a short lag in the response of job guarantee spending because of the existence of pay periods and payment schedules. For instance, if a worker switches from a job guarantee position to a role in the broader economy, the impact on income will precede the impact on job guarantee spending. The latter will be delayed because workers are usually paid at the end of a pay period rather than at the beginning. If we think of the time steps as fortnightly periods, then at time t = 0 there is an increase in autonomous demand with immediate impacts on income and its composition. Under present assumptions, this higher income can only be achieved through a transfer of some employment to sector b. At the end of the fortnight (time t = 1) these workers will be paid by sector b employers rather than receiving the job guarantee wage and at this point job guarantee spending will decrease.

**Job Guarantee Spending**

In a steady state, the level of job guarantee spending is

All terms on the right-hand side are exogenous variables or parameters (q is defined solely in terms of parameters).

An exogenous change in demand will cause G_{j} to diverge from its steady state. Its adjustment is described by

This looks a lot scarier than it actually is. Suppose the net marginal propensity to consume is 1/2, sector b productivity is ρ_{b} = 2, the job guarantee wage is w_{j} = 1/2 and the fraction of job guarantee spending going to wages is 2/3. This is all the information we need to work out the values of k, v and M and the change in job guarantee spending with respect to autonomous demand at each time step t and in total. The index n simply refers to the *n*_{ }th term in the equation for each time step.

In our example, k = 3/8, v = -1/8 and M = 3/8. In principle, the change in job guarantee spending can be calculated as

The changes for t = 1 to t = 10 (to four decimal places) are:

Although we are dealing with an infinite series, the total changes are pretty much spent at this point, being about 0.000014 away from the ultimate change, for which we possess a convenient formula:

This says that a one unit increase in autonomous demand ultimately causes job guarantee spending to decrease by half a unit.

Graphically, the adjustment looks roughly as shown below (the software assumes a constant rate of change within each time step):

The graph showing the level of G_{j} over time is based on an initial level of autonomous demand of 88 and total employment of 100. The initial level of 6 compares with total income of 188. The final level of 5.5 compares with total income of 189.

It was mentioned in the earlier post that convergence to a steady state is assured for plausible values of the parameters. It was also noted that, mathematically, divergence could occur if wages made up an unrealistically small fraction of job guarantee spending. For the fun of it, this is illustrated in the next two graphs. Holding all the other parameters at the same level, oscillation without a trend occurs if ϕ = 2/15 and divergence occurs for values of ϕ smaller than this (ϕ = 0.12 in the second graph).

**Sector b Income**

The behavior of the other endogenous variables can be considered in the same way. In what remains, we will mainly consider sector b income. In a steady state, the sector’s income satisfies

Once again, all terms on the right-hand side other than the summary term q are exogenous variables or parameters.

An exogenous change in demand will cause Y_{b} to diverge from its steady state, with its adjustment process described by

Assuming the same parameter values as earlier we once again have k = 3/8, v = -1/8 and M = 3/8. In principle, the change in sector b income can be calculated as

The changes for t = 0 to t = 9 are:

As before, the total changes are pretty much spent at this point. The ultimate change is given by the formula:

This says that a one unit increase in autonomous demand ultimately causes sector b income to rise by 4/3 units.

Graphically, the adjustment looks something like this:

As before, the graph showing the variable’s level is based on initial autonomous demand of 88 and total employment of 100. The initial level of 184 compares with total income of 188. The final level of 185 1/3 compares with total income of 189.

**Other Variables**

The behavior of total income and the other endogenous variables is in simple relation to the behavior of job guarantee spending and sector b income. In particular, the change in Y at time step t will be the change in sector b income plus ϕ times the change in job guarantee spending. Since job guarantee spending varies inversely to sector b income, the ultimate change in income is somewhat smaller than the corresponding impact on sector b income. The total change is

For the particular example we have considered, the behavior looks roughly like this:

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**Two Reference Points**

The presentation in the previous post was guided by a desire to have all key expressions share the same denominator. The common denominator was α + q, where α is the marginal propensity to leak to taxes, saving and imports and q is the ratio of job guarantee spending to the income gap.

In thinking about an economy with a job guarantee, there are a couple of obvious reference points. One is the maximum possible level of income given the labor-supply choices of workers. This is the level of income that could notionally be generated if all employment happened to be in sector b (the broader economy) since productivity in that sector is assumed to be higher than in sector j (the job guarantee sector). In reality, Y_{max} would not be tolerated by policymakers because of the inflationary pressures likely to emerge. To the extent that some employment must be located in sector j, income will fall short of Y_{max}, leaving an income gap.

Another reference point is the level of income that would be generated in the absence of a job guarantee. This is equal to A_{ }/_{ }α, where A is autonomous demand.

In short, there is a maximum possible income (reference point 1), the income that would be generated in the absence of a job guarantee (reference point 2), and income itself. Income will be at a level somewhere between the two reference points whenever an income gap exists.

The following way of expressing the steady state level of income makes this clear:

Here, ρ_{b} is sector b productivity and L is total employment. For now, both are taken to be exogenous. The expression depicts the level of income as a weighted average of the two reference levels, with the weights depending on the parameters α and q.

Job guarantee spending can be considered in a similar way:

This shows job guarantee spending as a fraction of the income that notionally could be generated beyond Y_{No JG}. Again the parameters α and q shape the relationship in question.

The reference points can also be considered in terms of employment:

In this expression, ϕ is the fraction of job guarantee spending going to wages and w_{j} the job guarantee wage. Both are exogenous. The expression says that job guarantee spending is just sufficient to generate the amount of employment L – L_{No JG}. Part of this employment is generated directly in sector j and part is generated indirectly through the multiplier impact of job guarantee spending on sector b income and employment.

**Alternative Way of Obtaining the Steady State Relationships**

The previous post discussed the notion of an income gap (or Y_{gap}) that represents the difference between Y_{max} and income Y. It was observed that job guarantee spending can be thought of as a fraction q of the income gap. This suggests a different way of arriving at the steady state relationships.

The steady state condition and demand function are reproduced below.

If job guarantee spending is regarded as a fraction of the income gap, then

Substituting this expression for G_{j} into the demand function and solving for steady state income gives the same expression for Y as presented in the previous post:

This expression can be substituted into the preceding one for G_{j} to get the steady state level of job guarantee spending and then the expressions for Y and G_{j} used to obtain the other relationships.

This might seem simpler than the approach adopted previously, but the make-up of q is left vague. The relevant expression for q can be obtained by noting that the income gap will be equal to the productivity differential (where w_{j} is taken to define sector j productivity) multiplied by the level of sector j employment:

Since G_{j} = qY_{gap},

Solving for q:

Noting that job guarantee spending per unit of sector j employment is w_{j}_{ }/_{ }ϕ, we have

which matches the definition for q given in the previous post.

In the end, this method does not really save effort. But perhaps it offers a somewhat different perspective on the various relationships.

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**1. Income Determination with a Job Guarantee**

It will be convenient to think of the economy as comprising just two sectors: the ‘job guarantee sector’ or sector j and the ‘broader economy’ or sector b. The broader economy is taken to include households, firms, the rest of the public sector and non-residents.

