The most subversive sentence I’ve ever written

In a paper on the “selection” of Mexican immigrants where we find that Mexican immigrants to the US are about the same as non-migrant Mexicans in terms of observable skills like education and age but, as it turns out, they have lower unobserved skills:

It may be the case that because many border crossings occur without documentation, there may be selection on certain unobserved characteristics (e.g. risk-taking, underestimating dangers, low respect for authority) that may have a negative correlation with productivity.

Man, I feel like running down the street with a black bandanna covering my face, breaking windows and burning cars!

More on immigration

Ok. I can’t wait anymore. Someday this paper (co-written with my advisor) will show up here. The paper reviews trends in immigration in California and summarizes the findings of one of Peri’s working papers. In that more technical paper, Peri found a clever way to control for all three confounding effects I’ve discussed before that can contaminate estimates of the effects of immigration on native employment outcomes. Consistent with most of the literature, he finds no negative effects of immigration in this respect.

Also, here’s Peri talking about immigration:

Immigrants and native wages

I know I’ve had you riveted with the literature review in the last few posts about the effect of immigrants on native employment outcomes (i.e. wages and employment levels). I thought it was important, though, to point out that academic economists don’t really contest the existence of this zero correlation. That said, we have learned a lot by trying to poke holes in the landmark “experimental” studies summarized here, here and here.

While those famous papers dealt with important measurement issues, we’ve also learned that experimental studies are inadequate to deal with at least two other factors, indicated by economic theory, that may be biasing the simple correlation one way or another.

First, and this is the measurement issue dealt with by the experimental studies, we want to be sure that there is not something that makes a particular area or job a more attractive place to work causing both foreigners and natives to migrate to that area or job. If such a third factor existed, it would hide the effect of immigrants on natives. Suppose, for example, there was a technological advance making a particular job more lucrative (e.g. an acceleration in computational power makes the wages of computer programmers go up) or suppose there was a surge in demand for a job (e.g. nurses are in more demand as the population ages). Because immigrants and natives would be attracted to these jobs, the increase in immigration would be positively correlated with the increase in wages and the increase in native employment in these jobs. These omitted variables, to use economic jargon, might mask the potentially negative effect of immigration on wages.

Second, natives relocating to other areas as a result of immigration can spread out any potential negative consequences of immigration among a wider population of natives, making those bad effects hard to detect. For example, when immigrants move to California, natives may move to other states. These spillover effects would cause the labor supply in those other states to increase putting pressure on wages there, too.

Third, we need to take into account the total effect of immigration. Immigrants with a particular set of skills will compete with natives with those same skills and decrease their wages, but they will make natives with complimentary skills more productive, increasing those natives’ wages. An immigrant that puts up drywall on a construction site, for example, competes with native drywall installers, but they compliment the native foreman who may be able to spend more time managing the construction site rather than helping put drywall up. Furthermore, when we properly account for all these indirect effects immigrants have on natives, we will want to pay special attention to the possibility that natives and immigrants, even those with the same skills, do not perfectly compete with each other. To return to the example: among drywall installers, natives may specialize in particular tasks like reading blueprints or leading work teams while immigrants specialize in hauling materials or the actual installation. To use the economic jargon again, we need to check to see if natives and immigrants are perfect substitutes or not.

In the last few years, researchers have shown that when all of these factors are taken into account, the surprising result is that immigrants don’t seem to have a negative effect on native wages or employment levels. In fact, its likely that immigrants have even been a net positive for natives, a result that this paper has replicated.

So there is not much debate about this non-correlation. Academic economists have moved on to try to explain why no correlation exists.

The total effect of immigration is positive

Last time, I said that nobody really cares about the direct or partial effect of immigration on natives. This isn’t strictly true. If immigration policy were changed to only allow immigrants of a particular skill-type to come into the country, this would probably upset the people of that skill-type. Each individual immigrant hurts the employment opportunities of natives with the same skills as the immigrant. Immigrants, in total though, can have a positive impact on natives because immigrants have different types of skills. People, immigrant or not, that have different skills tend to compliment each other in the production process. They make each other more efficient.

