1 Changes from previous version

  1. Added population as a RHS variable in basic coverage regressions.
  2. Weighted for population in basic coverage regressions.
  3. Use HC1 standard errors (i.e. same as you get with Stata’s “robust” option) for all regression coefficients

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”, “fsi”, “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    52.0620     -8.9381    0.2239    
##    2      dig_reg       addition       0.644       0.635    17.2740    -34.2834    0.1910    
##    3        eap         addition       0.675       0.663    11.0240    -39.8843    0.1836    
##    4     log_deaths     addition       0.711       0.696     3.5080    -47.6148    0.1743    
## -----------------------------------------------------------------------------------------
Dependent variable:
coverage
(1) (2) (3) (4) (5) (6) (7)
pre_coverage 1.147*** 0.849*** 0.731*** 0.673*** 0.637*** 0.620*** 0.635***
(0.117) (0.138) (0.134) (0.121) (0.119) (0.120) (0.068)
rGDPg2020 -0.005 -0.005 -0.005
(0.004) (0.004) (0.003)
dig_id 0.069 0.078 -0.193**
(0.078) (0.079) (0.075)
dig_reg 0.262*** 0.267*** 0.204*** 0.195*** 0.193*** 0.301***
(0.057) (0.054) (0.059) (0.063) (0.062) (0.041)
fsi 0.006 0.006 0.007
(0.017) (0.017) (0.020)
eap 0.164** 0.279*** 0.277*** 0.295*** 0.279***
(0.082) (0.077) (0.091) (0.092) (0.048)
log_deaths 0.040*** 0.035** 0.036** 0.058***
(0.013) (0.017) (0.017) (0.017)
pop_2018 -0.000
(0.000)
Constant 0.131*** 0.055** 0.046** -0.070* -0.144 -0.147 -0.134
(0.028) (0.022) (0.019) (0.037) (0.174) (0.176) (0.224)
Observations 83 83 83 83 82 82 82
R2 0.505 0.644 0.675 0.711 0.717 0.720 0.893
Adjusted R2 0.499 0.635 0.663 0.696 0.690 0.689 0.883
Residual Std. Error 0.224 (df = 81) 0.191 (df = 80) 0.184 (df = 79) 0.174 (df = 78) 0.176 (df = 74) 0.176 (df = 73) 771.234 (df = 74)
F Statistic 82.746*** (df = 1; 81) 72.416*** (df = 2; 80) 54.771*** (df = 3; 79) 48.029*** (df = 4; 78) 26.751*** (df = 7; 74) 23.477*** (df = 8; 73) 88.067*** (df = 7; 74)
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)
pre_coverage 0.739*** 0.641*** 0.735***
(0.115) (0.112) (0.121)
rGDPg2020 -0.004 -0.005 -0.004
(0.004) (0.004) (0.005)
eap 0.318*** 0.268*** 0.287***
(0.073) (0.076) (0.078)
log_deaths 0.052*** 0.035** 0.052***
(0.013) (0.015) (0.015)
dig_id 0.139**
(0.057)
dig_reg 0.205***
(0.059)
fsi -0.019
(0.016)
Constant -0.141*** -0.063* 0.086
(0.038) (0.038) (0.159)
Observations 83 83 82
R2 0.667 0.717 0.653
Adjusted R2 0.646 0.699 0.630
Residual Std. Error 0.188 (df = 77) 0.174 (df = 77) 0.192 (df = 76)
F Statistic 30.898*** (df = 5; 77) 39.021*** (df = 5; 77) 28.559*** (df = 5; 76)
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) (3)
pre_coverage 0.668*** 0.673*** 0.735***
(0.127) (0.121) (0.121)
dig_reg 0.257*** 0.204***
(0.051) (0.059)
eap 0.169** 0.279*** 0.287***
(0.084) (0.077) (0.078)
rGDPg2020 -0.008* -0.004
(0.004) (0.005)
log_deaths 0.040*** 0.052***
(0.013) (0.015)
fsi -0.019
(0.016)
Constant 0.034* -0.070* 0.086
(0.019) (0.037) (0.159)
Observations 83 83 82
R2 0.692 0.711 0.653
Adjusted R2 0.676 0.696 0.630
Residual Std. Error 0.180 (df = 78) 0.174 (df = 78) 0.192 (df = 76)
F Statistic 43.793*** (df = 4; 78) 48.029*** (df = 4; 78) 28.559*** (df = 5; 76)
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. 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       0.198       0.188     2.3480    -550.7298    0.0072    
##    2      dig_reg       addition       0.235       0.215     0.7880    -552.4523    0.0071    
##    3    pre_spending    addition       0.331       0.300    -0.6580    -484.0511    0.0069    
## ------------------------------------------------------------------------------------------
## 
##                              Stepwise Selection Summary                               
## -------------------------------------------------------------------------------------
##                      Added/                   Adj.                                       
## Step    Variable    Removed     R-Square    R-Square     C(p)        AIC        RMSE     
## -------------------------------------------------------------------------------------
##    1    dig_reg     addition       0.054       0.040    3.8880    -341.5569    0.0198    
## -------------------------------------------------------------------------------------
Dependent variable:
spending spending_pc
(1) (2) (3)
pre_coverage 0.011** -0.019
(0.005) (0.011)
dig_reg 0.005*** -0.009* -0.003
(0.002) (0.005) (0.006)
pre_spending 0.002 0.001
(0.002) (0.002)
expansion -0.006
(0.011)
Constant 0.0003 0.028*** 0.028***
(0.001) (0.005) (0.006)
Observations 69 69 60
R2 0.331 0.054 0.056
Adjusted R2 0.300 0.040 -0.013
Residual Std. Error 0.007 (df = 65) 0.020 (df = 67) 0.019 (df = 55)
F Statistic 10.728*** (df = 3; 65) 3.800* (df = 1; 67) 0.812 (df = 4; 55)
Note: p<0.1; p<0.05; p<0.01