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ETFsRule (99.90)

A look at the correlations between CPI & Real GDP

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March 11, 2011 – Comments (18)

            I am only posting the text here, but the whole thing with graphs is up on Scribd, which you can find here. You can download the file if you feel like it. I still have all the data sitting here in Excel, so if you have any questions feel free to ask.

            There has been a lot of debate over whether or not deflation is good for an economy. The two most important periods of deflation in modern history are the Great Depression and Japan's Lost Decade. These have already been studied in great detail, so I am not going to discuss them here.

            Many people, such as the folks at Mises.org have pointed out that price deflation was much more common in the 1800's, and did not always result in lower GDP growth. In this blog I will try to examine the relationship between yearly changes in the consumer price index (CPI), and yearly changes in real GDP. This data was downloaded from Measuring Worth. I will attempt to compare and contrast the years from 1790-1913, with years of the post-Federal Reserve era: 1914-2009.

            First I want to mention that the relationship between CPI and GDP can be seen very cleary, if nominal GDP is used instead of real GDP. But I am not going to discuss these graphs because I believe that would be misleading. If nominal GDP increases by 3%, but the CPI also increases by 3%, then we haven't really gained anything in terms of purchasing power. So I will stick to real GDP for my analysis.

First, here is the modern period:

Figure 1: A timeline showing the yearly percentage changes in both CPI and real GDP, from 1914-2009.

Now, we can contrast this with Figure 2, which shows the same data, for 1791-1913.

I have also divided Figure 2 into three smaller parts, which lets us see it more clearly:

Figure 3: Timeline, 1791-1830

Figure 4: Timeline, 1831-1871

Figure 5: Timeline, 1872-1913

For a quick history lesson, here are some key events which correspond with some of the various peaks and valleys of these graphs:

1812-1815 - War of 1812

1817 - NYSE founded

1819 - Panic of 1819 (some other panics can be seen here)

1861-1865 - American Civil War

1873-1879 (approx.) - Depression of 1873–79, AKA the "long depression"

1893-1897 - Depression of 1893

1907 - The Panic of 1907.

1913 - Creation of the Federal Reserve

There are a lot of ups and downs here, so rather than trying to squint at these graphs, I have made several scatter plots which allow us to analyze the data more easily.

For each of these plots, I am also going to give the Pearson Coefficient (to 2 decimal places). This is a way of measuring the degree of correlation between two variables using a scale of -1 to +1. Basically, a value of zero is randomness/no relationship. A value of +1 is a perfect 45-degree line: "/", and a value of -1 is a 45-degree line going the other direction: "\".

Here are the scatter plots:

Figure 6: CPI % Change vs Real GDP % Change, 1791-1913

Pearson = 0.18

We can contrast this with the more modern results:

Figure 7: CPI % Change vs Real GDP % Change, 1914-2009

Pearson = 0.18

It's interesting that the correlation came out exactly the same for both time periods. It's not the strongest correlation in the world, but what it means is that there tends to be greater real GDP growth in years with larger CPI increases.

Next, I split up the data from Figure 6 into 3 parts: inflationary years, deflationary years, and neutral years (believe it or not there were 18 years where the CPI stayed exactly the same).

Figure 8: Inflationary Years, 1791-1913

Pearson = 0.13

Figure 9: Deflationary Years, 1791-1913

Pearson = 0.13

Figure 10: Neutral Years, 1791-1913

Pearson = N/A

Again we see the exact same degree of correlation, which indicates that these numbers might actually mean something! More inflation (or, less deflation) generally results in higher GDP growth. Although, again I should point out that the correlation value of 0.13 is not very high.

To illustrate a point that I made earlier, I will post one plot that uses nominal GDP growth instead of real GDP growth:

Figure 11: CPI % Change vs Nominal GDP % Change, 1791-1913

Pearson = 0.85

This shows us conclusively that price inflation increases the growth rate of the nominal GDP, resulting in a much larger degree of correlation than what we saw in the real GDP plots.

