Is a municipal socio-economic ranking more influential than vaccination on daily growth in COVID-19 infection rate?

Figures & data

Table 1. Descriptive statistics.

Variable	Description	Obs	Mean	Std. Dev	Min	Max
t	Daily time variable from 1 (=11 March 2020; the first documentation of COVID-19 cases) to 560 (=21 September 2021)	95,427	281.444	161.1424	2	560
$\begin{array}{l}\Delta \mathit{\text{ln}}(\mathit{\text{Cum}}\_\mathit{\text{Infected}})=\mathit{\text{ln}}(\mathit{\text{Cum}}\_\mathit{\text{Infected}})\\ -\mathit{\text{ln}}{\left(\mathit{\text{Cum}}\_\mathit{\text{Infected}}\right)}_{t-1}\end{array}$	Approximated daily infected growth rate from SARS-COV2 virus where $\mathit{\text{Cum}}\_\mathit{\text{Infected}}\mathrm{ }$ is the accumulated number of infected persons	95,427	0.00950	0.0244847	0	0.7993
Dum_vaccine	1 = post-vaccine era (20 December 2020–21 September 2021); 0 = pre-vaccine era (21 March 2020–19 December 2020)	95,427	0.49458	0.4999732	0	1
MedianAge	Median age of municipal inhabitants in years.	95,427	28.3696	6.346089	11.44	40.73
PopulationSize	Population size of the municipality (city or town)	95,427	43,589	85,216	5,446	865,721
RANK2013	Socio-economic ranking on a scale of 1 = the lowest to 255 = the highest	95,427	116.803	75.34359	2	253

Notes: The dataset Refers to 171 Israeli municipalities ($i=1,2,3,\dots ,171$) and 559 days ($t=2,3,4,\dots ,560$), where $i\times t=95,427$.

Table 2. Skewness test.

Variable	Obs	Skewness	p Value (skewness = 0)	p Value (normal distribution)
Dum_vaccine×t	559	0.2186	0.0373	−
MedianAge	171	−0.2127	0.2222	0.1514
PopulationSize	171	6.3710	<0.01	<0.01
PopulationSize*	30	3.1709	<0.01	<0.01
RANK2013	171	0.28721	0.1381	<0.01

*Settlements above 52,000 persons.

Figure 1. Daily growth rate of infected persons ($\widehat{Y}$) vs. population size of the city ($X$).

Prior to vaccination ($\hat{Y}=0.0128151+\hspace{0.17em}3.27\times {10}^{-8}X$)

Figure 2. List of settlements above 52,000 persons and their population size.

Source: Google map. The settlements are arranged from north to south. The Population size reflects the number of persons at the settlement. Only settlements with a population above 52,000 persons are included.

*Settlements that appear on the map.

Table 3. Regression analysis and covariates weights.

	(1)	(2)			(3)
Variables	$\Delta \mathrm{\text{ln}}(\mathit{\text{Cum}}\_\mathit{\text{Infected}})$	$\Delta \mathrm{\text{ln}}(\mathit{\text{Cum}}\_\mathit{\text{Infected}})$	Variables		$\mathcal{Z}\left[\Delta \mathrm{\text{ln}}(\mathit{\text{Cum}}\_\mathit{\text{Infected}})\right]$
Constant	0.0124***	0.0124***	Constant		−
	(<0.01)	(<0.01)			−
	[0.0112–0.0137]	[0.0116–0.0133]
Dum_vaccine×t	−2.32 × 10^−5***	−2.32 × 10−^5***	$\mathcal{Z}\left[\mathit{\text{dum}}\_\mathit{\text{vaccine}}\times t\right]$	(1)	−0.2066569***
	(<0.01)	(<0.01)			(<0.01)
	[(−2.38 × 10^-5) - (−2.25 × 10^−5)]	[(−2.38 × 10^-5) - (−2.25 × 10^−5)]
MedianAge	6.41 × 10^-5**	6.41 × 10^-5***	$\mathcal{Z}\left[\mathit{\text{MedianAge}}\right]$	(3)	0.0166247***
	(0.0238)	(0.00168)			(0.00168)
	[8.54 × 10^−6 - 0.000120]	[2.41 × 10^−5 - 0.000104]
PopulationSize	1.59 × 10^−8***	1.59 × 10^−8***	$\mathcal{Z}\left[\mathit{\text{PopulationSize}}\right]$	(2)	0.0553647***
	(<0.01)	(<0.01)			(<0.01)
	[1.34 × 10^−8 - 1.84 × 10^−8]	[1.41 × 10−^8 - 1.77 × 10−^8]
RANK2013	−5.32 × 10^−6**	−5.32 × 10^-6***	$\mathcal{Z}\left[\mathit{\text{RANK}}2013\right]$	(4)	−0.0163568***
	(0.0249)	(0.00183)			(0.00183)
	[(−9.96) × 10^−6 - (−6.70) × 10^−7]	[(−8.66) × 10^−6 - (−1.97) × 10^−6]
Observations	95,427	95,427	Observations		95,427
CityCode	171		CityCode
between R-Square	0.502
Wald chi2(4)	4,449***

