used to proxy for the current production and use of inputs. To extend future analysis to include these estimations, the ES has started collecting information on these lagged variables of inputs. This will be used in the future as the data become available. Other, firm-level fixed effects methods have been used to estimate average firm-level productivity over time. The ES has constructed longitudinal/panel data for a large number of countries: TFP estimates based on the panel data will also be provided in the future.

Second, there are issues associated with the fact that often only monetary (as opposed to physical) output and input expenditure are observed in typical firm-level data. Such revenue-based TFP is often referred to as _TFPR_ ( _TFPRi_ = _Pi × TFPQi_ ), where R stands for revenue and Q for quantity, and _Pi_ denotes the firm’s product price. Market dynamics are inseparable within TFPR estimates, which incorporate clearing prices of inputs and revenue-based outputs and can conflate productivity and market (e.g. negotiating) power. As in the case for most firm-level datasets, the ES collect information on revenues and firm-level line item costs (rather than physical inputs and outputs), and hence TFPR is the only measure that can be estimated using the ES data. For a recent discussion of these and other issues in estimation see for instance Foster et al. (2008), Hsieh & Klenow (2009).

A third caveat relates to the importance of the functional form of the production function. The Cobb-Douglas specification in equation (1) assumes a constant elasticity of output, regardless of other output choices. These elasticities are constant and in the form of _βk_ and _βl_ . In other words, a firm’s elasticity of capital output, for example, does not depend on its use of labor: labor-intensive firms expect the same elasticity of output of capital as non-labor-intensive ones. This assumption may be unrealistic in two ways. First, imposing one production function on firms in different industries is almost surely too restrictive. And indeed, most of the empirical literature on productivity defines industries as narrowly as data permit (Syverson 2011). The ES estimations address this point with a very practical solution: TFPR is estimated separately for each industry — grouped by two-digit ISIC codes — over pooled economies.<sup>6</sup> Second, the assumption of constant elasticities of output for all three (or two) inputs may be too stringent even within industries defined at the two-digit level: so, we also consider a more flexible functional form, the translog specification, which does not impose this restriction.<sup>7</sup> Table A.3 in the Appendix presents the 16 industries with separate estimations.

Hence, the estimations assume that the production function, either Cobb-Douglas or translog, is sector-specific but common across countries. To address this rather restrictive assumption, the specification is enriched as follows. First, in order to control for potential differences in production technology between countries, wherever possible, the production coefficients are allowed to vary by the income-level grouping of the corresponding economy by adding interaction terms between income group and factor inputs. The income levels are grouped according to the WB classification (low-income and lower middle income grouped as low-income and upper-middle income and high income grouped as high income) as of the year in which each survey was conducted and are denoted with _Ic_ (equals 1 for high-income). Empirical investigation of the stability of our estimates revealed that this income grouping is appro-

> 6The production functions could in principle be estimated by country and sector. However, estimating production coefficients separately by country-sector is difficult with the ES data since there are few observations for most countries within each sector.

> 7Due to low number of observations in the current dataset, four groups of industries are defined: group 15 and 16: food, beverages and tobacco; group 23 and 24: refined petroleum, nuclear fuel and chemicals; group 30,31,32 and 33: electrical machinery and electronics; and group 34 and 35: transport equipment.

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