faster than the share-weighted sum of their inputs, even when their technology is constant. Thus, aggregate TFP rises when ...rms with above-average market power grow faster than average. At ...rst this result sounds counterintuitive, since it implies that welfare is enhanced by directing more capital and labor to the most distorted sectors. However, the logic is exactly the same as the usual result that ...rms with the greatest monopoly power should also receive the largest unit subsidies to increase their output.

A number of recent papers suggest that a substantial fraction of output growth within countries comes from reallocation, broadly de...ned. However, given the di¤erent de...nitions of “reallocation” used in the literature, it is not clear how much reallocation matters for welfare. Our work suggests that the literature should focus on quantifying the increment to aggregate TFP growth from reallocation. Furthermore, it shows that TFP is what matters, not technical e¢ ciency. TFP contributions can come from either higher technical e¢ ciency, by exploiting increasing returns to scale, or by allocating inputs more e¢ ciently across ...rms. When TFP and technical e¢ ciency diverge, it is TFP that matters for welfare. We have concentrated on aggregate TFP and capital accumulation without asking how individual ...rms and sectors contribute to these welfare-relevant variables. Domar (1961) and Basu and Fernald (2002) show how one can decompose standard TFP based on GDP into sectoral and ...rm-level contributions. However, our results above show that in an open economy one should base TFP measures on absorption rather than GDP. There is as yet no parallel to Domar’s (1961) decomposition for absorption or net investment, since that would require allocating the output of individual industries to particular components of ...nal expenditure. The approach of Basu, Fernald, Fisher and Kimball (2010), based on the use of input-output tables, may be helpful in this endeavor.

Finally, our work is closely related to the program of developing su¢ cient statistics for welfare analysis, surveyed by Chetty (2009). We have proposed such a statistic for a representative consumer in a macroeconomic context. As Chetty notes, such measures can be used to evaluate the e¤ects of policies. Suppose that one wishes to evaluate the e¤ect of a policy change— for example, a change in trade policy, as in Kehoe and Ruhl (2010). The usual method is to relate the policy change to a variety of economic indicators, such as GDP, capital accumulation, or the trade balance, and then try to relate the indicators to welfare informally. Our work suggests that one can dispense with these “intermediate targets,”and just directly relate the welfare outcome to a change in policy, or to some other shock.

# 7 Conclusions

We show that aggregate TFP, appropriately de...ned, and the capital stock can be used to construct su¢ cient statistics for the welfare of a representative consumer. To a ...rst order approximation, the change in the consumer’s welfare is measured by the expected present value of aggregate TFP growth (and its revision) and by the change in the capital stock. We also show that in order to create a proper welfare measure, TFP has to be calculated using prices faced by households 36