# Credibility of Labor Market

The currently revised monthly non-farm payroll numbers for the first half of the year is:
148k, 332k, 142k, 199k, 176k, 188k.

The average of these six data is 198k, with a standard deviation of 63k (an elevated level due to the outlier of February's 332k).  This is today's revision of the data, mostly similar to what was known to the FOMC during their July meeting.  See the calculated probability distribution below, with the labor data in units of thousands.

One can see there is a wide spread about 198k.  Also there are two additional payroll reports between this July meeting and the possible tapering event at the September meeting.  The first of these new reports is the July monthly payrolls, released today in August.  Today's July report came in at 162k, or roughly 1/2 a standard deviation below the statistical prior distribution.

How can one use statistical credibility to adjust from the higher previously known 198k, based on this new lower data of162k?  Full statistical credibility analysis is a Bayesian tool that uses the following formula to weight the new data:

credibility = sample size / [sample size + (v / a)]

The variable a represents the variation of all monthly labor reports this year, from both the first half of the year and the new reports between then and the September FOMC meeting (e.g., July and August monthly reports).  The v represents the weighted variations within these new monthly labor reports and the prior monthly labor reports.

What would be the impact of a second monthly labor report (e.g., August report known in September) of the same 162kfrom July, based only on the sample size now having increased?

Notice in this illustration above that there is now a double count of two hypothetical monthly reports at 162k (e.g., looking back at the time of the September FOMC meeting), and this shifts the probability curve lower towards 162k versus the top illustration of 198k.  But we still have more probability information here since the variations between these two sets of labor reports is analytically vital.  What additional impact is there from the assumption of consistency in both newly observed labor reports (e.g., July and August), versus from the first half of the year known at the July FOMC meeting?

So we see in this example how the credibility formula above works, if we see another 162k for the August report, released in September.  Assuming a zero variation in the new monthly reports would show the lowest possible value.  And lower vvalues reduce the credibility weight denominator (i.e., in the the bottom portion of the ratio in the credibility formula above).

Combined with a small increased sample size of months, and we see an increased credibility towards these lower 162kmonthly labor changes.  In conclusion, the effect of two addition labor reports (e.g., the 7th and 8th months of the year) is not 2/8, or 25%, but rather a greatly increased credibility weight of about 85%.  A short animation can be imagined on the Bayesian impact of this higher credibility weighting on the lower 162k monthly labor growth.

The following article is from one of our external contributors. It does not represent the opinion of Benzinga and has not been edited.

Posted-In: Economics Markets

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