Columbus Day tends to generate nostalgia for frontier, and the time when the possibilities seemed open for all on the American landmass. Some news that came out last Friday however underscores the fact that America remains a frontier, at least as far as opportunity is concerned. That news was contained in the monthly employment report from the Bureau of Labor Statistics.

The September jobs report at first seemed disappointing. Only 51,000 payroll jobs were created, compared to predictions of 120,000. Still, unemployment was down to 4.6% — a drop. And two surprises were in the report. The document also announced that an extra 62,000 jobs were created in the prior two months, bringing the total number of new payroll jobs to 113,000.

More important, tucked away on a back page, was the preliminary announcement that our economy had created 810,000 more payroll jobs over the period April 2005 to March 2006 than had been thought. This seemingly minor news contradicts the jobless recovery stories, shows why wages and compensation haven’t been growing faster, and explains the some of the difference between the household and payroll employment surveys.

A quick note of explanation: BLS issues two employment surveys each month. The payroll survey, based on 400,000 firms, produces data on jobs in the economy. This survey is revised two months in a row and “benchmarked” or recalibrated annually against a total administrative count of jobs in the economy.

The household survey, derived from monthly calls to 60,000 households, produces estimates of working Americans. Its estimates are never revised, lowering their accuracy. The household survey has recently produced consistently higher estimates of American employment than the payroll survey.

The surprise BLS announcement dealt with the annual benchmark revisions of the payroll survey. In the past, these revisions have been relatively small, plus or minus 0.2% of jobs. This year’s revision totaled 0.6% — the highest percentage on record. That means BLS’s statistical methodology has been systematically underestimating the number of jobs in the economy over that period of time.

This is vital because between April 2005 and March 2006, the number of jobs initially announced by BLS was lower than forecast in 7 out of 12 months. Over the past year, this was true in 9 out of 12 months. This gave rise to a steady stream of headlines such Friday’s “September Job Growth Below Expectations” and “US Jobs Figures Lower Than Hoped.” Many people, myself included, had been asking why the forecasters were so wrong. If forecast jobs came in regularly above numbers of jobs, why didn’t the forecasters lower their expectations?

It turns out that the forecasters were right.

They were not overpredicting jobs after all. The jobs were in the economy, but were not being recorded. Now that we know that an extra 67,500 jobs a month were being created, we can see that forecasters were actually underpredicting every month of the revised period except for two.

Needless to say, the Bush administration was blamed for not creating enough jobs to meet forecasts. The headlines about low job levels meant that administration’s economic policies, in particular tax cuts, were not working. With the new data, job creation exceeded the Administration forecast of 175,000 jobs per month in 2005. If the undercounting continues, the economy is well on its way also to exceed the 2006 job forecasts.

The discovery of the additional 810,000 jobs should put to rest the myth of the jobless recovery. With the creation of almost 3 million jobs over a 12-month period and an unemployment rate at 4.6%, the economy cannot be said to have a jobless recovery.

BLS reports that it does not know what is wrong with the sampling procedure and why the revision is so large. The error is systematic, across regions and industries. Hence, BLS could be making the same mistake now. So numbers that are coming in this month — such as the 51,000 number reported on Friday — could be revised up next year, as well as in the regular revisions that occur in the next two months.

One possible reason for the error is that entrepreneurs and small businesses are becoming more prevalent in our economy, aided by telecommuting, the internet, inexpensive printers and fax machines, and BlackBerries. These firms are harder for BLS to track down in their sampling procedure—although BLS does attempt to estimate their numbers using economic models.

Take the case of workers receiving buyouts from Ford Motor Company. Ford, an established company, reports to BLS that workers are off the payroll, resulting in a recorded loss of payroll jobs. But if some workers start new companies such as Joe’s Auto Repair, or Matt’s Tire Center, it’s unlikely that BLS will sample these new firms to see how many jobs have been created. The new jobs will only be captured in the final annual revision.

Finding more jobs in the economy means that American productivity, defined as output per unit of labor, is lower than we thought. This is not necessarily good news. Over the revised period, we have been producing the same amount of goods with 0.6% more workers.

This decline in productivity might clarify one of the mysteries regarding wage levels and compensation packages. Economists have been surprised that worker compensation took so long to catch up to increased employment. If productivity were lower, compensation would be slower to catch up, since compensation reflects productivity.

Another deciphered problem is the difference between the payroll and household surveys. Since the jobs recovery started in August 2003, the household survey has shown a gain of 7.3 million workers, compared to a gain of 5.8 million payroll jobs. The increased number of payroll jobs goes part of the way towards reconciling these numbers.

Friday’s news from BLS shows that our employment situation is strong, with almost a million more recorded jobs than previously thought. But it took us many months to learn this. Our economy is extensive and complicated, and our preliminary data estimates — not only for employment, but for all economic indicators — provide only an imperfect reflection of what is really occurring. Americans be reassured. When it comes to job creation, we are a job frontier.

Ms. Furchtgott-Roth is a senior fellow at the Hudson Institute, where she directs the Center for Employment Policy. From 2003 to 2005 she was chief economist of the U.S. Department of Labor.