### A look at the correlations between CPI & Real GDP

March 11, 2011
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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.