Monetarism is a hoary old myth that does its damage in two distinct ways. The first is that, piggybacking on Milton Friedman’s personality, basically an entire generation of economists are actually monetarist in their practical thinking. Greg Mankiw once remarked that New Keynesianism should more accurately be called New Monetarism and **a glance at the actual pronouncements of even the more self-critical the New Keynesians** shows this beyond a shadow of a doubt.

The second way in which monetarism does its damage is what might be called ‘man-in-the-street-monetarism’. Man-in-the-street-monetarism is the knee-jerk reaction you get from people who have no training in economics (and some people who actually do but obviously weren’t paying close attention!) but who nevertheless read about economic matters and so forth. When they hear ‘money printing’ they instantly think ‘inflation’. This can interfere with conversations at dinner parties but it also infects the journalistic media. In its more extreme forms it leads people into **economic cults** like the neo-Austrian school that has become so popular on the internet after the financial crisis. These poor suckers are then **sold gold and other dodgy investment vehicles by industry frontmen**.

The essence of monetarism is in the transformation of an identity put forward in Irving Fisher’s classic 1911 work *The Purchasing Power of Money* into a supposed causal relationship. In that work Fisher laid out the following identity:

That equation reads: “The amount of money, *M*, multiplied by its velocity, *V*, is equal by identity to the sum of the quantity of goods and services purchased, *Q*, times the sum of their prices, *p*.” Note the clause “equal by identity”. The equals sign with an extra bar indicates that this is a tautological statement. It simply must be true. In the book Fisher discusses a number of ways in which this identity might hold. I think that while Fisher’s discussion was far more nuanced than the monetarists that grew out of the 1960s and 1970s it is nevertheless quite misleading. I lay out this argument in the chapter on money **in my forthcoming book**.

The monetarists proper converted this identity into a behavioral equation. This equation ran as follows and should be read running from left to right:

Note two things. First, the fact that we have converted the “equal by identity” sign into a standard equals sign. This implies causality running from left to right. So, the left-hand side of the equation *causes* the right-hand side. Secondly, we have placed ‘hats’ on the velocity and quantity variables. This implies that they are to be thought of as fixed. Thus the equation reads: “The sum of prices is equal to the quantity of money”. We understand the sum of prices here to be the Consumer Price Index (CPI).

Even when Friedman first came out with these statements they were showed to be empirically vacuous in the classic empiricist, anti-monetarist text *The Scourge of Monetarism* by Nicholas Kaldor. But today we have easy access to these statistics and can quickly run the relevant regressions. So, let’s see how monetarism fairs when confronted with the facts today.

First it should be noted that one peculiar feature of monetarism is its vagueness. **When monetarist policies were implemented in the late-1970s and early-1980s** and did not have the intended effects, monetarist economists began to cast doubt on the measures being used to calculate the money supply. Any time the policy didn’t work the economists would say that the central banks were not measuring the money supply properly. This is a classic use of theoretical argument to immunise marginalist economic theories against empirical criticism and was a tendency much discussed by the neo-positivist philosopher Hans Albert. For this reason we will include three key measures of the money supply — M1, M2 and M3 — and plot them against the CPI to give the theory the best possible chance to come to empirically verifiable conclusions. All the data that follows comes from FRED and the years chosen are based on availability.

Let us first lay these out in a standard graph form to see if we can intuitively spot any correlation. All graphs measure percentage changes year-on-year of both variables mapped. The reader can click on the image to enlarge it.

Oh dear, oh dear. Typically we should be able to pick up any correlation intuitively but in the above graphs — which represent all the data that FRED provides on the various money supply measures — we really do not see much to be hopeful for. Nevertheless, let us run some simple regressions to see if there is a correlation hiding in plain view that our all-too-human faculties have missed.

Oh no! This is very bad news for our monetarist friends. First of all, we must note that if the monetarist theory is true we should see a *positive* correlation between the money supply and prices. That is, when the money supply rises so too should prices and vice versa. This would be indicated in the regressions by an *upward-sloping trendline*. But in all three regressions we see a *negative* correlation indicated by a *downward-sloping* trendline. Embarrassing!

Secondly, we should note that the correlation coefficient, annotated the R-squared, is very, very weak in all three regressions. This is reflective of the intuitive fact that the graphs we laid out previously showed no significant relationship between the variables. Thirdly, we should note that the generally favoured measure of the money supply by monetarists is the M3 and in our regressions the M3 had the *lowest* correlation coefficient and the most substantially *negative* relationship. If these regressions are anything to go by we should more so expect prices to *fall* when the M3 grows!

