# **5 Methodology**

In order to quantify the impact of the influx of forcibly displaced on the fiscal and labor market outcomes of native workers, most studies use the share of population (or working age population) of the forcibly displaced as the independent variable and acknowledges that there exists a limitation in identifying the causal impact in this way because of the potential endogeneity arising from the sorting of forcibly displaced to areas with certain characteristics and other time varying factors, such as public expenditure, that may lead to spurious correlation. Many studies try to address these endogeneity issues by using instrument variable methods (Verme and Schuettler, 2021).

This paper tries to evaluate the effect of the forcibly displaced by using the discontinuity that is observed in the population data, mainly the working age population, in the first quarter of 2018, in a regression discontinuity (RD) design to evaluate the fiscal and the labor market effects.<sup>8</sup> In the RD design, this paper uses a transformed variable (X) of the time quarters as the running or score variable. X is the distance between any time in quarter and the the first quarter of 2018. Since the PNADC data is from 2012-2020, there are 36 observations for X, with X being equal to zero in the first quarter of 2018, which is defined as the cutoff. The treatment is defined as when _X >_ = 0 and is denoted by _Di_ = _I_ ( _Xi >_ 0), where _I_ ( _._ ) is the indicator function. Since the fiscal data is monthly, the cutoff variable is the second bimonth of 2018 and X is defined as the distance in 2 months from the second bimonth of 2018. It should be noted here that assigning to the treatment condition does not mean receiving the treatment. For example, in this case, the Venezuelan refugees and migrants started coming in to Brazil in 2017, but the net influx did not become substantial till the first quarter of 2018, which witnessed a net inflow of about 20,000 that is 50% of the total Venezuelan influx in Brazil at that point in time (derived from Figure 2), which translated into 11000 increase in working age population that is observed in Figure 8. The sharp rise in both the population (Figure 8) and the working age population in Roraima in 2018 (Figure 8) add evidence for a sharp RD design, where it is assumed that the treatment condition assigned is identical to the treatment condition received. The results of the fuzzy RD design<sup>9</sup> , where there is noncompliance, or where the treatment condition assigned is not equal to treatment condition received is also estimated for robustness checks and the results are given in the appendix. This rest of this section focuses on sharp RD design.<sup>10</sup> .

Just like the fundamental problem in any causal inference, in RD design, one only observes the outcome under control, _Yi_ (0) for those units or quarters whose running variable or score is below the cutoff and the outcome under treatment, _Yi_ (1), for those units or quarters whose score is above the cutoff. The average potential outcome given the score, _E_ [ _Yi|Xi_ ] is observed for only _E_ [ _Yi_ (1) _|Xi >_ = _c_ ] for values where c is the cutoff and for _E_ [ _Yi_ (0) _|Xi < c_ ]. E[Y _i_ (1) _|Xi < c_ ] and _E_ [ _Yi_ (0) _|Xi > c_ ] are unobserved. Consequently, the sharp RD design exhibits an extreme case of lack of common support, as units in the control ( _Di_ = _I_ ( _Xi ≥ c_ ) = 0) and treatment ( _Di_ = _I_ ( _Xi ≥ c_ ) = 1) groups cannot have the same value of the running variable ( _Xi_ ). Thus, RD performs a local extrapolation in order to compare the control and the treatment units.

> 8It should be noted here that a bigger jump in total population is observed in the annual data series published by IBGE, but due to limited observations, the jump cannot be estimated by RD.

> 9The fuzzy RD involves a two stage estimation, where the first stage estimates the probability of treatment, while the second stage uses this estimated probability to find its effect on the outcome variable.

> 10Some evidences in support of the sharp RD design is given in the later sections of the paper.

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