Different Levels of Fixed E'ects Consider data on trade between countries over time. There are N countries. Index exporters by i, importers by j,...
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This is an econometrics problem.Screen Shot 2019-12-11 at 3.05.41 PM.png

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2. Different Levels of Fixed Efl'ects Consider data on trade between countries over time.
There are N countries. Index exporters by i, importers by j, and time by t. Let Sijt be the value of exports from i to j at time t: Let Xijt be the value of tariffs charged by j on i’s goods at time t. We are interested in the effect of tariffs on import values. a) Consider the following model:
Sijt = 5X17: + 5i + wj + At + Uijt And suppose that we have demeaned the data so that Xi; 6i 2 23:1 ng = 231:1 A; = 0. (a) Write down the OLS objective function.

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(b) Write out the FOC for di, v; and it.
(c) Define Si to be the mean of S over j and t. I.e.,
Si =
1
N T
NT
Sijt
j= 1 t=1
and define Xi similarly. Also define S; and X, to be the means of S and X over only i and
t, and the define St and Xt similarly. Then prove the following:
& = Si -BXi
bj = Sj - BX;
At = St - BXt
(d) Plug these values (without the hats) into the original regression and show that the regres-
sion is (approximately) equivalent to:
(Sijt - Si - Sj - St) = B (Xijt - Xi - Xj - Xt) + Uijt
b) Now consider the model:
Sijt = BXijt + bij + At + Uijt
Again assume things are demeaned so that En Elbij = Et- At = 0. Can you think of
what kind of factors are controlled for in part (b) that are not controlled for in part (a)?

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