Is there a race in environmental protection? A spatial econometric approach
MohammadHossein Sadeghi
2026-09-07
Abstract
This research aims to investigate spatial dependence among countries in the trajectories of their environmental policy and regulatory stringency, based on a theoretical framework that emphasizes politicians’ preferences and decision-making as well as the free movement of capital. Using panel data for 23 European Economic Area countries from 1990 to 2020, we found no compelling evidence of significant spatial dependence between the changes these European countries had in their environmental policy stringency index. The finding largely holds across alternative spatial specifications using inverse-distance and contiguity weights, as well as across different sample periods.
1. Introduction
Protecting the environment has been in the spotlight for decades, and its importance and significance have been increasing in recent years, as more attention has turned to issues of global warming, climate change, and sustainability. A widely used measure for protecting the environment and alleviating externalities, i.e., the adverse effects of economic activities on the environment, is environmental law and regulation. In this piece of research, we try to shed some light on the interdependence of environmental policy across countries, drawing on public choice theory and using a spatial econometric method. Considering the incentives of politicians and policymakers and based on the theory laid out in the following sections, we try to answer the question of whether there is an interdependence between the trajectory of environmental policy stringency that countries follow depending on their proximity and contiguity.
Similar topics and questions have attracted some attention among scholars. Two of the best examples are as follows: Zhang et al. (2020), using data from 36 Chinese provinces from 2000 to 2016, found spatial dependence among provinces in enforcing national environmental regulations. Similarly, Woods (2006) found that state-level enforcement of United States federal environmental regulations systematically depends on the enforcement behavior of regional competitor states.
This paper and relevant R codes are organized as follows. The next section is dedicated to the theory, theoretical conjectures, and the hypothesis we intend to test. In the third section, the data we use and its attributes are presented. In section four, we explain our estimation approach and our spatial model. Eventually, the fifth section presents the results and their interpretation, followed by the conclusion and research outlook in section six.
2. Theory
Public choice theory, as the extension of economic analysis and its methodological individualism to the study of politics and political behavior, has often been considered the cornerstone and the most important component of the new political economy, if not its equivalent (de Almeida, 2022; Besley, 2006, p. 29; Blankart & Koester, 2006). Public choice is built and developed based on the assumption that “voters, politicians and bureaucrats are mainly self-interested” (Tullock, 2018), criticizing the traditional so-called “benevolent politician” approach promoted by figures such as Arthur Pigou and James Meade (Besley, 2006; Persson et al., 1998, pp. 686-687). The following paragraphs reflect on environmental policymaking through a public choice and political economy lens.
One prevalent effect of introducing a measure that restricts industrial activity to reduce emissions and environmental damage could be reduced profitability in industrial economic activity. This, in turn, could result in closures or recession of the economic activity of firms or, in other words, reduced return on investment. This situation could lead to capital outflow, or even capital flight in severe cases, due to higher returns abroad, in addition to a reduction in the competitive advantage of the country’s producers against overseas competitors because of higher production costs. This effect could be more severe in places like EU member states with low costs of capital movement, due to freedom of capital movement and establishment, and low costs of shipping resources and products due to free movement of goods and people. Similarly, a decrease in the level of environmental protection in another country could have the same effects. Although in the long term, introducing and implementing environmental protection measures could be the optimal choice, it could put production and economic growth at a disadvantage in the short term.
On the other hand, politicians and policymakers often have time-inconsistent preferences (Kydland & Prescott, 1977; Voigt, 2020). In systems where decision makers face term limits, they lean toward measures and decisions that pay off in the short run but impose costs over time, when those decision makers are no longer in office, as politicians tend to maximize their own utility rather than society’s.
In this framework, considering a two-country world, when decision makers in country A take a step toward relaxing environmental regulations and policies, decision makers of country B may consider a similar change in their regulations to prevent the capital outflow country A’s move could trigger, since that could cause economic loss in country B and negatively affect the incumbent politicians through their popularity and the votes they could cast. The disadvantage that policy change puts country B’s producers at, compared with country A’s competitors, could also cause economic loss and strengthen lobbying efforts by the affected industries to take reciprocal measures. On the other hand, when country A decides to tighten environmental regulations, it could possibly cause a capital outflow from that country toward country B, which now has relatively lighter restrictions compared with before, and could create short-term economic gains for country B. This situation would reduce the costs of an advancement in protection of the environment for politicians and policymakers in country B. Moreover, the cost of staying in the status quo could possibly increase as pressure from civil society and environmental lobbies could rise, now that they have learned about changes in a relevant country and are aware that more polluting industries may relocate from that country to their own.
