Motivation
A challenge:
A case:
- Agricultural extension workers
- The 2013–2016 Ebola virus epidemic in West Africa
- Caught many by surprise, no early warning. Need for stronger decentralized bureaucracy.
- \(>\) 7/10 emerging infectious diseases spill over from animals
Motivation
Promising work on improving service provision:
Recruitment
Community monitoring
Financial incentives
We show:
- evidence 2. and 3. matter with limited crowding out.
- no good news on 1.
- we use a structural model to explore why and when these might be more effective.
Past Work on Recruitment
Theoretically:
Empirically:
Past Work on Financial Incentives
By and large a success:
Education: Muralidharan and Sundararaman (2011), Kahn et al (2014), Glewwe et al (2010), De Ree et al (2010), Leaver et al (2021)
Health status: Miller et al (2012) Mohanan et al. (2021)
Service delivery: Gertler and Vermeersch (2013), Desserano et al (2022)
Service provider inputs: teachers (Duflo et al, 2012, Leaver et al 2021), nurse attendance Banerjee and Duflo (2006)
The policy questions
- Are community monitoring mechanisms more or less effective than performance-based payment schemes?
- Are there interaction effects between recruitment strategies and incentive mechanisms?
- E.g. community monitoring may be less effective when service providers are selected by the state (and so, less embedded)
Design
We study these questions in the context of a randomized agricultural intervention in Sierra Leone.
Core design elements (more on context to come)
| T1 |
Agent is selected by community (T1 = 1) or by chief (T1 = 0) |
| T2 |
Community can impose social sanctions on agent (T2 = 1) or not (T2=0) |
| T3 |
Agents receive pay for performance (T3 = 1) or not (T3=0) |
Model
A worker has type \(\theta = (\eta,\mu)\) where:
- \(\eta \in \{ \underline{\eta} , 1 \}\) denotes embeddedness
- \(\mu \in \{ 0 ,\overline{\mu} \}\) denotes intrinsic motivation
Drawn according to:
| 0 |
\(\frac{1+ \rho}{4}\) |
\(\frac{1- \rho}{4}\) |
| \(\overline{\mu}\) |
\(\frac{1- \rho}{4}\) |
\(\frac{1+ \rho}{4}\) |
So \(\rho\) governs the correlation between embeddedness and motivation: embedded people are possibly more effective, but are they more likely to be highly motivated?
T1 and type
- Under chief selection (\(T_1=0\)) the worker is a random draw from the candidate pool.
- Under villager selection (\(T_1=1\)), the worker is drawn from the pool with high embeddedness.
So paramount chief is more likely to select workers with high intrinsic motivation if and only if \(\rho < 0\).
Villager (Monitoring)
- A representative villager selects a social sanctioning plan, which depend on the performance signal \(\sigma\): \[s=(s(0),s(1)) \in [-T_2, T_2]^2.\]
Interpretable as commitments to reward (\(s(\sigma)<0\)) or punish (\(s(\sigma)>0\)) performance.
Villager (Monitoring)
Punishment is possibly psychologically costly, according to \(\gamma\).
\[u(\pi, s) = \pi - \gamma s .\]
- \(\zeta\) is probability punishment is not costly for the villager
CAHW utility
Under pay-for-performance (\(T_3=1\)) and high performance signal (\(\sigma=1\)), the worker receives a payment normalized to 1
In addition:
- \(\phi\): sensitivity to social sanctions
- \(\mu\): intrinsic benefits from performing well
Putting it all together utility is:
\[w(e;s,\sigma;\theta = (\mu, \eta)) = \sigma (T_3) + \pi\mu - \phi s(\sigma) T_2 - \frac{e^2}{2 \kappa},\]
where \(\pi = e\eta\)
Timeline
The sequence of events is as follows:
- worker is selected by either village (\(T_1=1\)) or chief (\(T_1=0\)).
- villagers and worker learn whether the latter is subject to community monitoring (\(T_2=1\)) and/or P4P (\(T_3=1\)).
- if \(T_2=1\), villager with guilt parameter \(\gamma\) commits to a conditional plan of social sanctioning \(\{s(\sigma)\}_{\sigma \in \{0,1\}}\).
- The worker chooses effort \(e\).
- The worker’s performance signal \(\sigma\) is realized.
- Payoffs are realized and the game ends.
