A working paper exploring the idea that information equilibrium is a general principle for understanding economics. [Here] is an overview.

Tuesday, July 8, 2014

Why printing more money could have done nothing

I agree with everything this article says about preventing the Great Recession except for the fact that it should refer to a hypothetical Great Recession that happened in 1970 ([1], [2]).

Most of the colored paths are still going up for their duration and at their ends. And the Pink one is the only one curving over, the grey at the right is sky rocketing. So, the majority traces of the graph seem to state other wise than your title. The dotted line is drawing past most of the data points.

The majority of time printing more money increase prices. Even at the end of most of your traces.

(unlabled all of them, no ocasional dates, countries, towns, imaginary countries in other centries, etc.) But, that is not needed to see the relationship I stated above.

I complement you on ploting log(M/M0). So, the lines follow each other for good comparison. But I wouldn´t have any idea what p0 is given its some theoretical price of every thing.

[Except I realize that Switzerland is in the wrong location.]

"The majority of time printing more money increase prices. Even at the end of most of your traces."

This graph says that "printing" money increases prices at a decreasing rate as the amount of money that has been printed increases. It is a log-log graph so the actual slowing of the increase in the price level with increasing money is actually more dramatic. Monetary policy becomes less effective as the size of the monetary base grows.

p0 accounts for the arbitrary normalization of the price level.

I´m curios why are there no points at (0,0)? Shouldn´t all the lines run through (0,0)?

Why is that. If ln(P/P0) and ln(M/M0) are plotted an the time of P0 and M0 are in all the time series. Then the points (0,0) are where P=P0 ane M0=M0 would be.

Because those points give P/P0=1 and M/M0=1 and log(1)=0. Thus those time series should all run through (0,0). Like all those indexes crossing at 100%=1x at the same time.

p0 and m0 are independent fit parameters and the normalization of the price level p0 is completely arbitrary. There is no reason that P = p0 has to happen at M = m0.

Jason, how many P0s are there in the above plot? One for each country?

If P0 were larger for Russia say (the pink points in the lower left), then that would tend to move the data points for Russia down closer to the dashed black curve, which I take it represents a theoretical representative economy. So if P0 is completely arbitrary, wouldn't it "look better" to have a larger P0 for Russia? Or a smaller M00? Or some combination? In light of where all the other curves fall, why did you select the P0 you did for Russia? (I know there's nothing special about Russia, but I also know it's one of the latest curves you added, so that's why I'm framing my question around it).

Yes, there is one p0 for each country. What it's doing when I normalize is removing the arbitrary definition of the price level. The equation:

log P/p0 = (1/k - 1) log m/m0 - log k

becomes

y = (1/k - 1) x - log k

I could scale the price level data from a given country which would cause the price level fit to choose a different p0 but then P/p0 should be the same (in reality, the fit might change a little due to noise in the data).

There are m0's for each country as well, but m0 is not arbitrary. It sets the curvature of the curve.

You start off with bunch of data from a country: say N triplets of {m,NGDP,P} indexed by i. Now lets say we're using a pre-determined gamma. Is that reasonable?

Now, what do we do? Do we essentially minimize the following?

minimize over p0 and m0 { sum for i=1 to N of ( log P[i]/p0 - (1/k[i] - 1) log m[i]/m0 + log k[i] )^2 }

Where each k[i] is a function of m[i], NGDP[i], gamma, (and m0 and p0?)?

One you've performed the above minimization, then what? Use the m0 and p0 you found in the minimization to plot points {x,y} from your formula above?

Thanks Jason. But if that is essentially the process, why do you consider p0 to be an arbitrary parameter while m0 is not? Essentially you're solving:

minimize over p0 and m0: f(p0,m0)

Without knowing anything more about f(), I don't see how we deem one parameter to be arbitrary and the other non-arbitrary. So your rational for doing so must have something to do with the structure of f(). What is it about the structure of f() that allows you to do that?

Has my thinking gone off the rails yet? (Does it seem like I'm determined to go off the rails? :D)

It's just that the word "arbitrary" seems odd here to me. If it were truly arbitrary, then selection of a fixed p0, and then running the minimization over only m0 should result in the same m0 being selected no matter which fixed p0 was selected.

