Naureen Karachiwalla, University of Oxford
Albert Park, HKUST

Teachers are central to the learning process
 Often undermotivated in developing countries
 Exclusive focus on incentive pay (bonuses)
 China ideal case to study use of promotions to provide
incentives—sophisticated system, good performance


Incentives for civil servants, puzzle of governance
and rapid growth in China?
Empirical evidence on promotion incentives
 Previous evidence mostly on use of incentives (by
studying wage patterns) in US companies
 Little direct evidence on effort/performance (Gibbs,
1995; Campbell 2008, Kwon 2006)
Motivations
 Promotion of teachers in China
 Data
 Model of Promotions as Incentives
 Empirical model
 Results
 Conclusion

Four ranks in both primary and middle school
To apply for a promotion, need:
 To wait a certain number of years (depending on
education)
 Favourable annual evaluation scores (one ‘excellent’
or two ‘good’) in the last 5 years
 Promotion depends on the number of spaces available
in a township
 Wages are higher at higher rank levels


Rank change
Education level
Number of years to wait
Intern to Primary 2
Primary 2 to Primary 1
Doesn't matter
Vocational middle school
Normal college
University
Vocational middle school
Vocational college
University
Doesn't matter
Vocational middle school
Vocational College
University
Vocational middle school
Vocational college
University
Vocational middle school
Vocational college
University
PhD
2 years after starting teaching
4 years in the rank
3 years in the rank
1 year in the rank
10 years in the rank?
7 years in the rank
5 years in the rank
2 years after starting teaching
4 years in the rank
3 years in the rank
1 year in the rank
10 years in the rank? Let's say 8
7 years in the rank
5 years in the rank
25 years after starting teaching (and 5 years at Middle 1)
15 years after starting teaching (and 5 years at Middle 1)
5 years after Middle 1
1 year after Middle 1
Primary 1 to Primary
Intern to Middle 3
Middle 3 to Middle 2
Middle 2 to Middle 1
Middle 1 to Middle
Years considered
post promotion
6 years
5 years
4 years
18 years
17 years
11 years
5 years
4 years
3 years
16 years
13 years
9 years
13 years
13 years
11 years
5 years
Average salary
Standard
deviation
Increase
Primary 2
974.15
261.23
-
Primary 1
1289.63
230.19
32.4%
Primary high
1511.27
271.48
17.2%
Middle 3
1015.87
235.4
-
Middle 2
1270.69
229.79
25.1%
Middle 1
1534.88
233.46
20.8%
Middle high
1865.62
263.54
21.5%
Log monthly wage
Primary teachers
Control for
experience
Basic
coef
se
coef
se
Control for
experience +
county FE
coef
se
Primary 1
0.310***
0.031
0.219***
0.047
0.166***
0.047
Primary high
0.472***
0.031
0.316***
0.056
0.243***
0.057
Experience
0.017***
0.006
0.015**
0.006
Experience squared
-0.000**
0.000
-0.000
0.000
Middle school teachers
Middle 2
0.238***
0.026
0.107***
0.026
0.083***
0.025
Middle 1
0.435***
0.026
0.179***
0.033
0.176***
0.033
Middle high
0.634***
0.044
0.333***
0.050
0.343***
0.056
0.031***
0.004
0.023***
0.004
0.000 -0.000***
0.000
Experience
Experience squared
-0.001***





Annual evaluations on a four point scale: excellent, good,
pass, fail. Set proportions.
Based on four criteria: student test scores, attendance,
preparation and ‘attitude’. Committee chooses weights.
Classroom observation, questionnaires to teachers and
students, principal reports. Points for each component.
Points added, teachers are ranked. Top 10% get ‘excellent’,
next 10% get ‘good’ scores. Rest get a ‘pass’.
Results of ‘excellent’ and ‘good’ evaluation scores
announced at annual meetings
Criteria
Mean percentage
weight
Standard deviation
Attitude
23.22 %
10.57
Preparation
29.45 %
11.39
Attendance
13.16 %
5.82
Tests Scores
34.17 %
15.59





