1 Changes from previous version

  1. Drop FSI from (most of) the regressions
  2. For spending regs, only include countries which actually implemented in 2020.
  3. Dropped the regression which includes population on the RHS and the regression which weights by population.
  4. Dropped the regressions with spending per capita on LHS (the R squared was very low)

2 Coverage regressions

2.1 Stepwise selection of variables

Perform forward stepwise-selection on all variables included in Robert’s canonical specification (“pre_coverage”, “rGDPg2020”, “digIDcov”, “dig_reg”, “eap”, “log_deaths”). At each iteration, the variable which would have the the smallest p-value if added to the model is added. I add in the few variables which are not statistically significant all at once.

Note that the final regression on the right weights each observation by the country population.

## 
##                                Stepwise Selection Summary                                 
## -----------------------------------------------------------------------------------------
##                          Added/                   Adj.                                       
## Step      Variable      Removed     R-Square    R-Square     C(p)        AIC        RMSE     
## -----------------------------------------------------------------------------------------
##    1    pre_coverage    addition       0.505       0.499    55.3290     -8.9381    0.2239    
##    2      dig_reg       addition       0.644       0.635    19.6250    -34.2834    0.1910    
##    3        eap         addition       0.675       0.663    13.1690    -39.8843    0.1836    
##    4     log_deaths     addition       0.711       0.696     5.4160    -47.6148    0.1743    
## -----------------------------------------------------------------------------------------
Dependent variable:
coverage
(1) (2) (3) (4) (5)
pre_coverage 0.626*** 1.147*** 0.849*** 0.731*** 0.673***
(0.112) (0.117) (0.138) (0.134) (0.121)
rGDPg2020 -0.005
(0.004)
log_deaths 0.034** 0.040***
(0.015) (0.013)
dig_id 0.058
(0.065)
dig_reg 0.190*** 0.262*** 0.267*** 0.204***
(0.063) (0.057) (0.054) (0.059)
eap 0.268*** 0.164** 0.279***
(0.080) (0.082) (0.077)
Constant -0.089** 0.131*** 0.055** 0.046** -0.070*
(0.044) (0.028) (0.022) (0.019) (0.037)
Observations 83 83 83 83 83
R2 0.720 0.505 0.644 0.675 0.711
Adjusted R2 0.698 0.499 0.635 0.663 0.696
Residual Std. Error 0.174 (df = 76) 0.224 (df = 81) 0.191 (df = 80) 0.184 (df = 79) 0.174 (df = 78)
F Statistic 32.592*** (df = 6; 76) 82.746*** (df = 1; 81) 72.416*** (df = 2; 80) 54.771*** (df = 3; 79) 48.029*** (df = 4; 78)
Note: p<0.1; p<0.05; p<0.01

2.2 Only include one capacity variable

The following regressions include only one of the variables digital ID coverage, digital ID registration, and FSI each.

Dependent variable:
coverage
(1) (2) (3) (4)
pre_coverage 0.739*** 0.641*** 0.735*** 0.792***
(0.115) (0.112) (0.121) (0.101)
rGDPg2020 -0.004 -0.005 -0.004 -0.007
(0.004) (0.004) (0.005) (0.005)
eap 0.318*** 0.268*** 0.287*** 0.294***
(0.073) (0.076) (0.078) (0.063)
log_deaths 0.052*** 0.035** 0.052*** 0.058***
(0.013) (0.015) (0.015) (0.016)
dig_id 0.139**
(0.057)
dig_reg 0.205***
(0.059)
fsi -0.019
(0.016)
soc_reg_coverage 0.0003
(0.001)
Constant -0.141*** -0.063* 0.086 -0.089**
(0.038) (0.038) (0.159) (0.045)
Observations 83 83 82 78
R2 0.667 0.717 0.653 0.673
Adjusted R2 0.646 0.699 0.630 0.650
Residual Std. Error 0.188 (df = 77) 0.174 (df = 77) 0.192 (df = 76) 0.184 (df = 72)
F Statistic 30.898*** (df = 5; 77) 39.021*** (df = 5; 77) 28.559*** (df = 5; 76) 29.630*** (df = 5; 72)
Note: p<0.1; p<0.05; p<0.01

2.3 Only include one demand variable

The following regressions only include either GDP growth and deaths but not both.

Dependent variable:
coverage
(1) (2)
pre_coverage 0.647*** 0.667***
(0.135) (0.127)
dig_reg 0.252*** 0.200***
(0.065) (0.067)
eap 0.191** 0.283***
(0.086) (0.078)
soc_reg_coverage 0.0001 -0.001
(0.001) (0.001)
rGDPg2020 -0.012***
(0.004)
log_deaths 0.048***
(0.014)
Constant 0.028 -0.086**
(0.019) (0.038)
Observations 78 78
R2 0.710 0.723
Adjusted R2 0.690 0.704
Residual Std. Error (df = 72) 0.173 0.169
F Statistic (df = 5; 72) 35.269*** 37.651***
Note: p<0.1; p<0.05; p<0.01

2.4 Predicted versus actual coverage

The first figure below shows predicted versus actual coverage for a model with the following RHS vars: pre-COVID coverage, real GDP growth 2020, digital ID coverage, digital registration, and log of deaths. I wasn’t able to see any pattern in the outliers but I could be missing something. The next few graphs are partial adjustment graphs which are sometimes useful for checking if there are any important non-linearities that we should be taking into account. (There don’t seem to be any.)

3 Spending regressions

Perform stepwise forward selection to select independent variables in a regression of spending on other vars. Do the same thing with spending / coverage.

## 
##                                 Stepwise Selection Summary                                 
## ------------------------------------------------------------------------------------------
##                          Added/                   Adj.                                        
## Step      Variable      Removed     R-Square    R-Square     C(p)         AIC        RMSE     
## ------------------------------------------------------------------------------------------
##    1    pre_coverage    addition       0.194       0.180     1.7080    -409.7216    0.0077    
##    2    pre_spending    addition       0.244       0.217     0.1740    -411.5137    0.0075    
##    3      dig_reg       addition       0.291       0.253    -1.2420    -413.4207    0.0074    
## ------------------------------------------------------------------------------------------
## 
##                               Stepwise Selection Summary                               
## --------------------------------------------------------------------------------------
##                      Added/                   Adj.                                        
## Step    Variable    Removed     R-Square    R-Square     C(p)         AIC        RMSE     
## --------------------------------------------------------------------------------------
##    1      fsi       addition       0.046       0.029    -3.8090    -304.4924    0.0185    
## --------------------------------------------------------------------------------------
Dependent variable:
spending
(1) (2) (3) (4)
pre_coverage 0.016*** 0.019*** 0.015*** 0.010**
(0.006) (0.004) (0.005) (0.005)
pre_spending 0.001 0.002 0.002
(0.001) (0.002) (0.002)
dig_reg -0.001 0.004**
(0.002) (0.002)
expansion 0.021***
(0.005)
Constant -0.0001 0.004*** 0.003*** 0.001
(0.001) (0.001) (0.001) (0.001)
Observations 60 60 60 60
R2 0.501 0.194 0.244 0.291
Adjusted R2 0.465 0.180 0.217 0.253
Residual Std. Error 0.006 (df = 55) 0.008 (df = 58) 0.008 (df = 57) 0.007 (df = 56)
F Statistic 13.812*** (df = 4; 55) 13.991*** (df = 1; 58) 9.183*** (df = 2; 57) 7.675*** (df = 3; 56)
Note: p<0.1; p<0.05; p<0.01