Head-count ratio

Also called: HCR, Poverty headcount ratio · Topic: Poverty and Inequality: Measurement and Policy · NCERT: Beyond NCERT

Meaning

The head-count ratio (HCR) is the share of a country's population whose income or consumption is below the poverty line. It tells us how many people are poor. It says nothing about how poor they are.

H = q / n

• q = number of people below the poverty line (z)
• n = total population

It is the official headline poverty measure in India and the World Bank's headline measure. Most news reports use it, for example "1 in 5 Indians is poor". But it cannot see the depth of poverty or differences among the poor, so it should always be read together with other measures.

Explanation

How it works: identify the poor, then count them

• Step 1: Set the poverty line (z). This is a cut-off level of income or consumption. A person whose income or consumption (y) is below z is counted as poor.
• Step 2: Identification. Who is poor? Everyone with y < z.
• Step 3: Aggregation. How do we turn all the poor into one number? The HCR does this in the simplest way: it counts heads and divides by the total population.
• It measures incidence (how widespread poverty is), not depth or severity.
• It depends heavily on where z is drawn. Raise the line a little and many people near it suddenly become "poor". Lower it and they disappear from the count.

Place in the FGT family

• The Foster-Greer-Thorbecke (FGT, 1984) formula gives three poverty measures in one: Pα = (1/n) Σ (i = 1 to q) [(z − yᵢ) / z]^α

• α (alpha) is a "poverty-aversion" setting. The higher α is, the more weight the poorest get.

• When α = 0: every gap raised to the power 0 equals 1. The formula just counts the poor and gives q/n = HCR.

• α = 1 gives the poverty gap index (depth). α = 2 gives the squared poverty gap (severity).
• The World Bank confirms that the headcount, poverty gap and squared poverty gap all belong to the FGT class [4].
• Decomposability (can be split into parts): the HCR can be split by group, such as state, caste or rural/urban. National HCR = the population-weighted sum of the group HCRs. This shows which group adds the most to poverty.

Why HCR alone misleads

• It ignores depth. A person ₹1 below the line counts the same as a person ₹500 below it.
• It ignores differences among the poor. It cannot tell whether the poor are bunched just below the line or spread far below it.
• It breaks Sen's monotonicity axiom.
• Axiom (a basic rule a good measure should follow): if a poor person becomes poorer, measured poverty should go up.

• HCR does not change, because that person was already counted as poor.

• It breaks Sen's transfer axiom.

• Axiom: if income moves from a poorer person to a less-poor person, measured poverty should go up.

• Under HCR, poverty may stay the same. It may even fall, if the person who receives the money crosses the line.

• Perverse incentive (a reward for doing the wrong thing):

• A government is judged on HCR → it helps people just below the line, because they are the cheapest to push over
• → HCR falls fast

• → the poorest are left behind.

• Ratio vs number. The ratio can fall while the absolute number of poor goes up, if the population grows fast enough.

• Population 100 crore, HCR 30% → 30 crore poor.
• Later: population 125 crore, HCR 25% → 31.25 crore poor.
• The ratio fell, but 1.25 crore more people are poor. Always check both figures.

Worked example

Poverty line z = 100. Four people have incomes 60, 90, 120 and 150.

Person	Income	Poor?	Gap ratio (z − y)/z
1	60	Yes	0.40
2	90	Yes	0.10
3	120	No	0
4	150	No	0

• HCR = 2/4 = 50%
• For comparison, PGI = (0.4 + 0.1)/4 = 0.125 and SPG = (0.16 + 0.01)/4 = 0.0425

Test 1: monotonicity. Person 1 falls from 60 to 40.

• HCR stays at 50%. It does not notice.
• PGI rises to 0.175 and SPG rises to 0.0925. Only the gap measures see that the poorest person got poorer.

Test 2: transfer. Take 11 from person 1 (60 → 49) and give it to person 2 (90 → 101).

• HCR falls to 1/4 = 25%, so "poverty fell". Yet the poorest person is now worse off.
• PGI rises slightly to 0.1275. SPG rises sharply to 0.065 and clearly catches the harm.

