Average Observed Growth of Covid Mortality by Country
First, I conduct an observational analysis (Figure. 1), which shows that most typical trajectories are curvilinear in form, exhibiting accelerating growth across time points. All countries show increasing variability in Covid mortality over time. Notably, five countries that have highest mortality rates at initial status in 2020 (Belgium, Spain, Italy, Netherlands, and France) have relatively low slopes. On the other hand, the top five countries with the highest mortality rates at the ending point (Peru, Bulgaria, Bosnia and Herzegovina, Hungary, and Montenegro) exhibit relatively higher slopes than other countries. Despite some variation, all countries demonstrate positive growth over time, with notable differences in both linear rate of change and rate of curvature. These observations will be tested using multilevel statistical models in the next section.
Partitioning Within- and Between-country Components
To further analyze the data, the variance in the outcome variable, Covid mortality per million population, is partitioned into its within- and between-country components. The sample consists of 151 countries, with a total of 3384 points of measurement. There is some degree of imbalance in group sizes, as the number of monthly data point measurements for each country ranges from 11 to 23. However, this imbalance can be addressed effectively using multilevel modeling, where the maximum likelihood estimator accounts for variations in group size.
The fixed effect for the intercept indicates that the grand mean of Covid mortality rates per million population is 472.48 for the pooled data (across all time points in all countries). The level-1 residual variability is 299012, while the level-2 random intercept variance is 291718. The intra-class correlation (ICC) is calculated as 291718 / (291718 + 299012) = 0.494, indicating that approximately 49.4% of the variance in Covid mortality is associated with between-country differences. In other words, within a given country, Covid mortality rates have a meaningful correlation of 0.494. These results suggest that there is significant dependence in the Covid mortality per million population rates that requires further explanation based on countries' characteristics.
Linear and Quadratic Growth Curve Model
The estimated random effects reveal that the variance among the intercepts is 40216. When accounting for the time factor, this represents a substantial reduction (70%) compared to the unconditional model discussed earlier, where the variance associated with countries was 291718. Similarly, the variance among the slopes is 3297, and the level-1 residual variance is 20943. These results indicate variability among the country intercepts and slopes. Additionally, the random effects of the intercepts and slopes show a negative correlation of -0.53, suggesting that countries with high death tolls at the early phase tend to experience slower increases over time, while countries with lower death tolls tend to experience faster increases. Even after accounting for time, there remains significant variability at level 1. The fixed effects analysis reveals a significant mean linear slope (𝛾 = 52.02, sd = 4.68, p < 0.001), indicating an average increase of 52 deaths per month. However, the intercept with a negative value is not meaningful in this context and can be disregarded.
Moreover, the results from the quadratic growth curve model provide strong support for the inclusion of a quadratic component in the analysis. The fixed quadratic effect of 0.78 is statistically significant (sd = 0.06, p < 0.001). Furthermore, the formal test shows a significant improvement in model fit with the inclusion of the quadratic component (Chisq = 148.4, p < 0.001). Therefore, the quadratic term will be included in the succeeding models to better capture the data's curvilinear nature.
Systems of Internal Governance
Starting from this step, I expand the model to include level-2 predictors. The first predictor added is the system of internal governance of a country, i.e., a federal or unitary system, while controlling for GDP per capita (log) and health security index (standardized). Two methods of categorizing federal states, as mentioned in section 3.2.2, result in two distinct estimate outputs. Using the first method that identifies 22 states in the dataset as federals, no significant effect of the system of internal governance on Covid mortality is observed. However, when using the second method that recognizes 32 states in the dataset as federal, the system of internal governance becomes a significant factor associated with higher Covid deaths, even when controlling for GDP per capita (log) and health security index.
Regarding the fixed effect results, the main effect of internal governance system (federal coded 1) is significant. The model implies that federal states have an intercept higher than unitary states by 92.8 Covid deaths per million population (t = 2.42, SE = 38.2, p = 0.016). However, when including the cross-level interaction between time and federal, the regression of trajectory slopes on federal is not significant. This indicates that the model-implied slopes do not differ in magnitude between federal and unitary states. The figure below visually illustrates that the intercepts of the trajectory of Covid mortality are significantly higher for federal states compared to unitary states, while the slopes of the trajectories do not significantly differ from each other.
Democracy
In this section I added democracy as an additional predictor at level 2 to examine its effect on Covid mortality, while controlling for GDP per capita and Health Security Index. The original scale of democracy index is a continuous, with a 1-point incremental increase. To have a more meaningful interpretation, I standardized democracy.
M𝑜𝑟𝑡𝑎𝑙𝑖𝑡𝑦 𝑡𝑖 = (𝛾00 + 𝛾01𝑡𝑖𝑚𝑒 + 𝛾0Democracy) +
(𝛾01∗𝑡𝑖𝑚𝑒 + 𝛾0 ∗ Democracy) + (𝑢0𝑖 + 𝑢1𝑖 Democracy + 𝑟𝑡𝑖)
The fixed effects indicate significance in both main effect and interaction effect of democracy. Countries with higher democracy score have lower intercepts and steeper regression slopes. One standard deviation in the democracy score is associated with 63.89 less Covid deaths per million population (p = .004). The significant interaction between time and democracy (𝛾^ = 21.78) shows that the slope of the trajectory of Covid mortality increases by approximately 21.78 units for each one standard deviation increase in the predictor democracy (p < 0.001).
