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Usually economists say that in recession there is deflation, so increasing the money supply does not lead to a high level of inflation.

According to the Quantity theory of money, the price level is defined as such:

P = M*V/Y

Which implies that if the economy slows down, the V (velocity of money in circulation) goes down as well, leading to lower price level, hence lower inflation.

But what I don't understand, that at the same time the Y (Real GDP) goes down as well, cause of the recession, which should lead to a higher price level, hence higher inflation.

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  • $\begingroup$ When the real GDP goes down, is that a cause or an effect? Does the velocity go down because the factories stopped working, or do factories stop working because the velocity went down? $\endgroup$ – user253751 Jun 29 '20 at 13:32
  • $\begingroup$ The premise of the question is that the Quantity Theory of Money offers useful predictive content. The consensus of the economics profession appears to be that it does not. For example, all the major central banks target inflation, and they do not use the QTM in developing their inflation forecasts. $\endgroup$ – Brian Romanchuk Jun 29 '20 at 13:58
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    $\begingroup$ @BrianRomanchuk I agree that QTM is not useful for forecasting but that does not mean it has no useful predictive content. There is a difference between forecast and a prediction. For example theory of comparative advantage makes useful predictions yet it’s also not widely used for forecasting trade patterns where gravity models are much more prevalent. In fact I would say that the fact that QTM features explicitly or implicitly in many macro theoretical models shows that it’s important part of machinery that gives useful predictions and itself provides them even if it’s poor forecasting tool $\endgroup$ – 1muflon1♦ Jun 29 '20 at 14:26
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    $\begingroup$ @BrianRomanchuk definition of velocity is the number of times that average unit of currency is used to purchase G&S within given time period. In fact measuring V using $V=PY/M$ is an indirect method of measuring V. Also I totally agree it’s not constant. Also I think you keep mixing prediction that has a specific meaning when talking about formal theoretical models with its common English usage that is closer to what would be a forecast. As mentioned above I am in full agreement with you on that for forecasting purposes QTM equation is not useful $\endgroup$ – 1muflon1♦ Jun 30 '20 at 12:32
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    $\begingroup$ @BrianRomanchuk I agree that it’s not measured directly but just by talking about measuring it shows that you are coming at it from heavily policy relevant forecasting angle. That’s not all that good models should do. The QTM is not about creating accurate forecasting but about understanding the ‘black box’ in the background. For model to make predictions no measurement have to be taken you can just examine it completely analytically - in fact that’s what’s meant by model making predictions if you look at literature- i think we are coming at it from completely different angles $\endgroup$ – 1muflon1♦ Jun 30 '20 at 17:32
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First, let me address some incorrect premises in your question

Usually economists say that in recession there is deflation, so increasing the money supply does not lead to high level of inflation.

This statement is not really correct. First, I dont know many economists who would say that usually recessions are deflationary. For example, according to Romer's Advanced Macroeconomics 4th ed, the macroeconomic aggregates in 11 recessions between 1947:1 and 2009:3 can be summarized as follows:

enter image description here

So out of 11 recessions during the time period under considerations only 5 were characterized by deflation, and average change in inflation over all 11 recessions was only $-0.3\%$ which indicates that the recessions with deflation had on average slightly higher effect than the recession with inflation, but the datapoint is so close to zero that it would most likely be statistically insignificant. So the statement you say about most economists saying recessions are deflationary is simply not factually correct. Or at least if there are economists saying that they definitely cannot be in majority and assuming that statement was correctly representing their views they would not be factually correct.

In fact as you can read in this old Economics.SE question in economics we even distinguish between inflationary and deflationary recessions acknowledging both types of recessions exist. Generally speaking you will find that supply driven recessions are more on the inflationary side (good example are the 1970s energy crisis) and demand driven recessions on deflationary side (great example of deflationary recession is Great Depression or Great Recession both demand driven recession).

Second, the two effects are not mutually exclusive with each other. For example, it can be that velocity of money drops by $10\%$ while real output drops only by $8\%$ leading to deflation. If output would drop by more than velocity you would get inflation. Money supply also matters as it definitely does not stay constant during recession. For example, Fed with its dual mandate usually tries to expands money supply, directly or indirectly, during recessions to stimulate the economy. In addition as disused by Krugman (1998), what matters is not just the actual change in money supply or other quantities but what are peoples expectations about changes in money supply and so on. An increase of money supply that is not credible to be permanent and expected to be quickly reversed will have no effect on inflation as if it would never even happen.

One important thing to note here is that when nominal interest rates are at zero lower bound (ZLB) it is correct to say that even large monetary expansion wont necessary be inflationary. The reason for that is that if you would want to go significantly below ZLB the peoples will strictly prefer to hold cash and any increase in money supply will be completely offset by drop in velocity of money. In such cases indeed increasing money supply wont lead to higher level of inflation but that certainly does not apply to any or as data above show even most of the recessions.

