1 Introduction

Globally, one in every four individuals will experience mental health problems, and mental health challenges are a major cause of the overall disease burden worldwide (Steel et al. 2014). In Europe, the total estimated cost of mental health problems was equal to 3.5% of aggregate gross domestic product in 2010 (OECD 2016). Thus, tackling mental health concerns is becoming a key issue in social welfare, public health, and labor market policies in many countries. Several studies have shown that residents in economically deprived neighborhoods have worse mental health than residents in wealthier neighborhoods (Truong and Ma 2006), and studies on neighborhood effects suggest that mental health in particular is affected by neighborhood characteristics (Ludwig et al. 2001). Nevertheless, the empirical evidence of the causal effects of neighborhood economic deprivation on residents’ mental health is sparse.

This paper investigates the causal effect of exposure to an economically deprived neighborhood on mental health in Copenhagen, Denmark. To estimate the causal effect, we exploit the quasi-random assignment ofapplicants to apartments in different neighborhoods. The assignment is quasi-random because the Public Social Housing office matches applications with vacant apartments based on information on household size and financial means only, and thus, conditional on these characteristics, it is a matter of chance which neighborhood the applicant ends up in. We apply a measure of deprivation that captures a number of aspects of neighborhood deprivation, such as low labor force attachment, low income, high crime levels, and high percentages of people with mental health problems. To measure mental health, we use an indicator for whether the applicant was treated with psychiatric medications.Footnote 1

One reason for the limited literature investigating the causal inference of neighborhood deprivation on mental health is the empirical challenge of separating individual factors from neighborhood factors. People might choose where to live according to individual preferences or limited finances (Cheshire et al. 2014; Topa and Zenou 2015). If individual characteristics and preferences correlate with mental health, results based on observational data might not be sufficient for determining whether mental illness is caused by individual or neighborhood characteristics. Another reason is the limited access to detailed data measuring the characteristics of individuals and their physical and social environments over time. Such data are needed for distinguishing between the effect of social interaction and the institutional and structural environments of the neighborhood (Manski 1993).

Theories from sociology, psychology, and economics posit various hypotheses explaining why the characteristics and composition of residents in a neighborhood affect mental health. Two hypotheses predominate. The first hypothesis is that mental health problems can be spread through social interactions. Living among disadvantaged neighbors may affect new residents through a lack of residence-based social support (Carpiano 2007), through a greater acceptance of drug abuse, or through psychological imitation of people living nearby (Hatfield et al. 1993). Exposure to an economically deprived neighborhood may also increase the level of anxiety and fear of victimization by new neighbors, leading to greater social isolation and loneliness and, in turn, to deteriorating mental health (Popkin et al. 2002). Awaworyi Churchill et al. (2019) find that neighborhood ethnic diversity is associated with a decline in mental health and that neighborhood ethnic diversity influences mental health through a lower level of neighborhood trust. Mental health can also be affected by a change in the social comparison group, leading to a positive or negative effect on mental health, depending on the individual’s characteristics (Exline and Lobel 1997).

The second hypothesis is that mental health can be affected by structural or institutional factors. Physical neighborhood characteristics, such as neglected building maintenance or green and open spaces, can affect a person’s motivation to engage in physical activity and social interaction (Jones-Rounds et al. 2014). Structural factors related to the new neighborhood, such as the quality of local schools, grocery stores, public spaces, and health care institutions, can affect the mental health of newcomers.Footnote 2 Economically deprived neighborhoods may lack access to mental health care, or the quality of the health care services might be lower than in non-deprived neighborhoods (Bissonnette et al. 2012). In addition, the tendency of general practitioners (GPs) to prescribe psychiatric medications could depend on the characteristics of their group of patients.

To separate individual effects from neighborhood effects, several studies have used natural experiments in which individuals could not choose their residential location to evaluate neighborhood effects. These studies have evaluated the effect on, for example, mortality (Deryugina and Molitor 2020; Jacob et al. 2013), crime (Damm and Dustmann 2014; J. Ludwig et al. 2001; Rotger and Galster 2019), and labor market and educational outcomes (Beaman 2012; Chetty et al. 2016; Damm 2014; Edin et al. 2003; Jacob 2004; Åslund et al. 2011). To identify the causal effect of peers on mental health, Eisenberg et al. (2013), using a survey of first-year college students who were randomly assigned a roommate, find small effects on mental health measures. The effects differed by gender and pre-existing depression: For men with pre-existing depression, being paired with a roommate with the same symptoms had major negative effects on their mental health, whereas when paired with a depressed roommate, women with pre-existing depression appeared less depressed than men. These results indicate gender differences in exposure and reactions to new neighbors.