Suppose that most planned expenditure is exogenous and can be lumped together as autonomous demand A. The exceptions are induced household consumption net of endogenous imports, which rises with income, and job guarantee spending, which varies countercyclically. Steady state income in the absence of a job guarantee would be A_{ }/_{ }α, where α is the marginal propensity to leak to taxes, saving and imports. With a job guarantee, the system becomes:

The first equation is the steady state condition. Income Y must equal demand Y_{d} for activity to be stable. The second equation shows demand as the sum of induced net household consumption (1 – α)Y, autonomous demand and job guarantee spending G_{j}.

Income for the economy as a whole is composed of the sectoral incomes. The income of sector j can be regarded as the wages paid to job guarantee workers. This is in keeping with the national accounting treatment of public sector activity in general. If a fraction ϕ of job guarantee spending goes to wages, sector j income will be ϕG_{j}. It is assumed that the remaining fraction 1 – ϕ of job guarantee spending goes on materials supplied by the broader economy and so contributes to sector b income. These considerations are summarized as:

A preliminary expression for the steady state level of total income can be obtained by solving the system of equations (1) for Y. The result can be plugged in to the third equation in (2) to give a corresponding expression for sector b income:

To progress any further, we need an expression for job guarantee spending.

Let w_{j} be the exogenously set job guarantee wage. With ϕ defined as the fraction of job guarantee spending going to wages, w_{j}_{ }/_{ } ϕ must be the amount of job guarantee spending per unit of sector j employment L_{j}. This implies:

Sector j employment accounts for whatever employment is not located in the broader economy. This means we can write the above as

In the present discussion, total employment L is simply taken as given. This simplifying assumption means that variations in one sector’s employment translate one-for-one into inverse variations in the other sector: ΔL_{j} = -ΔL_{b}. A more sophisticated approach would factor in procyclical variation in labor force participation.

Unlike other entries on the right-hand side of (4), L_{b} is endogenous. It depends on the sector’s income and productivity ρ_{b}. Specifically, L_{b} = Y_{b}_{ }/_{ }ρ_{b}. Although it is possible to endogenize ρ_{b} to allow for procyclical variation in sector b’s productivity, here it will be considered exogenous. Additional complications can always be introduced at a later time.

Since L_{b} = Y_{b}_{ }/_{ }ρ_{b}, we can take the expression for Y_{b} in (3) and divide by ρ_{b}. The result can then be substituted for L_{b} in (4) to obtain an equation solvable for G_{j}. The solution is the steady state level of job guarantee spending:

Our expression for G_{j} can now be used in (3) to find the steady state levels of Y and Y_{b}:

Corresponding expressions for the other endogenous variables are easily obtained. The steady state level of Y_{j} is simply the expression for G_{j} multiplied by ϕ. The sectoral employment levels in a steady state will be Y_{b}_{ }/_{ }ρ_{b} and Y_{j}_{ }/_{ }w_{j}.

An exogenous change in autonomous demand will cause multiplied changes in the steady state levels of the endogenous variables. These multipliers can be obtained by differentiating or taking the first difference of the relevant expression with respect to A:

Exogenous changes in total employment also have multiplier effects, which can be found by differentiating the various steady state expressions with respect to L. An individual decision to enter the labor force and take a job guarantee position will activate government expenditure on the program, with a multiplier effect on the economy. This is a notable aspect of the job guarantee in that an increase in supply-side potential automatically translates into higher demand. An earlier post considers a couple of effects along these lines. The present focus, however, will be on the expenditure multipliers.

The expressions in (5) and (6) can be arranged in various ways. The above arrangement is chosen for its succinctness and to provide a common denominator. As displayed, the expressions tell us the steady state levels of the endogenous variables given the values of the exogenous variables and parameters. But the form of presentation is not conducive to understanding the likely dynamics involved in moving from one steady state to another. This is a different question and the focus of subsequent sections of the post.

Before turning to that question, though, the meaning of q requires some explanation. A cursory glance at (5) and (6) reveals that the term appears in both the numerator and denominator of all the main expressions. It is a positive constant defined as

The margin ρ_{b} – w_{j} is the additional income that is generated by having a unit of employment located in sector b rather than sector j. This margin is created because productivity in sector b is assumed to be higher than in sector j, where productivity is taken to equal the job guarantee wage on the basis that ρ_{j} = Y_{j}_{ }/_{ }L_{j} = w_{j}. The margin, then, is just the productivity differential.

Another way to think of the productivity differential is as the extra gap that is opened up between maximum possible income Y_{max} and income Y for every unit of employment that is located in sector j. In this interpretation, Y_{max} is taken to be the level of income that notionally could be generated if all employment were located in sector b. Looked at this way, the first term in q, which is the reciprocal of ρ_{b} – w_{j}, can be understood as the marginal response of sector j employment to a unit widening of the income gap.

The second term in q, w_{j}_{ }/_{ }ϕ, has already been encountered. As observed earlier, it represents job guarantee spending per unit of sector j employment.

Combining these observations, q can be expressed in terms of changes:

So q measures the endogenous response of job guarantee spending to a widening of the income gap. Under present assumptions, it also expresses job guarantee spending as a fraction of the income gap:

**2. A Representation of Dynamic Adjustment**

Here is a way to think about the dynamic adjustment process between two steady states that is analogous to the way the standard model’s dynamics are usually interpreted.

Beginning from a steady state, imagine a one-off exogenous change in demand that causes the economy to leave the steady state. Conceptually, we can suppose that this has an immediate impact on total income and sector b income but that the effects on job guarantee spending and household consumption are delayed.

Specifically, let ΔA denote the change in autonomous demand. At time t = 0, it is assumed that total income and sector b income change by the amount ΔA. At time t = 1, job guarantee spending and consumption respond to the events of time t = 0. This affects total income and sector b income in the same step. These changes in the level of income and its composition at time t = 1 then impact on job guarantee spending and consumption at time t = 2, with immediate impacts once again on income and its composition, and so on. The objective is to arrive at expressions describing the behavior of total income, sector b income, job guarantee spending and consumption (and, by implication, other endogenous variables) over time.

In general terms, the following process is envisaged.

The abbreviations are to save space and make the algebra easier, with c = 1 – α being the net marginal propensity to consume. It is also convenient to let m = 1 – ϕ represent the fraction of job guarantee spending going to materials.

The negative fraction k is constant, given the values of the parameters. It measures the inverse response of job guarantee spending to variations in sector b income. A unit increase in sector b income results in 1/ρ_{b} units of employment switching from sector j to sector b and so causes a reduction in job guarantee employment of 1/ρ_{b}. Since government spends w_{j}_{ }/_{ }ϕ per unit of sector j employment, the unit increase in sector b income causes job guarantee spending to change (negatively) by -(1/ρ_{b})(w_{j}_{ }/_{ }ϕ), or k. In terms of changes:

The immediate aim is to express changes in Y, Y_{b}, G_{j} and C in terms of exogenous variables and parameters. This can be done by writing down appropriate equations for the first step, t = 0, and then using these initial expressions to write down appropriate equations for the second step, t = 1, and so on, until a clear pattern emerges. Excel or a similar spreadsheet package is extremely useful for checking that the equations actually work. Setting up a spreadsheet is much easier than deriving the equations. The simple recursive rules outlined in (8) are all that are required for that purpose.

