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. /> Attachment 1 Attachment 2 ATTACHMENT PREVIEW Download attachment Screen Shot 2019-12-11 at 3.05.25 PM.png 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. ATTACHMENT PREVIEW Download attachment Screen Shot 2019-12-11 at 3.05.41 PM.png (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: &amp; = 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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