Annotations

lnPCGDP = log of Per Capita GDP

TR = Tax Revenue (% of GDP)

GE.EST = Government Effectiveness.

CC.EST = Control of Corruption.

PV.EST = Political Stability and Absence of Violence.

RQ.EST = Regulatory Quality.

RL.EST = Rule of Law.

VA.EST = Voice and Accountability.

Sig = p-value

Calculating Palma Ratio from the given data

## New names:
## * `` -> ...4
## * `` -> ...5
## * `` -> ...6
## * `` -> ...7

Making a data frame with relevant variables

Since the data frame has 12 columns, we are showing it in two parts.

Data has been taken from the World Bank.

Merging the datasets and showing specific columns

Regressing the Palma Ratio on several factors

All income levels included.

##                         Model Summary                          
## --------------------------------------------------------------
## R                       0.578       RMSE                0.598 
## R-Squared               0.334       Coef. Var          37.487 
## Adj. R-Squared          0.237       MSE                 0.358 
## Pred R-Squared          0.074       MAE                 0.403 
## --------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
## 
##                               ANOVA                                
## ------------------------------------------------------------------
##                Sum of                                             
##               Squares        DF    Mean Square      F        Sig. 
## ------------------------------------------------------------------
## Regression      9.890         8          1.236    3.452    0.0027 
## Residual       19.695        55          0.358                    
## Total          29.586        63                                   
## ------------------------------------------------------------------
## 
##                                   Parameter Estimates                                    
## ----------------------------------------------------------------------------------------
##       model      Beta    Std. Error    Std. Beta      t        Sig      lower     upper 
## ----------------------------------------------------------------------------------------
## (Intercept)     3.853         1.481                  2.602    0.012     0.885     6.820 
##     lnPCGDP    -0.142         0.159       -0.187    -0.896    0.374    -0.460     0.176 
##          TR    -0.046         0.017       -0.376    -2.704    0.009    -0.080    -0.012 
##      GE.EST    -0.412         0.451       -0.486    -0.912    0.366    -1.316     0.493 
##      CC.EST     0.494         0.283        0.717     1.742    0.087    -0.074     1.062 
##      PV.EST    -0.210         0.158       -0.230    -1.334    0.188    -0.526     0.105 
##      RQ.EST    -0.020         0.301       -0.023    -0.068    0.946    -0.623     0.583 
##      RL.EST    -0.417         0.440       -0.544    -0.947    0.348    -1.299     0.465 
##      VA.EST     0.487         0.191        0.592     2.549    0.014     0.104     0.869 
## ----------------------------------------------------------------------------------------

Here we have found ‘Control of Corruption’,‘Voice & Accountability’ and ‘Tax Revenue’(% of GDP) as significant variables to influence the palma ratio.

Regressing the Palma Ratio on several factors

Based on high income.

##                          Model Summary                          
## ---------------------------------------------------------------
## R                        0.518       RMSE                0.284 
## R-Squared                0.268       Coef. Var          22.789 
## Adj. R-Squared           0.002       MSE                 0.081 
## Pred R-Squared          -0.987       MAE                 0.193 
## ---------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
## 
##                               ANOVA                                
## ------------------------------------------------------------------
##                Sum of                                             
##               Squares        DF    Mean Square      F        Sig. 
## ------------------------------------------------------------------
## Regression      0.653         8          0.082    1.009    0.4573 
## Residual        1.780        22          0.081                    
## Total           2.433        30                                   
## ------------------------------------------------------------------
## 
##                                   Parameter Estimates                                   
## ---------------------------------------------------------------------------------------
##       model      Beta    Std. Error    Std. Beta      t        Sig      lower    upper 
## ---------------------------------------------------------------------------------------
## (Intercept)     1.197         2.361                  0.507    0.617    -3.699    6.093 
##     lnPCGDP     0.080         0.239        0.102     0.336    0.740    -0.414    0.575 
##          TR    -0.017         0.011       -0.314    -1.493    0.150    -0.040    0.007 
##      GE.EST    -0.309         0.540       -0.524    -0.573    0.573    -1.429    0.811 
##      CC.EST     0.301         0.234        0.773     1.287    0.212    -0.184    0.785 
##      PV.EST    -0.276         0.156       -0.437    -1.774    0.090    -0.599    0.047 
##      RQ.EST    -0.072         0.264       -0.127    -0.273    0.787    -0.620    0.475 
##      RL.EST    -0.088         0.524       -0.174    -0.167    0.869    -1.175    0.999 
##      VA.EST    -0.028         0.442       -0.031    -0.063    0.950    -0.945    0.890 
## ---------------------------------------------------------------------------------------

Here we have only found ‘political stability and absence of violence’ as a significant variable to influence the palma ratio.

