textwithmarginpar

How residence permits affect the labor market attachment of foreign workers:
Evidence from a migration lottery in Liechtenstein

Berno Buechel†, Selina Gangl†, Martin Huber†∗

†University of Fribourg, Department of Economics
∗Center for Econometrics and Business Analytics, St. Petersburg State
University

###### Abstract

We analyze the impact of obtaining a residence permit on foreign workers’
labor market and residential attachment. To overcome the usually severe
selection issues, we exploit a unique migration lottery that randomly assigns
access to otherwise restricted residence permits in Liechtenstein (situated
between Austria and Switzerland). Using an instrumental variable approach, our
results show that lottery compliers (whose migration behavior complies with
the assignment in their first lottery) raise their employment probability in
Liechtenstein by on average 24 percentage points across outcome periods (2008
to 2018) as a result of receiving a permit. Relatedly, their activity level
and employment duration in Liechtenstein increase by on average 20 percentage
points and 1.15 years, respectively, over the outcome window. These
substantial and statistically significant effects are mainly driven by
individuals not (yet) working in Liechtenstein prior to the lottery rather
than by previous cross-border commuters. Moreover, we find both the labor
market and residential effects to be persistent even several years after the
lottery with no sign of fading out. These results suggest that granting
resident permits to foreign workers can be effective to foster labor supply
even beyond the effect of cross-border commuting from adjacent regions.

Keywords: international migration, cross-border commuting, natural experiment,
lottery

JEL classification: F22, J61.

We are grateful to the Government of Liechtenstein for the permission to
realize this research project and to the Immigration and Passport Office as
well as the Office of Statistics of Liechtenstein for their valuable support
concerning data provision and processing. We have benefited from comments by
Andreas Brunhart and Andreas Steinmayr. Addresses for correspondence: Berno
Buechel, Selina Gangl, and Martin Huber, University of Fribourg, Bd. de
Pérolles 90, 1700 Fribourg, Switzerland<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
##  1 Introduction

Most labor markets rely on both locally-born and foreign-born workers. For
instance, the share of foreign-born persons in the U.S. labor market
corresponds to 17.4% in 2019, amounting to 28.4 million people.111Reported by
U.S. Bureau of Labor Statistics,
https://www.bls.gov/news.release/forbrn.nr0.htm/labor-force-characteristics-
of-foreign-born-workers-summary, retrieved 2021-02-11. World-wide, the number
of migrant workers is estimated to be 164 million in 2017, with 23% in North
America, 32% in Europe, and 13% Asia.222Reported by International Labour
Organization, https://migrationdataportal.org/themes/labour-migration,
retrieved 2021-02-11. While migration from low to higher income countries
receives a lot of attention in public and scientific discussions, an immense
amount of labor mobility is realized between rather developed nations, likely
competing for skilled workers. To address the high demand for foreign labor,
offering residence permits for migrant workers may seem a rather obvious
policy. In many regions and countries, however, alternative policies such as
admitting seasonal workers or cross-border commuters play an important role.
In France, for instance, about 438k workers commute to another country every
day for work.333Reported by EUROSTAT,
https://ec.europa.eu/eurostat/statistics-
explained/index.php?title=Archive:Statistics_on_commuting_patterns_at_regional_level&oldid=463740,
retrieved 2021-02-11. An interesting question that arises in this context is
whether residence permits increase foreign labor market attachment, relative
to alternatives such as cross-border commuting. This may be beneficial in an
environment of increased skill competition in order to attract and retain key
workers required for fostering economic growth.

In this paper, we assess the causal effect of obtaining a residence permit on
the labor market and residential attachment of foreign workers based on an
annual migration lottery that is unique in Europe. In Liechtenstein, a wealthy
microstate that is situated between Austria and Switzerland, two lottery draws
for residence permits are held every year. The lottery randomly assigns access
to residence permits among applicants from the European Economic Area
(EEA)444Iceland, Liechtenstein, and Norway plus all EU member states (Austria,
Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland,
France, Germany, Greece, Hungary, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Poland, Portugal, Romania, Slovakia, Slovenia,
Spain, and Sweden) are part of this free trade and movement agreement. who
hold an employment contract with a company in Liechtenstein.555For EEA
citizens who do not belong to the working population and can finance their
livelihood from their own resources, there is another lottery that is
conducted at the same time. We are the first to link European migration
lottery data with administrative data on individual labor market records. We
exploit the random assignment as instrument for the reception of a residence
permit that is conditional on actually moving to Liechtenstein. This allows us
to assess the local average treatment effect (LATE) of moving among compliers
of the first lottery they participated in, i.e. those whose migration behavior
complies with the assignment obtained in their first lottery participation,
making up 36% of our sample. We apply a flexible instrumental variable (IV)
estimator based on inverse probability weighting (IPW), in which we reweigh
the outcomes by the inverse of the conditional instrument probability given
the lottery year, the so-called instrument propensity score. This enables us
to control for the fact that the share of lottery winners changes over the
years as a function of lottery applicants, which is important in order to
avoid confounding, e.g. due to business cycle effects.

We find that receiving a residence permit statistically significantly
increases the employment probability by 24 percentage points on average over
our outcome periods 2008 to 2018. Likewise, it increases the activity level by
20 percentage points, and the employment duration in Liechtenstein by 1.15
years. These substantial labor attachment effects remain robust to the
inclusion of further covariates in the IPW estimator like gender, age, and
nationality. Assessing effect heterogeneity across previous cross-border
commuters and new labor market entrants who (despite holding a work contract)
have not worked in Liechtenstein yet when participating in the lottery, the
effects are stronger and statistically significant in the latter group. This
suggests that residents permits are more effective for attracting new labor
market entrants than for keeping previously commuting workers.

Moreover, we assess the effect of receiving the residence permit on residence
in Liechtenstein two and more years after the lottery. We find the residence
probability and duration to significantly increase by 71 percentage points and
3.44 years, respectively, on average, with little differences between previous
cross-border commuters and new labor market entrants. Finally, we consider the
labor market and residential effects separately for specific years after the
lottery and find them to be persistent with no sign of fading out. That is,
even in the tenth year after the first lottery participation, the impact on
the employment and residence probability is comparable to the respective
average effect across all periods and statistically significant at the 5%
level, albeit confidence intervals are large due to the smaller sample size.
We argue that tax advantages when moving to Liechtenstein are likely a very
important (if not the main) mechanism for driving our strong effects, as
confirmed by a survey among foreign workers in Liechtenstein.

Very broadly speaking, our paper fits into the literature on labor migration,
see for instance Fasani et al. (2020). More specifically, it is among a
relatively scarce number of studies that exploit migration lotteries to
convincingly assess the causal effect of residence permits on labor market
behavior or related outcomes. Gibson et al. (2011), for instance, investigate
a lottery in the Pacific island state of Tonga for residence permits in New
Zealand and study welfare effects on household members of families left
behind. Gibson et al. (2017) use the same lottery and find positive income
effects among migrants themselves. Clemens et al. (2012) analyze a lottery in
a specific multinational firm that allocated U.S. visas to Indian software
workers and conclude that migration to the U.S. entails a sixfold increase in
wages. Mergo (2016) considers the U.S. Diversity Visa lottery for Ethopians
and finds that their migration to the U.S. increases welfare (in particular
consumer expenditure) of the families left behind in Ethiopia. Mobarak et al.
(2020) examine a visa lottery for low-skilled workers from Bangladesh
intending to work in the palm-oil industry in Malaysia; and find that
migration leads not only to a substantial income rise among migrants, but also
to an increase in the household consumption of the family left behind.