In India

• Who sets the line: the Planning Commission set up expert groups to fix the poverty line. The HCR is then worked out from household consumption data.
• Tendulkar Expert Group:
• Set up in December 2005 under Prof. Suresh D. Tendulkar. It reported in December 2009 [1].
• It used a Mixed Reference Period (MRP) Poverty Line Basket. MRP means different recall periods for different items: 365 days for rarely bought items and 30 days for the rest. The basket was set to match an urban poverty ratio of 25.7% [1].

• HCR for 2004-05: rural 41.8%, urban 25.7%, all-India 37.2%. That was 407.6 million (40.76 crore) people [1].

• Trend (Tendulkar method): the HCR fell from 45.3% (1993-94) to 37.2% (2004-05) and then to 21.9% (2011-12) [2].

• Rangarajan Expert Group:
• Set up in June 2012 under Dr. C. Rangarajan. It reported on 30 June 2014 [3].
• Its poverty line was a monthly per capita expenditure of ₹1,407 (urban) and ₹972 (rural) [3].

• A different line gives a different head count. This shows how much the HCR depends on where z is drawn.

• Head-count inside the MPI: India's National Multidimensional Poverty Index (MPI) also uses a head-count. A person is "MPI poor" if deprived in one-third or more of 12 weighted indicators [5].

• The MPI combines this head-count (incidence) with the intensity of deprivation (how badly the poor are deprived).
• Multidimensional poverty fell from 29.17% (2013-14) to 11.28% (2022-23). 24.82 crore people escaped it in these 9 years [5].
• The biggest declines were in Uttar Pradesh (5.94 crore), Bihar (3.77 crore), Madhya Pradesh (2.30 crore) and Rajasthan (1.87 crore) [5].

Don't confuse with

• Poverty gap index (PGI, α = 1): HCR measures incidence (how many are poor). PGI measures depth, meaning the average shortfall from the line, with the non-poor counted as zero. PGI = H × I, where I is the income-gap ratio. PGI satisfies monotonicity. HCR does not.
• Squared poverty gap (SPG, α = 2): this measures severity. It squares each gap, so the poorest count much more. The World Bank calls it the "poverty severity index" [4]. Of the three FGT measures, only SPG captures inequality among the poor.
• Absolute number of poor: HCR is a ratio (q/n). The number of poor is q. When the population grows, the ratio can fall even while the number of poor rises.
• Multidimensional poverty index: HCR looks only at income or consumption. The MPI counts deprivation across 12 indicators of health, education and living standards [5], and it adds intensity to the head-count.

Prelims Hooks

• HCR = q/n. It measures incidence, and it is the FGT measure with α = 0. (α = 1 → poverty gap, depth; α = 2 → squared poverty gap, severity.)
• Trap: HCR violates both of Sen's axioms, monotonicity and transfer. It does not change when a poor person gets poorer. It can even fall when money moves from a poorer person to a less-poor one.
• Trap: a falling poverty ratio does not mean the number of poor is falling.
• Tendulkar (reported December 2009): used the Mixed Reference Period. All-India HCR in 2004-05 was 37.2% (rural 41.8%, urban 25.7%) [1].
• Tendulkar-method trend: 45.3% (1993-94) → 37.2% (2004-05) → 21.9% (2011-12) [2].
• Rangarajan (reported 30 June 2014): poverty line of ₹1,407/month urban and ₹972/month rural [3].

Mains Points

• Headline-measure bias in policy: India targets and reports on the HCR.
• This rewards schemes that lift the "near-poor" just over the line, while the poorest are left behind.

• Reporting PGI and SPG alongside HCR would direct welfare (PDS, MGNREGA, DBT) towards the poorest. This fits the Antyodaya idea of reaching the last person first.

• Line-setting debates: HCR depends on where z is drawn.

• The Tendulkar line (2009) and the Rangarajan line (2014) gave different poverty counts [1][3].

• This affects how many people qualify for schemes and how central funds are shared among states. Adding depth measures and the MPI makes policy less dependent on one line [5].

• Growth vs inclusion: growth alone can lower the HCR even while inequality among the poor rises. Severity measures (SPG, Sen index) show whether growth is truly inclusive. HCR should be read together with the absolute number of poor.

Related concepts

• Poverty gap index
• Squared poverty gap index

Read more

• Measuring poverty: head-count ratio, poverty gap and the FGT family