Several studies have taken advantage of the moving to opportunity (MTO) experiment from the USA, which randomly assigned participants to move to either a neighborhood with a low poverty rate or any other neighborhood and then compared them with non-movers (Sanbonmatsu et al. 2011). MTO results on mental health outcomes indicate that those who moved to a better neighborhood experienced a reduction in depressive periods (Katz et al. 2001; Kling et al. 2007; Leventhal and Brooks-Gunn 2003; Ludwig et al. 2013). However, as 98% of the adult sample in the MTO were women, this study could not estimate neighborhood effects for men.

Our study contributes to the literature on the effect of neighborhood characteristics on mental health by filling in these gaps in the literature. First, by using a natural experiment, the Copenhagen public social housing (PSH) program, we can isolate the neighborhood effect from the disruption effect (the impact of moving) by comparing households assigned to housing in an economically deprived neighborhood with households assigned to housing in a non-deprived neighborhood. Isolation of the neighborhood effect is critical in determining which housing policies are best and how they should be designed. Second, we estimate the effect of neighborhood deprivation on mental health by gender and immigrant status. Third, we estimate where in the distribution from most to least deprived neighborhood the effect originates. Fourth, we exclude the effect of physical and institutional neighborhood characteristics by controlling for local area characteristics and quality of housing and health care. Moreover, our study is the first to control for institutional and environmental effects related to health care. We do so by including fixed effects for general practitioners.

Fifth, as the compliance rate for the Copenhagen PSH program is significantly high (88%), we provide efficient estimates of the influence of neighborhood characteristics.Footnote 3Finally, we provide evidence of the impact of neighborhoods not only on mental health but also on various specifications of health care utilization and socioeconomic outcomes.

Our results indicate that being exposed to a deprived neighborhood increases the probability of being treated with psychiatric medication by 3.6 percentage points on average over five years. We conduct a series of tests to examine the randomness of the assignment process and our results. Our results are robust to various specifications, and we find that compared to the least deprived neighborhoods exposure only to the most deprived neighborhoods significantly increases the use of psychiatric medication. Furthermore, we find that being exposed to a deprived neighborhood increases health care utilization in general and the probability of being convicted of a crime and being non-employed.Footnote 4 The effects are positive (an increase in the use of health care treatments and the probability of being convicted of a crime and staying unemployed) and significant for men but insignificant for women.

2 Institutional context

2.1 Public social housing assignment system

Since 1950, the Municipality of Copenhagen has provided affordable housing to people with urgent housing needs through the PSH system. The assignment procedure was formalized in 1998, when the city council signed an agreement with all public housing associations—which account for 20% of the housing stock in Copenhagen and are located throughout the city.Footnote 5 Since 2000, these housing associations have made every third vacant apartment available to the municipality. The number of available apartments depends exclusively on the number of people moving out of apartments in the public housing sector at any given time.

The municipality assigns each applicant a local caseworker, who collects information on the applicant’s urgent housing need, financial means, and other issues (e.g., addictions), and health concerns. The caseworker verifies that the applicant has explored all options for finding an apartment, that the applicant has sufficient financial means for staying in the apartment that the PSH office offers, and that the applicant’s urgent housing problem is not simply a preference for moving to Copenhagen. The caseworker creates a budget, determines the applicant’s maximum affordable rent (based on household income and size, obtained from administrative databases), and determines whether the applicant meets the requirements for receiving a housing offer. When these criteria are met, the application goes to the PSH office, which matches the applicant’s household characteristics with the list of available apartments, according to household size (number of rooms needed) and financial means.

Applicants can request disability-accessible and pet-friendly apartments or specific locations. Approximately 4% of all apartments assigned by the Copenhagen PSH office allow pets. Anecdotal evidence from the PSH office indicates a low probability that a caseworker will consider individual preferences unless the applicant has been exposed to violence in the assigned neighborhood.

