to these estimates, labor market integration takes more time for refugees than for migrants. After 9–10 years, employment rates of refugees are 4 percentage points lower than those of migrants and this difference persists in the long run.

These integration profiles differ slightly from the (average) profile estimated by Fasani et al. (2020a, Figure 3) for 20 European countries (including Switzerland). The increase in employment rates seems to be more rapid in Switzerland since long-run levels are reached after 10 years in Switzerland, compared to 15 years in the 20 European countries. On the other hand, in Switzerland refugees never quite attain the same employment rates as migrants in the long run whereas this seems to be the case in other European countries according to the results in Fasani et al. (2020a), although this difference might not be statistically significant. If we compare the trajectories in Switzerland with those estimated by Bratsberg et al. (2014, Table 2) using comparable administrative data for Sweden, the long-run outcome in terms of employment rates for refugees (relative to natives) does not seem to be worse in Switzerland.

# **Selection and truncation**

Before turning to results by gender, we address two issues related to selection and truncation of our sample. First, many refugees leave Switzerland during the period of observation, either voluntarily or because all legal possibilities to remain in Switzerland have been exhausted. A problem of selective outmigration arises if out-migration and employment probabilities are correlated. Second, individuals in our panel are observed over different time spans, which implies that the variable _Years since migration_ is truncated in our sample. Before we discuss these issues further, it is worth asking when one should correct for selective out-migration. A policy maker who cares about the cost of social assistance and unemployment benefits paid to refugees would be interested in integration profiles of refugees without correcting for selective out-migration (Dustmann and Görlach 2016). Hence, the results discussed above are relevant in such a policy context. However, selective out-migration is of interest in the perspective of a more complete economic model that distinguishes between emigration behavior and the determination of employment in the labor market.

To check if selective out-migration plays a role in our context, we re-estimate equation (1) using individual fixed effects. This yields consistent estimates if selection depends on time-invariant unobservables.<sup>32</sup> The drawback of using individual fixed effects is that the vertical position of the integration profile is not identified in the regression (i.e. all coefficients of the integration profile are identified up to an additive constant). In other words, it is possible to compare the “speed” of integration but not the “level”. When comparing the estimates with individual fixed effects to those in Tables 3 and A.4, we can conclude that selective out-migration has a discernible but small influence on our results. On the one hand, the differences between the integration speeds that can be calculated from the estimates reported in these two tables and those obtained using individual fixed effects are small.<sup>33</sup> On the other hand, the speed of refugees’ labor market integration is slightly overestimated when comparing them to non-EU migrants in Table A.4. This seems to indicate that the probabilities of out-migration and employment are negatively correlated for refugees and/or positively correlated for non-EU migrants.

Now turn to the issue of truncation. If we consider the sample used to compare refugees with natives, the variable _Years since migration_ is truncated below a certain value for refugees arrived before 2010, and above a certain value for those arrived after 2000. Figure 6 shows clearly how the variable _Years since migration_ is truncated for different arrival cohorts. We already mentioned one implication of this truncation pattern: recently arrived cohorts determine the shape of the integration profile for the early

> 32. See Dustmann and Görlach (2016). If selection depends on time-variant unobservables, these authors propose to model out-migration explicitly in the context of a structural model, an approach which goes beyond the scope of our paper.

> 33. For example, regression (4) in Table 3 finds that the employment gap between natives and refugees decreases by 62 percentage points over 20 years: from 81 percentage points upon arrival to 18 percentage points after 19 to 20 years. The corresponding estimate with individual FE (available upon request) is 64.5 percentage points.

18