While the previously mentioned studies consider migration from a less
developed to a more developed country, a rather unique feature of our lottery
is that it exclusively concerns member states of the European Economic Area
(EEA). Therefore, our paper contributes to the literature by considering labor
migration between rather developed and wealthy countries. This is important,
because a large amount of labor mobility is realized between rather developed
nations, which are likely competing for skilled labor. A second important
distinction is that we focus on the labor force attachment of individuals that
could resume or start working in Liechtenstein even without living there, i.e.
by means of cross-border commuting, in particular from nearby Austria or
Switzerland, which is actually the most common form of labor in
Liechtenstein.666Indeed, about three thirds (76.9%) of the 29k foreigners who
work in Liechtenstein commute cross-border (Amt für Statistik Fürstentum
Liechtenstein (2018a), AS). Our paper therefore sheds light on whether
residence permits (and the associated amenities like tax reductions)
incentivize foreigners to remain in the labor market, which appears an
important piece of information for policy makers in a competitive open economy
with a high demand for foreign labor, as it is the case in
Liechtenstein.777See Huber and Nowotny (2013) for an empirical study on which
personal characteristics drive the willingness to commute and migrate across
borders in regions of the Czech Republic, Hungary, and Slovakia that are
situated close to Austria. The intention to commute or migrate is for instance
found to be significantly negatively associated with age and being a female,
and significantly positively associated with being single or feeling deprived
when comparing the own social status to peers. Also higher education has a
positive correlation, which is, however, not significant at the 5% level.
Therefore, personal factors most likely play a role for the question which
type of workers respond to specific incentives like cross-border work permits
or residence permits, even though it needs to be pointed out that the findings
in Huber and Nowotny (2013) do not necessarily directly carry over to the
context of Liechtenstein. As a motivation for the potential economic relevance
of labor migration regulations, see for instance Beerli et al. (2018). The
authors find for Switzerland that reducing restrictions for cross-border
workers increased the size and productivity of skill-intensive sectors (in
particular those with previous skill shortages) such that even the wages of
highly educated natives rose, despite the hike in foreign employment. Our
paper appears to be the first that relates the literature on migration
lotteries with the topic of commuting, in particular, cross-border commuting.

The remainder of the paper is structured as follows. Section 2 provides
information about Liechtenstein and its migration lottery. Section 3
introduces our data and provides descriptive statistics. Section 4 discusses
the empirical strategy. Section 5 presents and interprets the results.
Finally, Section 6 concludes.

##  2 Institutional background

This section gives a very brief overview of the economy, the labor market, and
the migration lottery of Liechtenstein.888More details about the institutional
background are provided in Appendix A.1. As illustrated in Figure 1,
Liechtenstein is a micro state situated in Central Europe, between Switzerland
in the West and Austria in the East. The official language is German.
Liechtenstein’s population amounts to almost 40k inhabitants, while its labor
force is of roughly the same size – in fact, slightly exceeding the
population. Liechtenstein is a small open economy. Since 1923 it has a customs
union with Switzerland and since 1995 it is member of the European Economic
Area (EEA), which includes all European Union (EU) states plus Norway and
Iceland, but not Switzerland. Export of goods, excluding trade with and via
Switzerland, account for 55% of its GDP. Its most important industries are
mechanical engineering and provision of financial and insurance services,
which account for 16.2% and 13.3% of the GDP, respectively (Amt für Statistik
Fürstentum Liechtenstein (2018c), AS). Liechtenstein is among the wealthiest
countries in the world with a nominal GDP per employed person of about 200k
USD. The official currency in Liechtenstein is the Swiss Franc (CHF), which
had an average exchange rate of 1.04 USD/CHF in the last decade.

Figure 1: Map of Liechtenstein (Source: Liechtenstein Marketing)

The labor market in Liechtenstein is characterized by a low unemployment rate
and a large demand for foreign labor. The strong economic growth in recent
decades in combination with the small size of the country fueled an ongoing
employment expansion. Table 1 documents the increase in the number of
employees from 1980 onwards and also distinguishes between employees residing
in Liechtenstein and cross-border commuters, which have grown even more
substantially than the total labor force. Since 2010 there are more cross-
border commuters in the work force than employees residing in Liechtenstein.
Most employees work in the service sector (61.9%) followed by the industrial
sector (37.4%).

Wages in Liechtenstein are relatively high when compared to other Western
European countries, which is most likely an important pull factor for
attracting foreign labor. The median gross wage per month is about 7k USD,
which is similar to the level of neighboring Switzerland, and substantially
higher than in most EU countries, including neighboring Austria. The gross
median income of cross-border commuters (CHF 6’723) is similar to that of
residents (CHF 6’612) (Amt für Statistik Fürstentum Liechtenstein (2018b),
AS). Cross-border commuters are predominantly male (64.4%), working in the
tertiary sector (55%), living in Switzerland or Austria (96%), and holders of
a citizenship of a member country of the EEA (62.2%) (AS, 2018b).

Table 1: Number of employees in Liechtenstein

| Employees in Liechtenstein
---|---
year | Residing in Liechtenstein | Cross-border commuters | Total
1980 | 11,543 | 3,297 | 14,840
1990 | 13,020 | 6,885 | 19,905
2000 | 15,605 | 11,192 | 26,797
2010 | 16,764 | 17,570 | 34,334
2017 | 17,362 | 21,299 | 38,661
2018 | 17,597 | 22,038 | 39,635

Source: Amt für Statistik Fürstentum Liechtenstein (2020) (AS); “residing in
Liechtenstein” is self-calculated

One important reason for the high share of cross-border commuters among the
labor force is regulated access to residence permits in Liechtenstein. Despite
being a member of the EEA, Liechtenstein is permitted to restrict residence of
EEA citizens in Liechtenstein. However, by the EEA treaty, Liechtenstein is
required to issue at least 56 residence permits for the purpose of employment
every year, half of which must be assigned by a lottery.999Despite the
restrictive rules for immigration to Liechtenstein there is an inflow of 17.0
(net inflow of 4.3) immigrants per 1,000 inhabitants (Amt für Statistik
Fürstentum Liechtenstein (2019b), AS). The dominant formal purpose for
immigration to Liechtenstein is family reunification. The fraction of
foreigners among the residents in Liechtenstein is 34% (Amt für Statistik
Fürstentum Liechtenstein (2020), AS).

Holding at least one lottery per year is required by law (see Law on the Free
Movement of Persons for EEA and Swiss nationals (2009), section 39, 1).
Usually, two lotteries take place per year, one in spring and one in fall
(Ausländer- und Passamt, 2020). Each lottery consists of two stages, namely
the pre-draw and the final draw (Landesverwaltung Fürstentum Liechtenstein,
2009, section 37, 2). Participants must win in both parts of the lottery to
receive a residence permit. Requirements for participation include holding an
EEA citizenship and paying the participation fees in time. In the final draw,
participants must also provide an employment contract of more than one year
with a minimum activity level of 80% or, else, an authorized permanent cross-
border business activity in case of self-employment (Ausländer- und Passamt,
2019b). After winning both the pre-draw and the final draw, the lottery
participant has six months time to relocate to Liechtenstein, otherwise the
residence permit expires (Landesverwaltung Fürstentum Liechtenstein, 2009,
section 37, 2). For this reason, our treatment is defined based on residing in
Liechtenstein in the year after the lottery, as obtaining the permit is tied
to actually moving there. The drawing of winners is done blindly by hand. This
procedure is monitored by at least one judge.

