Heterogeneous Firms and Substitution by Tasks: the Productivity Effect of Migrants

Economic debate about the consequences of immigration in Germany has largely focused on the wage effects for natives at an aggregate level. Especially the role of imperfect substitutability of migrants and natives gained importance. A new topic is to focus on the firm level by estimating production functions in an equilibrium framework to gain information about substitution elasticity. Additionally recent literature emphasizes the impact of the task dimension beside the qualification of workers: migrants are heavily concentrated in agglomerations and work in different jobs than natives do. This gives an explanation on the micro level for imperfect substitutability. The task approach is thus a key to understand imperfect substitution on the firm level. Our contribution in this article is manifold: we examine the effects of the relative (dis-)advantages in performing certain tasks and draw implications on the labor market outcomes. Using this we construct a simple model with a monopolistic competition framework a la Dixit-Stiglitz considering heterogeneous firms with different productivity levels and two types of jobs for migrants and natives. Firms differ in the ability to employ migrants which gives rise to wage differences between natives and migrants. This wage differences lead to wage cost advantages for firms. In the long run equilibrium only those firms with survive in the market which have a sufficiently high productivity level or can compensate their lower productivity level by wage cost advantages. We show that the increase of productivity might be explained by a higher migrant share. Regional disparities in our model stem from the unequal distribution of migrants. Thus part of the agglomeration advantages can be explained by the empirical stable observation that migrants tend to move to cities. The conclusions of the model are in line with three empirical facts in Germany. Firstly, the average productivity of firms is higher in cities where also the migrant share is higher. Secondly, the wage difference between migrants and natives in a region is increasing in the share of migrants in that region. Thirdly, less productive firms are more likely to employ a higher share of migrants, as wage advantages and productivity acts as a substitute.