Regressing the Palma Ratio on several factors.

Based on upper middle income.

##                         Model Summary                          
## --------------------------------------------------------------
## R                       0.844       RMSE                0.578 
## R-Squared               0.712       Coef. Var          27.987 
## Adj. R-Squared          0.534       MSE                 0.334 
## Pred R-Squared          0.147       MAE                 0.363 
## --------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
## 
##                               ANOVA                                
## ------------------------------------------------------------------
##                Sum of                                             
##               Squares        DF    Mean Square      F        Sig. 
## ------------------------------------------------------------------
## Regression     10.726         8          1.341     4.01    0.0132 
## Residual        4.346        13          0.334                    
## Total          15.073        21                                   
## ------------------------------------------------------------------
## 
##                                   Parameter Estimates                                    
## ----------------------------------------------------------------------------------------
##       model      Beta    Std. Error    Std. Beta      t        Sig      lower     upper 
## ----------------------------------------------------------------------------------------
## (Intercept)    11.799         4.840                  2.438    0.030     1.344    22.255 
##     lnPCGDP    -0.822         0.486       -0.267    -1.692    0.114    -1.871     0.228 
##          TR    -0.106         0.049       -0.488    -2.170    0.049    -0.212     0.000 
##      GE.EST    -0.182         0.620       -0.064    -0.293    0.774    -1.522     1.159 
##      CC.EST     0.294         0.546        0.155     0.538    0.600    -0.886     1.473 
##      PV.EST    -0.786         0.271       -0.607    -2.904    0.012    -1.371    -0.201 
##      RQ.EST    -0.541         0.521       -0.283    -1.038    0.318    -1.666     0.585 
##      RL.EST     0.227         0.680        0.102     0.333    0.744    -1.243     1.696 
##      VA.EST     1.219         0.270        1.080     4.507    0.001     0.635     1.803 
## ----------------------------------------------------------------------------------------

Here we have found ‘Tax Revenue’,‘Political Stability & Absence of Violence(PV.ESt)’ and ‘voice & accountability’ as significant to influence the Palma Ratio.

Regressing the Palma Ratio on several factors.

Based on lower middle income.

##                         Model Summary                         
## -------------------------------------------------------------
## R                       1.000       RMSE                 NaN 
## R-Squared               1.000       Coef. Var            NaN 
## Adj. R-Squared            NaN       MSE                  NaN 
## Pred R-Squared            NaN       MAE                0.000 
## -------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
## 
##                             ANOVA                             
## -------------------------------------------------------------
##                Sum of                                        
##               Squares       DF    Mean Square     F     Sig. 
## -------------------------------------------------------------
## Regression      1.874        7          0.268    NaN     NaN 
## Residual        0.000        0            NaN                
## Total           1.874        7                               
## -------------------------------------------------------------
## 
##                                Parameter Estimates                                 
## ----------------------------------------------------------------------------------
##       model      Beta    Std. Error    Std. Beta     t     Sig     lower    upper 
## ----------------------------------------------------------------------------------
## (Intercept)    -3.960           NaN                 NaN     NaN      NaN      NaN 
##     lnPCGDP     1.121           NaN        0.972    NaN     NaN      NaN      NaN 
##          TR    -0.238           NaN       -1.835    NaN     NaN      NaN      NaN 
##      GE.EST    -5.612           NaN       -3.495    NaN     NaN      NaN      NaN 
##      CC.EST     6.069           NaN        3.712    NaN     NaN      NaN      NaN 
##      PV.EST    -0.329           NaN       -0.508    NaN     NaN      NaN      NaN 
##      RQ.EST     2.553           NaN        1.351    NaN     NaN      NaN      NaN 
##      RL.EST    -1.593           NaN       -1.051    NaN     NaN      NaN      NaN 
##      VA.EST        NA            NA        0.829     NA      NA      NaN      NaN 
## ----------------------------------------------------------------------------------

From the table,we can see that there are several factors which has no standard error,t value or p-value (Sig).The reason behind is that our number of observation is very low to estimate the parameters.

OLS Assumption:

Number of estimators must be lower than number of observations.

Since our observation contains only 8 countries and number of parameters we wanted to estimate is also equal to 8,we don’t find any significant result. As our residual variation becomes 0, r square value becomes 1.