Similarly, when doing a regression trying to find a slope and intercept, fixing the intercept ahead of time at an arbitrary value, will lead to different slopes being calculated (one for each arbitrarily selected intercept). And only one slope-intercept pair gives the least mean squared error. Is this not a good analogy for some reason?

The value of p0 is arbitrary because the value of P is arbitrary; the ratio P/p0 isn't generally arbitrary.

If I choose to normalize the US CPI to today (237.8) rather than 1982-1984, then the fitted value of p0 is going to be 2.378 times bigger. If I choose to normalize to 1 instead of 100 for 1982-1984, then p0 is going to be 100 times smaller. The specific value of p0 is arbitrary, but the ratio P/p0 is meaningful.

m0 doesn't have the same freedom (although I can change both m0 and M by a scale factor, e.g. measuring M and m0 both in millions of dollars rather than billions). However m0 has units of dollars, so I can't arbitrarily set it to 15 billion dollars or 8 million dollars without scaling the monetary base.

I could change m0 for the US from ~ 800 billion dollars to 400 billion dollars, but then I would have to say there was half as much currency in circulation than there actually is (and that NGDP for the US was only 8 trillion dollars in 2014).

The arbitrariness of p0 is directly related to the arbitrariness of the definition of the value of the price level. Currency in circulation isn't arbitrary in the same way (however, if you recall your comment from awhile ago, adding two zeros on the dollar would just cause M and m0 to scale by 100).

Quote of previous reply of JS:"There is no reason that P = p0 has to happen at M = m0."

"There are m0's for each country as well, but m0 is not arbitrary. It sets the curvature of the curve."

So, does that mean for each line a point M equals an M0 and M0 is near an M in the time series? If so each line should pass throught the line of X=0 or equivalently pass 0 on the X axis. And if so, the US 1929-1944 line would not be more to right of the US modern line.

No, there is one m0 for each country, not each point. And there is no reason that an observed value of the available monetary base data has to exactly equal to m0 -- for example in Japan, all of the data has M > m0.

This is not that weird -- scientists determined what absolute zero was (-273 deg C, or 0 K) without having measured data from absolute zero.

""The study of money, above all other fields in economics, is one in which complexity is used to disguise truth or to evade truth, not to reveal it. The process by which banks create money is so simple the mind is repelled. With something so important, a deeper mystery seems only decent.[56]" – John Kenneth Galbraith writing in 'Money: Whence it came, where it went' (1975)." from: http://en.wikipedia.org/wiki/John_Kenneth_Galbraith

I'm not discussing the process by which banks create money (which I don't think is mysterious at all) ... I am talking about the relationship of money to the price level.

And apparently no one has understood the price level since no one has applied information theory ... ha! :)

Also, try to avoid the use of dollar signs as they interfere with my setup of mathjax. I left it set up that way because I think this is funny for an economics blog. You can use € or £ instead.

Lol, ... I knew what article by your title. I hope you left a comment on Sumner's blog.

ReplyDelete"Why printing more money could have done nothing"

ReplyDelete... and it turns out, nothing might be what we observed :D

It seems to fit the data :)

DeleteIn the latest post, we have a test of the model in Canada: it should start undershooting its inflation targets in the near term.

http://informationtransfereconomics.blogspot.com/2014/07/worthwhile-canadian-prediction.html

O/T: David Glasner made a comment about your Sraffa post that I can't help him with:

ReplyDeletehttp://uneasymoney.com/2014/07/07/a-new-version-of-my-paper-with-paul-zimmerman-on-the-hayek-sraffa-debate-is-available-on-ssrn/#comment-183761

I'm not sure I understand it either ... I will have to mull it a bit.

DeleteMost of the colored paths are still going up for their duration and at their ends. And the Pink one is the only one curving over, the grey at the right is sky rocketing. So, the majority traces of the graph seem to state other wise than your title. The dotted line is drawing past most of the data points.

ReplyDeleteThe majority of time printing more money increase prices. Even at the end of most of your traces.

(unlabled all of them, no ocasional dates, countries, towns, imaginary countries in other centries, etc.) But, that is not needed to see the relationship I stated above.

