of countries up to 2005. These countries are mostly, but not exclusively, European; the project also gives data for non-EU countries like Australia, Japan, Korea and the United States. The EU-KLEMS data are extensively documented by O’Mahony and Timmer (2009).

In addition to the non-parametric welfare-relevant index numbers presented in the next section, we will also estimate production functions using ...rm level data, allowing the coe¢ cients to vary across 2-digit industries for the period 1998-2005.<sup>9</sup> Before 1998 the number of ...rms in the survey is signi...cantly smaller in most countries. Between 1998 and 2000 many ...rms enter in the data set. The coverage provided by the dataset varies across these countries. In 2005 the aggregated sales of the ...rms represented in Amadeus represent between 20 percent and 45 percent of the manufacturing sector’s total production value, as documented in EU-KLEMS.

Our gross output proxy is (...rm level) revenues de‡ated by the sectoral value added de‡ator obtained from the EU-KLEMS data set, at the 2 digit level. All de‡ators used here will be at the 2 digit level and are obtained from EU-KLEMS. We are aware that using industry de‡ators in place of ...rm-level prices can cause problems (Klette and Grilliches (1996)), but ...rm-level price data for output are not available in Amadeus. Our proxy for labor input is manpower costs de‡ated by the labor services de‡ator. (For some countries, such as Italy, the number of employees ...gure is not reliable, since there is not a reporting requirement for the number of employees in the main section of the balance sheet.) Capital is the historical value of tangible ...xed assets divided by the price index for investment. We have also experimented with the perpetual inventory method, obtaining similar results. A measure for materials, intermediates and other services used in production has been computed using the following formula: materials = Operating Revenues - (Operating Pro...ts+Manpower costs+Depreciation). The ...gure obtained in this way is then de‡ated by the materials and services de‡ator. Given gross output and materials input, value added is constructed as a Tornqvist/Divisia index.

# 5 Sources of Welfare Di¤erences

Welfare change depends on the expected present discounted value of expected TFP growth as shown by equations (18) and (20). It is therefore important to investigate the time-series property of TFP growth. We do so in Table 1, using annual data from EU-KLEMS up to 2005 for the entire private economy for Belgium, France, Great Britain, Italy, and Spain. We use the measure of TFP developed in EU-KLEMS, based on the assumption of zero pro...ts and time varying distributional shares and present both country by country and pooled results. The persistence of TFP growth is a key statistic, since it shows how the entire summation of expected productivity residuals changes as a function of the new information about the TFP growth rate. For most countries the log level of the TFP index is well described by an AR(1) stationary process around a country-speci...c linear trend. Additional lags of log TFP are not signi...cant and the residual is white noise, as suggested by the Lagrange Multiplier test for residual serial correlation. The only exception is Spain, where

> 9 The use of a ...ner sectoral disaggregation is questionable if one wants to have enough ...rms in each sector for estimation purposes.

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