State capacity and Economic Development: A Network Approach

• Huge amount of variation in state capacity
• Rich historical data from the colonial history
• Topographical information can be used for network modeling

\[ f_{ij}=\frac{1}{1+\delta_1 d_{ij} (1+\delta_2 e_{ij})} \] \[ n_{ij}=\left\{\begin{array}{cc} 0, & j \not \in N(i)\\ f_{ij}, & j \in N(i) \end{array} \right. \]

• \( d_{ij} \) denotes the distance along the geodesic connecting the centroids of municipalities \( i \) and \( j \)
• \( e_{ij} \) is a measure of variability in altitude along the geodesic connecting the centroids of municipalities \( i \) and \( j \)
• \( N(i) \) denotes the set of municipalities connected to \( i \)

\[ p_i^j=(\kappa_i+\xi_i)s_i+\psi_1 s_i \mathbf{N(\delta)s}+\psi_2 \mathbf{N_i(\delta)s}+\epsilon_i^j \]

• \( p_i^j \) is the \( j \) th dimension of prosperity(a z-score)
• \( s_i\in [0,\infty) \) is municipality i's state capacity, \( \kappa_i \) is an observable fixed effect(a function of historical and other characteristics of a municipality), \( \xi_i \) a random effect
• \( \psi_1 \) captures the interaction effect between own capacity and neighbours' capacity
• \( \psi_2 \) captures the direct effect of neighbours' capacity on own prosperity

“Production” of state capacity in a certain municipality \[ s_i=[\alpha l_i^{\frac{\sigma-1}{\sigma}}+(1-\alpha)(\tau b_i)^{\frac{\sigma-1}{\sigma}}]^{\frac{\sigma}{\sigma-1}}, \sigma>0 \] Utility for municipality \[ U_i=E[\frac{1}{J} \sum \limits_{j} p_i^j - \frac{\theta}{2} l_i^2] \] Utility at the national level \[ W_i=E[\sum \limits_i (U_i \zeta_i-\frac{\eta}{2}b_i^2)] \]

• State capacity does have a positive impact on the prosperity of a region.
• General equilibrium effect is comparable to direct or spillover effect over a network.