Applying the first of the rules in (8) for time t = 0 gives:

The endogenous expenditures will begin to respond in the next step, with further ramifications for income and its composition.

At time t = 1:

In the last line, use is made of the definition m = 1 – ϕ to express k – ϕk as mk.

Before continuing, it is helpful to note that

An effective strategy is to group c + mk terms together and let M = c + mk. When a c + k term appears, it can be split into an M term and a ϕk term in accordance with (9). The ϕk terms will get multiplied by c to generate ϕkc = v terms. So for convenience:

In economic meaning, M is the spending induced by an increment in sector b income, taking into account both induced consumption and countercyclical variation in job guarantee spending on materials. v is the (negative) change in sector j workers’ consumption caused by a one unit increase in Y_{b} due to the latter’s effect on sector j employment and wages. This makes M + v the net marginal propensity to spend out of sector b income, taking into account both induced consumption and the inverse effects on consumption and materials expenditure of endogenous variation in job guarantee spending. So, in generating the equations, the net marginal propensity to spend out of sector b income will get decomposed into separate M and v terms. For given parameter values, M and v are constants.

Following this strategy, the expressions for ΔY_{1} and ΔY_{b1} can be restated as:

At time t = 2:

The overall pattern is not clear at this stage but emerges if we continue with the algebra for some more steps. Here, we will jump ahead a little and look at some of the expressions that emerge for early steps in the process. Energy can be conserved by focusing on the equations for Y_{b} and G_{j} since these are pivotal and can be used to obtain corresponding expressions for the other variables.

To save a bit more space, changes in Y_{b} and G_{j} will be divided by ΔA with the following notation adopted:

Continuing to work through the algebra gives the following changes in Y_{b} per unit change in A for steps 0 to 9. The purpose here is to notice a pattern.

The pattern followed by the coefficients in (12) relates to Pascal’s triangle. The integers involved are figurate numbers that can be read off the diagonals of the triangle. The first terms in each row are preceded by a 1. The second terms, from t = 2 onward, are preceded by ascending natural numbers (1, 2, 3, …). The third terms, from t = 4 onward, are preceded by ascending triangular numbers (1, 3, 6, …). The fourth terms, from t = 6 onward, are preceded by ascending tetrahedral numbers (1, 4, 10, …). The fifth terms, from t = 8 onward, are preceded by ascending pentatope numbers (1, 5, 15, …). The pattern continues through the simplex numbers.

With the pattern now evident, it is possible to form an equation that describes the behavior of Y_{b}. Focusing on the right-hand side of (12), the rows (or equations) can be numbered from t = 0 and the columns (or terms) from n = 0. The term in row t and column n will be

The first term in brackets is the binomial coefficient C(t – n, n). The change in Y_{b} with respect to A at time t will equal the sum of the terms in row t:

Summing across all time steps gives the total multiplier impact on Y_{b} of an exogenous change in demand:

Together, these last two expressions give a description of Y_{b}‘s behavior over time. Expression (13) enables us to calculate the change in Y_{b} at a given time step, while (14) can be used to find the cumulative change over all or a subset of time steps.

The behavior of the other variables can be considered in the same way. Fortunately, it is only really necessary to retread the above steps for job guarantee spending. Once the behavior of G_{j} becomes clear, it will be easy to infer the behavior of the other variables from the combined behavior of Y_{b} and G_{j}.

Working through time steps 1 to 9 for the changes in job guarantee spending gives:

The pattern is very similar to the behavior displayed by Y_{b} except that it is lagged a step, with each term multiplied by k. In view of the lag, we can number the rows from t = 1. To avert possible confusion, the columns can also be numbered from n = 1.

The value of the term in row t and column n will be

The change in G_{j} with respect to A at time t is given by the sum of the terms in row t:

Summing across all time steps gives the full multiplier impact:

The corresponding expressions for Y can be obtained using the following relationships:

The expressions for C are most easily obtained from the resulting expressions for Y:

**3. Conformity of the Dynamics to Steady State Requirements**

We now have expressions for the steady state levels of the endogenous variables. These were obtained in section 1. We also have expressions that describe the behavior of the endogenous variables at each step in time when they follow a simple set of recursive rules. These were obtained in section 2. But for the assumed dynamic behavior to be consistent with the underlying assumptions of the model, we need it to generate results that are the same as those implied by the steady state relationships. Specifically, the full multiplier impacts generated by the dynamic behavior should match the multipliers that are implicit in the steady state expressions and listed in (7). We need a way to compare the two sets of multipliers and verify that they are actually the same. For this purpose, it will be helpful to have formulas for the series sums developed in section 2 that are easy to compare with the multipliers in (7). Obtaining such formulas and showing that they are equivalent to the multipliers in (7) will verify that the assumed dynamics conform to the steady state requirements of the model.

A key to the exercise is to keep in mind that the sum of a geometric series with common coefficient *a* and factor r exists so long as r has an absolute value less than one.

When the absolute value of r is less than one, the terms in the series approach zero as t becomes large, and the sum of the series converges on a finite point that can be calculated using the formula on the far right-hand side.

It will be possible to obtain summation formulas for the endogenous variables in the form of (20). As in section 2, most effort can go toward obtaining formulas for Y_{b} and G_{j} because of the way they are connected with the other variables.

The full impact on Y_{b} of an exogenous change in demand has been found to be:

Recall that this sum relates to a system of equations for ΔY_{bt}_{ }/_{ }ΔA. The first equations in this system are shown in (12). In (14), terms in a given row of (12) are summed horizontally with the result added to the total of all previously summed rows. Each row pertains to a particular time step. This choice was useful for describing the behavior of Y_{b} over time, which was our aim in section 2, but it is not so helpful for obtaining a formula for the sum of the series. For that purpose, it is more convenient to sum vertically down columns and add the column sums together.

Some of the equations for y_{bt} = ΔY_{bt}_{ }/_{ }ΔA are reproduced below for easy reference:

To sum vertically, we fix the value of n (which denotes a column) and sum over all values of t. The same can be done for all other values of n to obtain an expression for the total change in Y_{b}.

In summing the columns, care is needed in setting up the summation. In (14), the summation only applies to values of n that are less than or equal to t/2. This implies that we need to take the column sums for values of t greater than or equal to 2n:

The sum of column n will be

The limits of this summation can be shifted so as to start each column sum from t = 0:

As was noted earlier, the coefficients in (12) are figurate numbers. These numbers can be represented in terms of rising and falling factorials. To match our notation, let n represent the “type” of number in Pascal’s triangle, with n = 0 denoting ones, n = 1 denoting natural numbers, n = 2 denoting triangular numbers and so on. The *t _{ }*th number (t = 0, 1, 2, …) of type n will be given by the formula

Here, n bar is the *n* th rising factorial of t and n! is the factorial of n. By definition, zero factorial equals 1.

