Given that economic targets are now interdependent with the Federal Open Market Committee (FOMC) projections of rate firming times, we can use statistical analysis to get a stronger sense of the likelihood of future FOMC activities. For example, macroeconomists generally expect rate firming in 2015 or later. And markets have recently responded, perhaps over-responded, to Federal Reserve Chairman Bernanke's recent communications. Nonetheless, not all market participants- notably equity investors- could state that there is some chance of rate firming prior to 2015, and that this chance can come from multiple quantitative analyses directly from the FOMC material. With a conclusion that the rate firming probability prior to 2015 has edged down to near 20%.

We begin with market participants before looking at data from the FOMC, and these participants have seen the typical FOMC future frequency data available for quite some time. The distribution is somewhat unchanged from the previous projection summaries, while the markets have recently priced in a substantially greater probability of government-bonds rate firming sooner than 2015. We start with the more traditional probabilistic approach of calculating the relevant portion from the future frequency data (e.g., Figure 2 here) that was released in the June meeting. With 4 of 19 participants judging a rate firming by 2015, we can get the 20% chance. And the important binomial variance equation is appropriate to determine the confidence interval associated with this 20% chance. Keep in mind that the variance associated with these discrete categorical probabilities is equal to *n*p*q*, when *n* is 19 participants, *p* is 20%, and *q* is *100%-p*.

This gives a symmetrical confidence interval, which is better served for estimates closer to 50%, and not for those on either end (e.g., near 20%). In this case where the estimate is closer to 0% than it is to 50%, an asymmetrical confidence interval would better fit the lower end of this probability distribution better. We'd also suffer from having an overall small sample size of 19 similarly trained economists, where the statistically relevant minimal sample size would be magnitudes greater than this. Nonetheless, geometrically extrapolating our confidence interval would get a range of 20%+/-5%, for the standard range about the 20% FOMC projection estimate. In order to get this geometric process on the confidence interval surrounding the 20% probability, we take the interval from *p^(1/U)*, to *p^U*, with *U* being the exponential rate of the arithmetic (symmetrical) standard error solved above. The objective is an upward error that will clearly be slightly larger than the downward error in cases where the central estimate is well below 50% (e.g., our case of 20%). In this case, the upward and downward errors are different by such a fractional amount that it would be absorbed into the rounding of +/-5%.

Another approach to this probability problem is through the more recent economic thresholds being communicated by the FOMC. Now what do we learn about these "barriers", which provide the chance for the FOMC to discuss rate firming? In this case one main threshold is a 6.5% unemployment rate. Let's see how the 2014 FOMC's unemployment rate forecast has evolved over time. We are using the 2014 unemployment rate forecast, since it is just "prior to 2015." See the chart below.

The 2014, the FOMC unemployment rate forecast has improved over time (see **purple** projection data in the chart above) since they began releasing this forecast in late 2011. However it has not been a gradual reduction in the forecasted unemployment rate, reflecting a similar 0.2% standard error in each FOMC report's forecast error among the 19 FOMC participants. Bear in mind that the reduction in the central unemployment rate forecast reflects only a temporary optimistic bias in the FOMC's past forecast of this 2014 value. Additionally, another recent pattern is that as the FOMC forecast evolves over time, the downward standard error is about 0.05% less than the upward standard error. This is parallel to the above topic of asymmetry in the frequency distribution. And it is particularly unfortunate in the case of economic thresholds, since financial market participants are trying to understand the likelihood of being on the other side of an economic threshold at various times in the future. In our case we see, through the **red** single-data in the chart above, that the 6.5% unemployment rate threshold would be demanding for prior to 2015.

The most recent May unemployment rate was 7.6%, or 1.1% above the 6.5% threshold. And the 7.6% level on the recent unemployment rate was known at the time of the June FOMC survey projections. See the **blue** data in the chart above to see the underlying unemployment rate over this time.

The standard errors associated with this rate are more symmetrical and reflect a mixture of the historical U.S. Department of Labor's survey sampling error, with the contemporaneous standard error in the unemployment rate trend in-between the FOMC meetings. This standard error is roughly half that of the FOMC standard error, though closer to two-thirds the FOMC standard error more recently. This shows the reduced accuracy of the FOMC in projecting future unemployment rates, relative to the survey errors themselves. Meanwhile the underlying unemployment rate had rapidly fallen during the recent recovery from the financial crisis, but would need to maintain something close to this fast rate of descent still, in order to achieve the 6.5% unemployment rate threshold prior to 2105.

So with the FOMC central tendency of the end of 2014 unemployment rate is 6.6%, and a 0.1% downward standard error, this implies a one standard deviation exception from forecast for the FOMC to cross the 6.5% unemployment rate threshold prior to 2015. Despite the small trending bias we discussed on the FOMC 2014 unemployment rate forecast, there is still 60% to 65% of this typical probability distribution residing within one standard deviation. Therefore about half of the remainder (i.e., about 20%) would be the FOMC probability of crossing the economic threshold prior to 2015. To be clear, the Federal Reserve Chairman Bernanke did state that this target would only start the conversation about rate firming. So looking at the rate firming frequency distribution from the participants (see Figure 2 from the link above), we see that we are able to better narrow the statistical confidence intervals about the near 20% probability of rate firming prior to 2015. And at least a three-quarter chance of rate firming in 2015 or later.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.