Considering the abovementioned theoretical considerations and theoretical conjectures, we can frame our theoretical response to the research question and the hypothesis we test. As explained in the previous paragraph, regarding the environmental regulations, we expect the countries’ policymakers to follow and reciprocate the acts of countries that affect their country. Assuming the same level of restriction on free movement of capital and goods, we expect the countries to react more to the changes in closer countries because of lower costs of moving capital and possibly easier access to the previously established supply chains and markets. Also, due to easier diffusion and more likely cultural, linguistic, and legal similarities, we expect this spatial interdependence to be particularly stronger between contiguous countries. Our hypothesis therefore would be: There is a spatial interdependence between the trajectory of environmental policy stringency of contiguous and closer countries; this relationship is positive as environmental policy stringencies move in the same direction.
3. Data
To test the abovementioned hypothesis, we rely on OECD data on climate and environmental policies (Botta & Koźluk, 2014; Kruse et al., 2022). The OECD Environmental Policy Stringency Index (EPS) is designed to capture the stringency of environmental policy as an internationally comparable measure, ranging from zero (least stringent) to six (most stringent). The index is measured annually for a group of 40 countries (including 23 countries from the European Economic Area [EEA]) from 1990 to 2020, with a focus on climate change and air pollution mitigation policies (Botta & Koźluk, 2014; Kruse et al., 2022). The graph below depicts the EPS index of 23 EEA countries over time.
library(tidyverse)
library(rnaturalearth)
library(sf)
library(spdep)
library(splm)
# 1. LOAD DATA
EPS <- read_csv("EPS.csv")
# 2. ANALYSIS SAMPLE
EEA_UK <- c(
"AUT", "BEL", "CZE", "DEU", "DNK", "ESP", "EST", "FIN",
"FRA", "GBR", "GRC", "HUN", "IRL", "ISL", "ITA", "LUX",
"NLD", "NOR", "POL", "PRT", "SVK", "SVN", "SWE"
)
EPS_EEA_UK <- EPS %>%
filter(REF_AREA %in% EEA_UK)# 3. EPS LEVELS: 1990–2020, 23 COUNTRIES
EPS_plot <- EPS_EEA_UK %>%
filter(TIME_PERIOD >= 1990, TIME_PERIOD <= 2020)
country_colors <- c(
"AUT" = "#E41A1C",
"BEL" = "#377EB8",
"CZE" = "#4DAF4A",
"DEU" = "#984EA3",
"DNK" = "#FF7F00",
"ESP" = "#A65628",
"EST" = "#F781BF",
"FIN" = "#00A6A6",
"FRA" = "#FFD92F",
"GBR" = "#666666",
"GRC" = "#1F78B4",
"HUN" = "#33A02C",
"IRL" = "#FB9A99",
"ISL" = "#6A3D9A",
"ITA" = "#B2DF8A",
"LUX" = "#CAB2D6",
"NLD" = "#FDBF6F",
"NOR" = "#FF1493",
"POL" = "#00CED1",
"PRT" = "#8B4513",
"SVK" = "#7B68EE",
"SVN" = "#32CD32",
"SWE" = "#DC143C"
)
ggplot(
EPS_plot,
aes(
x = TIME_PERIOD,
y = OBS_VALUE,
group = REF_AREA,
color = REF_AREA
)
) +
geom_line(linewidth = 0.8) +
scale_color_manual(values = country_colors) +
scale_x_continuous(
breaks = seq(1990, 2020, 5)
) +
labs(
title = "Environmental Policy Stringency, 1990–2020",
x = "Year",
y = "EPS",
color = "Country"
) +
theme_minimal() +
theme(
plot.title = element_text(face = "bold", size = 15),
legend.position = "right",
legend.title = element_text(face = "bold"),
legend.text = element_text(size = 9)
)
In our data, except for EEA countries, most other countries are geographically scattered. Moreover, our theory is based on the assumption that capital can easily move between territories with low transaction costs. Consequently, we limit our sample to those 23 countries. From our sample of 23 countries, eight (Belgium, Denmark, France, Germany, Italy, Luxembourg, the Netherlands, and the United Kingdom) were part of the European Economic Community (EEC) and subject to free movement of capital. Other countries (Ireland [1993], Portugal [1993], Spain [1993], Iceland [1994], Norway [1994], Austria [1995], Finland [1995], Greece [1995], Sweden [1995]) joined the free movement of capital regime over time until 2004, when Czech Republic, Estonia, Hungary, Poland, Slovakia, and Slovenia joined the EU. From 2004 to the end of our data time period, all countries were subject to EU regulations on the free movement of capital. The UK formally left the EU on 31 January 2020, though between 1 February and 31 December 2020 it was in the Brexit transition period and therefore remained in the Single Market with its four freedoms, including free movement of capital (European Commission, 2022). So, it would be reasonable to remove the observations (country-year) from our sample that fall in periods when the assumption of our model is not fully satisfied, creating an unbalanced panel. The problem that would arise, though, is that the splm package and its spml design do not support unbalanced panels (Millo & Piras, 2012). Facing this problem, we use a subsample covering the years 2004-2020, when all countries are subject to the free movement of capital regime, and also the full sample from 1990. It should be noted that although some countries were not subject to free movement of capital regulations during the entire period, in many cases, due to other agreements in place or preliminary phases of joining the EU, capital mobility was still relatively easy. Nevertheless, the differences in results between these two samples could be informative as well.
