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Friday, March 22, 2013

The Choice of Price Indexes Can Matter

I recently ran across a reference to a BLS study looking at the divergence of real wages and labor productivity growth over the past 30 years, and I decided to look at one aspect of it.  The study uses the Consumer Price Index (CPI) to deflate wages and the Non-Farm Business Output Price Deflator (NFBODef) to deflate the value of non-farm business output.  There is an alternative index for consumer prices, the Personal Consumption Expenditure Deflator (PCEDef), and I wondered if we would see (essentially) the same pattern if we used that measure of consumer prices instead of the CPI.  Let me anticipate my conclusions.  Between 1947 and 1978, there was little divergence in the rate of increase in prices regardless of which measure one chose to use.  But from 1978 to 2012, the rate of inflation calculated using the CPI has been noticeable faster, and thus real wage growth has been noticeable slower, when calculated using the CPI than when using either of the other two price indexes.

It took me a while to figure out how to put all three indexes on the same chart.  For one thing, the CPI has a base period of 1982-84, while the PCEDef and the NVBODef share 2005 as a base period.  As a result, they have markedly different starting values in 1947.  What I finally did was start all three indexes at the same value (about 15) at the beginning of 1947 (January 1947 for the CPI and 1947.Q1 for the other two) and then changed then at the period-to-period rate of change calculated from the original indexes.  Then I converted all three index values to natural logarithms.  This gave me the following chart.
Click to enlarge.
Until about 1978 or 1979, the three indexes move almost identically,  But then the CPI begins to increase at a faster rate than either of the other two.  Using it as a deflator, then, will deflate nominal labor compensation more than using the PCEDef, and therefore will show slower growth in real compensation than would using the PCEDef.  And until about 1993, the two deflators continue to move closely (but not as closely) together, but then diverge slightly, with the PCEDef rising (slightly) faster.  The following table shows annual rates of change for all three price indexes for the entire 1947-2012 period, for the 1947-1978 period, for the 1978-1995 period, and for the 1995 – 2012 period.


CPI Inflation

PCE Inflation

NFBO Inflation

















Remember that I scaled all three price indexes so that they begat at the same value.  By the end of 1978 (see the table below), the PCEDef was 3.6% below the NFBODef, while the CPI was 4.9% higher.  But over 31 years, neither of these difference seems particularly notable.  By 1990, the PCEDef was 3.6 higher than the NFBODef—but the CPI was 36.4% higher.  The divergence over that 12-year period was significant.  And by 2012, the CPI was 40.7% higher, while the PCEDef was about 7.9% higher.  So the essential period of divergence was from 1978 to 1990, when the CPI rose (as can be seen in the table above) considerably more rapidly than the other two price indexes. 




End of 1978



End of 1990



End of 2012



The problem, however, is simple.  The degree of divergence between growth in real wages and the growth in the value of real non-farm business output growth will be strikingly different if we use the PCE deflator or the CPI.  The following chart shows median real weekly earnings, with nominal wages deflated by the PCE deflator, on the one hand, and by the CPI on the other.  (The readily available data series on earnings is available from the BLS only back to 1979; however, since the primary divergence of the price indexes dates from 1978, this should not be that much of a problem.)  At the beginning of 1979, real wages calculated by using the CPI were 8% below real wages using the PCE deflator; by 2004, that gap had widened to 20%, and has been roughly unchanged since (at the end of 2012, it was 21%).  To put it another way, between 1979 and 2012, real median weekly wages calculated using the CPI rose by 4%.  Using the PCE deflator, they rose by 15.5%.  (In either case, average annual wage growth has been slow—0.1% per  year if calculated using the CPI and 0.4% using the PCE deflator.)
Click to enlarge
This is not the place (or the time) to get into why the CPI and the PCE deflator have varied so much over the past 35 years.  But they have varied.  And that variation matters quite a bit.


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