Formal AER Model: Institutional Redesign and Human Capital Accumulation under Capacity Constraints
1. Environment
Time is discrete t = 0,1,2,\dots
Agents are households with one child.
Each child has innate ability a_i \sim F(a).
Households choose schooling investment s_t \in \{0,1\} (enroll or not).
2. Human Capital Technology
Human capital evolves as:
H_{t+1} = (1 - \delta)H_t + \phi \cdot s_t \cdot q_t
where:
H_t: human capital stock
s_t: schooling decision
q_t: education quality
\delta: depreciation
3. Education System Constraint (Key Innovation)
Education access is constrained by system capacity:
s_t = 1 \quad \text{iff} \quad D_t \leq \bar{C}_t
where:
D_t: demand for schooling
\bar{C}_t: system capacity (schools × teachers × institutional design)
4. Pre-Reform Regime (Rigid Capacity System)
Before reform:
\bar{C}_t = \bar{C}_0
\quad \text{(slow-growing, exogenous)}
and:
\frac{d\bar{C}_t}{dt} \approx 0
Implication:
excess demand persists
rationing equilibrium
D_t > \bar{C}_t \Rightarrow \text{binding constraint}
5. Institutional Redesign Shock (Sukavichinomics Shock)
At time t = T^*:
\bar{C}_t = \bar{C}_0 + \Delta R_t
where:
\Delta R_t = g(\text{institutional redesign})
Key mechanism:
school role reallocation
administrative decentralization
capacity redefinition (not physical capital only)
6. Post-Reform Regime (Nonlinear Capacity Expansion)
After shock:
\bar{C}_t = \bar{C}_0 \cdot e^{\lambda R_t}
where:
\lambda > 0: scalability of institutional redesign
This introduces:
nonlinear jump in system capacity
7. Household Optimization
Households maximize:
U = u(C_t) + \beta E[H_{t+1}]
subject to schooling constraint:
s_t \in \{0,1\}, \quad s_t \leq \mathbb{1}(D_t \leq \bar{C}_t)
8. Equilibrium
Pre-reform equilibrium:
s_t^{*} = \frac{\bar{C}_0}{D_t}
\quad \Rightarrow \text{rationed education}
Post-reform equilibrium:
s_t^{*} = 1 \quad \forall D_t \leq \bar{C}_t^{new}
9. Aggregate Human Capital
H_t = \int H_i(t) \, di
Growth rate:
g_H =
\begin{cases}
g_0 & t < T^* \\
g_0 + \Delta g(R_t) & t \geq T^*
\end{cases}
where:
\Delta g(R_t) > 0
10. Key Theoretical Proposition (AER-style)
Proposition 1 (Capacity Regime Shift)
If institutional redesign increases effective capacity elasticity:
\frac{\partial \bar{C}_t}{\partial R_t} > 0
then the economy experiences a discrete jump in steady-state human capital level:
H^{SS}_{post} > H^{SS}_{pre}
and linear extrapolation of pre-reform capacity growth is invalid.
11. Empirical Mapping
Observable variables:
Table: Variable Definitions and Empirical Proxies
Variable Empirical proxy
C̄_t school slots, enrollment capacity
H_t years of schooling
s_t enrollment rate
R_t 1995–1997 reform dummy
12. Identification Strategy (AER Standard)
(1) Structural Break:
Y_t = \alpha + \beta \cdot \mathbb{1}(t \geq T^*) + \epsilon_t
(2) Event Study:
Y_t = \sum_{k \neq -1} \beta_k D_{t+k}
(3) Synthetic Control:
Y^{SC}_t = \sum w_j Y_{j,t}
ATT:
ATT = Y_t - Y^{SC}_t
13. Main Empirical Prediction
Sharp increase in enrollment at T^*
No pre-trend violation
Persistent higher steady-state H_t
Drop in dropout rate driven by capacity relaxation (not income)
14. Core Contribution (what AER cares about)
This model shows:
Human capital accumulation is not only a function of investment, but also a function of institutional capacity constraints that can shift discretely through redesign shocks.
