I finally finished the paper that addresses the latest Mariel-related brouhaha–the claim that the large drop in the wage of high school dropouts in post-Mariel Miami was spuriously created by a change in the racial composition of the March CPS sample. As I documented in earlier blog posts here and here, not much happens to the results of my Mariel paper when one uses race-adjusted data to look at wage trends in Miami and comparison cities. The new technical paper summarizes much of this evidence, shows that the before-after wage drop remains even if we were to start the analysis in calendar year 1979 (*after* the unexplained change in the racial composition of the survey), compares what happened in Miami to what happened in over 123,000 alternative placebos, and adds even more data/discussion. Put simply, the claim that the post-Mariel drop in Miami’s low-skill wage was spuriously produced is fake news.

I realize that it is the type of fake news that will be accepted unquestioningly by those who are ideologically wedded to–or financially dependent on–the notion that a 20 percent increase in supply does not change prices (at least in the immigration context). But the paper lays out all the facts and even the most cursory look at the actual data demonstrates the inescapable conclusion that something indeed did happen to low-skill wages in post-Mariel Miami. (All the programs used in the preparation of the paper are here).

One part of the paper is worth discussing more fully now, as it seems to be the direction in which the debate is headed. The point is a bit on the geeky side, but definitely worth thinking about as it shows just how easy it is to torture the data into screaming “PLEASE! STOP! THERE IS NO WAGE EFFECT!” by making what seem to be innocuous assumptions.

In a recent response to my blog posts, Clemens finally estimated the statistical model that corresponds to my analysis and concluded that although he can replicate my regression showing the drop in the “race-adjusted wage,” the ultimate answer depends on just how the race-adjusted wage is calculated. In an important sense, the blog response subtly moves the “goalpost” of the Clemens-Hunt criticism. **It is no longer that the change in the black share of the workforce induced a spurious correlation that led to lower wages in post-Mariel Miami; just look at the figures in my paper or the regression evidence and it’s obvious that this particular argument is just plain wrong. It is now instead that the measured wage impact of Mariel could be zero if we calculated the race-adjusted wage in a different way.**

Let me explain what a **race-adjusted wage** is. It is the wage we would see a black worker earn if his employer suddenly became color-blind and saw him as just another white worker. The trend in the race-adjusted wage would then show what happened to Miami’s low-skill wage in a world where race was no longer relevant.

Obviously, the race-adjusted wage is not available in survey data. It needs to be calculated somehow, usually by estimating a regression model. And this is where all kinds of tricks can be played to get different answers. So I cooked up a trivial numerical example in my new paper to get the point across in the simplest way possible.

I’m going to tell a hypothetical tale of two cities, Miami and New York. In this tale, New York did not receive any immigrants, but Miami did. The table shows the average wage of black and white low-skill workers in the two cities before and after the supply shock. Panel A at the top gives the unadjusted wage data–the data that would be available in the CPS. By construction, immigration had a much larger impact on black workers in Miami, reducing their wage from $7 to $4, while the wage of white workers fell by only $1, from $10 to $9.

Panel B shows the race-adjusted wage in each city. As I said earlier, we need to calculate that wage, and to do so we are going to use all the low-skill wage data available across cities, across race groups, and over time. We would then look at the available data in the top panel of the table, see that there is a $3 racial wage gap among low-skill workers in Miami prior to the supply shock, and use that information to infer that the race-adjusted wage of a black worker in Miami in that period should be $10. After the supply shock, we would see a $5 racial wage gap, and use that information to infer that the race-adjusted wage of a black worker in Miami should be $9. (In fancy econometrics jargon, we just ran a fully interactive regression model, allowing wages to fully vary by city × education × race × year).

Suppose that half of Miami’s workforce is black. The average race-adjusted wage in Miami fell only from $10 to $9, or 10 percent. In fact, the average wage in Miami fell from $8.50 to $6.50, or nearly a 25 percent drop. The drop in Miami’s race-adjusted wage is not all that big for a simple reason: If the calculation of the race-adjusted wage ignores that the racial wage gap in Miami might have increased *because* of immigration we are going to greatly understate the impact of immigration.

Panel C at the bottom of the table shows what would happen if we used an alternative calculation of the race-adjusted wage that does not throw the baby out with the bathwater. Suppose that Miami is a very small city relative to New York. We are now going to use *national* data on how the racial wage gap for low-skill workers changed over time to calculate the race-adjusted wage. We would again look at the actual data in the top panel and see that the average black worker nationwide earns $3 less than the average white worker both before and after the supply shock. This would imply a race-adjusted post-migration wage for black workers in Miami of $6 (or $3 less than what whites get). If we use this approach, the average race-adjusted wage in Miami fell from $10 to $7.50, or 25 percent. (In econometrics jargon, we ran a regression that allows wages to vary by education × race × year).

In short, the mechanics of calculating the race-adjusted wage matter a lot. But is it proper to calculate the race-adjusted wage by netting out the change in the racial wage gap in Miami when that change could have been caused by immigration? It seems plausible that Mariel affected the wage of black and white workers in Miami differently. There were substantial differences in the jobs the two groups held, in the occupations they entered, and in the industries that employed them. The *Marielitos* obviously penetrated some sectors more than others, affecting the magnitude of the racial wage gap for a particular education group in Miami relative to other cities. A “race-adjusted wage” that nets out this differential impact removes much of the effect that immigration might have had on the local labor market. As a result, it would not be surprising if the measured impact of immigration became much smaller, perhaps near zero.

The two panels of the table below shows how the bias shows up in real-world data when I calculate the actual wage impact of the *Marielitos* using alternative calculations of the race-adjusted wage. The top panel uses the fully interactive model, netting out the fact that the racial wage gap for high school dropouts in Miami changed over time (perhaps *because* of Mariel). As in my cooked-example, the measured wage effects are small, though some are still statistically significant in the ORG.

The bottom panel instead allows for the racial wage gap at a particular point in time to vary across age groups, across education groups, and across cities–*but does not net out that the racial wage gap for high school dropouts in a particular city (like Miami) might have changed over time.* Note that the wage effects of the Mariel supply shock are strongly negative and statistically significant.

So the question now becomes: do we know anything about whether immigration into a particular city affects the low-skill racial wage gap in that city? In other words, does immigration affect the wages of low-skill blacks and low-skill whites differently? Amazingly enough, only a handful of papers estimate the wage impact of immigration separately for black and white workers. And out of that handful, as far as I know, there is only one paper that estimates the impact for *low-skill* blacks and whites. Ironically, this happens to be the classic paper by Joe Altonji and David Card. This is the relevant page from the Altonji-Card study (click to enlarge, and the relevant numbers are the ones furthest to the right in the bottom row of each table):

It sure seems as if the negative impact of immigration on the low-skill black wage is about twice as large as the impact on the low-skill white wage, making my numerical example quite relevant. In fact, this very large estimate of the impact of immigration on low-skill blacks was the one specifically cited in Table 5-2 of the recent National Academy of Sciences report.

I know that this geeky discussion may not be particularly gripping to those who just want to know *the* answer (especially if one is looking for a different answer). But the statistical exercise used to compute the race-adjusted wage in a city at a point in time should not follow blindly from a kitchen-sink approach to regressions. Careful thought must be given to *why* racial wage differences might arise, and how the time trend of those racial differences in a particular city might be affected by immigration. It is entirely possible (and much too easy for those tempted to do so) to hide away the wage impact of Mariel by using the wrong conceptual approach.