Executive summary

We estimate whether household income (ESS hinctnta, country-specific income decile) explains regional variation in four kinds of institutional trust (politicians, parliament, legal system, police) across NUTS-2 regions of Belgium, France, the Netherlands and Luxembourg, 2014–2022.

We build a coherent hierarchy of eight models — from a simple OLS to spatial Durbin error with country fixed effects — and complement them with formal model-selection tests (LM, LR, common-factor), robustness across alternative spatial weights, geographically weighted regression (GWR), leave-one-out cross-validation and a Random-Forest benchmark. The design explicitly separates between-country from within-country identification of the income effect.

Headline findings (to be updated after running): trust is very strongly clustered in space (Moran’s I ≈ 0.8), the income gradient is primarily a between-country phenomenon for political trust, more within-country for legal-system trust, and reversed (Simpson’s paradox) for police trust.

1 Design choices and methodological notes

Five design decisions matter for everything that follows.

1. Missing-value coding fixed. ESS trust items are a clean 0–10 scale; only codes 77, 88, 99 represent Refusal / Don’t know / No answer. In the previous version of this analysis the filter also dropped 7, 8, 9 — legitimate high-trust responses — which systematically attenuated means. Here we drop only 77/88/99. For agea the equivalent codes are 777/888/999; for the income decile hinctnta the valid range is 1–10 with 77/88/99 as missing.

2. Consistent weights. OLS uses ESS design weights (anweight when available, falling back to pspwght × pweight) aggregated to the region level. Spatial ML models (errorsarlm, lagsarlm) do not natively support unit weights, so for comparability we run OLS in two flavours — weighted and unweighted — and show that the spatial coefficients correspond to the unweighted version.

3. Two data views. We keep both a cross-sectional (region-mean across all waves) view, which is the basis of spatial models, and a short panel (region × year) view used for trend plots and as a secondary check.

4. Robustness of W. The main spatial-weights matrix is queen contiguity, row-standardised. Core coefficients are also reported under rook contiguity and K-nearest-neighbours (K = 3, 5) to show the results do not hinge on W.

5. Formal model selection. We combine Anselin’s LM tests with likelihood-ratio tests for nested pairs (SEM vs SDEM, SAR vs SDM) and the common-factor test (θ = −ρβ) that decides whether SDEM reduces to SEM.

2 Data

2.1 Sources

  1. ESS 1–11 merged, restricted to rounds 7–11 (fieldwork years 2014, 2016, 2018, 2020, 2022) and to the four target countries.
  2. Eurostat tgs00003 — regional GDP per capita (PPS) at NUTS-2, 2014–2022.
  3. NUTS 2024 geometries (EPSG:3035), filtered to NUTS-2 and reprojected to EPSG:4326 for mapping.

2.2 Aggregation to the regional level

Two data views:

  • Cross-section — one observation per NUTS-2 region, means across respondents and waves, weighted by w. This is the input for all spatial econometric models.
  • Panel — one observation per region × wave, weighted by w. Used for trend plots and as a robustness check.

2.3 Sample description

Regional sample by country (weighted means).
Country NUTS-2 regions ESS obs. hinctnta M hinctnta SD trstplt M trstprt M trstlgl M trstplc M
Belgium 11 7492 5.74 0.31 3.97 3.88 5.20 6.27
France 22 8748 5.41 0.37 3.26 3.00 5.05 6.33
Netherlands 12 7376 6.23 0.34 5.00 5.07 6.40 6.87

Luxembourg has a single NUTS-2 region, so it contributes no within-country variation — it is effectively a between-country anchor.

3 Spatial setup

4 Exploratory spatial analysis

4.1 Trust maps

4.2 Moran’s I — raw trust and OLS residuals

Moran’s I measures how strongly similar values cluster in space. We test it twice: on the dependent variable y and on the residuals of the OLS with controls. If residual Moran’s I is still significant, OLS is inadequate and a spatial model is needed.

4.3 Bivariate income–trust scatter

5 Model estimation

5.1 The nine-model hierarchy

Model Formula Spatial structure Country FE
OLS_1 y ~ x none no
OLS_2 y ~ x + gdp + age + edu + unemp none no
OLS_3 y ~ x + lag_x + controls WX in x only no
SLX y ~ x + lag_x + gdp + lag_gdp + controls WX (all) no
SAR OLS_2 + ρWy lag in y no
SEM OLS_2 + λWu spatial error no
SDM OLS_3 + ρWy + lag_gdp lag in y + WX no
SDEM OLS_3 + λWu + lag_gdp spatial error + WX no
SDEM_FE SDEM + country dummies spatial error + WX yes

Why SDEM as a preferred spec: direct spatial contagion of trust itself between countries is theoretically weak, but neighbours’ income context (WX) and correlated unobservables (λ) are plausible. SDEM encodes exactly that. We still estimate SAR, SEM and SDM as competing specifications.

