the coe¢ cient of log TFP (t-3) is signi...cantly di¤erent from zero at the 5% level and the LM test rejects the hypothesis of no serial correlation (up to the third order). Thus, for most countries the growth rate of TFP is well described by an ARMA(1,1) model. We henceforth focus on the current TFP growth rate, since for most countries the data do not reject the proposition that the current growth rate (or its innovation) gives all necessary information about the entire future path of TFP, and hence welfare.

We ...rst ask which sectors contributed the most to welfare change in these countries over the period of our study through their contribution to aggregate TFP growth. The results are in Table 2. We look at the contributions of ...ve major industry groups: Manufacturing, Utilities, Construction, Wholesale and Retail Trade and FIRE. For each country, we present in line 1 the mean of the Tornqvist index of TFP growth for these industries, which represent the overwhelming majority of private output. Interestingly, average TFP growth over this period is less than 1 percent per annum, even for the leading economies, France and Britain. The sectoral decompositions are also interesting. The next ...ve lines give average sectoral TFP growth rates (not growth contributions, which would multiply the growth rates by the respective sectoral weights, and give a mechanical advantage to large sectors). Manufacturing makes a positive contribution for each country. The contribution of FIRE (Finance, Insurance, Real Estate), on the other hand, is often negative, especially in Britain, which has become a ...nancial hub for the world.<sup>10</sup> But the humble utility sectors are the largest source of productivity growth on average (in every country other than Italy). Alesina et al (2005) suggest an explanation for this pattern based on deregulation of the utilities sectors in many European countries (with Italy a laggard in terms of the timing and pace of deregulation).

In Table 3, we look at the contributions of di¤erent groups of ...rms to welfare growth, now using our ...rm-level data from Amadeus for these countries. We now look at the average TFP growth rates of small and large ...rms, from 1998-2004. No very clear pattern emerges. Large ...rms have higher TFP growth rates in two countries (Belgium and Spain); small ...rms have higher growth rates in two others (Italy and Great Britain), and the contributions are basically identical in the remaining country, France.

We can further decompose productivity di¤erences across countries by applying the following decomposition, based on Griliches and Regev (1995). We wish to ask whether the di¤erence in the productivity growth rate of any pair of countries is due to di¤erences in their sectoral compositions or to di¤erences in the growth rates for each sector. Let i now index sectors (not ...rms) and C be one of the countries in our sample other than the UK.

> 10 However, measures of both nominal and real ...nancial sector output are often unreliable. See Wang, Basu and Fernald (forthcoming) for a model-based method for constructing ...nancial sector output. Basu, Inklaar and Wang (forthcoming) apply this theory to construct nominal bank output measures, and Inklaar and Wang (2007) provide a theory-consistent measure of real bank output in the United States.

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