On the effects of immigration on African American migration to the North, there is an article by William J. Collins, "When the Tide Turned: Immigration and the Delay of the Great Black Migration", The Journal of Economic History, Vol. 57, No. 3 (Sep., 1997), pp. 607-632.
https://www.jstor.org/stable/2951192
Here's how I summarized it in soc.history.what-if:
Anyway, Collins notes that Euroepan immigration as a deterrent to black
migration from the South to North has often beeen mentioned, and certainly
seems a plausible hypothesis, but had never really been tested rigorously.
Collins attempts to do this through regression analysis. Some of his
findings:
"Finally, the issue at the heart of this article is the extent to which
European immigrants to the North deterred potential black migrants from
the South. Does a closer look at the data support Brinley Thomas's rough
correlation, and if so, does the magnitude of the relationship suggest that
the prevalence of immigrants delayed the Great Migration? All of the
regressions reported in Table 3 estimate a statistically significant negative
coefficient relating foreign-born immigration and black migration-a strong
confirmation of the immigrant-as-deterrent hypothesis. But are the
coefficients of such a magnitude that they place immigration at the center of
our understanding of black migration to the North?
"The size of the coefficient varies from one specification to another
(especially with respect to the fifth column), and for the following
calculations the coefficient from the second column will be used to size up
the impact of immigration on the magnitude of black migration. In the
hypothetical million-person state, an additional 100,000 foreign-born
migrants over the course of a decade are associated with 8,400 fewer black
migrants, an impact that at first glance might appear small. The impact
appears to be much more substantial if one compares the number of actual
black migrants with the number that might have migrated in the absence of
foreign immigration. For example, supposing this hypothetical state had the
sample's average foreign-born migration rate of 54.88, the coefficient
predicts that the black migration rate would have been 4.60 lower than
would have prevailed without immigration. Given that the average black
migration rate was approximately 8.76, it appears that the size of the black
migrant flow might have been 50 percent larger were it not for labor market
competition from recently arrived foreign immigrants.
"The impact appears even more substantial when considering states that
received huge influxes of foreign-born migrants. For example, between 1900
and 1910 New York received 1,195,000 foreign-born, implying that 100,000
potential black migrants might have been crowded out of the labor market.
In fact only 40,000 black migrants came to New York in this period, and the
regression suggests that this flow might have more than tripled in the
absence of foreign-born immigration.
"Finally, suppose immigration quotas had been established in 1900 at
165,000 immigrants per year; also suppose that all of these immigrants
would have located in the set of northern states employed in this study.
Between 1900 and 1910 the immigration rate would have been 49.87 compared to
the actual rate of 106.85, implying, ceteris paribus, that more than 150,000
more black migrants would have moved north in that decade with earlier
immigration quotas, an enormous addition to the 161,000 who actually did
move. Supposing instead that foreign immigration had been banned altogether
in 1900, then 295,000 more blacks might have migrated than in the free
immigration case. *Indeed, it appears that the Great Migration could have
been greater and occurred earlier had there been controls on foreign
immigration before the 1920s.* [emphasis in original]
"What if foreign immigration had continued unimpeded in the 1920s? The
average foreign-born migration rate to the northern states in this sample
from 1880 to 1920 was 81.61 per thousand population, but the rate in the
1920s was only 38.64. If the rate of 81.61 had prevailed in the 1920s, the
coefficient estimate suggests that about 165,000 fewer blacks would have
migrated to the North than with the foreign migration rate at 38.64. This
would have reduced black migration by about 20 percent. If the 1920s
foreign-born migration rate had achieved the rate that prevailed in the
1900s, then about 260,000 fewer blacks might have moved northward than when
the foreign-born rate was 38.64, reducing the black migration rate by about
30 percent...."
Collins then uses the same type of analysis on individual northern cities, and
again finds a significant negative correlation between European immigration
and black migration. Collins' conclusions are as follows:
"The Great Migration stands as one of the great watersheds in African
American economic history, and the complexity of its causes and consequences
merits study from a variety of perspectives. This particular study focuses on
northern labor markets and attempts to account for the dispersion of black
migration rates across space and over time using a straightforward empirical
strategy. Of special interest is the econometric evaluation of the immigrant-
as-deterrent hypothesis that until now has stood as a plausible though
unexplored assertion in the Great Migration literature. From the analysis of
state and city level data, it is clear that on average blacks moved at times
and to places where foreign-born immigrants were less prevalent. In fact, the
size of the estimated coefficients suggests that the Great Migration would
have gotten underway earlier than it did if strict immigration controls had
been adopted earlier. Given the political environment of turn-of-century
America the adoption of such a counter-factual policy is not at all far-
fetched, and the ramifications of an earlier Great Migration for black
economic progress in the twentieth century might have been considerable."
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