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Wednesday, January 8, 2020

MMT And Price Level Determination

What determines the price level is a theoretical topic that pops up in Mosler's White Paper on Modern Monetary Theory (MMT - link to my discussion). Mosler's argument is that only MMT provides a proper understanding of price level determination. That is a strong claim, and difficult to assess. However, the discussion of price level determination is a distinctive part of MMT, and should receive greater prominence in discussion.


I want to offer my interpretation of the following statements that are in his white paper (link):
Only MMT recognizes the source of the price level.  The currency itself is a public monopoly.  Monopolists are necessarily “price setters”.
Therefore: The price level is necessarily a function of prices paid by the government’s agents when it spends, or collateral demanded when it lends. [emphasis in original]
In a market economy the government need only set one price, letting market forces continuously determine all other prices as expressions of relative value, as further influenced by institutional structure.   
Based on some offline discussions (which I may discuss elsewhere), the first sentence "Only MMT recognizes the source of the price level" is a statement that can easily be disputed. In this piece, I will put aside its validity. Modern Monetary Theory is supposed to be a school of thought, and we should not spend too much time debating the wording in one document, even though Warren Mosler is one of the founders of MMT.

I will instead focus on the substantive content in the following sentences. If one looks at them, one can see that they sound exactly like what someone who has spent a career doing fixed income relative value would write -- and that has some similarities to neoclassical macro. (I discussed this topic with Warren Mosler years ago, and he characterised dynamic stochastic general equilibrium (DSGE) models as arbitrage-free relative value pricing models, and I agree with that assessment.)

This is perhaps not a phrasing that would come naturally to those of a post-Keynesian bent. I think there is no contradiction, but it is probably easier to explain the implications of these statements if we start from (neo-)classical models. Since many of my readers may not be familiar with those models, I will sketch out what matters.

Basic Macro Models

There are many possible mathematical models that can be used in economics, but I am interested here in what I refer to as macro models. These are models that are meant to simulate economic aggregates. There are a few sectors, that interact via markets. Both (neo-)classical models and post-Keynesian stock-flow consistent (SFC) models can fit within this class of models; the differences show up in sector behaviour.
  • There is a household sector, that works for nominal ("dollar") wages, produces a aggregate good, and then purchases those goods for consumption. (The difference between DSGE and SFC models mainly revolve around the function used to determine consumption, and to a lesser extent, how many hours are worked.)
  • The business sector hires the household sector, paying an hourly wage W, and charging a price P for goods. The amount of goods produced in a period is determined by the production function, which will include the amount of hours worked, and quite often, the capital stock. The business sector sells the goods at a price that generates a profit. The classical/post-Keynesian debate is about the price-setting process.
  • There is a government sector, which I am largely putting aside for this discussion. It issues money, which is not pegged to anything ("fiat currency"). 
  • I will not worry about other features that commonly show up, such as bonds, or the external sector.
From the perspective of selling goods at a profit, we see that the ratio of wages (W) to goods prices (P) is extremely important. For example, if the only cost of production is wages and workers produce one widget per hour, the break-even ratio for P/W is 1. However, only the ratio matters, not the level of W and P. For example, the firm will break even if both prices are $1, or $10.

From the perspective of households, they are mainly concerned about the P/W ratio. If they work N hours, their total wages is WN, and this allows them to buy P/W N units of goods. If we scale both P and W by the same amount, the number of goods that can be purchased is unchanged. 

In other words, other than for one very key exception (discussed next), we can scale all prices in model solution and end up with another valid solution. This can be thought of as being equivalent to the re-denomination of a currency. 

The problem with this is that we have an infinite number of solutions: we can just pick one solution, and scale all prices by one of the infinite possible non-zero scalars, and end up with another solution. Real quantities (hours worked, goods consumed, etc.) are the same, but dollar amounts are different. This is worrisome theoretically, and makes it extremely difficult if not impossible to compute solutions. We need a way to fix (determine) the price level. (Since relative prices are fixed, we need only fix one, and the others are pinned down. People usually equate the price level to the price of goods, but from this perspective, fixing the wage accomplishes the same thing.)

The Price of Money is Fixed

The exception to being able to scale prices arbitrarily does not apply to money -- one dollar is always worth one dollar. In particular, the value of the inherited stock of money does not scale along with other prices.

The implication is that the inherited stock of money is a key variable to determine the price level, at least in classical models. (In a post-Keynesian model, more variables are inherited from the past, and so help act as an anchor for the price level.)