Gansu Survey of Children and Families (GSCF),
focussed on rural schools
3 waves, we use 2007. Child, teacher, principal
etc.
Sampled 100 villages in 42 townships in 20
counties
Sampled the main primary and middle school in
each village
Sample of 2,350 teachers
Primary 2 Primary 1
Number of teachers
Total
Female
Basic characteristics
Average Age
Average Years teaching
Years of education
Number of teachers
competing
Number of teachers (in
the township for Primary
school, in the school for
Middle school)
Primary
high
Middle 3
Middle 2
Middle 1
Middle
high
163
58%
553
45%
354
25%
133
49%
525
37%
281
17%
13
15%
28.3
7
12.42
36.7
16.3
12.2
48
27.6
12.02
26.8
4
13.82
32.3
10.1
13.63
40.6
19.7
13.05
47.2
27.6
14.14
124
219
148
33
42
22
3
1.00
Primary 1 - Kaplan-Meier survival estimate
0.00
0.00
0.25
0.25
0.50
0.50
0.75
0.75
1.00
Primary 2 - Kaplan-Meier survival estimate
25
10
20
Number of years until promotion to Primary high
0
5
10
Number of years until promotion to Middle 2
15
30
Middle 1 - Kaplan-Meier survival estimate
0.50
0.25
0.00
0.25
0.50
0.75
1.00
Middle 2 - Kaplan-Meier survival estimate
0.00
0.00
0.25
0.50
0.75
1.00
Middle 3 - Kaplan-Meier survival estimate
0
1.00
5
10
15
20
Number of years until promotion to Primary 1
0.75
0
0
5
10
15
20
Number of years until promotion to Middle 1
25
0
5
10
15
Number of years until promotion to Middle high
20
Promotions as tournaments, Lazear and Rosen (1981).
Wage gap that can induce first best effort exists.
 Macleod and Malcolmson (1988) model of skill and
effort as private information. Employees sort into ranks
according to ability.
 Fairburn and Malcolmson (1994) sorting into different
jobs. Promotions can be made incentive compatible.
 Gibbs (1989) multi-person tournaments with
heterogeneous competitors. Predictions on ability,
number of competitors, time after promotion, beliefs
on ability etc.

School offers promotions, teachers hired in
lowest rank, n teachers compete for k
promotion slots at each rank level
 School offers ΔEU  (W2 - W1)*tenure after
promotion
 Teachers have different skill, s with B(s) and
b(s), E(s)=0
 Cost of effort (e) is C(e) where C’ , C’’ >0
 p(e, s, e) is probability of promotion


Teacher solves:

First order condition:

dp/de is marginal probability of promotion
(MPE)

qi = si + ei + πi where πi = εi + μ, CDF R(q) PDF r(q)

E(πi)=E(εi)=E(μ)=0, CDF F(ε), PDF f(ε)


Probability teacher i beats teacher g:
pr(qi > qg) = pr(ei + si + εi + μ > eg + sg + εg + μ) = pr(eg + sg + εg
+ < ei + si + εi) = R(ei + si + εi)
Probability of promotion:




Incentives higher with higher wage increases
when promoted
Incentives decline with age
Incentive highest when skill percentile = 1 – p*,
and declines with distance from 1-p*
When n increases but p* stays the same,
incentives increase for those close with skill
percentile close to 1 - p* (and decrease for
those with very high or very low skill)
Teachers have careers of T periods, eligible for promotion in year t
=X
 Probability of promotion, pt is based on performance in past 5
years
 Normalize per period utility before promotion to zero, define Uh > 0
utility from wages after promotion
 In year j, lifetime expected discounted utility is:

T
EV j  c(e j )  Ep j 1   U h  (1  Ep j 1 )( Ep j 2
t  j 1
T
t j
T
T
t j

 U h  (1  Ep j2 )( Ep j3
t  j 2
T
t j

U

(
1

Ep
)(
Ep

U

(
1

Ep
)
Ep

U h )))

h
j 3
j 4 
h
j 4
j 5 
t j
t  j 3


t  j 4
t j
t  j 5
Prior belief on skill, s1, 1/N ≤ s1 ≤ 1. True relative rank s.
Teachers update beliefs on skill rank st , adjust st downward when
passed over for promotion