Lottery losers of either stage may participate again in subsequent lotteries,
while multiple applications to the very same lottery are not allowed
(Landesverwaltung Fürstentum Liechtenstein, 2009, section 38, 1) c)). As the
decision to repeatedly take part in the lottery is most likely endogenous to
the first lottery outcome, our main evaluation strategy relies on the first
lottery participation of an individual in our data window. Furthermore, as
participation in the final draw is conditional on succeeding in the pre-draw
only, we base our instrumental variable approach on the pre-draw alone.

The incentives to participate in the lottery are arguably related with the
costs and benefits of residing in Liechtenstein. For most lottery
participants, the relevant alternative is to reside in a neighboring country
and commute cross-border.101010For other participants it can be the case that
they will stop working in Liechtenstein or not start working in Liechtenstein,
despite holding an employment contract. In a survey of cross-country commuters
to Liechtenstein Marxer et al. (2016, p. 57) ask about the reasons to move to
Liechtenstein, given the presumption that the respondents would move there in
the future. The top answer is “taxes and duties” (86% of respondents), which
is even ticked more often than “proximity to the workplace” (80% of
respondents), while all other categories are ticked by less than 22% of
respondents. Indeed, taxes are substantially lower in Liechtenstein than in
Switzerland such that the net disposable income of given gross incomes and
given household types is about 10 percentage points higher in Liechtenstein
(Brunhart and Buechel, 2016). In Austria taxes are even substantially higher
than in Switzerland such that the net disposable income there is likely even
lower, despite the lower costs of living. Accordingly, Marxer et al. (2016)
find that 31% of the cross-border commuters living in Switzerland and 75% of
those living in Austria are not satisfied with their tax system; while there
is a is a particularly low willingness to move to Liechtenstein for those
employees who pay taxes in Liechtenstein (these are employees who reside in
Austria and work in Liechtenstein’s public sector).

The second motivation to participate in the lottery, living closer to the
workplace, appears obvious, but must be put in perspective: most cross-border
commuters have quite short commutes. 59% of them travel less than 30 minutes
to work and only 6% more than 1 hour (Marxer et al., 2016, p. 36). Still,
residing in Liechtenstein can lead to more convenient commutes, be it because
of even shorter commuting times, fewer bus or train changes when using public
transport, or different means of transport (e.g. biking instead of driving).
Given these advantages of residing in Liechtenstein over commuting to
Liechtenstein, we note that financial incentives are probably the most
important factor for participating in the lottery, while distance to the
workplace also matters.

##  3 Data

This section provides a description of our data set and the key variables
along with descriptive statistics. Our data base was created by linking
records from the migration lottery with employment statistics in
Liechtenstein. The lottery records cover all lottery participants from 2003 to
2019. In particular, they include information on when and how often an
individual applied to the migration lottery. This enables us to define the
instrument based on whether an applicant has won the pre-draw or not in the
first lottery participation. In addition, the data contain personal
characteristics such as the year of birth, nationality, and gender, which are
asked in the application form for the lottery.

The employment statistics cover the years 2005 to 2018. Every employer in
Liechtenstein is obliged to report new employment entries and exits on a
monthly base. At the end of each year, companies receive a list of their
reported employees for proofreading and are obliged to resubmit a corrected
version (Amt für Statistik Fürstentum Liechtenstein (2019a), AS). The
employment statistics contain variables characterizing the labor market
behavior of the applicants. This includes information on whether an individual
has worked in Liechtenstein in the year prior to lottery participation and
whether she or he has started or continued dependent or self-employment in the
years after lottery participation. For each year, also the activity level in
percent is reported, as well as the country of residence. Finally, several
personal characteristics are observed that are also available in the migration
lottery records, namely the year of birth, nationality, and gender. Whenever
there are differences in these variables across the two data sources, we
prioritize the employment statistics which we suspect to be of higher quality,
as they are repeatedly provided and checked. In contrast, the lottery records
only contain information that was originally handwritten in the application
form. Linking both data sets is based on a unique personal identifier and the
created data base is fully anonymized.

In total, the migration lottery data contain 9,906 observations from 2003 to
2019. While each lottery draw is random, the possibility to repeatedly
participate in case of losing might induce a selection problem, as more
persistent applicants who participate more than once in the lottery likely
differ in terms of their characteristics from the initial pool of applicants.
We overcome this concern by exclusively considering the first lottery
participation in our data window, which reduces the sample to 5,091
observations. Hence, we compare individuals who won when first participating
in the lottery with those who lost, but might have participated again and won
in a later lottery. This strategy yields conservative effects in the sense
that they likely provide a lower bound to those of a hypothetical comparison
of winning vs. losing and being prevented from any further lottery
participation. Since the employment statistics are only available from 2005
onwards, we restrict the sample of first lottery participants to the years
2006 or later, in order to observe the labor market state of each applicant in
the year prior to the lottery. This will be important for our analysis of
effect heterogeneity across previous cross-border commuters and new labor
market entrants. Another sample restriction comes from the fact that the last
period in which outcomes are observed in the employment statistics is 2018.
This requires us to consider 2016 as last lottery year, because outcomes are
measured at the earliest 2 years after the lottery, as it will become clear
from the discussion further below. Figure 2 shows the annual number of the
first lottery participants from 2006 to 2016, separately for the spring and
fall lotteries. Moreover, Figure 2 indicates that this number varies across
years, which is also true for the number of all lottery participants, with a
peak during the financial crisis in 2008.111111The high number of lottery
applications may partly be driven by more applications from individuals
previously not working in Liechtenstein, aiming to escape the crisis-induced
deteriorating labor market conditions in their home country, as suggested by
descriptive statistics in Table 4 below. Furthermore, the higher number might
partly be caused by cross-border commuters suspecting a larger chance of
losing employment when being a commuter rather than a resident, in line with
findings in Kuptsch (2012) that migrants face disproportionately higher risks
of job loss in case of economic woes. Thus, the odds of winning change over
time, as the amount of lottery-assigned permits is not deterministic in the
number of (first) applications. This implies that the lottery year is a likely
confounder of our instrument variable assignment, as the year is likely
associated with labor market outcomes through the business cycle. We therefore
control for lottery year dummies in our IV approach and include the additional
control variables age, nationality, and gender in a robustness check. In sum,
our evaluation data set contains 3,145 participants, out of which 350 win the
pre-draw in their first participation.

Figure 2:  Annual number of first lottery participations

Figure 3 provides a timeline for the measurement of the key variables in our
analysis, with $t$ denoting a specific year. The instrument, namely the
lottery assignment which we henceforth denote by $Z$ (with $Z=1$ for winning
and $Z=0$ for losing), is measured in the year of the first lottery
participation, which is our baseline period ($t=0$). The treatment (denoted by
$D$), namely whether someone has moved to Liechtenstein ($D=1$) (and is thus
in possession of a residence permit) or not ($D=0$), is measured one year
later ($t=1$). The outcome periods start two years after the lottery (t $\geq$
2) and continue until the end of the data window for the respective
observation, at most up to 12 years after the lottery for someone
participating in 2006 with the final outcome being observed in 2018. All in
all, our evaluation sample includes 20,009 outcome observations. Personal
characteristics (e.g. nationality) are generally measured in the year prior to
the first lottery participation ($t=-1$), even though those variables that are
independent from or deterministic in time (gender and age) may also be
obtained from different periods. In some cases there are differences between
the personal characteristics in the migration lottery records (stemming from
the application form) and the employment statistics (regularly provided by the
employer). As the data quality of the employment statistics appears to be
higher than that of the lottery records, priority is given to the former when
measuring these characteristics. We henceforth denote the control variables by
$X$, which either only contain period dummies for the lottery years in the
main specification, or also additional characteristics in our robustness
checks.

