How Errors in Seasonal Adjustment Factors for US GDP contributes to misleading National Accounts Data

World Economics - July 2015

Speed Read
  • US Q1 GDP data may seriously under record economic growth.
  • Survey evidence suggests US GDP annual growth in Q1 2015 was closer to 2% than the -0.2% official third estimate.
  • Analysis suggests that faulty seasonal adjustment methods are responsible for the problem.
  • Improved and timely advance estimates of US GDP growth are available from the Sales Managers’ Index produced and published monthly by World Economics.

Official Estimates of Q1 GDP Growth

The rapid deceleration of US economic growth indicated in the three estimates of Q1 2015 GDP over the previous year released by the Bureau of Economic Analysis (BEA) was disappointing. The first release showed real GDP rising by only 0.2% year-on-year in Q1 compared to an increase of 2.2% in Q4, while the second estimate registered a fall to -0.7% and the third estimate was a -0.2%.


Evidence of Expected Q1 Growth

In contrast to the BEA figures released many economic forecasts of GDP Q1 annual growth were predicting an expansion of over 1%. Most economic indicators did not signal a fall in economic growth. Consumer confidence remained high during Q1 2015 and the employment market was buoyant. [1] Despite the weak first estimate of growth the Federal Reserve Bank of San Francisco maintained its prediction of 1.8% growth in Q1 arguing that the official estimates were wrong.[2]


The Federal Reserve Bank of San Francisco’s figure is very close to the 2.2% estimated by the World Economics Sales Managers’ Index (SMI)[3]. The SMI is the first all sector monthly economic activity index release covering the US economy and is based on a representative panel of sales managers. Sales Managers are unique as an occupational group in being at the front line of economic activity. The SMI headline value provides probably the most sensitive barometer of changes in economic activity available and it has demonstrated a close relationship with GDP growth. (See Figure 1) Growth also fell in Q1 2013 and rebounded in Q2 2014, but in this case the SMI values anticipated the falling and rising pattern.

      Figure 1: Monthly US SMI Index and Quarterly Real GDP Growth %

 Why Official Data Under-records Growth

There is evidence that the predictions of the SMI panel data were correct and that the seeming fall of GDP growth in Q1 of this year was a statistical anomaly brought about by inadequate seasonal adjustment.

Barclays Bank and the Federal Reserve Bank of San Francisco, Rudebusch et al (2015), have noted the existence of regular changes in quarterly US GDP data that should have been ironed out by the seasonal adjustment methods employed, a phenomenon termed ‘residual seasonality’. In May 2015 Rudebusch et al (2015) found that an unusual seasonal pattern existed in the BEA estimates of seasonally adjusted real GDP growth over the last few decades. GDP growth in Q1 averaged 1 percentage point lower than in Q2-Q3 for many years, but the Q1 shortfall increased to 2.3 percentage points on average from 2000 to 2014. 

A research note also published in May by Barclays[4] noted that many components of GDP displayed residual seasonality including state and local investment, residential and non-residential investment and exports. In order to correct for this problem both studies applied a second seasonal adjustment to the BEA’s adjusted series from Q1 1960 to 2015 in order to discover how much Q1 GDP had been affected by residual seasonality. The authors find that after making corrections, published GDP data for Q1 is pushed upwards by approximately 1 percentage point in the late 1990s and by around 1.5 percentage points more recently. However, after removing residual seasonality real GDP growth in Q2, Q3 and Q4 is lowered. The results of this procedure are shown in Figure 2. The authors find that the year-on-year GDP growth for the advance estimate of Q1 2015 would have been 1.8% rather than the BEA’s 0.2%[5]. Barclay’s arrived at the same estimate for Q1 GDP growth having used the same technique to eradicate residual seasonal influences.

Figure 2: Quarterly GDP annual rate and Doubly Seasonally Adjusted Growth %

How to Track US GDP
The BEA now recognises the problem and is trying to account for ‘residual seasonality’ by undertaking a number of corrective measures. These include adjusting federal government defence expenditure to take account of unanticipated lower growth rates in Q4 and Q1 and testing for seasonality in series that now have sufficient time spans to allow adjustment techniques to be applied, BEA (2015). The changes will be included in the July 30, Q2 GDP advance release.

However, given the importance of the release of GDP estimates in moving markets and in setting economic policy all those interested in the direction of the US economy would be better off studying the GDP estimates of private surveys, such as the SMI, at least as far as Q1 estimates are concerned. US SMI data is produced 2 months in advance of the 1st estimate of official US GDP data. The SMI has an excellent trend record over the last 3 years, and is very likely to be more accurate than official data for the first quarter data that is to be amended on 30 July.


BEA (2015), BEA Works to Mitigate Potential Sources of Residual Seasonality in GDP, BEA Blog, May 22:

Rudebusch, G.D, Wilson,D. and Mahedy, T. (2015), The Puzzle of Weak First-Quarter GDP Growth, Reserve Bank of San Francisco Economic Letter, May 8, May 18

World Economics, (2015) Sales Managers’ Index: United States



[3] The Sales Managers’ Index results are calculated by taking the percentage of respondents that report that the activity has risen (“Increasing") and adding it to one-half of the percentage that report the activity has not changed (“Unchanged"). Using half of the “Unchanged" percentage effectively measures the bias toward a positive (above 50 points) or negative (below 50 points) index. An example of how to calculate a diffusion index: if the response is 40% “Increasing," 40% “Unchanged," and 20% “Reducing," the Diffusion Index would be 60 points (40% + [0.50 x 40%]). A value of 50 indicates "no change" from the previous month.

[4] Reported by Matthew Klein, Another lingering cost of the bubble: weirdly seasonal GDP data?, FT Alphaville, Financial Times, May 13, 2015:

[5] Rudebush et al calculations are based on the BEA’s 1st estimate of GDP. 3rd estimate GDP data was revised to -0.2%