n?u=RePEc:cep:sercdp:0208&r=his

Proposition 1. There exists a ¯V h∗ > 0 such that worker-l**and** 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 l**and** 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 l**and** 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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