interactive, non-routine and analytic, and non-routine and manual. Since the 1980’s, the United States has been specializing more in tasks that are non-routine and either interactive or analytic, and less in the other three categories of tasks.

Spitz-Oener (2006) has conducted a similar exercise using German data. She ...nds that the pattern of specialization across tasks has evolved similarly in Germany as in the United States, except that Germany is performing more tasks that are non-routine and manual over time, unlike the United States. The evidence supports the plausible conclusion that routine tasks are migrating to low-income countries like China, India and Mexico, with the high-income countries specializing increasingly in the set of non-routine tasks. But the evidence also suggests that Germany is specializing in a di¤erent set of non-routine tasks than the United States, namely, those that are more manual in nature. Given that Germany is smaller than the United States in terms of aggregate output and it has lower wages, our theory predicts that it should specialize in tasks that are relatively easier to o¤shore. Our prediction accords with the available evidence to the extent that (non-routine) manual tasks can more readily be organized and coordinated from a distance than interactive or analytic tasks. This ranking of relative o¤shoring costs seems plausible to us, but we could ...nd no direct evidence to con...rm it.

Ideally, empirical research on task trade would begin by classifying tasks according to the relative ease of o¤shoring. More data on o¤shoring are becoming available as awareness of this phenomenon grows, so it may soon be possible to measure the o¤shoring costs for di¤erent tasks. Once that is possible, it will also be possible to study the pattern of specialization by task. We hope that our theory can help guide such e¤orts.

# 5 Appendix

In this Appendix, we prove Propositions 3, 4, 5, and 7.

Proof of Proposition 3. Equations (1), (3) and (2) de...ne thresholds I; I<sup>�</sup> ; and J as continuous functions of the two triplets (n; x; w) and (n<sup>�</sup> ; x<sup>�</sup> ; w<sup>�</sup> ) : For values of w such that w = w<sup>�</sup> ; Proposition 1 uses these thresholds to determine uniquely the three sets fE; W; Dg as functions of (n; x; w) and (n<sup>�</sup> ; x<sup>�</sup> ; w<sup>�</sup> ). Furthermore, M (Z) and T (Z) for Z = fE; W; Dg are continuous functions of the set of thresholds (I; I<sup>�</sup> ; J) by the Theorem of the Maximum. We can then use the eight equations (5) to (11) plus (13) to solve for n; n<sup>�</sup> ; x; x<sup>�</sup> ; s; s<sup>�</sup> ; c and c<sup>�</sup> as functions of the wage in East w, after normalizing w<sup>�</sup> = 1. Substituting these solutions into what results from dividing equation (12) by (13) yields an expression of the form �(w; L; L<sup>�</sup> ) = L=L<sup>�</sup> , where �(w; L; L<sup>�</sup> ) denotes the relative quantity of labor demanded in East as a function of the relative wage (given endowments). To show existence, we need to guarantee that there exists a value of w (including, possibly, w = 1)such that this equation is satis...ed. Given that all expressions in the eight equations (5) to (11) plus (13) are continuous in all variables, �(w; L; L<sup>�</sup> ) is continuous as long as w = 1.

For w = 1, the task allocation is not pinned down by Proposition 1. In this case, it must be that nx = n<sup>�</sup> x<sup>�</sup> , because otherwise all tasks would be performed in the same country, which is 26