# 4. MAPS
world <- ne_countries(
scale = "medium",
returnclass = "sf"
)
EPS_MAP <- EPS %>%
filter(
REF_AREA %in% EEA_UK,
TIME_PERIOD %in% c(1990, 2004, 2020)
) %>%
left_join(
world %>%
st_drop_geometry() %>%
select(iso_a3, name),
by = c("REF_AREA" = "iso_a3")
) %>%
mutate(
map_name = ifelse(
is.na(name),
`Reference area`,
name
)
) %>%
select(-name)
ggplot() +
geom_sf(
data = world %>%
left_join(
EPS_MAP,
by = c("name" = "map_name")
) %>%
filter(REF_AREA %in% EEA_UK),
aes(fill = OBS_VALUE)
) +
facet_wrap(~ TIME_PERIOD) +
scale_fill_gradient(
low = "#E8F3E8",
high = "#176B3A",
name = "EPS"
) +
coord_sf(
xlim = c(-25, 35),
ylim = c(34, 72)
) +
labs(
title = "Environmental Policy Stringency in Europe",
subtitle = "1990, 2004 and 2020"
) +
theme_minimal() +
theme(
strip.text = element_text(size = 14, face = "bold"),
plot.title = element_text(size = 16, face = "bold"),
plot.subtitle = element_text(size = 12),
axis.text = element_blank(),
axis.title = element_blank(),
panel.grid = element_blank()
)
4. Methodology and estimation approach
Since we are concerned with the trajectory environmental policy stringency, not the determinants of environmental policy stringency levels, we use the yearly changes in EPS index as our dependant variable which would also make our spatially lagged independent variable. Therefor this study employs the following baseline specification: \[ \Delta EPS_{i,t} = \alpha + \lambda W\Delta EPS_{i,t} + \gamma_t + \varepsilon_{i,t} \] We use the spatial panel estimation method in a pooled panel framework. We refrained from including individual (country) fixed effects because, as mentioned before, we use annual changes in the EPS Index, not its level, and we do not expect most time-invariant factors to play a crucial role in determining changes to environmental policy stringency.
On the other hand, we control for time (year) fixed effects in our baseline model, as we expect waves of environmental policy actions, coordinated policymaking, and universal EU regulations to significantly affect countries’ environmental policy stringency trajectories. However, we couldn’t use the usual time fixed-effects approach with the splm package and its spml function, since the only explanatory variable we have is the spatially lagged variable, and the panel-structured implementation does not handle that specification. Therefore, we included a year dummy variable to account for time fixed effects in a pooled specification.
To test the hypothesis mentioned in Section 2, two types of spatial weight matrices are used. To test for proximity of countries, we used the inverse distance spatial weight matrix based on the distance (in kilometers) between the centroids of countries. We did not row-standardize it, as our theoretical framework emphasizes distance, and we expect remote countries to be less affected by other countries’ policy changes. To test for contiguous countries, as specified in our theory section, a row-standardized contiguity matrix is used.
# 5. COUNTRY CENTROIDS
centroids <- world %>%
filter(
iso_a3 %in% EEA_UK |
name %in% c("France", "Norway")
) %>%
st_centroid()
# France: metropolitan France only
france <- world %>%
filter(name == "France") %>%
st_geometry()
france_parts <- st_cast(france, "POLYGON")
france_main <- france_parts[2]
france_centroid <- st_centroid(france_main)
# Replacing centroid
st_geometry(centroids)[centroids$name == "France"] <-
france_centroid
# Correcting ISO codes
centroids <- centroids %>%
mutate(
iso_a3 = case_when(
name == "France" ~ "FRA",
name == "Norway" ~ "NOR",
TRUE ~ iso_a3
)
)
# 6. DISTANCE MATRIX
dist_matrix <- st_distance(centroids)
dist_km <- matrix(
as.numeric(dist_matrix),
nrow = nrow(dist_matrix),
ncol = ncol(dist_matrix)
) / 1000
rownames(dist_km) <- centroids$iso_a3
colnames(dist_km) <- centroids$iso_a3
# 7. INVERSE-DISTANCE WEIGHT MATRIX
W <- 1 / dist_km
diag(W) <- 0
# W in same country order as the data
country_order <- sort(unique(EPS_EEA_UK$REF_AREA))