Although approved applicants have the right to decline the first offer, few applicants in our sample did so, likely due to the waiting time for a new housing offer (which varied from 7 to 10 months from 2000 to 2007).Footnote 6In our sample, only 12% of the applicants who received a housing offer did not move into the assigned apartment (i.e., 7% declined the offer, and 5% never moved into the apartment).Footnote 7

The assignment procedure suggests that in which neighborhood applicants with similar household size and financial means end up it is a matter of chance. Thus, we can consider the assignment procedure as quasi-randomly distributed in terms of neighborhoods. We exploit this quasi-randomness and compare the differences in outcomes for applicants who are allocated to deprived and non-deprived neighborhoods.

2.2 The Danish health care system

A brief introduction to the Danish health care system is necessary at this point, as the main outcome variable is based on public health care records and as access to health care can contribute to differences in our main outcome. The Danish health care system is universal, with most services free of charge. The GP acts as the gatekeeper to specialist consultations with, for example, a psychiatrist or psychologist. GPs and psychiatrists prescribe medication, which is highly subsidized (Pedersen 2003). When people move, they are asked to choose a new GP from the list of available GPs within 5 km of their residence if their current GP does not live within this distance. If they do not choose a GP, the municipality assigns them one. In our study, descriptive analyses show no systematic differences between residents assigned to deprived and non-deprived neighborhoods in changing GPs.Footnote 8

3 Definitions and data

3.1 Definition of neighborhood

Previous studies indicate that social interaction appears on a relatively small geographical scale, such as census tracts (Chetty and Hendren 2018) or housing blocks (Bayer et al. 2008; Grossman and Khalil 2019; Rotger and Galster 2019). Thus we define a neighborhood on a small scale and use physically contiguous housing blocks as neighborhoods, i.e., a neighborhood consists of a block comprising contiguous buildings delimited by the four intersections that constitute the corners of the block.Footnote 9 In our sample, 281 physically contiguous housing blocks fit our definition of a neighborhood, and on average, 333 people reside in each block.Footnote 10 All housing blocks belong to one of 25 non-profit housing associations in Copenhagen.

Our goal is to identify the most economically deprived neighborhoods in the Copenhagen municipality. If we base the definition on the income of the residents, as in the MTO experiment, and apply the poverty threshold used in official Danish statistics, four of 281 neighborhoods in our sample are categorized as being deprived (i.e., 0.44% of the sample is treated).Footnote 11 Thus this definition produces an extreme case in Denmark. If we were to follow Damm (2014) and Musterd and Anderson (2006) and define a deprived neighborhood based only on employment information, we would pool heterogeneous groups with very different income levels, including students, homemakers, and residents receiving a disability pension, unemployment, or social benefits. Thus, neighborhoods with a high concentration of non-employed people do not necessarily capture the most deprived neighborhoods.

In this paper, we base our definition of a deprived neighborhood on the concentration of non-employed and low-income residents.Footnote 12 We categorize a neighborhood as deprived when the percentage of non-employed residents, aged 18–64, is in the highest quartile of the non-employment distribution and when the average annual gross income per adult resident is in the lowest quartile of the gross income distribution for residents living in the public housing block in 2013.Footnote 13 In Section 5.3, we present various sensitivity tests of our definition, including tests of the thresholds of the percentage of non-employed and low-income residents and tests of other combinations of neighborhood characteristics, following definitions used in previous studies (Iversen et al. 2019; Kauppinen 2007; Wodtke et al. 2011). As the neighborhood characteristics changed relatively little over the period we study, we use the same neighborhood classification throughout 1996–2013 (Weatherall et al. 2016).

Using our preferred definition of a deprived neighborhood, we categorized 12% of the neighborhoods (34 of 281) as deprived, and, in our sample, 9% of the applicants were offered an apartment in such a neighborhood. On average, nine applicants were assigned to each of the 34 deprived neighborhoods per year.

3.2 Data

To identify the effect of a deprived neighborhood on mental health, we used combined administrative data from the PSH system (from 2000 through 2007) in Copenhagen and national administrative registry data (from 1996 through 2013). The data from the PSH system includes the records of each applicant’s date of the assignment (and acceptance or rejection) of the PSH offer, unique (national) identification (ID) number, and the full address of the offered apartment. Using each individual’s ID number, we merged the data from numerous Danish administrative registries with the PSH records to identify family members and relatives in the household both before and after they received the PSH offer. For the full population aged 18–60, the administrative registers provide information annually between 1996 and 2013 on both health care use and demographic and socioeconomic characteristics, such as age, current residence, moving patterns, country of origin, income, job status, and education level.