Notes: $\Delta \mathrm{\text{ln}}(\mathit{\text{Cum}}\_\mathit{\text{Infected}})$ approximates the daily growth rate of COVID-19 infected persons. t is the time variable (where $t=1,2,3,\dots ,560$ where 1 = 11 March 2020 (Beginning of the COVID-19 pandemic; 285 = 20 December 2020 (first date of vaccination); 560 = 21 September 2021. Column (1) reports the outcomes obtained from the random-effect regression. This procedure corrects for serial correlation due to the fact that the same municipality appears in consecutive periods over time (see, for example, Wooldridge, 2009: 489–491). Column (2) reports the outcomes obtained from a simple regression analysis. Column (3) reports the regression analysis where each variable is converted to the standard normal distribution function ($z\left(X_i\right)=\frac{X_i-\overline{X}}{{\sigma }_X}$ where $\overline{X}$ is the average and ${\sigma }_X$ is the standard deviation of $X_i$. The relative weight of each variable is given in the left side of column (3). p Values are given in parentheses and 95% confidence intervals are given in square brackets. **p < 0.05, ***p < 0.01.

Figure 3. Relative contributions of explanatory variables.

Notes: The figure describes the relative contribution of each variable to the daily infection rate from COVID-19, namely, projected STD increase of the dependent variable–the daily infection growth rate, following a one standard deviation increase in each independent variable in absolute value ($-\mathcal{Z}\left[\mathit{\text{dum}}\_\mathit{\text{vaccine}}\times t\right]$; $\mathcal{Z}(\mathit{\text{PopulationSize}})$; $\mathcal{Z}\left[\mathit{\text{MedianAge}}\right]$; $\left[-\mathcal{Z}\left(\mathit{\text{RANK}}2013\right)\right]$). The Figure is based on the outcomes obtained from column (3) in Table 2. $\mathcal{Z}\left(X_i\right)=\frac{X_i-\overline{X}}{{\sigma }_X}$ where $\overline{X}$ is the average and ${\sigma }_X$ is the standard deviation of $X_i$.

Table 4. Dickey–Fuller unit root tests for panel data.

Test	Statistic	p Value
Inverse chi-squared(342)	1.03 × 10^−4	<0.01
Inverse normal	−95.7094	<0.01
Inverse logit t(859)	−218.0766	<0.01
Modified inv. chi-squared	382.24	<0.01

Notes: The sample includes 171 panels and the average number of periods is 558.05. The Dickey–Fuller test for each panel is based on the following model (if there is a drift): $\Delta u_t=\alpha +\theta u_{t-1}+{ϵ}_t$ where $\theta =\rho -1$ (Wooldridge, 2009: 630–632). The null hypothesis is that all panels contain unit roots. The alternative hypothesis is that at least one panel is stationary.

Table 5. Cross validate.

Folds	Time	480	520	560
10	r	0.3165***	0.6527***	0.3717***
	p Value	<0.01	<0.01	<0.01
5	r	0.2936***	0.6526***	0.3664***
	p Value	0.0001	<0.01	<0.01
2	r	0.3160***	0.5970***	0.1782**
	p Value	<0.01	<0.01	0.0197

Notes: Vaccine–from t = 285. To test the predictive power of the model, the procedure randomly assigns an on-sample and off-sample groups and generates a vector of predictions based on off-sample observations. The number of folds is the number of regressions the procedure uses to generate this vector of predictions. We then test whether the Pearson correlation between this vector of predictions obtained from the off-sample group and the observed dependent variable. **p < 0.05; ***p < 0.01 for the rejection of the null hypothesis that the Pearson correlation is zero.