But before we take our leave from monetarist fantasyland let us zoom in on the best ‘natural experiment’ of the thesis that we find in the data: namely, the extreme events surrounding 2008. Here is the data for the M1 and the M2 plotted against the CPI for that era (data for M3 is not available as it was discontinued in 2005):

Again, the data seems to run entirely contrary to the monetarist theory. Recall that above we read the monetarist equation to say that an increase in the money supply *causes *a rise in prices. But here we see both money supply measures *rising* toward the end of the 2008 as prices *fell*. This runs exactly contrary to what the monetarists would have you believe. Indeed, the *negative* relationship between the M1 monetary base and the price level is extremely statistically significant. Here is a regression plotting that important 12 month period:

All we can conclude from this is that monetarist theory — whether in academic form or in its man-in-the-street variant — is deeply, deeply misleading. The real world facts seem to run exactly contrary to the theory. Indeed, I do not think you could hope for a stronger refutation of any theory by engaging in data analysis. And yet the theory will continue to live on, zombie-like in the minds of academic economists, the media and the general public. Why? Why did this doctrine impose itself on the minds of men, especially in the 1970s and 1980s?

This, I think, is when ideology comes to play a role. **I have documented some reasons for the rise of monetarist doctrine in this era on this blog before** and readers can consult that particular post. But that post mainly focused on the case of the UK. With regards to the US James Galbraith and William Darity Jr. put forward the following argument as to monetarism’s supposed adoption by the Federal Reserve in the late-1970s and early-1980s in their excellent textbook *Macroeconomics*:

The Federal Reserve was no more monetarist in the early 1980s than it had ever been; it merely found for a time that monetarist arguments could be used to justify a severe credit crunch, and resulting recession, when these were felt necessary to bring a rapid end to inflation. (p244)

Amen to that!

There is one sense in which “Inflation is Always and Everywhere a Monetary Phenomenon”. If the CB didn’t increase the monetary base then the scope for inflation under fiat money would be very much limited. There is nothing pre-ordained about the fact that most CBs currently accommodate any increased demand for base money at the target interest rate – that is a policy choice.

Um… the evidence shows that increases in M1 are not positively correlated with inflation. Indeed, they seem to be weakly negatively correlated. If you want to make your quasi-monetarist case you must provide evidence. Otherwise it is just assertion.

Well, velocity clearly jumps around a lot during the economic cycle – which is why there is no direct correlation between M and P. But surely you would agree that if the CB kept M1 fixed then it is unlikely that you would get consistently high levels of inflation – this could only happen if V increased or Q decreased over time.

No I would not think that. Nor would the evidence show that.

The main mistake monetarists seem to make is to assume all of ‘M’ is always in flow. It isn’t. I have £20 in my wallet now that isn’t flowing anywhere.

The notion of ‘MV’ makes sense because in normal language that is ‘Turnover’, and of course turnover = price * quantity, because that’s how you calculate turnover!

It’s the decomposition of turnover that is at fault. The amount of the money that is available that has been in flow is not stable, and neither is the amount of times it is spent in a time period.

And I’m not sure what sort of belief you’d have to have to think that they ever could be.

So you have some evidence from history of economies with steady inflation and a fixed monetary base ?

All the evidence we have shows that these are not correlated. So, there is no reason to assume that if you held one constant then the other would remain constant.

Excellent Phil!Nice job! No correlation money sypply-inflation what so ever,clearly stated in this regression plain and simple! Well i have hard to find that monetarism ever rise again after this! Well i find it little amazing that neo-classicel ,at least some of them,stick to both Says Law and QTM,allthough allready Neoclassical Knut Wicksell in his critique of Irving Fischer round year 1900 showed it do not fit together! http://en.wikipedia.org/wiki/Cumulative_process .God lord they living in the past!

Velocity should play more important role in Fisher equation. I checked up FRED data about velocity of monetary base during crieses in USA and i see massive decrese. So i think that velocity shouldnt be taken as fix. So if we print a lot o money like Fed did it wont have any effect because money doesnt move. But when velocity is high printing money will have positive corelation on inflation.