W <- W[
country_order,
country_order
]
# 8. SPATIAL WEIGHTS OBJECT
W_listw <- mat2listw(
W,
style = "M"
)
# 9. CONSTRUCTING dEPS
EPS_PANEL <- EPS_EEA_UK %>%
arrange(REF_AREA, TIME_PERIOD) %>%
group_by(REF_AREA) %>%
mutate(
dEPS = OBS_VALUE - dplyr::lag(OBS_VALUE)
) %>%
ungroup()
# 2004+ Sample
EPS_PANEL_2004 <- EPS_PANEL %>%
filter(TIME_PERIOD >= 2004)
# Remove first observation of each country
EPS_PANEL <- EPS_PANEL %>%
filter(!is.na(dEPS))
# ============================================================
# 10. INVERSE DITANCE Models
# ============================================================
model_1 <- spml(
dEPS ~ 1,
data = EPS_PANEL,
index = c("REF_AREA", "TIME_PERIOD"),
listw = W_listw,
model = "pooling",
spatial.error = "none",
lag = TRUE)
model_2 <- spml(
dEPS ~ factor(TIME_PERIOD),
data = EPS_PANEL,
index = c("REF_AREA", "TIME_PERIOD"),
listw = W_listw,
model = "pooling",
spatial.error = "none",
lag = TRUE)
model_1_2004 <- spml(
dEPS ~ 1,
data = EPS_PANEL_2004,
index = c("REF_AREA", "TIME_PERIOD"),
listw = W_listw,
model = "pooling",
spatial.error = "none",
lag = TRUE)
model_2_2004 <- spml(
dEPS ~ factor(TIME_PERIOD),
data = EPS_PANEL_2004,
index = c("REF_AREA", "TIME_PERIOD"),
listw = W_listw,
model = "pooling",
spatial.error = "none",
lag = TRUE)
# 11. CONTIGUITY WEIGHT MATRIX
# Country polygons in same order as the panel
countries_sf <- world %>%
filter(
iso_a3 %in% EEA_UK |
name %in% c("France", "Norway")
) %>%
mutate(
iso_a3 = case_when(
name == "France" ~ "FRA",
name == "Norway" ~ "NOR",
TRUE ~ iso_a3
)
) %>%
filter(iso_a3 %in% EEA_UK) %>%
slice(match(country_order, iso_a3))
# Create Queen-contiguity neighbors
nb_queen <- poly2nb(
countries_sf,
queen = TRUE)
# Row-standardized matrix
W_neighbour <- nb2mat(
nb_queen,
style = "W",
zero.policy = TRUE)
# Adding country names
rownames(W_neighbour) <- country_order
colnames(W_neighbour) <- country_order
# Convert to listw object
W_neighbour_listw <- nb2listw(
nb_queen,
style = "W",
zero.policy = TRUE)
# ============================================================
# 12. CONTIGUITY Models
# ============================================================
model_1_neighbour <- spml(
dEPS ~ 1,
data = EPS_PANEL,
index = c("REF_AREA", "TIME_PERIOD"),
listw = W_neighbour_listw,
model = "pooling",
spatial.error = "none",
lag = TRUE)
model_2_neighbour <- spml(
dEPS ~ factor(TIME_PERIOD),
data = EPS_PANEL,
index = c("REF_AREA", "TIME_PERIOD"),
listw = W_neighbour_listw,
model = "pooling",
spatial.error = "none",
lag = TRUE)
model_1_neighbour_2004 <- spml(
dEPS ~ 1,
data = EPS_PANEL_2004,
index = c("REF_AREA", "TIME_PERIOD"),
listw = W_neighbour_listw,
model = "pooling",
spatial.error = "none",
lag = TRUE)
model_2_neighbour_2004 <- spml(
dEPS ~ factor(TIME_PERIOD),
data = EPS_PANEL_2004,
index = c("REF_AREA", "TIME_PERIOD"),
listw = W_neighbour_listw,
model = "pooling",
spatial.error = "none",
lag = TRUE)5. Results and interpretation
This section presents the empirical findings. Results are reported for both inverse distance (W1) and contiguity spatial weight matrices (W2), across four model specifications depending on the sample used (entire sample or post 2004 sub-sample) and accounting for year fixed effects (1 and 2).
As is visible in the table below, the results of our estimation based on the inverse distance spatial weight matrix do not support our hypothesis. The results are very similar across samples. In the first and third specifications, where we have not controlled for country fixed effects, the coefficient on the spatial lagged Variable is positive, though very small and insignificant. It is also worth noting that, since we are using inverse distances (in Kilometers) without standardization or any modification, the estimated coefficient is very small. As can be seen in the table, by introducing time fixed effects through year dummy variables, even that small positive coefficient vanishes, as the estimated coefficient is negative, though still very weak.