$t=-1$Time-dependent covariates $t=0$First lottery participation
$t=1$Treatment $t\geq 2$Outcome periods  Figure 3: Timeline of measured
variables

To check for violations of the random assignment of residence permits through
the lottery, Table 2 reports descriptive statistics on personal
characteristics separately for winners ($Z=1$) and losers ($Z=0$) of the first
lottery in our evaluation sample. For either group, the mean and the standard
deviation (std.dev) of the variables are reported as well as the mean
differences across groups along with t-values and p-values. Among those with
non-missing information in the respective personal characteristics, age,
gender, and the various dummy variables for nationality do not differ
importantly or statistically significantly (at any conventional level of
significance) across groups, thus pointing to a fair lottery. We also see from
the table that the majority of the lottery participants is male, of either
Austrian or German nationality, and on average 37 to 38 years old.121212In
this context, we note that Swiss nationals are not allowed to participate in
the lottery. The reason that their share amounts to 1% in our data is most
likely due to holding a second citizenship from the EEA but reporting the
Swiss nationality in the employment statistics.

In contrast to the observed characteristics, the probability of missing
information in nationality and age is statistically significantly different
across winners and losers, albeit very small in absolute terms (amounting to
only 1 percentage point). This difference is, however, most likely caused by
an imbalance in missingness across our two data sources rather than a failure
of the lottery. To see this, note that for any individual already working in
Liechtenstein prior to the lottery participation, we have access to
information from the employment statistics, in which case there is no missing
information. For those not working in Liechtenstein prior to the lottery, we
need to rely on the variables from the migration lottery, in which missings do
occur. Albeit some of the missing information can be used based on the
employment statistics in later (i.e. treatment or outcome) periods in
particular for determining the age in the year of the lottery, this is
dependent on entering the labor market in Liechtenstein at some point in time.
As lottery losers enter the labor market less frequently than lottery winners,
their share of missing covariates is endogenously higher even under a
satisfaction of randomized assignment. This issue does not affect our main
results since we do not drop any observations with missing covariate
information, in order to avoid jeopardizing randomization through an
endogenously selected subsample.

Table 2: Descriptive statistics: First participation from 2006 to 2016

| $Z=1$ | $Z=0$ |  |  |  |
---|---|---|---|---|---|---
| mean | std.dev | mean | std.dev | mean difference | t-value | p-value | observations
Female | 0.29 | 0.45 | 0.30 | 0.46 | -0.01 | -0.51 | 0.61 | 3,145
Nationality |  |  |  |  |  |  |  |
Missing Dummy | 0.00 | 0.00 | 0.02 | 0.13 | -0.02 | -6.76 | 0.00 | 3,145
Austria | 0.38 | 0.49 | 0.37 | 0.48 | 0.01 | 0.40 | 0.69 | 3,100
Germany | 0.39 | 0.49 | 0.42 | 0.49 | -0.02 | -0.88 | 0.38 | 3,100
Italy | 0.06 | 0.24 | 0.07 | 0.26 | -0.01 | -0.88 | 0.38 | 3,100
Switzerland | 0.01 | 0.09 | 0.01 | 0.08 | 0.00 | 0.53 | 0.59 | 3,100
Others | 0.16 | 0.37 | 0.14 | 0.34 | 0.02 | 1.11 | 0.27 | 3,100
Age |  |  |  |  |  |  |  |
Missing Dummy | 0.01 | 0.09 | 0.02 | 0.15 | -0.01 | -2.52 | 0.01 | 3,145
Age | 37.25 | 9.25 | 37.49 | 9.62 | -0.24 | -0.46 | 0.65 | 3,078
First lottery participation |  |  |  |  |  |  |  |
Dummy 2006 | 0.09 | 0.29 | 0.10 | 0.30 | -0.01 | -0.31 | 0.76 | 3,145
Dummy 2007 | 0.09 | 0.29 | 0.10 | 0.30 | -0.01 | -0.57 | 0.57 | 3,145
Dummy 2008 | 0.09 | 0.29 | 0.14 | 0.35 | -0.05 | -2.97 | 0.00 | 3,145
Dummy 2009 | 0.10 | 0.30 | 0.09 | 0.28 | 0.01 | 0.84 | 0.40 | 3,145
Dummy 2010 | 0.06 | 0.24 | 0.09 | 0.28 | -0.02 | -1.74 | 0.08 | 3,145
Dummy 2011 | 0.11 | 0.31 | 0.09 | 0.29 | 0.01 | 0.85 | 0.39 | 3,145
Dummy 2012 | 0.09 | 0.28 | 0.07 | 0.26 | 0.02 | 1.02 | 0.31 | 3,145
Dummy 2013 | 0.08 | 0.28 | 0.06 | 0.25 | 0.02 | 1.17 | 0.24 | 3,145
Dummy 2014 | 0.10 | 0.30 | 0.08 | 0.27 | 0.03 | 1.50 | 0.13 | 3,145
Dummy 2015 | 0.09 | 0.28 | 0.08 | 0.27 | 0.01 | 0.75 | 0.45 | 3,145
Dummy 2016 | 0.08 | 0.28 | 0.09 | 0.29 | -0.01 | -0.73 | 0.46 | 3,145
Number of observations | 350 |  | 2,795 |  |  |  |  |

Sources: Lottery data (2005 - 2016) and employment statistics (2005 - 2016);
calculations are done by ourselves

Table 2 also reports the year dummies for the first lottery participation
across instrument values, providing information about variation in the ratio
of pre-draw winners and losers across different years. For year 2008, the mean
difference in dummies is statistically significant at the 1% level, owing to
the large number of lottery applicants in that year (see Figure 2), a likely
consequence of the financial crisis of 2007-2008. Such potential business
cycle-related confounding motivates controlling for period dummies in our IV
approach.

##  4 Econometric approach

In this section, we discuss our instrumental variable (IV) approach for
evaluating local average treatment effect (LATE), see Imbens and Angrist
(1994) and Angrist et al. (1996), among lottery compliers, i.e. among those
who are induced to move to Liechtenstein in the year after the lottery by
winning. Following Abadie (2003), we assume that our lottery $Z$ is a valid
and relevant instrument conditional on covariates $X$, which either include
the lottery year dummies (main specification) or both the year dummies and
additional personal characteristics (robustness check). To formally state the
identifying assumptions, we make use of the potential outcome notation, see
for instance Rubin (1974). We denote by $Y(z,d)$ the potential outcome (e.g.
hypothetical employment) under specific instrument and treatment states $z,d$
$\in$ $\\{1,0\\}$, and by $D(z)$ the potential treatment state as a function
of the instrument assignment.

Conditional IV validity, as formally stated in equation (4.1), consists of two
parts: The first part (i) implies that the lottery assignment is as good as
random given $X$ and thus not associated with other factors affecting the
treatment and/or the outcome. For reasons discussed in Section 3, this appears
plausible conditional on the year dummies. The second part (ii) states that
the lottery assignment must not have a direct effect on the outcome other
through the treatment, such that the IV exclusion restriction holds. This
assumption is satisfied if winning or losing the lottery does not directly
affect the employment decision conditional on the moving decision. Hence, the
assumption excludes, for instance, that winning or losing the lottery induces
sufficiently strong feelings of appreciation or disappointment that would make
the participant change her labor market status.