If we assume that a model has a single "steady state" solution in terms of real variables, we can then see one corollary. If there is a unique solution to the model, then the ratio of GDP to the initial money stock (the velocity of money) has to be a constant. Otherwise, there could be multiple possible solutions for the same initial money stock, violating the uniqueness assumption. By implication, we end up with the Quantity Theory of Money. This explains why the Quantity Theory of Money keeps popping up in discussions of neoclassical theory -- it pretty much has to.

Pinning Down the Price Level

Within neoclassical theory, there are at least two main ways of pinning down the initial price level. The first is to sneak in assumptions that create a mechanism to force the Quantity Theory Money to hold, and the second (the Fiscal Theory of the Price Level) I will discuss in an appendix. The existence of these techniques is contrary to Mosler's claim that "only" MMT recognises the source of the price level. Presumably, Mosler believes that other theories do not recognise the correct source of the price level. I see no value in debating that particular claim, as I would need to look at every other economic theory in existence.

Proponents of MMT reject the Quantity Theory of Money for a number of reasons. For myself, the data are enough to deal with that issue. This means that one cannot use it to pin down the price level. Instead, Mosler's summary points at an alternative means: the government transacts now ("in the spot markets") in some markets at prices it administers. It is a monopoly issuer of the currency, and has the capacity to set at least some prices.

letting market forces continuously determine all other prices as expressions of relative value [classical -BR], as further influenced by institutional structure [post-Keynesian - BR].   
As noted, this sounds like a mixture of classical and post-Keynesian thinking -- which could easily draw the ire of academics of all persuasions.

If we look at the Job Guarantee, we can easily see where this logic leads.
  • Private sector wages would be expected to be set as a markup over the Job Guarantee wage, except for positions where people may be willing to work at lower pay in order to get work experience (e.g., interns). 
  • Wages are a major component of production costs, and post-Keynesian theory argues that selling prices are a markup over those costs. 
  • The markup of private wages over the Job Guarantee wage, as well as profit margins, will vary over the cycle. Nevertheless, there should be some linkage between the Job Guarantee wage -- which is a directly-controlled policy variable -- and the price level.
This leads us to the preferred framing of MMT proponents: they want to control the price level by creating jobs for everyone who wishes to work, whereas the conventional response is to keep the unemployment rate at a level close enough to the NAIRU to stabilise prices.

From a technical perspective, if we view a DSGE model as a relative pricing model, we could imagine model where setting some prices leads to pinning down the other prices. This sounds quite similar to the above phrasing, which is how post-Keynesians would phrase the process. The difference lies in how markups are determined: classical models are based on the premise that optimisation will determine the hedging ratios, whereas post-Keynesians argue that markup are based on convention. As noted in an appendix, dealing with a Job Guarantee forces a blurring between classical and post-Keynesian approaches.

Models of this Behaviour

Warren Mosler's white paper references two papers that discuss how the government as a monopolist determines the price level. The papers include fairly simple models of the behaviour. For reasons of time, I will not cover them here. However, I would note that my description of how markups would transfer from the Job Guarantee wage to the overall price level is much less abstract (but reliant upon the existence of the Job Guarantee).

Should Government be a Price Taker?

This rather abstract topic then turns into an interesting practical discussion -- should the government be a price taker? Although the Job Guarantee wage is the most obvious way to influence the price level, all government provisioning matters. To the extent that the government is concerned about inflation, its spending patterns should reinforce those goals.

At present, governments are probably reinforcing the generally disinflationary slant of the developed economies. However, this was not always the case. One could argue that poorly-structured spending programmes were an important driver of the inflation in the 1970s, which does not fit traditional narratives about that episode.

Concluding Remarks

One needs to step away from never-ending debates about the fiscal constraint in order to assess the depth of MMT.

Link to the next article in this sequence: the monetary monopoly model.

Appendix: The Fiscal Theory of the Price Level

The Fiscal Theory of the Price Level (FTPL) is an interesting beast (my primer). It is one of the few areas where neoclassical economists are stuck arguing over arcane theoretical points like heterodox economists. There are some interesting links between the FTPL and MMT.

To summarise, the FTPL suggests that expectations about fiscal policy determine the price level (as the name suggests). From 30,000 feet, this sounds similar to MMT arguments about "taxes drive money."

As noted earlier, Mosler's white paper uses the language of relative value, and DSGE models are ultimately relative value models. Is there a deeper relationship? Perhaps, but the key difference is that the MMT formulation has the governments transacting in the spot markets to drive the price level. In the FTPL variant, the threat of future taxes (primary fiscal surpluses) is the driver. To be blunt, that mechanism appears implausible, since households cannot truly hope to estimate the path of their tax burden on an infinite planning horizon.