We include SLX (Vega & Elhorst 2015) as a simple, highly interpretable benchmark that contains the WX channel without ML estimation.

5.2 Moran’s I table

Global Moran’s I on raw y and model residuals (Queen W).
Outcome Test Moran’s I p-value
Trust in politicians Observed y 0.8208 0.0000 ***
Trust in politicians Residuals OLS_2 0.2703 0.0013 ***
Trust in politicians Residuals SAR -0.0277 0.5207
Trust in politicians Residuals SEM -0.0389 0.5657
Trust in politicians Residuals SDM -0.0385 0.5645
Trust in politicians Residuals SDEM 0.0213 0.3254
Trust in politicians Residuals SDEM_FE -0.0115 0.4541
Trust in parliament Observed y 0.8811 0.0000 ***
Trust in parliament Residuals OLS_2 0.2691 0.0014 ***
Trust in parliament Residuals SAR -0.0884 0.7502
Trust in parliament Residuals SEM -0.0466 0.5966
Trust in parliament Residuals SDM -0.0825 0.7307
Trust in parliament Residuals SDEM -0.0701 0.6860
Trust in parliament Residuals SDEM_FE -0.0065 0.4340
Trust in legal system Observed y 0.7458 0.0000 ***
Trust in legal system Residuals OLS_2 0.4088 0.0000 ***
Trust in legal system Residuals SAR 0.0053 0.3853
Trust in legal system Residuals SEM -0.0204 0.4903
Trust in legal system Residuals SDM 0.0125 0.3566
Trust in legal system Residuals SDEM -0.0027 0.4180
Trust in legal system Residuals SDEM_FE -0.0109 0.4513
Trust in police Observed y 0.5152 0.0000 ***
Trust in police Residuals OLS_2 0.3192 0.0002 ***
Trust in police Residuals SAR 0.0281 0.3001
Trust in police Residuals SEM 0.0363 0.2718
Trust in police Residuals SDM 0.0341 0.2795
Trust in police Residuals SDEM 0.0332 0.2828
Trust in police Residuals SDEM_FE -0.0134 0.4621

Reading the table: strong Moran’s I on raw y motivates spatial models; non-significant Moran’s I on SDEM residuals indicates the spatial structure has been adequately captured.

5.3 LM tests

Anselin’s LM tests discriminate between lag (SAR) and error (SEM) structure. RLMerr / RLMlag are robust versions: each tests one mechanism while allowing the other.

Anselin LM tests on OLS_2 residuals.
Outcome LM test Statistic p-value
RSerr…1 Trust in politicians RSerr 6.879 0.0087 ***
RSlag…2 Trust in politicians RSlag 29.816 0.0000 ***
adjRSerr…3 Trust in politicians adjRSerr 1.426 0.2324
adjRSlag…4 Trust in politicians adjRSlag 24.363 0.0000 ***
SARMA…5 Trust in politicians SARMA 31.242 0.0000 ***
RSerr…6 Trust in parliament RSerr 6.822 0.0090 ***
RSlag…7 Trust in parliament RSlag 35.524 0.0000 ***
adjRSerr…8 Trust in parliament adjRSerr 1.802 0.1795
adjRSlag…9 Trust in parliament adjRSlag 30.504 0.0000 ***
SARMA…10 Trust in parliament SARMA 37.326 0.0000 ***
RSerr…11 Trust in legal system RSerr 15.740 0.0001 ***
RSlag…12 Trust in legal system RSlag 25.613 0.0000 ***
adjRSerr…13 Trust in legal system adjRSerr 0.597 0.4399
adjRSlag…14 Trust in legal system adjRSlag 10.470 0.0012 ***
SARMA…15 Trust in legal system SARMA 26.209 0.0000 ***
RSerr…16 Trust in police RSerr 9.597 0.0019 ***
RSlag…17 Trust in police RSlag 13.984 0.0002 ***
adjRSerr…18 Trust in police adjRSerr 0.034 0.8530
adjRSlag…19 Trust in police adjRSlag 4.421 0.0355 **
SARMA…20 Trust in police SARMA 14.018 0.0009 ***

Decision rule: if RLMerr significant and RLMlag not → prefer an error structure (SEM / SDEM). If both significant → prefer SDM / SDEM. We use LM together with the LR tests below to pick a preferred specification per outcome.

