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# GDP Deflator vs. Consumer Price Index

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While reviewing Robert Gordon's book The Rise and Fall of American Growth for Regulation, I found it relevant to dig into the GDP deflator and the Consumer Price Index. The reasons why would take me too far afield.

I knew and know that the CPI still overstates inflation by a substantial annual percentage. But I didn't know as much about the GDP deflator.

So I looked at the GDP deflator from the first quarter of 1950 to the fourth quarter of 2015, and the CPI in roughly the same period, from February 1950 to January 2016.

GDP Deflator
1950 Q1: 13.49
2015 Q4: 110.29

CPI
Feb. 1950: 23.6
Jan. 2016: 238.1

So now we can compute the annualized growth rate of each.

For GDP Deflator:
13.49(1 + x)^65.75 = 110.29
(1 + x) )^65.75 = 110.29/13.49 = 8.176
65.75ln(1 +x) = ln8.176 = 2.1012
ln(1 + x) = 2.1012/65.75 = 0.03196
1 + x = 1.0325
x = 0.0325
So annualized rate of growth of GDP deflator = 3.25%.

For CPI:
23.61(1 + x)^65.92 = 238.11
(1 + x)^65.92 = 238.11/23.61 = 10.085
65.92ln(1 +x) = ln10.085 = 2.311
ln(1 + x) = 2.311/65.92 = 0.03506
1 + x = 1.0357
x = 0.0357
So annualized rate of growth of CPI = 3.57%.

The difference is about 0.3 percentage points annually.

So if the CPI overstates annual inflation by 0.8 to 0.9 percentage points, then the GDP deflator overstates annual inflation by about 0.3 percentage points less.

Caution: Jeff Hummel tells me that the computers of the GDP deflator regularly reach back and adjust earlier data, unlike the case for the CPI. So take the above with a grain of salt.

CATEGORIES: Macroeconomics

Richard A. writes:

For the GDP Deflator you have
22.6(1 + x)^65.75 = 238.0

Shouldn't that be
13.49(1 + x)^65.75 = 110.29

And for the CPI you have
23.6(1 + x)^66 = 10.08

Shouldn't that be
22.6(1 + x)^65.92 = 238.0
where the time between Feb 1950 ans Jan 2016 is 65 11/12 years.

David R. Henderson writes:

@Richard A.
Good catches. I screwed up big time in transcribing from some scratch paper that I then threw away. Will correct later. I know that my bottom line is right.

James Alexander writes:

The link to the Boskin article for the 0.8-0.9% overstatement of inflation is very helpful. It does show some thought being given to the issue.

The "no revision" policy is simply incredible. More importantly, the estimate overstatement is hardly scientific. It could be a lot more or less. No error bars are mentioned. Housing and services make up the majority of he basket and little is known about quality changes in these areas. There is no mention of zero cost services like marginally more internet use, that consumers now consume voraciously.

The big message from your article and the Boskin work is that it is foolish for central banks to target something as unmeasurable as inflation, or anything that relies on it such as real GDP, or worse the gap between real GDP and an optimal real GDP.

David R. Henderson writes:

@Richard A.
Redone, and I took your suggestion on the 65.92. See if I got it right.

writes:

GDP deflator is a problem because of the minus sign in the equation. This has paradoxical result of seeing HIGH import prices deflate negative contribution to real GDP by a greater amount and so shrink the difference between its sum and that of the nominal number, hence REDUCING the overall deflator

David R. Henderson writes:

@SeanCorrigan,
What minus sign?

Jule R Herbert writes:

That's a big "if." But is there a market for "correct" index numbers, given the government's willingness to give the stuff away?

writes:

the GDP deflator adjusts for prices of imports, exports, investment, inventories, construction, and government outlays that the CPI does not...import prices are a negative

Andrew_FL writes:

So, over this period cumulative real GDP growth was underestimated by over 30%?

David R. Henderson writes:

@Andrew_FL.
So, over this period cumulative real GDP growth was underestimated by over 30%?
Actually, well over 30% because according to the Boskin Commission, the CPI, before the reforms after 1996 that brought the overstatement down to 0.8-0.9 annually, overstated inflation by well over 1.0 percentage point.

DOR writes:

[Comment removed. Please consult our comment policies and check your email for explanation.--Econlib Ed.]

Dallas Weaver Ph.D. writes:

Considering the technological change between the 50's and today, how can either number be considered real or significant.

How do you correct for the differences between that IBM super-computer of the day with my i-phone, or even the super-computer of the late 50's that at least used solid state transistors and magnetic memories. (factors of millions in cost/performance)

Meanwhile, we have gone from paying a kid (me) less than \$0.50 to mow and edge the yard to paying almost \$50 (a factor of 100 increase).

We have also gone from a society where a new idea could be implemented in almost no time to a society where it can take 12 years to get "permission" to build a desalinization plant in water short Southern California using technology developed in the 50's and tested with no questions or regulations. Meanwhile, the educated elite running the regulatory agencies, as highly paid bureaucrats, earn huge amounts to prevent the creation of jobs for the Joe Median's of our society who build, operate, and maintain facilities. Meanwhile, these same bureaucrats cry about income inequality and lack of jobs for Joe Median.

Ricardo writes:

No mention of the chained CPI, which *does* restate inflation using actual expenditures (with a 10-12 month lag)? Revising the (unchained) CPI makes no sense, as no new data will have arrived in the meantime.

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