Perhaps this is the source of the assumption of substitution I asked about before: we tend to imagine groups of people as being homogeneous masses, not individuals with a variety of skills. If immigrants were all the same, with the same skills, and natives all the same, with the same skills, and if those skills perfectly overlapped, then immigrants would compete directly with natives and hurt their employment opportunities. In reality, though, a random immigrant has different skills than a random native. Because they have different sets of skills, this random pair do not compete with each other in the labor market. In fact, on average, a random pairing of natives and immigrants would be more productive than the sum of its parts.

Even in the extreme case where all immigrants had exactly the same skills, this would only hurt the group of natives that had those skills. Everyone else would benefit from having co-workers with complimentary skill sets. Its a common belief that all recent immigrates have been very low educated. This, it is imagined, would hurt very low educated natives. The distribution of education among recent immigrants, however, has been U-shaped. There have been many very low educated immigrants and many very highly educated immigrants.

Even among natives with no high school degree, the pain of immigration has not been felt. There are two reasons for this. First, because it turns out that workers with no high school degree are strong competitors with those with a high school degree in the labor market, very low educated immigrants compete with a much bigger pool of natives, spreading out the pain of direct competition. Second, the pool of low educated natives benefit from the large group of highly educated immigrants as highly educated workers make the low educated much more productive. In other words, the negative effects of low educated immigrants on low educated natives are small and spread out, but the gains from high educated immigrants are acute. On net, the gains swamp the losses and even low educated natives benefit from immigration.

Capital accumulation also plays a key role. Like the Econ 101 growth theory would tell us, immigration, by increasing the labor supply, increases the return to capital. This will give investors an incentive to invest more and the capital stock will grow. Because capital makes labor more efficient, it would increase wages until they returned to their long-run value ((This means when capital fully adjusts, the average wage effect of immigration is zero. Different groups might be affected differently, but its a wash on net. It turns out all groups of natives benefit even if slightly from immigration. The only group that is hurt by new immigration is old immigrants.)). This undoes some of the negative direct effects of immigration, too.

All of these empirical claims were verified in a paper by Ottaviano and Peri just a couple of years ago ((A good discussion of that paper can be found here. The author reproduces many of Ottaviano and Peri’s findings using a slightly different data set.)). A random immigrant makes a random native more productive because the native is unlikely to have the same skills as the immigrant and because natives and immigrants, even if they have the same education and experience, are not perfect substitutes. Next time we’ll see that this is because immigrants specialize in different tasks than natives and because they induce innovations that complement their skills.

Partial derivatives are not total derivatives

When Borjas says, “immigration lowers the wage of competing workers,” he is only looking at the direct effect of immigrants on similarly skilled natives controlling for spillover effects. Immigrants affect natives in other indirect ways.

Please indulge my equation writing. How else am I to demonstrate my intellectual superiority make my point as concretely as possible?

Wages for a particular worker in a particular skill group are w. Those wages are affected by the number labor market competitors of that worker, Comp. These are the workers with exactly the same skills as the worker. But wages are also affected by other types of workers. For example, if the number of total workers, Lab, goes up it would probably increase wages for the worker because other workers on average make him more productive. Also, an increase in the number of workers with the same education but not the same experience, Educ, or workers with the same level of experience but different educations, Exp, may increase or decrease his wages. Finally, capital, Cap, makes the worker more productive.

(In general, there’s a ton more of these cross-labor group effects. Each education group, for example, may have a different impact on each of the other education groups. Its possible that high school workers and non-degreed workers are competitors but high school workers and college workers make each other more productive. Also, there may be skill-specific capital and so there may be additional cross-labor-capital group terms.)

Borjas’ skill group-based analysis is only estimating A. It is only estimating the direct effect of immigrants on natives in their own skill group. He ignores all the other effects of immigration and almost without exception these cross-effects are positive. The “area” studies, like Card’s Mariel boatlift study and the myriad cross-section studies, suffer similar problems. While all of them ignore spillover effects, some are estimating some terms in the equation but ignoring others. The difference between those studies (and perhaps the source of the variation in their estimates of the effect of immigration on wages) is in which subset of the terms they estimate ((It would be neat to see this hypothesis tested formally. Can we get the observed variation in estimates by adding and removing various fixed effects?)).

The hitch is that nobody cares about A. Analysts, policy makers and lay people care about the total effect of immigration on natives. To get the total effect, we need estimates of A, B, C, etc; estimates of the relevant cross-effects.