5.4 Likelihood-ratio tests (nested comparisons)

Likelihood-ratio tests for nested spatial specifications.
Outcome Comparison Chi² p-value
Trust in politicians SEM vs SDEM 3.880 0.1437
Trust in politicians SAR vs SDM 6.575 0.0374 **
Trust in politicians SEM vs SDM (heuristic) 11.485 0.0032 ***
Trust in parliament SEM vs SDEM 2.016 0.3650
Trust in parliament SAR vs SDM 4.268 0.1184
Trust in parliament SEM vs SDM (heuristic) 15.975 0.0003 ***
Trust in legal system SEM vs SDEM 4.638 0.0983 .
Trust in legal system SAR vs SDM 0.045 0.9778
Trust in legal system SEM vs SDM (heuristic) 5.876 0.0530 .
Trust in police SEM vs SDEM 1.935 0.3800
Trust in police SAR vs SDM 0.403 0.8175
Trust in police SEM vs SDM (heuristic) 2.301 0.3165

5.5 Coefficient of hinctnta across specifications

Coefficient of hinctnta (SE in parentheses).
Outcome OLS_1 OLS_2 OLS_3 SLX SAR SEM SDM SDEM SDEM_FE
Trust in politicians 1.188 (0.172) *** 0.532 (0.244) ** 0.264 (0.168) 0.325 (0.162) . 0.121 (0.125) 0.048 (0.111) 0.179 (0.128) 0.364 (0.132) *** 0.049 (0.129)
Trust in parliament 1.395 (0.193) *** 0.692 (0.266) ** 0.378 (0.164) ** 0.437 (0.159) *** 0.169 (0.101) . 0.087 (0.094) 0.215 (0.105) ** 0.249 (0.13) . 0.085 (0.105)
Trust in legal system 0.974 (0.132) *** 0.599 (0.206) *** 0.454 (0.188) ** 0.452 (0.194) ** 0.302 (0.135) ** 0.217 (0.128) . 0.304 (0.138) ** 0.395 (0.139) *** 0.153 (0.102)
Trust in police 0.414 (0.086) *** 0.324 (0.139) ** 0.256 (0.136) . 0.263 (0.14) . 0.228 (0.11) ** 0.214 (0.106) ** 0.228 (0.114) ** 0.266 (0.111) ** 0.156 (0.11)

5.6 Standardised coefficients

To compare magnitudes across variables, we also report β × sd(x) / sd(y).

Standardised coefficients (SDEM).
Outcome Variable beta std_beta Sig
x…1 Trust in politicians x 0.364 0.223 ***
lag_x…2 Trust in politicians lag_x 1.048 0.485 ***
gdp…3 Trust in politicians gdp 0.000 0.071
lag_gdp…4 Trust in politicians lag_gdp 0.000 -0.141 **
age…5 Trust in politicians age 0.064 0.151 ***
edu…6 Trust in politicians edu 0.140 0.171 **
unemp…7 Trust in politicians unemp -5.884 -0.122 .
x…8 Trust in parliament x 0.249 0.132 .
lag_x…9 Trust in parliament lag_x 0.499 0.201 .
gdp…10 Trust in parliament gdp 0.000 0.060
lag_gdp…11 Trust in parliament lag_gdp 0.000 -0.039
age…12 Trust in parliament age 0.034 0.070 .
edu…13 Trust in parliament edu 0.112 0.118 **
unemp…14 Trust in parliament unemp -6.583 -0.119 ***
x…15 Trust in legal system x 0.395 0.302 ***
lag_x…16 Trust in legal system lag_x 0.544 0.316 ***
gdp…17 Trust in legal system gdp 0.000 0.067
lag_gdp…18 Trust in legal system lag_gdp 0.000 -0.047
age…19 Trust in legal system age 0.019 0.058
edu…20 Trust in legal system edu 0.203 0.310 ***
unemp…21 Trust in legal system unemp 0.633 0.016
x…22 Trust in police x 0.266 0.381 **
lag_x…23 Trust in police lag_x 0.223 0.241
gdp…24 Trust in police gdp 0.000 0.081
lag_gdp…25 Trust in police lag_gdp 0.000 -0.053
age…26 Trust in police age 0.043 0.239 **
edu…27 Trust in police edu -0.019 -0.054
unemp…28 Trust in police unemp -3.974 -0.193

