in each country, we can readily construct the ...rst two terms in equation (57), the present value of expected TFP growth, and the change in expectations of that quantity. The third term, which depends on the change in the capital stock can also be constructed using data from EU-KLEMS. We assume that the composite discount rate, �; is common across countries and we set it equal to 0:95:<sup>18</sup> For the expenditure and distributional shares, we use their country speci...c averages over the sample period.

The results are in Table 2. We see that assumptions about ...scal policy a¤ect the results in signi...cant ways. We ...rst illustrate our methods by discussing the results for the US, which are given in the last row. We then broaden our discussion to draw more general lessons from the full set of countries. In the ...rst column of Table 2, we construct the output data and the capital and labor shares under the assumption that government expenditure is wasteful and taxes are lump-sum. In this column, "utility-relevant output" comprises just consumption and investment, aggregated using weights that sum to less than one.<sup>19</sup> In this case, the average annual growth rate of welfare in the US is equivalent to a permanent annual increase in consumption of about 2.5 percent. Recall from Section 4.4 that this result applies whether we think of the US as an open or a closed economy. The same is true for all the other results in Table 2–all apply to open as well as closed economies. Now we study the case of optimal government spending, still under the assumption that taxes are not distortionary. Thus, at the margin the consumer is indi¤erent between an additional unit of private consumption and an additional unit of government expenditures. In this case, output consists of consumption, investment and government purchases, aggregated using nominal expenditure shares that sum to one. In a closed economy this concept of TFP corresponds to the standard Solow residual. Note that in all cases our output concepts correspond to di¤erent measures of absorption; this is why they are relevant for both closed and open economies.

Welfare growth for the US is only slightly higher when we assume that expenditures are optimal: 2.6 versus 2.5 percent for the lump-sum tax cases. (We will see that this result is not universal within our sample of countries.) On the whole, the di¤ering assumptions about the value of government expenditure do not change the calculated US growth rate of welfare signi...cantly. Note, however, that this result does not mean that the US consumer is indi¤erent between wasteful and optimal government spending. Steady-state welfare is surely much lower in the case where the government wastes 20 percent of GDP. However, our results show that the di¤erence in welfare in the two cases is almost entirely a level di¤erence rather than a growth rate di¤erence.

We repeat our welfare calculations under the assumption that the government raises revenue via distortionary taxes. The results are in columns 3 and 4 of Table 2. As shown above, if taxes are distortionary we need to construct the factor shares in the Solow residual using the after-tax wage and capital rental rate perceived by the household, implying that the shares will sum to less

> 18 We construct our measure of � following the method of Cooley and Prescott (1995), who ...nd � = 0:947.

> 19 The weight on consumption is the nominal value of consumption divided by nominal expenditures on consumption, investment and government purchases. The weight on investment is the nominal value of investment, divided by the same denominator.

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