To give a couple of examples, the fourth triangular and seventh tetrahedral numbers are

This way of representing the numbers in Pascal’s triangle can be applied to the equations in (12). Column n in that system of equations contains numbers of type n. The *t _{ }*th nonzero entry in the column will be the

Using this notation, (21′) can be written as

As has been noted, this is the sum of column n. We want to find a simple formula for this sum. A way to find the formula is to substitute successive values for n into (22) and look for a pattern. The strategy is as follows. Each time a value for n is substituted into (22), treat the resulting expression as a function of M. By integrating the function n times with respect to M, it will be possible to isolate a ΣM^{t} term. The formula for the sum of a geometric series given in (20) can then be applied, with *a* = 1 and r = M, to replace ΣM^{t} with 1/(1 – M). With this replacement made, the function can be differentiated n times with respect to M to eliminate any constants of integration and solve for *f*_{ }(M) = ΔY_{bn}_{ }/_{ }ΔA.

When n = 0, (22) becomes:

When n = 1,

Since n =1, we now integrate once with respect to M. The t + 1 term will cancel:

K_{1} is a constant of integration. Differentiating with respect to M and solving:

A pattern is emerging. We can go over some of the procedure one more time to check.

Letting n = 2,

Without actually performing the integrations it is clear that the first integration will eliminate the t + 1 term and the second integration will eliminate the t + 2 term. M will be raised to the power of t + 2. M^{2} can be taken outside the summation, leaving only ΣM^{t} on the inside, which can be replaced with 1/(1 – M). This will give:

where K_{1} and K_{2} are constants of integration. Differentiating twice with respect to M gives:

The procedure gets more laborious as n is increased because of the need to integrate and differentiate n times, but the pattern is clear. All terms in the numerator other than v^{n} cancel out after the *n*_{ }th differentiation and we are left with an expression in the form:

This expression gives the sum of column n in the set of equations abbreviated in (12).

The total multiplier impact on Y_{b} is obtained by summing the totals of all the columns:

Conveniently, (24) is in the form of a geometric series, as shown in (20), with *a* = 1/(1 – M) and r = v/(1 – M). Plugging into the formula in (20) gives:

So long as the system converges to a steady state, this formula gives the full multiplier impact on Y_{b} of a change in autonomous demand when behavior follows the simple recursive rules outlined in (8).

For Y_{b} to converge, it is necessary that:

Keeping in mind that M + v is the net marginal propensity to spend out of sector b income, convergence will occur for appropriate values of the parameters.

Mathematically, divergence would occur if either M + v > 1 or M + v < -1. But neither of these cases is plausible. The first case is impossible so long as there is a positive marginal propensity to leak (α > 0) because M always takes a value less than one and v is defined to be negative. The second case would make no sense from a policy perspective. For M + v to be negative at all, let alone less than -1, a unit increase in sector b income would need to be accompanied by a withdrawal of job guarantee spending that more than offset the extra induced consumption. The main way it could happen mathematically would be for the fraction of job guarantee spending on wages (ϕ) to be unrealistically small. For example, for α = 1/2, ρ_{b} = 2 and w_{j} = 1/2, divergence would occur for a value of ϕ less than 2/15. For ϕ of exactly 2/15, the system would oscillate from one time step to the next with sector b income showing no tendency either to rise or fall. Or with α = 1/5, ρ_{b} = 3 and w_{j} = 1/2, the system would diverge for values of ϕ less than 5/63. These choices for ϕ would be inapplicable from the policy perspective. On economic considerations, the system will always converge.

We are now in a position to compare the multiplier impact generated by our assumed dynamic behavior, given in (25), with the multiplier for Y_{b} that was derived from the steady state relationships and listed in (7). If the two multipliers happen to be the same, the assumed dynamics will not violate steady state requirements. Our conceptualization of the dynamics will be consistent with the underlying assumptions of the model.

The steady state relationships imply a multiplier for Y_{b} that is shown in (7):

We need to compare our formula in (25) with (26). To do so, it is necessary to substitute in the actual expressions for M and v, since these terms are abbreviations chosen to conserve space. It is also necessary to recall the definition of q. For convenience, these are reproduced below:

It needs to be shown that:

This verifies that the multiplier impact on Y_{b} generated by the assumed dynamic process matches the multiplier impact implied by the corresponding steady state expression. In other words, the dynamics of sector b income conform to steady state requirements. For given values of the exogenous variables and parameters, the assumed system behavior will cause Y_{b} to converge on its steady state level, as depicted in (6).

**Convergence of Other Variables**

The approach just taken for sector b income can also be applied in the case of job guarantee spending. By summing vertically down each column of the system of equations for g_{jt} = ΔG_{jt}_{ }/_{ }ΔA it is possible to arrive at a simple formula for the sum of a series. This formula will be equivalent to the multiplier derived for G_{j} on the basis of steady state relationships. Once equivalence is established for the multipliers of both Y_{b} and G_{j}, it is straightforward to handle Y, C and, by implication, Y_{j} and other endogenous variables because their expressions can all be obtained from those for Y_{b} and G_{j}. Specifically,

It is unnecessary to go into the same detail for G_{j} as we did for Y_{b} as the steps and algebra are almost identical. But there are a few points that might be unclear without some elaboration.

The g_{jt} for t = 1 to t = 9 are reproduced below:

Before summing vertically, it is once again important to consider the limits of summation in the expression for the total change in G_{j}:

The summation only applies to values of n that are less than or equal to (t + 1)/2. So we need to take the column sums for values of t greater than or equal to 2n – 1:

The sum of column n will be

Left as it is, this would be inconvenient for integrating and differentiating n times. It helps to shift the limits of the summation so as to start each column sum from t = 0:

Replacing the binomial coefficients with equivalent expressions involving rising and falling factorials and treating ΔG_{jn}_{ }/_{ }ΔA as a function of M gives us a convenient starting point:

From here there are no surprises. For each n, we integrate n times to get a ΣM^{t} term by itself that can be replaced with 1/(1 – M). We then differentiate n times to eliminate the constants of integration and solve for *f*_{ }(M).

As might be guessed, the end result is a formula that is almost identical to the one for the total change in Y_{b} except that the numerator is multiplied by k.

Similar expressions for the other variables can be obtained from those for Y_{b} and G_{j}. The resulting formulas are all equivalent to the corresponding multipliers implied by the steady state expressions. The various multipliers resulting from the assumed dynamics are shown below.

**4. Concluding Remark**

The focus has been on a model economy with a job guarantee. Adopting the income-expenditure model as a base, we identified characteristics of a steady state and described a dynamic process – analogous to the usual dynamic interpretation of the base model – that would tend to bring the system, when outside a steady state, back toward it.

**Appendix**

A fair bit of notation has been used. For easy reference, it is summarized below.