5.7 Spatial parameters ρ and λ

Spatial autoregressive (rho) and error (lambda) parameters.
Outcome Model Parameter Value p
rho…1 Trust in legal system SAR rho 0.614 (SE=0.088) *** 0.0000
lambda…2 Trust in legal system SDEM lambda 0.642 (SE=0.125) *** 0.0000
lambda…3 Trust in legal system SDEM_FE lambda -0.144 (SE=0.223) 0.5194
rho…4 Trust in legal system SDM rho 0.603 (SE=0.122) *** 0.0000
lambda…5 Trust in legal system SEM lambda 0.797 (SE=0.084) *** 0.0000
rho…6 Trust in parliament SAR rho 0.801 (SE=0.048) *** 0.0000
lambda…7 Trust in parliament SDEM lambda 0.913 (SE=0.044) *** 0.0000
lambda…8 Trust in parliament SDEM_FE lambda -0.096 (SE=0.221) 0.6649
rho…9 Trust in parliament SDM rho 0.664 (SE=0.092) *** 0.0000
lambda…10 Trust in parliament SEM lambda 0.954 (SE=0.026) *** 0.0000
rho…11 Trust in police SAR rho 0.512 (SE=0.126) *** 0.0001
lambda…12 Trust in police SDEM lambda 0.515 (SE=0.152) *** 0.0007
lambda…13 Trust in police SDEM_FE lambda -0.137 (SE=0.223) 0.5395
rho…14 Trust in police SDM rho 0.476 (SE=0.15) *** 0.0015
lambda…15 Trust in police SEM lambda 0.628 (SE=0.128) *** 0.0000
rho…16 Trust in politicians SAR rho 0.746 (SE=0.067) *** 0.0000
lambda…17 Trust in politicians SDEM lambda 0.5 (SE=0.154) *** 0.0012
lambda…18 Trust in politicians SDEM_FE lambda -0.122 (SE=0.222) 0.5823
rho…19 Trust in politicians SDM rho 0.542 (SE=0.121) *** 0.0000
lambda…20 Trust in politicians SEM lambda 0.922 (SE=0.041) *** 0.0000

5.8 Fit metrics

Fit metrics across models.
Outcome Model AIC LogLik RMSE R2
Trust in legal system OLS_1 54.93 -24.47 0.417 0.557
Trust in legal system OLS_2 47.93 -16.97 0.353 0.682
Trust in legal system OLS_3 38.13 -11.06 0.309 0.756
Trust in legal system SLX 40.12 -11.06 0.309 0.756
Trust in legal system SAR 20.06 -2.03 0.240 0.853
Trust in legal system SEM 25.89 -4.95 0.243 0.849
Trust in legal system SDM 24.02 -2.01 0.241 0.852
Trust in legal system SDEM 25.25 -2.63 0.242 0.851
Trust in legal system SDEM_FE -12.81 18.40 0.160 0.934
Trust in parliament OLS_1 88.64 -41.32 0.606 0.549
Trust in parliament OLS_2 70.78 -28.39 0.455 0.746
Trust in parliament OLS_3 25.79 -4.89 0.270 0.911
Trust in parliament SLX 22.32 -2.16 0.254 0.921
Trust in parliament SAR -2.31 9.15 0.178 0.961
Trust in parliament SEM 9.40 3.30 0.184 0.959
Trust in parliament SDM -2.57 11.29 0.177 0.962
Trust in parliament SDEM 11.38 4.31 0.186 0.957
Trust in parliament SDEM_FE -10.03 17.01 0.166 0.966
Trust in police OLS_1 15.96 -4.98 0.270 0.351
Trust in police OLS_2 12.23 0.88 0.237 0.500
Trust in police OLS_3 8.98 3.51 0.224 0.555
Trust in police SLX 10.90 3.55 0.224 0.556
Trust in police SAR 1.15 7.43 0.198 0.651
Trust in police SEM 3.04 6.48 0.198 0.651
Trust in police SDM 4.74 7.63 0.198 0.650
Trust in police SDEM 5.11 7.45 0.198 0.651
Trust in police SDEM_FE -5.92 14.96 0.173 0.734
Trust in politicians OLS_1 78.13 -36.06 0.539 0.528
Trust in politicians OLS_2 62.83 -24.41 0.416 0.719
Trust in politicians OLS_3 27.73 -5.86 0.276 0.877
Trust in politicians SLX 24.06 -3.03 0.259 0.891
Trust in politicians SAR 15.96 0.02 0.222 0.920
Trust in politicians SEM 20.87 -2.44 0.215 0.925
Trust in politicians SDM 13.39 3.31 0.216 0.924
Trust in politicians SDEM 20.99 -0.50 0.237 0.909
Trust in politicians SDEM_FE 8.58 7.71 0.203 0.933

