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Wednesday, August 24, 2005

Update: Explaining the Systematic Statistical Discrepancy

This is about explaining the statistical discrepancy in the NIPAs so many of you will want to skip it (and it's a bit long so I'll tuck it into the continuation frame).  There's progress.  I think.

I’ve found another paper by Klein and Makino that reports somewhat similar findings to those reported here and notes the correlation of the discrepancy with product side variables.  There is also a paper commenting on the Klein and Makino findings.

The paper by Klein and Makino finds significant correlations between the sum of corporate profits and proprietors’ income, exports, and government consumption expenditures, and the statistical discrepancy. This earlier post on this site indicates that such correlations do exist as claimed by Klein and Makino, but the paper by Fixler and Grimm using a longer data set could not confirm these results. Here are the papers.  The paper links are followed by one quote bearing on this issue from Fixler and Grimm. The Klein and Makino abstract follows and then a section from Fixler and Grimm is presented. I’ve also included a paper on this issue in Australia if anyone is interested, the third on the list. This paper finds that in the Australian national income accounts private investment appears to be the source of the discrepancy:

Here is footnote 17 from the Fixler and Grimm article in Survey of Current Business:

footnote 17. According to a study of the statistical discrepancy in 1947–97 by Klein and Makino (2000), the discrepancy was statistically significant in explaining its values four quarters later, and after the discrepancy was adjusted to remove trends, the sum of corporate profits and proprietors’ income, exports, and government consumption expenditures were statistically significant in explaining the statistical discrepancy. Replication of their work by BEA for 1983–2002 and using data from the 2003 comprehensive NIPA revision found that none of the explanatory measures were statistically significant and that the four-quarter-lag effects of the discrepancy were also not significant.

As noted above, it seems clear that such correlations do exist. The question is why they are correlated which has yet to be answered.

Here’s the abstract from Klein and Makino:

Abstract: Through many comprehensive revisions of the National Income and Product Accounts (NIPA) of the US, a significant discrepancy has persisted, namely that between the estimate of the headline total now called Gross Domestic Product (GDP) from the side of expenditures or from the side of imcome payments. This discrepancy is not trivial (now in the neighborhood of -\$100^+ bn.); it is not random; it is wrongly attributed exclusively to the income side estimates. There have been interesting proposals for systematically allocating it among NIPA entries according to some statistical rule. Students of the discrepancy, over the years, have noted systematic variation with respect to international trade, inventory investment, total output and other variables. In recent years, the income side total has given a different estimate of the historical rate of change of output per worker, obviously an extremely important statistic. In a fresh examination of the discrepancy through 1996 (quarterly), we find, in this paper, suggestive correlation with business earnings, itself a very important but difficult magnitude to measure. If the NIPA data are to be used in an important way for policy guidance, a more careful treatment based on economic and statistical analysis is called for.

And finally, section 5 from Fixler and Grimm. Note the warning at the end on the use of quarterly data (I don’t think the annual/quarterly issue at the end is a problem for what I’ve presented so far):

5. The Statistical Discrepancy In principle, GDP and GDI should be equal. However, they usually differ because they rely on different source data that are not necessarily compatible. The statistical discrepancy is defined as the difference between GDP and GDI. The statistical discrepancy may be regarded as the net sum of offsetting, unknown, measurement errors. For example, if the output of drycleaning and laundry services is measured in a Census Bureau survey, and the income for this activity is measured in IRS income tax documents, a discrepancy might arise. This is true of many income-side and product-side measures.

In theory, an econometric analysis should be able to determine which income-side and product-side measures have the greatest ability to explain the statistical discrepancy. In practice, most major GDP components are highly correlated with one another, and most major GDI components are only slightly less highly correlated with one another. All of the measures are considerably less correlated with the statistical discrepancy.

As a result of the correlations among GDP and GDI components, the principal contributors to the statistical discrepancy are difficult to identify. Revisions to each component of GDP and of GDI will pass through one-for-one to the statistical discrepancy, but the effects of the revisions partly offset one another, and multicollinearity is again a substantial problem. BEA’s statistical findings about the relationships between the movements in the statistical discrepancy and those in GDP and GDI components have been inconclusive. Research on the statistical discrepancy and related topics is continuing at BEA.

For the latest annual estimates, the statistical discrepancy has large positive values in 1989–97; it dips sharply to negative values in 1998, and then it recovers to a near-zero value in 2002 (chart 3).

Annual data should be used to study the statistical discrepancy and revisions to it; if quarterly data are used, two factors act to obscure the relationships between the statistical discrepancy and the income-side and product-side components:

Seasonal adjustments. Although these adjustments remove regular fluctuations from seasonally unadjusted source data, the adjustments are not made in lockstep, and the adjustment process includes some judgments that might not be the same for related income-side and product-side measures.

Interpolation and extrapolation. The use of methodologies to interpolate or to extrapolate quarterly estimates by less-than-perfect indicator series may lead to incompatible quarterly estimates for income-side and product-side components. In addition, revisions to the indicator series or the use of different indicator series in later estimates may lead to revisions to the estimates of the statistical discrepancy.

    Posted by on Wednesday, August 24, 2005 at 02:07 PM in Academic Papers, Economics, Methodology | Permalink  TrackBack (0)  Comments (0)


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