# =========================================================
# 13. TABLE OF ALL 8 Models
# =========================================================
get_results <- function(m) {
b <- m$coefficients
se <- sqrt(diag(m$vcov))
lambda <- m$arcoef
se_lambda <- sqrt(diag(m$vcov.arcoef))
p_lambda <- 2 * pnorm(-abs(lambda / se_lambda))
p_const <- 2 * pnorm(-abs(b["(Intercept)"] / se["(Intercept)"]))
stars <- function(p) {
if (p < 0.001) "***"
else if (p < 0.01) "**"
else if (p < 0.05) "*"
else if (p < 0.10) "."
else ""
}
c(
"Spatial lag (λ)" = sprintf("%.4f%s (%.4f)",
lambda, stars(p_lambda), se_lambda),
"Constant" = sprintf("%.4f%s (%.4f)",
b["(Intercept)"], stars(p_const),
se["(Intercept)"]),
"N" = nrow(m$model)
)
}
models <- list(
model_1,
model_2,
model_1_2004,
model_2_2004,
model_1_neighbour,
model_2_neighbour,
model_1_neighbour_2004,
model_2_neighbour_2004
)
table_8 <- as.data.frame(do.call(cbind, lapply(models, get_results)))
colnames(table_8) <- paste0("(", 1:8, ")")
table_8 <- rbind(
table_8,
"Year FE" = c("No", "Yes", "No", "Yes", "No", "Yes", "No", "Yes"),
"Spatial weights" = c("W1", "W1", "W1", "W1", "W2", "W2", "W2", "W2"),
"Sample" = c("Full", "Full", "2004+", "2004+",
"Full", "Full", "2004+", "2004+")
)
table_8## (1) (2) (3)
## Spatial lag (λ) 0.9990 (3.3033) -0.9990 (3.3607) 0.9990 (3.9626)
## Constant 0.0826*** (0.0088) 0.1023* (0.0428) 0.0788*** (0.0125)
## N 690 690 391
## Year FE No Yes No
## Spatial weights W1 W1 W1
## Sample Full Full 2004+
## (4) (5) (6)
## Spatial lag (λ) -0.9990 (4.9761) 0.2812*** (0.0387) 0.0847. (0.0437)
## Constant 0.1653*** (0.0462) 0.0641*** (0.0084) 0.0920* (0.0426)
## N 391 690 690
## Year FE Yes No Yes
## Spatial weights W1 W2 W2
## Sample 2004+ Full Full
## (7) (8)
## Spatial lag (λ) 0.2314*** (0.0545) 0.0256 (0.0624)
## Constant 0.0644*** (0.0122) 0.1576*** (0.0463)
## N 391 391
## Year FE No Yes
## Spatial weights W2 W2
## Sample 2004+ 2004+The situation is somewhat different in specifications where we used the contiguity matrix. In specifications 5 and 7, where we did not control for year fixed effects, we received strong and highly significant positive results. However, year fixed effects proved very strong, as controlling for them more or less revealed the insignificance of the spatial lag variable in determining the trajectories of environmental policy stringency of countries in our sample.
The difference between the results for the inverse distance and contiguity matrices was expected to some extent, as explained in the theory section, emphasizing that the factors we mentioned may especially contribute to spatial interdependence among contiguous countries.
Overall, the estimation results for the post-1990 sample were slightly more in line with our hypothesis, contrary to what we expected based on the aforementioned theoretical considerations. The estimation results for year dummy variables (available in the appendix) show a higher frequency of significant year effects post-2004. Based on this, one explanation could be that since as we go backward from 2004 the number of countries in the free movement of capital bloc decreases, the year effects affecting the bloc countries are not captured as year effects in our estimation as they did not affect all the countries, and therefore are accounted as spatial interdependence of countries, given the eastward expansion of the bloc from 1990 To 2004 so the bloc countries have been relatively close and contiguous to each other at each time. This explanation, however, does not apply to the estimation results without year fixed effects control.
6. Conclusion and outlook
Roughly speaking, the results obtained in this research, though not totally dismissive, do not support the hypothesis that countries are spatially dependent on other countries in determining changes in the stringency of their environmental policies. The rejection of the hypothesis is pronounced regarding spatial interdependence based on proximity.
Nevertheless, the estimation results for our year dummy variables (available in the appendix) could be an informative source in the way we approach the issue and for the direction of future research, especially in the context of the EU. We had multiple years with significant effects, both positive and negative, showing widespread simultaneous changes across our sample. They could involve a wide variety of incidents, as briefly mentioned in section 4. If we could identify these sorts of incidents, both independently or based on the results here, studying them individually and the dynamics involved, could expand our understanding of environmental policy-making practices and probable interdependencies. What could have gone wrong in the case of our sample, for testing our hypothesis, is the extent to which EU environmental policies and regulations dominate this policy-legal domain, in a way that most changes and updates to laws and policies are driven at the EU level, especially in more recent years. In that case, even though the EU and EEA are favorable for satisfying our assumption about capital mobility, it wouldn’t be conducive to a theoretical framework based on interaction between countries. Another issue with our sample could be the special relations between EU countries. As these countries are in a highly cooperative mode of relations with each other, are very well connected, are constantly communicating bilaterally and multilaterally at various levels in the context of international organizations with dedicated mechanisms and channels, and have a long history of coordinated action and acting as a unified bloc.
Future research could focus on testing other samples of countries, as well as differentiating between different types of environmental policies at the theoretical level, which could in turn lead to more targeted empirical tests.