“All the evidence we have shows that these are not correlated”

there’s a general correlation between the monetary base and CPI: basically CPI keeps increasing and so does the monetary base. This doesn’t mean that there is a causal relationship from money to prices however, as the recent massive increase in the monetary base has indicated.

I also want to add that an increase in the monetary base does not necessarily and always lead to a corresponding increase in the money supply and inflation. We could have, during a financial crisis, an increase of the monetary base and deflation at the same time as banks do not make any new loans.

I think that the Feds action during the financial crisis was (or is) to increase the monetary base to the extreme and in this way hinder a collapse of the money supply. The banks, in this environment, will feel safe enough to not too severely cut borrowing.

Historically, though, and during “normal circumstances” increases of the monetary base has led to increases of the money supply and inflation.

The problem with Monetarism is that it is so “mechanical”.

True, if the monetary base (which is narrower than M1) did not increase at all, we would, sooner or later, have a small deflation.

If that was not true we all should have a printing press, we all would be rich.

But Monetarism is dead in another way and that is that we can not define which money supply is relevant with regard to inflation and fluctuation of output and that the velocity of money is not stable.

I think that the new school “Market Monetarism” is therefore a lot better.

This is an excellent post.

This, in particular, is such a damning statement for so-called New Keynesianism:

“Greg Mankiw once remarked that New Keynesianism should more accurately be called New Monetarism”Also, if you have the time or interest, I wonder if you can answer some queries on the history of the quantity theory itself and the various versions:

(1) Fisher’s equation of exchange as I normally see it written (e.g., in Thirlwall’s entry on “monetarism” in the Encyclopedia of Political Economy: L-Z):

MV = PT

This doesn’t agree with the version you give above from Fisher’s

The Purchasing Power of Money(1911), where Q is in the place of T. What is going on here?Was Fisher the first to state the quantity theory in an equation?

(2) Cash balance equation: M = kPY.

Who was it who first formulated this? is it true that there was an earlier version M = kPT formulated by Marshall?

cheers

(1) Yes. Fisher was the first to state the quantity theory in equation form. I know that people generally use T rather than Q today but they also leave out the summation sign which is actually a nice addition to the original equation. As I said in the piece: Fisher’s discussion of the equation is actually of a fairly high quality. I especially like his use of the picture metaphor of a balance when showing how he conceives the identity to work. See: Section 3, II.29 in this chapter.

(2) I recall from memory that Pigou was the first to formulate the cash balances version during WWI. But apparently Marshall was giving lectures on this before that. Keynes discussed the theory extensively in his

Tract on Monetary Reform. Then he turned very critical of it in hisTreatise on Money.Congratulations, you have debunked short-run money neutrality, something (almost) no economist would defend. Of course, the quantity equation, if understood causally, is almost always taken to refer to the long-run, not monthly fluctuations. And in the long run, the positive relationship is clearly there, see e.g. figure 1 in McCandless & Weber (1995) [1], or just plot say 5-year growth rates for money and inflation data from FRED.

[1] http://www.minneapolisfed.org/research/qr/qr1931.pdf

Wow… the regression in that paper is one of the dodgiest I’ve ever seen. I’ll pass thanks.

As for averaging over five years, I don’t buy it either. It’s just statistical tomfoolery. Why five? Why not two? Why not ten? I’ll get very different relationships for each. This is called data-mining and its the equivalent to the old monetarist discussions about “lags”.

In fact, its worse than lags. At least with lags you could test a hypothesis rather than just aggregate the data in whatever arbitrary way gets the best fit.

So any contradicting evidence is just “statistical tomfoolery”? How convenient.

Averaging is justified by the fact that the theory describes a long-run relationship. Taking monthly data on year-on-year growth rates (seems to be your favorite data transformation) as some sort of sacred benchmark is not justified by anything.

Also, please explain what’s dodgy about McCandless & Weber results (which is not even a regression, just a scatter-plot of data).

The theory must posit causality. Therefore W amount of money at time X must produce Y amount of inflation at time Z. Averaging over any given period does not capture this dynamic. That is why the monetarists discussed lags. Not averages.

Pretty obvious really.

The scatterplot is way too aggregated to be trusted. I’d want to see a breakdown.

Out of interest here is the five year averaged regression for M3 for the whole period of measurement.

Looks pretty negatively correlated to me.

Ooops, its actually four year averages. But it’ll come out basically the same if you do five years.

