Exercise 8.4

Using the file CAN4, compute the concentration indices of each of B and T, and compare them to the Gini index of gross income X. Then, compute an estimate of TR progressivity of the tax and benefit system in Canada.

Answer

  • Gini coeffiction of gross income (X)

STEP 1: Use the DAD Application: INEQUALITY|S-GINI INDEX

  • After choosing the appropriate variable(s) and parameters, click on the  COMPUTE button.

RESULTS

 

Gini / S-Gini  (I)

Session Date Fri Jul 09 14:54:20 EDT 2004
Execution Time 0.125 sec
FileName CAN6.daf
OBS 1000
Sampling Weight No Selection
Variable of interest X
Size variable Without size
Group variable No Selection
Group Number 1
Parameter ρ=2.0

Estimated value

Standard deviation

Lower bound

Upper bound

Confidence Level in (%)

0,50845586

0,01630584

0,47649699

0,54041472

95,00000000

 

 
 

  • Coefficient of concentration

STEP 1: Use the DAD Application: REDISTRIBUTION|COEFFICIENT OF CONCENTRATION

  • After choosing the appropriate variable(s) and parameters, click on the  COMPUTE button.

RESULTS

Coefficient of Concentration (IC)

Session Date Fri Jul 09 14:56:41 EDT 2004
Execution Time 0.203 sec
FileName CAN6.daf
OBS 1000
Sampling Weight No Selection
Variable of interest B1
Size variable Without size
Group variable No Selection
Group Number 1
Parameter ρ=2.0
rho 2.0
Estimate -0,26485826
  (0,04945408)

 

Progressivity coefficients

Component IC difference
B1 -0,2648 I-IC 0.7733

B2

 -0,4395 I-IC 0.9480
B3 -0,3647 I-IC 0.8732
T 0,5953 IC-I 0.0868

We can also find these results by using:

 

STEP 1: Use the DAD Application: REDISTRIBUTION|TAX OR TRANSFER

  • After choosing the appropriate variable(s) and parameters, click on the  S-GINI button.

RESULTS
 

Redistribution (Tax Or Transfer) - S-Gini

Session Date Fri Jul 09 15:16:21 EDT 2004
Execution Time 0.266 sec
FileName CAN6.daf
OBS 1000
Sampling Weight No Selection
Variable of interest X
Size variable Without Weigths
Group variable No Selection
Group Number 1
Vector of Tranfer B1
Options STD = Yes / Approach = TR
Parameters p=0.5 / rho=2
Estimate 0,77331412
  (0,05207858)