The data starts in 2000, when the registration of housing offer rejections began. The data ends in 2007, when the assignment rules of the PSH system changed. As of 2007, the PSH office is not allowed to assign applicants without employment to neighborhoods where the share of residents without employment is 40% or higher.Footnote 14 We imposed four restrictions on our sample. First, for households assigned to more than one address in the same year, we assumed that any assignment in a given year is quasi-random and therefore used the later address.Footnote 15 Second, to control for mental health problems up to 5 years before assignment, we restricted the dataset to individuals older than age 21 in the year of assignment, because prescription data was available only for individuals ages 18 or older.Footnote 16 Third, we restricted the assigned residents to a maximum age of 55 years during the assignment year, because we followed the residents up to 5 years after the assignment.Footnote 17 Fourth, we excluded residents who emigrated or died over the period we study, because we lacked information on their mental health for the 5 years after the assignment.

The final sample comprises 8175 individuals, 48% of whom are women. Compared to the general population living in Copenhagen, PSH system applicants are predominantly immigrants, single, without children, and non-employed, with lower income and fewer years of education.

Table 1 presents descriptive statistics of the analysis sample.Footnote 18 Approximately 47% are non-Western immigrants, 70% have fewer than 10 years of formal education, 70% are non-employed, 48% have been treated with psychiatric medications, and 7% had at least one psychiatric hospital admission during the five years prior to the assignment.The characteristics of the groups assigned to deprived or non-deprived neighborhoods do not differ significantly from one another at the 5% significance level. However, the families assigned to a deprived neighborhood have 0.1 more family members, on average, than those assigned to a non-deprived neighborhood. This difference is significant at a 10% significance level. When the PSH office assigns apartments to applicants, it takes the number of family members into account, see Section 2.1. Among the assigned applicants who accepted the housing offer, 55% still lived in the apartment 5 years after the assignment.

Table 1 Descriptive statistics
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Table 1 also presents descriptive statistics of the neighborhood characteristics measured the year before assignment. Differences between deprived and non-deprived neighborhoods illustrate the neighborhood characteristics to which the applicants are exposed when moving into different areas. Compared to non-deprived neighborhoods, deprived neighborhoods are characterized by having a significantly higher percentage of non-employed (24 percentage points higher) and a higher percentage of residents treated with psychiatric medication (10 percentage points higher). Furthermore, the average household income is about 26% lower among residents in deprived neighborhoods than in non-deprived ones. Although not significantly different, deprived neighborhoods also have a higher percentage of non-Western immigrants (12 percentage points higher) and a higher percentage of residents convicted of a crime (4.3 percentage points higher).

4 Empirical strategy

Given that the PSH program included a quasi-random assignment of applicants and had a high acceptance rate, we estimate the intention-to-treat (ITT) effect of neighborhood characteristics on mental health. As the ITT approach does not rely on the applicant’s decision as to whether to accept a PSH offer, it allows us to estimate unbiased parameter estimates. To the extent that some individuals are affected by neighborhood characteristics, our ITT estimates produce a lower (or conservative) bound for the “true” effect of neighborhood characteristics on mental health. We estimate the following model:

$${MH}_{i}= \alpha + {\beta }_{t}+ \delta {assign\_dep}_{i}+\tau {X}_{i}+{\mu }_{p}+{\mu }_{yc}+{\mu }_{gp}+{\varepsilon }_{i. }$$
(1)

In Eq. (1), \({MH}_{i}\) is the mental health outcome, where i denotes the individual. In our main specification, mental health is the average of years being treated with psychiatric medications up to 5 years after the assignment. The treatment dummy assign_dep equals 1 when the individual is assigned to a deprived neighborhood and 0 when assigned to a non-deprived neighborhood. The parameter of interest, δ, indicates the average effect for individuals assigned to a deprived neighborhood.

