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The Integration Paradox

First Results of a Meta-Analysis &
Proposal of a New Experimental Design

Merlin Schaeffer & Judith Kas (WZB)

2023-04-21

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Tocqueville's Paradox




The hatred that men bear to privilege increases in proportion as privileges become fewer and less considerable,
[...]
the love of equality should constantly increase together with equality itself [...].

-- Alexis de Tocqueville (2015 [1840])

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Tocqueville's Paradox

Source: European Union Agency for Fundamental Rights. (2014)

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Tocqueville's Paradox

Source: European Union Agency for Fundamental Rights. (2014)

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An integration paradox?

Single family home in Berlin's suburb Rudow





Do immigrants and their descendants who established themselves among the middle-class mainstream report
less or more
discrimination than those who remain at the margins of society?

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An integration paradox?

Single family home in Berlin's suburb Rudow




[...] greater familiarity with the culture and language and some economic advancement can lead to greater consciousness of the reality of discrimination.

-- Portes, Parker, and Cobas (1980)

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The integration paradox Synthesized theoretical model

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Meta-analysis Which reliable patterns has the literature produced so far?

Sample definition

  1. Outcome: perceived (ethnic) discrimination.
  2. Population: Immigrants, descendants of immigrants, or members of an ethnic, religious, or racial minority.
  3. Correlation or regression coefficient & associated inference statistic: Perceived discrimination and one of the following types of indicators of immigrant integration:
    • Education, length of residence or generational status,
    • Labor market attainment (e.g., income), exposure to persons of native-born parents (e.g., neighborhood share),
    • Indicators of familiarity with public discourse (e.g., news media consumption),
    • Indicators of (downward) social mobility
  4. Published in English & no MA theses.




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Meta-analysis Which reliable patterns has the literature produced so far?

Sample definition

  1. Outcome: perceived (ethnic) discrimination.
  2. Population: Immigrants, descendants of immigrants, or members of an ethnic, religious, or racial minority.
  3. Correlation or regression coefficient & associated inference statistic: Perceived discrimination and one of the following types of indicators of immigrant integration:
    • Education, length of residence or generational status,
    • Labor market attainment (e.g., income), exposure to persons of native-born parents (e.g., neighborhood share),
    • Indicators of familiarity with public discourse (e.g., news media consumption),
    • Indicators of (downward) social mobility
  4. Published in English & no MA theses.

Sampling

  • 766 non-duplicate studies from WoS & Google Scholar via search string, 7 April 2021:

    ("integration paradox" OR "Paradox of Integration") AND discrimination

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Sample Cleaning & pre-reg training

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Sample Cleaning & pre-reg training

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Coding

Outcome

ρyx⋅z=Cov(ex⋅z,ey⋅z)SDex⋅zSDey⋅z,=t√t2+df.

Source: Gustafson (1961)

Advantage: Can get t and df from every kind of model (e.g., logit, probit, poisson, OLS).

Disadvantages: ρyx⋅z depends on z & is probably not accurate for estimates from GLMs.

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Coding

Outcome

ρyx⋅z=Cov(ex⋅z,ey⋅z)SDex⋅zSDey⋅z,=t√t2+df.

Source: Gustafson (1961)

Advantage: Can get t and df from every kind of model (e.g., logit, probit, poisson, OLS).

Disadvantages: ρyx⋅z depends on z & is probably not accurate for estimates from GLMs.

Predictors

  • Original predictor:
    • Broad indicators of integration
      • Education
      • Generation
      • Length of residence
    • Social exposure
      • Contact to mainstream members
      • Labor market attainment
    • Awareness
      • Media consumption
      • Language skills
    • Disillusion & relative deprivation
      • Downward social mobility
  • Identifiability of immigrant population studied
  • MIPEX by country-year
  • Data analyzed.
  • Nr. of good/bad controls.
  • Nr. mediators.
  • ...
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Meta-analysis

ˉρyx⋅z=∑ni=1wiρ(yx⋅z)iwi,min

  1. Fixed effects: w_{i} = \frac{1}{\color{orange}{\text{Var}(\rho_{(yx \cdot z)i})}}.

  2. Random effects: w_{i} = \frac{1}{\text{Var}(\rho_{(yx \cdot z)i}) \color{orange}{+ \tau^2}},

where \tau^2 is the between-studies variance of \rho_{(yx \cdot z)i}. Commonly, \tau^2 is estimated via REML.

