literature (Andrews et al. 2019; Lee et al. 2020). We conclude that the first-stage regressions are generally strong.

The second key assumption to have a valid IV is the exclusion restriction: the instrument cannot be correlated with the error term _εi_ in equation (1), conditionally on covariates.

We carefully represent the causal model we have in mind using a directed acyclic graph (DAG), in order to identify possible sources of endogeneity (Figure 1). The perceptions that survey respondents have about refugees depend on three categories of factors. First, the characteristics of the respondents and their households. For example, the employment status and wealth of the respondent might directly influence the perceptions of refugees as competitors or economic contributors. Second, the perceptions that other hosts living around have about refugees can influence the perception of the respondent. Gossips, rumours, and discussions can certainly forge the perceptions that hosts have about refugees. Finally, whether the respondent frequently interacts with refugees may influence perceptions, in line with contact theory. This latter variable is our main explanatory variable of – interest but this variable is likely to be endogenous. The respondent’s interactions with refugees also depends on three factors. First, the characteristics of the respondents and their households. For example, language skills may directly affect respondents’ ability to interact with refugees. Second, the level of refugee-host interactions among kin and neighbours may influence respondents’ level of interaction with refugees, either through emulation or competition. Finally, the share of refugees in the locality of the respondent should directly affect the possibility and frequency of interactions.<sup>13</sup> The latter two variables are our chosen instruments.

– The characteristics of individuals living in an EA including the proportion of refugees – is expected to depend on the characteristics of the EA. In refugee camps and settlements, the initial placement of refugees is determined by camp authorities. The allocation process first and foremost depends on space availability, arrival date, and administrative decisions that are often quasi-random (MacPherson and Sterck 2021; Siu et al. 2021). Movements within settlements and camps are possible but not frequent. For example, our panel data for Kenya shows that in any given year around 1.7% of refugees in Kakuma relocate within the camp (Betts et al. 2021). In cities, the process is completely different. Refugees decide where to live and usually co-locate with fellow nationals. For these reasons, our presumption was that the exclusion restriction would be more likely to be satisfied in refugee camps.

We draw two conclusions from this DAG. First, controlling for kin and neighbours’ perception of refugees ( _PHH_ and _PEA_ ) is essential to limit omitted variable bias in OLS

> 13A fourth possible factor influencing respondents’ interactions with refugees is the perceptions that other hosts living around have about refugees ( _PEA ⇒ Ii_ ). For example, if refugees have a bad reputation, respondents may avoid contact with them to protect their own reputation. While such a link is certainly possible, it would not affect the validity of the IV specification. However, a strong link going the other way around ( _Ii ⇒ PEA_ ) would be more problematic. Implicitly, our empirical strategy assumes that the effect of one particular individual (here the respondent) on group behaviour (here the perceptions of the respondent’s contacts) is negligible (assumption of “atomicity”).

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