In Eq. (1), β is a dummy for the year of the assignment t, and Xi is a vector of control variables for improving the estimation precision. The variables include demographic and socioeconomic characteristics, information on whether the individual previously lived in a deprived neighborhood, and dummy variables for the parish code µp, which measures the time-constant structural and institutional characteristics operating at the geographical level surrounding the neighborhood.Footnote 19 In addition, to measure the quality of housing, we include µyc, a set of dummy variables for the year of construction of the building block.Footnote 20 Moreover, µgp denotes the post-assignment GP fixed effects measuring health-related institutional factors that can influence mental health. Finally, εi is the idiosyncratic error term. To circumvent the “bad control” problem (Angrist and Pischke 2008), we measured all individual control variables in the pre-assignment period. Because the sampling occurs at the household level, we clustered this unit (Abadie et al. 2017).

We estimated a local average treatment effect (LATE) and used the PSH offer in a deprived or non-deprived neighborhood as an instrument for actual residence in a two-equation system is shown in Eqs. (2) and (3):

$${MH}_{i}= \alpha + {\beta }_{t}+ \delta \widehat{{act\_dep}_{i}}+\tau {X}_{i}+{\mu }_{p}+{\mu }_{yc}+{\mu }_{gp}+{\varepsilon }_{i}$$
(2)
$${act\_dep}_{i}= \mu + \gamma {assign\_dep}_{i}+\lambda {X}_{i}+{\mu }_{p}+{\mu }_{yc}+{\mu }_{gp}+ {\nu }_{i}$$
(3)

In Eq. (3), \(\gamma\) is the coefficient for the instrumental variable, the first-stage effect, which captures the effect of receiving a PSH offer on actual residence. In Eq. (2), \(\delta\) is the parameter of interest: the effect of the exposure to the actual neighborhood where the individual lives.

Several conditions are needed for a causal interpretation of the parameter \(\delta\) to be possible. First, the first-stage condition requires that the instrumental variable affects the variable of interest, i.e., the actual residence. This condition is tested in the first stage regression (3). Second, the independence condition requires that the assignment to an apartment in a deprived neighborhood is random and, thus, independent of unobservable characteristics of residents who moved into deprived neighborhoods. While this condition is inherently untestable, we explore the exogeneity of assignment in a number of balance tests in Section 5.1. Third, the exclusion condition requires that the instrument does not affect the outcome directly but only through the actual residence. While this condition is not testable, it seems likely that the outcomes depend on the actual neighborhood characteristics (treatment) and depend on the assigned neighborhood through the actual residence only. Finally, the exposure to the neighborhood must be (monotonically) increasing with the PSH offer. Given that the population offered an apartment through the PSH office is often in no position to reject the offer, we expect the last assumption to be fulfilled.

We include a number of robustness tests of the model specification. First, we exploited the panel data structure of our data and estimate a random effect model (Baltagi 2008). Second, we tested the model specification with a propensity score matching model.Footnote 21

5 Results

5.1 Exogeneity of neighborhood assignment

As described in Section 2.1, the assignment of applicants to different neighborhoods relies on which apartments become available when the application reaches the top of the waiting list. Given the assignment procedure, we expect that the match of applicants and neighborhoods is quasi-random. To test whether this procedure is quasi-random, we compare differences between the groups allocated to deprived and non-deprived neighborhoods according to their pre-assignment characteristics.

Table 2 presents the results from estimating the probability of being assigned to an apartment in a deprived or non-deprived neighborhood, conditioned by individual applicant characteristics observed prior to applying and by year of assignment fixed effects. In the probability model, we included two variables measuring mental health: whether the applicant was treated with psychiatric medications or had been admitted to a psychiatric hospital before the assignment.Footnote 22 In column 1, we measure individual characteristics either one or up to five years before assignment. In column 2, we include information on all pre-years, i.e., we boost the sample. Except for age in the pooled sample (which is significant at a 10% significance level), none of the included variables are significantly related to the probability of being assigned to a deprived neighborhood and all parameter estimates are small in magnitude.Footnote 23 The F-test on joint significance excluding only the number of family members, household income, and year fixed effects is not rejected, suggesting that assignment to a deprived neighborhood is quasi-random.Footnote 24

Table 2 Probability of being assigned to a deprived (versus non-deprived) neighborhood
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To investigate further the independence between assignment and the applicants’ characteristics, we conducted additional balance tests. Electronic Supplementary Material Table 7 presents six balance tests of the assignment to neighborhoods with distinct characteristics. In all six regressions, the F-test on joint insignificance is not rejected.Footnote 25 Electronic Supplementary Material Table 8 presents the results from 11 regressions, where we regress the applicants’ individual characteristics on assignment into a deprived neighborhood. In all 11 regressions, we find no significant relationship between the individual characteristics (measured before assignment) and assignment to a deprived versus a non-deprived neighborhood. Drawing on the results from Tables 2, 7, and 8, we find that the assignment of households through the PSH office in Copenhagen municipality is quasi-random for the assignment of neighborhoods.

