The Bureau of Economic Analysis today

released its advance estimates for the second quarter, reporting real GDP growth of 3.4%, implying

a very slight increase in the recession probability index to 4.7%.

Although June manufacturing and housing figures were extremely

strong, the 3.4% GDP growth rate for 2005:II is a little weaker than one might have hoped for

at this point in an expansion, and was assigned

a tentative grade of C+ on voluntaryXchange’s academic grading system.

Using the new data, I’ve calculated the real-time GDP-based recession probability index for the

first quarter of 2005 to be 4.7, a slight increase from the value of 3.4 for 2004:IV. This marks

the seventh

consecutive quarter that the index has remained below 5%.

The index can be interpreted as the probability that the economy was experiencing an economic

recession at any given date. Like the business cycle dates assigned by the National Bureau of Economic

Research, this is a backward-looking index, describing where the economy appears to have been

in 2005:I, rather than a forward-looking prediction of where it will be at the end of the year.

NBER announcements of business cycle turning points are often made long after the event; for

example, the NBER waited until July, 2003 to announce that the most recent recession had actually

ended in November, 2001. By contrast, the real-time GDP-based recession probability index is

available with only a 4-month delay.

This index employs a pattern-recognition algorithm that compares the recent history of GDP

growth with the values that have been observed during historical recessions. Technical details of

the construction and historical performance of the index can be found here.

pglTim Duy (Economist’s View) and I (at Angrybear) were a little delighted that fixed investment demand was growing at 9.3% per year and final sales at 5.8% per year. Tim suspects that the FED will see this as proof it was right to raise interest rates. Of course, I still think we are below full employment – but that’s the labor market debate all over again.

Joe DoyleJim – I scanned your referenced paper, and it is clear the approach might have widespread use. I am a big fan of describing probabilities in a forecast as opposed to issuing brave but foolhardy point estimates. I was especially intrigued with the graphics reviewing the recessionary periods in your data set. (I can handle pictures more easily than the math). A few questions:

1. Re figure 11, 2001 recession, the data shows a bigger spike in recession prob in late 2002 (up to 70%) than your chart above shows. Monthly v quarterly data, I’m guessing?

2. The objective of the paper is essentially to come up with an algorithm to improve the NBER’s reaction time to historical data (fair characterization?) Or said another way, to forecast the NBER’s pronouncements. Have you attempted to extend the analysis to forecasting, say, turning points in S&P operating earnings; or turning points in strategists estimates of GNP growth or S&P operating earnings; or (dare I say it) turning points in Fed behavior? If so, tell me and no one else

Hank RiehlSince the massive inventory draw down penalized 2Q GDP growth by 2.3-2.4% (the shelves have been picked clean) and 2Q “core GDP (consumption + fixed investment) rose by about 4.4% while the shrinking trade deficit added 1.6% to GDP as the budget deficit also plunged–and all this without an uptick in inflation–just how does that combine to increase the odds of recession? Seems like the economy rates at least a B+ and that the odds of recession have been significantly reduced.

Then again I don’t have the background on your formula. But like all of the monthly consumer confidence surveys of the past 2-3 years, it appears to be totally worthless.

JDHThanks for your comments, Joe. The figure I displayed is identical (up until the new data from the last year) to the top panel of Figure 7 in that paper (though it may appear a little different because of the different scales). You can look up the actual numerical values in Table 3 of that paper. Figure 11, as you stated, bases the inference not on quarterly GDP but rather on the combined signal from four different monthly indicators. The two inferences are similar but not identical.

As for keeping other applications a secret between me and thee, it’s a little late for that. Since I first proposed this basic idea in 1989, there have been many hundreds of applications to all kinds of different data sets. You can follow active links to a few of these at http://ideas.repec.org/e/c/pha60.html (first scroll down to the section after “working papers” to “articles,” then go to item 9). Even so, I don’t recall anybody looking at S&P earnings this way. But there have been lots of studies of various aspects of what the Fed is up to.

The main new thing in the paper I link to is the use of real-time data. Essentially all of the academic studies I’m referring to use the fully revised data as it’s available today. That’s OK for academics, who usually just want to document some of the regularities of how different variables move together over the cycle or describe what happens when there are changes in regime. But, if you’re trying to make calls in real time, the difference between the data as originally released and what later become available can be quite important. The main thing we show in the paper is that the method seems to be pretty reliable for making real-time calls with real-time data.

JDHHank, I’ll comment some more on the issues you raise in a post next week.

HalI know it’s just a widely used shorthand, but the GDP did not actually grow 3.4% in the second quarter this year, did it? It grew about 0.85%; the 3.4% is an annual rate. It’s always confusing to the layman to hear the figure misquoted as it so often is.

JDHYes, you’re exactly correct, Hal. The 3.4% is found by multiplying the actual growth by four in order to quote it at an annual rate.

CalculatedRiskHal, the GDP is reported in real terms at an annual rate because this is thought to be easier to understand and compare across periods. They are not trying to mislead anyone.

Hopefully I’m not being too nitpicky, but … the nominal quarterly increase in GDP for Q2 (advanced estimate) was 1.45%. To calculate the reported real annual GDP rate:

1) Adjust the GDP by the GDP price deflator. This is given in table 6. Here is the calcuation:

Q1 GDP (nominal annual rate) = $12,198.80 Billion

Q2 GDP (nominal annual rate) = $12,376.20 Billion

Q1 GDP price deflator = 110.905

Q2 GDP price deflator = 111.578

Q2 GDP(r) (real annual) = Q2 GDP(n) X Q1 deflator / Q2 deflator.

So Q2 GDP (real annual) = $12,301.6 Billion

This adjusts Q2 for inflation (makes Q2 real compared to Q1).

2) Divide Q2 GDP (real annual) by Q1 (GDP nominal) = 1.0084 or 0.84%.

3) Raise quarterly rate to the fourth power (you can multiply – at these low rates you get the same answer). So 1.0084^4 = 3.4%

I hope that didn’t make it even more confusing.

Best Regards.

Joe DoyleOh – you’re Mr. Markov Switching – nice to meet you! To be honest, I’ve heard of the techinque, but never took the time to expose myself to work that relied on it. My bad! I’m now reconsidering my opposition to AIMR CE credits.

The references you’ve provided were extremely helpful, Jim. I’m not sure how effective this technique is in forecasting, but in terms of characterizing the relative certainty that a given market is a certain “state” (ie bull or bear, recession or recovery, value v growth v large v small cap) on a real time basis I am very intrigued, especially when it begins to move from 95% certainty (as we are now wrt GDP growth) to something much less. Do you know of any sources (other than yourself wrt GDP) that analyze markets in this manner? I suppose “market professionals” know these states when they see them, but a rigorous methodology that compares the present to the past, and is honest about uncertainty when it is present, would be valuable.

JDHJoe, I wonder if the paper by Gabriel Perez-Quiros and Allan Timmermann, “Firm Size and Cyclical Variation in Stock Returns,” might be an example of what you’re looking for:

http://www.econ.ucsd.edu/%7Eatimmerm/small.pdf

Joe DoyleJim, spot on. I found about six other papers from your list, including this one from Massimo Guidolin & Allan Timmerman, 2005. “Size and value anomalies under regime shifts,” Working Papers 2005-007, Federal Reserve Bank of St. Louis. http://research.stlouisfed.org/wp/2005/2005-007.pdf

You’ve given me a lot to chew on. Many, many thanks!!