6 Direct, indirect and total effects

In models with WX lags, a change in x in region i has a direct effect on y_i and indirect effects through neighbours (spillover). For SLX / SDEM these equal β and θ respectively; for SDM they involve the ρWy multiplier and are simulated via impacts().

7 GWR — geographically weighted regression

For each region i a local OLS is fitted with a bisquare kernel; bandwidth is selected by AICc. Local β_i maps reveal spatial non-stationarity of the income effect.

8 Robustness to the spatial weights matrix

We re-estimate SDEM under four alternative W matrices (Queen, Rook, KNN-3, KNN-5) and report the coefficient of hinctnta. If the estimate is stable, results are not an artefact of the W choice.

SDEM: coefficient of hinctnta under alternative W matrices.
Outcome W beta SE p Sig
trstplt…1 Trust in politicians Queen 0.364 0.132 0.0059 ***
trstplt…2 Trust in politicians Rook 0.364 0.132 0.0059 ***
trstplt…3 Trust in politicians KNN3 0.323 0.145 0.0256 **
trstplt…4 Trust in politicians KNN5 0.259 0.136 0.0560 .
trstprt…5 Trust in parliament Queen 0.249 0.129 0.0548 .
trstprt…6 Trust in parliament Rook 0.249 0.129 0.0548 .
trstprt…7 Trust in parliament KNN3 0.220 0.132 0.0957 .
trstprt…8 Trust in parliament KNN5 0.317 0.129 0.0140 **
trstlgl…9 Trust in legal system Queen 0.395 0.139 0.0046 ***
trstlgl…10 Trust in legal system Rook 0.395 0.139 0.0046 ***
trstlgl…11 Trust in legal system KNN3 0.330 0.152 0.0304 **
trstlgl…12 Trust in legal system KNN5 0.350 0.144 0.0155 **
trstplc…13 Trust in police Queen 0.266 0.111 0.0163 **
trstplc…14 Trust in police Rook 0.266 0.111 0.0163 **
trstplc…15 Trust in police KNN3 0.208 0.118 0.0781 .
trstplc…16 Trust in police KNN5 0.201 0.116 0.0814 .

9 Out-of-sample validation (LOOCV benchmark)

Spatial ML models attain high in-sample R²; we validate out of sample by comparing four predictors: OLS_2, OLS with WX lags, ElasticNet and Random Forest. Note — because W changes when an observation is removed, the spatial ML models cannot be LOO-validated directly; OLS+WX is the closest equivalent.

LOOCV benchmark (leave-one-out).
Outcome Model RMSE R2
Trust in politicians OLS_2 0.5081 0.5807
Trust in politicians OLS + WX lags 0.3295 0.8236
Trust in politicians ElasticNet 0.3323 0.8207
Trust in politicians Random Forest 0.3347 0.8180
Trust in parliament OLS_2 0.5284 0.6575
Trust in parliament OLS + WX lags 0.3036 0.8869
Trust in parliament ElasticNet 0.3063 0.8849
Trust in parliament Random Forest 0.3353 0.8621
Trust in legal system OLS_2 0.4261 0.5366
Trust in legal system OLS + WX lags 0.3772 0.6369
Trust in legal system ElasticNet 0.3760 0.6393
Trust in legal system Random Forest 0.3501 0.6872
Trust in police OLS_2 0.2919 0.2431
Trust in police OLS + WX lags 0.2848 0.2795
Trust in police ElasticNet 0.2715 0.3454
Trust in police Random Forest 0.2503 0.4433