5.2 The effect on mental health of being assigned to a deprived neighborhood

Table 3 presents the estimates of the effect of the initial assignment to a deprived versus a non-deprived neighborhood on mental health, measured by treatment of psychiatric medication. In column 1, the parameter estimate in the baseline model is 0.028. When we follow some previous studies (e.g., Rotger and Galster 2019) and condition on individual characteristics and local area-fixed effects, the parameter estimate is 0.030 (column 2). In column 3, we control for the quality of housing and health care by including the year of construction of the building block and GP fixed effects and the parameter estimate increases to 0.035. In column 4, we present the results from a linear probability random effects (RE) model where we exploit the panel data structure in the outcome variable. The parameter estimate from the RE model is very similar to the one we estimate with the cross section OLS model. These fairly similar parameter estimates suggest that the quasi-random assignment does align unobserved heterogeneity between treated and control units. The parameter estimate from the RE model is 0.036, corresponding to a 3.6 percentage points increase over five years after assignment, i.e., an effect size of 11.5%.Footnote 26

Table 3 Effect of being assigned to a deprived (versus non-deprived) neighborhood on mental health outcome (treated with psychiatric medication), intention-to-treat effects
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To the extent that some individuals did not move into the apartments they were assigned to, the ITT estimates are a lower bound for the effect of exposure to a deprived neighborhood. Table 3, column 5, presents the two-stage least square (2SLS) estimates for treatment with psychiatric medication for those moving into the assigned neighborhood. The first-stage result (Eq. 3) indicates a positive and significant relationship between being assigned to a deprived neighborhood and living in it. The parameter estimate on deprived is 0.041 when we apply the 2SLS model.

Two studies suggest that becoming acquainted with the neighborhood takes time and therefore display the results of an interaction between the treatment variable and each year after the assignment (Damm 2014; Edin et al. 2003). In Fig. 1, we use the panel data and present the parameter estimates of the interactions between being assigned to a deprived neighborhood and time since assignment (one to 5 years) while controlling for the variables specified in Eq. 1. All parameter estimates are positive but only significant in the fifth year after the assignment, suggesting that the effect of neighborhood deprivation on mental health is cumulative.

Fig. 1
figure 1

Effect of being assigned to a deprived (versus non-deprived) neighborhood, intention-to-treat effects. Notes: The figure plots the parameter estimates with the 95 % confidence intervals based on a linear probability panel model with random effects. The sample is based on 8,175 applicants aged 23–55 at the time of assignment. The regression includes outcome measures one to five years after assignment and 40,769 observations. The regression includes the full set of control variables as described in Table 3. The following fixed effects are included: local area-fixed effects measured at parish level, year of construction of the building block, identifier code for general practitioner at the time of assignment and year of assignment. Standard errors are clustered at the household level.

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5.3 Alternative model specifications and sensitivity checks

We conducted various analyses to assess the sensitivity of our definition of a deprived neighborhood. First, we tested the deprivation measure based on income and non-employment by drawing different thresholds, i.e., the 20% and 30% lowest and highest values, in the distribution of income and non-employment. We present the results using the two different deprivations measures in Electronic Supplementary Material Fig. 5. Using these alternative thresholds, the results are similar to the main results in Table 3. Furthermore, using the principal component method we generated a deprivation score based on the two neighborhood characteristics, i.e., income and non-employment, and divided the score into quartiles. Compared to the least deprived neighborhoods, only the most deprived quartile significantly increases the use of psychiatric medication, see Electronic Supplementary Material Table 9.

