Cities, Shocks & Theories: Locational Fundamentals vs Increasing Returns

Key Motivating Questions

• Why do cities exist?
  • Why is economic activity geographically concentrated rather than evenly spread?
• What determines where that concentration occurs?
  • What makes some places densely populated and economically vibrant while others remain sparsely settled?
• Why is the spatial distribution of activity persistent?
  • Once a place becomes important, why does it often stay important for centuries?
  • Japanese regions, for example, show millennia-long durability of population ranks.

Three Core Theories of Urban Location

• Locational Fundamentals
  • Physical or natural advantages (rivers, harbors, fertile valleys, pleasant climate).
  • Man-made but fixed features also count in practice (Roman roads, aqueducts, inherited housing stock).
  • Simple intuition: if the place itself confers productivity, people cluster there.
• Increasing Returns (Agglomeration Economies)
  • Productivity rises with local scale: more firms & workers → thicker labor markets, sharing of inputs, knowledge spillovers, specialized services.
  • Paraphrasing Yogi Berra: “A city is where the people are because…that’s where the people are.”
  • Generates multiple equilibria & path dependence (lock-in).
  • Coordination problems: nobody moves first because individual migration is costly if others stay.
  • Example: World Bank builds a new Kenya coast road.
  – If fundamentals dominate, lower travel cost shifts density coast-ward.
  – If increasing returns dominate, interior cities keep their people; new road under-used.
• Random Growth (Gibrat/Proportionate-Growth Process)
  • Each city draws an iid growth rate each period from some distribution.
  • Over time this random multiplicative process yields a city-size distribution obeying Zip’s Law.
  $\log\text{(rank)} = c - \log\text{(population)}$
  → slope ≈ $-1$ in a log–log plot.
  • Found not only in cities but in word frequencies, firm sizes, etc.
  • Economists struggle to tether the process to micro foundations, though New Economic Geography (Krugman) hints geography may shape the underlying variance structure.
  • Historical deviations (Europe pre-1600, Japan during autarky) show “missing megacities” when trade frictions or institutions limit very large centers.

Policy & Conceptual Implications

• Choice of theory matters for infrastructure policy, regional aid, and urban planning.
  • Under fundamentals, improving access to superior sites can shift activity.
  • Under strong increasing returns, existing concentrations persist unless a mass migration or coordinated relocation occurs.
  • Potential for welfare-reducing lock-in when history traps populations in sub-optimal spots.

Empirical Case Study 1: 8,000 Years of Japanese Regional Density (Davis & Weinstein, “Bones, Bombs, and Breakpoints”)

Data Construction

• 39 regions (prefectures) observed at multiple archaeological & historical horizons, 6000 BC → 1998.
• Variables assembled: total population, population density, Zip coefficient, variance measures, correlations with 1998 ranks.

Stylised Facts

• High dispersion throughout history
  • Share of top-5 regions rarely < $20\%$; peaks at $\approx 40\%$ (6000 BC) and $\approx 41\%$ (1998).
  • Relative variance of log density generally high; modern benchmark normalised to $1$.
• Zip coefficients
  • Hover near $-1$ (Zip’s Law) for most epochs.
  • Become more negative (≈ $-1.25$) when Japan closes to trade (≈ 1600–1850), indicating flattened upper tail (large cities too small).
• Striking persistence
  • Rank correlation between Jōmon-period densities and 1998 ≈ $0.71$.
  • Raw correlation climbs steadily over time.
• Interpretation
  • Large long-run variance ⇢ consistent with locational fundamentals.
  • High rank persistence ⇢ could stem from either fundamentals or agglomeration.
• Need sharper identification → natural experiment.

Empirical Case Study 2: WWII Bombing of Japanese Cities

Identification Strategy

• Sudden, massive & spatially heterogeneous population shocks.
  • U.S. B-29 incendiary raids (McNamara & LeMay strategy) burned $\approx$ 50 mi² of Tokyo; single-night deaths ≈ $100{,}000$.
  • 303 cities > 30 000 residents (1925) form sample.
• Key variables
  • $\text{Casualties}<em>i / \text{Pop}</em>{1940,i}$
  • $\text{BuildingsDestroyed}<em>i / \text{Pop}</em>{1940,i}$
  • Government reconstruction spending per capita (1947) – control.
• Logic
  • If fundamentals dominate: larger wartime losses ⇒ higher post-war growth → city snaps back.
  • If increasing returns dominate: severe losses break agglomerations ⇒ city stays small.

