Pollution and Persistent Neighborhood Sorting



Proposition 1. There exists a ¯V h∗ > 0 such that worker-land clearing condition is

satisfied. High-skilled workers sort into those locations with amenities above A ∗ =

¯V h∗ /(θ h − θ l ). Imperfect sorting at the neighborhood level can occur in equilibrium

if amenity levels overlap.

Proof. See Appendix A.

Sorting and pollution Following Proposition 1, we denote F (A) the cumulative

density of land with amenity level less than or equal to A within the city, and we

define S l (j) as the equilibrium share of low-skilled workers in neighborhood j.

In the absence of pollution, we have a(W ) = a(E) = 0 and d(W ) = d(E) = 0, so

F (A) = 2A. The amenity level that satisfies (5) is where A ∗ = γ. The low-skilled

share in neighborhood j is the share of land in the neighborhood with A ≤ A ∗ , that

is, S l (j, t) = A ∗ − min l {A(j, l, t)}. Without pollution, neighborhoods are symmetric

and S l (j, t) = γ for j ∈ {W, E}.

Pollution takes the form of emission of an air contaminant that causes air quality

to decline. Pollution emitted in each neighborhood is ρ, but a Westerly wind blows

a portion η ∈ (0, 1) of the pollution emitted in neighborhood W into the air of

neighborhood E:

a(W ) = −(1 − η)ρ,

a(E) = −(1 + η)ρ.

Lemma 1. With imperfect sorting, pollution causes the East to have a larger proportion

of low-skilled workers. More intense pollution causes more sorting.

Proof. See Appendix A.

The impact of pollution is depicted in Figure I. The disamenity causes equilibrium

rents paid by high-skilled workers to increase compared to the benchmark without

pollution. Since the lowest 2γ amenities are now disproportionately in the East, the

East has a larger share of low-skilled workers.

In our empirical exercise, we will provide evidence on the spatial relationship

between pollution and the share of low-skilled workers at the peak of industrial

pollution, relying – as in the model – on the asymmetric dispersion of pollution

implied by wind patterns (and topography).

3 Historical context

The start of the Classical Industrial Revolution is dated to around 1760 by the arrival

of new technologies in key growth sectors such as textiles, iron and steam. However,


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