Solution concept
An equilibrium is a pair of strategies \(\{ s,e(s;\theta) \}\) such that
- effort is individually rational for each type given the sanctioning strategy
- the sanctioning strategy maximizes the villager’s expected payoff given anticipated effect on the workers’ effort \(\hat{e}(s;\theta)\), and
- expectations are correct (\(\hat{e}(s;\theta)=e(s;\theta)\) for each \(\theta\)) :
\[e(s;\theta) \in \arg \max_{e \in [0,1]} \mathbb{E}_{\pi } \Big\{ w(e,s,\sigma;\theta) \Big\}\] \[s \in \arg \max_{\{ (s(0),s(1)) \in [-T_2,T_2]^2 \}} \mathbb{E}_{\theta,\pi} \Big\{ u(\pi,s) \mid \hat{e}(s;\theta) \Big\}\]
Results
- Sanctioning.
- following a high signal: always praise the worker
- following a low signal: choose maximal shaming \(s(0)=1\) if susceptibility to guilt is low (\(\gamma=0\)) and minimal shaming \(s(0)=-1\) otherwise.
- Effort (depending on citizen guilt):
\[e(s^*;\gamma,\theta) = \left\{\begin{array}
.\kappa \eta (\mu + T_3 + T_2 2 \phi) & \mbox{if} \quad \gamma =0 \\
\kappa \eta (\mu + T_3) \quad & \mbox{otherwise}.
\end{array}\right.\]
Results
Full closed form solution for all treatment conditions:
| \(\frac{\pi^*(T_1,0,0)}{\kappa}\) |
\(\frac{\overline{\mu}}{2} \frac{1 + \rho + \underline{\eta}^2(1-\rho)}{2}\) |
\(\frac{\overline{\mu}}{2} (1 + \rho)\) |
| \(\frac{\pi^*(T_1,0,1)}{\kappa}\) |
\(\frac{\overline{\mu}}{2} \frac{1 + \rho + \underline{\eta}^2(1-\rho)}{2}+ \frac{1+ \underline{\eta}^2}{2}\) |
\(\frac{\overline{\mu}}{2} (1 + \rho)\) \(+1\) |
| \(\frac{\pi^*(T_1,1,0)}{\kappa}\) |
\(\frac{\overline{\mu}}{2} \frac{1 + \rho + \underline{\eta}^2(1-\rho)}{2} +(1+ \underline{\eta}^2) \phi \zeta\) |
\(\frac{\overline{\mu}}{2} (1 + \rho) +2 \phi \zeta\) |
| \(\frac{\pi^*(T_1,1,1)}{\kappa}\) |
\(\frac{\overline{\mu}}{2} \frac{1 + \rho + \underline{\eta}^2(1-\rho)}{2} +(1+ \underline{\eta}^2) \phi \zeta + \frac{1+ \underline{\eta}^2}{2}\) |
\(\frac{\overline{\mu}}{2} (1 + \rho) +2 \phi \zeta +1\) |
Hypotheses inspired by model
Hypothesis 1: Village selection increases performance.
- Explanation: Requires gains from embeddedness not crowded-out by any reductions in intrinsic motivation
Hypothesis 2: Community monitoring increases performance.
- Explanation: Community monitoring (T2=1) incentivizes worker performance through the associated probability of being publicly shamed for poor performance.
Hypothesis 3: Pay-for-performance increases performance.
- Explanation: Pay for performance (T3=1) increases performance due to the probability of receiving a monetary reward.
Hypotheses
Hypothesis 4: There is a positive interaction between village selection and pay-for-performance.
- Explanation: More productive workers (because embedded) are more responsive to extrinsic incentives (T3=1).
Hypothesis 5: There is a positive interaction between village selection and community monitoring.
- Explanation: More productive workers (i.e. those with higher embeddedness, T1=1) as it is easier (less risky!) for villagers to commit to sanctioning (as long as embeddedness does not crowd-out intrinsic motivation too much).
Hypotheses
- [Hypothesis 6: There is a positive interaction between community monitoring and pay-for-performance.
Explanation: The expected improvement in performance driven by the monetary incentive (T3=1) makes it easier for the village to commit to punish low performance (T2=1).]
Structural model
- Our model provides predictions for effort as a function of parameters and treatments
- We integrate these into a model with chiefdom level fixed effects and random errors
- We then estimate model parameters using
stan
\[e_{ij} = \alpha_{j} + \kappa \times p(T_1, T_2, T_3 | \bar{\mu}, \underline{\eta}, \rho, \nu, \phi, \zeta) + \epsilon_i\]
