<table><caption>Table A7: Immigrant/Asylum seekers flows and informal sector, first-difference model (IV)</caption><thead><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th></tr><tr><th></th><th>Δ M&S index<br>1997-2017</th><th>Δ E&Ö index<br>1997-2020</th><th>Δ M&S index<br>1997-2017</th><th>Δ E&Ö index<br>1997-2020</th></tr></thead><tbody><tr><td>Immigration flow share <i>t</i></td><td>0.061***<br>(0.023)</td><td>0.037***<br>(0.012)</td><td></td><td></td></tr><tr><td>Asylum seekers flow share <i>t</i></td><td></td><td></td><td>0.327**<br>(0.160)</td><td>0.167**<br>(0.082)</td></tr><tr><td>GDP per capita <i>t</i>-1</td><td>-3.392***<br>(0.684)</td><td>-0.359<br>(0.356)</td><td>-3.741***<br>(0.757)</td><td>-0.885*<br>(0.490)</td></tr><tr><td>Credit market regulation index <i>t</i>-1</td><td>-0.048<br>(0.051)</td><td>0.013<br>(0.011)</td><td>-0.005<br>(0.061)</td><td>0.010<br>(0.009)</td></tr><tr><td>Labor market regulation index <i>t</i>-1</td><td>-0.010<br>(0.029)</td><td>0.003<br>(0.006)</td><td>-0.007<br>(0.035)</td><td>0.000<br>(0.004)</td></tr><tr><td>Democracy index <i>t</i>-1</td><td>0.022<br>(0.036)</td><td>0.029<br>(0.031)</td><td>-0.054*<br>(0.033)</td><td>0.046**<br>(0.021)</td></tr><tr><td>Time dummies</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Observations</td><td>485</td><td>550</td><td>504</td><td>571</td></tr><tr><td>F statistic KPW</td><td>2,259.86</td><td>5,096.10</td><td>279.54</td><td>432.81</td></tr></tbody></table>

Standard errors clustered at the country level in parentheses. * p<0.10, ** p<0.05, *** p<0.01.

<table><caption>Table A8: Immigrant/Asylum seekers flows and informal sector, first-difference model (not instrumented)</caption><thead><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th></tr><tr><th></th><th>Δ M&S index</th><th>Δ E&Ö index</th><th>Δ M&S index</th><th>Δ E&Ö index</th></tr></thead><tbody><tr><td>Immigration flow share <i>t</i></td><td>0.065***<br>(0.018)</td><td>0.037***<br>(0.012)</td><td></td><td></td></tr><tr><td>Asylum seekers flow share <i>t</i></td><td></td><td></td><td>0.295**<br>(0.127)</td><td>0.170***<br>(0.061)</td></tr><tr><td>Controls</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Time dummies</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Observations</td><td>596</td><td>697</td><td>629</td><td>733</td></tr></tbody></table>

Standard errors clustered at the country level in parentheses. * p<0.10, ** p<0.05, *** p<0.01.

<table><caption>Table A9: Immigrant flows, labor regulations restrictiveness and informal sector, first-difference model (IV)</caption><thead><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th></tr><tr><th></th><th>Δ M&S index</th><th>Δ E&Ö index</th><th>Δ M&S index</th><th>Δ E&Ö index</th></tr></thead><tbody><tr><td>Immigration flow share <i>t</i></td><td>0.063***<br>(0.019)</td><td>0.036**<br>(0.015)</td><td>0.031<br>(0.027)</td><td>0.041<br>(0.025)</td></tr><tr><td>Immig. flow share <i>t</i> × Ext. Reg. Index above median</td><td>-0.031<br>(0.038)</td><td>0.028<br>(0.029)</td><td></td><td></td></tr><tr><td>Immig. flow share <i>t</i> × Int. Reg. Index above median</td><td></td><td></td><td>0.029<br>(0.034)</td><td>0.006<br>(0.031)</td></tr><tr><td>Controls</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Time dummies</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Observations</td><td>568</td><td>599</td><td>568</td><td>599</td></tr><tr><td>Sum coeff.</td><td>0.032</td><td>0.064</td><td>0.059</td><td>0.046</td></tr><tr><td>P-value</td><td>0.299</td><td>0.011</td><td>0.002</td><td>0.015</td></tr><tr><td>F statistic KPW</td><td>1,071.69</td><td>1,165.13</td><td>1,134.56</td><td>1,510.40</td></tr></tbody></table>

Standard errors clustered at the country level in parentheses. * p<0.10, ** p<0.05, *** p<0.01.
<figure><img src="image_4.png" /><figcaption>Figure A1: First-stage correlates of predicted versus observed migrant and asylum seeker inflows</figcaption></figure>

## A.2 Discussion of the empirical specification

Our choice of a quasi first-difference model<fnref n="19" /> is first justified by the stationarity properties or our dependent variables. Ignoring the non-stationarity of time series may lead to spurious regression results. Results from a panel unit root test based on individual Augmented Dickey-Fuller (ADF) regressions (Im et al., 2003) reported in Table A10 show that our two measures of the informal economy are non stationary. The same test however concludes that the unit-root hypothesis can be rejected for the first-difference of the two variables. By first-differencing our dependent variable, we are thus able to address this non stationarity issue.<fnref n="20" />

Second, as argued by Aleksynska and Tritah (2015), based on Wooldridge (2010), the choice of a first-difference model may be justified by the time persistence of migration due to network effects (Pedersen et al., 2008).

<footnote n="19">¹⁹Our model is not, strictly speaking, a first difference model in that our main independent variable of interest - immigrant or asylum seeker variations in stock - is proxied by immigrant inflows.</footnote>

<footnote n="20">²⁰While first introduced in studies based on time series, the detection of non-stationarity has become a matter of great importance in panel data analysis since the seminal works of Levin and Lin (1992) and Quah (1994). The advantage of panel data in the detection of unit roots is linked to the increase in the number of observations owing to the double individual and time dimension. Non-stationarity may lead to spurious results, as it may indicate relationships between variables when they do not exist. By definition, a data series is defined as non-stationary if its statistical properties are time dependent.</footnote>
<table><caption>Table A10: Panel unit-root Im et al. (2003) test</caption><thead><tr><th>Variables</th><th></th><th>Without trend</th><th>With trend</th></tr></thead><tbody><tr><td rowspan="2">Informal economy - M&S</td><td>Levels</td><td>1.021</td><td>-3.844</td></tr><tr><td>Differences</td><td>-12.574***</td><td>-12.764***</td></tr><tr><td rowspan="2">Informal economy - E&O</td><td>Levels</td><td>3.853</td><td>-0.832</td></tr><tr><td>Differences</td><td>-5.929***</td><td>-4.619***</td></tr></tbody></table>

<footnote>*** p<0.01</footnote>