$\displaystyle(i)\quad
Z\bot\left(D(1),D(0),Y(1,1),Y(1,0),Y(0,1),Y(0,0))|X\right.$
$\displaystyle(ii)\quad\Pr(Y(1,d)=Y(0,d)=Y(d)|X)=1\quad\textrm{for
}d\in\\{1,0\\}$ (4.1)

Equation (4.2) formalizes the conditional monotonicity assumption, which rules
out the existence of so-called defiers, i.e. of individuals that would move to
Liechtenstein in the year after the lottery if losing it, but would not move
if winning. Since lottery losers are generally not allowed to move to
Liechtenstein,131313Exceptions are that someone gets married or has a common
child with a resident of Liechtenstein. this assumption holds by design in our
context.

$\Pr(D(0)>D(1)|X)=0$ (4.2)

Equation (4.3) is a common support assumption, implying that for any value of
$X$, both lottery winners and losers do exist. Indeed we find in our data that
winners and losers appear in any lottery year and as well across age groups,
nationalities and gender.

$0\textless\Pr(Z=1|X)\textless 1$ (4.3)

Finally, equation (4.4) states that the instrument is relevant in the sense
that it affects the treatment decision conditional on $X$. As discussed in
Section 5 below, winning the pre-draw does indeed importantly and
statistically significantly affect the decision to move to Liechtenstein given
the control variables.

$\Pr(D=1|Z=1,X)-\Pr(D=1|Z=0,X)\neq 0$ (4.4)

Under these assumptions, the LATE is nonparametrically identified, see Frölich
(2007), for instance by reweighing observations based on the inverse of the
conditional instrument probability $\Pr(Z=1|X)$, known as the instrument
propensity score. Equation (4.5) presents the identification result based on
such an inverse probability weighting (IPW) approach as suggested in Frölich
(2007) and Tan (2006). It is worth noting that the nominator provides the
intention-to-treat effect (ITT) or reduced form effect of the lottery
assignment $Z$ on the outcome $Y$, which is a weighted average of the LATE on
compliers and a zero effect of $Z$ among non-compliers (whose treatment does
not react to the instrument). The denominator consists of the first-stage
effect, i.e. the impact of the lottery assignment $Z$ on the decision to
reside in Liechtenstein one year after the first lottery participation $D$.

$\centering LATE=\frac{E[Y\cdot
Z/\Pr(Z=1|X)-Y\cdot(1-Z)/(1-\Pr(Z=1|X))]}{E[D\cdot
Z/\Pr(Z=1|X)-D\cdot(1-Z)/(1-\Pr(Z=1|X)]}\@add@centering$ (4.5)

For the estimation of (4.5), we use the ‘lateweight’ command of the
‘causalweight’ package (Bodory and Huber, 2018) for the statistical software
R, with 1999 bootstrap replications for computing the standard error and the
default trimming rule of dropping observations with propensity scores smaller
than 0.05 or larger than 0.95 to ensure common support in the sample. The
instrument propensity score $\Pr(Z=1|X)$ is estimated by means of a probit
specification. However, we point out that our estimator is fully nonparametric
when controlling for lottery period dummies only, which amounts to a fully
saturated model. Our estimator is semiparametric when additionally controlling
for further covariates and in particular age, whose inclusion in the linear
index of the probit model imposes parametric assumptions on $\Pr(Z=1|X)$ (but
in contrast to two-stage least squares neither on the treatment, nor on the
outcome model).

##  5 Results

This section provides the empirical results. First, the average LATE estimates
when pooling all outcome periods; second, the outcome period-specific LATE
estimates; and third, an analysis of effect heterogeneity.141414We also
briefly discuss the results when considering the second and third (rather than
the first) lottery participation as instrument and present the results of
these further analyses in Appendix A.2. Pooling the outcome periods provides a
weighted average of effects over different complier groups and outcome
periods, in which compliers who first participate in the lottery in an earlier
period obtain a larger weight due to having a longer outcome window than
compliers participating in a later period. Furthermore, earlier outcome
periods obtain a larger weight than later ones, as earlier outcome periods
(e.g. two years after first lottery participation, $t=2$) are also observed
for first lottery participants in later periods, while the observability of
later outcome periods (e.g. ten years after first lottery participation,
$t=10$) is conditional on a relatively early participation in the lottery.
While pooling and its implied weighting of observations might be considered as
hampering the interpretability of the results, our outcome period-specific
results presented further below suggest that the LATEs on the binary
employment and residence decision as well as the activity level (in %) are
quite persistent across different choices of $t$. Given that the effects are
quite stable across periods, pooling yields a concise and informative LATE and
at the same time entails a higher statistical power (or a smaller standard
error) than outcome period-specific estimations that rely on a relatively
small subsample of the data.

Table 3 reports the LATE estimates for pooled outcome periods. The upper panel
reports the effects along with bootstrap-based standard error and p-values
obtained from t-tests. As an individual might be observed in multiple outcome
periods, we cluster observations on the personal identifier by using the
cluster or block bootstrap (which resamples individuals with all related
observations in any outcome period rather than single observations) when
computing standard errors. We find that having moved to Liechtenstein one year
after the first lottery participation increases the probability of residing in
Liechtenstein by 71 percentage points and the probability of being employed in
Liechtenstein by 24 percentage points among compliers when averaging over all
outcome periods. Similarly, the effect on the activity level, which is
measured in percent and by definition zero if not working in Liechtenstein,
amounts to almost 20 percentage points. Furthermore, the duration of residing
and being employed in Liechtenstein increases by 3.44 and 1.15 years on
average, respectively, across the outcome periods, which start with $t=2$ and
are restricted by the time window of the data set. These important labor
market and residential effects are highly statistically significant, as
p-values are close to zero. The intermediate panel reports the first-stage
effect of the instrument on the treatment, which implies that 36% of the
participants in the sample are compliers. The group of non-compliers also
contains participants who won the pre-draw of the lottery but not the final
draw, as we use the pre-draw as our instrument. The p-value of the first-stage
is close to zero and the instrument is therefore strongly associated with the
treatment, thus supporting the relevance assumption postulated in (4.4). For
completeness, the lower panel of Table 3 reports the intention-to-treat effect
(ITT) of the instrument on the outcome, which is smaller than the
corresponding LATE due to the presence of non-compliers for whom the effect is
zero by definition (if defiers do not exist). All effects are highly
statistically significant. As no extremely high ($>$0.95) or extremely low
($<$0.05) probabilities of winning the lottery occur in any year of first
lottery participation, no observation was trimmed such that the estimates are
based on all 20,009 pooled observations, as indicated at the bottom of Table
3.

Table A.1 in Appendix A.2 provides the results for pooled outcome periods when
including age, gender, nationality, and missing dummies for these variables as
covariates in addition to the lottery period dummies. The effect estimates are
rather similar and again highly statistically significant. Furthermore, Tables
A.2 to A.5 in Appendix A.2 report the estimates for pooled outcome periods
when considering the second and third lottery participation (rather than the
first one) as instrument, respectively, when either using the lottery period
dummies alone or additionally the personal characteristics as control
variables. Also in these cases, the findings are all qualitatively similar to
our main results.

