We employ an instrumental variable (IV) approach as identification strategy for identifying and estimating the effect of receiving on-the-job training within the first year of arrival on language course and labor market outcomes for Danish refugees. Therefore, our empirical model is specified as follows:
(1) 𝑇𝑇𝑖𝑖1=𝛼𝛼2+𝜂𝜂𝑍𝑍𝑖𝑖1+𝜋𝜋2 𝑋𝑋𝑖𝑖0+𝜃𝜃2𝑈𝑈𝑚𝑚𝑚𝑚+𝛾𝛾2𝑚𝑚+𝛾𝛾2𝑚𝑚+𝑢𝑢𝑖𝑖1
(2) 𝑌𝑌𝑖𝑖𝑖𝑖=𝛼𝛼1+𝛿𝛿𝑇𝑇𝑖𝑖1+𝜋𝜋1 𝑋𝑋𝑖𝑖0+𝜃𝜃1𝑈𝑈𝑚𝑚𝑚𝑚+𝛾𝛾1𝑚𝑚+𝛾𝛾1𝑚𝑚+𝜖𝜖𝑖𝑖𝑖𝑖
where Y is an outcome measured t months after arrival (t=13, …, 48), T1 is a dummy for being treated in the first year, and X are individual characteristics measured in the year of arrival (see Table 4.1). Z is an instrumental variable, and 𝛾𝛾𝑚𝑚 and 𝛾𝛾𝑚𝑚are municipality- and semester-of-arrival fixed effects. The fixed effects wipe out common time trends and time invariant unobserved determinants of the outcomes in a given municipality. U is the local unemployment rate meas-ured at the municipality level in the year of arrival, to control for the possibility that the instru-ment is related to the possibility of getting a job (see discussion below), which may affect later language course and labor market outcomes.
The instrumental variable is a measure of the local inclination to use early on-the-job training as part of the integration program. For refugee i arriving in a municipality in a given month, the instrument is calculated as the job training participation rate in the first year after arrival among the refugees who arrived at the same municipality during a certain period prior to refugee i’s arrival. We use municipality-month pairs where at least 10 refugees arrived during the previous 20 months. The number 20 has been chosen to ensure a sufficient number of municipality-month pairs. As described in Section 2 and showed in Section 3, early job training has been used increasingly over time in most municipalities, and we utilize this gradual rollout to identify its effect. Since we observe actual on-the-job training participation we can measure local aver-age treatment effects rather than intent-to-treat effects using the instrumental variables esti-mator15. The identifying variation henceforth relies on the different growth-rates between mu-nicipalities in their inclination to use early job training as measured by the instrument. By relying on this rollout design, we are able to rule out any correlation driven by fixed municipality char-acteristics or general correlated time varying trends in outcomes and use of job-training.
5.1 Validation of the instrument
The validity of the instrumental variable requires it to be independent of the refugees’ charac-teristics (the independence condition) but also that it affects the probability of participating in early on-the-job training (the first-stage condition). We argued in Section 2 that immigrants with asylum with no family members already living in the country are randomly allocated across municipalities due to the dispersal policy (see also Edin et al., 2003; 2004; Damm, 2009;
Damm, 2014; Azlor et al., 2020).16 The plausibility of the independence assumption for the entire sample is examined using a balance test reported in Table 5.1.
15 Rollout designs have been used extensively to estimate the impact of various US welfare programs (e.g. Ludwig and Miller 2007;
Almond, Chay and Greenstone 2007; Bailey and Goodman-Bacon 2015; Hoynes, Schanzenbach and Almond 2016; Johnson and Jackson 2017). In the absence of data on participation in the programs, most of these studies estimate intent-to-treat effects.
16 Immigrants with asylum based on reunification with refugees who are still in the integration period are also randomly allocated across municipalities, unless their application for reunification is depending on settlement location.
Table 5.1 Balance test: Regression of instrument on refugee characteristics measured one
Coefficient Std. error Coefficient Std. error Coefficient Std. error
Woman -0.0018 (0.0024) -0.0016 (0.0040) -0.0002 (0.0028)
Woman with children 0.0037 (0.0031) -0.0010 (0.0053) 0.0155*** (0.0037)
Married 0.0036* (0.0016) 0.0039 (0.0027) -0.0043* (0.0019)
Maternity within first 12 months 0.0012 (0.0025) 0.0121** (0.0042) 0.0024 (0.0030)
Age 18-25 -0.0033 (0.0055) -0.0146 (0.0093) 0.0056 (0.0066)
Family reunification status -0.0005 (0.0020) -0.0022 (0.0034) 0.0217*** (0.0024) Country of origin:
Health care utilization 1st Year:
General practitioner (1000 DKK) -0.0000+ (0.0000) 0.0000 (0.0000) -0.0000 (0.0000) Emergency care (1000 DKK) -0.0000** (0.0000) -0.0000+ (0.0000) -0.0000* (0.0000) Psychiatry (1000 DKK) 0.0000 (0.0000) 0.0000 (0.0000) 0.0000+ (0.0000) Hospitalized (days) -0.0007 (0.0006) -0.0013 (0.0011) -0.0033*** (0.0008) Course module (within level) at arrival†:
Level 1:
Local unemployment rate -0.0406*** (0.0029) -0.0345*** (0.0012) -0.0866*** (0.0018)
Observations 20303 20303 20303
Adjusted R2 0.742 0.256 0.633
Number of covariates 138 44 130
Notes: OLS estimates with controls for municipality dummies and dummies for semester of arrival. † The three course levels are sub-divided into six sequential modules. Standard errors in parentheses. + p < 0.1, * p < 0.05, ** p < 0.01, *** p <
0.001.
