1 Coverage regressions

1.1 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.

## 
##                                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)

pre_coverage	1.147^***	0.849^***	0.731^***	0.673^***	0.637^***
	(0.126)	(0.120)	(0.123)	(0.118)	(0.127)

rGDPg2020					-0.005
					(0.004)

dig_id					0.069
					(0.070)

dig_reg		0.262^***	0.267^***	0.204^***	0.195^***
		(0.047)	(0.045)	(0.047)	(0.053)

fsi					0.006
					(0.015)

eap			0.164^***	0.279^***	0.277^***
			(0.060)	(0.068)	(0.073)

log_deaths				0.040^***	0.035^**
				(0.013)	(0.014)

Constant	0.131^***	0.055^*	0.046	-0.070	-0.144
	(0.032)	(0.030)	(0.029)	(0.047)	(0.155)


Observations	83	83	83	83	82
R²	0.505	0.644	0.675	0.711	0.717
Adjusted R²	0.499	0.635	0.663	0.696	0.690
Residual Std. Error	0.224 (df = 81)	0.191 (df = 80)	0.184 (df = 79)	0.174 (df = 78)	0.176 (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)

Note:	p<0.1; p<0.05; p<0.01

1.2 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^***
	(0.128)	(0.121)	(0.136)

rGDPg2020	-0.004	-0.005	-0.004
	(0.004)	(0.004)	(0.004)

eap	0.318^***	0.268^***	0.287^***
	(0.072)	(0.068)	(0.079)

log_deaths	0.052^***	0.035^**	0.052^***
	(0.013)	(0.013)	(0.014)

dig_id	0.139^**
	(0.065)

dig_reg		0.205^***
		(0.047)

fsi			-0.019
			(0.014)

Constant	-0.141^**	-0.063	0.086
	(0.057)	(0.047)	(0.138)


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

1.3 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^***
	(0.125)	(0.118)	(0.136)

dig_reg	0.257^***	0.204^***
	(0.045)	(0.047)

eap	0.169^***	0.279^***	0.287^***
	(0.059)	(0.068)	(0.079)

rGDPg2020	-0.008^**		-0.004
	(0.004)		(0.004)

log_deaths		0.040^***	0.052^***
		(0.013)	(0.014)

fsi			-0.019
			(0.014)

Constant	0.034	-0.070	0.086
	(0.029)	(0.047)	(0.138)


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

1.4 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.)

2 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    
## -------------------------------------------------------------------------------------