Private Signals and Group Affiliations in the Recruitment Process

Question 1

What is the heterogeneity challenge of human capital?

Answer 1

heterogeneity: the quality or state of being diverse in character or content

neither employers nor employees are identical. Some couples “fit” better than others,

Question 2

What is the asymmetry challenge of human capital?

Answer 2

Asymmetry: employers and employees do not have the same goals and they do not tend to share private information.

Question 3

What are the key challenges that firms face?

Answer 3

1. Recruitment: hire the “right” workers
2. Train: develop their skills
3. Produce: extract effort and benefit from their expertise.
4. Separate: “divorce” when “marriage” is no longer working

Question 4

What is the premise for statstical discrimination literature?

Answer 4

Firms have limited information about the skills of job applicants.

This gives firms an incentive to use easily observable characteristics such as school, degree, work experience, to infer the expected productivity of applicants (if these characteristics are correlated with productivity).

We should not discriminate on the basis of gender, race, ethnicity, preferences, beliefs etc.

Question 5

Equation for the productivity of a job applicant?

Answer 5

V_Gi = V_G + ε_Gi

V_G = group average (known to employers)

ε_Gi = person-specifi productivity above and beyond group mean (unknown to employers)

V_Gi = productivity of candidate

Question 6

Notation for normal distribution of the productivity of a candidate?

Answer 6

V_Gi ~ N(V_G, σ²_v)

Question 7

Equation for the test scores of a candidate?

Answer 7

S_Gi = V_Gi + η_Gi

V = productivity

η = “luck” during the exam, it can be good or bad but sums to 0

Question 8

Combine equations for test scores and productivity

Answer 8

V_Gi = V_G + ε_Gi

S_Gi = V_Gi + η_Gi

S_Gi = V_G + η_Gi

Question 9

What is the key challenge for the productivity equation?

Answer 9

We cannot identify why candidate i scored better than the average: might reflect her productivity or her luck.

Question 10

What does γ_G stand for?

Answer 10

“signal to noise ratio”

How much useful info there is in proportion to the entire contents.

The optimal weight ranges between 0 to 1.

Question 11

What is the equation for γ_G?

Answer 11

γ_G = σ²_Gε /(σ²_Gε + σ²_Gη)

γ= signal to noise ratio

σ²_Gε = variance for person-specific productivity

σ²_Gη = variance for luck

Question 12

Equation for Joe’s expected productivity given

(1) the weighted average of his group average productivity (V_G)
(2) his private signal (S_Gi)

?

Answer 12

E| V_Gi | S_Gi | = (1 - γ_G)V_G + γ_GS_Gi

Question 13

What is Joe’s productivity assuming the following:

Joe’s score = 90

Group mean = 60

variance in productivity = 1

variance in the noise of the signal = 1

Answer 13

In that case, γ_G = 1/2

the best prediction of Joe’s productivity is:

(1 - γ_G) V_G + γ_G S_Gi = (0.5*60) + (0.5*90) = 75

Question 14

Predict Carolina’s productivity given the following:

Score = 85

Group mean = 70

variance of productivity = 1

Variance of noise signal = 1

Answer 14

γ_G = 1/2

(1 - γ_G) V_G + γ_G S_Gi = (0.5*70) + (0.5*85) = 77.5

Question 15

What can we learn from the equation for private signals/group affiliations?

Answer 15

• Both private signals and group affiliation should not be ignored.
• The best prediction is a weighted average of both. The weights depend on the “noise to signal ratio”.
• We the “noise to signal ratio” is 1 then we use only group affiliation to project candidates’ productivity.
• When the “noise to signal ratio” is 0 then we use only candidates’ private signals to project candidates’ productivity.