Masked Statistical Recalibrations in GDP Revisions

The annual comprehensive benchmark revision to real GDP can be decomposed into: (A) the traditional statistical enhancement, (B) components of definitional changes to the national growth accounts, and (C) changes in the price deflator.  For this analysis, we look at the revisions post the revision to the price deflator.  This is an additional layer of statistical manipulation, but allows one to more carefully focus on the primary econometric interest of these annual benchmark revisions.  And from here we see that the largest and most novel component of this particular release is the definitional change associated with the consumption of fixed capital.

Now the statistical revisions, which we are most comfortable with, had a typical change of 0.0% annually.  This is from 2003 through 2012, a period that the Bureau of Economic Analysis (BEA) had provided the most readily available complete data.  The standard deviation of this statistical revision was 0.5%.  On the other hand, the non-statistical revisions were typically 0.2%, with the same standard deviation of 0.5%.  Together, the total revisions were the typical 0.2%, but maintained a standard deviation of 0.5%.  So we see very large deviations in the annual revisions for both component groups, yet a clear and unexpected dependence in the BEA's statistical errors between the two groups.  It is this dependence that allows for the total error of two 0.5% components together to still equal 0.5%.  And this makes interpreting each component variable in isolation difficult, from a any perspective.  It also points to a source of possible methodological error in the model development of these revision series.

Let's look at the annual revisions to real GDP, from three disaggregated sources, as shown in the illustration below.  We also show, in the purple dashed line, the total revision aggregated from these three "error" sources.

This is not the random noise that would give us confidence.  It is instead obvious from the illustration above that the total error is dependent on time, and specifically it is cyclical.  We must point out, for example, that the periods that were most improved versus earlier reports were during expansionary periods as opposed to recessionary periods.  This again can provide more questions as it does provide answers.  We also see an uncomfortably large statistical errors of -1.0% in 2009.  This is clear outlier just happens to be offset by non-statistical errors totaling a similar magnitude.  In this case 1.1%.  This unfortunate dependency and counteractivity among the large non-statistical errors, making the study of these revisions open to more questions about the BEA than it provides answers.

To add clarity on these revisions, we represent the two major revisions, in a time series chart below.  This way one can better understand the cyclical development of the statistical and non-statistical revisions in this BEA report.  The two error variables do not independently move roam at will in the chart, but rather we see have an eye-opening -86% correlation between the two variables.  The relationship if fairly uniform as well across the 2003 through 2012 period.

To describe this chart with words, we start with the 2003 period that is represented at 0.1% non-statistical revision rightward along the horizontal axis, and 0.2% statistical revision upward along the vertical axis.  One can also mostly match up the data in the chart below, with the original chart above.  The most recent annual errors terminate in 2012 at 0.5% non-statistical revision along the horizontal axis, and 0.2% statistical revision along the vertical axis.