trade openness can affect overall volatility through changing the configuration of ai’s. In
particular, making the simplifying assumption that all sectors have the same σ2 , we can
rewrite equation (1) as:
II
σA = hσ + ai aj σij , (5)
i=1 j=1
j6=i
where h is the Herfindahl index of production shares in the economy.8 A higher value of
h represents a more specialized (less diversified) economy, and thus, at a given level of
σ2 , leads to a higher aggregate volatility. We call this the Specialization Effect. We use
industry-level production data to compute indices of specialization directly at the country
level, and relate them to trade openness in the following empirical specification:
Specializationc = α0 + α1Xc + βTradec + εc. (6)
Here, c indexes countries, and the left-hand side variable is the log of the Herfindahl index
of production shares of sectors in total manufacturing output, h, averaged over the sample
period.9 Tradec is the log of total manufacturing trade divided by total manufacturing
output in our data. Xc are controls such as per capita GDP.
2.1.1 Discussion
As mentioned above, we estimate the Sector Volatility and Comovement Effects in both
cross-sectional and ten-year panel specifications. The advantage of the cross-sectional spec-
ifications is that they allow us to calculate our left-hand side variables - variances and
correlations - over a long time series, reducing measurement error. The advantage of the
panel specifications is that they make it possible to control for a much richer array of fixed
effects.
The ability to employ a variety of fixed effects is a major strength of our empirical
approach. Specifically, the fixed effects greatly help in alleviating simultaneity issues by
controlling for omitted variables in the variance and correlation regressions. For exam-
ple, in both cross-sectional and panel specifications, country fixed effects will control for
any potential omitted variable that varies at country level, such as overall macroeconomic
volatility, level of development, or institutions. Sector fixed effects will do the same for any
sector characteristics correlated across countries, such as inherent volatility, factor inten-
sity, or tradability. In the panel specifications, the use of fixed effects becomes even more
8The Herfindahl index is defined as the sum of squared shares of each sector in total production: h =
Pi ai2.
9 There are gaps in the sector coverage in some countries and years. We only used country-years in which
at least 20 sectors were available to calculate the Herfindahl. Varying this threshold does not affect the
results.