Given that sustained price inflation requires a growing money supply, it is not at all surprising that there would be general positive relationship.

But why are empirical studies on whether there is a *proportional* relationship between money supply growth and the price level so contradictory if the “positive relationship” is (according to you) “clearly there”?:

“The quantity theory of money is based on two propositions. First, in the long run, there is proportionality between money growth and inflation, i.e., when money growth increases by x% inflation also rises by x% …. We subjected these statements to empirical tests using a sample which covers most countries in the world during the last 30 years. Our findings can be summarised as follows. First, when analysing the full sample of countries, we find a strong positive relation between the long-run growth rate of money and inflation.However, this relation is not proportional. Our second finding is that this strong link between inflation and money growth is almost wholly due to the presence of high-inflation or hyperinflation countries in the sample. The relation between inflation and money growth for low-inflation countries (on average less than 10% per year over 30 years) is weak, if not absent”De Grauwe, P. and Polan, M. 2005. “Is Inflation Always and Everywhere a Monetary Phenomenon?,” Scandinavian Journal of Economics 107: 239–259, at p. 256.

————

Why the astonishing lack of consensus?

And that is why I said I wouldn’t trust the scatterplot that ivansml provided. WAY too aggregated.

Also, assume one finds some limited cases in some nations in specific periods where there does seem to be a *proportional* relationship between money supply growth and the price level, even though lots of other studies, both general and specific, do not show this proportionality: doesn’t it ever occur to people that the few cases where it is proportional could be sheer accidents? Statistical flutes? — given how contradictory at best the data is?

Given how complex and variable inflation can be, it wouldn’t be surprising at all.

Of course. The point is that for the “inflation is everywhere a monetary phenomenon” to hold I would have to not be able to produce ANY data that shows an instance to the contrary. And yet, I can.

Mainstreamers like ivansml avoid these problems by fudging their research methods. Think for a moment about what it means to aggregate data over five year periods (arbitrarily) to get different results. Does this really show a “long-run trend”? Of course not. It just reduces the number of observations.

A “long-run trend” is, for example, a correlation between real income growth and population growth in the industrial revolution. Do we chart this relationship by taking five year averages? Of course not. We plot the two and see if they rise together. These guys don’t know what they mean when they say “long-run”. As I keep insisting, it is a mystical phrase that you would not get away with in either history or the hard sciences.

I wasn’t aware of this paper, so thanks. First of all, if you read their literature review section, most of previous research does support positive relationship, so there was a consensus (and De Grauwe & Polan frame their paper as questioning said consensus). Second, even in their paper, the relationship is positive over the whole sample, and disappears only after throwing out more than half of observations. Even in a subsample of low-inflation countries, output and money growth are not correlated, so money is neutral in the long run and lack of positive relationship between money growth and inflation must be thus explained by unaccounted differences in velocity growth. Overall, I don’t think their results present a strong evidence against QTM, although they do indicate that the situation is perhaps less clear than thought about previously.

“First of all, if you read their literature review section, most of previous research does support positive relationship, so there was a consensus”Yes, but not a universal *proportional* relationship between money supply growth and the price level, if read the literature review on pp. 241-244.

Of the 2 major previous groups of empirical studies of the 3 they mention:

(1) the “crosssection data on a large number of countries over a long time span” only show one study — Vogel (1974) — that finds a proportional relationship. The rest only find strong or very strong positive relationships.

(2) the “single country time-series” analyses “tend to confirm the proportionality

prediction of the quantity theory, although their

methodology has been“.criticised by McCallum (1984) and Rolnick and Weber (1995). McCallum

(1984) warns us that associating high-frequency time series with long-run

economic propositions is not always warranted

————————

So I am not sure how anyone can speak of a “consensus” here. It looks to me that their literature review, at best, finds contradictory results.

@Phil:

“A “long-run trend” is, for example, a correlation between real income growth and population growth in the industrial revolution. Do we chart this relationship by taking five year averages? Of course not. We plot the two and see if they rise together.”

Oh really? M2 and CPI seem to grow together pretty well: http://research.stlouisfed.org/fred2/graph/?g=GZG . On the other hand if you take yearly changes in population and income, I don’t think you’ll find much of a relationship.

