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)

MotivationsPromotion of teachers in ChinaDataModel of Promotions as

IncentivesEmpirical modelResultsConclusion

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 Years considered post promotion

Intern to Primary 2 Doesn't matter 2 years after starting teachingPrimary 2 to Primary 1 Vocational middle school 4 years in the rank 6 years

Normal college 3 years in the rank 5 yearsUniversity 1 year in the rank 4 years

Primary 1 to Primary Vocational middle school 10 years in the rank? 18 yearsVocational college 7 years in the rank 17 yearsUniversity 5 years in the rank 11 years

Intern to Middle 3 Doesn't matter 2 years after starting teachingMiddle 3 to Middle 2 Vocational middle school 4 years in the rank 5 years

Vocational College 3 years in the rank 4 yearsUniversity 1 year in the rank 3 years

Middle 2 to Middle 1 Vocational middle school 10 years in the rank? Let's say 8 16 yearsVocational college 7 years in the rank 13 yearsUniversity 5 years in the rank 9 years

Middle 1 to Middle Vocational middle school 25 years after starting teaching (and 5 years at Middle 1) 13 yearsVocational college 15 years after starting teaching (and 5 years at Middle 1) 13 yearsUniversity 5 years after Middle 1 11 yearsPhD 1 year after Middle 1 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 coef se coef se 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

Experience 0.031*** 0.004 0.023*** 0.004

Experience squared -0.001*** 0.000 -0.000*** 0.000

BasicControl for experience

Control for experience +

county FE

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

CriteriaMean percentage

weightStandard deviation

Attitude 23.22 % 10.57

Preparation 29.45 % 11.39

Attendance 13.16 % 5.82Tests 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 1Primary

high Middle 3 Middle 2 Middle 1Middle

highNumber of teachers

Total 163 553 354 133 525 281 13Female 58% 45% 25% 49% 37% 17% 15%

Basic characteristicsAverage Age 28.3 36.7 48 26.8 32.3 40.6 47.2Average Years teaching 7 16.3 27.6 4 10.1 19.7 27.6Years of education 12.42 12.2 12.02 13.82 13.63 13.05 14.14

Number of teachers competing

Number of teachers (in the township for Primary school, in the school for Middle school) 124 219 148 33 42 22 3

0.0

00.2

50.5

00.7

51.0

0

0 5 10 15 20 25Number of years until promotion to Primary 1

Primary 2 - Kaplan-Meier survival estimate

0.00

0.25

0.50

0.75

1.00

0 10 20 30Number of years until promotion to Primary high

Primary 1 - Kaplan-Meier survival estimate

0.0

00.2

50.5

00.7

51.0

0

0 5 10 15Number of years until promotion to Middle 2

Middle 3 - Kaplan-Meier survival estimate

0.0

00.

25

0.5

00.

75

1.00

0 5 10 15 20 25Number of years until promotion to Middle 1

Middle 2 - Kaplan-Meier survival estimate

0.0

00.2

50.5

00.7

51.0

00 5 10 15 20

Number of years until promotion to Middle high

Middle 1 - Kaplan-Meier survival estimate

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’’ >0p(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:

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

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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

X-5 X-4 X-3 X-2 X-1 X

Theory predicts no effort incentive after achieving highest rank, decline suggests olderteachers slowing down (rising cost of effort?)

Variable Coefficient Standard errorNumber of teachers 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

Ability top 10% -0.054 0.074

• 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

From same village 0.658** 0.334

From same township 0.588* 0.332

From same county 0.568* 0.320

From same province 0.689** 0.337

Spouse's education - vocational college 0.109 0.103

Spouse's education - college 0.208 0.146

Number of children under 18 0.146** 0.067

Spouse's salary -0.000 0.000

Ability bottom 10% -0.201** 0.088

Ability top 10% 0.056 0.080

Log of total hours 0.227** 0.102

Constant -2.119*** 0.640

Number of observations 1,286

R2

Marginal effect, log of total hours 0.022** 0.032 note: *** p<0.01, ** p<0.05, * p<0.1

Basic With p* Marginal effect - evaluation score (instrumented with change in log wages) 0.299*** 0.302***

(0.053) (0.039)

Rho -1.499*** -1.535***

(0.541) (0.421)

Sigma -0.321*** -0.322***

(0.010) (0.011)

Promotion rate quintiles included No Yes County fixed effects included Yes Yes Number of observations 5,111 5,111 note: *** p<0.01, ** p<0.05, * p<0.1

• Effort responds to promotion incentives• Implications for design

• Optimal contest size and promotion rate?• Incentivizing teachers falling behind• Combining pay for performance (within-

rank incentives) with promotion incentives(happening in China!)