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The standard model can be summarized in the following set of equations:

For the system to be in a steady state, output and income (both denoted Y) must equal demand Y_{d}. Demand is defined as the sum of planned expenditures. These expenditures include household consumption C, private investment I, government expenditure G and net exports (exports X minus imports M). The other expressions are behavioral equations. In the simplest versions of the model, private investment, government spending and exports are all considered exogenous (denoted with a 0 subscript). Private consumption, taxes T and imports are endogenous. They are largely induced by income, though with autonomous components (C_{0}, T_{0} and M_{0}). The marginal propensities to consume, tax and import (c, t and m, respectively) are all assumed to be constants that take values between zero and one.

Through a series of substitutions the system can be solved for Y to obtain the steady state level of income:

The numerator of this expression is net planned autonomous expenditure, or ‘autonomous demand’. The denominator is the ‘marginal propensity to leak’. It is the fraction of an increment in income that drains to taxes, saving and imports. The model therefore depicts steady state income as a multiple of autonomous demand, where the ‘expenditure multiplier’ is the reciprocal of the marginal propensity to leak.

To condense the model, let A represent autonomous demand and α the marginal propensity to leak. The model can then be depicted more succinctly as

Demand, in (2), is the sum of induced consumption net of endogenous imports, represented by (1 – α)Y, and autonomous demand.

Substituting the expression for demand into steady state condition (1) and solving for Y gives:

As before, steady state income depends on the level of autonomous demand (now denoted A) and the marginal propensity to leak α. The multiplier, found by differentiating (3) with respect to A, is 1/α.

The model can be used to consider how a change in either the exogenous variable A or the parameter α will affect the steady state level of Y. If autonomous demand changes by the amount ΔA, the steady state level of income will change by ΔY = (1/α)ΔA.

As it stands, the model says nothing about how the system might get from one steady state to another. There are many conceivable ways this could occur. The one that is usually taken to make most sense goes along the following lines. An exogenous change in demand of ΔA will be the result of either an ‘injection’ (from one or more of government spending, private investment and/or exports) or autonomous household consumption, or some combination of the two. The extra exogenous spending will be received as income. This will induce additional household consumption on domestic output, as well as result in leakage or ‘withdrawal’ from the circular flow of income to taxes, saving and imports. In this way, a given increase in exogenous spending will initiate a multiplier process in which the newly created income induces consumption which, in turn, creates still more income, again inducing consumption, and so on. But the multiplier process associated with a particular act of autonomous spending eventually runs out of steam because withdrawals to taxes, saving and imports occur on each round of the process. Given the new value of autonomous demand and the marginal propensity to leak, there will be a stable (steady state) level of activity to which income converges.

The process just described suggests a power series. The idea is implicit in the expression for the multiplier. Since α is always between zero and one, 1/α can be interpreted as the sum of a convergent series. The sum of the series will be

The change in income caused by a change in autonomous demand can now be found by multiplying through by ΔA:

So, in the economic process envisaged, a change in autonomous demand of ΔA occurring at time t = 0 will be received as income. At time t = 1, a fraction 1 – α of this new income will go to consumption and be received as new income of (1 – α)ΔA. At time t = 2, a fraction 1 – α of this new income will go to consumption and create still further new income of (1 – α)^{2}ΔA. And so on.

The basic logic of the model will remain fundamentally the same when a job guarantee is included. But interaction between the broader economy and job guarantee program – which entails endogenous, countercyclical spending – modifies the steady state relationships and can especially complicate plausible representations of the system’s behavior when outside of a steady state.

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At the present time, of course, there is no job guarantee in the comprehensive form articulated by its proponents. The job guarantee is a proposal rather than an existing policy. In today’s economies, some people are relegated to unemployment for the sake of containing inflation. So long as there is excess capacity and unemployment, it is possible to expand production through an increase in employment and the rate of capacity utilization. When appropriate, expansionary demand-side policies can be implemented to this end. At a certain point, however, bottlenecks are likely to emerge due to shortages of particular kinds of workers and raw materials. Although these bottlenecks are often possible to address through additional investment in capacity, this takes time. Meanwhile, the presence of bottlenecks can cause a bidding up of some wages and prices. Potentially, this could also intensify distributional conflict between workers and capitalists as both attempt to protect real income shares. In any case, as the economy gets closer to full employment, the proportion of sectors affected by bottlenecks is likely to rise, adding to the risk of inflation.

In the absence of an incomes policy involving direct wage and price controls, or a job guarantee, the likely government response to an inflation threat will be to adopt contractionary macroeconomic policies aimed at weakening demand in general, and with it, demand for labor-power and raw materials. Given time, this policy approach can succeed in eliminating inflationary pressure. But it comes at the considerable economic and social cost of unemployment. To the extent the policy approach works through a generalized slowdown in demand rather than attempting to address specific areas of the economy directly, it is likely to require more pronounced macroeconomic contraction and job loss than might be necessary under better designed policy.

The job guarantee is proposed as a way of making full employment compatible with price stability. Rather than sacrifice some employment as a means of moderating inflation, it is contended that price stability can be achieved without inflicting the costs of involuntary unemployment. Under a job guarantee, there would still be voluntary unemployment in cases where laid off skilled workers preferred to wait for a similar position to become available rather than accept a job guarantee position. But anybody who was willing and able to take a job at minimum wage (including defined benefits) would be employed. There would be zero involuntary unemployment: a situation described as ‘loose full employment’.

According to the logic of the proposal, the pay and conditions of job guarantee employment would serve as a floor under the economy’s relative wage structure and set the value of the currency in terms of simple labor. A minimum wage (with benefits factored in) of $w per hour would mean that one unit of the currency commanded 1/w hours of simple labor power. Other employers would need to offer pay and conditions that were competitive with the job guarantee as well as commensurate with the complexity of labor involved in the roles required to be performed. Given the economy’s average level of productivity and on an assumption that firms largely set prices as a mark up over wage and materials costs, the wage floor set by the job guarantee would act as a nominal price anchor for the economy’s wage and price structure.

It is argued that the anchoring effect will be strongest when job guarantee employment as a proportion of total employment (referred to as the ‘buffer employment ratio’ or BER) is at its highest. During booms, the BER will tend to decline as some job guarantee workers are attracted into better paying positions in the broader economy. As the job guarantee sector contracts, the nominal price anchor will lose some of its influence on the broader economy, and other wages and prices might rise relative to the job guarantee wage as employers compete for workers. Because government would not compete on wages in an attempt to retain job guarantee workers, these wage payments would not contribute to the inflationary pressures developing elsewhere in the economy. Even so, a boom that continued long enough might result in demand-side inflationary pressure.

Much like under the current policy approach, this situation would be addressed by contractionary policies to moderate activity. But importantly, these policies would not cause involuntary unemployment. The negative impact on employment in the broader economy would instead cause a net migration of workers into job guarantee employment. The consequent increase in the BER would reinforce the nominal price anchor and help to keep inflation in check.