The presented coefficients are obtained from a regression of the instrument on characteristics of the refugees and the local unemployment rate at the time of arrival as well as municipality dummies and dummies for each arrival semester.
Table 5.1 shows that most of the individual characteristics that are likely to be strongly related to job finding abilities are unrelated to the instrument, once we have controlled for municipality and time fixed effects in column 1. Thus, neither demographics (gender, age, and children) nor use of most types of health care have a significant relationship to the instrument. Four charac-teristics are significantly related to the instrument on a 5% level, but given that the model con-tains 39 estimated coefficients this could be due to chance. In general, the number of significant correlations do not change considerably when the municipality fixed effects are excluded, whereas a number of individual characteristics become significant when the time trend meas-ured as half-year (semester) fixed effects is excluded. This is probably due to changes in the composition of the refugee group during the period and it shows how important it is to correct for time trends.
It is potentially a larger concern that the local unemployment rate is strongly related to the instrument in all three specifications: The last row shows that a high unemployment rate is associated with a lower use of early job training. This may not only violate the independence assumption of the instrument but may also violate the exclusion assumption (Imbens and An-grist 1994). The exclusion restriction requires that being assigned to a municipality with a his-torical high level of on-the-job training among refugees has an impact only on outcomes that operate through the probability of being assigned to on-the-job training. In our case, we could imagine that municipalities with better general labor market conditions find it easier to find on-the-job training positions. If the better labor market conditions also affect future job and lan-guage acquisition, then the exclusion restriction is violated. To assess how important this is, we conduct a robustness analysis, where we include total time in the labor market during the first year, either in on-the-job training or regular employment, as the treatment. Then, the ex-clusion restriction is only violated if the fact that a refugee is assigned to a municipality with a high level of on-the-job training has an impact on outcomes, independently of the refugee’s own labor market behavior, which seems more implausible. The exclusion restriction is also violated if the language course in municipalities with a higher use of early on-the-job training is of a different quality than in other municipalities. This is examined by inclusion of language course provider dummies in a robustness analysis at the end of the paper. As we shall see, both of these analyses show that the results are robust and that the correlation with the local unemployment rate therefore does not seem to be a concern.
Table 5.2 First stage: The effect of the instrument on the probability of receiving on-the-job training in the first year
Early job training
Instrument# 0.489***
(0.0336)
Observations## 20,303
Cragg-Donald Wald F test 212.3
Notes: OLS estimates with controls for background characteristics, municipality dummies and dummies for semester of arrival.
# The instrument is calculated as the degree of job training in the municipality of arrival in the 20 months prior to arrival.
## The regression is based on the sample of refugees who can be followed for at least 42 months. P-value in parenthes.
* p < 0.05, ** p < 0.01, *** p < 0.001.
Table 5.2 tests whether the instrument affects the treatment (the first-stage condition). The table contains the first-stage coefficients on the instrument, i.e. the coefficient 𝜂𝜂 in equation (1).
It shows that the instrument is strongly correlated with the likelihood of participating in early job training.17 We also report the Cragg-Donald Wald F statistic for weak identification. It is very large and therefore there is no indication that the instrument is weak (Stock and Yogo 2005).
To be able to interpret the IV estimates as local average treatment effects (LATE), an tion of monotonicity of the instrument is also required (Imbens and Angrist 1994). The assump-tion rules out the presence of defiers. As the first-stage coefficient is positive, this assumpassump-tion requires that the likelihood of receiving early job training is not lower for an individual when assigned to a municipality with higher levels of past use of early job training. This could be the case if, for instance, the number of on-the-job training positions is constrained, and a new refugee therefore has less on-the-job training options when arriving just after a period with a high level of on-the-job training. Figure 5.1 plots a local linear regression of the probability of participating in early on-the-job training in period t on the rate of use of early on-the-job training in the municipality in the previous period (i.e., the instrument). The function shows a highly monotonic relationship between the instrument and the refugees’ probability of receiving on-the-job training, which indicate that the first stage is not merely driven by outliers, which again supports the assumption that there are no defiers.
Figure 5.1 Local linear regression of the probability of early on-the-job training on the instru-ment
17 The coefficient increases by around 50 percent when municipality dummies and annual local unemployment rates are excluded, which suggests that municipality-specific factors play a sizeable role for the correlation between the instrument and treatment.