It’s easy to create examples when two series share common trend and move together in the long run, and yet correlation between their short-run changes is low, or even negative (hint: let z be a random walk, and x and y be defined as sum of z and random noise, with shocks to x and y possibly correlated). Which is one of the reason why analyzing time series data usually requires something more than eyeballing FRED charts.

@LK:

Of course you will find always find papers that criticize some previous research. But from those papers where De Grauwe and Polan explicitly discuss their results, most of them confirm positive correlation (see their Table 1). In any case, I don’t think this is the most relevant thing to focus on here.

More interesting is – what’s the alternative hypothesis? If long-run variations in money growth are not associated with proportional changes in prices, they must be associated either with variations in real output growth or velocity. So what exactly are you arguing here for?

Now that is a long-run trend. But it doesn’t say what you seem to think that it says. It just says: “Since 1960 both the money supply measured in dollars terms and CPI indexed to 1982=100 have both risen continuously”. That’s not saying much, to be honest. And if you indexed the CPI to, say, 1959 you would get a somewhat different picture. If you index both to 1959 you get a VERY different picture. See, you can generate these so-called ‘long-run trends’ in any number of arbitrary ways. What you’re really doing is finding what you want to find. I’ll do a post on this tomorrow.

In the meantime, I’ve done some five year averages of the M3 versus the CPI from 1983 to 2003 and I’m still getting a negative relationship. You know why? Because economic ‘laws’… they ain’t like physics laws. If I were able to produce such results for a real scientist he would be taken aback. You do it in economics and you get the sort of vague woolly responses that you’re giving to LK. Shift the goalposts. Say that there is a consensus. And so on. It’s a terrible show.

The graph I linked to has log scale, so indexing to a different year will amount to shifting the series by a constant, i.e. it won’t change a thing.

Regarding M3, by all means do post those pictures. Although one must wonder, why choose that particular period (FRED has monthly series that go to 1959) and that particular money measure? Are you mining for negative correlation, by any chance? See, that’s very easy game to play.

Here:

And no, M3 goes back to ’81. Look it up.

But this is the point: even if I can mine a counterexample, if that counterexample is 20 years then I have proved your ‘law’ doesn’t work for those 20 years!

In science a law either holds or it doesn’t. But you’re not a scientist so I wouldn’t expect you to appreciate that. Move goalposts. Ceteris paribus immunizing conditions. Re-average the data. Set arbitrary lags. We know all the tricks, ivansml. I was taught them, for Godssake. I just had the cahones to call BS on what I saw being done.

Fitting line through 4 points, seriously? Please do compute also confidence interval on that one, so we can have some fun. Also, here you go, M3, January 1959 – February 2006: http://research.stlouisfed.org/fred2/series/M3SL

The rest – you’re just starting to repeat yourself. if anyone else reads this, they can judge for themselves who is more honest in considering evidence.

20 years. Done using your criteria. Negative relationship. Sorry. They’re the facts. You can close your eyes and pray to Milton if you so wish.

I look forward to your input tomorrow on justifying these long-run averages.

But then, we both know what’s really going on here, right? Duck and dodge. Say that there isn’t enough observations (even though you told me to reduce them). Cast doubt on the reliability of the regression. ANYTHING to not have to face the fact: 20 years; on your terms; the opposite results to what the theory predicts.

Again, in science a law either holds or it doesn’t. Either you stay stuck to the Earth’s gravitational pull or you float into space and refute Newton. But in economics? It’s just a game. Played by people who can’t do real economic analysis.

Ivanml. Monetarism in all it´s variations,is a regression in economic thinking to a time before Knut Wicksell´s formulation of the Cumulative Process round year 1900.Please read this: Axel Leijonhufvud, The Wicksell Connection http://www.econ.ucla.edu/workingpapers/wp165.pdf

Very important subject of course, but I don’t think your regression model captures the monetarist causal version of Fisher’s equation. When you say that the relationship M V.bar = Sum P Q.bar implies a causal relationship between M and P, V.bar and Q.bar being held constant, this implies that reasoning is done ceteris paribus (ie. all other variables being equal), as so often in economics.

A univariate linear regression (like the one you present) cannot capture such a relationship, because it does not include V or Q. In this sense, the lack of two-way correlation you find between M and P does not reject the monetarist theory, because the variations of P might be due to variations of V and Q that were not taken into account in the two-way model. It is often seen in linear regression settings that a zero two-way correlation between explained variable Y and a regressor X1 becomes significantly non-zero once you add other regresors X2, X3…

A more correct interpretation of the monetarist hypothesis would be the following (notating m, v, p, q the logarithm or the change rate of levels M, V, P, Q, with P an aggregate price index and Q a corresponding aggregated consumption quantity):

p= alpha + beta m + gamma v + delta q + error

where a monetarist would like to find alpha=0, beta = gamma = 1, and delta= -1.