Table 6. Spatial autocorrelation.

	(1)	(2)
	OLS	Prais–Winsten
Variables	$\Delta \mathrm{\text{ln}}(\mathit{\text{Cum}}\_\mathit{\text{Infected}})$	$\Delta \mathrm{\text{ln}}(\mathit{\text{Cum}}\_\mathit{\text{Infected}})$
Constant	0.00927***	0.00905***
	(5.25 × 10^−5)	(0.000114)
MedianAge	5.12 × 10^−5	5.34 × 10^−5
	(0.549)	(0.617)
PopulationSize	−1.12 × 10^−8***	−1.00 × 10^−8**
	(0.000553)	(0.0431)
RANK2013	−3.47 × 10^−5***	−3.38 × 10^−5***
	(3.51 × 10^−7)	(0.000223)
Observations	166	166
R-squared	0.206	0.182
F-Statistics	14.67***	12.05***
Durbin Watson	1.7625	2.0029

Notes: The critical values for the Durbin Watson Statistics with 150 settlements and 3 regressors (excluding the constant term) at the 1% significance level are (Kmenta, 1997: 767):

p values are given in parentheses. **p < 0.05; ***p < 0.01.

Table

$\rho >0$	dL	dU	$\rho =0$	4 − dU	4 − dL	$\rho <0$
0	1.584	1.665	2	2.335	2.416	4

The critical values for the Durbin Watson Statistics with 200 settlements and four regressors (excluding the constant term) at the 1% significance level are (Kmenta, 1997: 767):

Table

$\rho >0$	dL	dU	$\rho =0$	4-dU	4-dL	$\rho <0$
0	1.643	1.704	2	2.296	2.357	4

Table 7. Regression with interacted variables.

	(1)		(2)
Variables	$\Delta \mathrm{\text{ln}}(\mathit{\text{Cum}}\_\mathit{\text{Infected}})$	Variables	$\mathcal{Z}\left[\Delta \mathrm{\text{ln}}(\mathit{\text{Cum}}\_\mathit{\text{Infected}})\right]$
Constant	0.0139***	Constant	−
	(<0.01)		−
	[0.0135–0.0143]	−	−
Dum_vaccine×t	−2.32 × 10^−5***	$\mathcal{Z}\left(\mathit{\text{Dum}}\_\mathit{\text{vaccine}}\times t\right)$	−0.2066554***
	(<0.01)		(<0.01)
	[(−2.38 × 10^−5) - (−2.25 × 10^-5)]
MedianAge	−	−	−
	−	−	−
PopulationSize	−	−	−
	−	−	−
$\mathit{\text{MedianAge}}\times \mathit{\text{PopulationSize}}$	5.79 × 10^−10***	$\mathcal{Z}\left(\mathit{\text{MedianAge}}\times \mathit{\text{PopulationSize}}\right)$	0.0593993***
	(<0.01)		(<0.01)
	[4.94 × 10^−10 - 6.64 × 10^−10]	−	−
RANK2013	−3.02 × 10^−6***	$\mathcal{Z}\left(\mathit{\text{RANK}}2013\right)$	−0.0092981***
	(0.00396)		(0.00396)
	[(−5.85 × 10^−6)- (−1.99 × 10^−7)]	−	−
$\mathit{\text{MedianAge}}\times \mathit{\text{RANK}}2013$	−	−	−
	−	−	−
$\mathit{\text{PopulationSize}}\times \mathit{\text{RANK}}2013$	−	−	−
	−	−	−
$\mathit{\text{MedianAge}}\times \mathit{\text{PopulationSize}}$ $\times \mathit{\text{RANK}}2013$	−	−	−
	−	−	−
Observations	95,427		95,427
CityCode	171
Between R-squared	0.518
F-Statistics	1,537.29***		1,537.29***

Notes: Column (1) reports the outcomes obtained from a stepwise random effect regression analysis. This procedure gradually omits variables with insignificant coefficients. The random effect procedure corrects for serial correlation due to the fact that the same municipality appears in consecutive periods over time (see, for example, Wooldridge, 2009: 489–491). Column (2) reports the regression analysis where each variable is converted to the standard normal distribution function ($z\left(X_i\right)=\frac{X_i-\overline{X}}{{\sigma }_X}$ where $\overline{X}$ is the average and ${\sigma }_X$ is the standard deviation of $X_i$. The relative weight of each variable is given in the left side of column (2). p Values are given in parentheses and 95% confidence intervals are given in square brackets. **p < 0.05; ***p < 0.01.

