Notesale: Turn your study into money

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LECTURE NOTES ON SPENCE’S JOB
MARKET SIGNALLING

1

SIMPLIFIED MODEL
The Set-Up
Two “types” of workers: HIGH ability (θ = 2),
and LOW ability (θ = 1), where θ measures
ability
...

3
Productivity of worker is 2θ
e
Cost of education e is C (e) = θ
...
The employer, upon observing e, chooses wage
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Simplify Analysis: Assume wage equals to expected productivity
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Then it must be the case
that:
In a separating PBE the two types of workers
choose different education levels: Let e H and
e L denote the levels chosen by high and low
ability types, respectively, where e H = e L
...
e
...

Indeed, thus, for any e such that e = e H and
e = e L : Pr(θ = 1 | e) can be any number between zero and one
...

Suppose, then, (to most easily see whether a
separating PBE exists), assume: Pr(θ = 1 | e) =
1 for any e such as e = e H and e = e L
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4

Given the above, the wages in this PBE must
be as follows (since assumed above wages equal
expected productivity):
w(e = e H ) = 2(2) = 4 and for any e = e H , w(e) =
2(1) = 2
...

2
2
This implies the High type IC condition becomes:
e
4 − H ≥ 2
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LOW Type’s IC conditions:
For any e = e H ,
e
e
2− L ≥ 2−
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1
1
The first one implies that e L = 0
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Consequently for the proposed separating
PBE to exist it must also be the case that
e H ≥ 2
...

In each such PBE, e L = 0 and e H ∈ [2, 4]
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Then it must be the case
that:
In a pooling PBE the two types of workers
choose the same education level: e H = e L = e∗
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Cannot apply Bayes rule following zero probability events — i
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, in the pooling PBE when
education level e is observed different from e∗
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The PBE concept does not restrict outof-equilibrium beliefs
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That is: we assume that when employers observe education e = e∗ , they believe worker is
Low type for sure
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w(e = e

3

3

3

And for any e = e∗ , w(e) = 2(1) = 2
...

3
2
2

This is iff

10 e∗
− ≥ 2
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LOW-type Incentive-Compatibility Condition is:

For any e = e∗ ,

10 e∗
e
− ≥ 2−
...

3
1
Thus, for the pooling PBE to exist it must
also be the case that e∗ ≤ 4
...
In each PBE,
4
e H = e L = e∗ ≤ 3

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