Inflation and the Phillips curve · Lesson 2 of 12
Measuring unemployment: stocks, flows and the natural rate
The Phillips curve puts inflation against unemployment, so the second number needs the same care as the first. Who counts as unemployed? Out of how many? And why does a healthy economy still have some unemployment? This lesson answers all three, and ends with the one idea the whole module builds on: a rate of unemployment that flows of workers settle at.
A question to hold on to
Given for 2010: unemployment rate 15%, unemployed 30 million, labour force participation rate 70%. For 2020: unemployment rate 20%, unemployed 50 million, labour force participation rate 80%. The percentage change in the working-age population from 2010 to 2020 is ________ (rounded to two decimal places).
IIT JAM 2024Solved at the end ↓
Definitions
Who counts
Take every adult in the economy. Each is in exactly one of three groups: employed (has a job), unemployed (has no job but is looking for one) or not in the labour force (has no job and is not looking: studying, caring for a family, retired, or discouraged). The employed and the unemployed together are the labour force.
The unemployment rate
The denominator is the labour force, not the population and not the employed (Hyderabad 2011, 2014). Someone outside the labour force is not unemployed.
Two ratios sit beside it, and the second is a trap in Indian papers:
- The labour force participation rate is the labour force over the working-age population, L/N.
- The worker ratio is the employed over the population, E/N. In Indian usage this is called the workforce or worker participation rate, which is not the same thing as the labour force participation rate: it leaves the unemployed out of the numerator.
Pause and predict
Employed 140 million, unemployed 10 million, outside the labour force 50 million. The unemployment rate is
Interactive
Try it: counting and flows
The Counting tab splits a population three ways. Press “A worker gives up looking” and watch the rate fall though nobody found a job. The Flows tab sets the same economy in motion: each month some of the employed lose their job and some of the unemployed find one.
Every adult is employed, unemployed (without a job and looking for one) or outside the labour force. Numbers are in millions. Press a case or set the three groups.
EmployedOutside
Unemployment rate
6.67%: 10 out of the labour force of 150.
Labour force participation
75% of the 200 million adults are in the labour force.
Worker ratio (employed over population)
70%. In Indian usage this is the “workforce participation rate”.
What changed
Employed 140, unemployed 10, outside the labour force 50 (millions). The rate is 10 out of the labour force of 150, not out of 200.
A subtle point
When the rate moves the wrong way
Because the rate is a ratio, both its parts can move. If the number employed rises and the population does not change, does the unemployment rate fall? Not necessarily (IIT JAM 2021). If the new jobs draw people into the labour force from outside, the labour force grows, and the unemployed can rise even as employment does. Equally, if discouraged workers stop looking, unemployment falls and no job has been created.
This is why the unemployment rate is read beside the participation rate, never alone. It is also why the arithmetic of one question can be quite different from another that sounds the same: when a paper says “workforce participation rate of 60%” of a population of 100 million with 6 million unemployed, it means 60 million are working (IIT JAM 2021), and the rate is 6 out of 66, which is 1/11. Read as the labour force participation rate it would be 6 out of 60, which is 1/10. The word “workforce” fixes the reading.
Pause and predict
The number of employed workers rises and the population does not change. The unemployment rate
Why people are unemployed
Kinds of unemployment
| Kind | What it is | The exam’s clue |
|---|---|---|
| Frictional | Short spells between jobs while workers and employers find one another | “Between jobs”; “imperfect information about the labour market” (Hyderabad 2012, 2015) |
| Structural | A mismatch between workers’ skills or location and the jobs that exist, often after a fall in demand for some industries | “Mismatch of skills”; a fall in demand for some industries’ products (Hyderabad 2013, 2021) |
| Cyclical | Unemployment above its normal level because total demand is low in a recession | The gap between actual and natural unemployment (Hyderabad 2021) |
Add the first two and you have the natural rate of unemployment, the rate that remains when the economy is at its normal level of activity: frictional plus structural (CUET 2022, Hyderabad 2018). Cyclical unemployment is the actual rate less this natural rate, positive in a slump and negative in a boom. The next lessons build the Phillips curve on that gap, and Lesson 8 explains what sets the natural rate itself.
Two traps. The definitions of frictional and structural are easy to swap, and an exam statement that swaps them is false (IIT JAM 2023: “structural arises between two jobs” is frictional). And voluntary non-participation is not unemployment: a person who prefers to stay at home at the equilibrium wage is outside the labour force, so that reason does not explain any natural unemployment (JNU 2021).
Stocks and flows
Why there is always some
Unemployment is a stock (how many are unemployed now) fed and drained by flows. Each month a share s of the employed lose or leave their jobs, and a share f of the unemployed find one. If the unemployment rate is u, then next month it is u plus the new separations, minus the hires:
The steady state
Set the change to zero: s(1 − u) = f·u, so u = s/(s + f). The rate settles at this value from any starting point, and the gap closes by the share s + f each month.
With s = 2% and f = 30% a month, u* = 2/32 = 6.25%. Raise s or lower f and the steady-state rate rises. A low job-finding rate is what frictions and mismatch do: workers searching slowly, vacancies in the wrong place or for the wrong skills. That is the idea behind frictional and structural unemployment, and it is why the natural rate is never zero.
