Promotion Incentives in the Public Sector: Evidence from

Chinese SchoolsNaureen Karachiwalla, University

of OxfordAlbert Park, HKUST

Motivations

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)

Outline

MotivationsPromotion of teachers in ChinaDataModel of Promotions as

IncentivesEmpirical modelResultsConclusion

Promotion of Teachers in China

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

Promotion eligibility rules

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

Mean wages by rank

 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%

Wage regressions

Log monthly wage

Primary teachers coef se coef se coef sePrimary 1 0.310*** 0.031 0.219*** 0.047 0.166*** 0.047Primary high 0.472*** 0.031 0.316*** 0.056 0.243*** 0.057Experience 0.017*** 0.006 0.015** 0.006Experience squared -0.000** 0.000 -0.000 0.000Middle school teachersMiddle 2 0.238*** 0.026 0.107*** 0.026 0.083*** 0.025Middle 1 0.435*** 0.026 0.179*** 0.033 0.176*** 0.033Middle high 0.634*** 0.044 0.333*** 0.050 0.343*** 0.056Experience 0.031*** 0.004 0.023*** 0.004Experience squared -0.001*** 0.000 -0.000*** 0.000

Basic Control for experience

Control for experience +

county FE

Teacher evaluations 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

Teacher evaluation criteria

CriteriaMean percentage

weightStandard deviation

Attitude 23.22 % 10.57

Preparation 29.45 % 11.39

Attendance 13.16 % 5.82Tests Scores 34.17 % 15.59

Data

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

Data Primary 2 Primary 1

Primary high Middle 3 Middle 2 Middle 1

Middle high

Number of teachersTotal 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

Data0.

000.

250.

500.

751.

00

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

0.00

0.25

0.50

0.75

1.00

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

Middle 3 - Kaplan-Meier survival estimate

0.00

0.25

0.50

0.75

1.00

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

Middle 2 - Kaplan-Meier survival estimate

0.00

0.25

0.50

0.75

1.00

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

Middle 1 - Kaplan-Meier survival estimate

Literature – Theory 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.

Model of Promotions as Incentives

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

Model of Promotions as Incentives Teacher solves:

First order condition:

dp/de is marginal probability of promotion (MPE)

Model of Promotions as Incentives

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:

Model of Promotions as Incentives

Model of Promotions as Incentives

Model of Promotions as Incentives

Predictions

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)

Multiperiod Model 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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More Predictions 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

Empirical Specification

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.

Empirical specification

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)

Empirical results 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

Results – X-5 to X

-0.100

-0.050

0.000

0.050

0.100

0.150

0.200

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

Results – post-eligibility

0 2 4 6 8 10 12

-2.500

-2.000

-1.500

-1.000

-0.500

0.000

0.500

Primary High0 2 4 6 8 10 12 14 16

-1.400

-1.200

-1.000

-0.800

-0.600

-0.400

-0.200

0.000

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

Other resultsVariable Coefficient Standard errorNumber of teachers 0.001** 0.000Number of teachers * ability bottom 10%

-0.002*** 0.001

Number of teachers * ability top 10% -0.001** 0.000

Ability bottom 10% 0.192*** 0.067Ability top 10% -0.054 0.074

Evaluations as a proxy for effort

• 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

Robustness

• 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)

Evaluation scores and time spent on teaching

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

Do higher evaluation scores increase promotion probability?

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

Conclusion

• 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!)