Averages: This seems like as good a time as any to throw some numbers at you, so here they are: 

Average CPI % change, 1791-1913: 0.23%

Average real GDP % change, 1791-1913: 3.85%

Average real GDP % change, 1791-1913 (during the 50 inflationary years): 4.64%

Average real GDP % change, 1791-1913 (during the 54 deflationary years): 3.39%

Average real GDP % change, 1791-1913 (during the 18 neutral years): 5.50%

 

Average CPI % change, 1914-2009: 3.41%

Average real GDP % change, 1914-2009: 3.37%

Average real GDP % change, 1914-2009 (during the 82 inflationary years): 4.06%

Average real GDP % change, 1914-2009 (during the 13 deflationary years): -1.18%

Average real GDP % change, 1914-2009 (during the 1 neutral year): 6.05%

Stable prices seem to be the best possible scenario for high real GDP growth. Inflation is the second-best option, and deflationary years produce the worst results.

Looking Ahead: 

Now, I will examine the effect that inflation has on future GDP growth. Fig. 12 shows the CPI % change for the current year, compared to the real GDP % change for the next year. Fig's 13-15 compare current-year CPI changes to the average annual GDP growth over the next 3, 5, and 10 years:

Figure 12: Current Year CPI % Change vs Next Year's Real GDP % Change, 1791-1913

Pearson = -0.04

Figure 13: Current Year CPI % Change vs Next 3 Year's Real GDP Average % Change, 1791-1913

Pearson = -0.23

Figure 14: Current Year CPI % Change vs Next 5 Year's Real GDP Average % Change, 1791-1913

Pearson = -0.30

Figure 15: Current Year CPI % Change vs Next 10 Year's Real GDP Average % Change, 1791-1913

Pearson = -0.23

And I did the same thing for the post-1914 era:

Figure 16: Current Year CPI % Change vs Next Year's Real GDP % Change, 1914-2008

Pearson = -0.03

Figure 17: Current Year CPI % Change vs Next 3 Year's Real GDP Average % Change, 1914-2006

Pearson = -0.12

Figure 18: Current Year CPI % Change vs Next 5 Year's Real GDP Average % Change, 1914-2004

Pearson = -0.13

Figure 19: Current Year CPI % Change vs Next 10 Year's Real GDP Average % Change, 1914-2004

Pearson = -0.16

Figures 12-19 all had negative correlations, which makes perfect sense: a high rate of price inflation in the current year results in slower GDP growth in subsequent years. This shows that there were "boom and bust" cycles, which behaved similarly in both time periods.

Conclusions:

            Comparing the two time periods (1790-1913 and 1914-2009), I have not found many fundamental differences. Deflation has become much less common since 1914, but the behavior of the economy seems very similar. In both periods, higher inflation generally correlates with higher real GDP growth in that year. Periods of high growth and high price inflation are generally followed by periods of slower growth, or even negative growth.

            Bear in mind that these are just correlations, so if you try to draw conclusions, it leads to a lot of chicken-or-the-egg types of problems. Is GDP influencing the CPI, or is it the other way around? Probably both, and sometimes maybe neither. Two variables can show a correlation if certain events influence both of those variables in a similar way. But that doesn't mean that the two variables are necessarily influencing each other.

            Even when you look at the correlation between current-year inflation and future GDP growth, that still doesn't necessarily mean that high inflation is the cause of lower GDP growth in the future. It just illustrates that boom-and-bust cycles are a real phenomenon; if the economy is growing at a high rate in one year, then it will probably grow at a slower rate over the next few years (and vice versa). In future blogs I'll try to dig deeper and hopefully gain a better understanding of causality. That's it for now.

18 Comments – Post Your Own

#1) On March 11, 2011 at 3:54 PM, Slider08 (45.56) wrote:

Interesting, but I think you're using a flawed metric (GDP) that is hopelessy bound to correlation instead of causation.