Pause and predict
Each month 1% of the employed lose their jobs and 19% of the unemployed find one. The steady-state unemployment rate is
The idea the module builds on
The unemployment rate has a resting point set by how fast people lose jobs and how fast they find them. Recession pushes the rate above it and boom below it, but it is the resting point, the natural rate, that Lessons 5 to 8 are about.
A growth-accounting detour
Output, productivity and jobs
Output is jobs times output per worker, so in growth rates, output growth = employment growth + productivity growth. If the unemployment rate is constant, the labour force and employment grow at the same rate, so a country must grow its labour force at output growth less productivity growth to keep unemployment steady. Economy A grows output at 4% and productivity at 2%, so employment, and with a constant rate the labour force, grows at 2%; economy B at 8% and 4% gives 4%, so B has the higher labour force growth (JNU 2017).
One more curiosity the papers like: the ratio of the employment rate to the unemployment rate is (1 − u)/u, which grows without bound as u falls to zero, so it has no maximum (JNU 2018). And two rates plus a count give a population: the labour force is the number unemployed over the rate, and the working-age population is the labour force over the participation rate. That is the puzzle.
Traps
What examiners are fishing for
Watch out for
The mistakes examiners are fishing for
- The wrong denominator. Unemployed over the labour force. Not over the population, the employed or the skilled (Hyderabad 2011, 2014).
- Workforce against labour force. “Workforce participation” in Indian usage counts only the employed.
- Frictional against structural. Between jobs is frictional; a mismatch of skills or industry is structural.
- A falling rate is not always good news. Discouraged workers leaving the labour force lower it with no new job.
- A rising employment is not always a falling rate. New participants can push the rate up.
- The natural rate is not zero. It is frictional plus structural, and it is the rate at which cyclical unemployment is zero.
Worked questions
Worked questions
IIT JAM 2024 · standard (the opening question)
For 2010: u = 15%, unemployed 30 million, participation 70%. For 2020: u = 20%, unemployed 50 million, participation 80%. What is the percentage change in the working-age population?
- Labour force from the unemployed.2010: 30 ÷ 0.15 = 200 million. 2020: 50 ÷ 0.20 = 250 million.
- Population from the participation rate.2010: 200 ÷ 0.70 = 285.71 million. 2020: 250 ÷ 0.80 = 312.5 million.
- The change.312.5 ÷ 285.71 − 1 = 9.375%.
Answer
9.38% (the key accepts 9.30 to 9.40).
IIT JAM 2025 · standard
Employed 140 million, unemployed 10 million, not in the labour force 50 million. The rate of unemployment is?
- Labour force.140 + 10 = 150.
- Rate.10 ÷ 150 = 6.67%.
Answer
6.67%.
IIT JAM 2021 · standard
The workforce participation rate is 60%, the population is 100 million and 6 million are unemployed. The unemployment rate is?
- Workers.“Workforce” participation is employed over population: 0.60 × 100 = 60 million employed.
- Labour force.60 + 6 = 66 million.
- Rate.6 ÷ 66 = 1/11.
Answer
1/11. (Reading it as the labour force rate would give 1/10, which is also an option: the wording decides.)
JNU 2017 · standard
Economy A has unemployment 5%, output growth 4% and productivity growth 2%; economy B has 10%, 8% and 4%, all constant. Which has the higher labour force growth?
- Employment growth.Output growth less productivity growth: A 2%, B 4%.
- Constant rate.With u constant the labour force grows as fast as employment.
Answer
B.
Revise
The lesson on one screen
The lesson on one screen
- Three groups
- Employed, unemployed (jobless and looking), not in the labour force. Labour force = employed + unemployed.
- Unemployment rate
- U / L. The denominator is the labour force.
- Participation
- Labour force participation = L/N. Worker ratio (Indian 'workforce participation') = E/N.
- Perverse moves
- Discouraged workers lower the rate; new entrants can raise it even as jobs grow.
- Frictional
- Between jobs; imperfect information.
- Structural
- Skills or industry mismatch.
- Cyclical
- Actual rate less the natural rate.
- Natural rate
- Frictional plus structural: not zero.
- Steady state
- u* = s/(s + f) from separation s and job-finding f.
Practice
Check yourself
Quick questions
1The unemployment rate is the number unemployed as a percentage of
2A worker who has been out of work for months stops looking. The unemployment rate
3A fall in the demand for the products of some industries leaves workers with skills nobody wants. This is
4The natural rate of unemployment equals
5The job-finding rate falls and nothing else changes. The steady-state unemployment rate s/(s + f)
Numerical problems
The rate from counts
Employed 180 million, unemployed 20 million, outside the labour force 100 million. What is the unemployment rate, in percent?
The participation rate
In the same economy, what is the labour force participation rate, in percent?
A steady state
Each month 1.5% of the employed lose their jobs and 28.5% of the unemployed find one. What unemployment rate does the economy settle at, in percent?
The population from two figures
12 million are unemployed, the unemployment rate is 8% and the labour force participation rate is 60%. What is the working-age population, in millions?
Real questions
Past papers, by level
Foundation
Definitions, formulas and one-step problems. Most CUET, UGC NET and Hyderabad questions on this topic sit here.
9 questionsPractise →
Standard
Statements to judge, matching lists and calculations with several steps, up to the hardest JNU, JAM and GATE questions.
9 questionsPractise →
All 18 past-paper questions for this lesson, easiest first: practise the full set →
These are questions from the TestStop bank. A free account answers 10 a day, each with its worked solution; All-Access opens every set with no daily limit.
Read next
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