of mining in GDP, and share of agriculture in GDP. Two points are worth mentioning here.
First, we do not control for the amount of risk sharing across countries, but this omission
is not crucial given the common finding in the literature that economies do not share risk
at the country level (cf. Backus et al. 1992, Kalemli-Ozcan et al. 2003). Second, we
follow Imbs and Wacziarg (2003) and include GDP per capita and its square to capture the
U-shaped pattern of diversification over the development process. This specification does
not significantly affect our results.
4 The Impact on Aggregate Volatility
In the preceding section we estimated the effect of trade on the variance of individual sectors
(σi2 ), the correlation coefficient between an individual sector and the rest of the economy
(ρi,A-i), and the Herfindahl index of sectoral concentration of production shares (h). In this
section we use our estimates to quantify the impact of each of the three effects on aggregate
volatility, as well as their combined impact.
We do this in a number of ways. First, we calculate the effect of moving from the 25th
to the 75th percentile in the distribution of trade openness we observe in our sample. This
exercise is meant to capture mainly the consequences of cross-sectional variation in trade
across countries. Second, we calculate the average increase in trade openness in our sample
over time, from the 1970s to the 1990s, and use it to calculate the expected impact of this
trade expansion on aggregate volatility, through each channel as well as combined. Third,
we calculate how the estimated impact of trade openness on aggregate volatility differs
across countries based on observed characteristics of these countries. The final exercise we
perform is to examine how the nature of the relationship between trade and volatility has
changed over time. To do so, we reestimate the three sets of equations from the previous
section by decade. We then use the decade-specific coefficients to calculate how the impact
of trade on aggregate volatility changes over time.
The aggregate variance, σA2 , can be written as a function of σi2 and ρi,A-i as in equation
(3), which we reproduce here:
II
σA = ai σi + ai (1 - ai)ρi,A-iσiσA-i . (7)
i=1 i=1
In order to evaluate the estimated effect of trade-induced changes in σi2 , ρi,A-i , and h, we
assume for simplicity that for all sectors, the variances and correlations are equal: σi2 = σ2 ,
ρi,A-i = ρ, and σA-i = σA- for all i. This allows us to write equation (7) in terms of σ2 , ρ,
and h as:
σA2 = hσ2 + (1 - h)ρσσA- . (8)
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