George Borjas and the national approach

It has taken me too long to introduce the hero of this story. Borjas has had a series of papers, books and editorials since the mid-80’s that have each challenged the consensus economist’s view on immigration in support of the popular view. His work in the late 80’s uncovered the pattern of a secular decline in the quality of immigrants (in terms of educational attainment, work experience and unobserved skills) since WWII, a trend that is common sense today. He also introduced the idea of self-selection of immigrants and gave conditions for when we’d expect immigrants to be higher or lower quality. In the nineties, while setting the ground work for the work I’ll describe below, he started the conversation on the costs and benefits of immigration, sitting on a panel of the National Academy of Sciences evaluating the economic impact of immigration. He wrote papers encouraging researchers and policy makers to balance the fiscal costs of immigrants (welfare, schooling, etc) against any potential production gains.

In his 2003 paper called “The labor demand curve is downward sloping,” Borjas challenged the consensus that immigration has a zero effect on native employment outcomes. He worried that studies comparing regions did not properly account for spillover effects from trade, capital movements and labor mobility. The problem with goods, capital and labor movements is that they all tend to equalize wages across regions. This means that when you compare regions that have had more or less immigration, you won’t be able to find a difference in wages even as everyone’s wages have gone down.

He suggested, instead, to compare groups that do not admit mobility. Specifically, he looked at the effect of immigration across skill groups where skill is defined by a combination of education and years of work experience. Intranational trade in goods doesn’t operate in this context. Add to that the fact that international trade is probably not important here and the trade channel for spillovers is shut down. Also, workers can only increase work experience one year at a time (thus they can’t decrease it or move to a level of experience more than one year ahead of their own), so its extremely hard for them to change it to respond to incentives and, in the short run, workers can’t change their education. These things suggest the labor mobility channel is shut down, too. Finally, if you assume, as Borjas does, that capital is not skill specific (or at least to the degree it is, it has a small spillover effect) then there’s no role for capital movement to cause spillover effects.

Below I reproduce his suggestion. On the x-axis is the change in the proportion of immigrants from 1990 to 2000 and the y-axis is the change in native wages. Each dot is a education-experience group ((Actually, I cheated and used age instead of work experience which gives the same results but is much easier to calculate.)).
skill_groups
The slope here is negative (-0.35) and quarter standard deviation more negative than the mean found by Longhi, Nijkamp and Poot. This result, which controls for spillover effects, confirms what Borjas says: “immigration lowers the wage of competing workers”.

There are three ways to critique these findings. First, attack the premise. If spillover effects are creating the zero correlation at the local level, we should be able to detect them. We should see native workers fleeing areas of high immigration or we should see industries in high immigration areas reshuffle to take advantage of the skills of immigrants, as trade theory would predict. David Card took up both of these challenges. In 2001, he wrote a paper finding no native flight and in 2007 he wrote a paper finding that least one type of trade spillover doesn’t seem to be emperically important ((That said, there is an opportunity for us to look for other ways trade affects native workers. For example, perhaps immigrants produce new varieties of goods. Much attention in trade theory these days — someone got a Noble for his work on this — is on the trade effects of new varieties. This wouldn’t be a spillover channel, I don’t think there’s factor price equalization in New Trade models, as much as a possible explanation for native/immigrant complementarity, which I haven’t talked about yet. I’m no trade theorist but perhaps the production based models used by Ottaviano and Peri, e.g., are isomorphic to the love of variety trade models. So where those authors see complementarity in production, trade models would see love of new immigrant produced varieties. We’d need micro evidence on immigrant entrepreneurship to differentiate to see which of these models best explains the evidence.)). If spillovers are a problem, they don’t appear to work through the trade and labor mobility channels.

Second, attack the assumption that capital isn’t skill specific or that international trade doesn’t matter. To be honest, I haven’t found any work that does either of these things…

So moving right along. Third, point out that there are much more important indirect effects of immigration than spillover effects. This will be the focus of my next post.

For those of us that believe immigration has a net positive benefit on society, Borjas is the perfect enemy ((He’s also a model academic. Besides his volumes of academic papers, he’s written a well-used textbook, several popular books on immigration and dozens of editorials on the subject)). He has applied honest, fair and constant pressure on our sure beliefs about immigration. His challenges have inspired reams of rebuttals; reams that could not otherwise have been used in support of immigration.

Slam dunk?