But of course putting numbers and measurements to these subjective values is nonsense. As Ludwig von Mises wrote, "The attempts to determine in money the wealth of a nation or of the whole of mankind are as childish as the mystic efforts to solve the riddles of the universe by worrying about the dimensions of the pyramid of Cheops."

Should We Believe the GDP?

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#2) On March 12, 2011 at 12:48 AM, ETFsRule (99.90) wrote:

Slider:

My advice is that when someone resorts to using that much anti-government rhetoric in one article, it is probably best to stop reading and just move on. They appear to be incapable of looking at the issue objectively.

If they had a legitimate gripe with the GDP figure they should be able to explain themselves calmly, rationally, and analytically. Instead they rely almost entirely on condescension and political rhetoric.

It's interesting that the author didn't mention any other possible alternatives to the GDP. I guess he also lacks faith in other indicators: manufacturing, exports, consumer sales, etc. These must all be phony numbers too right? Because in his mind, everything is part of a vast government conspiracy.

Notice how they conveniently only give credence to one indicator: the "new index project" - but they only support this one because they know that the project has already been discontinued. It makes you wonder if they really have any interest in looking at numbers at all, doesn't it?

They describe the concept behind the New Index Project:

"more-reliable metrics for measuring change in our health, education, the environment — the many ways that human beings make themselves better or worse off."

Well, someone should inform the author that such an index already exists: it's called the human development index. There are some others as well, including the gross national happiness and the genuine progress indicator. Of course, I'm sure he would just ignore all of these, since their results do not support his preconceived notions of what should work.

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#3) On March 12, 2011 at 4:23 PM, Slider08 (45.56) wrote:

Hmm... my biggest gripe with the Mises Institute is how inbred they are. That probably shows in this article. The author's the president of the Mises Institute, and I'm sure he could calmy and rationally explain his gripe with GDP; he's just preaching to the choir and glazing over the real issues, though.

I have a feeling this will boil down to a positivist vs. theoretical view of economics (cardinal vs ordinal utility, etc.) French, the article's author, was merely pointing out that even non-Austrian economists are flirting with the inadequacies of GDP as a metric.

Here, I think, is the most relevant part of the article:

The GDP framework cannot tell us whether final goods and services that were produced during a particular period of time are a reflection of real wealth expansion, or a reflection of capital consumption.  

French is actually quoting from the article I was originally seeking. That probably does a better job explaining GDP's deficiencies than I can, but I'll try:

1. Individuals have differing economic preferences, making the idea of a standard of living inherently relative to an individual. Trying to find an agregate number to measure this seems silly and bound to fail.

2. GDP includes consumption in a metric meant to measure wealth. Tthe only way to create wealth is through saving/investment. As the newly-linked article says, the supply of goods is taken for granted.

3. GDP fails to differ between good and bad consumption/investment. Breaking and fixing a window and building too many houses are considered good things.

3.5. GDP poorly accounts for time. The resulting goods deflation from #3 adversely affects GDP in a future time period.

As to an Austrian replacement for GDP: 

One is tempted to ask, why it is necessary to know the growth of the so-called "economy"?  What purpose can this type of information serve? In a free unhampered economy, this type of information would be of little use to entrepreneurs. The only indicator that any entrepreneur relies upon is profit and loss. How can the information that the so-called "economy" grew by 4 percent in a particular period help an entrepreneur make profit?

One more:

 So what are we to make out of the periodical pronouncements that the economy, as depicted by real GDP, grew by a particular percentage? All we can say is that this percentage has nothing to do with real economic growth and that it most likely mirrors the pace of monetary pumping. 

As a rule, the more money created by the central bank and the banking sector, the larger the monetary spending will be. This in turn means that the rate of growth of what is labeled as the real economy will closely mirror rises in money supply. 