In terms of the discretionary policy response to inflation, clearly there is a resemblance between the current policy approach and the way policy would be conducted in the presence of a job guarantee. Under the current regime, policymakers think in terms of a rate of unemployment (the ‘non-accelerating inflation rate of unemployment’ or NAIRU) at which inflationary pressures first become problematic. With a job guarantee in place, the focus would shift to the proportion of job guarantee employment in total employment (the BER) instead of the unemployment rate. In principle, reference could be made to a ‘non-accelerating inflation buffer employment ratio’ (NAIBER). The NAIBER would be the lowest level of the BER still consistent with stable inflation.

Although the notion of the NAIBER is conceptually clear, Modern Monetary Theorists do not propose attempting to pinpoint its actual value. In reality, and as is true of the NAIRU, its actual value would be difficult to determine. Structural changes, by affecting the likelihood and distribution of bottlenecks, would affect the value of the NAIBER. Institutional changes, by affecting whether bottlenecks were likely to initiate wage-price spirals, could also alter the NAIBER. For instance, combining a job guarantee with an incomes policy might lower the NAIBER by enabling overall demand to be kept stronger without causing inflation. Pronounced distributional changes, by altering the pattern of demand relative to the economy’s present structure, could also alter the likelihood of bottlenecks appearing. Rather than trying to identify the precise value of the NAIBER, the point of relevance to policy is simply that demand-side inflation would be taken as evidence that the BER was too low and that contractionary policies were required. Of course, in the reverse scenario of a generalized slump or deflation, discretionary expansionary policies would be appropriate.

Modern Monetary Theorists maintain that the introduction of a job guarantee would give the economy a more effective nominal price anchor than currently exists. In comparison to the current policy approach, they point out that:

**Job guarantee spending would be highly targeted.**Anyone wanting a job but unable to find one in the broader economy would be able to register for a job guarantee position. This individual act would automatically trigger the minimum level of government spending necessary to generate employment for the worker, given the fixed job guarantee wage. It would be the minimum necessary public expenditure to get the worker back in employment because other forms of spending would only generate the same employment, if at all, indirectly through a multiplier process in which, at each step of the process, some of the newly created income drained to taxes, saving and imports. Since the spending would be kept to a minimum, the inflation risk would likewise be minimized relative to less direct methods of generating the extra job. This argument is not about financial considerations, but demand pressure and potential for inflation.**Much job guarantee spending would be at a fixed price.**In contrast to other spending, which is typically conducted at market prices, the hiring of job guarantee workers would occur at a fixed wage. This spending, unlike most other public and private spending, would not directly participate in any bidding up (or bidding down) of wages and prices that might occur elsewhere in the economy. This spending rule would provide a stable floor under other wages and, given the economy’s level of productivity and a prevalence of mark up pricing, influence prices in general. During booms, other wages might spread higher above the floor, but they would do so to a lesser degree than if government competed on wages to retain workers in the job guarantee program. In a slump, other wages might decline relative to the wage floor, but the floor would limit their fall. In this way, the fixed job guarantee wage would be a source of stability in the economy’s nominal wage and price structure. There would be some job guarantee spending undertaken at market prices. Most notably, materials used in the production processes of the job guarantee sector might mostly or entirely be purchased at market prices from the broader economy. But with wages being a substantial fraction of total job guarantee spending, the stability provided by the wage floor would still be significant.**A more job-ready labor force.**Unemployment, especially when long term, can affect the employability of individuals due to skill atrophy and the loss of work habits, self-esteem and social networks. Employers, for their part, display a marked preference for hiring employed rather than unemployed individuals. It is likely that the job guarantee, by enabling people to maintain continuous employment, would make it easier for laid off workers to transition back into the broader economy as well as make the process more cost-efficient for firms. The relevance of this argument from the perspective of price stability is that job-guarantee workers would be more competitive in job applications than unemployed workers, and so exert more competitive pressure on wages in the broader economy. In other words, the nominal price anchor built in to the job guarantee would exert more influence on other wages and prices than if employers instead were hiring from a pool of unemployed workers.

**A Simple Depiction of the Theory**

The theory just described emphasizes two main sources of inflation. First, there are structural, institutional and supply-side factors (such as the skill profile of the workforce) that affect the likelihood and consequences of bottlenecks. These factors determine the NAIBER. Second, inflationary pressure is conceived as inversely related to the buffer employment ratio rather than the unemployment rate. When the BER gets too low, bottlenecks can arise, resulting in inflation.

A third potentially relevant factor, not touched on above, is a role for inflation expectations. These can conceivably influence the pricing behavior of firms and wage demands of workers. It is not clear, though, that expectations really play an independent causal role in the inflation story that has been outlined. Workers or firms might well expect inflation of five percent, but if they lack the capacity to raise their own wages and prices by five percent, prices in the end will not mirror their expectations. Conversesly, if workers or firms find that they can raise their wages or prices by ten percent, they will hardly be constrained in their actions by an expectation that inflation will only be five percent. In either scenario, the critical factor will not actually be expectations. The critical factor will be whether workers and firms actually have the capacity to raise their wages or prices, and this capacity – in the theory briefly outlined – will depend on demand conditions (summarized as the value of the BER relative to the NAIBER) along with the structural, institutional and distributional aspects of the economy that influence the likelihood and consequences of bottlenecks.

The job guarantee would put an end to the inverse Phillips Curve relationship between inflation and unemployment for the simple reason that there would be no involuntary unemployment. Rather than accepting some unemployment as the price of containing inflation, loose full employment would be maintained at all times.

Although there would be no Phillips Curve, we could, if we wished, draw a similar curve to depict the situation with a job guarantee. I’m not sure if such an exercise would be exactly MMT kosher but it seems that we could define a function with inflation inversely related to the buffer employment ratio (BER) rather than the unemployment rate. A simple representation would be:

with π_{t} the inflation rate of the current period, π_{0} exogenous inflation and *f* a function describing the sensitivity of inflation to excess or deficient demand.

With BER < NAIBER, there would be excess demand and inflationary pressure. Demand deficiency and decelerating inflation would occur with BER > NAIBER.

Graphically it might look something like this:

The curve gets flatter as the BER increases to reflect the view that the influence of the job guarantee’s nominal price anchor will be at its weakest when the BER is near zero and stronger when the BER is high.

During a boom, the economy would move along the curve, up and to the left, as the job guarantee program was deprived of workers and the BER decreased. If policymakers did nothing to constrain demand, the theory suggests inflation would rise. If, instead, policymakers implemented contractionary policy, as appropriate, this would help to bring the economy back down along the curve toward the NAIBER.

An increase in exogenous inflation emanating from the supply side of the economy (for instance, an oil shock) would cause an upward shift of the entire curve. For any given BER, there would then be a higher rate of inflation. Here, too, it might be necessary for policymakers to implement contractionary policy to compel a less inflationary resolution to conflict heightened by real income losses associated with the supply shock.

A significant change in the economy’s structure or institutions could cause the NAIBER to shift either left or right, depending on whether the structural change made the economy less or more prone to inflation.