Second, we tested four alternative definitions of a deprived neighborhood used in other studies based on other neighborhood characteristics: a Danish study (Damm 2014), which categorizes a neighborhood as deprived when the employment rate is lower than 60%, and a US (Wodtke et al 2011), a Finish (Kauppinen 2006), and a Danish study (Iversen et al. 2019) using multiple factors to construct indices of deprivation. Electronic Supplementary Material Fig. 5 shows that in all models using alternative definitions of deprivation, the parameter estimates of being assigned to a deprived neighborhood are positive, the parameter estimates varying between 0.02 and 0.11. The share of treated observations varies significantly depending on the definition. When we base the definition on employment using a 60% threshold, we increase the number of treated applicants and decrease the level of deprivation significantly, and as expected, the parameter estimate is smaller than that in Table 3 (and insignificant). Overall, the results from these sensitivity analyses lend further support to the validity of our main definition of a deprived neighborhood.

We conducted several additional tests of the validity of the main results in Table 3. First, we estimated Eq. 1 for a sample including deaths and emigrants with at least one observation after assignment. Second, we estimated Eq. 1 on a balanced sample, i.e., we exclude observations that we cannot track 5 years prior to the assignment. Third, because no clear consensus exists as to which level one should adjust standard errors for in studies similar to ours (Chetty et al. 2016; Damm and Dustmann 2014; Kling et al. 2007; Rotger and Galster 2019), we replicated the results in Table 3 and clustered the data at the neighborhood level. Fourth, as the dependent variable is bivariate, we tested a panel probit model with random effects. Fifth, we estimate a propensity score matching model. Electronic Supplementary Material Table 10 presents the results for the five alternative sample and model specifications. Changing the sample, the level of clustering, and the empirical model affects the point estimates modestly, with little effect on the qualitative conclusions in Table 3.

5.4 Heterogeneous effects by gender and immigrant status

We investigate the heterogeneous effects by gender and immigrant status because significant differences exist in health care use for these groups. Electronic Supplementary Material Table 11 presents descriptive statistics by gender and immigrant status.

In Table 4, we estimate the impact of being assigned to a deprived neighborhood separately by gender and immigrant status. The parameter estimate is positive and significant only for men and non-Western immigrants. For men, the parameter estimate is 0.062 in the OLS model and 0.073 in the 2SLS model. For non-Western immigrants, the parameter estimates are 0.046 in the OLS model and 0.052 in the 2SLS model. The corresponding results for ethnic Danes and Western immigrants are 0.030 and 0.037.Footnote 27 However, these latter results are not statistically significant.Footnote 28

Table 4 Effect of being assigned to a deprived (versus non-deprived neighborhood) on mental health outcome (treated with psychiatric medication) by gender and immigrant status, intention-to-treat effects
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In Figs. 2 and 3, we present the cumulative results of being assigned to a deprived neighborhood by gender and immigrant status, corresponding to the results in Fig. 1. The effect of assignment to a deprived neighborhood is significant for men in year four and five and for non-Western immigrants in year 5. The effect is not significant for women and for the group including ethnic Danes and Western immigrants (Figs. 2 and 3).

Fig. 2
figure 2

Effect of being assigned to a deprived (versus non-deprived) neighborhood by gender, intention-to-treat effects. Notes: The figure plots the parameter estimates with the 95 % confidence intervals based on two linear probability panel models with random effects. The sample is based on 8,175 applicants aged 23–55 at the time of assignment. The regressions include outcome measures one to five years after assignment and 40,769 observations. The regressions include the full set of control variables as described in Table 3. The following fixed effects are included: local area-fixed effects measured at parish level, year of construction of the building block, identifier code for general practitioner at the time of assignment and year of assignment. Standard errors are clustered at the household level.

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Fig. 3
figure 3

Effect of being assigned to a deprived (versus non-deprived) neighborhood by immigrant status, intention-to-treat effects. Notes: The figure plots the parameter estimates with the 95% confidence intervals based on two linear probability panel models with random effects. The sample is based on 8,175 applicants aged 23–55 at the time of assignment. The regressions include outcome measures one to five years after assignment and 40,769 observations. The regressions include the full set of control variables as described in Table 3. The following fixed effects are included: local area-fixed effects measured at parish level, year of construction of the building block, identifier code for general practitioner at the time of assignment and year of assignment. Standard errors are clustered at the household level.