Preliminary Visual Evidence

• Scatter: $g<em>{47–60}$ (vertical) vs $g</em>{40–47}$ (horizontal)
  • Downward line with slope ≈ $-1$
  • Tokyo: −47 % in war, then rapid rebound ≈ +45 %.
  • Suggests one-for-one snap-back.

Econometric Framework

1. Baseline OLS
   $g^{47–60}<em>i = \alpha + \beta g^{40–47}</em>i + \varepsilon_i$
   • Endogeneity concern: pre-war trend or amenities that drive both periods.
2. Instrumental Variables (2SLS)
   • First-stage instruments:
   – $Z<em>{1i} = \text{Casualties}</em>i / \text{Pop}<em>{1940,i}$ – $Z</em>{2i} = \text{BuildingsDestroyed}<em>i / \text{Pop}</em>{1940,i}$
   • Relevance: heavy bombing strongly predicts $g^{40–47}_i$ (first-stage $R^2$ high, F-stat ≫ 10 for buildings destroyed).
   • Validity: Instruments assumed orthogonal to latent productivity trends after controlling for reconstruction aid.

Main IV Results

• Second-stage coefficient
  $\hat\beta \approx -1.048 \;(SE = 0.097)$
  • Statistically different from 0 (|t| ≈ 10.8) and not different from −1.
• Robust to
  • Adding reconstruction spending and 1925–40 pre-trend controls.
  • Extending horizon to 1947–65.
• Interpretation
  • Losing $10\%$ of population raises subsequent growth by ≈ $10\%$ → cities regain pre-war size.
  • Evidence favors locational fundamentals; agglomeration alone would predict persistent scars.

Additional Check: Atomic Bomb Cities

• Hiroshima & Nagasaki (near-total devastation; refugee return less likely).
• Plot $\log\text{(population)}$ vs year:
  • Pre-trend slow incline → 1945 atomic blast → sharp drop → faster post-45 growth slope.
  • Both trajectories converge back to old trend lines within ~15 years.
• Supports fundamentals: even extreme shocks do not permanently dislodge cities.

Caveats & Counter-arguments

• Refugee Return vs Geography
  • Possibly still increasing returns if displaced residents simply move home once war ends.
  • Authors argue atomic cases & sheer casualty magnitude reduce but cannot entirely rule out this channel.
• Infrastructure also bombed (roads, factories) ⇒ shock not purely demographic.
  • Controls for aid; still results hold.
• Contrast with “pure” mortality shocks (e.g.
  Black Death) where infrastructure intact but demographic data sparse.

Connections to Broader Literature

• Similar natural-experiment papers: U.S. bombing of Vietnam; German WW II bombing; Katrina’s impact on New Orleans; Mount St Helens eruption, etc.
• Krugman’s New Economic Geography links market access & increasing returns but allows fundamentals (transport cost gradients) to underlie core–periphery outcomes.

Ethical & Historical Reflections

• Strategic bombing raised profound moral questions (proportionality, civilian targets).
  • McNamara’s retrospective: “Proportionality should be a guideline of war.”
  • Illustrates how human tragedy inadvertently yields quasi-experimental variation for economists.

Practical Take-aways

• Persistent urban hierarchies are hard to overturn with temporary shocks; place-specific advantages matter greatly.
• Infrastructure investment aimed at new locations must account for potential lock-in of existing centers.
• Recovery policy: if fundamentals remain, rebuilding efforts can expect rapid population return; if not, subsidies may be wasted.

Key Numbers & Equations At A Glance

• Zip distribution: $\text{slope} \approx -1$.
• Share of 5 largest Japanese regions: $0.39$ (6000 BC) → $0.41$ (1998).
• Main IV estimate: $\hat\beta = -1.048 \;(SE=0.097)$.
• Tokyo incendiary raid: $\approx 100{,}000$ deaths in one night; $50$ square miles burned.
• Atomic bomb city rebound visible within < $20$ years.

Study Checklist

• Understand definitions & differences among locational fundamentals, increasing returns, random growth.
• Be able to explain Zip’s Law derivation and graphical test.
• Reproduce intuition of Davis-Weinstein bombing experiment and why $\beta = -1$ supports fundamentals.
• Know IV conditions (relevance, validity) and why casualties & buildings destroyed satisfy them (or might fail).
• Recognize policy relevance: road-building in Kenya example; post-disaster urban recovery.
• Reflect on moral/ethical dimensions of using wartime devastation in economic research.