Trade Openness and Volatility

Using a Taylor approximation, the effect of changes in the three variables (∆σ² , ∆ρ, and
∆h) on the aggregate volatility is:

₂   ∂σ_A²   ₂ ∂σ_A²      ∂σ_A²

∆σA ≈ TΓ2∆σ² + _:iA∆ρ + —A∆h.

∂σ² ∂ρ ∂h

We can compute the partial derivatives using equation (8):

Each of the three terms represents the partial effect of the three channels we estimated on
the aggregate volatility, and their sum is the combined impact.

We obtain the values of ∆σ² , ∆ρ, and ∆h as a function of changes in openness from
our estimated equations as follows:

∆σ² = β^bσσ²∆Log(Openness)                       (11)

∆ρ = β^bρ∆Log(Openness)                         (12)

∆h = β^bhh∆Log(Openness),                       (13)

where β^bσ is the coefficient on the trade openness variable in equation (2), β^bρ is the coefficient
on trade openness obtained from estimating equation (4), and β^bh comes from estimating
our specialization equation (6).²⁰

The various exercises we perform in this section differ only in the kinds of values we
plug in for ∆Log(Openness), σ², ρ, h, σA-, βσ, βρ, and β_h.

4.1 The Impact Across Countries and Over Time

In the first two exercises, we use the average values of σ² , ρ, and h found in our sample.
These are reported in the first row of Table T1. The average Herfindahl index in our sample
is h = 0.12. The average comovement of a sector with the aggregate, ρ = 0.35. The average
variance of a sector, σ² = 0.038. For the variance of the entire economy minus one sector,
σ_A² _-, we simply use the average aggregate volatility in our sample of countries, which is
0.0086. This is a sensible approximation of the volatility of all the sectors except one, since
the mean share of an individual sector in total manufacturing is just under 0.04, and thus on
average, subtracting an individual sector from the aggregate will not make much difference.

The dispersion in the overall manufacturing trade as a share of output in our sample
implies that moving from the 25^th to the 75^th percentile in overall trade openness is equiv-
alent to an increase in total trade to manufacturing output from about 40 percent (e.g.,
²⁰Note that in the estimation equations (2) and (6) the left-hand-side variable is in logs. Hence, in order
to get the change in its level in equations (11) and (13), we must multiply the estimated coefficients by the
average level of the variable.

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