Discussing ‘Reshaping Infrastructure: Evidence from the Division of Germany’ by Marta Santamaria

Regional and Urban Economics Workshop @ PSE

Florian Oswald
florian.oswald@sciencespo.fr

SciencesPo Paris

25 March, 2024

Overview

  • Impressive QSM model with an endogenous investment decision.
  • Interesting historical setting: Helpful to think about path dependency of large infrastructure projects.
  • Paper seems fairly matured by now, under revision at a prestigious journal…so, not many comments left to make?

👍

  • Will try with a few clarifying questions.
  • Some comments about computation.

Questions

Questions

What is Reshaping?

  • “Very Similar”
  • But: “Important differences”
  • 👈 allocation to different district?
  • 1463 Edges?

Questions

What is Reshaping?

Some help with Table 1 please:

This decomposition shows that the highway network in 1974 was considerably reshaped from what had been set out in the plan designed 40 years earlier.

  • Talking only about West, right?
  • Map (even only part) would be super helpful
  • Appendix C was not enough. Are there more higways than in figure 1?

Questions

How does Path Dependence counterfactual work?

I solve for the unconstrained infrastructure allocation in West Germany by assuming that no highway had been built before division

  • Why is assuming that no highway had been built in West Germany the right thing to do here?
  • I understand the infrastructure part (compare wrongly built network with optimal one).
  • But are you not kind of ignoring the population distribution? Some cities may exist only because they got the wrong highways in the first place.
  • I may not properly understand how the dynamics play out here. How does one transition from 1949 to 1974?

Questions

What is Investment into Highways actually?

Once a highway is built, the main cost has been incured? What exactly is highway investment?

  • Maintainance?
  • Adding a lane?
  • Renewing surface?
  • Some background would be helpful. Like, how important is \(\phi_{i,j}\) once the highway exists?

Computation

Computation

This is a hard problem

\[ \begin{align} \max_{\phi_n} & \left[ \sum_n \left(\frac{v_n}{P_n^\alpha r_n^{1-\alpha}}\right)^\epsilon \right]^{1/\epsilon} \\ s.t. \quad & (10)-(13) \quad \text{(SE)}\\ & (17) \quad \text{(TC)} \\ & (18) \quad \text{(BC)} \end{align} \]

simplified into 👉 \(\max_{\phi_n} U^{eq} = f(w^{eq}(\phi),P^{eq}(\phi),r^{eq}(\phi),L^{eq}(\phi),T^{eq}(\phi),\phi)\quad (21)\)

    1. not clear. What is \(f\)? no constraints? \(w^{eq}(\phi)\) fixed at step \(k\)?
  • Seems a nested fixed point strategy.

Computation

Suggestions (👋 hand-waving alert)

  • No Analytic Gradients
  • Use a language with good AD support. julia + JuMP.jl + IPopt.jl
  • Su and Judd (2012)
  • JuMP.jl Lubin et al. (2023)
  • You would solve the full constrained problem on previous slide, no iteration.
  • I.e. you choose \(\{\phi_n,w_n,P_n,r_n,L_n\}\) at the same time.
  • You could combine steps 1 and 3 of your algorithm. Maybe even step 2 as well (not sure about complexity of this)

Computation

Suggestions 👋

# not tested. (of course.)
using JuMP, Ipopt
function MartaSteps1and3(T::Matrix)
    N = size(T,1)  # T is the current transport costs matrix
    m = Model(Ipopt.Optimizer)
    @variable(m, 1 <= ϕ[1:N])
    @variable(m, 0 <= w[1:N])
    . . . # define all choice variables
    @constraint(m, eq10[n=1:N], 
        sum( (L[i] / (σ*F) (σ/(σ-1)) w[i]/A[i] * T[n,i]) * P[i]^(σ-1) * w[i] * L[i]     
    for i in 1:N)
    . . . # define all constraints (10-13)
    @expression(m, v[i=1:N], . . . ) # define
    @objective(m, sum( (v[n] / (P[n]^α * r[n]^(1-α)))^ϵ for n in 1:N)^(1/ϵ))

    optimize!(m)  
    # build's AD gradient+hessian+sparsity structure
    # and hands over to Ipopt
end

End 👋

😉

References

Lubin, Miles, Oscar Dowson, Joaquim Dias Garcia, Joey Huchette, Benoı̂t Legat, and Juan Pablo Vielma. 2023. “JuMP 1.0: Recent Improvements to a Modeling Language for Mathematical Optimization.” Mathematical Programming Computation. https://doi.org/10.1007/s12532-023-00239-3.
Su, Che-Lin, and Kenneth L Judd. 2012. “Constrained Optimization Approaches to Estimation of Structural Models.” Econometrica 80 (5): 2213–30.

RUES workshop March 2024