The plot above provides further insights into the relationships between democracy and Covid mortality. It displays three lines representing the democracy values at the mean, one standard deviation above the mean and one standard deviation below the mean. Notably, one standard deviation of democracy index in the dataset is equivalent to 21.75 points.
The plot reveals that countries with higher democracy scores exhibit lower number of Covid deaths per million population at initial time point. However, as time progresses, their mortality rates increase at a quicker pace. On the other hand, countries with lower democracy index scores started out with higher death rates, but their mortality rates increase at a slower rate overtime. In other words, higher democratic countries had lower death rates early in the pandemic, but as time went on, their mortality rates increased faster compared to those of less democratic countries. This trend becomes apparent starting at around time point 3, which corresponds to July 2020. From that point onwards, higher democratic countries experienced a greater impact from Covid deaths in comparison to their less democratic counterparts.
Government effectiveness
Subsequently, government effectiveness was added to the model as an additional predictor, and it was also standardized for ease of interpretation. The results of the model highlight the significant impact of government effectiveness on Covid mortality. Specifically, one standard deviation increase in government effectiveness was associated with 68.77 fewer Covid deaths (p = 0.043).
Additionally, a model with a cross-level interaction term between the slope (time) and government effectiveness was examined, but it yielded no significant effect of this predictor. This suggests that while government effectiveness plays a crucial role in influencing the overall Covid mortality rates, it does not significantly influence the trajectory of mortality rates over time.
Trust in Government
Next, trust in government was included as an additional predictor, and it was found to have a negative effect on the slope of Covid mortality. For each standard deviation increase in trust in government, the slope decreased by 1.78 units (p = 0.026). It is important to note that the model now consists of 873 observations from 38 countries, as opposed to the previous 147 countries, due to the limited availability of the indicator trust in government. Consequently, caution should be exercised when comparing variance estimates in the random effects with the previous models. Both the between-country variance (31278) and within-country variance (1874) were reduced in this smaller sample size. Additionally, the correlation between time in months and the intercept, -0.46, is smaller than in the previous models.
Interestingly, in this smaller sample size, democracy shows a significant negative effect on the slope of the Covid trajectory, which is in the opposite direction compared to the previous model. Specifically, one standard deviation increase in democracy is associated with a 2.78 lower unit in the rate of change of Covid mortality. This difference in the effect of democracy on Covid mortality may be attributed to the distinctiveness in the scores in the two groups of countries. In the smaller sample of 38 countries, democracy is much less varied, ranging from 31.1 (Russia) to 98.7 (Norway), with a mean of 78.18 and standard deviation of 13.61. This is in contrast to the score in the larger sample size of 148 countries, which ranges from 13.2 to 98.7, with a mean of 56.04 and standard deviation of 21.75. Essentially, the subgroup of countries classified as democracies in this model comprises those with much higher levels of democracy than those in the larger sample.
In this joint model using the smaller sample size, the government effectiveness factor maintains its negative main effect on Covid deaths. That is, one standard deviation increase in government effectiveness is associated with 2.67 fewer deaths (p = 0.025). The table below summarizes the results of hypotheses testing.
Table 2
Variables | Model 1 | Model 2 | Model 3 | Model 4 |
time_month | 34.644***(5.01) | 34.800***(4.69) | 34.912***(4.714) | 109.285***(15.06) |
I(time_month^2) | 0.793***(0.065) | 0.794***(0.065) | 0.797***(0.065) | 0.014(0.146) |
GDP per capita (log) | 2.683(13.345) | 5.907(14.172) | 31.251(18.718) | 228.876**(80.442) |
Health Security Index | 2.682(1.494) | 3.106(1.611) | 4.680**(1.753) | 5.753(3.922) |
Federal system (Yes = 1) | 92.857*(38.272) | 93.612*(38.349) | 87.149*(38.956) | 159.318**(61.088) |
scale(democracy) | | -63.891**(22.2) | -50.582*(23.645) | 153.128*(77.777) |
time_month:scale(democracy) | | 21.777***(4.46) | 21.581***(4.482) | -27.869*(12.216) |
scale(gov_eff) | | | -68.772*(33.759) | -266.969*(113.229) |
scale(trust_gov) | | | | -9.196 (37.384) |
time_month:scale(trust_gov) | | | | -17.894*(7.640) |
Num.Obs. | 3315 | 3315 | 3293 | 873 |
RMSE | 136.50 | 136.50 | 136.94 | 161.43 |
* p < 0.05, ** p < 0.01, *** p < 0.001 Notes: Standard errors shown in parentheses. |
Table 3
The study's hypotheses and summary of findings
H1 | Countries with higher level of democracy tend to have lower Covid mortality rates. | Partially supported by the data. In the sample of 148 countries, countries with higher level of democracy have lower death rates at the beginning, but the death tolls tend to increase faster than those with lower level of democracy. In the group of 38 OECD countries, those in higher democracy experience slower rate of Covid deaths. |
H2 | Federal states tend to have lower Covid mortality rates than unitary states. | Data shows an opposite effect. Federal states tend to have higher rate of Covid deaths compared to those in unitary system. |
H3 | Countries with higher score of governance effectiveness tend to have lower Covid mortality rates. | Supported by the data. Government effectiveness significantly associated with lower rate of Covid deaths. |
H4 | Countries with higher level of trust in government tend to have lower Covid mortality rates. | Supported by the data. In the groups of 38 OECD countries, those with higher level of trust in government experience significantly slower rate of Covid deaths. |