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Meta-analysis

\begin{align*} \bar{\rho}_{yx \cdot z} &= \frac{\sum_{i=1}^n \color{orange}{w_{i}}\rho_{(yx \cdot z)i}}{\color{orange}{w_{i}}}, \\ \min \text{RSS} &= \min \sum_{i=1}^{n} \color{orange}{w_{i}} R_{i}^{2}. \end{align*}

  1. Fixed effects: w_{i} = \frac{1}{\color{orange}{\text{Var}(\rho_{(yx \cdot z)i})}}.

  2. Random effects: w_{i} = \frac{1}{\text{Var}(\rho_{(yx \cdot z)i}) \color{orange}{+ \tau^2}},

where \tau^2 is the between-studies variance of \rho_{(yx \cdot z)i}. Commonly, \tau^2 is estimated via REML.

Nested estimates:

  1. Code estimates for:
    • strongest dummy contrast,
    • full-sample, unless subsamples informative about identifiability,
    • racial > ethnic > national > religious > linguistic discrimination,
    • composite scale if available,
    • max demographic (e.g., gender) & min subsequent outcomes (e.g., mental health) & altern. predictors as controls,
    • No moderated/conditional coefficients.
  2. Use multilevel random effects meta-analytic models (Konstantopoulos, 2011), as implemented in R's metafor package (Viechtbauer, 2010).
rma.mv(yi = yi, V = as.matrix(vi), 
       data = sample_1, test = "t",
       mods = ~ pred,
       random = list(~ 1 | Study_ID/ID), ~ 1 | data))
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Overall meta-estimate

# Sample definition
#------------------
sample_1 <- meta_data %>%
  # Only broad integration indicators,
  filter(pred == "Education" | 
           pred == "Generation" |
           pred == "Length of residency") %>%
  # Within each indep. sample & type of predictor,
  group_by(study_ID, data, context, pred) %>%
  # Use sub-sample if available,
  filter(full_sample_num == 
           max(full_sample_num, na.rm = TRUE)) %>%
  # Use model with least number of mediators
  filter(nr_mediators == min(nr_mediators)) %>%
  # Use model with min number of bad controls
  filter(nr_bad_controls == min(nr_bad_controls)) %>%
  # Use model with max number of good controls
  filter(nr_good_controls == max(nr_good_controls)) %>%
  # Use model with minimum number of integration predictors
  filter(nr_preds == min(nr_preds)) %>%
  ungroup()
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Overall meta-estimate

# Sample definition
#------------------
sample_1 <- meta_data %>%
  # Only broad integration indicators,
  filter(pred == "Education" | 
           pred == "Generation" |
           pred == "Length of residency") %>%
  # Within each indep. sample & type of predictor,
  group_by(study_ID, data, context, pred) %>%
  # Use sub-sample if available,
  filter(full_sample_num == 
           max(full_sample_num, na.rm = TRUE)) %>%
  # Use model with least number of mediators
  filter(nr_mediators == min(nr_mediators)) %>%
  # Use model with min number of bad controls
  filter(nr_bad_controls == min(nr_bad_controls)) %>%
  # Use model with max number of good controls
  filter(nr_good_controls == max(nr_good_controls)) %>%
  # Use model with minimum number of integration predictors
  filter(nr_preds == min(nr_preds)) %>%
  ungroup()

Note: 20 partial correlation coefficients and overall meta-estimate with associated 95% confidence intervals, based on five coded studies.

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Overall meta-estimate

# Sample definition
#------------------
sample_1 <- meta_data %>%
  # Only broad integration indicators,
  filter(pred == "Education" | 
           pred == "Generation" |
           pred == "Length of residency") %>%
  # Within each indep. sample & type of predictor,
  group_by(study_ID, data, context, pred) %>%
  # Use sub-sample if available,
  filter(full_sample_num == 
           max(full_sample_num, na.rm = TRUE)) %>%
  # Use model with least number of mediators
  filter(nr_mediators == min(nr_mediators)) %>%
  # Use model with min number of bad controls
  filter(nr_bad_controls == min(nr_bad_controls)) %>%
  # Use model with max number of good controls
  filter(nr_good_controls == max(nr_good_controls)) %>%
  # Use model with minimum number of integration predictors
  filter(nr_preds == min(nr_preds)) %>%
  ungroup()

Note: Results are based on a multilevel random effects meta analysis. n = 20 partial correlation coefficients based on five coded studies and five different data sets.

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Signs of mediation?

# Sample definition
#------------------
sample_2 <- meta_data %>%
  # Only broad integration indicators,
  filter(pred == "Education" | 
           pred == "Generation" |
           pred == "Length of residency") %>%
  # Within each indep. sample & type of predictor,
  group_by(study_ID, data, context, pred) %>%
  # Use sub-sample if available,
  filter(full_sample_num == 
           max(full_sample_num, na.rm = TRUE)) %>%
  # Use model with least number of mediators
  # filter(nr_mediators == min(nr_mediators)) %>%
  # Use model with min number of bad controls
  filter(nr_bad_controls == min(nr_bad_controls)) %>%
  # Use model with max number of good controls
  filter(nr_good_controls == max(nr_good_controls)) %>%
  # Use model with minimum number of integration predictors
  filter(nr_preds == min(nr_preds)) %>%
  ungroup()
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Signs of mediation?