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  • $\begingroup$ What I meant are mainstream economist, who are invited into talk shows, and who argue that money printing is good in recession, because it offsets the potential deflation. This point was made during the 2008 and covid crisis. I believe the reason for their argument is to decrease the potential expectation, like you were talking about. $\endgroup$ – curiousTrader Jun 29 '20 at 14:49
  • $\begingroup$ And what I still don't understand is that based on QTM inflation and GDP has a negative relation, while based on the Phillips curve, there is a positive relation. Could you clarify for me which one is right and why? $\endgroup$ – curiousTrader Jun 29 '20 at 14:53
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    $\begingroup$ @curiousTrader but I am sure those mainstream economist were talking about 2009 Great Recession and Covid crisis specifically not about all crisis as you made it sound. Also the standard New Keynesian Phillips curve does not imply consistent relationship between inflation and output (or rather I should more correctly say output gap) - see chapter 6 pp 259-261 in that Romer handbook I referenced. Moreover, those two effects are not necessary exclusive. The Phillips curve is basically an equivalent to an aggregate supply relationship (see for example Lucas model in Romer's book) where Y $\endgroup$ – 1muflon1♦ Jun 29 '20 at 15:28
  • $\begingroup$ ncreases with inflation the same way as a Q supplied on any market such as market for lets say potatos increases with price. However, you also have aggregate demand which also depends on money market equilibrium, for example after some derivations in Lucas model aggregate demand could be given as y=m−p (which actually is ultimately based on the QTM) where output varies negatively with prices the same way as a Q demanded. In equilibrium aggregate supply should equal aggregate demand AS=AD so both effects exist - increase in price lowers Q demanded and hence also the total national product y $\endgroup$ – 1muflon1♦ Jun 29 '20 at 15:45
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    $\begingroup$ but at the same time higher price induces producers to produce more of the national product. A macro-economy is an open and endogenous system. Looking only at MV=PY gives you only partial picture of what is happening (although that does not make the QTM any less useful). I think this is also one of the reasons why generally it seems that supply side recessions are associated with inflation while demand driven recession by deflation $\endgroup$ – 1muflon1♦ Jun 29 '20 at 15:46
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The quantity theory of money (QTM), $$P=\frac{MV}{Y},$$ is usually used to say this:

Consider these three Assumptions:

  1. Output $Y$ is growing at some fixed rate (for simplicity, let's say $0\%$ per annum).
  2. Velocity of money $V$ is constant (i.e. also growing at $0\%$).
  3. Money supply $M$ is growing at some fixed rate (let's say $2\%$ per annum).

Suppose the above three Assumptions hold. Then the price level $P$ must also grow at $2\%$.

Now, suppose that for Some Reason, Assumption #1 fails to hold and $Y$ instead grows by $-5\%$ (i.e. $Y$ falls by $5\%$). Your reasoning is this:

Assuming Assumptions #2 and #3 continue to hold, we'd expect $P$ to rise by about $7\%$.†

Your reasoning is incorrect because the Some Reason that caused $Y$ to fall (and Assumption #1 to fail) will probably also have some effect on $V$ and $M$ (and so cause Assumptions #2 and #3 to fail).

Your error is in assuming that all else is equal (the behavior of $V$ and $M$ does not change). But that is probably false during a recession.

(This is one reason why trying to use the above simple version of the QTM to predict $P$ from mere movements in $Y$ will usually not work. Cf. Brian Romanchuk's comment above.)

†More precisely, your incorrect reasoning would be that $P$ will rise by $$\frac{1.02}{0.95}-1\approx1.0736-1=0.0736=7.36\%.$$

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In my informal, colloquial understanding, the thinking behind your assertion is that during a downturn, the populous has less money to spend, thus, less product is sold. In order to attempt to sell product, vendors reduce prices as much as they can. This is classic supply and demand, where the supply exceeds demand.

Inflation is only really measured by some people wandering around stores making notes of the prices being asked for a range of products (yeah, it's a little more complicated than that, but you get the idea). If those prices get collectively discounted enough then you have deflation. The "basket" of goods that are price checked are usually picked to be broad across the economy, yet be things that "most people buy".

The basket method of inflation/deflation measurement means that for deflation to become truly likely, then the downturn needs to affect pretty much all sectors of the economy - and actually, analysis of most downturns shows that some sectors are hit harder than others. As a result, official deflation doesn't actually happen nearly as often as the simple assertion you make would suggest - even though vast swathes of people may be close to destitution, others may be working in fairly stable circumstances.

By way of example, during Covid lockdowns, many people have found themselves without work to do (leaving some unpaid or on government support), yet others have been employed as normal, or possibly be even busier than normal. Thus, whatever longer term downturns may occur as a result of it, we may not see official deflation because some sectors of the economy are (for the time being) still working roughly normally. The fact that many people have dramatically less disposable income, and so are consuming dramatically less is somewhat hidden by a single number describing the state of the economy (ie. the inflation figure) - arguably a case of over-simplification of a complex system.

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It is always easier to go back to the basics so first think of it in terms of plain old supply and demand. Most recessions are triggered by some sort of demand shock (war ends, Fed raises interest rates, pandemics). So demand contracts rapidly and supply stays roughly the same. That causes price and aggregate demand to fall. Price falling is deflation and aggregate demand falling is a recession. (Side note: notice how if it is a recession caused by a supply shock this is not true)

Demand decreasing]

In the case of the quantity theory of money you assume too many constants. M usually goes up as central banks often print money during recessions, V will go down as people go out and spend less, Y decreases because it is a recession. With so many variables and no values it becomes difficult to consider. Let's make up some numbers for an example. Suppose some made up numbers for before the recession M = 2, V = 2, and Y = 2. Then $P = \frac{2 * 2}{2} = 2$. Let us say after the recession there is a little more money because the central bank stepped in and M = 2.1, V = 1.8 and Y = 1.9. Now $P = \frac{2.1 * 1.8}{1.9} = 1.989$ which implies there is deflation.

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