Appendix: The Job Guarantee and Utility Maximisation

In standard classical models, households are assumed to optimise some utility function. Consuming goods increases utility, while being forced to work reduces utility, as the worker could instead pursue leisure activities. Post-Keynesians argue (correctly, in my view) that this is pernicious; human beings are social animals, and it is better to be working in a group that sitting at home alone (playing video games, or whatever). There is also the argument that taking the models literally is silly; for example, one might call the recession after the Financial Crisis "The Great Vacation."* However, if we argue that these are mathematical models, and this is just a mechanism to generate unemployment in the model, one can say that the lesson is to not take the models too literally.

Simulating a Job Guarantee does not immediately fit such a framework.

In the real world, we would expect that if a Job Guarantee were implemented with a wage near prevailing minimum wages, a good portion of the unemployed would sign up (at least after unemployment benefits expire, assuming they still exist). Meanwhile, people may quit terrible jobs that paid the minimum wage to take up a Job Guarantee wage. In other words, the number of people in the Job Guarantee programme would not be zero, even though the wages and benefits are well below the average for the private sector.

Conversely, if we added the equations/terms associated with a Job Guarantee to a standard classical model, the model would result in zero hours allocated to the Job Guarantee, under the assumption that the private wage is strictly greater than the Job Guarantee wage (and we assume that benefits are embedded in the wage, since they are not normally modelled).

The reasoning is straightforward: the Job Guarantee is a job, not leisure, and so it will not add to utility. Meanwhile, with a wage that is strictly lower than the private wage, households have strictly less to spend on consumption. There is no way a utility-maximising household would voluntarily choose a strictly positive allocation of time to working in the Job Guarantee. Since the defining characteristic of a DSGE model is that it is an equilibrium generated by meshing together voluntary  allocations of "endowments" by actors, there is no way to get an involuntary allocation.

In order to get the model to fit what we expect to happen in the real world, the only way forward is to throw a factor into the utility function to force a non-zero allocation of hours to the Job Guarantee. One can argue that there is some form of "community service aura" that makes spending some time working at a lower wage equivalent to receiving a higher wage in the private sector.

Unfortunately, such a change could easily disrupt the model solution properties, forcing other changes. The notion of "leisure" in standard models covers plausible reasons to voluntarily leave the labour market (e.g., take early retirement) as well as involuntary unemployment. The core of standard DSGE models are a flexible price Real Business Cycle (RBC) model. In those models. random movements in productivity result in changing the hours worked; that is, the real change to productivity drives the business cycle (hence the name). If a model hews closely to that existing behavioural pattern, business cycles would mainly be driven by changes to the leisure allocation, whereas the proportion of working hours devoted to Job Guarantee work would be stable. Since someone pursuing leisure is not considered part of the labour force, the prediction of the model is that the percentage of the working population in the Job Guarantee pool ought to be very stable. That not what MMT proponents argue will happen: the "Job Guarantee rate" would behave empirically like the unemployment rate does under current institutional arrangements. Further fixes may be needed to the utility function to force such an outcome, on the argument that the MMTers' view seems to be the most plausible (in the absence of observed data).

If we put these metaphysical concerns to the side, we end up with a model that appears operationally equivalent to post-Keynesian arguments: a fudge factor is inserted into the model to generate a markup of the private sector wage over the Job Guarantee wage, which will presumably vary with the other cyclical factors.

I am fatigued by the macro wars, and so I do not have strong opinions either way on such an approach. However, from a practical perspective, we are still in the dark as to the practical effects of a Job Guarantee. In the absence of an actual Job Guarantee, we have no idea what the parameter values are on the implied utility function, so we do not know what the markup relationship would be between the Job Guarantee wage and private sector wages. At best, one could compare the empirical quality of predictions about the markup between approaches after the Job Guarantee is implemented.


* Not sure who to credit with coining that phrase; I first saw it in an article by Paul Krugman.

(c) Brian Romanchuk 2020


  1. Brian: Where do you see the bank-credit system in all this, that is, loans that don't go to productivity enhancing projects but instead create credit-money for consumption and speculation?

    1. This is a very abstract question: how do we pin down the price level in a mathematical model in the economy? In order for these models to be tractable, thinks like the banking system are abstracted out of existence.

      Mosler's argument is that private sector prices are set as a markup over prices that are being determined by the government. (Right now, governments do their best to be price takers, so this effect is extremely weak.) The state of the business cycle will affect those markups. Bank lending is a function of the business cycle.

