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Sunday, October 1, 2017

The Price Level Does Not Exist

It appears to be a mistake to refer to the price level when discussing the theoretical properties of an economy; at best, there are a few price levels in play at a given time. If we are referring to the measured level of a price index, such as the Consumer Price Index (CPI) there is no difficulty, however this aggregate price index should not be expected to correspond to any useful theoretical construct. This article explains my logic, and then looks at the practical implications of what appears to be yet another hand-wringing post-Keynesian article about the difficulties with mathematical economics.

Update: Based on some reader feedback, I realise that I need to fill out parts of my logic in more detail. To repeat what I wrote below, I am unsure how my thinking fits in with the existing academic literature in this area. I am looking at this from the point of view of building a model that fits observed data, and there's some purist theoretical issues about price indices that I am not concerned about. Merijn Knibbe left this reference, which overlaps some of my thinking. The more detailed version will probably have to follow this weekend, since Professor Wren-Lewis caused yet another internet discussion that I want to weigh in on...

As a disclaimer, I have no idea how my comments fit in with the existing academic literature. I had a very brief discussion with Professor Randall Wray at the Modern Monetary Theory Conference on this topic, and it was an issue that he was well aware of. I would guess that it would cause greater anguish among mainstream economists, as it suggests that their preferred policy of inflation targeting is theoretically incoherent.

The Aggregation Problem

I originally started pondering this topic when I ran across the writings of a non-economist who simultaneously argued that we ought to look at the empirical data and not start with theory, and meanwhile did time series analysis of aggregate time series such as the CPI. (Since these origins are not critically important to my argument, I will not try to track down references.) My view was that this was incoherent: the empirical data was the millions of price measurements that get boiled down to the CPI time series, and we need to use to theory to justify how the aggregation is done. If one wants to build a theory of macroeconomics in the absence of theory, you need to start with disaggregated data, which most researchers do not have access to.

For example, I have recently purchased some craft beer in Kansas City, and bulk kitty litter in the Greater Montréal area. Since I am a consumer, why not directly aggregate time series of the prices of these items to create a consumer price index? We have good theoretical reasons to argue that these items should not be directly aggregated (left as an exercise to the reader), and so we instinctively would not try to create such a price index. However, we are relying on theory to determine which items we can aggregate.

Not Completely Austrian

I believe that this sounds somewhat similar to the Austrian economist critique of aggregation. (I have only seen the internet Austrian version of the argument, so I am unsure exactly how it is expressed.) The argument as I have seen it presented was that any aggregation in economics was not justified; we are adding unlike quantities together (such as apples and oranges).

I do not think that we can can take this argument too far; it is reasonable to aggregate similar items together. Defining similar is tricky; take the previously mentioned apples and oranges (which may be aggregated into "fresh fruits"). For a Canadian, oranges are imported, mainly from Florida, where the prices are susceptible to extreme weather. Meanwhile, apples are available domestically. We have reasons to suspect that apple and orange prices have different drivers. However, we have less reason to be concerned by processed cereal prices.

The belief that we cannot aggregate items at all is a curious argument, since we do it all the time. This is why we have a unit of account (that is, money) in the first place. Firms need to plan, and they are highly reliant on monetary aggregation in their financial plans. The issue is that we cannot lose sight of the underlying real constraints on activity. For example, if you are an owner of department stores in Montréal, having $1 million of clothes on display is not helpful if those clothes are parkas and it is July.

In other word, my complaint is not that the sub-indices of the CPI are theoretically meaningless, rather the act of aggregating them into a single number. We obviously can do the final aggregation calculation, but we should not expect that single aggregate to correspond to any useful theoretical concept.

Why Aggregation Breaks Down

The 1970s experience is suggestive of the problems. Why would we expect the price of crude oil to move in a coordinated fashion with the prices of domestically produced services? Yes, energy prices are embedded into the cost structure of almost everything, but at the same time, doubling the price of oil would only add a few percent to the cost of most items, so there is no reason to believe that they will move proportionally (which a unitary price level would suggest).

For example, Warren Mosler argues that the deregulation of natural gas prices created a massive demand shock for oil (as U.S. utilities switched from oil to natural gas), which destroyed OPEC's pricing power. He argues that this deregulation accounted for the breaking of the back of the 1970s inflation, and that Volcker's rate hikes were actually counter-productive. (Please note that I have not studied his arguments, and so I cannot say that I agree with him, but I find no reason to reject them on a theoretical basis. However, his argument would likely cause most mainstream economists to become apoplectic.)

More Than One Hidden Variable

The entire premise of macroeconomics is that we can relate low-level observations to a few aggregate variables. We can make definite statements about some aggregates on the basis of accounting logic, but in order to make useful forecasts and statements about policy, we need to make assumptions about the behavioural relationships between aggregates.

The usual assumption is that the calculated (observed) CPI is a proxy for a theoretical price level, and we can can then relate this singular theoretical price level to other hidden variables, such as the output gap. (Note that post-Keynesians generally object to the particular definitions of the output gap used by the mainstream, but there generally is the belief in a similar concept, which can be also viewed as a hidden variable that is to be estimated. I discuss this in Interest Rate Cycles: An Introduction.)

