There's something I don't get about the CPI.

When you go to the bls.gov website, they list the CPI as being .5% for April.  

Annualized, that would be 6% inflation per year.

But nobody seems worried about this.  In fact, everybody (i.e., the
WSJ, the Economist) are saying that inflation's "on track" and "at the
speed limit" between 2 to 3%

I don't get it.  Where does that other 3% go?  One cannot claim, it
seems to me, that the final inflation figure for previous years is
"adjusted for inflation," because the CPI IS the measure of inflation?

So what's happening?  .5% per month seems like it's gonna wind up
being 6% per year, but instead it ends up only being 3% per year. 
What happened?

Anyhow.  Ten bucks if you can dispel my confusion.

Hi gnossie:

Thanks for the interesting question. 

The key to answering your question is that when CPI vlaues are
reported for any particular month (in this case April 2005) the figure
that is reported is not an *average* monthly rate but an *actual*
monthly rate. In fact, the individual monthly rates vary, sometimes
significantly from month to month.

So, when they say that inflation is on the way to 2 - 3% for the year,
they are looking at each of the previous months separately and adding
up the figures (plus probably making some educated guesses about
upcoming months).

To illustrate this, have a look at "Table A - Percent changes in CPI
for All Urban Consumers (CPI-U) - Seasonally adjusted" near the top of
the following document:

Consumer Price Index Summary 
URL: http://bls.gov/news.release/cpi.nr0.htm

As you can see the figure for Dec. 2004 was 0.0% and that for January
0.1%. If you look in the very last column, you'll see that the last
twelve months added to 3.5%. If you see someone quoting a yearly rate
that will likely be lower than that, they are most likely projecting
some months into the future.

You can also see from the second last column in Table A that if just
the last three months were taken into account AND those monthly rates
were compounded into an annual rate, the CPI would be 6.2%!
    
However, the most reliable figure is the one that takes each month's
actual rate for the last year and adds them straight up - 3.5%.

I hope this clears your confusion. 

Search Strategy (on Google):
* CPI monthly 2004 site:.gov 

websearcher

---

Request for Answer Clarification by gnossie-ga on 29 May 2005 04:35 PDT

Okay, thanks websearcher.  But I'm still a little cloudy on a few
points, thought I have been poring carefully over that table and what
you wrote about it.

1.  I'm not sure what the last column:  "Unadjusted" 12 months means
by "adjusted."  What would "adjusting" consist of?  The months that
are there add up to 2.5.  Added to that, the missing months presumably
bring the figure to 3.5, but why would you need to "adjust" it from
that?

2.  I'm not sure what the second-to-the-last column means by
"compound" annual rate.  Presumably they mean annualized...?  If so,
how did they arrive at 6.2 (mathematically), since when I monkey with
the figures from the previous 3 months (.4, .5, .6) I can annualize at
only 6.0.

3.  Could you define what you mean by "actual" and "average" in this
case?  For the top line of Table A, the "average" monthly rate would
seem to be .29 (i.e., actual rate 3.5 divided by 12).  Am I getting
that right?

Thanks again.

---

Clarification of Answer by websearcher-ga on 29 May 2005 06:19 PDT

Hi gnossie:

Thanks for the clarification requests. 

I'll tackle your questions one at a time. 

1. The "unadjusted" in the last column refers to the "seasonally
adjusted" mentioned in the title of the table. So, for the last colum,
the figures are *not* seasonally adjusted.

For more on how and why they seasonally adjust figures, see: 

Fact Sheet on Seasonal Adjustment in the CPI
URL: http://www.bls.gov/cpi/cpisaqanda.htm

I would imagine that they don't seasonally adjust the last solumn
because it represents a *full-year* of figures (i.e., a full cylce of
seasons) - thus any seasonal adjustments they would make would cancel
themselves out.

2. No, annualized and compounded are two different things (or, at
least, the latter is an additional step to the former). To annualize,
you would - as you noted - add up the three months (1.5) and multiply
by 4 (6.0). If you were compounding, you would create a year-long
table which had the last three months repeated four times ( .4 .6 .5
.4 .6 .5 .4 .6 .5 .4 .6 .5 ) and then you'd compound the running total
to account for the fact that the previous months' inflation affect the
current month. So, the calculation would go as the following:

Month 1:  1.000 * 1.004 = 1.004
Month 2:  1.004 * 1.006 = 1.010024
Month 3:  1.010024 * 1.005 = 1.01507412 
Month 4:  1.01507412 * 1.004 = 1.01913441648
Month 5:  1.01913441648 * 1.006 = 1.02524922297888
Month 6:  1.02524922297888 * 1.005 = 1.0303754690937744
Month 7:  1.0303754690937744 * 1.004 = 1.0344969709701494976
Month 8:  1.0344969709701494976 * 1.006 = 1.0407039527959703945856
Month 9:  1.0407039527959703945856 * 1.005 = 1.045907472559950246558528
Month 10: 1.045907472559950246558528 * 1.004 = 1.050091102450190047544762112
Month 11: 1.050091102450190047544762112 * 1.006 = 1.056391649064891187830030684672
Month 12: 1.056391649064891187830030684672 * 1.005 =
1.0616736073102156437691808380954

From this, I would assume they would round to the nearest tenth of a
percent (which is the accuracy they use in reporting) to 6.2%.

3. All that I meant by "average" in my original response was that you
-incorrectly - were (in your original question) treating the .5%
figure for April like average when you extrapolated that the rate for
the year would be 6.0%. They don't figures for a *single* month like
this - as average figure that would be spread out for an entire year.
They obviously do use averages (of a sort) in their 3-month
extrapolation. "Actual" figures are the exact values calculated each
month. They do re-calculate the entire CPI figure for each month -
quite the process!

I hope this clears things up. :-)

websearcher