bj <u>�</u> be calculated as (1 � b<sup>Takingconstantreturnsasourmodalestimate,themarkuprangejust</sup> �<sup>Q</sup> i<sup>).</sup> discussed corresponds to pro...t rates in the range of 9 to 20 percent, expressed as a percentage of gross output.

Our estimates of the markup and thus of the pro...t rate are probably upper bounds. We do not control for variations in ...rm-level input utilization (changes in the number of shifts or variations in labor e¤ort), except through our use of time ...xed e¤ects. Thus, we remove variations in utilization due to common industry e¤ects but not due to ...rm-speci...c demand variation over time. Basu (1996) suggests that variable utilization is likely to bias upward the output elasticity of materials in particular, which is the parameter that has the largest impact on our estimates of markups and pro...t rates. Unfortunately, we do not have the ...rm-level data on hours worked per employee that would be necessary to implement the utilization control derived from the optimizing model of Basu, Fernald and Kimball (2006). Thus, our estimates of the average distortions coming from markup pricing, as summarized by the ...rst two terms in equation (34) are likely to be on the high side. But the fact that our estimated average markups are large does not create any particular bias in our estimates of the reallocation terms, which are our particular focus, since the reallocation terms involving markups depend on the gaps between ...rm-level and average markups.

In light of this discussion, it is interesting to look at the estimates of the various reallocation terms for our sample of six countries, which are presented in Tables 10 and 11. In Table 10 we report for each country in our sample, average productivity growth, d log pr, the sum of aggregate distortions, <u>(�</u> � 1)d log X + <u>(�</u> � 1)d log M=Q, the sum of the reallocation terms for primary factors and materials, R� + RM , and technology growth, d log T . The last column reports as residual the di¤erence between productivity, on the one hand, and the sum of aggregate distortions, of the reallocation terms, and of technological progress, on the other, i.e. the di¤erence between the left hand side and the right hand side of (34). This equation may not hold as an equality for three reasons: ...rst we do not observe the true value of the markup, but only its estimated value; (ii) whereas the labor share is observed in the data, calculations of the capital share depends upon a zero pro...t assumptions or an estimate of the markup and of the degree of returns to scale; (iii) as Basu and Fernald (2002) show, if the price paid for capital and labor di¤ers across ...rms, additional terms involving the di¤erence of factor prices for each ...rm from the average, multiplied by each factor growth rate will appear on the right hand side of (34).<sup>13</sup> First of all, we see from Table 10 robust average annual productivity growth for all countries in our sample of large ...rms. The case of Italy is particularly striking, since our sample of ...rms has an average productivity growth rate, d log pr, of 2.8 percent, while the EU-KLEMS database shows that for all of Italian manufacturing average TFP declined at a rate of 1.2 percent per year over our sample period. Second, we see that technical change was also positive for all countries, and

> 13 See footnote 11. Petrin, Reiter and White (2009) argue that changes in ...xed costs create yet another gap between the two sides of equation (34). However, changes in ...xed costs are equivalent to an additive technology shock, and to a ...rst-order approximation both additive and multiplicative technology shocks are already incorporated into the estimate of dlogT . Thus, changes in ...xed costs are not an additional gap between productivity growth and technological change.

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