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The start and end of recessions are determined by the NBER, a “private, nonprofit, nonpartisan research organization” (see here for more). While there has been much debate about why this group has the power to determine the dating of recessions, their proclamations are generally accepted by most economists.
The NBER determines what are the peaks and troughs of business cycles, that is, the date at which the economy started to decline and the date at which the economy hit bottom and started rising again. Their announcement of the end of the 2001 recession provides a clear illustration of their thinking:
In determining that a trough occurred in November 2001, the committee did not conclude that economic conditions since that month have been favorable or that the economy has returned to operating at normal capacity. Rather, the committee determined only that the recession ended and a recovery began in that month. A recession is a period of falling economic activity spread across the economy, lasting more than a few months, normally visible in real GDP, real income, employment, industrial production, and wholesale-retail sales. The trough marks the end of the declining phase and the start of the rising phase of the business cycle. Economic activity is typically below normal in the early stages of an expansion, and it sometimes remains so well into the expansion.
The committee waited to make the determination of the trough date until it was confident that any future downturn in the economy would be considered a new recession and not a continuation of the recession that began in March 2001.
The key point to note relative to the end of a recession is that it representts the end of the decline. So the NBER will declare that the recession has ended at the point when economic activity stops declining; the obvious problem is that you can only tell that the decline has stopped when economic activity has started to rise again.
Recessions are not like sporting events, where a winner is declared immediately after the match ends, because the end of the match is itself uncertain. Economic commentators often describe recesssions as V or U shaped, depending on whether the rapidity of the rise in economic activity from the bottom, A U shaped recovery (or even worse a W or L) means that activity remains low for some time before the recovery starts; in such situations (as in 2002-2003), the NBER will delay its determination of the end of a recession until the ensuing recovery is clear and the end of the recession was announced a year and a half later.
On another page on this site I am tracking some of the variables that the NBER uses to analyze the current recession. As of the time I am writing (June 2009) most of the variables are low and still falling (personal income has been up a bit due to the increase in transfer payments associated with the government’s stimulus plan). The NBER will most likely wait until the evidence is completely clear, that is when employment, sales, income and production are all rising and well above current levels. Forecasters seem to expect that the economy will begin to improve in the second half of 2009, but the evidence that the recession has ended may not be clear until a year or so later.