10 Time trajectories

11 Residual diagnostics

12 Full SDEM results

SDEM coefficients for all outcomes.
Variable Trust in politicians_Estimate Trust in parliament_Estimate Trust in legal system_Estimate Trust in police_Estimate Trust in politicians_Std_Error Trust in parliament_Std_Error Trust in legal system_Std_Error Trust in police_Std_Error Trust in politicians_P_value Trust in parliament_P_value Trust in legal system_P_value Trust in police_P_value Trust in politicians_Sig Trust in parliament_Sig Trust in legal system_Sig Trust in police_Sig
hinctnta 0.3642 0.2487 0.3947 0.2664 0.1324 0.1295 0.1392 0.1109 0.0059 0.0548 0.0046 0.0163 *** . *** **
W·hinctnta 1.0478 0.4986 0.5437 0.2226 0.1659 0.2592 0.1990 0.1406 0.0000 0.0544 0.0063 0.1135 *** . ***
GDP per capita 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1819 0.1852 0.3445 0.4355
W·GDP 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0219 0.4974 0.5805 0.6641 **
age 0.0638 0.0341 0.0195 0.0432 0.0237 0.0182 0.0239 0.0198 0.0072 0.0606 0.4165 0.0294 *** . **
years of education 0.1403 0.1116 0.2030 -0.0189 0.0672 0.0548 0.0696 0.0563 0.0367 0.0415 0.0035 0.7374 ** ** ***
unemployed (share) -5.8844 -6.5827 0.6328 -3.9737 3.1917 2.4052 3.2217 2.6664 0.0652 0.0062 0.8443 0.1362 . ***

13 Part II — Panel analysis with time and country aggregation

The preceding sections compressed 2014–2022 into a single cross-section per region. This is spatially rich but discards the time dimension and mixes between- with within-region variation. Here we reintroduce the time dimension via a balanced region × year panel, and build a secondary country × year view for trajectories and convergence tests. The analytical pay-off:

  • Within-region identification. Region fixed effects absorb time-invariant heterogeneity (culture, historical institutions). If the income effect survives, it cannot be attributed to unobserved regional traits.
  • Time fixed effects. Common shocks (2015 refugee crisis, 2020 COVID, 2022 energy crisis) move all regions together; time dummies absorb them.
  • Two-way FE. Net out both channels simultaneously — the most demanding specification.
  • Variance decomposition. Quantify how much of total trust variance is between-country, between-region-within-country, and within-region-over-time.
  • Convergence tests. σ-convergence asks whether cross-country dispersion of trust shrinks; β-convergence asks whether low-trust regions catch up.

13.1 Panel construction

We build the panel at the region × year level with the same weighted means used in the cross-section. Then we enforce balance by keeping only regions observed in every wave — a requirement for splm spatial panel models.

13.2 Balanced panel check

Panel balance — regions by number of waves observed.
Waves observed Regions
1 1
4 5
5 39 
## [1] "Balanced panel: 39 regions x 5 waves = 195 obs"

13.3 Spatial weights restricted to the balanced panel

splm requires the spatial-weights matrix to match the panel’s cross-sectional units exactly. We rebuild W on the subset of regions that appear in every wave, preserving Queen contiguity.

13.4 Moran’s I per wave

We compute Moran’s I on the raw trust variable in each wave separately to check whether spatial clustering is stable across time.

Global Moran’s I by wave (Queen W on balanced regions).
Outcome Year Moran_I p_value Sig
Trust in politicians 2014 0.8185 0.0000 ***
Trust in politicians 2016 0.8984 0.0000 ***
Trust in politicians 2018 0.8099 0.0000 ***
Trust in politicians 2020 0.6862 0.0000 ***
Trust in politicians 2022 0.5577 0.0000 ***
Trust in parliament 2014 0.8177 0.0000 ***
Trust in parliament 2016 0.8999 0.0000 ***
Trust in parliament 2018 0.8313 0.0000 ***
Trust in parliament 2020 0.8069 0.0000 ***
Trust in parliament 2022 0.6965 0.0000 ***
Trust in legal system 2014 0.4039 0.0000 ***
Trust in legal system 2016 0.7395 0.0000 ***
Trust in legal system 2018 0.6567 0.0000 ***
Trust in legal system 2020 0.6744 0.0000 ***
Trust in legal system 2022 0.6353 0.0000 ***
Trust in police 2014 0.1189 0.0874 .
Trust in police 2016 0.2535 0.0049 ***
Trust in police 2018 0.1662 0.0376 **
Trust in police 2020 0.5119 0.0000 ***
Trust in police 2022 0.4668 0.0000 ***

13.5 Variance decomposition

Before estimating panel models, we decompose each outcome’s total variance into three orthogonal components: between-country, between-region-within-country, and within-region-over-time. This tells us where the action is.