Predictions on teacher performance over time
 If t ≤ X – 5 effort is zero
 Effort is increasing from t=X – 4 to X
 Teachers update beliefs on s based on whether or not
they are promoted. When teachers are not promoted, s
is revised downwards, effort is decreasing for every year
of non-promotion

From the one-period model’s FOC:

Estimate as:

We will estimate with fixed effects so w and p will
drop out. We will also add in the time dimension.





ev = evaluation scores for t = 2003, 2004, 2005, 2006
a = ability index, dummies for top and bottom 10%
n = number of teachers, also interacted with ability
in top and bottom 10%
w = fixed effect
D – dummies for:
 t = X – 5 or greater
 t = X – 4, t = X – 3, t = X – 2, t = X – 1 , t=X
 t > after half the other teachers are promoted (dummies
from one to ten years after half of colleagues are
promoted)




Evaluation scores increase with higher expected
wage increases
Evaluation scores increase in the years
preceding promotion eligibility and decrease
after not being promoted (inverted U) or
reaching the highest rank
Evaluation scores increase with competition
(number of teachers) for those in the middle of
the skill distribution but do not for those in the
tails of the skill distribution
Promotion probability positively affected by
high evaluation scores
0.150
0.100
0.050
0.000
X-5
-0.050
-0.100
X-4
X-3
X-2
X-1
X
0.500
0.000
0
-0.500
-1.000
-1.500
-2.000
-2.500
2
4
6
8
10
12
0.000
0
2
4
6
8
10
12
14
16
-0.200
-0.400
-0.600
-0.800
-1.000
-1.200
-1.400
Theory predicts no effort incentive after achieving highest rank, decline suggests older
teachers slowing down (rising cost of effort?)
Variable
Number of teachers
Coefficient Standard error
0.001**
0.000
Number of teachers *
ability bottom 10%
-0.002***
0.001
Number of teachers *
ability top 10%
-0.001**
0.000
Ability bottom 10%
0.192***
0.067
-0.054
0.074
Ability top 10%
One could argue that the evaluation scores capture
both ability and effort
• However, the use of the fixed effect and the ability
index mitigate this problem
• A regression was also run of the probability of
obtaining an ‘excellent’ or ‘good’ evaluation score on
measures of teacher time use
•
• This was done for 2006 only since that is what we have data
on
• Coefficient on number of hours (spent with students,
preparing lesson plans, marking homework etc.) is positive
and significant
•
What if principals are just awarding high scores to
teachers who are nearing eligibility for promotion?
• Again, evaluation scores are related to time use
• Restricted the sample to counties that have high
correlations between time use and evaluation scores
and the effect remains
• Ranks strongly predict test scores (other studies)
•
Or, teachers could be learning and that would also
produce an upward trend pre-eligibility
• The teachers in the sample have already been teaching
for many years (average experience is 12 years)
Excellent or
Good evaluation
score
coef
se
Education - vocational college
0.004
0.111
Education - college
0.061
0.132
Age
0.011
0.007
0.658**
0.334
From same township
0.588*
0.332
From same county
0.568*
0.320
0.689**
0.337
Spouse's education - vocational college
0.109
0.103
Spouse's education - college
0.208
0.146
0.146**
0.067
-0.000
0.000
-0.201**
0.088
0.056
0.080
0.227**
0.102
-2.119***
0.640
From same village
From same province
Number of children under 18
Spouse's salary
Ability bottom 10%
Ability top 10%
Log of total hours
Constant
Number of observations
1,286
R2
Marginal effect, log of total hours
note: *** p<0.01, ** p<0.05, * p<0.1
0.022**
0.032
Marginal effect - evaluation score (instrumented
with change in log wages)
Rho
Sigma
Promotion rate quintiles included
County fixed effects included
Number of observations
note: *** p<0.01, ** p<0.05, * p<0.1
Basic
With p*
0.299***
(0.053)
-1.499***
(0.541)
-0.321***
(0.010)
No
Yes
5,111
0.302***
(0.039)
-1.535***
(0.421)
-0.322***
(0.011)
Yes
Yes
5,111
•
•
Effort responds to promotion incentives
Implications for design
• Optimal contest size and promotion rate?
• Incentivizing teachers falling behind
• Combining pay for performance (withinrank incentives) with promotion incentives
(happening in China!)