# Sample definition
#------------------
sample_2 <- meta_data %>%
  # Only broad integration indicators,
  filter(pred == "Education" | 
           pred == "Generation" |
           pred == "Length of residency") %>%
  # Within each indep. sample & type of predictor,
  group_by(study_ID, data, context, pred) %>%
  # Use sub-sample if available,
  filter(full_sample_num == 
           max(full_sample_num, na.rm = TRUE)) %>%
  # Use model with least number of mediators
  # filter(nr_mediators == min(nr_mediators)) %>%
  # Use model with min number of bad controls
  filter(nr_bad_controls == min(nr_bad_controls)) %>%
  # Use model with max number of good controls
  filter(nr_good_controls == max(nr_good_controls)) %>%
  # Use model with minimum number of integration predictors
  filter(nr_preds == min(nr_preds)) %>%
  ungroup()

Note: Results are based on a multilevel random effects meta analysis. n = 27 partial correlation coefficients based on five coded studies and five different data sets.

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Scope condition Citizenship rights?

Note: Results are based on a multilevel random effects meta analysis. n = 20 partial correlation coefficients based on five coded studies and five different data sets.

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Publication bias? p-curve analysis

# Sample definition
#------------------
pubbias_sample <- sample_1 %>%
  mutate(
    pred_num = case_when(
      pred == "Education" ~ 3,
      pred == "Generation" ~ 2,
      TRUE ~ 1)) %>%
  # Within each independent sample:
  group_by(study_ID, data, pop, context) %>%
  # Use preferable predictor,
  filter(pred_num == 
           max(pred_num, na.rm = TRUE)) %>%
  # Finally, choose one at random.
  sample_n(1) %>%
  ungroup()

Note: n = 12 and 6 p-values respectively.

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Synthesized theoretical model


[...] greater familiarity with the culture and language and some economic advancement can lead to greater consciousness of the reality of discrimination.

-- Portes, Parker, and Cobas (1980)

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Fundamental flaw of prior research


[...] greater familiarity with the culture and language and some economic advancement can lead to greater consciousness of the reality of discrimination.

-- Portes, Parker, and Cobas (1980)

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Fundamental flaw of prior research


[...] greater familiarity with the culture and language and some economic advancement can lead to greater consciousness of the reality of discrimination.

-- Portes, Parker, and Cobas (1980)

False Consciousness: Are the less integrated under-perceiving the true extent of discrimination they face?

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Limitation of correspondence studies

Fake CV's
have no experiences and feelings

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A new experimental design

The Trust game
Two persons' mutual evaluation of their trustworthiness

We'll have endowments of €10
Respondents will play both roles & we define actual role randomly afterwards

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A new experimental design

The Trust game
Two persons' mutual evaluation of their trustworthiness

We'll have endowments of €10
Respondents will play both roles & we define actual role randomly afterwards

Non-anonymous games
Profile photo & spoken sentence

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Actual discrimination

Non-anonymous games
Profile photo & spoken sentence

  1. €_{\text{Judith}} - \bar{€}_{\text{Co-ethnics}}, or €_{\text{Judith}} - €_{\text{anonymous}}
    • Single measure: May be ethnic or not.
    • Aggregated across 10 game partners: Ethnic discrimination.
  2. After all 11 games: Which two of the overall ten (non-anonymous) games do you want to have paid out?
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Expected & perceived discrimination

Non-anonymous games
Profile photo & spoken sentence

Expected discrimination After all games are played: What do you think,

  1. Expected \Delta€ (incentivized, €4 for correct guess)
    • how much did that game partner send you? \rightarrow €3
    • how much did that game partner send other players? \rightarrow €5
    • why did that game partner send you €2 less than the others?
  2. Do you think, that game partner chose your game as one of the two that are being paid out (incentivized, €2 for correct guess)

Perceived discrimination Three months later, respondents are informed about their aggregate personal and overall average payoffs.

  1. Why did you make less / more?
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Implementation in three steps

1) Pre-game online survey
May 2021

  • Photo & recorded sentence.
  • Berlin, Hamburg, Cologne, Frankfurt, Munich.
  • 1,500 Germans with native-born parents.
  • 900 immigrants or children of immigrants.
  • 600 Turkish immigrants or children of Turkish immigrants.

