July 9 (Bloomberg) -- Illegal immigrants may lie at the heart of one of the persistent puzzles of the U.S. labor market.

Overall payroll jobs rose by 132,000 in June, while the gains in April and May were revised to show 75,000 more jobs than reported earlier, the Labor Department said. The increase in jobs for the second quarter totaled 444,000, up modestly from the first quarter's 427,000.

The unemployment rate remained at 4.5 percent, unchanged from April and May.

The mystery is why the collapse of the bubble in the housing market hasn't been a much greater drag on payroll employment than it has.

``Something isn't right,'' said economist Ray Stone of Stone & McCarthy Research Associates. ``We think that the BLS monthly payroll estimate is overstating the pulse of labor market conditions.''

The number of housing starts and units under construction have both plunged over the past year, while residential construction employment fell a scant 3.5 percent. Last month the number of people at work on homes was unchanged from May at a little more than 3.3 million, the department said.

Federal Reserve officials have been waiting for months for construction employment to fall, but it hasn't. Of course, the decline in housing construction has been a major drag on gross domestic product growth.

As Janet L. Yellen, president of the San Francisco Federal Reserve Bank, said in a July 5 speech, ``Over the past four quarters, the level of residential investment spending declined more than 16 percent in real terms. And during that period, this sector -- which represents only a little more than 5 percent of U.S. GDP -- has taken a large toll on overall activity, subtracting a full percentage point from real GDP growth.''

Data Accuracy

Yellen also expressed some skepticism about the accuracy of the construction jobs data, and the way in which it has depressed growth in productivity, the output per hour worked.

``Most of the recent slowdown in labor productivity growth can be accounted for by such lags in just one sector -- residential construction. Although this sector has experienced huge drops in spending, employment has been remarkably well sustained,'' she said.

``Going forward, as the adjustment lags work themselves out, residential construction employment may post significant declines and productivity in that sector and the economy as a whole may rebound,'' Yellen said.

Different Times

Aside from construction, Stone also questioned why the 42,000 drop in temporary-help agency jobs since June 2006 hasn't been reflected in a pronounced slowing in overall payroll jobs gains.

Historically, changes in temp services payrolls have led overall payroll trends, Stone said.

``Early in the recovery stage of a business cycle, employers often contract temp workers given the uncertainty of any pick up in demand,'' he said. ``At late stages of a cycle when layoffs may become necessary, the contract or temp workers are the first out the door.''

This time it's different. Temporary employment stopped growing at the beginning of last year and then began to decline. Overall payrolls growth has slowed, though not by all that much. In the last 12 months, 2 million jobs have been added.

The big discrepancy, though, remains in residential construction.

Small Numbers

Stone said he thinks the problem lies in the combination of a relatively small number of construction firms in the Bureau of Labor Statistics' sample of business establishments -- on which the payroll estimates are based -- and the extensive use of undocumented workers in the industry.

``It may be that these payrolls are declining quickly, but the decline may be most pronounced among illegal immigrants that were not officially counted in the payroll data,'' he said.

Stone, like most analysts, normally regards the payroll figures as a more reliable guide to the state of the labor market than the data from the BLS household survey, from which the unemployment rate is derived. At the moment, he's not sure that's true.

``It is noteworthy that household employment, when adjusted for differences in definition with payroll employment, has slowed in a fairly pronounced fashion over the past six months, averaging only 45,000 a month, in sharp contrast to the payroll series, which has averaged 145,000 a month,'' Stone said.

Slower Growth

The slower increase of jobs in the household survey hasn't caused the unemployment rate to rise because growth of the labor force also has slowed. There are a number of possible explanations for that, of course, including that jobs aren't quite as easy to come by as a 4.5 percent unemployment rate would normally indicate.

Put all this together and there are some major analytical uncertainties facing anyone, including Fed Chairman Ben S. Bernanke and his colleagues as they try to figure out where the economy is headed.

He will provide an update on the collective forecast of all the Fed policymakers when he gives his semi-annual monetary policy report to the House Financial Services Committee on July 18.

(John M. Berry is a Bloomberg News columnist. The opinions expressed are his own.)

To contact the writer of this column: John M. Berry in Washington at berry5@bloomberg.net

Last Updated: July 9, 2007 00:27 EDT