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The answers to these questions depend, above all, on whether the government in question is a currency issuer or a mere currency user. The simple tale traced below illustrates some basic aspects of a society in which government issues its own currency. It is important to understand that the illustration does not apply to governments that use a currency issued by some other entity. For example, it does not apply to a state or local government that is required to transact in a currency issued by its national government. Such governments are mere currency users, much like households and private businesses. They do not issue their own currencies. Equally, the illustration does not apply to a national government that has given up its prerogative to issue a currency and has instead agreed to use what is essentially a foreign currency. This is currently the predicament of those European governments who have committed to using the euro. At least for now, such governments have reduced themselves to the status of mere currency users. If, at some point in the future, these European governments decide to go off the euro and reintroduce their own currencies, the following illustration will then become applicable to them, but not until then.

Most national governments, however, do issue their own currencies. This is true of the national governments of countries such as China, the US, Russia, the UK, Japan, Brazil, India and too many others to mention.

To illustrate in very simple terms the position of such governments and the nature of their currencies, consider Buckwell Island. It is an imaginary island. Its people have just voted to form a nation. Elected representatives from each region of the island have gathered to discuss some basic needs of the new nation.

After much discussion and consultation it is agreed that there need to be some common rules governing access to natural resources, ownership or stewardship of property, and the conduct of business activities. It is decided that the newly formed government will need to see to the effective defense of the island and develop key public services in education, child and aged care, health care and civil administration as well as build or oversee the building of roads, a public transport system and a modern communications network. All this will take time and much effort.

The island government realizes that it will need to hire some people to perform roles in the public sector. It also needs a way for private sector activity to be integrated into the economy. To this end, it decides to introduce a national currency called the ‘buck’.

The currency is established in two basic steps:

First, the government officials return to their local electorates and announce that all citizens of at least working age will be required to pay taxes. A tax authority will be established to monitor and enforce payment. Significantly, it is specified that all taxes and other government charges will have to be paid in bucks. No other currency or item will be accepted. In addition, all income and wealth generated on the island will be evaluated in bucks, with taxes imposed accordingly. Court settlements will also be specified in bucks.

Since people require an income, and since income and wealth will be evaluated in bucks and subject to tax, this first step in establishing a national currency creates a need within the community for its members to earn or otherwise obtain bucks.

The effect of this first step is to ensure at least some demand for the currency. Since people need bucks to pay taxes and other government charges, they will accept the currency in payment for goods and services that they are able and willing to supply either to government or to fellow Buckwellians.

With a basic demand for the currency now created, the second step in establishing the currency is for the government to open up various channels through which members of the community can actually get hold of the currency. In partial fulfillment of this objective, nominated government representatives release a list of public sector job positions. It is announced that there will be jobs for teachers, health practitioners, administrators, police officers, defense and peacekeeping forces and other important roles. Suitable applicants are free to apply for these jobs. If successful, they will be paid in bucks.

The officials also announce a list of goods and services that the government would like to purchase from private businesses. This opens up opportunities for prospective businesses to sell output to a large customer (the government). To obtain finance, competing businesses will be able to approach a newly established public bank for loans. These loans will be issued in bucks. In time, private banks may also be permitted to operate. For now it is left as a future question for the voters to decide.

The effect of these measures is to ensure that citizens can get hold of the currency. Some people will accept a job offer from the government to work in the public sector. Business operators, financed at least initially by public loans, will be able to start production and sell their products or services to customers, generating revenues in bucks. The rest of the working-age population will be able to seek employment in the private sector in exchange for bucks.

The government also announces a Job Guarantee program. Anyone who cannot find a job elsewhere can accept a job-guarantee position financed by government and administered by local government or perhaps community organizations. Those who are unable to work due to age or sickness will receive a pension paid by government. For accounting purposes, the pension payments are treated as negative taxes rather than spending, because they do not constitute direct spending on goods and services.

With these policies in place, everyone can get hold of bucks. They will be obtained either as newly issued currency when the government spends, pays pensions or lends, or as circulating currency when households or businesses make payments with bucks yet to be extinguished by taxation.

To facilitate economic activity as well as saving, citizens are granted the right to hold accounts at the public bank. Payments for goods and services can be made through the direct debiting and crediting of bank accounts or the exchange of hard currency.

To summarize, there is a basic two-step logic involved in Buckwell Island’s introduction of a currency. First, by requiring taxes and similar charges to be paid in bucks, the government ensures that people are willing to accept the currency. This step ensures at least some demand for bucks since people need them, at minimum, to pay taxes. Second, the currency is issued. The government issues bucks by hiring workers, providing pensions, extending loans to businesses and purchasing some of their output.

It may be noticed that it would be impossible for anyone to pay taxes before the currency had actually been issued. Until government spent on goods and services, or paid pensions, or the public bank lent, there would be no way for anyone to obtain bucks. An implication is that government spending and public lending are logically prior to the payment of taxes. The government’s spending and lending are not constrained by the amount of taxes paid in the past. To the contrary, the capacity of citizens to pay taxes originates from government spending and lending. A currency-issuing government, such as Buckwell Island’s government, can always afford to purchase whatever is available for sale in its own currency. In other words, if something has a sale price in bucks, the island government can always afford to purchase it, since it is the sole issuer of bucks.

A system of accounting and basic bookkeeping is put in place with the aid of spreadsheets maintained by the public bank. Whenever the government decides to spend or lend bucks, the public bank types in the appropriate new numbers in its spreadsheets. If the government pays 100 bucks for office stationary, the public bank marks up the account of the stationary supplier by that amount. The new deposit will be an asset of the stationary supplier and a liability of government.

The stationary supplier is one entity in what can be called the non-government sector. This sector includes all households and private businesses on the island as well as any foreigners making transactions in bucks.

When the government spends 100 bucks on office supplies, the financial assets of the non-government sector, taken as a whole, increase by the same amount. This increase in non-government financial assets is offset exactly by an increase in government liabilities of the same amount. In this way, bucks (which are government liabilities and non-government assets) are created out of nothing.

Conversely, when the stationary supplier pays perhaps 30 bucks in tax, this amount is subtracted from its bank account. This action destroys 30 bucks. They no longer exist. The stationary supplier’s assets go down by 30 bucks as do government liabilities. As a whole, the financial assets of the non-government sector decrease by this amount, as do outstanding government liabilities.

In short, government spending and lending create bucks, which are a financial asset of non-government and financial liability of government. Taxation eliminates bucks. Loan repayments to the public bank also function as tax payments, and so eliminate bucks. The discharge of any other government charges, such as through the payment of licensing fees or fines, also eliminates bucks.

As a matter of logic, something cannot be destroyed before it exists. Bucks must be created through government spending or lending before they can be eliminated through taxes, the repayment of public loans or the discharge of other financial obligations to government. Or, to put it another way, the government must issue its financial liabilities before they can be extinguished.

Clearly, there is no limit to how many financial liabilities the government can issue in its own currency. For Buckwell Island’s government, there is never a question of financial affordability when it comes to anything that is available for sale in bucks. To issue its liabilities, the government simply makes a decision to spend, pay pensions or lend. With the decision made, the bucks are keystroked into existence when the public bank types them into the accounts of spending recipients, pensioners or borrowers.