But then again this model does not take into account the time aspect of the data, and the probable autocorrelation of errors (the fact that the change in the price index is probably caused in part by its change in recent periods), and that’s where things get really messy. When you take this autocorrelation into account, the linear model is ill-specified, and if you try to estimate it by instrumental variables and such you’ll have to take a lot of additional (and often hard to justify) hypotheses…

My interpretation of all this is that the monetarist hypothesis is untestable by itself, as the only way of seriously fitting the monetarist model to empirical data will require additional hypotheses, which means that rejection of the model would mean rejection of the monetarist hypothesis OR the additional hypotheses.

The real question here, as so often, is how can economists place so much faith in absolutely undecidable hypotheses, and yet claim scientific status? The monetarist hypothesis is unfortunately but one example among many, rational expectations and stable preferences come to mind.

PS: absolutely nothing can be concluded from graphic https://fixingtheeconomists.files.wordpress.com/2014/08/m3-5-year-average-83-03.jpg, five data points is no way near enough to assess correlation.

The hypothesis was that V and Q were fixed. That is clearly stated.

That would be a preposterous hypothesis: fixed consumed quantities and circulation velocity, for the last thirty years? Even for monetarists that seems a bit too much, doesn’t it? I think you are confused by the meaning of “constant”. So here we go again, with a simpler example:

Saying “the body mass index of individuals is strongly correlated with weight when height is held constant” does not imply that the whole population is supposed to have the same height! It simply means that of two persons of same height, the heaviest one is likely to have a higher body mass. It also means that just correlating weight with BMI will yield very misleading results.

These examples are extremely obscure. I think you guys are going way down the rabbit hole on this one. This always happens when I bring up stats.

@ ivansml : The problem with the quantity theory is that it completely misunderstands how prices are set in capitalist economies. As someone who has been a price setter, an ‘estimator’, for an industrial firm, I can tell you that the money supply has no short-run or long-run relation to prices except in the trivial sense that a means of payment is necessary. Instead, as any heterodox economist can tell you, the firm set selling prices according to cost plus markup; the former depending to a large degree on management’s control of the labour process and the latter depending to a large degree on the firm’s share of the market. Questions of power, in other words.

@ Phil : Good piece – I’m looking forward to your book!

@ Philip – NICE POST! As an economics noob, it was simple and accessible. Looking forward to your book. Anyway, I just checked the FRED site and it has economic data about M1,M2 and M3 from before 1976(which is the earliest date you have plotted for). Why have you not included that? Also, it would be really cool if you could upload files you used to make your graphs. Apart from adding credibility, noobs like me could play around with it to learn more.

I’ll think about it next time. I’m somewhat hesitant. People get all finicky about statistics even if you don’t post them. When you do it tends to generate debates which, frankly, I don’t have the time or the energy to engage with. Recall the FT vs. Piketty. That was high-level and look how much energy it took. I’m not sure if I want to do that for a blogpost. People can contact me if they cannot replicate my results.

Thanks for the reply. And about not including data before 1976. Why that?

Reblogged this on economics for the million and commented:

Good post – Inflation is NOT Always and Everywhere a Monetary Phenomenon

Phil, JuBo has a point. I know you think monetarists believe velocity is fixed but that isn’t so. Rather, for practical purposes, they said velocity was predictable (eg, can be known by looking at other indicators such as interest rates and output growth).

Monetarism was fully and completely discredited in the early 80s when velocity crashed, contrary to previous decades when it was it could be predicted fairly precisely). Accordingly, that period saw disinflation alongside significant growth in the money supply.

Phil, you and Irving Fisher have confused equal by definition with substantive equality. The first, depicted by a triple line, indicates that the left-hand side of the “equation”, the definiens, is identical ex vi terminorum to the right-hand side of the “equation”, the definiendum, by definition. Hence, it is neither true nor false, just useful or not, as the case may be. Thus, it isn’t a tautology, which in this context is a misleading term, and this is because, logically, definitions have no truth value.