You’d think the question of whether there is an effect of immigration on native employment opportunities would be an open and shut case. Carefully comparing nations, states, cities and occupations using cross-sectional and quasi-experimental (here, here and here) data has shown there to be no correlation. Nations, states, cities and occupations with higher proportions of immigrants, all else equal, do not have lower native wages.

Houston was one of of the cities Card compared to Miami to see if immigrants had an effect on wages after the Mariel boatlift. At any given moment, there are quite a few investors in Houston that are willing to invest their money somewhere besides Houston. Miami perhaps. If those investors catch wind that several tens of thousands of low-skill workers are going to flood the Miami labor force, they may decide to invest in factories in Miami to take advantage of this new labor supply. Or they may invest in service businesses there to service a new batch of customers. Perhaps some less efficient businesses in Miami, who would have otherwise gone out of business, get new injections of capital. In any case, because capital is mobile, it flows to Miami in short order. What would the impact of this capital mobility be on the Houston labor market and so what would its impact be on what Card saw?

Machines make workers more productive. If you take machines away, workers become less productive. By our normal assumption that productivity equals wages, this means that when capital leaves Houston and goes to Miami, wages in Houston go down. Assume, too, that through the mechanisms of the simple supply and demand story, the Mariels decrease native wages in Miami. So natives have two effects on natives. They directly reduce wages in Miami and they indirectly, through induced capital flows, reduce wages in Houston.

Now Card comes along and compares wage changes between Houston and Miami. He simply subtracts the change in Houston wages before and after the boatlift from the change in Miami wages. He gets a zero and concludes the Mariels had no effect. But that is wrong. He is wrong because he assumes there is no indirect effect of immigrants on native wages.

Capital moves from nation to nation, state to state, city to city and even occupation to occupation relatively easily. Goods move relatively easily too across political borders. Trade, then, is another channel for immigrants to have an indirect effect on native wages because changing trade patterns change the patterns of derived demand for labor. Textile companies in Miami, for example, may find that their production process is cheaper. This reallocates resources towards textile companies in Miami and, because there’s now less demand for Houston produced textiles, away from textile companies in Houston. Textile workers in Houston see a reduction in their wages. The same effect is at play for workers in general (relative to capital) and so trade can cause wages in Houston to decline. Trade is another source of indirect costs of immigration for native workers.

Finally, labor is mobile too, at least within a country’s borders. Like capital mobility, labor movement — geographic or otherwise — can result in equalization of wages across regions and even occupations. Natives in Miami, on the realization of the horde of immigrants thundering upon them from Cuba, may have just lost hope, packed up and moved to other cities. Houston perhaps. Then the increase in labor supply induced by the new Cuban immigrants would seep throughout the country, rising wherever forlorn natives chose to resettle. At the national level, then, analysts would see an effect of immigrants but at the local level no effect could be detected.

And all of the studies we’ve looked at have assumed no indirect effects of immigration. The zero effects found by those studies, then, become negative when indirect effects are added in. Borjas, in his 2003 paper, suggest the only way to account for indirect effects is by looking at relatively closed markets; to look at the nation as a whole.

So its not a slam dunk case. Economics intervenes. People respond to incentives.

A little better

Here’s the cross-state plot of the effect of immigrants on native wages:
diffed
This time you’ll notice that I plotted the changes in the proportion of immigrants against the change in wages (these are changes from the 1990 to 2000 censuses). In effect, I’m controlling for fixed features of states. This makes the effect size (a slope of about 0.25 and statistically insignificant) a little closer to the average effect size reported by Longhi, Nijkamp and Poot.

Non-experimental evidence

Angus Deaton recently said that all the attention that natural (and actual) experiments are getting is over blown. He claims experimental data has no special status in a hierarchy of evidence. I agree to the extent that I don’t think we should favor one form of evidence to the exclusion of other types of evidence ((I tenured member of the Cult of Identification told me once that she wouldn’t write a paper about a topic unless there was a clear source of exogenous variation. She proudly told me that she hadn’t used an instrumental variable in years.)). Evidence is evidence.

A readily available form of evidence about the relationship between native employment opportunities and immigration is cross-section data ((In applied micro seminars, you often hear Cult members hiss something to the effect, “But those estimates are from cross-sectional data”. With grimaces around the table at the mention of the taint.)). These data describe various geographical regions or worker skill groups. For each region or skill group, the analysts assigns average wages (or other employment outcome) and the percentage of the group that is immigrants. Then the analyst checks to see if there’s a correlation among the groups between wages and the number of immigrants.

