Monday, January 19, 2009

GDP: getting the reported growth numbers straight

World economies are expected to post dismal fourth quarter 2008 economic growth rates. For those of you who are slightly confused across world growth reports, here is a primer on GDP growth: annual average growth rates, quarterly growth rates, quarterly growth rates on an annualized basis... If not, then you will want to skip this post.

Tough times ahead are expected for the European Union (EU) and t
he US

The EU Commission released its interim forecast for the European Union, which detailed some bad economic news. EU economic growth is expected to mark just a 1.0% growth rate in 2008 and -1.8% in 2009. Furthermore, its forecast for US GDP growth is expected to be 1.2% in 2008 and -1.6% for 2009. And that includes a 200 billion euro fiscal stimulus (1.5% of GDP), and a $775 billion plan in the US.

The Bureau of Economic Analysis will report its advanced estimate (first out of three releases) of fourth quarter 2008 US GDP growth on January 30. The EU's interim forecast shows the US economy contracting at a 1.2% rate over the quarter, which would be reported by the BEA as -4.7% annualized growth. This translates into a 1.2% growth rate for 2008 as a whole and -1.6% growth in 2009. (I believe that the fourth quarter economic will be slightly worse than -4.7%; but for the purpose of this analysis, let's use the EU's numbers.)

A 1.8% drop EU growth and 1.6% fall in US growth for the year 2009 is horrendous. The average EU annual growth rate from 1997-2001 was 2.9%, while since 2004, it has grown at least 2.0% every year (see page 44 for these and the US statistics). In the US, 1991 was the last time to post negative annual growth, which was just -0.2%. An annual growth rate of -1.8% is very ugly.
And here is where I know that it gets slightly confusing: the EU reports q4 2008 US growth as -1.2%, while the BEA would report it as -4.7% (again, it will probably be worse on Jan. 30). And furthermore, why is -1.8% so bad when the quarterly pattern is -4.7%?

A primer on reported GDP numbers:
  • The EU reports quarterly growth rates on a quarter over quarter basis (q/q), not annualized.
  • The US reports quarterly growth rates on a quarter over quarter and annualized basis (q/q, annualized).
  • Annual growth rates (ex: 2008 growth) represent the pattern of growth for each year on an yearly average basis, not a q4/q4 growth pattern.
  • The EU defines a recession as two consecutive quarters of negative economic growth; and therefore, it was officially in a recession immediately following the release of q3 2008 GDP, since q2 was also negative.
  • The US uses a more broad-based approach, as defined by the Business Cycle Dating Committee (BCDC) at the NBER. A recession was reported on December 1, even though the US contracted in the third quarter of 2008 only.
  • A contraction in economic activity is represented as a negative growth rate.
How the EU reports quarterly growth: on a q/q basis, which is simply the quarterly growth pattern for each quarter of reported GDP.

How the BEA reports quarterly growth : on a q/q, annualized basis
, which is the annual growth rate that would occur if each q/q rate was the same over four quarters.

A simple lesson on compounded annualized growth.
Assume that the same growth rate, g, occured for each quarter, starting from the initial point X0. Note that g*100 = g%.
  1. X1 = (1+g) X0 and X1/X0 = (1+g)
  2. X2 = (1+g) X1
  3. X3 = (1+g) X2
  4. X4 = (1+g) X3

Therefore, substituting 1. into 2., and 2. into 3., and 3. into 4., you get: X4 = (1+g)^4 * X0.

In this simple example, X4/X0 = (1+g)^4 = (1+ga), where ga is the annual growth rate, and (X4/X0-1)= ga. If we only know two consecutive periods, then solve for the annual growth rate, ga, to get the compounded annualized growth rate (CAR) for the whole year: (X1/X0)^4 - 1= ga = (1 + g)^4 - 1. This is what the BEA reports, the annualized growth rate, ga, or ga * 100 in percentages. It does this for ease of comparison across quarters.

Let's say that q4 growth occurs as the EU Commission forecasts, so q4/q3 = (1+g) = (1 - 0.012), then the annualized growth rate is (1-0.012)^4 -1 = -0.047, or -4.7%. Now you can understand the lunacy that CR describes in this post.

Annual US growth

Year over year growth is reported as the percentage change of each year's average over the 4 quarters of reported GDP. The BEA's reported 2008 real GDP will be the average of the following:

  1. q1 = $11646.0 real chained 2000 dollars
  2. q2 = $11727.4
  3. q3 = $11712.4
  4. q4 = $11571.85 (calculated using the EU's forecast of -4.7% quarterly annualized growth)

Average 2008 GDP = (q1+q2+q3+q4)/4 = $11664.4, and 2007 GDP = $11523.9. The 2008 growth rate = ($11664.4/$11523.9 - 1) * 100 = 1.2%.

US annual growth of -1.6% in 2009 is truly dismal

It is not uncommon for reported annualized quarterly economic activity to contract more than 1% - especially during a recession. But it is unusual for overall economic activity to fall by more than 1% on average over a year (see charts above). In fact, 2009 growth is likely to be the worst since 1982. And the way things are looking now, it may even be worse than that. Wachovia forecasts US economic activity to contract 2.3% in 2009.

Rebecca Wilder


  1. GDP should be measured on the rate-of-change basis that corresponds to the fixed, unvarying, economic lags for rates-of-change in nominal-gdp, real-gdp, and the deflator.

    The BEA doesn't capture changes in gdp between quarterly reporting periods. It averages the numbers.

    I.e., it doesn't report based on economic lags. If they did, the sharp decline in real-gdp in 1987 between sept & oct would have captured black monday 1987.