The second equation, which could be considered to be a real equation, can be viewed as a substantive assertion that could be true or false. You could view the left-hand side of the equation as the independent variable and the right-hand side as the dependent variable. This would support your the causal interpretation you place on the equation.

However, the equation could be interpreted differently. It could be viewed as stipulating only a correlation between two sets of variables, or factors. This is because a functional identity on its own is not indicative of a causal relationship. More information is required. Mill’s test is an elementary means of assessing the presence or absence of a causal relationship. And to satisfy Mill’s test, you need more than a functional identity.

Moreover, one of your statements suggests that the assertion could be interpreted as a definition. If so, this would indicate that you and Fisher are equivocating in the use of the identity term.

The regressions you have run in your second set of graphs appear to me to be statistically non-significant. Which tells me that there is no relationship whatsoever between the respective pairs of variables. The regression lines are not needed to see this. They merely emphasize what is obvious. You contend that you don’t want to get into the details of statistical argumentation. I can understand that, but in this case, your reluctance has led you to see what isn’t really there, which further statistical analysis would have told you outright. Whatever negative correlation there is is trivial and statistical non-significant.

Definitions and tautologies are the same thing.

If I define X as not-Y then within my system the sentence “X is Y” is untrue while the sentence “X is not the same as Y” is true.

Definitions imply truth relations.

Example: mathematics is a language. Languages require definitions to function. But mathematics and all languages make true and false statements. But these rely on prior definitions which undergird the language in question.

No, Phil, they are not. A tautology is a statement that is always true, like if A, then A. Or (A or not-A). A definition tells you the meaning of a term or other grammatical entity. You are confusing a definition with a statement that is trivially derivable from the definition.

Using your own example, You define X and Y in the following way. X =df not-Y. What this means is that in any sentence in which X occurs, not-Y can be substituted and preserve the truth-value of the sentence. Let me use a slightly more complicated example than you have to show how this works.

X – Z + 3C = 6X^4. if we substitute not-Y for X as our definition allows us to do, we obtain the equation, not-Y – Z +3C = 6(not-Y)^4 (adding parentheses for readability). While both of these sentence may not “say” quite the same thing, they have exactly the same truth-value, which is all the definition accommodates.

Your final paragraph is somewhat confused. While it is true that mathematics is a language or set of languages, the role of definitions in these languages is more psychological than logical. Let me use the theory of arithmetic as an example. Peano arithmetic is set out by adumbrating a set of axioms or statements that are unproved in that theory, that is, they are assumed to be true and they utilize a set of primitive terms, terms that are undefined in the theory under construction, which in this case is Peano arithmetic. You also assume a grammar and a set of rules of inference, but I am taking these for granted. You begin with primitive axioms and primitive terms to set out your theory. No definitions are needed yet.

All mathematical theories begin in this way or a slightly related way (as set out in the latter part of Patrick Suppes’ Introduction to Logic), but for our purposes here we can ignore this complication. Some of these axioms are 1) zero is a number; 2) if the successor of a number X = the successor of a number Y, then X = Y. 3) X + 0 = X (zero is the identity element for addition). And so forth. “Zero” is a primitive term. “Successor” is a primitive term. “Plus” is a primitive term. That is, these terms are undefined within Peano arithmetic. As mentioned, no definitions are needed, at least not yet. However, in order to prove results where more concision is needed in order to facilitate understanding, you need to introduce definitions.

To summarize, to set up the theory of Peano arithmetic, you formulate a set of axioms that are unproved within the theory you are constructing. And you use primitive terms that are undefined within the theory you are constructing to formulate the axioms. You then begin proving all the things you need your theory to say, like 2 + 2 = 4, using the axioms, subsequently proved theorems, and any definitions you have introduced to extend the ease of expression of your theory.

If you do not set out your theory in this way, it will end up being trivially circular and, therefore, end up saying nothing substantive.

To prove a particular theorem, on the other hand, you might find it helpful to begin with some definitions. The utility, not the truth-value, of these definitions depends on previously defined terms, for example, or theorems whose proofs utilize these definitions. None of the definitions that any theory uses possess a truth-value; their only value is semantical or psychological. If a definition has no truth-value, it, therefore, can never be true or false.