Table 3: Empirical results based on first participation and year dummies

| Outcomes
---|---
| Residing (binary) | Employed (binary) | Activity level (%) | Years residing | Years employed
LATE
Effect | 0.71 | 0.24 | 19.72 | 3.44 | 1.15
Standard error | 0.05 | 0.08 | 7.43 | 0.27 | 0.39
P-value | 0.00 | 0.00 | 0.01 | 0.00 | 0.00
First-stage
Effect |  |  | 0.36 |  |
Standard error |  |  | 0.03 |  |
P-value |  |  | 0.00 |  |
ITT
Effect | 0.25 | 0.09 | 7.06 | 1.23 | 0.41
Standard error | 0.03 | 0.03 | 2.92 | 0.15 | 0.15
P-value | 0.00 | 0.00 | 0.02 | 0.00 | 0.01
Number of observations |  |  | 20,009 |  |
Trimmed observations |  |  | 0 |  |

Note: Standard errors are estimated by cluster bootstrapping.

In a next step, we investigate the effects in specific outcome periods defined
relative to the year of the first lottery participation. Figure 4 displays the
estimates for the various outcomes from period $t=2$ (i.e. two years after the
lottery) up to period $t=12$. The dots represent the period-specific LATEs and
the bands correspond to the pointwise 95% confidence intervals based on the
standard bootstrap. The triangles depict the estimated mean potential outcome
among compliers under-nontreatment, see for instance Huber and Wüthrich (2019)
for a discussion of its computation, in order to judge the importance of the
effects relative to not moving to Liechtenstein. The effects on the binary
residence and employment dummies as well as the activity level are positive
throughout all periods and statistically significant at the 5% level in most
cases. However, many of the effects are imprecisely estimated in particular in
later outcome periods with a the limited number of observations, which results
in wider confidence intervals. Nevertheless, the positive point estimates
appear to be quite persistent with no sign of fading out at the end of the
data window. Relatedly, the LATEs on the durations of residing or being
employed in Liechtenstein from $t=2$ on monotonically increase as we consider
later outcome periods and due to the persistence of the residence and labor
market decisions over time, they appear to roughly follow a linear path. Panel
(f) of Figure 4 provides the number of observations per outcome period as well
as the number of trimmed observations, which is equal to zero just as for the
pooled estimations. We also inspected the plots when controlling for age,
gender, nationality, and missing dummies in addition to the lottery period
dummies and obtained similar results.

(a) Residing (binary)

(b) Employed (binary)

(c) Activity level (%)

(d) Years residing

(e) Years employed

(f) Number of observations

Figure 4: Effects over years. Dots represent LATEs, bands correspond to 95%
confidence intervals, triangles depict mean potential outcome among compliers
under non-treatment

Approximately half of the observations in our evaluation data consist of
participants that had already worked as cross-border commuters one year prior
to their first lottery, the other half of potentially new labor market
entrants were not employed in and thus, not commuting to Liechtenstein in the
previous year. Tables 4 and 5 report descriptive statistics about personal
characteristics separately for cross-border commuters and non-commuters in our
evaluation sample. We see from the tables that the majority of applicants is
male, on average 36 to 38 years old, and of either Austrian or German
nationality. However, the share of the nationalities differs in both groups:
German is the most frequent nationality among the non-commuters (on average
47%), whereas the Austrian nationality dominates among the cross-border
commuters (on average 44%).151515As mentioned in Section 3, nationality is
missing for some non-commuters, due to missing information in the lottery data
that could not be compensated by information in the employment statistics.

Table 4: Descriptive statistics for non-commuters: First participation from
2006 to 2016

| $Z=1$ | $Z=0$ |  |  |  |
---|---|---|---|---|---|---
| mean | std.dev | mean | std.dev | mean difference | t-value | p-value | observations
Female | 0.29 | 0.46 | 0.31 | 0.46 | -0.02 | -0.43 | 0.67 | 1,530
Nationality |  |  |  |  |  |  |  |
Missing Dummy | 0.00 | 0.00 | 0.03 | 0.18 | -0.03 | -6.82 | 0.00 | 1,530
Austria | 0.29 | 0.45 | 0.29 | 0.45 | 0.00 | 0.03 | 0.97 | 1,485
Germany | 0.43 | 0.50 | 0.48 | 0.50 | -0.05 | -1.21 | 0.23 | 1,485
Italy | 0.08 | 0.27 | 0.07 | 0.25 | 0.01 | 0.35 | 0.72 | 1,485
Switzerland | 0.00 | 0.00 | 0.01 | 0.08 | -0.01 | -2.83 | 0.00 | 1,485
Others | 0.20 | 0.40 | 0.16 | 0.36 | 0.05 | 1.42 | 0.16 | 1,485
Age |  |  |  |  |  |  |  |
Missing Dummy | 0.02 | 0.14 | 0.05 | 0.21 | -0.03 | -2.22 | 0.03 | 1,530
Age | 37.06 | 9.46 | 38.74 | 10.12 | -1.67 | -2.06 | 0.04 | 1,463
First lottery participation |  |  |  |  |  |  |  |
Dummy 2006 | 0.11 | 0.31 | 0.11 | 0.32 | -0.00 | -0.17 | 0.86 | 1,530
Dummy 2007 | 0.11 | 0.32 | 0.11 | 0.32 | 0.00 | 0.04 | 0.97 | 1,530
Dummy 2008 | 0.09 | 0.29 | 0.16 | 0.36 | -0.07 | -2.71 | 0.01 | 1,530
Dummy 2009 | 0.10 | 0.30 | 0.09 | 0.29 | 0.01 | 0.45 | 0.65 | 1,530
Dummy 2010 | 0.06 | 0.24 | 0.09 | 0.28 | -0.02 | -1.02 | 0.31 | 1,530
Dummy 2011 | 0.12 | 0.33 | 0.09 | 0.28 | 0.03 | 1.18 | 0.24 | 1,530
Dummy 2012 | 0.10 | 0.29 | 0.07 | 0.25 | 0.03 | 1.13 | 0.26 | 1,530
Dummy 2013 | 0.07 | 0.26 | 0.05 | 0.22 | 0.02 | 1.00 | 0.32 | 1,530
Dummy 2014 | 0.07 | 0.26 | 0.06 | 0.24 | 0.01 | 0.31 | 0.76 | 1,530
Dummy 2015 | 0.10 | 0.29 | 0.08 | 0.27 | 0.02 | 0.65 | 0.51 | 1,530
Dummy 2016 | 0.07 | 0.26 | 0.09 | 0.29 | -0.02 | -1.06 | 0.29 | 1,530
Number of observations | 157 |  | 1,373 |  |  |  |  |

Sources: Lottery data (2005 - 2016) and employment statistics (2005 - 2016).

