Yes, there was such an instance in 1947 (q2 and q3) where official GDP registered a decline,
but the NBER US Business Cycle Expansion and Contractions data does not define it as a recession.
Apart from 1947, there was only one period (Q4 1969 - Q1 1970) with comparably low declines in real GDP in two consecutive quarters (see the original BEA source for example). That time was declared a recession though. More on that below.
There have also been 3 quarters where the first and third were negative, but the second positive. These periods were either declared recessions (e.g. 1960) or not (e.g. 1956).
Excursion:
A recession can even be shorter than 2 quarters. For the most recent recession, the committee has determined
"that a trough in monthly economic activity occurred in the US economy
in April 2020. The previous peak in economic activity occurred in
February 2020. The recession lasted two months, which makes it the
shortest US recession on record."
Following this definition, the recession was declared over before the second quarterly decline in GDP occurred. that said, these announcements come with a significant lag. Also, all other recessions (apart from one in 1980) lasted longer than two quarters, which makes it very difficult to show that the two quarter rule of thumb is not followed.
James D. Hamilton computes the so called GDP-based recession indicator and the associated Dates of U.S. recessions with a mathematical model solely based on GDP data. You may also find James D. Hamilton's The Econbrowser Recession Indicator Index interesting to read. It states that:
Of the 45 quarters up to the date that paper was written for which the
NBER said the U.S. was in recession, 19 were actually characterized by
at least some growth of real GDP.
This indicator never changed its methodology since it was created 17 years ago (it was computed retrospectively for longer periods). It showed 5 out of 8 times that there is a recession before the first decline in GDP. The remaining 3 times, the start of the recession coincided with the first negative GDP number. Interestingly, this time, the indicator does not yet say it is a recession. Noteworthy, James D. Hamilton's indicator flagged the aforementioned Q4 1969 - Q1 1970 period as a recession two quarters in advance.
Similar measures also show little increase in recession probabilities yet. For example, Smoothed recession probability usually increases prior to recessions. Since we do not know yet if and when NBER will call this a recession it is not yet possible to claim this time is different.
Last but not least, GDP is subject to measurement error. For example, BEA computes using a 90 percent confidence criterion based on data from 1996 - 2018, that the revision between the advance and second estimates is in the interval (−0.94, 1.14). This means that if the advance estimate for some quarter was 1 percent at an annual rate, one could say that with 90 percent confidence, the second estimate would be between −0.04 percent and 2.04 percent. Insofar, a negative GDP value itself need not mean a recession, even if you were to only look at GDP.
In any case, it will be interesting to see what happens going forward. High energy prices, declining consumer sentiment (which often goes hand in hand with increases in energy prices), interest rate hikes, which in turn will likely impact constructing spending, and so forth will all have a dampening effect on the economy.
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