If we argue that there are at least two "price levels" in a theoretical model, we cannot cover both with a single time series proxy. Furthermore, the idea of a single "generalised output gap" that drives all of these price levels appears to break down.

The various outlandish assumptions that mainstream economists make in their "microfounded" models are there for one reason: to make it look respectable to pretend that there is only one good in the economy, with a single price level, which can then be controlled by manipulating a single price expectations series and a single output gap series. (Wages effectively disappear as a concept. The wage level is determined entirely by the price level and the marginal productivity of labour, and hence is a redundant variable.) Needless to say, this entire edifice collapses if we believe there is more than one price level in the economy.

(I am not arguing that I have a theory that can magically take the mainstream's place, and offer an easy way to forecast economic outcomes. Instead, my argument is that we should not expect economic forecasting (as it is currently understood) to be feasible, and we can demonstrate this by looking at the properties of theoretical models. All we can hope for is to extract general principles, and use them to guide policy.)

The rest of this article looks at various implications of these arguments.


Wages and salaries are a significant portion of the cost structure of domestically-produced goods and services. To what extent labour costs are correlated, we would expect them to act as a single unified variable that looks like a singular price level. As a result, it is not a mistake that the Fed is singularly interested in a tightening job market, even though their (loose) mandate is presumably to look at consumer price inflation.

However, the market for labour is regional and fragmented; there is little relationship between the bonuses paid to traders on Wall Street and the people who toil at minimum wage jobs in retail. Any realistic depiction of the labour market needs to take this into account. Even if we ignore the extreme top end of the income distribution, there is a big gap between the pay trends for workers in information technology and the minimum wage.

Nevertheless, if a tight labour market manages to buoy the wages across the employment spectrum, we would expect inflationary pressures. This was certainly the case in the 1970s, and during the mild cyclical upswing in the late 1990s.


 The widespread practice of indexing prices to some variable would tend to eliminate the divergences between multiple theoretical price levels. Such indexation could be tied to a domestic price index, or it could be through tying prices to those in a foreign (hard) currency (in which case the value of the domestic currency acts as the indexation variable).

In such an environment, we would expect that it would be much easier to move the entire price structure in one direction or another. Hence, much more susceptible to widespread inflation (as traditionally defined). Correspondingly, the decline of indexation (via union bargaining) may be the main explaining factor for the stability of observed CPI inflation, and not the switch to inflation-targeting.


Inflation-linked bond market participants have an extremely large vested interest in getting inflation forecasts right. Based on my observations, the usual practice is to forecast each component of the CPI separately, and then aggregate those forecasts to get the CPI forecast. Mainstream academic economists would presumably sneer at such a methodology, since they do not glorify the role of expectations in the steering of "the" price level. However, it is exactly the right procedure to follow if there is no unified price level as a theoretical concept.


Inflation control is the key goal of mainstream economics, a common view regardless of their political leanings. Even Modern Monetary Theory argues that one of its advantages is that it allows for control of inflation.

However, if there is no single theoretical price level, there is no single inflation series. What exactly is the policy objective, and why?

I am certainly not a spokesman for Modern Monetary Theory. However, I would phrase the objective as follows (which I think is compatible with existing formulations). The role of money in the economy is to allow the government to provision itself. (The alternative is to seize what it needs, such as conscripting soldiers or seizing goods and services.) The government should aim to keep the prices it pays for wages, goods, and services stable, and have those prices act as a pricing anchor for other domestic prices. As a result, the hope is that citizens would face stable prices during their day-to-day lives, although this cannot be guaranteed. (In this case, stable prices could either be stable levels, or a stable inflation rate.)

The Job Guarantee wage would be a critical price anchor. It would act as the effective minimum wage in the economy, and one would normally expect that at least 2% of the labour force would be employed at that wage. This would keep private sector wages for unskilled labour near that wage, although it may require the automatic stabilisers to induce a recession if private sector wages were outstripping that level.

Concluding Remarks

We need to be very careful when attempting to infer what is happening in the economy by just looking at the aggregate CPI.

(c) Brian Romanchuk 2017


  1. "Nevertheless, if a tight labour market manages to buoy the wages across the employment spectrum, we would expect inflationary pressures"

    Only if firms in any particular market segment runs out of price competition, i.e. they all start to do things in the same way at the same time. (If there is effective competition then quantity adjusters should always out-compete price adjusters.)

    However once you start to see inflation happen then the benefits of capitalism on that market segment (you can do more with less by investing capital) have expired and the segment ought to be nationalised (i.e. you lay off the capitalists since their job is clearly redundant).

    So you could argue that any inflation is an indication that the competition authorities ought to get involved and start laying off capitalists. This is an inversion of the current method where if there is any inflation the central bank gets involved to cause the lay off of workers.