Table 5: Descriptive statistics for cross-border commuters: First
participation from 2006 to 2016

| $Z=1$ | $Z=0$ |  |  |  |
---|---|---|---|---|---|---
| mean | std.dev | mean | std.dev | mean difference | t-value | p-value | observations
Female | 0.28 | 0.45 | 0.29 | 0.45 | -0.01 | -0.25 | 0.81 | 1,615
Nationality |  |  |  |  |  |  |  |
Austria | 0.45 | 0.50 | 0.44 | 0.50 | 0.01 | 0.24 | 0.81 | 1,615
Germany | 0.36 | 0.48 | 0.36 | 0.48 | 0.00 | 0.13 | 0.90 | 1,615
Italy | 0.05 | 0.21 | 0.08 | 0.26 | -0.03 | -1.70 | 0.09 | 1,615
Switzerland | 0.02 | 0.12 | 0.01 | 0.07 | 0.01 | 1.08 | 0.28 | 1,615
Others | 0.12 | 0.33 | 0.12 | 0.32 | 0.00 | 0.19 | 0.85 | 1,615
Age | 37.40 | 9.11 | 36.35 | 8.99 | 1.05 | 1.50 | 0.13 | 1,615
First lottery participation |  |  |  |  |  |  |  |
Dummy 2006 | 0.08 | 0.28 | 0.09 | 0.28 | -0.00 | -0.17 | 0.87 | 1,615
Dummy 2007 | 0.08 | 0.27 | 0.09 | 0.29 | -0.02 | -0.79 | 0.43 | 1,615
Dummy 2008 | 0.10 | 0.30 | 0.13 | 0.34 | -0.04 | -1.50 | 0.13 | 1,615
Dummy 2009 | 0.10 | 0.31 | 0.09 | 0.28 | 0.02 | 0.74 | 0.46 | 1,615
Dummy 2010 | 0.06 | 0.24 | 0.09 | 0.29 | -0.03 | -1.43 | 0.15 | 1,615
Dummy 2011 | 0.09 | 0.29 | 0.09 | 0.29 | 0.00 | 0.02 | 0.98 | 1,615
Dummy 2012 | 0.08 | 0.28 | 0.08 | 0.27 | 0.01 | 0.30 | 0.77 | 1,615
Dummy 2013 | 0.09 | 0.29 | 0.08 | 0.27 | 0.01 | 0.59 | 0.56 | 1,615
Dummy 2014 | 0.13 | 0.34 | 0.09 | 0.29 | 0.04 | 1.52 | 0.13 | 1,615
Dummy 2015 | 0.08 | 0.28 | 0.07 | 0.26 | 0.01 | 0.43 | 0.67 | 1,615
Dummy 2016 | 0.09 | 0.29 | 0.10 | 0.29 | -0.00 | -0.11 | 0.92 | 1,615
Number of observations | 193 |  | 1,422 |  |  |  |  |

Sources: Lottery data (2005 - 2016) and employment statistics (2005 - 2016).

In a next step, we check whether cross-border commuters who apply for the
lottery are in terms of their personal characteristics similar to or different
from cross-border commuters to Liechtenstein in general. For this reason, we
compare the average age, gender, and nationality of the cross-border commuters
in our sample with those respective average values in the administrative
statistics (Amt für Statistik Fürstentum Liechtenstein (2018a), AS; Amt für
Statistik Fürstentum Liechtenstein (2019a), AS). Male (71% versus 74%) and
younger (37 years versus 41 years) occur more frequently in our lottery data.
While Austrian and Germans cross-border commuters are the most frequent
applicants in our data, they are still “underrepresented,” as 55% of the
cross-border commuters with EEA nationality are Austrian and 24% German.
Intuitively, Austrians and Germans who can commute from their home country are
less likely to apply for the lottery than cross-border commuters with other
nationalities. Additionally, we use the cross-border survey to draw
conclusions about what the average educational level might be in our
evaluation data, in which information on education is not available. Marxer et
al. (2016) report that cross-border commuters are on average highly educated,
as 57.5% of them hold a degree from a higher education institution. Based on
these findings, we suspect that cross-border commuters applying for the
migration lottery have an average education that is likely considerably higher
than that of the general population in Austria, Switzerland, and
Liechtenstein.

From a policy perspective, it appears interesting whether treatment effects
are heterogeneous across cross-border commuters and non-commuters, i.e. if
residence permits are rather effective for attracting new or keeping existing
foreign workers that have already decided to enter Liechtenstein’s labor
market at an earlier point in time. If permits were more effective among one
rather than the other group, policy makers might want to consider to adapt
targeting of immigration policies accordingly.

Table 6: Effects among non-commuters

| Outcomes
---|---
| Residing (binary) | Employed (binary) | Activity level (%) | Years residing | Years employed
LATE
Effect | 0.71 | 0.34 | 29.78 | 3.31 | 1.56
Standard error | 0.13 | 0.15 | 13.83 | 0.60 | 0.79
P-value | 0.00 | 0.02 | 0.03 | 0.00 | 0.05
First-stage
Effect |  |  | 0.28 |  |
Standard error |  |  | 0.05 |  |
P-value |  |  | 0.00 |  |
ITT
Effect | 0.20 | 0.10 | 8.35 | 0.93 | 0.44
Standard error | 0.04 | 0.04 | 4.13 | 0.21 | 0.23
P-value | 0.00 | 0.03 | 0.04 | 0.00 | 0.06
Number of observations |  |  | 10,081 |  |
Trimmed observations |  |  | 0 |  |

Note: Standard errors are estimated by cluster bootstrapping.

For this reason, Tables 6 and 7 report the results with pooled outcome periods
separately for applicants working (cross-border commuters) and not working
(non-commuters) in Liechtenstein one year prior to the lottery. We find that
in both subsamples, the residence permit has a similarly positive and highly
significant effect on the compliers’ probability to reside in Liechtenstein
(71 vs. 69 percentage points) and their residence duration (3.31 vs. 3.46
years). In contrast, we find heterogeneous effects for the LATEs on the labor
market outcomes: The effects for previous cross-border commuters are
insignificant, whereas the effects for people not working in Liechtenstein are
significant at conventional levels. For the latter group of potential new
labor market entrants, we find that a residence permit leads to an increase in
the employment probability of 34%, in the activity level of almost 30%, and in
the employment duration of 1.56 years in the outcome periods. We therefore
conclude that the policy is more effective in raising labor supply among
individuals previously not working in Liechtenstein than among cross-border
commuters, while effects on residential choices are similar among both groups.

Table 7: Effects among cross-border commuters

| Outcomes
---|---
| Residing (binary) | Employed (binary) | Activity level (%) | Years residing | Years employed
LATE
Effect | 0.69 | 0.11 | 6.75 | 3.46 | 0.56
Standard error | 0.06 | 0.09 | 8.83 | 0.28 | 0.42
P-value | 0.00 | 0.21 | 0.44 | 0.00 | 0.18
First-stage
Effect |  |  | 0.42 |  |
Standard error |  |  | 0.04 |  |
P-value |  |  | 0.00 |  |
ITT
Effect | 0.29 | 0.05 | 2.86 | 1.47 | 0.24
Standard error | 0.04 | 0.04 | 3.75 | 0.20 | 0.18
P-value | 0.00 | 0.23 | 0.45 | 0.00 | 0.20
Number of observations |  |  | 9,928 |  |
Trimmed observations |  |  | 0 |  |

Note: Standard errors are estimated by cluster bootstrapping.

##  6 Conclusion

In this paper, we analyzed the effect of a residence permit on the labor
supply and residential decisions of foreign workers by an instrumental
variable approach exploiting a migration lottery in Liechtenstein. Our results
pointed to substantial effects on the labor market and residential attachment
of compliers, whose migration decision complies with the permit assignment in
their first lottery. We also found the labor market effects to be more
strongly driven by individuals previously not working in Liechtenstein than by
previous cross-border commuters. This implies that residence permits are more
effective for attracting new labor market entrants than for keeping previously
commuting workers in the labor market and therefore suggests stronger effects
at the extensive rather than intensive margin of labor supply. In future
research following up on our findings, one would ideally link our current data
base with tax data to examine the effect of resident permits on the income (at
least) of current cross-border commuters or on the tax revenues in
Liechtenstein.

