How to Avoid Mis-interpreting GDP Data (Or How the Second Derivative Does not Predict the First)
From 1929 to 1930, the GDP growth rate was -8.62%. From 1930 to 1931, it was a somewhat less ominous -6.5%. If today’s economists and journalists were interpreting the release of this news in early 1932, papers may have printed headlines like this:
“In Hopeful Sign, Output Declines at a Slower Pace” or “Economy Turning Out of Steep Dive.”
These headlines are not from 1932 but from today’s print editions of the New York Times and Washington Post, respectively. By the way, GDP growth from 1932 to 1933 did not usher in the start of recovery; it was -13.1%, which is the worst year on record in the Bureau of Economic Analysis’s historic data.
If you saw the report that GDP in the second quarter of 2009 fell, you may be wondering how to reconcile negative GDP growth with such rosy pronouncements from the media, but if journalists themselves had the same question, their doubts were quickly put to rest, it would seem, from prominent economists. Who are these bulls, who insist that a positive change in the rate of decline is a sure sign that the worst is behind us? Christina Romer of the Council of Economic Advisors and chief economists from private investment firms offered quotes predicting recovery. One should note, however, that both parties have incentiveswhether political or financialto encourage recovery.
So, to be clear the news release from the Bureau of Economic Analysis, which is the agency responsible for calculating GDP, was that the economy continued to decline in the second quarter of 2009 (April through June). More precisely, when compared to the previous quarter, real GDP fell by another 0.26% (or an “annualized” 1% decline in the parlance of the BEA, which, for some queer reason, reports GDP percentage changes as “annualized rates.” This means that they take the real data and multiply it by 4, as if it happened for a year, even though it only happened for one fourth of a year).
Why was a decline in economic activity interpreted as sign that economic activity will soon start increasing? The answer is that the previous quarter-to-quarter growth rates were more negative. They were -1.7 and -1.4 for the first quarter of 2009 and the fourth quarter of 2008 respectively (multiply those by four to get the BEA figures).
The question is: does an increase in the rate of decline guarantee positive growth in the next quarter? Does it even increase the probability? The answer is no, but one can answer this question by doing the following simple experiment, which I did in Microsoft Excel:
- Download the BEA data (real GDP by quarter);
- Calculate the growth rate for each quarter and the change in the growth rate for each quarter (the growth rate this quarter - growth rate last quarter);
- Code the change in the growth rate as positive or negative (1=positive and 0=negative) and call it “Change-in- the-Growth-Rate Index;”
- Cut and paste the growth rate so that you match the next period’s growth rate with the index;
- Run a regression, where the growth rate of the next quarter is a function of the change in the growth rate index. ΔGDPt+1 = β*Indext
What were the results of this exercise? There was no significant relationship between Change-in-the-Growth-Rate Index and the actual growth rate in the next period. More precisely, the 95% confidence interval was between -0.2% and 0.3%. We can be 95% confident that the actual effect of the previous period’s Change-in-the-Growth-Rate on the current growth rate falls within this range.
In non-economists prose, there is no reason to be optimistic
about the BEA figures. There is nothing in our nation’s history, nor in
economic theory, that justifies interpreting a slower decline in GDP as a sign
of recovery. If there is room for optimism it is this: negative quarters of
growth are quite rare in
It would be nice if journalists, administration economists, and Wall Street economists would be clearer about interpreting the GDP data. If there are indeed signs of recovery in the data, such as trends in housing prices or some leading indicator, then great, but don’t tell us that a more positive change in the rate of change predicts that a growth increase is likely to follow.