ECON 102: Unemployment Formulas
In this document, we present the most important formulas used in Module 6.
Labour Market Characteristics
The variables are
• U: The number of unemployed workers.
• E: The number of employed workers.
• LF: The labour force which is equal to U+E.
• WAP: Number of individuals in or out of the labour force that are old enough to work. When studying the characteristics of a particular group (males, females, 24 to 35 year old, etc.), WAP is the number of working age individuals that belong to that group. The working age in Canada is 15 years and over.
Unemployment Rate (UR)
Participation rate (PR)
Employment rate (ER)
UR= U ×100% LF
PR= LF =×100% WAP
ER= E ×100% WAP
Relationship Between UR, PR and ER
UR = 1 − ER PR
Duration of Unemployment
The variables are
• D: Duration of unemployment, which is the average time new unemployed workers remain un- employed.
• I: Incidence of unemployment is the proportion of workers in the labour force that become unemployed over a given period. In other words, it is the number of new unemployed workers divided by the labour force.
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Unemployment Rate Versus Duration
Dynamics of the Labour Market
UR = D × I
We illustrate the dynamics with this numerical example:
• LF = 1,000.
• Every month, 10 workers become unemployed for 1 month. • Every month, 20 workers become unemployed for 2 months. • Every month, 15 workers become unemployed for 3 months. • Every month, 12 workers become unemployed for 6 months.
Incidence of Unemployment (I)
It is the total number of workers who become unemployed each month divided by the labour force: I = 10+20+15+12 =5.7%
1, 000
Steady State
The steady state is reached when the number of workers who become unemployed is equal to the number of unemployed workers who become employed. It is a steady state because the UR is constant. If UR=0 in month 0, and the above dynamics starts on month 1, the steady state is reached during the sixth month (the highest of all duration lengths)
The Number of Unemployed at the Steady State in Each Group
At the steady states we have the following number of unemployed workers from each group: • Number of unemployed workers that remain unemployed for 1 month: 10 × 1 = 10.
• Number of unemployed workers that remain unemployed for 2 months: 20 × 2 = 40.
• Number of unemployed workers that remain unemployed for 3 months: 15 × 3 = 45.
• Number of unemployed workers that remain unemployed for 6 months: 12 × 6 = 72. The Unemployment Rate at the Steady State
At the steady states, the unemployment rate is the total number of unemployed workers in each group divided by LF:
UR= 10+40+45+72 = 167 =16.7% 1, 000 1, 000
The Average Duration at the Steady State
The average duration can be computed using the UR and I:
D = UR = 16.7% = 2.9298 months
I 5.7%
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Alternative Approach
The duration can be computed directly as the total number of months new unemployed workers will remain unemployed divided by the number of new unemployed each month:
(10×1 month)+(20×2 months)+(15×3 months)+(12×6 months) 10+20+15+12
167 months
57 new unemployed workers
= 2.9298 months per new unemployed workers
Then, the steady state UR can be computed using the duration formula
UR = 2.9298 × 5.7% = 16.7%
D= =
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