This post is a little more technical than my usual blather. It applies simple statistical theory to explain why most announcements of employment reports have almost no real significance. Notice how the market went berserk recently after the payroll jobs number for May 2010 came in under expectations. But if one examines the probability distribution of monthly employment changes, you see that most monthly changes fit into a category of “not-statistically significant” or not statistically different from zero percent. That is, I show below why even if the May figure had been closer to 500,000 jobs, the statistical interpretation would have been that this change was not different from zero! The nature of the employment probability distribution is that it will take monthly employment increases of more than 520,000 to be significant at the usual 95% level. That means that it would take even larger gains to be significantly different from zero at the more exacting 99% confidence level. The upshot is that there is a good statistical basis for why the markets do not react optimistically to most employment announcements…and why they might react negatively if they had hoped for real progress.
To come to these conclusions I used monthly data from Jan 2000 to May 2010 – a total of 125 months of data. I used the Total Non-Farm Employment from the Current Employment Statistics Survey (http://www.bls.gov/ces/#tables ) . Employment started at 130.8 million in January 2000 and ended at 130.6 million in May of 2010. Employment experienced some cycles – a peak at 132 million in 2001….falling to 129.8 in 2003 and then rising to 138.0 million in 2007. It hit bottom again at 129.6 million in 2010 and rose to 130.6 million in May.
The average monthly change was .002%. The mode and median were also approximately zero percent. The distribution of percent changes were gathered around zero percent – with 80 of the 125 monthly observations ranging between -0.1 percent and +0.1 percent. This means most monthly changes, if annualized (without compounding), were about 1.2%. In all, 55 observations were plus – ranging from 0.1 percent to 0.4 percent. There were 36 negative changes ranging from -0.1 percent to -0.6%. This implies that the distribution ranges farther to the left but the mass is to the right of zero.
The distribution is not symmetrical but it looks normal with the fewest number of observations at the extreme left and right. The standard deviation of the percent changes is 0.19 percent. To be two or more standard deviations from the mean implies a monthly percent change of more than 0.38 percent. That is, it takes a monthly change of about plus or minus 0.4 percent to be statistically different from the mean. Since the change in May 2010 was about 0.3 percent, it was not outside the 95% confidence interval and thus was not statistically different from zero. With a current level of employment near 130 million workers, it would take an increase of about 520,000 jobs to be statistically different from zero. .
I also evaluated the probability distribution function for private jobs, which exclude government employment. With a current level of about 107.6 million jobs, it would take an increase of 471,000 jobs in one month to be statistically significant. Job increased by about 41,000 in May.
The upshot is that employment changes are tightly clustered around a mean of zero percent. Not many months between 2000 and 2010 have shown large percentage increases. A change of around 600,000 jobs in a month would represent a change of about 0.45 percent and would be statistically significant. It would also imply an annual increase – if kept up for 12 months – of more than 7 million jobs. It will take employment increases in this range to wow the market.
Larry,
ReplyDeleteA little heady for a guy like me to read so early in the morning but well done. I have always felt that the attention the market pays to the monthly employment numbers is way more than what the data really shows. With that said, what data do you look at on a monthly/quarterly basis to get a true idea of how the economy is doing with regards to employment? Is it as simple following the unemployment rate and projecting from there?
Hi Bob -- thanks for the nice comments. The Bureau of Labor Statistics publishes several series. The key ones are the payroll survey and the household survey. One of my earlier blogs talked about the differences and you can learn all you want about their differences at www.bls.gov . From there are tons of very specific pictures of the employment and unemployment pools. For example, you can break down the unemployed by sex or race or by duration. Or you can categorize the employment by industry. One of these days we can sip some whiskey and I will show you some of the websites I use.
ReplyDeleteWhile I understand the point you are trying to make I have to disagree with your premiss. The reason for this is (IMHO) the underground economy buffers and distorts the employment picture. By all the accounts I have seen there has been a statistically significant change in employment of illegal aliens. It is not easy to quantify numbers in the underground economy, but it is interesting to note that remittances from the US to Mexico have dropped by at least 1/3 according to records for places like Western Union, a figure that seems statistically significant to me. There also seem to be real changes in the increase of part time (as opposed to full time as qualifying for benefits) workers. Bottom line is whatever statistics say about employment it is clear to most people that we are in hard economic times and there is a real sea change in the jobs available in this country.
ReplyDeleteTom,
ReplyDeleteThose are good points about changes in data. This is a bad recession and therefore the past data might not be a great indicator. But it is the best we have. My point was to reveal some facts about the probability distribution of monthly changes. It has a wide variance and, therefore, it will take a large swing in employment to convince people that anything positive is happening.