The last quote may not be so obvious due to my point 3.5 

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#4) On March 12, 2011 at 4:41 PM, whereaminow (73.81) wrote:

ETF's,

You did a good job here. You put in a lot of work. I respect you for that, without a doubt. I'm just coming across this now. I've been busy with work and only have to time to call Larry Summers an idiot :)

I hope your positivist approach to studying this issue is helping you discover some of the difficulties with using empirical study to uncover the complex web of economic activity.

Real GDP = GDP/Price (Index)

GDP = private consumption + gross investment + government spending + (exports − imports)

Now, consider that you are on a gold standard. How can one suffer from prolonged (price) inflation on a gold standard? (I would consider anything over 6 consecutive quarters as prolonged, but opinions vary)?

One way would be for the government to go off the gold standard to pay for something it wants (money for killing enemies being the usual reason.) Ceteris paribus, GDP will rise. (There are other ways of course, so each case needs to examined individually.)

Often times, a rise in GDP is the reason for rising CPI, not the other way around, since the rise in GDP occured primarily because of a rise in government spending.

Fraught with difficulties, we are.

All that being said, no one in the Austrian School denies that inflation can increase economic activity. Malinvestment is investment, after all, but a bust will inevitably follow.

Our original discussion focused on the question, is (price) deflation a certain disaster? This is impossible to prove either way using empirical data. I hoped to bridge the gulf between theoretical and positivist approaches by speaking some of your language. But no study using empirical research is likely to result in definitive proof of any economic theory in either support or disproof. That's just the way it goes. Milton Friedman, on the other hand, was convinced that no economic argument could be settled through deductive reasoning.  We may never find out who is right.

But if you and I continue to take into consideration the framework from which each other operates, maybe we can find that we have some common ground.

David in Qatar

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#5) On March 13, 2011 at 3:29 PM, ETFsRule (99.90) wrote:

As to an Austrian replacement for GDP: 

"One is tempted to ask, why it is necessary to know the growth of the so-called "economy"?  What purpose can this type of information serve? In a free unhampered economy, this type of information would be of little use to entrepreneurs. The only indicator that any entrepreneur relies upon is profit and loss."

This is a problem I often have with Austrian economists. They spend so much time asking questions and criticizing the government, that they don't have enough time left over to come up with their own, practical answers. If they want a better index, then they should make one! Be pro-active, people!

I agree that the GDP isn't perfect, but historically I believe it has done a good job of corresponding with "real economic growth".

Maybe in a future blog I'll compare real GDP to the HDI, to try and get a feel for how well the GDP correlates with real, meaningful "development" of a country. This should get rid of the more controversial aspects of GDP, because breaking a window and then re-building again it would not cause the HDI to increase.

"How can the information that the so-called "economy" grew by 4 percent in a particular period help an entrepreneur make profit?"

It would also be trivially easy to graph real GDP against personal incomes or corporate incomes, to see if they really do correlate with one another. I would guess that they probably do.

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#6) On March 13, 2011 at 3:48 PM, ETFsRule (99.90) wrote:

"You did a good job here. You put in a lot of work. I respect you for that, without a doubt. I'm just coming across this now. I've been busy with work and only have to time to call Larry Summers an idiot :)"

It's all good... I've been too busy watching the living legend known as Kemba Walker

"How can one suffer from prolonged (price) inflation on a gold standard?"

Well, if the increase in the gold supply was faster than the increase in our population, then the value of gold should decrease, shouldn't it? That's probably the case right now, actually. The US population is currently growing at a rate of less than 1% per year, while I believe the gold supply grows at around 2% per year. So, theoretically the purchasing power of gold should be decreasing.

As for malinvestment, we should also consider that the private sector makes mistakes too. Even in a world with no government at all, we would still have to find a way to adjust our economic figures to account for malinvestments.

"Our original discussion focused on the question, is (price) deflation a certain disaster?"

I don't think it causes certain disaster, but I believe it is usually a bad thing.

