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Table 2 Regression results – OLS compared with spatial autoregressive model, Germany

From: Deaths during the first year of the COVID-19 pandemic: insights from regional patterns in Germany and Poland

 

COVID-19 deaths

Excess deaths

Difference: excess minus COVID-19 deaths

OLS

Spatial error model

Spatial lag model

OLS

Spatial error model

Spatial lag model

OLS

Spatial error model

Spatial lag model

coeff

SE

coeff

SE

coeff

SE

coeff

SE

coeff

SE

coeff

SE

coeff

SE

coeff

SE

coeff

SE

Pop. aged 50-69 (%)

0.012

(0.012)

0.024**

(0.011)

0.008

(0.009)

− 0.022

(0.018)

− 0.009

(0.019)

− 0.010

(0.016)

− 0.034**

(0.014)

− 0.034**

(0.015)

− 0.026*

(0.014)

Pop. aged 70-84 (%)

−0.017

(0.021)

−0.004

(0.021)

0.001

(0.015)

0.030

(0.031)

0.049

(0.036)

0.025

(0.027)

0.047**

(0.023)

0.050*

(0.027)

0.037

(0.022)

Pop aged 85+ (%)

0.302***

(0.086)

0.207**

(0.081)

0.150**

(0.064)

0.300**

(0.126)

0.141

(0.137)

0.172

(0.111)

−0.002

(0.095)

−0.044

(0.105)

−0.008

(0.092)

Employed in agricul. (%)

−0.030*

(0.016)

−0.021

(0.013)

−0.014

(0.012)

0.014

(0.023)

0.015

(0.023)

0.008

(0.020)

0.045**

(0.018)

0.039**

(0.018)

0.035**

(0.017)

Hospital beds (per 1 K)

−0.005

(0.006)

− 0.002

(0.004)

− 0.004

(0.004)

− 0.035***

(0.009)

− 0.028***

(0.008)

− 0.034***

(0.008)

− 0.030***

(0.007)

− 0.027***

(0.007)

− 0.030***

(0.006)

Pop. density (p/1000 sqm)

0.020

(0.039)

0.060*

(0.033)

0.029

(0.029)

−0.052

(0.057)

−0.055

(0.057)

−0.047

(0.050)

−0.072*

(0.043)

−0.100**

(0.046)

−0.073*

(0.042)

Constant

−0.321

(0.293)

−0.626**

(0.291)

−0.526**

(0.216)

0.217

(0.430)

0.029

(0.481)

−0.057

(0.378)

0.538*

(0.326)

0.617*

(0.364)

0.477

(0.315)

[depvar]

  

0.803***

(0.042)

  

0.619***

(0.061)

  

0.326***

(0.079)

e.[depvar]

 

0.821***

(0.040)

  

0.643***

(0.060)

  

0.358***

(0.083)

 

var(e.[depvar])

 

0.075

(0.005)

0.077

(0.006)

 

0.233

(0.017)

0.236

(0.017)

 

0.163

(0.012)

0.164

(0.012)

Diagnostics:

Measures of fit:

AIC

364.044

161.350

168.395

670.503

593.035

596.511

447.569

434.763

435.959

BIC

392.002

197.296

204.341

698.460

628.981

632.457

475.527

470.708

471.905

Tests for spatial error dependence:

Lagrange multiplier stat.

417.418

  

148.799

  

25.007

  

Lagrange multiplier p-value

0.000

  

0.000

  

0.000

  

Moran’s I z-value

21.534

  

12.978

  

5.498

  

Moran’s I p-value

0.000

  

0.000

  

0.000

  

Tests for spatial lag dependence:

Lagrange multiplier stat.

382.926

  

138.228

  

23.996

  

Lagrange multiplier p-value

0.000

  

0.000

  

0.000

  

Wald test of spatial terms:

chi2

 

414.614

373.045

 

113.218

104.213

 

18.728

16.862

Prob > chi2

 

0.000

0.000

 

0.000

0.000

 

0.000

0.000

  1. Source: own calculations based on county level data as described in Source notes for Figs. 1 and 3
  2. Notes: Number of observations: 401. *p < 0.1, **p < 0.05, ***p < 0.01. Spatial error model – with spatially lagged errors, maximum likelihood estimator. Spatial lag model – with spatially lagged dependent variable, maximum likelihood estimator. The estimated variance inflation factor for conditioning variables varies between 1.55 and 3.77