ปรัชญาเศรษฐศาสตร์ทฤษฎีใหม่/ Human Capital Technology
1. Environment
Time is discrete t = 0,1,2,\dots
Agents are households with one child.
Each child has innate ability a_i \sim F(a).
Households choose schooling investment s_t \in \{0,1\} (enroll or not).
2. Human Capital Technology
Human capital evolves as:
H_{t+1} = (1 - \delta)H_t + \phi \cdot s_t \cdot q_t
where:
H_t: human capital stock
s_t: schooling decision
q_t: education quality
\delta: depreciation
3. Education System Constraint (Key Innovation)
Education access is constrained by system capacity:
s_t = 1 \quad \text{iff} \quad D_t \leq \bar{C}_t
where:
D_t: demand for schooling
\bar{C}_t: system capacity (schools × teachers × institutional design)
4. Pre-Reform Regime (Rigid Capacity System)
Before reform:
\bar{C}_t = \bar{C}_0
\quad \text{(slow-growing, exogenous)}
and:
\frac{d\bar{C}_t}{dt} \approx 0
Implication:
excess demand persists
rationing equilibrium
D_t > \bar{C}_t \Rightarrow \text{binding constraint}
5. Institutional Redesign Shock (Sukavichinomics Shock)
At time t = T^*:
\bar{C}_t = \bar{C}_0 + \Delta R_t
where:
\Delta R_t = g(\text{institutional redesign})
Key mechanism:
school role reallocation
administrative decentralization
capacity redefinition (not physical capital only)
6. Post-Reform Regime (Nonlinear Capacity Expansion)
After shock:
\bar{C}_t = \bar{C}_0 \cdot e^{\lambda R_t}
where:
\lambda > 0: scalability of institutional redesign
This introduces:
nonlinear jump in system capacity
7. Household Optimization
Households maximize:
U = u(C_t) + \beta E[H_{t+1}]
subject to schooling constraint:
s_t \in \{0,1\}, \quad s_t \leq \mathbb{1}(D_t \leq \bar{C}_t)
8. Equilibrium
Pre-reform equilibrium:
s_t^{*} = \frac{\bar{C}_0}{D_t}
\quad \Rightarrow \text{rationed education}
Post-reform equilibrium:
s_t^{*} = 1 \quad \forall D_t \leq \bar{C}_t^{new}
9. Aggregate Human Capital
H_t = \int H_i(t) \, di
Growth rate:
g_H =
\begin{cases}
g_0 & t < T^* \\
g_0 + \Delta g(R_t) & t \geq T^*
\end{cases}
where:
\Delta g(R_t) > 0
10. Key Theoretical Proposition (AER-style)
Proposition 1 (Capacity Regime Shift)
If institutional redesign increases effective capacity elasticity:
\frac{\partial \bar{C}_t}{\partial R_t} > 0
then the economy experiences a discrete jump in steady-state human capital level:
H^{SS}_{post} > H^{SS}_{pre}
and linear extrapolation of pre-reform capacity growth is invalid.
11. Empirical Mapping
Observable variables:
Table: Variable Definitions and Empirical Proxies
Variable Empirical proxy
C̄_t school slots, enrollment capacity
H_t years of schooling
s_t enrollment rate
R_t 1995–1997 reform dummy
12. Identification Strategy (AER Standard)
(1) Structural Break:
Y_t = \alpha + \beta \cdot \mathbb{1}(t \geq T^*) + \epsilon_t
(2) Event Study:
Y_t = \sum_{k \neq -1} \beta_k D_{t+k}
(3) Synthetic Control:
Y^{SC}_t = \sum w_j Y_{j,t}
ATT:
ATT = Y_t - Y^{SC}_t
13. Main Empirical Prediction
Sharp increase in enrollment at T^*
No pre-trend violation
Persistent higher steady-state H_t
Drop in dropout rate driven by capacity relaxation (not income)
14. Core Contribution (what AER cares about)
This model shows:
Human capital accumulation is not only a function of investment, but also a function of institutional capacity constraints that can shift discretely through redesign shocks.