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If you think looking under the hood is vital when you buy a used car, take it from me: It goes double when you’re reading reports on the economy, and the White House’s new report on the economic effects of President Obama’s Executive Amnesty plan is a vivid reminder why.

One of the most controversial claims made by the President and his supporters is that Executive Amnesty and the broader immigration reform bill passed by the Senate in 2013 would actually raise wages in America and reduce income inequality. These claims have been especially crucial for the politics of immigration reform. How else could liberals, Democrats, and others who profess to champion “the common man” support measures that both logic and economic theory strongly indicate would have the opposite effects, since they will greatly increase the supply of U.S. labor available to employers, especially for jobs requiring relatively modest education and skills?

Despite the best efforts of The Economic Effects of Executive Action on Immigration, however, that’s still a challenge these supposed middle- and working-class advocates haven’t met. The study contends that the President’s decision would increase wages for native-born American workers by 0.1 percent on average over the next decade. In 2014 dollars, that’s $40 – not a king’s ransom, but at least not a decline.

Here’s where the problems start, though. That prediction isn’t based on original research by the White House’s own economists at the Council of Economic Advisors. It’s based largely on the results of a single academic study. And there’s more: This study doesn’t break down the wage effects by education level, as the CEA acknowledges. So the CEA offers no evidence on how evenly distributed – or not – these miniscule economy-wide wage gains might be. Given that less than a third of U.S. workers hold a B.A. or more advanced degree, and given the huge, rising wage premium produced by higher education, that’s a huge omission.

The CEA leaves the matter there. But no one with any common sense needs to, or should. Other Open Borders-friendly analysts have addressed the issue recently, and Jared Bernstein (who has done excellent work on subjects like the impact of offshoring-friendly trade deals on U.S. wages and living standards) sums up their case:

[T]he undocumented workers who will gain temporary legal status are already here, so we’re not talking about increased supply effects. In fact, by entitling them to leave the shadows of the undocumented workforce, their own pay could get a boost, especially as they may now be more mobile across both geography and sectors of the economy. And the pay of those with whom they compete is also helped by this change. If you’re competing with someone who can be exploited by dint of their undocumented status, that hurts you too.

Sounds great – until you start thinking beyond the textbook. For Executive Amnesty is unlikely to leave the supply of new foreign-born labor frozen at today’s levels. First, deportation relief is not extended to all illegal immigrants, so those left out will still be able to undercut the wages both of illegal workers who are brought out of the shadows and of native-born workers who compete with them. In principle, effective enforcement measures, like harsh sanctions on the business owners that hire them, takes care of this problem.  But when has Washington ever taken this approach seriously?

Does this mean that the main shortcoming of Executive Amnesty is its failure to include all illegal immigrants? Only if you forget the magnet issue and the aims of Mr. Obama and his supporters. After all, as the President has just reminded, the Senate-backed immigration reform bill would protect most of the rest of the illegal population from deportation. Although support in the incoming Senate arguably will be weaker, over the longer-term, as so many political analysts believe, the American electorate seems to be changing in ways that boost the pro-reform vote.  Therefore, a more lenient immigration policy is at least a distinct possibility.

As a result, powerful incentives still exist for foreigners to enter the United States illegally, in full confidence that they’ll find work as well as schooling and other government benefits for their children, as well as that, sooner or later, they’ll receive amnesty whether from new executive orders or from legislation. So there’s every reason to expect that the illegal population will keep growing – unless you believe in the fairy tale that the border will become much more secure.

In fact, as the CEA inadvertently makes clear, the Congressional Budget Office has already provided evidence that the reformers’ version of immigration policy will reduce, not raise wages, at least for the next decade. According to the CBO, implementation of the Senate reform bill will depress average wages on average for newcomers and native-born workers alike through 2024, and start raising them thereafter. The nearer-term wage decline is not big – 0.1 percent – and CBO emphasizes that all the gains will accrue to the native-born.

Interestingly, although CBO doesn’t break down the effects according to educational attainment, it does provide a breakdown by skill levels. Its findings: “The legislation would particularly increase the number of workers with lower or higher skills but would have less effect on the number of workers with average skills. As a result, the wages of lower- and higher-skilled workers would tend to be pushed downward slightly (by less than ½ percent) relative to the wages of workers with average skills.”

So the foreseen effects of greater immigration inflows again are not large, but at least for America’s native-born poor, they’re harmful. But the CBO doesn’t seem to account adequately for the magnet effect, either. I could discuss additional problems with its findings, like the reliance on estimates of overall economic growth and productivity growth that entail enormous uncertainties – to put it kindly.

Yet one final reason for skepticism is even stronger: The same kinds of models and other methodologies that are generating only modest wage effects from greater immigration flows also long showed few if any wage effects from the kinds of trade expansion policies pursued by Washington for the past twenty years. Now this conventional wisdom, which of course helped fuel and legitimate these policies is changing substantially – though arguably too late to undo the decisive damage. Benign projections of conventional immigration reform’s economic impact serve powerful agendas, too – both on the Left and on the Right. The difference is that there’s still a chance to save the economy from its effects.