I complement you on ploting log(M/M0). So, the lines follow each other for good comparison. But I wouldn´t have any idea what p0 is given its some theoretical price of every thing.

I dropped the labels for aesthetic reasons; the labeled graph is here:

Deletehttp://informationtransfereconomics.blogspot.com/2014/06/output-and-price-level-behavior-across.html

[Except I realize that Switzerland is in the wrong location.]

"The majority of time printing more money increase prices. Even at the end of most of your traces."

This graph says that "printing" money increases prices at a decreasing rate as the amount of money that has been printed increases. It is a log-log graph so the actual slowing of the increase in the price level with increasing money is actually more dramatic. Monetary policy becomes less effective as the size of the monetary base grows.

p0 accounts for the arbitrary normalization of the price level.

One way for the prices to go down according to the graph is if the moeny supply decreased.

ReplyDeleteYes, that is typical quantity theory: decrease the money supply and you get deflation.

DeleteI´m curios why are there no points at (0,0)? Shouldn´t all the lines run through (0,0)?

ReplyDeleteWhy is that. If ln(P/P0) and ln(M/M0) are plotted an the time of P0 and M0 are in all the time series. Then the points (0,0) are where P=P0 ane M0=M0 would be.

Because those points give P/P0=1 and M/M0=1 and log(1)=0. Thus those time series should all run through (0,0). Like all those indexes crossing at 100%=1x at the same time.

p0 and m0 are independent fit parameters and the normalization of the price level p0 is completely arbitrary. There is no reason that P = p0 has to happen at M = m0.

DeleteCorrection:

ReplyDeleteWhy is that? P0 an M0 should be in all your time series. So, at some time for each series P(t)=P(t0) (P=P0) and M(t)=M(t0) (M=M0),

So, log(P/P0) and log(M/M0) are each equal to log(1)=0. Then the points (0,0) are where P=P0 and M0=M0 would be.

And

Thus the data in this graph seems to be graphed falsely.

p0 has nothing to do with P(t = t0)

Deletem0 has nothing to do with M(t = t0)

The source of p0, m0 are the equations here:

http://informationtransfereconomics.blogspot.com/2014/07/how-good-is-price-level-function.html

Would it help if I relabeled p0 to be "A" and m0 to be "B"?

I must stress: p0 is completely arbitrary. The price level P is usually given as P = 100 in some year; see for example here:

http://research.stlouisfed.org/fred2/series/CPILFENS

CPI = 100 for the average 1982-1984. That is a completely arbitrary designation. Much like the EU:

http://research.stlouisfed.org/fred2/series/CP0000EZ17M086NEST

HICP = 100 for 2005 (end of May)

Why 1982? Why 2005? It is arbitrary, so that makes p0 arbitrary.

Jason, how many P0s are there in the above plot? One for each country?

DeleteIf P0 were larger for Russia say (the pink points in the lower left), then that would tend to move the data points for Russia down closer to the dashed black curve, which I take it represents a theoretical representative economy. So if P0 is completely arbitrary, wouldn't it "look better" to have a larger P0 for Russia? Or a smaller M00? Or some combination? In light of where all the other curves fall, why did you select the P0 you did for Russia? (I know there's nothing special about Russia, but I also know it's one of the latest curves you added, so that's why I'm framing my question around it).

Yes, there is one p0 for each country. What it's doing when I normalize is removing the arbitrary definition of the price level. The equation:

Deletelog P/p0 = (1/k - 1) log m/m0 - log k

becomes

y = (1/k - 1) x - log k

I could scale the price level data from a given country which would cause the price level fit to choose a different p0 but then P/p0 should be the same (in reality, the fit might change a little due to noise in the data).

There are m0's for each country as well, but m0 is not arbitrary. It sets the curvature of the curve.

Jason, tell me where I go off the rails here:

DeleteYou start off with bunch of data from a country: say N triplets of {m,NGDP,P} indexed by i. Now lets say we're using a pre-determined gamma. Is that reasonable?

Now, what do we do? Do we essentially minimize the following?

minimize over p0 and m0 { sum for i=1 to N of ( log P[i]/p0 - (1/k[i] - 1) log m[i]/m0 + log k[i] )^2 }

Where each k[i] is a function of m[i], NGDP[i], gamma, (and m0 and p0?)?

