Poverty Calculations

Poverty Calculations Overview

• The video presents a sequence of eight poverty calculations starting from the poverty headcount to the Foster Greer Thonbruger index (FGT index).

Society and Poverty Line

• There are seven individuals in the studied society.

• The established poverty line is set at $1,000.

• Individuals with incomes below $1,000 are categorized as poor.

• Four out of seven individuals have incomes below this threshold.

Poverty Headcount

• Definition: The poverty headcount (h) represents the total number of individuals whose income is below the poverty line.

• Calculation: Four people fall below the poverty line.

  • Thus, the poverty headcount, h, equals 4.

Poverty Headcount Index

• Definition: The poverty headcount index measures the percentage of the total population living below the poverty line.

• Calculation:

  • Formula: $ext{Poverty Headcount Index} = rac{ ext{Number of Poor}}{ ext{Total Population}}$

  • Applying to our data: $ext{Poverty Headcount Index} = rac{4}{7} times 100 <br>ightarrow 57.14\%$

• Interpretation: 57.14% of the society's population is considered poor.

Total Poverty Gap

• Definition: The total poverty gap is the sum of the income shortfalls for all individuals below the poverty line.

• Calculation approach:

  • The income shortfall for each individual is calculated as: $ext{Poverty Line} - ext{Individual Income}$

  • For four individuals:

  • Individual 1: Income is $100 → Shortfall = $900 (\$1,000 - \$100)

  • Individual 2: Income is $400 → Shortfall = $600 (\$1,000 - \$400)

  • Individual 3: Income is $700 → Shortfall = $300 (\$1,000 - \$700)

  • Individual 4: Income is $900 → Shortfall = $100 (\$1,000 - \$900)

• Summation of shortfalls:
  $ext{Total Poverty Gap} = 900 + 600 + 300 + 100 = 1,900$

• Interpretation: It would require $1,900 to raise the four individuals’ incomes to the poverty line.

Average Poverty Gap

• Definition: The average poverty gap indicates the mean contribution required per person to elevate the poor to the poverty line.

• Calculation:

  • Formula: $ext{Average Poverty Gap} = rac{ ext{Total Poverty Gap}}{ ext{Total Population}}$

  • Applying data:
    $ext{Average Poverty Gap} = rac{1,900}{7} <br>ightarrow 271.43$

• Interpretation: Each person in society would need to contribute $271.43 to assist the four individuals below the poverty line.

Normalized Poverty Gap (NPG)

• Definition: The normalized poverty gap is a unitless measure that expresses the average shortfall as a percentage of the poverty line.

• Calculation:

  • Formula: $ext{NPG} = rac{ ext{Average Poverty Gap}}{ ext{Poverty Line}}$

  • Application:
    $ext{NPG} = rac{271.43}{1,000} <br>ightarrow 27.14\%$

• Interpretation: On average, the income of the poor is 27.14% short of the poverty line.

Average Income Shortfall

• Definition: The average income shortfall gives the mean shortfall for individuals below the poverty line specifically.

• Calculation approach:

  • Formula: $ext{Average Income Shortfall} = rac{ ext{Total Poverty Gap}}{h}$ (where h = number of poor individuals)

  • With values:
    $ext{Average Income Shortfall} = rac{1,900}{4} = 475$

• Interpretation: On average, each of the four individuals is $475 short of the poverty line.

Normalized Income Shortfall

• Definition: The normalized income shortfall indicates the average income shortfall relative to the poverty line in percentage form.

• Calculation:

  • Formula: $ext{Normalized Income Shortfall} = rac{ ext{Average Income Shortfall}}{ ext{Poverty Line}}$

  • Application:
    $ext{Normalized Income Shortfall} = rac{475}{1,000} <br>ightarrow 47.5\%$

• Interpretation: On average, the incomes of the poor are about 47.5% below the poverty line.

Foster Greer Thonbruger (FGT) Index

• Definition: The FGT Index is a comprehensive measure of poverty, factoring in the depth and severity of poverty among a population.

• Formula:

  • $FGT( ext{index}) = rac{1}{n} imes ext{summing from } i = 1 ext{ to } h \bigg( rac{P - Y_i}{P} \bigg)^ ext{α}$ where:

  • P = poverty line

  • Yi = income of individual i

  • n = total population

  • h = number of poor individuals

• Alpha Variants:

  • Alpha = 0: Calculates the headcount, which counts the number of individuals below the poverty line.

  • Alpha = 1: Calculates the average poverty gap.

  • Alpha = 2: Assess the squared poverty gap, providing weight to more severe income shortfalls.

• Example Calculations:

  • Alpha = 0:

  • For each poor individual (0.9, 0.6, 0.3, 0.1) raised to the power 0 gives 1, sum yields 4.

  • $rac{4}{7} <br>ightarrow 57.14\%$ (matches the earlier headcount index).

  • Alpha = 1:

  • Summing gives 1.9.

  • $rac{1.9}{7} <br>ightarrow 27.14\%$ (same as average poverty gap).

  • Alpha = 2:

  • Squaring each calculated value before summing gives 1.27.

  • $rac{1.27}{7} <br>ightarrow 11.04\%$

• Interpretation: The squared poverty gap reveals that the poorest individuals are 11.04% worse off than the average poor individual, indicating the severity of poverty and economic inequality within this subgroup and society.

Conclusion

• The presented calculations provide a nuanced understanding of poverty within a defined population, highlighting both the basic poverty measures and the deeper issues surrounding income inequality and economic disparity. Visual representations of these calculations, values, and indices play a crucial role in poverty analysis and welfare policies.