## Wednesday, November 21, 2012

### "Updated Summary of NIPA Methodologies" versus Nick Rowe

From: Survey of Current Business (Online) November 2012, Bureau of Economic Analysis, Volume 92 Number 11:
Updated Summary of NIPA Methodologies (PDF)

The data and methods used to prepare current-dollar and real estimates of GDP as well as current-dollar estimates of gross domestic income, reflecting the 2012 annual NIPA revision.

From the PDF:
Updated Summary of NIPA Methodologies

The Bureau of Economic Analysis (BEA) has recently improved its estimates of current-dollar gross domestic product (GDP), current-dollar gross domestic income (GDI), and real GDP as part of the 2012 annual revision of the national income and product accounts (NIPAs). The sources of data and the methodologies that are now used to prepare the NIPA estimates are summarized in this report...

Estimates of real GDP

BEA uses three methods to estimate real GDP: the deflation method, the quantity extrapolation method, and the direct valuation method. These methods and the source data that are used for estimation are listed in table 2.

The deflation method is used for most components of GDP. A quantity index is derived by dividing the current-dollar index by an appropriate price index that has the base year—currently 2005—equal to 100. The result is then multiplied by 100.

The quantity extrapolation method uses quantity indexes that are obtained by using a quantity indicator to extrapolate from the base-year value of 100.

The direct valuation method uses quantity indexes that are obtained by multiplying the base-year price by actual quantity data for the index period. The result is then expressed as an index with the base year equal to 100.

For most components of GDP, they divide the actual (so-called nominal) number by a price index. They divide the price change out of the number in order to get a quantity-of-output number. They start with the actual-price output number, divide by a price number, and take the result to be "real" output.

I'm not saying it is wrong to do this. I'm just pointing out that they do it. I'm sure that for most components of GDP, there is no other practical way to do it. Okay?

So now, here's what Nick Rowe said:

Places like Statistics Canada measure *both* NGDP and RGDP to calculate P. P is the "derived" value, in practice.

But according to the NIPA PDF, they do not do it the way Nick Rowe says. For most components of GDP, according to NIPA, RGDP is the derived value. Not P.

Nice to know.

Nick Rowe said...

Hmmm. I thought they used the "direct valuation" method. Multiply this period's vector of quantities by last period's vector of prices.

What they don't explain in the "deflation" method is how they get that "appropriate price index". How do they convert a vector of prices into a scalar, so they can divide it into nominal GDP for that component? Do they use last period's vector of quantities, and multiply it by this period's vector of prices, like with the CPI? If so, my understanding was wrong.

Nick Rowe said...

So, I went to the Statistics Canada website, and found this (pdf), which told me more information than I can handle.
http://www.statcan.gc.ca/pub/15-547-x/15-547-x2002001-eng.pdf

Chapter 4 is the relevant one. I had thought that StatsCan uses the "Chain Laspeyres" index for GDP (see page 32). That's what I described above. But it sounds like they are maybe using Fisher, which is a geometric average of Laspeyres and Paasche.

If I understand it right (I may not):

In Laspeyres you first multiply today's vector of quantities by yesterday's vector of prices, to get real GDP today. Then you divide NGDP by RGDP to get the price index. (That's what I had thought they all did, so that RGDP comes before P.)

In Paasche you first multiply today's vector of prices by yesterday's vector of quantities to get a price index. Then you divide NGDP by P to get RGDP. (Which is the opposite).

And Fisher takes a geometric average of those two methods.

Maybe the US means "Fisher" when it says "the deflation method"?

Nick Rowe said...

Yep. Reading the bottom of page 34, it sounds like I am 10 years out of date. They switched from chained Laspeyres to chained Fisher for RGDP, and the US probably switched around the same time. That means it's a mix of the two. Which makes sense. Laspeyres is biased in one direction, and Paasche is biased in the other direction, so Fisher takes an average.

Which is the limit of my understanding of index number theory.

Nick Rowe said...

Hmmm. Now I'm changing my mind again, after reading a much clearer Statistics Canada document. Look at section 2.135 on down in this pdf:

http://www.statcan.gc.ca/pub/13-017-x/2008001/pdf/5220040-eng.pdf

It shows how to calculate Fisher RGDP directly, without first calculating a Fisher price index.

I'm now starting to think that this is a non-question. Like debating whether the chicken or the egg comes first. You can do the math either way around. You can calculate P first, or you can calculate RGDP first. It doesn't matter.

Look at equation 2.6, where they calculate Paasche RGDP directly, without first calculating a Paasche price index.

Or 2.7, where they calculate Fisher RGDP directly, without first calculating a Fisher price index.

But you could equally well calculate a price index directly, without first calculating RGDP.

I now think me and Scott were (stupidly, in retrospect) arguing about nothing. We were both wrong, because we thought there was a difference, when there isn't.

The Arthurian said...

Wow, I got that the little q was the quantity of some arbitrary product, but I didn't get that big Q was the summed quantity RGDP until you said "Look at equation 2.6, where they calculate Paasche RGDP directly..."
So, thank you Nick. I learned something today.

"Laspeyres is biased in one direction, and Paasche is biased in the other direction, so Fisher takes an average."
Yes, I got that from something I read at Statistics Canada. That much made a lot of sense to me. But let me not dwell on this topic, for I read until my brain was full, and now my brain is full.

Thanks, Nick, for letting me watch you think about things.

The Arthurian said...

An example in a Reddit comment offers a different perspective: