1. AN APPROACH TO IDENTIFYING AN OPTIMAL GUARANTEED BASIC INCOMEby
Harvey Stevens
for
the 2018 NABIG Congress

2. THE CHALLENGE: WHICH OPTION IS THE BEST?
These options have the same common features:
They are financed by the removal of the following non-refundable tax credits: Basic, Age, Pension Income, Education, Tuition and Interest on student loans, the transfer of unused education tax credits and the elimination of the GST credit.
The nuclear family is the administrative unit for calculating the net benefit.
Total family income less allowable CRA deductions is used as the basis for clawing back the value of the Guarantee. As such the value of all federal transfers are included.
The Guarantee for a single adult is increased by the square root of family size for larger size units.
A top-up to the value of the Guarantee is provided for those in receipt of a tax credit for a disability and for caring for an infirm dependent.

3. The Potential for an Optimum Design
The design of a GAI involves trade-offs due to the formula that determines the net benefit and cost:
Net Benefit/Cost = Guarantee – (Other Income x Benefit Reduction Rate)
Given this formula, to remain within the same budget constraint, raising the value of the Guarantee (G) requires raising the Benefit Reduction Rate (BRR).
In turn, a higher G and a higher BRR generates the following trade-offs:
A reduction in the rate and depth of poverty;
A reduction in income inequality;
A reduction in labour supply and earnings;
Reduction in the number of winners.
To see the nature of these trade-offs, we can look at the previous chart of the four equal-cost options.
These trade-offs suggest that there may be an optimum combination of a G and BRR that maximizes poverty reduction while minimizing the loss of earnings and the number of winners.

4. The Methodology for Determining an Optimal Design
Identify the criteria for assessing each G/BRR combination. With the SPSDM package, it is possible to measure the following: rate and depth of poverty/total poverty gap, degree of income inequality and the percent winners. By applying consensus estimates of substitution and income elasticities to the changes in marginal tax rates induced by the financing of the GAI and the G and BRR parameters, it is possible to estimate the change in earnings due to the GAI.
Measure each of the criteria under the current tax and transfer system.
Generate a range of equal cost G and BRR combinations and measure the criteria for each combination.
For each criteria and for each G and BRR combination, calculate the per cent change from the current system. The ‘per cent change’ calculation provides a common metric across the criteria.
Aggregate the per cent changes to create a total or average score for each combination.
Compare the aggregate score across the range of combinations to see if it reaches a maximum value.
If there is a maximum value , then that indicates the optimal design.

5. An Example – Canada 2015 BRR & G Combination % change in Poverty Rate
% change in Poverty Depth
% change in GINI Index
% change in Earnings
% change in Winners
Average % Change – Equal Weights (1)
0%/G=$2083
-8.7%
-4.3%
-1.4%
-0.8%
+13.8%
+5.46%
7%/G=$5,061
-32.7%
-7.5%
-5.3%
-3.3%
+6.4%
+9.71%
10%/G=$5,978
-36.5%
-10.4%
-5.6%
-4.2%
-1.3%
+9.41%
20%/G=$8,420
-44.2%
-21.9%
-5.8%
-7.6%
-15.9%
+9.68%
39%/G=$8,420/TP=$11,635
-55.8%
-19.2%
-11.6%
-28.4%
+8.11%
35%/G=$11,243
-50.0%
-37.3%
-5.7%
-29.2%
+10.46%
50%/G=$13,606
-51.2%
-5.5%
-14.7%
-37.6%
+10.89%
58%/G=$14,749
-49.0%
-57.9%
-5.4%
-15.7%
-41.2%
+11.09%
60%/G=$15,024
-48.1%
-59.2%
-15.6%
-42.2%
+10.97%
70%/G=$16,344
-47.1%
-64.0%
-5.2%
-46.0%
+10.92%
Note: (1) The changes in the rate and depth of poverty and the GINI index have been scored as positive, in
calculating the average change.
These results are particular to the population covered by the GAI, the method of financing it and the indicators used.
Preliminary work on an Alberta and Manitoba GAI indicates that the optimum is a 7 per cent BRR.
A different method of financing the GAI also would lead to different results as it would affect the METRs and the per cent winners.
Other indicators also could affect the results. For example, instead of two measures of poverty, one could use a composite measure – the total poverty gap measured in dollars.
As for the results for Canada, the following should be noted:
- There is a local maximum at a 7% BRR and a global maximum at 58%, likely reflecting the shape of the income distribution.
The big trade-offs are between poverty reduction and the per cent winners.
The impact on income inequality is minimal and it peaks at a 20% BRR.
A comparison of the two options with a G=$8,420 show that the option featuring no turning point results in a higher average change score than the one with a turning point.
Very high BRRs reduce the impact on the rate of poverty but continue to improve the depth of poverty impact.
Reductions in earnings increase as the BRR and G increase but seem to plateau at the 58%/$14,749 combination.

6. A Second Example – Canada 2017
BRR & G Combination
% change in Total Poverty Gap
% change in GINI Index
% change in Earnings
% change in Winners
Average % Change – Equal Weights (1)
Average % Change – Unequal Weights (2)
0%/G=$2083
-14.2%
-1.4%
-0.8%
+13.8%
7.15
7.17
7%/G=$5,061
-40.8%
-5.3%
-3.3%
+6.4%
12.30
14.02
10%/G=$5,978
-46.6%
-5.6%
-4.2%
-1.3%
11.67
14.06
20%/G=$8,420
-59.4%
-5.8%
-7.6%
-15.9%
10.43
14.19
35%/G=$11,243
-70.5%
-5.7%
-11.6%
-29.2%
8.84
13.83
50%/G=$13,606
-77.2%
-5.5%
-14.7%
-37.6%
7.59
13.33
60%/G=$15,024
-80.0%
-5.4%
-15.6%
-42.2%
6.90
13.02
70%/G=$16,344
-82.0%
-5.2%
-15.7%
-46.0%
6.37
12.77
Note: (1) The changes in the rate and depth of poverty and the GINI index have been scored as positive, in
calculating the average change. Each criteria has a weight of 0.25, such that they add to 1.00
Note: (2) Weights are: 0.30 for Total Poverty Gap; 0.25 for GINI index and % change in earnings; and, 0.20 for %
change in winners.
Replacing the two poverty measures with the aggregate total poverty gap measure results in the optimum BRR/G combination dropping from 58% & $14,479 to 7% & $5,601 when equal weights are applied to each criterion. This is because the % change in the total gap is less than the combined per cent change in the rate and depth of poverty.
However, if poverty reduction is weighted more heavily and the % winners weighted less heavily, the optimum BRR/G combination increases to 20% & $8,420.
Thus, the results are sensitive to both the outcome measures used to rate the combinations and the weights assigned to each criteria.
Conclusions:
It is possible to compare equal cost combinations of BRR & G on several outcome criteria and, calculating the % change score for each combination across the several criteria, then rank the combinations according to their total or average score.
For Canada, this comparison suggests that a high BRR and G combination is the optimum if both the rate and depth of poverty measure is used. However, if just the total poverty gap measure is used, then the optimum BRR & G combination is a low BRR and G.
Shifting more policy weight to poverty reduction and less to maximizing the number of winners results in a more generous G and higher BRR.
While such shifts indicate that the choice of an optimum is dependent upon the criteria used and the weights applied, the application of the method permits a more disciplined approach to selecting a GAI design, based on policy makers objectives and policy preferences.