I hope it is clear from this that definitions neither say nor imply anything about truth. All that is required of them is that they be self-consistent and consistent with the axioms, theorems, plus any other definitions to which they will be related in some way. After all, you expect all the elements of your theory to be consistent with one another. And you hope that your theory as a whole is true, which means that all of its substantive statements (axioms plus theorems) are true. Notice that definitions are not included in this specification, as they have no truth-value nor do they, indeed nor can they, lend truth-value to any statement with which they are associated.

Definitions do imply truth. And if you do not think so I would encourage you to consult your nearest lawyer.

If I say that a cat is a “large untamed herbivore bred in a single variety” then you will rightly say that my definition is

wrongorincorrector, what is the same,untrue. If I am silly enough to dispute this you will direct me to a dictionary which will tell me that a cat is, in fact, a “a small domesticated carnivore bred in a number of varieties”.If definitions do not imply truth then I cannot give an incorrect definition. This would also imply that the law cannot function as it relies on the idea of incorrect and correct definition. Human language and society cannot function without giving truth value to definitions.

Your philosophical system (probably some sort derivative of early Wittgenstein which he firmly rejected in later work) cannot capture this. But that is the fault of your philosophical system. You can say that I am “wrong”. But I am only wrong under your system. Which, it should be said, you define.

Phil, I should have added to the end of my final sentence in order to be strictly correct “except indirectly”, but I thought this would only add more confusion while contributing only a kind of formal completeness. I thus say it now only for the sake of formal completeness, but feel free to ignore it.

I am quite familiar with Wittgenstein’s work and I have not made that simple error. You are now bringing into the discussion which for the sake of simplicity I will designate as a theory that is already in use. The situation you describe exists also in mathematics and logical systems and their applied versions. But whereas you want to say definitions are correct or incorrect, I think it more appropriate to say that they are consistent or inconsistent, or good or bad, or useful or useless.

Just like your example of the cat, if you are adding to the general theory of relativity and you add a definition that is inconsistent with one or another aspect of the theory that has already been developed and tested, you may be accused of being incorrect. But you are incorrect only in the sense that the new definition you have introduced is inconsistent in some way with the body of theory (including the definitions already introduced) previously developed.

The logical character of the situation has not altered. Your new definition is not being disputed because it is false, except in a certain odd sense, it is being disputed and claimed to be wrong because it is inconsistent with previous usage, say. Just as with your example of the cat. Someone takes you to task about your new definition because it is inconsistent with previous usage, not because it has conveyed any aberrant sort of truth-value. And anyone who says that that is why they are criticizing you is making an elementary logical error.

Since definitions are used in derivations, the addition of an aberrant definition to a set of theorems of a theory may lead, via a set of derivations utilizing your new definition, to substantive statements to which there may be objections, substantive statements which will possess truth-value. As there may be objections to such substantive statements, for whatever reason, which are derived using your new definition, it may well be your new definition that will be singled out for criticism. But the problem is not that your definition carries any truth-value, it is being critiqued because it is linked to statements that do carry truth-value and it is this linkage that brings about the problem.

A definition to work well must be consistently integrated with the elements that comprise a theory that is already in use. If this integration goes awry for some reason, then problems will arise. In your example of the cat, the new definition leads to derivations of statements that are inconsistent with already accepted statements concerning biological systems. The new definition is linking up elements of the theory that the experts in the field, or everyday life, find unacceptable.

If your definition is incorrect, it is incorrect because it incorrectly links theoretical elements that when used in derivations lead to what are considered to be false substantive statements. It is not incorrect because it is itself false. A definition can be deviant and lead to unacceptable results as a consequence of being incompatible with the context into which it is integrated. And this can happen to any definition. Problems of truth and falsity, should there be any, are the consequence of linkages the definition has with other elements of the system and are not attributable to the definition itself.

That’s what I said in my first response when I wrote:

We all speak various languages. Within these languages you have correct and incorrect definitions. If you say that definitions are neither true nor untrue you are laying wreckage to all languages. Indeed, the irony that you might SAY this at all should not be lost as you are obviously using a language to SAY it, thus rendering the statement internally inconsistent. If it were true that definitions had no inherent truth-value then you would not even be able to make this statement because the words you are using to express it would have no true meaning.

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I disagree Phil.

http://moneymarketsandmisperceptions.blogspot.com/2014/08/endogenous-money-growth-and-prices.html

Monetary base vs. CPI.

I left this out because I assumed that everyone knew that they had no relationship to each other (especially after QE!).

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