## Thursday, May 31, 2012

### A Prediction

How does NGDP Targeting work? Nick Rowe says:

If real GDP falls 10% below what was expected, the price level rises 10% above what was expected...

David Andolfatto says something similar:

Adopting a NGDP target implies that policymakers can commit to (say) a 5% NGDP growth rate. But what if inflation turns out to be 4% and RDGP growth turns out to be 1%? (Or how about 7% inflation and -2% RGDP growth?)

I summarize:

NGDP targeting does nothing for growth.

The goal of NGDP targeting is to stabilize the path of Aggregate Demand (AD). Using "P" for "prices" and "Y" for "real output", Nick Rowe says:

When a negative AD shock hits, both P and Y will fall. When AD recovers both P and Y will rise. But we know very little about how that rise in AD will be divided into a rise in P and a rise in Y.

Rowe says we do not know how the increase will be distributed between inflation and real growth. But I think we have a pretty good idea. If cost-push forces exist, as I claim, then NGDP Targeting will give us lots more inflation than real growth.

So I got thinking about how to see that on a graph: to see how AD (or something) is distributed between inflation and real growth. I came up with a graph, and I'll show it to you. But it's crude. It's a first draft. So take it for what it's worth.

I started by getting quarterly data for Real GDP, the Consumer Price Index, and U.S. recession dates from FRED.

The US Recessions column shows a "1" -- TRUE -- when there is a recession, and "0" otherwise. I wanted to look at just the peak-to-peak data for RGDP and prices, so I wanted to look at the last "0" before a "1". So I deleted all the rows from the worksheet except the rows with the last "0" before a "1". That left me with a dozen rows.

Starting with the second data item, from the date I subtracted the previous date; this gave me the number of days from peak to peak. From the RGDP I subtracted the previous RGDP, to get the increase in real output. And from the CPI I subtracted the previous CPI, to get the increase in prices for the peak-to-peak period.

Next I divided the increase in real output by the number of days, to get the average daily increase in real output. (This is crude, so again: take it for what it's worth.) And I divided the increase in prices by the number of days, to get the average daily increase in prices for the period.

Finally, I normalized these series. I divided each of the Average Daily RGDP values by the first of them; and each of the Average Daily CPI values by the first of them. Then I made my graph.

 Graph #1: Distribution of Growth and Inflation across business cycle peaks
The blue line shows RGDP data; the red line shows price data. The dots on each line represent business cycle peaks -- dates of the last "0" values before the recession's "1" in the original FRED data. (Except, the last dot is just the most recent data.)

For the first few dots -- 1953, 1957, 1960, and even 1969 -- prices and output travel close together. (For 1953, normalization forces them to be identical; my reason for doing that was to see whether the lines move together or move apart.)

For the first few dots, prices and output move together. Then suddenly in the 1970s -- the Great Inflation -- the red line shoots up. It peaks in 1981, about the same time inflation and interest rates also peaked.

Then the red line falls, but only about half as much as it rose. Thereafter, the two lines run more or less parallel.

The peak represents the Volcker squeeze. The two lines running parallel thereafter suggests that there is a fairly stable division between what adds to real growth and what fizzles away as inflating prices. Note, however, that after the Volcker squeeze the red line never again comes close to the blue.

Before the Great Inflation, the two lines travel together. This suggests that out of every \$4 gain, \$2 ended up as real growth and \$2 ended up as inflation.

After the Volcker squeeze, the red line values are roughly three times the blue. This suggests that out of every \$4 gain, \$1 ended up as real growth and \$3 ended up as inflation.

I expect the 3-to-1 ratio to continue under NGDP targeting, unless the gap widens again.

So, there's my prediction.

To see if the above story fits other peoples' reality, I went back to FRED and graphed RGDP and the CPI with less manipulation of the numbers. All I did was express each series as "Index (Scale value to 100 for chosen period)". For each series, the chosen period I picked was the 1953 business cycle peak. That is as close as I could get to mimicking the normalization I used in Graph #1.

 Graph #2: Real GDP (blue) and the CPI (red)

Normalized to 1953, the two lines start out together and run close at first. When first they separate, prices run below real output: Growth increased faster than prices.

By the mid-1970s the lines come together again, and cross. Thereafter, prices run higher than real growth. A sign of cost-push, I might say.

It's not an exact match to my Graph #1. But it's not that far off.

Woj said...

Obviously there are many caveats, but if we take your ratio and the recommended 5% NGDP growth, the result is consistent inflation of 3.75% and real GDP growth of 1.25%. Sounds like a terrible trade off for nominal stability.

The Arthurian said...

Hi Woj. Nice, I didn't think of that.

But ponder me this... Does it seem to be true, that over the last 30 years prices have gone up three times as much as 'real' output?

That's what the numbers tell me. But it is a hard thing to believe, without some practical examples.

Okay. I bought a Sentra...

FOUND IT! This post shows me figuring long-term (1983-2007) inflation at 3.715% annual, compounded.

Pretty close to what you got.

I wonder how many more cars are sold each year in the US...

Okay, FRED has ALTSALES, showing "Light Weight Vehicle Sales: Autos & Light Trucks" here:

http://research.stlouisfed.org/fred2/graph/?g=7C1

The first value was about 12.5 million (for 1975). I divided the whole series by 12.5 and now the graph shows 1.0 vehicles for 1975, and less than 1.4 for 2007. Again, pretty close to what you got.

I gain confidence...

Jazzbumpa said...

I like what you're doing here, but will have to reread, and give it more thought.

To what extent is the relative magnitudes of your curves an artifact of normalization?

You hint that it is in the 50's.

Your graph suggests about a 3:1 inflation/GDP ratio for several years. The FRED graph suggests about 1.5.

Tell me again what the purpose of normalization was.

Cheers!
JzB

The Arthurian said...

"Tell me again what the purpose of normalization was."

To make the two lines comparable, as Milton Friedman would say. (And I objected like crazy to that.)