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The Pew Research Center is out with its latest estimates of the role played by both immigrants and illegal immigrants in the American job market. So that has enabled me to crunch some reasonably reliable numbers to find out whether illegals-friendly immigration policies like some form of amnesty are, as often claimed, desperately needed if the nation is to avoid a crippling labor shortage.

When I performed this exercise roughly a decade ago, I found that similar claims being made in that period were wildly overblown at best. Why? Because the data showed that real wages in the industries employing the most illegal immigrants were generally stagnant or going down. That’s exactly the opposite of what should happen if economists (and common sense) are right in contending that when anything – including workers – is scarce relative to demand, the price of that thing should go up.

And the verdict for 2014 – the year for which Pew’s latest statistics come? Labor shortage claims are still mainly hokum.

According to Pew, the sectors where illegal aliens make up the greatest share of workers are (in order of the total immigrant share of their workforces: private households; textile and apparel manufacturing; agriculture; accommodation; food manufacturing; computer and electronics manufacturing; personal and laundry services; administrative and support services; construction, and miscellaneous manufacturing.

Are there many signs of the kinds of labor market tightness that should be sending pay soaring out of sight? I couldn’t find data for domestic workers, but here are the current-dollar wage figures for the other sectors during the current recovery so far. That means from June, 2009 through February, 2016, except where noted. They cover non-supervisory workers, on the assumption that few illegal aliens are finding managerial jobs in these parts of the economy:

Private sector overall: +17.78 percent

Construction: +15.93 percent

Computer and electronic manufacturing: +12.55 percent

Miscellaneous manufacturing: +16.55 percent

Food manufacturing: +17.31 percent

Textile mill manufacturing: +14.93 percent

Textile products mill manufacturing: +24.76 percent

Apparel manufacturing: +18.05 percent

Administrative and support services (through January): +14.33 percent

Accommodation (through January): +7.56 percent

Personal and laundry services: +21.61 percent

Farm workers: +24.53 percent

I sure don’t see any broad-based wage explosion in these statistics. In only four of the eleven illegal alien-heavy sectors have wages even been rising faster than those in the overall private sector – which hasn’t been terribly fast given that the current recovery is more than seven years old. Two of them, moreover, are in labor-intensive manufacturing industries that have been so decimated by foreign competition for so long that what’s left of them might indeed be facing labor shortages. The reason? Who in his or her right mind would assume they have much of a future in this country?

But what about more recent developments? Can signs of widespread labor shortages be seen in the current stage of the recovery? You be the judge, based on these February (or January, where noted above) year-on-year developments:

Private sector overall: +2.48 percent

Construction: +3.38 percent

Computer and electronic manufacturing: +2.73 percent

Miscellaneous manufacturing: +3.13 percent

Food manufacturing: +3.70 percent

Textile mill manufacturing: -1.07 percent

Textile products mill manufacturing: +8.04 percent

Apparel manufacturing: -3.02 percent

Administrative and support services (through January): +4.13 percent

Accommodation (through January): +1.50 percent

Personal and laundry services: +3.88 percent

Farm workers: +3.00 percent

Bottom line: The illegal immigrant-heavy sectors have seen some wage acceleration since last year. But two of the manufacturing sectors where wages had separated themselves from the pack are now experiencing wage decline. And it’s important to keep two other considerations in mind for many of the rest: First, their wages have been boosted artificially during this period by numerous sizable minimum wage increases in major states and localities. That’s not to say that such hikes per se are undesirable in any way. Indeed, I personally don’t see any reason why they shouldn’t be much more tightly linked to inflation nationwide than they’ve been till now.

When it comes to the labor shortage claims, however, they greatly distort the picture – because they represent wage developments based not on the labor supply and demand situation in these parts of the economy, but on political decisions.

Second, if the relatively strong wage increases that have taken place continue much longer, expect the sectors in question to start automating fast — or faster. That’s been a major feature of American economic history. And if economists are right, the resulting technological progress will wind up simply being delayed (perhaps partly accounting for the economy’s recent sluggish productivity growth?), rather than stopped, by the continuing easy availability of illegal immigrant labor.

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