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Appendix:
Full estimation results, including year dummy variables:
summary(model_1)## ML panel with spatial lag and iid errors
##
## Call:
## spreml(formula = formula, data = data, index = index, w = listw2mat(listw),
## w2 = listw2mat(listw2), lag = lag, errors = errors, cl = cl)
##
## Residuals:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.77702 -0.08257 -0.05479 0.00189 0.08410 1.41743
##
## Spatial autoregressive coefficient:
## Estimate Std. Error t-value Pr(>|t|)
## lambda 0.9990 3.3033 0.3024 0.7623
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## (Intercept) 0.0825706 0.0087753 9.4094 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model_2)## ML panel with spatial lag and iid errors
##
## Call:
## spreml(formula = formula, data = data, index = index, w = listw2mat(listw),
## w2 = listw2mat(listw2), lag = lag, errors = errors, cl = cl)
##
## Residuals:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.73821 -0.10230 -0.02105 -0.00189 0.06435 1.19436
##
## Spatial autoregressive coefficient:
## Estimate Std. Error t-value Pr(>|t|)
## lambda -0.9990 3.3607 -0.2973 0.7663
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## (Intercept) 1.0227e-01 4.2788e-02 2.3901 0.0168420 *
## factor(TIME_PERIOD)1992 -6.3034e-03 6.0511e-02 -0.1042 0.9170341
## factor(TIME_PERIOD)1993 -9.1397e-02 6.0511e-02 -1.5104 0.1309362
## factor(TIME_PERIOD)1994 -7.1327e-02 6.0511e-02 -1.1788 0.2384965
## factor(TIME_PERIOD)1995 -9.4889e-02 6.0511e-02 -1.5681 0.1168483
## factor(TIME_PERIOD)1996 -5.2959e-02 6.0511e-02 -0.8752 0.3814690
## factor(TIME_PERIOD)1997 -8.1217e-02 6.0511e-02 -1.3422 0.1795318
## factor(TIME_PERIOD)1998 -6.2651e-02 6.0511e-02 -1.0354 0.3004958
## factor(TIME_PERIOD)1999 -1.0980e-01 6.0511e-02 -1.8145 0.0696010 .
## factor(TIME_PERIOD)2000 2.4614e-01 6.0511e-02 4.0676 4.749e-05 ***
## factor(TIME_PERIOD)2001 -4.9172e-02 6.0511e-02 -0.8126 0.4164419
## factor(TIME_PERIOD)2002 1.1151e-01 6.0511e-02 1.8428 0.0653566 .
## factor(TIME_PERIOD)2003 1.2116e-01 6.0511e-02 2.0023 0.0452569 *
## factor(TIME_PERIOD)2004 6.3068e-02 6.0511e-02 1.0423 0.2972921
## factor(TIME_PERIOD)2005 2.0337e-01 6.0511e-02 3.3609 0.0007768 ***
## factor(TIME_PERIOD)2006 6.6918e-02 6.0511e-02 1.1059 0.2687785
## factor(TIME_PERIOD)2007 -1.9163e-01 6.0511e-02 -3.1669 0.0015408 **
## factor(TIME_PERIOD)2008 1.7795e-01 6.0511e-02 2.9408 0.0032740 **
## factor(TIME_PERIOD)2009 1.2043e-01 6.0511e-02 1.9902 0.0465672 *
## factor(TIME_PERIOD)2010 -2.9616e-02 6.0511e-02 -0.4894 0.6245325
## factor(TIME_PERIOD)2011 7.7361e-03 6.0511e-02 0.1278 0.8982699
## factor(TIME_PERIOD)2012 -2.1301e-01 6.0511e-02 -3.5203 0.0004311 ***
## factor(TIME_PERIOD)2013 -3.0724e-02 6.0511e-02 -0.5077 0.6116352
## factor(TIME_PERIOD)2014 -7.5488e-02 6.0511e-02 -1.2475 0.2122088
## factor(TIME_PERIOD)2015 -1.0134e-01 6.0511e-02 -1.6747 0.0939890 .
## factor(TIME_PERIOD)2016 -1.3403e-01 6.0511e-02 -2.2150 0.0267626 *
## factor(TIME_PERIOD)2017 -1.0122e-01 6.0511e-02 -1.6727 0.0943783 .
## factor(TIME_PERIOD)2018 -5.3937e-02 6.0511e-02 -0.8914 0.3727388
## factor(TIME_PERIOD)2019 -4.5142e-02 6.0511e-02 -0.7460 0.4556610
## factor(TIME_PERIOD)2020 4.3862e-05 6.0511e-02 0.0007 0.9994216
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model_1_2004)## ML panel with spatial lag and iid errors