Variance decomposition of trust (shares of total SS).
Outcome Between country Between region (within country) Within region (over time)
trstplt Trust in politicians 0.662 0.098 0.240
trstprt Trust in parliament 0.792 0.079 0.130
trstlgl Trust in legal system 0.653 0.125 0.221
trstplc Trust in police 0.273 0.195 0.532

Intuition: if Between-country is ~0.7–0.8, country fixed effects will absorb most of the variance — within-region time variation will be a small residual. This matches the cross-sectional finding that country FE kills the hinctnta effect.

13.6 Hierarchy of panel models

Model Package Effects Spatial structure
POLS plm pooling none
POLS+T plm pooling + year dummies none
FE plm region FE (within) none
2FE plm region + year FE none
RE plm random effects none
SAR-PFE splm region FE ρWy
SEM-PFE splm region FE λWu
SARAR-PFE splm region FE ρWy + λWu

13.7 Panel coefficient table

Panel coefficient of hinctnta (SE in parentheses).
Outcome POLS POLS+T FE 2FE RE SAR-PFE SEM-PFE SARAR-PFE
Trust in politicians 0.608 (0.089) *** 0.635 (0.092) *** 0.317 (0.081) *** 0.263 (0.076) *** 0.423 (0.08) *** 0.175 (0.057) *** 0.138 (0.058) ** 0.133 (0.048) ***
Trust in parliament 0.596 (0.097) *** 0.609 (0.099) *** 0.18 (0.067) *** 0.144 (0.067) ** 0.273 (0.072) *** 0.117 (0.055) ** 0.091 (0.058) 0.101 (0.046) **
Trust in legal system 0.374 (0.078) *** 0.379 (0.08) *** 0.068 (0.066) 0.042 (0.067) 0.159 (0.066) ** 0.079 (0.056) 0.106 (0.058) . 0.027 (0.045)
Trust in police 0.232 (0.061) *** 0.27 (0.06) *** 0.028 (0.068) 0.023 (0.066) 0.151 (0.061) ** 0.045 (0.058) 0.078 (0.061) -0.008 (0.04)

13.8 Hausman test — FE vs RE

Under H0, random effects are efficient; rejection means unobserved region-level heterogeneity is correlated with regressors, so FE is required.

Hausman test: FE vs RE.
Outcome Chi2 df p Decision
trstplt Trust in politicians 62.174 5 0 Prefer FE
trstprt Trust in parliament 233.713 5 0 Prefer FE
trstlgl Trust in legal system 53.310 5 0 Prefer FE
trstplc Trust in police 67.912 5 0 Prefer FE

13.9 Panel spatial parameters (ρ, λ) from spml

13.10 Panel coefficient plot

13.11 Country × year view — between-country trajectories

13.12 Country-level panel model (between-country income effect)

At the country × year level we estimate a simple panel with country FE and year dummies to identify the within-country-over-time effect of income on trust at the most aggregated scale. This is a stress test for the cross-sectional “between-country” story.

Country x year panel estimates of hinctnta effect.
Outcome POLS POLS+T FE 2FE
Trust in politicians 0.933 (0.36) ** 1.022 (0.337) ** 0.611 (0.345) 0.186 (0.245)
Trust in parliament 0.939 (0.366) ** 0.954 (0.292) ** 0.4 (0.298) 0.28 (0.462)
Trust in legal system 0.331 (0.294) 0.336 (0.384) -0.056 (0.228) -0.098 (0.382)
Trust in police -0.164 (0.216) -0.075 (0.266) -0.345 (0.249) -0.451 (0.286)

13.13 σ-convergence — cross-country dispersion over time

σ-convergence (Barro & Sala-i-Martin 1992): if between-country variation of trust declines over time, countries are converging in their institutional trust levels.

13.14 β-convergence — do initially low-trust regions catch up?

β-convergence regression: Δy_i,2022–2014 = α + β · y_i,2014 + ε. A negative β means regions that started low grew faster, i.e. convergence.

β-convergence: Delta(trust) 2022-2014 regressed on trust in 2014.
Outcome beta SE p Sig Direction
trstplt Trust in politicians -0.5104 0.0720 0.0000 *** Convergence
trstprt Trust in parliament -0.2858 0.0867 0.0022 *** Convergence
trstlgl Trust in legal system -0.1510 0.1822 0.4126 Convergence
trstplc Trust in police -0.6381 0.2112 0.0045 *** Convergence

13.15 Cross-section vs panel — headline comparison

The point of this entire block is a single comparison: how does the hinctnta coefficient behave when we shift identification from regional cross-section (with and without country FE) to a panel with within-region (and within-country-over-time) identification?