Table 8. Robustness test: regression analysis and covariates weights.

	(1)	(2)			(3)
Variables	$\Delta \mathrm{\text{ln}}(\mathit{\text{Cum}}\_\mathit{\text{Infected}})$	$\Delta \mathrm{\text{ln}}(\mathit{\text{Cum}}\_\mathit{\text{Infected}})$	Variables		$\mathcal{Z}\left[\Delta \mathrm{\text{ln}}(\mathit{\text{Cum}}\_\mathit{\text{Infected}})\right]$
Constant	0.0119***	0.0119***	Constant		−
	(<0.01)	(<0.01)			−
	[0.00985–0.0141]	[0.0108–0.0131]
Dum_vaccine×t	−2.32 × 10^−5***	−2.32 × 10^−5***	$\mathcal{Z}\left[\mathit{\text{dum}}\_\mathit{\text{vaccine}}\times t\right]$	(1)	−0.2066626***
	(<0.01)	(<0.01)			(<0.01)
	[(−2.41 × 10^−5) - (−2.22 × 10^−5)]	[(−2.41 × 10^−5) - (−2.22 × 10^−5)]
MedianAge	0.000112***	0.000112***	$\mathcal{Z}\left[\mathit{\text{MedianAge}}\right]$	(2)	0.0289189***
	(0.00289)	(3.65 × 10^−8)			(3.65 × 10^−8)
	[1.51 × 10^−5- 0.000208]	[5.94 × 10^−5 - 0.000164]
PopulationSize	−	−	$\mathcal{Z}\left[\mathit{\text{PopulationSize}}\right]$	−	−
	−	−		−	−
RANK2013	−6.65 × 10^−6**	−6.65 × 10^−6***	$\mathcal{Z}\left[\mathit{\text{RANK}}2013\right]$	(3)	−0.0204486***
	(0.0351)	(9.85 × 10^−5)			(9.85 × 10^−5)
	[(^−1.48 × 10^−5) - 1.48 × 10^−6]	[(−1.10 × 10^−5) - (−2.25 × 10^−6)]
Observations	95,427	95,427	Observations		95,427
CityCode	171		CityCode
Wald chi^2(4)	4,287***

Notes: $\Delta \mathrm{\text{ln}}(\mathit{\text{Cum}}\_\mathit{\text{Infected}})$ approximates the daily growth rate of COVID-19 infected persons. t is the time variable (where $t=1,2,3,\dots ,560$ where 1 = 11 March 2020 (Beginning of the COVID-19 pandemic; 285 = 20 December 2020 (first date of vaccination); 560 = 21 September 2021. Column (1) reports the outcomes obtained from the random-effect regression with dummies to 171 Israeli municipalities. Column (2) reports the outcomes obtained from a simple regression analysis. Column (3) reports the regression analysis where each variable is converted to the standard normal distribution function ($z\left(X_i\right)=\frac{X_i-\overline{X}}{{\sigma }_X}$ where $\overline{X}$ is the average and ${\sigma }_X$ is the standard deviation of $X_i$. The relative weight of each variable is given in the left side of column (3). p Values are given in parentheses and 99% confidence intervals are given in square brackets. **p < 0.05; ***p < 0.01.

Wooldridge, J. M. (2009). Introductory econometrics: A modern approach. South Western, a part of cengage learning (4th ed.). ASCO

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Kmenta, J. (1997). Elements of econometrics (2nd ed.). Ann Arbor the University of Michigan Press.

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Availability of data and materials

This research is based on information downloaded from the Israeli Ministry of Health website. After publication, supplementary materials which permit replications of the outcomes in Stata version 16.1 software package will be provided.