One you've performed the above minimization, then what? Use the m0 and p0 you found in the minimization to plot points {x,y} from your formula above?

That is essentially the procedure. You can see it in the Mathematica code here:

Deletehttp://informationtransfereconomics.blogspot.com/2014/06/answering-some-technical-questions.html

And for the last question, yes, the numbers m0 and p0 then normalize the data in the graph above.

Thanks Jason. But if that is essentially the process, why do you consider p0 to be an arbitrary parameter while m0 is not? Essentially you're solving:

Deleteminimize over p0 and m0: f(p0,m0)

Without knowing anything more about f(), I don't see how we deem one parameter to be arbitrary and the other non-arbitrary. So your rational for doing so must have something to do with the structure of f(). What is it about the structure of f() that allows you to do that?

Has my thinking gone off the rails yet? (Does it seem like I'm determined to go off the rails? :D)

It's just that the word "arbitrary" seems odd here to me. If it were truly arbitrary, then selection of a fixed p0, and then running the minimization over only m0 should result in the same m0 being selected no matter which fixed p0 was selected.

Similarly, when doing a regression trying to find a slope and intercept, fixing the intercept ahead of time at an arbitrary value, will lead to different slopes being calculated (one for each arbitrarily selected intercept). And only one slope-intercept pair gives the least mean squared error. Is this not a good analogy for some reason?

The value of p0 is arbitrary because the value of P is arbitrary; the ratio P/p0 isn't generally arbitrary.

DeleteIf I choose to normalize the US CPI to today (237.8) rather than 1982-1984, then the fitted value of p0 is going to be 2.378 times bigger. If I choose to normalize to 1 instead of 100 for 1982-1984, then p0 is going to be 100 times smaller. The specific value of p0 is arbitrary, but the ratio P/p0 is meaningful.

m0 doesn't have the same freedom (although I can change both m0 and M by a scale factor, e.g. measuring M and m0 both in millions of dollars rather than billions). However m0 has units of dollars, so I can't arbitrarily set it to 15 billion dollars or 8 million dollars without scaling the monetary base.

I could change m0 for the US from ~ 800 billion dollars to 400 billion dollars, but then I would have to say there was half as much currency in circulation than there actually is (and that NGDP for the US was only 8 trillion dollars in 2014).

The arbitrariness of p0 is directly related to the arbitrariness of the definition of the value of the price level. Currency in circulation isn't arbitrary in the same way (however, if you recall your comment from awhile ago, adding two zeros on the dollar would just cause M and m0 to scale by 100).

OK, got it. Thanks.

DeleteQuote of previous reply of JS:"There is no reason that P = p0 has to happen at M = m0."

ReplyDelete"There are m0's for each country as well, but m0 is not arbitrary. It sets the curvature of the curve."

So, does that mean for each line a point M equals an M0 and M0 is near an M in the time series? If so each line should pass throught the line of X=0 or equivalently pass 0 on the X axis. And if so, the US 1929-1944 line would not be more to right of the US modern line.

No, there is one m0 for each country, not each point. And there is no reason that an observed value of the available monetary base data has to exactly equal to m0 -- for example in Japan, all of the data has M > m0.

DeleteThis is not that weird -- scientists determined what absolute zero was (-273 deg C, or 0 K) without having measured data from absolute zero.

Also, ment to this resent quote in the above coment.

ReplyDelete"There are m0's for each country as well, but m0 is not arbitrary. It sets the curvature of the curve."

Should have written the word recent instead of resent.

ReplyDelete""The study of money, above all other fields in economics, is one in which complexity is used to disguise truth or to evade truth, not to reveal it. The process by which banks create money is so simple the mind is repelled. With something so important, a deeper mystery seems only decent.[56]"

ReplyDelete– John Kenneth Galbraith writing in 'Money: Whence it came, where it went' (1975)."

from:

http://en.wikipedia.org/wiki/John_Kenneth_Galbraith

I'm not discussing the process by which banks create money (which I don't think is mysterious at all) ... I am talking about the relationship of money to the price level.

DeleteAnd apparently no one has understood the price level since no one has applied information theory ... ha! :)