    The mistake in the Beveridge form of Keynesianism, from what I can tell, was to assume that firms would do the right thing under wage pressure rather than sticking their prices up.

  2. I basically agree with the points made in this post, but I would put it a different way. The price level is a fine ex-post measure of the average price mark up in an economy. Minsky has a good chapter on this in Stabilizing and Unstable economy. But like you say, it is most useful looking at the components of the mark up instead of just looking at the aggregate level.

    The real problem is when the price level is considered an ex-ante behavioral variable. In particular, the concept of "inflation expectations" is totally incoherent, yet is the dominant paradigm for mainstream central bank policy.

    This also means that the real interest rate is only useful as an ex-post measure.

    Indexation is an under studied topic. They have insane pro-cyclical indexation policies in brazil, that I suspect add to their inflation problems.

  3. "The government should aim to keep the prices it pays for wages, goods, and services stable, and have those prices act as a pricing anchor for other domestic prices. As a result, the hope is that citizens would face stable prices during their day-to-day lives"

    "The Job Guarantee wage would be a critical price anchor. It would act as the effective minimum wage in the economy"

    I agree 100% with that. That's also my interpretation of MMT, although I'm also not a spokesman for MMT.

    I believe that stable government prices would guarantee a stable value for the currency.

    But if some sort of disease affects the tomatoes crops, than tomatoes value would probably rise, while the value of currency wouldn't change. Tomatoes price would rise, even with the stability of government prices.

    Currency value stability is not the same as price stability.


  4. I actually published a bit on this (link below). One point: there is no such thing as the purchasing power of money. What we measure (consumer price index) is the inverse of the purchasing power of income. At the end of my article, I come to the same conclusion as Keynes, in his General theory: it is not about the price level persé, it is about the relation between price levels, for instance wages and consumer prices (i.e. real wages. Which is why Keynes warned against lowering real wages.

    Which does not mean there is no order to prices. Based upon the national accounts it is for instance possible to establish a taxonomy of price levels: spending prices (government spending, consumer spending, investments, exports, imports); income price levels (mainly wages) and price levels of production (agriculture. manufacturing, restaurants etc.). Aside from these flow prices we have 'stock' prices: houses, stocks, bonds etc. It is clearly not right to use consumer prices as 'the' price level.

    Metrological arguments are also important. Using the consumer price level to gauge 'real' spending poweris based upon the assumption that preferences, incomes and relative prices do not change too much. This is, contrary to many complaints, imo not a drawback! It enables us to investigate the influence of changes in incomes etc.! But it is at odds with ideas about the existence of something like the stability of currency... As money is, in different sectors, by different people and in different times, used for different purposes, it is utterly misleading to talk about the purchasing power of money. Again: we use money to spend our income! The purchasing power of income or production is hence the important metric.

    Looking at it from this spending of income angle the enigma of the value of capital also becomes easier to understand. As relative prices as well as interest rates change over the years, it becomes quite difficult to arrive at a 'real' value of a capital good in a base year as this is supposed to be a function of these every changing relative cost and product prices in the future. It's all quite confusing. But remember that any price index is a construct, unlike nominal production and income.

    1. Thanks. Like I wrote, I had no idea how this fit in with the existing literature. I was going to offer more details on my thinking in a followup.

  5. " however this aggregate price index should not be expected to correspond to any useful theoretical construct."


    I can envision a theoretical link between money supply (when we include government bonds as part of the money supply), the price of houses, and the price of profitable production organizations. I can envision a theoretical link from production to wages and the price of resources.

    The actual measurement of these links would require a judgement about what to measure, as you suggest. Certainly taxes would affect the price level of each production item and, by extension, would affect the CPI.

    One thing that has always bothered me about the Job Guarantee Wage was how to determine a 'fair wage'. How would you differentiate between skill, willingness to work, individual handicaps, and locations of workers to create anything but an arbitrarily-decided bureaucratic distribution?

    Our current system of competitive prices measures (rather directly) willingness to sacrifice to achieve reward. Some of us hope that CPI measures sacrifice or at least the movement of the standard of sacrifice.

    If there are links between money supply and CPI (as I have suggested), then measurement of 'willingness to sacrifice' is complicated by changes in money supply.

  6. informative post! I really like and appreciate your work, thank you for sharing such a useful facts and information about labour process theory and employement relationship strategies, keep updating the blog, hear i prefer some more information about jobs for your career hr jobs in hyderabad .

  7. I wrote a similar post in mid july called "Are General Price Level Indices Theoretically Coherent?"

  8. Forward inflation expectations follow the business cycle almost perfectly. Hard to see how this could be a "random" series.

    1. 1) Forward inflation expectations are determined by a handful of market participants’ views about fair value. There is no guarantee that they are correct.

      2) If central banks react to the aggregated inflation value, and cause recession when it gets “too high”, forward inflation expectations ahould do exactly what they have done for their limited lifespan - stick around 2% (plus an added premium due to market structure). This is just telling us about central bankers, not the usefulness of the aggregate inflation measure.


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