cross-sectional specifications include both country and sector fixed effects. The panel spec-
ifications include country×sector fixed effects, country×time fixed effects, and sector×time
fixed effects in alternative specifications.
To analyze the second effect, rewrite equation (1) as:
II
σA2 = ai2σi2 + ai (1 - ai)ρi,A-iσiσA-i , (3)
i=1 i=1
where the subscript A - i is used to denote the sum of all the sectors in the economy except
i. Thus, ρi,A-i is the correlation coefficient of sector i with the rest of the economy, and
σA-i is the standard deviation of the aggregate output growth excluding sector i. This
way, rather than writing the aggregate variance as a double sum of all the covariances of
individual sector pairs, equation (3) rewrites it as the sum of covariances of each sector
i with the rest of the economy. (Note that we can express aggregate variance this way
without any loss of generality.)
The effect of trade on the correlation between an individual sector and the rest of the
economy, ρi,A-i , is the subject of our second empirical exercise. We call this the Comove-
ment Effect.6 Just like σi2, we calculate ρi,A-i for each country, sector, and time period, and
thus we can estimate the relationship between trade openness and ρi,A-i using industry-level
data in the cross section and in ten-year panels:
Correlationict = α0 + α1Outputict + βTradeict + uict + εict. (4)
The right-hand side variables are the same as in the volatility specifications (see above).
The left-hand side variable is the correlation of output per worker growth in sector i with
the overall manufacturing excluding that sector, ρi,A-i . In the cross-sectional specifications,
these correlations are computed over thirty years. In the panel, we compute correlations over
non-overlapping ten-year periods.7 In contrast to the volatility estimation in the previous
section, the left-hand side is in levels rather than in logs because correlation coefficients can
be negative. Note also that we use correlation rather than covariance. This is because the
correlation coefficient is a pure measure of comovement, whereas changes in the covariance
are influenced by changes in the sector-level variance. These are themselves affected by
trade, as we show when we estimate the impact of trade on sector-level volatility.
We next analyze whether trade leads to increased specialization in a small number of
sectors. Going back to equation (1), we see that aside from its effect on σj,s and σij’s,
6 Note that this effect is different from the cross-country comovement analyzed in the international business
cycle literature (Backus, Kehoe and Kydland 1992, Baxter and Kouparitsas 2002, Burstein, Kurz and Tesar
2004, Frankel and Rose 1998, Kose and Yi 2006).
7We also estimated five-year panel specifications for both the volatility and correlation regressions. As
the conclusions are remarkably similar to the ten-year panel specifications, we report only the cross-sectional
and ten-year panel results to conserve space.