Stephen Hawking tells us that "philosophy is dead". So, for the most part I will probably stick to my numbers-based approach to these issues.

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#7) On March 13, 2011 at 4:48 PM, whereaminow (73.81) wrote:

Well that's interesting ETF's. I suspect Hawking had more to say than those three words, and since he's not the Pope, I don't think he speaks infallibly.  (I'm kidding of course about the Pope. Not about infallibility.)

It's kind of sad to watch you use tools which arose from deductive reasoning (mathematical logic) to denounce deductive reasoning. Kind of like biting the hand that fed you.

All I can say is good luck with that. The witch doctors made the same choice many years ago. They now preside over the "dismal science." 

David in Qatar

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#8) On March 13, 2011 at 6:48 PM, ETFsRule (99.90) wrote:

That quote was just to illustrate a point, I never claimed that he was infallible.

Good luck with your deductive reasoning. Your attitudes towards the scientific community are about on par with Mao Zedong's.

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#9) On March 13, 2011 at 10:49 PM, whereaminow (73.81) wrote:

And you resort to cheap shots. You just can't help yourself. Oh well. I happen to love science. You never cared to ask. I just read Dawkins' Greatest Show on Earth.  You don't care to know.

You admit defeat when you reduce a perfectly reasonable argument into a war of cheap shots. You know I love those. But here, we tried to be reasonable with each other.

You know what you have never done?  Grasped and defeated a single a priori position of the Austrian School. You didn't even know that the term malinvestment (the cornerstone of Austrian Business Cycle Theory) does not refer to government spending.

Your attitude to theories that make you uncomfortable resembles Mao's attitude towards science. Look in the mirror.

I think I've had enough. Fire your last parting words. Here's another Austrian School prediction that is about to come true:  Your last words will have nothing to do with subjective value scales, human action, economic calculation, malinvestment, or anything that is central to Austrian Economic Theory.  

Enjoy the comfort of never learning anything too upseting. 

David in Qatar 

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#10) On March 14, 2011 at 8:39 AM, ETFsRule (99.90) wrote:

"And you resort to cheap shots. You just can't help yourself. Oh well. I happen to love science. You never cared to ask. I just read Dawkins' Greatest Show on Earth.  You don't care to know."

I've heard your thoughts on science in the past. I know that you believe the global scientific community is nothing more than a tool used by governments to legitimize themselves. That's not a cheap shot - those were your words.

I guess you only adopt that position when it is convenient? Scientists are only part of a wide-reaching conspiracy, when that is what you want to believe? How do you know Dawkins isn't a puppet of some government conspiracy?

"You know what you have never done?  Grasped and defeated a single a priori position of the Austrian School. "

That's because an a priori position cannot be defeated. Nor can one ever be proven. Do you understand what an a priori position is?

There is nothing more dangerous than having an absolute, infallible belief in something, which you can never let go of.

"You didn't even know that the term malinvestment (the cornerstone of Austrian Business Cycle Theory) does not refer to government spending."

I understand this completely. I was merely pointing out that Austrians have never taken appropriate measures to account for malinvestment. There is a lot of hot air, but no productive action on their part.

"Your attitude to theories that make you uncomfortable resembles Mao's attitude towards science. Look in the mirror. "

At least you admit that they are theories, and not absolute truths. Maybe there is hope for you.

"Here's another Austrian School prediction that is about to come true:  Your last words will have nothing to do with subjective value scales, human action, economic calculation, malinvestment, or anything that is central to Austrian Economic Theory. "

Economic calculation! Ha!

Austrians are good at spewing rhetoric... but calculation? Not so much.

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#11) On March 15, 2011 at 12:17 AM, whereaminow (73.81) wrote:

Wow, that must have been embarrasing to re-read.  I'm having trouble not laughing as I type.  I think you need psychological help. In all serious. 

You still don't understand what malinvestment means (or economic calculation, or logic, or philosophy.) 

But you sure can call the stock market. Oh wait, I almost forgot.... 

