average of firm-plant-level INF and IC variables instead of the crude variables,<sup>13</sup> which is a common solution in panel data studies at the firm level<sup>14</sup> (see Veeramani and Goldar, 2004, for other use of industry-region averages with IC variables).

Using industry-region-size averages also mitigates the effect of having certain missing individual INF and IC observations at the plant level, which—as mentioned in section 3—represent one of the most important difficulties of using ICSs. As an alternative, we also follow a second strategy to deal with the missing values of some INF and IC variables. In order to keep as many observations in the regressions as possible to avoid losing efficiency, when the response rate of the variables is large enough, we decided to replace those missing observations with the corresponding industry-region-size 15 average. Thus, we gain observations, efficiency, and representativity at the cost of introducing measurement errors into some variables.<sup>16</sup> The econometric methodology applied for the selection of the variables (INF and IC) goes from the general to the specific. The otherwise omitted variables that we encounter—starting from a toosimple model—generate biased and inconsistent parameter estimates. We start the selection of variables with a wide set compounded by up to 90 variables (depending on the country). We avoid simultaneously using time variables that provide the same information and are likely to be correlated, mitigating the problem of multicollinearity that could otherwise arise. We then start removing the less significant variables from the regressions one by one, until we obtain the final set of variables, all significant in at least one of the regressions and with parameters varying within a reasonable range of values. Once we have selected a preliminary model we test for omitted INF and IC variables.

The robust coefficients of the INF and IC variables in productivity, along with their level of significance, are available upon from request. The parameters estimated in the two step procedure with restricted input-output elasticites can be found in figures 6.1 to 6.23.

# _Infrastructure assessment based on O&P decompositions_

According to the O&P (1996) decomposition, aggregate productivity for a given country, industry, or region may be decomposed into two terms: (a) average productivity, and (b) a covariance term measuring whether the economy is able to efficiently reallocate resources from less productive establishments to more productive ones. Once we have estimated a robust set of parameters for the IC

> 13 Because of the low number of available regions in most of the countries, we had to use the industry-region-size variables instead of the region-industry averages. For the creation of cells a minimum number of firms are imposed—there must be at least 15 to 20 firms in each industry-region-size cell to create the average, otherwise we apply the region-industry averages. If the problem persists, we apply the industry-size or the region-size average.

> 14 This two-step estimation approach is a simplified version of an instrumental variable (IV) estimator (two-stage least squares, 2SLS).

> 15 Notice that this replacement strategy has a straightforward weighted least squares interpretation since we are giving a greater weight to those observations with more variance (Escribano et al., 2008).

> 16 The measurement error introduces a downward bias in the parameters that depends on the ratio between the variances of the variables and the measurement error. Since those explanatory variables are constant within regions, sizes, and industries we expect their variances will be small.

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