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5.5 Other outcomes: health care use, crime, and remaining non-employed

In this subsection, we investigate whether the negative impact of exposure to a deprived neighborhood applies to health care use, crime, and socioeconomic outcomes. Table 5 contains the results of Eq. 1 estimated on five outcome measures: number of GP visits and the probability of being admitted to a hospital (somatic and psychiatric), convicted of a crime, and remaining non-employed. The results in column 1 suggest that, in the full sample, assignment to a deprived neighborhood increases the number of GP visits by on average 0.9 visits over five years after the assignment. The probability of being admitted to a somatic and psychiatric hospital increases, but the impact on admission to a psychiatric hospital is not statistically significant.

Table 5 Effect of being assigned to a deprived (versus non-deprived) neighborhood on various outcomes by gender and immigration status, intention-to-treat effects
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Moreover, being assigned to a deprived neighborhood increases the probability of being convicted of a crime and remaining non-employed (parameter estimates of 0.02 and 0.021, respectively). While the impact on the remaining non-employed is not significant, the impact on the probability of being convicted of a crime is relatively large and significant. In columns 2 and 3, the results are presented for men and women. The impact of being assigned to a deprived neighborhood on the outcomes number of GP visits, admitted to a somatic hospital, and staying non-employed are significant for men (for convicted of a crime, the parameter estimate is significant at the 15% significance level). For women, the parameter estimates are small and insignificant. We find only one significant result on these alternative outcomes when we split the sample by immigrant status, i.e., among etnic Danes and Western immigrants, assignment to a deprived neighborhood increases the probability of being convicted of a crime.

6 Conclusion

This study investigates the effect of neighborhood deprivation on mental health by using a unique quasi-experiment that assigns people in need of housing to different neighborhoods. The average estimated effect 1 to 5 years after the assignment on being treated with psychiatric medication is 3.6 percentage points, corresponding to an effect size of 11.5. The parameter estimate increases over time and is positive and significant in the fifth year after the assignment, suggesting that the effect of neighborhood deprivation on mental health is cumulative. The significant impact of exposure to a deprived neighborhood on being treated with psychiatric medication is robust to several sensitivity checks, including various definitions of neighborhood. Based on a continuous deprivation score, we find that compared to the least deprived neighborhoods only exposure to the most deprived neighborhoods significantly increases the use of psychiatric medication.

We estimate the effect without disruption costs and control for institutional and structural factors by including indicators for housing quality and for local area and health care fixed effects. Consequently, our results suggest that differences in institutional factors—such as access to and quality of health care and housing quality—are not the driving forces through which neighborhood characteristics affect mental health. Instead, our results point to social interactions with the new neighbors as the mechanism though which the neighborhood affects mental health. Previous literature finds a negative association between ethnic diversity in a neighborhood and mental health and points to neighborhood trust as an important mitigating factor (Awaworyi Churchill et al. 2019). However, without highly detailed information on (a) individuals’ choices and preferences and (b) the characteristics of the neighborhood in which they are placed, including, e.g., the level of trust, we cannot identify the precise type of social interactions through which neighborhood deprivation affects mental health.

While the studies based on the MTO experiment cannot estimate the effect on men, estimating the effect on this group may prove essential, as the literature on social networks suggests that men and women differ somewhat in their exposures and responses to new peers (Eisenberg et al. 2013). Our results show significant gender differences. For men, the average estimated effect on being treated with psychiatric medication one to five years after the assignment is 0.062. In contrast, the effect is not significant for women. The gender differences in our study may partly be explained by the socioeconomic characteristics of the men and women assigned to housing through the PSH system, as well as by the exposure of these groups, and their responses, to new neighbors. Descriptive statistics in our sample indicate that male applicants appeared more vulnerable than female applicants.

The MTO experiment revealed positive effects on mental health from moving from a high- to low-poverty neighborhood in the adult sample, which consisted of 98% women (Katz et al. 2001; Kling et al. 2007; Leventhal and Brooks-Gunn 2003). Several explanations exist for the different results for women in studies based on MTO and in our study. In particular, while the MTO results included both a disruption and a neighborhood effect (comparing movers with stayers), it did not account for housing quality or access to health care. Furthermore, the geographic scale of a “neighborhood” was much larger in the MTO than in our study.

The main empirical results of our paper imply that, for a society’s vulnerable populations, economically deprived neighborhoods create externalities that contribute to maintaining the poor mental health status of their residents. Consequently, policies aimed at providing affordable housing for individuals with housing needs should consider neighborhood characteristics when matching individuals with available apartments.