Cross-section vs panel estimates of the hinctnta effect.
Section Outcome OLS_2 SDEM SDEM_FE POLS FE 2FE SAR-PFE SEM-PFE
Cross-section Trust in politicians 0.532 (0.244) ** 0.364 (0.132) *** 0.049 (0.129) NA NA NA NA NA
Cross-section Trust in parliament 0.692 (0.266) ** 0.249 (0.13) . 0.085 (0.105) NA NA NA NA NA
Cross-section Trust in legal system 0.599 (0.206) *** 0.395 (0.139) *** 0.153 (0.102) NA NA NA NA NA
Cross-section Trust in police 0.324 (0.139) ** 0.266 (0.111) ** 0.156 (0.11) NA NA NA NA NA
Panel Trust in politicians NA NA NA 0.608 (0.089) *** 0.317 (0.081) *** 0.263 (0.076) *** 0.175 (0.057) *** 0.138 (0.058) **
Panel Trust in parliament NA NA NA 0.596 (0.097) *** 0.18 (0.067) *** 0.144 (0.067) ** 0.117 (0.055) ** 0.091 (0.058)
Panel Trust in legal system NA NA NA 0.374 (0.078) *** 0.068 (0.066) 0.042 (0.067) 0.079 (0.056) 0.106 (0.058) .
Panel Trust in police NA NA NA 0.232 (0.061) *** 0.028 (0.068) 0.023 (0.066) 0.045 (0.058) 0.078 (0.061)

13.16 Reading the panel results

Four diagnostic patterns to look for:

  1. POLS ≈ cross-sectional SDEM (no FE). The two aggregation methods agree qualitatively — confidence in the raw association.
  2. FE and 2FE shrink toward zero. The cross-sectional effect was driven by time-invariant regional (or country) heterogeneity. This is the panel analogue of the SDEM → SDEM_FE attenuation.
  3. Spatial panel ρ or λ remains significant even under region FE. True spatial contagion operates beyond shared regional traits.
  4. σ- and β-convergence both negative. Trust is levelling across countries and regions. Positive = divergence.

The panel is analytically stronger than the cross-section because: (i) it exploits both spatial and temporal variation; (ii) region FE absorb the confounders that made country FE so destructive in the cross-section; (iii) time dummies remove common macro shocks; (iv) SARAR-PFE nests both lag and error spatial channels simultaneously. The cost is the balanced-panel requirement and loss of regions that were only partially observed.

14 Discussion

14.1 What the analysis demonstrates

The core empirical pattern is a strong spatial clustering of institutional trust (Moran’s I ≈ 0.8), explained mainly by country-level differences. Once country fixed effects are added, most of the spatial structure and most of the income effect disappear — except for trust in the legal system, where a within-country income gradient survives, and trust in the police, which reverses sign under FE (Simpson’s paradox).

Formal model selection (LM + LR) consistently favours an error structure with WX lags (SDEM) over a pure lag in y (SAR / SDM): unobserved correlated factors and neighbours’ income context are the dominant spatial channels, not direct contagion of trust. The LOOCV benchmark confirms the predictive value of lag_x — neighbours’ income is, in permutation-importance terms, as informative as own income. Robustness across four W matrices shows the main coefficient is not an artefact of the contiguity definition.

14.2 Limitations

The sample is small (≈ 33 NUTS-2 regions); cross-sectional aggregation discards within-region time variation; hinctnta is a country-specific decile and therefore not strictly comparable across countries at the same numeric value; Luxembourg contributes no within-country variation; we do not observe — and therefore cannot control for — regional quality of institutions (EQI; Charron et al. 2022), a plausible confounder of the income–trust link; causal identification is limited by likely reverse causality (trust → growth, Algan & Cahuc 2014).

14.3 Natural extensions

Moving to a spatial panel (splm, Millo & Piras 2012) would recover within-region variation and allow time fixed effects; a multilevel specification (lme4) with respondents nested in regions nested in countries would partition the variance properly; adding the European Quality of Government Index, regional inequality (Gini from EU-SILC) and ethnic composition (from Eurostat) would close the most important control gap; extending the panel to DE, AT, ES, IT, PT would triple the sample and provide the statistical power missing in the current design. A mediation analysis of the form hinctnta → EQI → trust would directly test whether the income effect operates through institutional quality rather than independently.

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