powerful, as our panel has three dimensions. In addition to country, sector, and decade
fixed effects, we also employ interacted fixed effects rich enough to control for a wide vari-
ety of omitted variables. For instance, country×time fixed effects control for time-varying
characteristics of countries, such as external and domestic aggregate shocks, overall trade
opening, financial liberalization, or any other reforms. Sector×time effects absorb any vari-
ation in sector characteristics over time. Finally, the use of country×sector effects allows
us to control for unobservable characteristics of each individual sector in each country, and
identify the effect of trade purely from the time variation in trade and volatility within a
sector. Including a plethora of fixed effects may still not resolve simultaneity problems at
the country×sector×time level, however.10 We therefore reestimate our core specification
with the most conservative set of fixed effects, while adding a variety of controls and inter-
action terms. The list of variables includes terms-of-trade (TOT) volatility, the volatility of
trade at the sector level, the share of the manufacturing sector trade to total trade, and a
measure of financial development interacted with the Raddatz (2005) sector-level measure
of liquidity needs.
As another robustness check, the growth-volatility nexus must also be considered. The
macroeconomics literature finds a negative relationship between growth and volatility (Ramey
and Ramey 1995), though recent work shows that at sector level the opposite is true
(Imbs 2006). In addition, faster growing sectors may also be more open to trade. Therefore,
besides including initial output per worker as a proxy for growth potential in the baseline
estimations, we also control for average levels and growth rates of output per worker as a
further robustness check. Finally, while in our main specifications the dependent variables
are variances and correlations of output per worker growth, we also use a quantity index
and a constructed sector-level price index to check robustness of the results.
To examine the Specialization Effect, we must rely on cross-country regressions because
h is measured at country level. We therefore use the Frankel and Romer (1999) measure of
natural openness to instrument for trade in our sample, and also consider numerous controls
previously suggested in the literature.
10 The following example can illustrate what we can and cannot control for using fixed effects. Suppose
that a natural disaster damages the petroleum refineries inside a country. This shock temporarily drives
down production in the sector. It also forces consumers to substitute from domestic to foreign fuel, increasing
imports, and therefore trade openness. Within that period, these effects would push up both volatility of
output and average openness simultaneously, biasing the relationship between sector-level volatility and trade
openness positively away from zero. If these shocks are frequent (say they occur in each decade in our data),
we can capture this feature of the petroleum sector in this particular country using country×sector effects.
If, in addition to the petroleum industry, all of the other industries in that country experienced declines
in production and increases in trade as a result of that natural disaster, then the impact is economywide
and we control for it using country×time effects. However, if neither is the case, and what is driving the
observed relationship between volatility and trade are country×sector×time-specific domestic supply shocks,
our fixed effects cannot go all the way in helping us identify the impact of trade.