##  Appendix A Appendix

###  A.1 Detailed institutional background

This section provides information about the conditions of participation in the
lottery and the draw in more detail. Lottery participants must hold an EEA
citizenship and transfer the required application documents as well as the
participation fees prior to a specific deadline (Landesverwaltung Fürstentum
Liechtenstein, 2009, section 38). The amount of the fee varies between the
pre-draw (100 CHF) and the final draw (500 CHF) (Ausländer- und Passamt,
2020). Persons with an entry ban, posing a threat to public safety, or
providing false statements are already excluded from the first draw of the
lottery (Landesverwaltung Fürstentum Liechtenstein, 2009, section 38, 3).

In the final draw, participants must be of full age and must not hold a
permanent residence permit (Ausländer- und Passamt, 2019b). Importantly, they
must also provide an employment contract of more than one year with a minimum
activity level of 80% or an authorized permanent cross-border business
activity in case of self-employment (Ausländer- und Passamt, 2019b). After
winning both the pre-draw and the final draw, the lottery participant must
relocate to Liechtenstein within six months, otherwise the residence permit
expires (Landesverwaltung Fürstentum Liechtenstein, 2009, section 37, 2). For
this reason, our treatment is defined based on residing in Liechtenstein in
the year after the lottery, as obtaining the permit is tied to actually moving
there. The drawing procedure can be described as follows. All submitted
applications (see Figure A.1) are put into a box and even include participants
not fulfilling all conditions (to give them the chance to appeal against a
later denial of a residence permit due to a violation of the conditions). In
the presence of a national judge and media representatives, the winners are
blindly drawn from the box and the person who draws announces the total number
of winners as well as their nationality (see Figure A.2). Lottery losers may
participate again in subsequent lotteries, while multiple applications to the
very same lottery are not allowed (Landesverwaltung Fürstentum Liechtenstein,
2009, section 38, 1) c)) .

Figure A.1: Participation voucher (of 2019). Interested candidates fill out
this form to participate in the pre-draw
Source: Ausländer- und Passamt (2019a) Figure A.2: Final draw (of spring
lottery 2016) monitored by a judge
Source: Michael Zanghellini, Liechtensteiner Volksblatt

###  A.2 Further analyses and robustness checks

Table A.1: Empirical results based on first participation and further
covariates

| Outcomes
---|---
| Residing (binary) | Employed (binary) | Activity level (%) | Years residing | Years employed
LATE
Effect | 0.70 | 0.21 | 16.70 | 3.43 | 1.02
Standard error | 0.06 | 0.08 | 7.54 | 0.27 | 0.39
P-value | 0.00 | 0.01 | 0.03 | 0.00 | 0.01
First-stage
Effect |  |  | 0.35 |  |
Standard error |  |  | 0.03 |  |
P-value |  |  | 0.00 |  |
ITT
Effect | 0.25 | 0.07 | 5.88 | 1.21 | 0.36
Standard error | 0.03 | 0.03 | 2.86 | 0.15 | 0.15
P-value | 0.00 | 0.01 | 0.04 | 0.00 | 0.02
Number of observations |  |  | 20,009 |  |
Trimmed observations |  |  | 392 |  |

Note: Standard errors are estimated by cluster bootstrapping.
Only observations whose first lottery participation was after 2005 are
included.

Figure A.3: Second participation; Propensity score; Assignment=1 Figure A.4:
Second participation; Propensity score; Assignment=0

Table A.2: Empirical results based on second participation and year dummies

| Outcomes
---|---
| Residing (binary) | Employed (binary) | Activity level (%) | Years residing | Years employed
LATE
Effect | 0.78 | 0.31 | 27.39 | 3.24 | 1.29
Standard error | 0.12 | 0.15 | 13.91 | 0.53 | 0.72
P-value | 0.00 | 0.04 | 0.05 | 0.00 | 0.07
First-stage
Effect |  |  | 0.40 |  |
Standard error | 0.06 | 0.07 | 0.07 | 0.07 | 0.07
P-value |  |  | 0.00 |  |
ITT
Effect | 0.31 | 0.12 | 10.84 | 1.28 | 0.51
Standard error | 0.06 | 0.06 | 5.13 | 0.29 | 0.26
P-value | 0.00 | 0.03 | 0.03 | 0.00 | 0.05
Number of observations |  |  | 6,771 |  |
Trimmed observations |  |  | 1,251 |  |

Note: Standard errors are estimated by cluster bootstrapping.
Only observations whose first lottery participation was after 2005 are
included.

Table A.3: Empirical results based on second participation and further
covariates

| Outcomes
---|---
| Residing (binary) | Employed (binary) | Activity level (%) | Years residing | Years employed
LATE
Effect | 0.70 | 0.25 | 26.16 | 2.81 | 0.84
Standard error | 0.11 | 0.14 | 13.58 | 0.47 | 0.66
P-value | 0.00 | 0.07 | 0.05 | 0.00 | 0.20
First-stage
Effect |  |  | 0.38 |  |
Standard error |  |  | 0.06 |  |
P-value |  |  | 0.00 |  |
ITT
Effect | 0.26 | 0.09 | 9.82 | 1.06 | 0.32
Standard error | 0.06 | 0.05 | 5.02 | 0.25 | 0.25
P-value | 0.00 | 0.08 | 0.05 | 0.00 | 0.20
Number of observations |  |  | 6,771 |  |
Trimmed observations |  |  | 1,727 |  |

Note: Standard errors are estimated by cluster bootstrapping
Only observations whose first lottery participation was after 2005 are
included.

Figure A.5: Third participation; Propensity score; Assignment=1 Figure A.6:
Third participation; Propensity score; Assignment=0

Table A.4: Empirical results based on third participation and year dummies

| Outcomes
---|---
| Residing (binary) | Employed (binary) | Activity level (%) | Years residing | Years employed
LATE
Effect | 0.77 | 0.22 | 15.19 | 2.99 | 0.88
Standard error | 0.17 | 0.18 | 16.16 | 0.89 | 0.82
P-value | 0.00 | 0.22 | 0.35 | 0.00 | 0.28
First-stage
Effect |  |  | 0.61 |  |
Standard error |  |  | 0.10 |  |
P-value |  |  | 0.00 |  |
ITT
Effect | 0.47 | 0.13 | 9.21 | 1.81 | 0.53
Standard error | 0.10 | 0.09 | 8.26 | 0.53 | 0.39
P-value | 0.00 | 0.16 | 0.27 | 0.00 | 0.17
Number of observations |  |  | 3,369 |  |
Trimmed observations |  |  | 1,088 |  |

Note: Standard errors are estimated by cluster bootstrapping.
Only observations whose first lottery participation was after 2005 are
included.

Table A.5: Empirical results based on third participation and further
covariates

| Outcomes
---|---
| Residing (binary) | Employed (binary) | Activity level (%) | Years residing | Years employed
LATE
Effect | 0.80 | 0.24 | 13.87 | 3.58 | 0.98
Standard error | 0.18 | 0.20 | 18.68 | 0.94 | 0.98
P-value | 0.00 | 0.22 | 0.46 | 0.00 | 0.32
First-stage
Effect |  |  | 0.50 |  |
Standard error | 0.10 | 0.11 | 0.10 | 0.11 | 0.11
P-value |  |  | 0.00 |  |
ITT
Effect | 0.39 | 0.12 | 6.87 | 1.77 | 0.49
Standard error | 0.09 | 0.10 | 8.94 | 0.50 | 0.45
P-value | 0.00 | 0.22 | 0.44 | 0.00 | 0.27
Number of observations |  |  | 3,369 |  |
Trimmed observations |  |  | 1,193 |  |

Note: Standard errors are estimated by cluster bootstrapping.
Only observations whose first lottery participation was after 2005 are
included.

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