##
## Call:
## spreml(formula = formula, data = data, index = index, w = listw2mat(listw),
## w2 = listw2mat(listw2), lag = lag, errors = errors, cl = cl)
##
## Residuals:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.77324 -0.10658 -0.02324 0.00183 0.08787 1.42120
##
## Spatial autoregressive coefficient:
## Estimate Std. Error t-value Pr(>|t|)
## lambda 0.9990 3.9626 0.2521 0.801
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## (Intercept) 0.078801 0.012518 6.295 3.073e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model_2_2004)## ML panel with spatial lag and iid errors
##
## Call:
## spreml(formula = formula, data = data, index = index, w = listw2mat(listw),
## w2 = listw2mat(listw2), lag = lag, errors = errors, cl = cl)
##
## Residuals:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.73821 -0.11355 -0.00157 -0.00183 0.08582 1.19436
##
## Spatial autoregressive coefficient:
## Estimate Std. Error t-value Pr(>|t|)
## lambda -0.9990 4.9761 -0.2008 0.8409
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## (Intercept) 0.1653359 0.0462482 3.5750 0.0003503 ***
## factor(TIME_PERIOD)2005 0.1403052 0.0654049 2.1452 0.0319384 *
## factor(TIME_PERIOD)2006 0.0038498 0.0654049 0.0589 0.9530626
## factor(TIME_PERIOD)2007 -0.2546989 0.0654049 -3.8942 9.853e-05 ***
## factor(TIME_PERIOD)2008 0.1148803 0.0654049 1.7564 0.0790117 .
## factor(TIME_PERIOD)2009 0.0573616 0.0654049 0.8770 0.3804741
## factor(TIME_PERIOD)2010 -0.0926839 0.0654049 -1.4171 0.1564595
## factor(TIME_PERIOD)2011 -0.0553316 0.0654049 -0.8460 0.3975601
## factor(TIME_PERIOD)2012 -0.2760815 0.0654049 -4.2211 2.431e-05 ***
## factor(TIME_PERIOD)2013 -0.0937915 0.0654049 -1.4340 0.1515681
## factor(TIME_PERIOD)2014 -0.1385558 0.0654049 -2.1184 0.0341385 *
## factor(TIME_PERIOD)2015 -0.1644063 0.0654049 -2.5137 0.0119482 *
## factor(TIME_PERIOD)2016 -0.1970968 0.0654049 -3.0135 0.0025826 **
## factor(TIME_PERIOD)2017 -0.1642865 0.0654049 -2.5118 0.0120104 *
## factor(TIME_PERIOD)2018 -0.1170043 0.0654049 -1.7889 0.0736272 .
## factor(TIME_PERIOD)2019 -0.1082094 0.0654049 -1.6545 0.0980351 .
## factor(TIME_PERIOD)2020 -0.0630239 0.0654049 -0.9636 0.3352482
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model_1_neighbour)## ML panel with spatial lag and iid errors
##
## Call:
## spreml(formula = formula, data = data, index = index, w = listw2mat(listw),
## w2 = listw2mat(listw2), lag = lag, errors = errors, cl = cl)
##
## Residuals:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.7585 -0.0641 -0.0363 0.0204 0.1026 1.4359
##
## Spatial autoregressive coefficient:
## Estimate Std. Error t-value Pr(>|t|)
## lambda 0.281177 0.038717 7.2624 3.803e-13 ***
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## (Intercept) 0.064070 0.008393 7.6337 2.28e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model_2_neighbour)## ML panel with spatial lag and iid errors
##
## Call:
## spreml(formula = formula, data = data, index = index, w = listw2mat(listw),
## w2 = listw2mat(listw2), lag = lag, errors = errors, cl = cl)
##
## Residuals:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.73291 -0.09201 -0.02094 0.00614 0.07742 1.21978
##
## Spatial autoregressive coefficient:
## Estimate Std. Error t-value Pr(>|t|)
## lambda 0.084653 0.043742 1.9353 0.05296 .
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## (Intercept) 0.0920105 0.0426462 2.1575 0.0309642 *