      MMTers are not believers in the Quantity Theory of Money. The creation of money - whether is governmental money, or bank money - is not assumed to have an inflationary impact.

  2. There is quite a lot in this post--rather wide ranging. That said, I think I will comment on the Job Guarantee program as a cost of labor device.

    Leading into that, we can consider how government pays for skills commonly used in the private sector. Here we can think about secretaries, janitors, and mid-level office workers. Now, I am thinking that government tends to advertise job openings and people apply. This is true even if the jobs are short term, such as census workers.

    If government advertises for workers, is it likely to offer so little that the jobs remain unfilled? Or is it more likely to offer a wage packet intended to result in qualified hires? If the latter is the usual method, I think government becomes a labor price-setter.

    Naturally, I have an opinion comparing minimum wage efforts with the MMT Job Guarantee proposal. A quantified opinion awaits details on how the JG might be constructed. So many minimum wage jobs are part-time without benefits!

    And of course, what would the JG workers do?

    I think we need to be braced for the possibility that annual government deficits boost asset prices while having little effect on labor prices. Relative prices might depend upon competition within each market sector.

    1. I'm only familiar with the Canadian system, but pages paid by governments are highly bureaucratised. A manager who hires someone might be able to bump the ranking of a position by fooling around with the job description, but pay scales within a rank are a narrow range - and there is a tight budget constraint on a department's total spending. As far as I can tell, the US and other countries have a very similar culture. Meanwhile, wages are "medium term" contracts - set for at least a year, and negotiations might conducted only every few years.

      This means that governmental wages are administered - they do not jump around on a daily basis, like gasoline prices. If they want to fill positions, the wages need to be near the market - but short-term shocks can be ignored.

      The MMT argument is that if the governmental wage is getting too far from "the market", if the government is truly concerned about inflation, it should tighten fiscal policy, and not ratify higher prices by raising wages.

  3. Neil Wilson comments:

    The way it works is this.

    Government sets a price for a commodity it wants – say £50K for a nurse. Then it simply refuses to spend that money until it gets the price it demands. That leaves the system short of money, taxation continues to drain, and because under MMT policies the banks are constrained in what they can lend for they can’t replace the money in circulation. Bidding for nurses in competition to the democratic choice of the nation isn’t “capital development of the economy”.

    Additionally government can use its other coercive power to force bids at its price (banning private hospitals for example – which is the only place spare nurses can be found incidentally. Surprisingly taxing the rich doesn’t causes nurses to pop into being fully formed from the ether). The result is a bot of a recession in part of the economy and a price squeeze until sufficient bids for those nurse places come into to release the money into circulation – at which point the squeeze is automatically lifted.

    One of the reasons mainstream economic types can’t get their head around MMT is that in their world all resource conflicts are resolved via a bid-up auctions – people pay higher and higher prices until all bar one entity pulls out. MMT theory understands that there are several other ways that resource conflicts can be handled when you have a democratic government that is something more than “just another market player”.

    Incidentally bid up auctions degrade transitively into “how much money can you persuade the banks to create for you?”. Again something mainstream economists struggle to get their head around.

    In terms of oil, the question is ‘who is the oil producer going to sell their oil to if not you?’ In aggregate all demand is already satisfied at the price people are willing to pay, so your only choice is to leave the oil in the ground – or drop the price to encourage more bids.

    The floating exchange rate helps here, because again if the government is withholding spending, there are fewer units of currency in circulation, which makes them harder to get. Therefore the exchange rate tends to move in that direction. So although the government paid fewer £s to get the oil, it’s likely that the exchange rate as moved so the oil seller ends up with the same amount of money in US dollar terms (assuming that is their base unit of account).

    In terms of taxation liability, it’s not the tax bills that come first. It’s the *expectation* of a tax bill. I know I’m going to get a council tax bill in £s in April. Hence I’m working today for £s so I can pay it then. Or I’m talking to the bank about a £ loan so I can get that in place to pay the bill in April (loans take time to turn up – something else mainstream can’t seem to get their head around: time effluxion). Either way my actions today have been driven by a future event.

    Happy New Year everybody.

    1. Hey! You left out the most important word in that comment. I could be biased though.

      Happy New Year to the Unknowns also.

  4. Prices are such a delightful lock of contrasts:

    Labor is a renewable resource in chaotic supply.
    Natural resources are location-locked.
    Money has controllable durability.
    Money can be created at a whim.
    Government can introduce a tax at a whim.

    And it all comes together to a single transaction price.

    1. That's pretty damn good Roger.

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