However, the absence of a financial limit does not mean that there are no limits to what can be achieved in real terms. It would be pointless for Buckwell Island’s government to keep increasing its spending if there were no actual goods and services that could be produced to meet the extra demand. Acting in this way would merely bid up the prices of various goods and services. And since the prices of these goods and services might also enter into the costs of producing other goods and services, there could potentially be a bout of excessive inflation in which prices, on average, rose rapidly and continued to rise for some time. Inflation causes the currency to lose some of its purchasing power. A unit of the currency – one buck for the islanders – would purchase less than before.

Fortunately, Buckwell Island’s government and citizens understand that the level of total spending – which includes the spending of government, the island’s households and businesses, and foreigners – needs to be kept in sensible proportion to the capacity of the society as a whole to produce real goods and services. This does not necessarily mean that taxes must be as high as government spending. To the extent that households, businesses and foreigners wish to spend less than their incomes, this subtracts from the overall level of demand and makes it possible for government to spend somewhat more than it taxes without causing excess demand.

Although our tale is very simple compared with the complexities of modern economies, it does highlight some basic points that will help address the questions posed at the outset. Introducing more real-world factors, such as a private banking sector, would greatly complicate the details of the story but not change the basic issues presently under consideration. Returning to the questions:

**Question 1.** Where does a national currency come from?

**Answer.** In a society with a currency-issuing government, the currency originates from governmental decisions to spend or lend. Whenever Buckwell Island’s government follows through with its decision to spend or lend, bucks are created. As has been discussed, the bucks so created are a financial liability of government – a form of liability that the government can issue without limit – and a financial asset of non-government.

**Question 2.** How does a currency system basically work?

**Answer.** The currency originally comes from government. When the Buckwell Islanders sell goods or services (including labor services) to government, they receive bucks in exchange as income. When businesses borrow from the public bank to invest in production or hire workers, these expenditures likewise go to somebody as income. In this way, bucks enter the economy and can be used for various purposes within the economy. Some of the bucks received as income will be used by households and businesses to pay taxes. Some will be saved in accounts at the public bank or in hard currency. Some will be used to buy goods and services from foreigners. And some will be used to buy goods and services from others in the island community, creating additional income in the process. In this way, bucks circulate from one household or business to another until at some point they are eliminated through taxation.

**Question 3.** Why might people agree to accept a national currency in the first place?

**Answer.** An important reason is that people must obtain the currency in order to pay taxes or meet other financial obligations imposed by government. This ensures that the Buckwell Islanders will accept bucks in particular, in preference to some other currency. The imposition of taxes and other government charges is not necessarily the only reason people might accept the currency. But this factor is sufficient to ensure at least a base level demand for the currency.

**Question 4.** How can we be confident that a national currency won’t collapse and that people will continue to accept it in economic transactions?

**Answer.** A complete collapse of the currency would mean that it was no longer possible to buy goods and services with the currency. It would mean that nobody was willing any longer to accept the currency in payment for anything. A complete breakdown of the currency will not happen so long as the government effectively enforces taxes and other obligations denominated in its currency. It is the successful enforcement of these obligations that guarantees the currency remains acceptable in exchange at least to some extent.

Even so, we have also recognized that the currency can lose some of its purchasing power when the tax burden becomes too light relative to the level of government spending. If taxes were kept very low but the government chose to spend a great deal in comparison, this could cause (in combination with other spending) more demand than the economy could cope with in a timely fashion and result in a bidding up of prices for many goods and services. A unit of the currency – one buck for the islanders – would then buy less than before. The purchasing power of the currency would decline.

What matters, in this respect, is the strength of spending in general, whether by government or non-government. All spending carries some risk of inflation if it causes demand to outstrip the capacity of the economy to supply additional output. The more households, businesses and foreigners wish to save bucks (rather than spend them), the more it is possible for government spending to exceed tax payments without causing undue inflation.

The solution to an outbreak of severe inflation would be for government either to cut its spending, raise taxes or do a combination of both. These actions would constrain the level of public and/or private spending and help to keep inflationary pressures in check. In the absence of a Job Guarantee, the policies would almost certainly create some unemployment. Fortunately, Buckwell Island has a Job Guarantee. This program ensures that full employment can be maintained despite any reduction in total spending on goods and services that might occasionally be necessary to curb inflation.

**Question 5.** Can a government ever go broke and leave citizens footing the bill?

**Answer.** A currency-issuing government can never go broke so long as it sticks to operating in its own currency and refrains from borrowing in foreign currencies. (To the extent that a government becomes indebted in a foreign currency, it reduces itself to the status of a currency user and can run into financial difficulties.) A government that sticks to its own currency faces no financial constraint. It can always create more currency if and when this is deemed appropriate.

**Question 6.** Can financial affordability even be an issue for government?

**Answer.** A currency-issuing government can always purchase whatever is available for sale in its own currency. By the same token – and at the risk of stating the obvious – the government cannot purchase what is unavailable for sale. Put simply, there can be a shortage of natural resources. There can be a shortage of workers. There can be a shortage of knowledge and technical know-how that prevents certain goods or services from being supplied within a particular time frame. These constraints place limits on what can be done in real terms. But, importantly, anything that can be done within these real limits is affordable for a currency-issuing government.

**Related Posts**

Consider a currency-issuing government that requires itself either to deduct taxes from non-government accounts or to issue debt to non-government before it spends. This is quite typical of governments today. At first glance, these requirements may seem problematic. From inception, it would clearly be impossible for a currency issuer to receive tax payments in its own currency or to auction off public debt in exchange for its own currency before the currency itself had actually been issued. The resolution to this apparent conundrum is that government can always (and currently does) advance to non-government the currency it requires to purchase newly issued public debt.

More specifically, the central bank, as the monetary arm of government, issues currency in the form of reserves (by crediting reserve accounts) while requiring collateral in the form of previously issued government bonds. Non-government is then in a position to purchase newly issued government bonds, with reserve accounts debited in settlement.

Typically, there will be a bidding process at a Treasury auction. The bonds will go to the participants with successful bids – all those bids that offer an interest rate on government debt that is at or below the cutoff. If the central bank is prohibited from purchasing bonds directly from the Treasury (which may or may not be the case, depending on the country in question), it will be necessary to auction off all newly-issued debt to non-government. In that case, the cutoff between successful and unsuccessful bids will be determined in the auction itself.

Considering that the sale of public debt is typically subjected to a bidding process, it may be wondered how government can nonetheless maintain control over the terms on which it spends. In particular, it may be unclear what prevents the rate of interest on public debt from rising above the rate that government actually wants to pay.

The answer is simple. The central bank can always purchase public debt in the secondary market (the market for previously issued bonds) and signal an intention to do so at a particular price. This means that official bond dealers participating in the Treasury auction know that bonds purchased in the primary issue on slightly more attractive terms can be sold to the central bank in the secondary market at a profit. It also means that the central bank can control interest rates on all government debt (of varying duration) by purchasing as much of each type as necessary in the secondary market. This pushes up bond prices and lowers yields, making newly issued bonds more attractive than otherwise. There is no limit to the central bank’s capacity to create reserves. For this reason, it can always drive interest rates on public debt lower through secondary-market transactions.

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