## factor(TIME_PERIOD)1992 -0.0034273 0.0603108 -0.0568 0.9546827
## factor(TIME_PERIOD)1993 -0.0803333 0.0603108 -1.3320 0.1828641
## factor(TIME_PERIOD)1994 -0.0638595 0.0603108 -1.0588 0.2896727
## factor(TIME_PERIOD)1995 -0.0844395 0.0603108 -1.4001 0.1614914
## factor(TIME_PERIOD)1996 -0.0478701 0.0603108 -0.7937 0.4273566
## factor(TIME_PERIOD)1997 -0.0710676 0.0603108 -1.1784 0.2386548
## factor(TIME_PERIOD)1998 -0.0569756 0.0603108 -0.9447 0.3448123
## factor(TIME_PERIOD)1999 -0.0980249 0.0603108 -1.6253 0.1040924
## factor(TIME_PERIOD)2000 0.2248993 0.0603108 3.7290 0.0001922 ***
## factor(TIME_PERIOD)2001 -0.0413791 0.0603108 -0.6861 0.4926512
## factor(TIME_PERIOD)2002 0.0947035 0.0603108 1.5703 0.1163552
## factor(TIME_PERIOD)2003 0.1115467 0.0603108 1.8495 0.0643812 .
## factor(TIME_PERIOD)2004 0.0558791 0.0603108 0.9265 0.3541766
## factor(TIME_PERIOD)2005 0.1882110 0.0603108 3.1207 0.0018043 **
## factor(TIME_PERIOD)2006 0.0613383 0.0603108 1.0170 0.3091363
## factor(TIME_PERIOD)2007 -0.1714218 0.0603108 -2.8423 0.0044788 **
## factor(TIME_PERIOD)2008 0.1639073 0.0603108 2.7177 0.0065735 **
## factor(TIME_PERIOD)2009 0.1081851 0.0603108 1.7938 0.0728461 .
## factor(TIME_PERIOD)2010 -0.0224541 0.0603108 -0.3723 0.7096642
## factor(TIME_PERIOD)2011 0.0050406 0.0603108 0.0836 0.9333933
## factor(TIME_PERIOD)2012 -0.1949902 0.0603108 -3.2331 0.0012246 **
## factor(TIME_PERIOD)2013 -0.0257672 0.0603108 -0.4272 0.6692049
## factor(TIME_PERIOD)2014 -0.0662652 0.0603108 -1.0987 0.2718867
## factor(TIME_PERIOD)2015 -0.0885919 0.0603108 -1.4689 0.1418538
## factor(TIME_PERIOD)2016 -0.1213309 0.0603108 -2.0118 0.0442451 *
## factor(TIME_PERIOD)2017 -0.0903529 0.0603108 -1.4981 0.1341016
## factor(TIME_PERIOD)2018 -0.0528768 0.0603108 -0.8767 0.3806283
## factor(TIME_PERIOD)2019 -0.0416844 0.0603108 -0.6912 0.4894650
## factor(TIME_PERIOD)2020 -0.0012669 0.0603108 -0.0210 0.9832407
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model_1_neighbour_2004)## ML panel with spatial lag and iid errors
##
## Call:
## spreml(formula = formula, data = data, index = index, w = listw2mat(listw),
## w2 = listw2mat(listw2), lag = lag, errors = errors, cl = cl)
##
## Residuals:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.75883 -0.09217 -0.00883 0.01625 0.10228 1.43561
##
## Spatial autoregressive coefficient:
## Estimate Std. Error t-value Pr(>|t|)
## lambda 0.231405 0.054493 4.2465 2.171e-05 ***
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## (Intercept) 0.064387 0.012183 5.2848 1.258e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model_2_neighbour_2004)## ML panel with spatial lag and iid errors
##
## Call:
## spreml(formula = formula, data = data, index = index, w = listw2mat(listw),
## w2 = listw2mat(listw2), lag = lag, errors = errors, cl = cl)
##
## Residuals:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.73557 -0.10624 -0.00414 0.00180 0.08468 1.20716
##
## Spatial autoregressive coefficient:
## Estimate Std. Error t-value Pr(>|t|)
## lambda 0.025575 0.062359 0.4101 0.6817
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## (Intercept) 0.1576225 0.0462679 3.4067 0.0006575 ***
## factor(TIME_PERIOD)2005 0.1352222 0.0654327 2.0666 0.0387733 *
## factor(TIME_PERIOD)2006 0.0041779 0.0654327 0.0638 0.9490900
## factor(TIME_PERIOD)2007 -0.2422995 0.0654327 -3.7030 0.0002130 ***
## factor(TIME_PERIOD)2008 0.1110226 0.0654327 1.6967 0.0897450 .
## factor(TIME_PERIOD)2009 0.0545739 0.0654327 0.8340 0.4042554
## factor(TIME_PERIOD)2010 -0.0868799 0.0654327 -1.3278 0.1842527
## factor(TIME_PERIOD)2011 -0.0532876 0.0654327 -0.8144 0.4154225
## factor(TIME_PERIOD)2012 -0.2645913 0.0654327 -4.0437 5.261e-05 ***
## factor(TIME_PERIOD)2013 -0.0887237 0.0654327 -1.3560 0.1751143
## factor(TIME_PERIOD)2014 -0.1313016 0.0654327 -2.0067 0.0447853 *
## factor(TIME_PERIOD)2015 -0.1557468 0.0654327 -2.3803 0.0173005 *
## factor(TIME_PERIOD)2016 -0.1883949 0.0654327 -2.8792 0.0039867 **
## factor(TIME_PERIOD)2017 -0.1562788 0.0654327 -2.3884 0.0169224 *
## factor(TIME_PERIOD)2018 -0.1129282 0.0654327 -1.7259 0.0843713 .
## factor(TIME_PERIOD)2019 -0.1036468 0.0654327 -1.5840 0.1131891
## factor(TIME_PERIOD)2020 -0.0602503 0.0654327 -0.9208 0.3571557
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1