In “Immigration, search and redistribution: A quantitative assessment of native welfare,” a paper by Battisti et al. published in the August 2018 issue of the Journal of the European Economic Association, the authors inquire about how migration to 20 Organization for Economic Cooperation and Development countries affects the welfare of the countries’ native workers. We raise several concerns regarding the analytical and the empirical parts of the Battisti et al.’s inquiry that bear on this effect. Calibration of a corrected model reveals that our concerns affect measurably the empirical results regarding the impacts on the welfare of native workers of skill-neutral migration and of migration by low-skill workers. A particular concern is that our calibration of a corrected model yields estimates of the tax rate on workers’ wages that are far too high to be considered feasible. We calibrate a version of the corrected model, which involves “reasonable” tax rates on wages and a budget deficit. The results yielded by this counterfactual version lend support to the results of the corrected model regarding the negative impact of skill-neutral migration and of migration by low-skill workers on the welfare of native workers.