## Tuesday, October 9, 2012

### Again: "real" output is calculated

Marcus Nunes quotes David Beckworth, who quotes Mark Sadowski, who says:

RGDP is an artificial concept requiring that we estimate an index of the aggregate price level.

Yes.

Beckworth links back to Sumner, where George Selgin quotes the same words of Sadowski, and expands the thought:

The occasional, if tacit, treatment of NGDP as a value that is “derived” by taking the product of two directly observable magnitudes, real output and the price level, is as mischievous as it is wrong.

I'm not sure about the mischief. But it is definitely wrong.

I'm sure he means no harm. But if I were to respond to Nick Rowe's Simple thoughts on NGDP = RGDP x P, I would begin by quoting him:

1. NGDP = RGDP x P. In words: nominal GDP = real GDP times the GDP deflator (which is one way to measure the price level).

What Nick is saying in words, it seems to me, is that Nominal GDP is calculated from Real GDP and the price level. But that is wrong, as Sadowski and Selgin assert.

In every computer language I ever used, the equal sign assigns the value on the right to the variable on the left: Result <-- Value. So, when I see

I naturally read it as: Take Real GDP, factor prices in, and you get Nominal GDP. Sure, the math is correct. But you don't start with "real GDP". You start with GDP at actual prices -- called "nominal" -- and figure out real GDP. Rowe's arrangement of terms suggests that real output and the price level are "two directly observable magnitudes". But it is nominal GDP which is the directly observed measure.

Maybe it's harmless, like I said. I know Nick Rowe knows what's real and what's not, despite the confusing application of the word "real" to a calculated value and "nominal" to the actual value.

That's what I would have said, if I were responding to Nick's post.

Does it matter which is the actual value and which is calculated?

Oh yeah, it matters. Because if the "real GDP" number was really real, then Milton Friedman's "money relative to output" graphs would be perfectly valid. His graphs are not valid, because the only way to figure "real output" is by starting with "nominal" output and dividing out the price changes.

Once you do that, the price numbers are part of the "real output" numbers. And then when you divide the quantity of money by real output, you are actually multiplying the quantity of money by the price level. Arithmetic makes your numbers similar to the price numbers. Economics has nothing to do with it.

When you compare "money relative to output" to prices, as Milton Friedman did in his book Money Mischief, you are really comparing prices to prices-and-some-other-stuff. That's where the similarity comes from, similarity that Friedman erroneously offers as evidence to explain the cause of inflation.

Mischief, indeed.

#### 4 comments:

Nick Rowe said...

Arthur: If you read what I said immediately below that bit you quoted:

"2. It is easier to measure NGDP (nominal growth) than it is to measure RGDP (real growth) and P (inflation). To say the same thing another way, it is not easy to figure out how to decompose nominal growth into real growth and inflation. Because it's hard to measure things like quality changes. In that sense only, NGDP is more "real" than RGDP."

Places like Statistics Canada measure *both* NGDP and RGDP to calculate P. P is the "derived" value, in practice. You can't just measure one of the three. You need two out of the three.

Jazzbumpa said...

Yes.

Correctly stated, RGDP = NGDP/P.

To Nick's point, this illustrates why using "real" to mean "inflation adjusted" is a real bad vocabulary choice.

But I'm surprised to learn that RGDP is measured and P is calculated.

P = NGDP/RGDP (??!??)

Truly, that is a head scratcher.

Where does one obtain raw RGDP data? Isn't the price level directly measurable?

JzB

The Arthurian said...

Thanks, Nick. Clarity & brevity help me understand.
"P is the "derived" value, in practice."
But you're making me work! I have been to Statistics Canada before and found it helpful. I will go there again and study it this time.

Oh, and I re-read the Selgin quote. He doesn't really say the same thing Sadowski does. I shall go back to those source posts as well.

The Arthurian said...

So Nick, I went back to StatCan and did some reading:
In the Canadian National Accounts, the volume effect is determined using the deflation method, which eliminates the price effect from each component of the aggregate and then aggregates the components thus deflated to obtain the "total" volume effect.

1. Start with the component information that is added up to get NGDP.
2. Remove the PRICE effect from each component.
3. Add the components to get RGDP.

So maybe they use NGDP and RGDP to figure the overall price change. But they use component price information to figure RGDP. It does seem perfectly reasonable. But it doesn't seem right to say "P is the 'derived' value".

A little more reading:
If there were an "average" GDP price then it would be quite simple to divide the change in GDP (given by Equation (1)) by this average price to obtain the average change in quantities. Most of the time in the National Accounts, there is no such average price. Thus, the total change in quantities can only be calculated by adding the changes in quantities in the economy.

But in the next paragraph they remind us that you can't add apples and oranges. What StatCan does is add the VALUES of apples and oranges. In other words, they introduce money into it again.

So even if they had all the information on all the quantities of everything that counts as a year's output, they couldn't add it up unless they multiplied those quantities by the respective prices.

That means they have to know the prices -- the "before inflation" prices *and* the "after inflation" prices -- before then can figure RGDP. Looks like Jazz was right about that.