Same reason also goes for 3 low income countries.There’s no use running regression on that.

Classifying countries based on regions

## 
##        East Asia & Pacific      Europe & Central Asia 
##                          4                         40 
##  Latin America & Caribbean Middle East & North Africa 
##                         11                          2 
##              North America                 South Asia 
##                          1                          2 
##         Sub-Saharan Africa 
##                          4

Regressing the Palma Ratio on several factors in Europe & Central Asia.

##                          Model Summary                          
## ---------------------------------------------------------------
## R                        0.614       RMSE                0.249 
## R-Squared                0.376       Coef. Var          20.339 
## Adj. R-Squared           0.216       MSE                 0.062 
## Pred R-Squared          -0.224       MAE                 0.165 
## ---------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
## 
##                               ANOVA                                
## ------------------------------------------------------------------
##                Sum of                                             
##               Squares        DF    Mean Square      F        Sig. 
## ------------------------------------------------------------------
## Regression      1.163         8          0.145    2.339    0.0428 
## Residual        1.927        31          0.062                    
## Total           3.090        39                                   
## ------------------------------------------------------------------
## 
##                                   Parameter Estimates                                   
## ---------------------------------------------------------------------------------------
##       model      Beta    Std. Error    Std. Beta      t        Sig      lower    upper 
## ---------------------------------------------------------------------------------------
## (Intercept)    -1.444         1.397                 -1.034    0.309    -4.294    1.406 
##     lnPCGDP     0.231         0.138        0.511     1.678    0.103    -0.050    0.513 
##          TR     0.009         0.010        0.173     0.978    0.335    -0.010    0.029 
##      GE.EST     0.332         0.264        0.961     1.257    0.218    -0.207    0.870 
##      CC.EST    -0.195         0.171       -0.716    -1.140    0.263    -0.543    0.154 
##      PV.EST    -0.159         0.086       -0.435    -1.845    0.075    -0.336    0.017 
##      RQ.EST     0.487         0.183        1.317     2.659    0.012     0.114    0.861 
##      RL.EST    -0.488         0.299       -1.608    -1.634    0.112    -1.098    0.121 
##      VA.EST    -0.075         0.136       -0.222    -0.555    0.583    -0.353    0.202 
## ---------------------------------------------------------------------------------------

We have found ‘Political Stability & Absence of Violence’ & ‘Regulatory quality’ as significant to influence the Palma Ratio.

Regressing the Palma Ratio on several factors in Latin America & Carribean.

##                          Model Summary                          
## ---------------------------------------------------------------
## R                        0.978       RMSE                0.321 
## R-Squared                0.957       Coef. Var          11.855 
## Adj. R-Squared           0.785       MSE                 0.103 
## Pred R-Squared          -0.315       MAE                 0.101 
## ---------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
## 
##                               ANOVA                                
## ------------------------------------------------------------------
##                Sum of                                             
##               Squares        DF    Mean Square      F        Sig. 
## ------------------------------------------------------------------
## Regression      4.582         8          0.573    5.551    0.1616 
## Residual        0.206         2          0.103                    
## Total           4.789        10                                   
## ------------------------------------------------------------------
## 
##                                    Parameter Estimates                                    
## -----------------------------------------------------------------------------------------
##       model      Beta    Std. Error    Std. Beta      t        Sig       lower     upper 
## -----------------------------------------------------------------------------------------
## (Intercept)    10.680        17.848                  0.598    0.610    -66.112    87.472 
##     lnPCGDP    -0.625         1.612       -0.263    -0.388    0.736     -7.559     6.309 
##          TR    -0.062         0.091       -0.351    -0.688    0.562     -0.453     0.328 
##      GE.EST    -0.991         1.846       -0.521    -0.537    0.645     -8.936     6.953 
##      CC.EST    -0.636         0.736       -0.630    -0.864    0.479     -3.803     2.531 
##      PV.EST    -0.936         0.621       -0.853    -1.509    0.270     -3.606     1.734 
##      RQ.EST    -0.627         0.721       -0.310    -0.869    0.477     -3.731     2.477 
##      RL.EST     3.706         1.228        2.665     3.019    0.094     -1.576     8.989 
##      VA.EST    -0.589         2.165       -0.389    -0.272    0.811     -9.904     8.725 
## -----------------------------------------------------------------------------------------

Here we have only found the ‘Rule of Law’ as a significant variable to influence the Palma Ratio.

For the same reason mentioned above,we are not able to show the impact of our factors on Palma Ratio based on rest of the regions.