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Implementation in three steps

2) Online trust games
October 2021

  • n = 2,000.
  • Not simultaneously but strategy method.
  • Guaranteed €20, Average win €60, maximum €100.

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Implementation in three steps

3) Final survey
January 2022

  • Information about personal and overall payoffs.

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Envisioned data n = 1,500 X 8 = 12,000

Minority Pot. discriminator €_{i} - \bar{€}_{j(\text{Co-ethnics})} Exp. \Delta_i€ j selected i i exp. selection i Education i ...
i=1 (Judith) j=1 (Merlin) -3 -5 0 0 ... ...
i=1 (Judith) j=2 0 0 1 0 ... ...
i=1 (Judith) j=3 1 0 1 0 ... ...
i=1 (Judith) j=4 -1 0 1 1 ... ...
i=1 (Judith) j=5 -2 0 1 0 ... ...
i=1 (Judith) j=6 -4 0 1 0 ... ...
i=1 (Judith) j=7 3 0 0 0 ... ...
i=1 (Judith) j=8 0 0 0 0 ... ...
i=2 j=1 (Merlin) ... ... ... ... ... ...
i=2 j=4 ... ... ... ... ... ...
i=2 j=9 ... ... ... ... ... ...
i=2 j=10 ... ... ... ... ... ...
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Conclusion

  • Tocqueville's / integration paradox:
    • Interesting phenomenon & maybe rather pervasive.
    • Related to (Marxist) claims about false consciousness.
    • Hefty implications for interview/survey based reports.
    • No good toolbox to study these phenomena.
  • Training pre-reg (multilevel) meta-analysis:
    • Interesting tool for sociology despite violated assumptions?
    • Integration paradox seems credible.
  • The new experimental design:
    • Artificial, but first attempt to measure & predict individuals' under- and over-perceived discrimination.
    • Mis-perceptions may also be used as predictor, e.g. of political mobilization.
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Conclusion

  • Tocqueville's / integration paradox:
    • Interesting phenomenon & maybe rather pervasive.
    • Related to (Marxist) claims about false consciousness.
    • Hefty implications for interview/survey based reports.
    • No good toolbox to study these phenomena.
  • Training pre-reg (multilevel) meta-analysis:
    • Interesting tool for sociology despite violated assumptions?
    • Integration paradox seems credible.
  • The new experimental design:
    • Artificial, but first attempt to measure & predict individuals' under- and over-perceived discrimination.
    • Mis-perceptions may also be used as predictor, e.g. of political mobilization.


Thank you for your attention!

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References

European Union Agency for Fundamental Rights. (2014). Violence against women :an EU wide survey : results at a glance. LU: Publications Office.

Gustafson, R. L. (1961). "Partial Correlations in Regression Computations". In: Journal of the American Statistical Association, pp. 363-367.

Konstantopoulos, S. (2011). "Fixed effects and variance components estimation in three-level meta-analysis". In: Research Synthesis Methods, pp. 61-76.

Portes, A., R. N. Parker, and J. A. Cobas (1980). "Assimilation or Consciousness". In: Social Forces, pp. 200-224.

Tocqueville, A. d. (2015). Democracy in America - Vol. I. and II. Read Books Ltd.

Viechtbauer, W. (2010). "Conducting Meta-Analyses in R with the metafor Package". In: Journal of Statistical Software, pp. 1-48.

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Appendix

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Which social / psychological process?

## Sample definition
sample_3 <- meta_data %>%
  # Only broad integration indicators and full samples.
  filter(pred == "Social exposure" |
           pred == "Labor market attainment" |
           pred == "Cognitive awareness" |
           pred == "Disillusion") %>%
  # Within each independent sample & type of predictor,
  group_by(study_ID, data, context, pred) %>%
  # Use sub-sample if available,
  filter(full_sample_num == max(full_sample_num, na.rm = TRUE)) %>%
  # Use model with least number of mediators
  filter(nr_mediators == min(nr_mediators)) %>%
  # Use model with min number of bad controls
  filter(nr_bad_controls == min(nr_bad_controls)) %>%
  # Use model with max number of good controls
  filter(nr_good_controls == max(nr_good_controls)) %>%
  # Use model with minimum number of integration predictors
  # filter(nr_preds == min(nr_preds)) %>%
  ungroup()

Note: n = 34 partial correlation coefficients based on five coded studies and five different data sets.

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Small-sample publication bias? Trim and fill analysis

Note: Results are based on (multilevel, Original model) random effects meta analyses.

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Tocqueville's Paradox




The hatred that men bear to privilege increases in proportion as privileges become fewer and less considerable,
[...]
the love of equality should constantly increase together with equality itself [...].

-- Alexis de Tocqueville (2015 [1840])

2 / 33
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