What is the average inflation rate in the United States? An examination of historical data.

One of the most annoying things in finance is the tendancy to use wildly different numbers for assumptions based on different historical data. It drives me absolutely nuts. I always see calculations where they say the average return of the stock market is between 7%. Or 10%. Or 12.2%. Now wait a damned minute here. It can't be all three at the same time.

Let's look at those examples briefly. Say we invest $10,000 and leave it for 30 years.

7%: $76,122.55
10%: $174,494.02
12.2%: $316,071.77

That's one heck of a difference, isn't it? Now what if we want to adjust that for inflation and find the return of the investment in today's dollars? I see inflation rates used from anywhere from 2% to 4%.

Maximum return range is (12.2% return - 2% inflation) = 10.2% = $552,801.34
Minimum return range is (7% return - 4% inflation) = 3% = $72,817.87

Difference: $479,983.47

What's a half million dollars between friends though, huh? I mean, it only is the difference between eating top ramen and living in a beat down trailer home at retirement and living in your own home and eating well.

Obviously the future is murky at best and historical returns are no indicator of future performance. But we damn well should be able to agree on a few of the numbers. What is the right length of time to look at? How do you adjust the data?

To try to answer this, let's look at an interesting web site called measuring worth.com that does much of the number crunching. I believe much of their data came from the Bureau of Labor Statistics.

1906 - 2006 (100 years): 3.19%
1931 - 2006 ( 75 years): 3.50%
1956 - 2006 ( 50 years): 4.09%
1966 - 2006 ( 40 years): 4.67%
1976 - 2006 ( 30 years): 4.30%
1986 - 2006 ( 20 years): 3.09%
1996 - 2006 ( 10 years): 2.54%
2001 - 2006 ( 5 years): 2.63%
2003 - 2006 ( 3 years): 3.09%

That's one heck of a range, huh? 4.67% to 2.54%. Not particularily useful either. So I pulled some source data (CPI-U All Urban Consumers) and ran some numbers on it.

1914-2006 (93 years):
Data points: 93
Annualized Dec-Dec: 3.2688%
Annualized Avg-Avg: 3.2831%
Average Dec-Dec: 3.40%
STDEV Dec-Dec: 5.14%
Average Avg-Avg: 3.41%
STDEV Avg-Avg: 5.02%

1932-2006 (75 years):
Data points: 75
Annualized Dec-Dec: 3.7099%
Annualized Avg-Avg: 3.6511%
Average Dec-Dec: 3.63%
STDEV Dec-Dec: 3.88%
Average Avg-Avg: 3.57%
STDEV Avg-Avg: 3.77%

1957-2006 (50 years):
Data points: 50
Annualized Dec-Dec: 3.9950%
Annualized Avg-Avg: 4.0190%
Average Dec-Dec: 4.10%
STDEV Dec-Dec: 2.97%
Average Avg-Avg: 4.12%
STDEV Avg-Avg: 2.83%

1982-2006 (25 years):
Data points: 25
Annualized Dec-Dec: 2.9400%
Annualized Avg-Avg: 2.9900%
Average Dec-Dec: 3.10%
STDEV Dec-Dec: 1.13%
Average Avg-Avg: 3.25%
STDEV Avg-Avg: 1.12%

1997-2006 (10 years):
Data points: 10
Annualized Dec-Dec: 2.2500%
Annualized Avg-Avg: 2.3000%
Average Dec-Dec: 2.45%
STDEV Dec-Dec: 0.74%
Average Avg-Avg: 2.55%
STDEV Avg-Avg: 0.67%

Summary:

Over a 93 year span, inflation averages 3.4%.
68.2% (+/- 1 SD) of the data falls within the range of 8.49% to 1.68%
95.4% (+/- 2 SD) of the data falls within the range of 13.57% to -6.76%
2 SD range = 20.3%

Over a 75 year span, inflation averages 3.6%
68.2% (+/- 1 SD) of the data falls within the range of 7.43% to -0.22%
95.4% (+/- 2 SD) of the data falls within the range of 11.25% to -4.05%
2 SD range = 15.3%

Over a 50 year span, inflation averages 4.1%
68.2% (+/- 1 SD) of the data falls within the range of 7.01% to 1.21%
95.4% (+/- 2 SD) of the data falls within the range of 9.91% to -1.69%
2 SD range = 11.6%

Over a 25 year span, inflation averages 3.2%
68.2% (+/- 1 SD) of the data falls within the range of 4.30% to 2.05%
95.4% (+/- 2 SD) of the data falls within the range of 5.43% to 0.92%
2 SD range = 4.51%

Over a 10 year span, inflation averages 2.5%
68.2% (+/- 1 SD) of the data falls within the range of 3.20% to 1.80%
95.4% (+/- 2 SD) of the data falls within the range of 3.91% to 1.09%
2 SD range = 2.82%

Discussion and Conclusion:

The range of inflation appears to be smaller and smaller over time. Whether this is the effect of the Fed doing better at their job, the extreme prosperity of the United States over the period, or just the fact that there is less data is hard to say.

Based on on the data, I don't think 2.5% is a fair number to use. It seems that we've been very lucky lately, but even as recently as 50 years ago we were not so lucky. I also don't think 50 year number of 4.1% is a fair number to use either. It's really too high.

In my estimation, the 93 year 3.4% number is probably the best to use for a long term estimate of inflation. This number includes such events as World War I, the Great Depression, World War II, the post war boom, Korea and Vietnam, the Cold War, the tech boom, 9/11, and a big chunk of Iraq. It's hard to imagine that anything more unstable than those events can occur in the future without resulting in the end of the world.