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.