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Revising “Yield Curve and Predicted GDP Growth”

Note: A recent verification of the data supporting the yield curve and predicted GDP growth indicator revealed minor errors in the calculation of quarterly averages of yield curves dating back to 2013. The deviation between the original and revised averages is no more than 60 basis points in any quarter and has averaged 20 basis points in the period since September 2013; three months in 2015 were reported correctly.

The error in computing the quarterly yield curve average led to errors in predicted GDP growth starting in September 2013, with a maximum difference of 0.30 percent. (The average difference was 0.04 percent, and the average absolute difference was 0.07 percent.) Since the numbers reported on the website were rounded, some of the calculated differences did not affect the reported numbers—of the 30 months with errors, 11 resulted in different real GDP growth numbers at the precision reported on the website. The verification also revealed three transcription or rounding errors between the calculated values previously reported and the corrected reported values, each of -0.1 percent. Reported recession probabilities were not affected. A spreadsheet with the originally reported and corrected data is available for download. Archived reports will not be adjusted, but the June report references the corrected data and the errors are posted on the archives page.

The program used to calculate predicted real GDP growth regresses four-quarter growth rates in real GDP against (lagged) quarterly averages of the yield spread. For any given month, the most recent quarter is of course incomplete, so the program calculates an average yield spread using the completed weeks of the quarter in lieu of the complete quarterly average. For example, in March 2015, the quarterly average computed for that quarter (2013:Q1) was based on data from 1/2/2015 to 3/20/2015.

However, from September 2013 on, the quarterly average was computed inconsistently, not always using the starting date of the current quarter. So in March 2015, for example, the quarterly average was based on data from 7/5/2013 to 3/20/2015 instead of 1/2/2015 to 3/20/2015. The running quarterly average calculated from 7/5/2013 to 3/20/2015 was 2.487667, while the corrected average (from 1/2/2015 to 3/20/2015) is 1.964167. This resulted in a difference in predicted real GDP growth of 2.094006554 (previously reported version) versus 2.086489564 (corrected version), though note that both would have been rounded to 2.1 percent on the website.

In addition to the table and text, the error affects one of the charts, “Yield-Curve Predicted GDP Growth,” specifically the plot line for projected GDP growth. The error was identified only in the calculation of the average yield spread for the most recent quarter in each report, when complete data for that quarter were not available. That average yield spread was not shown on the charts, so the only thing that needs to be corrected on the charts is the GDP growth projections. Once the quarter became complete, the quarterly average was correct, as the value was taken directly from the data source. Thus, in any one report the error affected only one data point used in predicting GDP growth.

The following charts compare the originally calculated quarterly averages and the revised averages. Since the program replaced the incomplete quarterly average as soon as the quarter was completed (and the new data were saved over the old), recovering the older unrevised numbers involved reconstruction, and in some months the unrevised numbers are our best estimates.

Sources: Bureau of Economic Analysis; Federal Reserve Board; ALFRED; Author' calculations
Bureau of Economic Analysis; Federal Reserve Board; ALFRED; Author' calculations

Likewise, because real GDP data are frequently revised, obtaining revised real GDP predictions for past months required using unrevised GDP numbers, which were obtained by consulting legacy files and using the real-time data set from ALFRED.

The verification of the program and files also uncovered several typographical errors in the archives, separate from the incorrect calculation. We list the corrected values in the table below.

Errors in Archived Reports
Release date Data date Previously Reported GDP Growth on Web Previously Obtained GDP Growth Prediction Corrected GDP Growth Prediction
May 2011 April 2011 April: 1.0 1.1 NA
November 2011 October 2011 August: 0.08 0.8 NA
March 2013 February 2013 February: 0.4 0.5 NA
November 2013 October 2013 October: missing
September: 1.1
August: 0.9
October: 1.2
September: 1.2
August: 1.1
October: 1.1
September: 1.2
August: NA
March 2014 February 2014 February: missing 1.4 1.5
April 2014 March 2014 February: 1.3 1.4 1.4
May 2014 April 2014 February: 1.3 1.4 1.4
November 2015 October 2015 October: 1.9 2.0 1.9
May 2016 April 2016 April: 1.8 1.9 1.7