As you can imagine, there’s a lot for the interested analyst to play with. Every country has its own data sources. You can change the definition of skill group. You can look at larger geographic regions like states or smaller ones like cities. And, like always, you can choose from the palette of statistical techniques to calculate your estimated correlation and effect size. Longhi, Nijkamp and Poot did a meta-analysis of 18 papers that reported 348 estimates of this correlation.

As a quick demonstration of what these papers look like, I’ve downloaded some Census 2000 data from IPUMS USA. For each state, I calculated the percent of workers that are foreign born and the average wage for native workers. Here’s the plot:
raw
I’ve drawn the regression line. Surprisingly, the line has an upward slope, suggesting a positive correlation. The slope of the line is about 1.5.

One thing that’s wrong with this plot, besides the fact that I haven’t controlled for a bunch of obvious things, is that this simple correlation conflates the impact of immigration on native wages with the shared economic incentives of natives and immigrants to move to states that have positive wage growth. Both immigrants and natives will want to move to states that have good wage prospects; they select themselves, to use the jargon. We really only care about the first thing, the impact of immigrants on natives, and so we’d like to wash this correlation to get the stain of “selection” out.

A neat regularity among immigrants is that they tend to move to regions where previous immigrants had already called home. We’ll leave it to sociologists to tell us why this might be the case and for the moment just exploit this fact for our statistical purposes. We can predict the percentage of immigrants in a state in the year 2000 by looking at the percentage of immigrants in that state several years before. Here’s a plot:
first_stage

The red line is the regression line and the black line is the 45 degree line. As you can see, the percentage of immigrants has uniformly increased in those 40 years, but the red line is positively sloped and the dots cluster pretty well around the regression line. The immigrate ratios in 2000 are predicted pretty well by their ratios in 1960(!).

So what? Well, suppose the percentage of immigrants in a state does not have an impact on the relative wage prospects in that state 40 years later. The prediction of the year 2000 immigration ratios using the red line, then, should be unrelated to the wage prospects for immigrants (and natives) in that year. This prediction is just the detergent we needed to get rid of the stain of selection. Basically, we’re taking the variation of immigrant ratios due to selection out and only looking at the variation due to immigrant clustering. Here’s a plot of native wages versus predicted year 2000 immigrant ratios:
second_stage
The slope on the regression line is 1.8. That this slope is close to the slope of the one where I didn’t correct for selection suggests that selection isn’t that big of a deal.

While its size is a bit big and so makes me think I did something wrong, the sign of the slope I’ve estimated isn’t surprising. Longhi, Nijkamp and Poot found that almost as many estimates of the effect of immigration on native wages are positive as negative. Here’s their figure 1 which shows the distribution of estimates across analyses:
lnp_fig1
The estimates seem to cluster around zero. My estimates are 1.5 standard deviations away from the mean; not too bad for a quick and dirty analysis!

So even the non-experimental evidence suggests immigrants have little impact on native wages.

Even more zeros

There’s more experimental-like evidence that immigrants have little or no negative effect on native employment opportunities, if you need it.

In 1962, 900,000 pied-noirs repatriated to France after fleeing Algeria following their loss in the country’s war of independence. These repatriates settled in the warmer departments of France with climates more similar to their former home country. And as evidence that this was an exogenous shock to the labor force, they tended to settle in those departments with the higher unemployment and lower wages.

This exogenous shock to the French labor force that increased the number of workers by 1.7% was studied by Jennifer Hunt in her 1992 paper. She found a small but significantly negative effects on native unemployment six years after the mass repatriation. However, she found no effect on native participation rates. Her data on wages is a bit of a mess, but with what she had she found at most a small negative effect ((She worries that given her data limitations, she’s not able to properly control for the fact that the repatriates happened to have chosen to migrate to departments that were having bad economic outcomes unrelated to the mass migration. Interestingly, the migrants didn’t seem to have an effect on internal migration patterns, i.e. their presence didn’t discourage the native French from migrating to departments heavily populated by the new immigrants.))

Another crumbling empire provides us with another immigration experiment: the returnados from Angola and Mozambique in the mid-1970s increased Portugal’s work force by 10%. In a study design similar to Card’s Mariel paper, Carrington and Delima find the Europe-wide recession of those years swamps out any effect the the immigrants might have had.