David in Qatar 

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#12) On March 15, 2011 at 12:11 PM, ETFsRule (99.90) wrote:

"You admit defeat when you reduce a perfectly reasonable argument into a war of cheap shots."

And you have waived the white flag, as usual. You could have learned something if you had taken the time to understand why Mr. Hawking said what he did.

You're right that I hadn't bothered to look up malinvestment before. And now that I have, I wish I hadn't wasted my time.

You admitted yourself that Austrian economists have no way of determining the optimal amount by which the money supply should be increased each year. IAs a result, they are incapable of identifying when monetary inflation is occuring. So, their incessant whining about it is nothing but hot air.

Malinvestment is the same story. Austrian economists have no way of quantitatively determining what the true cost of credit should be. So, they have no way of even determining when malinvestment is taking place. It's an empty idea, nothing but rhetoric.

You refer to the dismal science and witch doctors. Well then, why don't you tell me about the illustrious track record of Austrian economists? Where are their achievements, and their meaningful contributions to the world? Hmm, that's what I thought. There are none.

"But you sure can call the stock market. "

Thanks.

Say, David, what annual inflation rate is the MIT billion prices project reporting today? If you're going to spread lies, you may as well get your money's worth. Just be careful you don't get sued for libel.

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#13) On March 15, 2011 at 3:03 PM, whereaminow (73.81) wrote:

The white flag? What did you accomplish here, besides making a fool of yourself?

Sometimes I feel bad for you. You spend so much time denying other viewpoints and giving horrible stock market advice that I have to wonder if you have any money left at all.

Tell me, ETF's, what did you actually accomplish here? 

David in Qatar 

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#14) On March 15, 2011 at 4:38 PM, ETFsRule (99.90) wrote:

Do you even invest in stocks? I've never seen you discuss investing.

I learned about the correlation between CPI and Real GDP. This is valuable stuff, and it was a glaring omission from the economic data that was readily available. I'll continue to look at other correlations in the future, and hopefully determine what type of environment is truly best for the economy. Unlike some people I don't pretend to have all the answers unless I have studied the issues first.

I'm not denying other viewpoints. I looked into the ideas that you presented, but I found that they were riddled with serious flaws.  "Malinvestment" could have been a useful concept, but they haven't done anything useful with it. It's just another word that they use to complain about inflation.

I'm still waiting to hear what Austrian economists have accomplished. Just think: instead of writing all those books, those dead trees could have been used to make valuable toilet paper.

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#15) On March 15, 2011 at 4:49 PM, whereaminow (73.81) wrote:

I learned about the correlation between CPI and Real GDP.

Is this what you claim I waived a white flag at?  

David in Qatar 

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#16) On March 15, 2011 at 5:17 PM, ETFsRule (99.90) wrote:

The Hawking quote. You got defensive over it, dismissed it, and came back with your "witch doctor" comment. By your own standards that constitutes admitting defeat.

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#17) On March 15, 2011 at 5:28 PM, whereaminow (73.81) wrote:

The Hawking quote. 

LOL, ok. That's why I made a joke about it.

"Your attitudes towards the scientific community are about on par with Mao Zedong's." - ETFsRule 

That's the cheapshot, if I have to remind you.

Are we seriously doing this? Doesn't this seem just a bit stupid to you?  Does this have anything to do with matters of importance?  I can think of a million trivial things we can argue about.  Are we just arguing for argument's sake?

Is this how you approach all debates? Do you ever get anywhere with these tactics? 

David in Qatar 

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#18) On March 15, 2011 at 6:03 PM, ETFsRule (99.90) wrote:

"Are we seriously doing this? Doesn't this seem just a bit stupid to you?  Does this have anything to do with matters of importance?  I can think of a million trivial things we can argue about.  Are we just arguing for argument's sake?

Is this how you approach all debates? Do you ever get anywhere with these tactics?"

Me? Look in the mirror. I'm done with this.

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