where _INF_ is the observable fixed effects vector of infrastructure variables, and _IC_ is the observable fixed effects vector of other IC and control variables listed in table A.2 in the Appendix. In all the panel data regressions, we always control for several sector-industry dummies (Dj, j = 1, 2, . . ., qD), and in the cases having more than one year of observations we also include a set of time (Dt, t = 1, 2, . . ., qT) dummy variables and always a constant term ( α _P_ ).

For cross-country comparisons based on TFP we use the concept of demeaned TFP,<sup>12</sup> which gets rid of the constant term as well as the constant effects by industry and by year, concentrating therefore on the part of TFP that is influenced by INF, IC, and the other plant-level control variables, In the single-step estimation approach, we consider the parametric estimation by OLS and RE of the extended PF (4.2). To address the well-known problem of the endogeneity of inputs, we follow the approach proposed by Escribano and Guasch (2005, 2008). That is, we proxy the usually unobserved firm-specific fixed effects (which are the main cause of inputs’ endogeneity) by a long list of observed firm-specific fixed effects coming from the ICSs. Controlling for the largest set of IC variables and plant characteristics, we can get—under standard regularity conditions—consistent and unbiased least squares estimators of the parameters of the PF and the INF and IC elasticities. Furthermore, we use two different functional forms of the PF—Cobb-Douglas and Translog—under two different assumptions on the input-output elasticities: equal input-output elasticities in all industries (restricted case) and different input-output elasticities by industries (unrestricted case).

Notice that even if we are only interested in assessing the impact of infrastructure on TFP, we do not limit the scope of the control analysis to only this subset of IC variables. We include (and therefore control for) all the IC factors because of the crucial role IC variables play as proxies for the unobserved fixed effects; this is the key feature of this methodology in order to provide robust empirical results. If we tried to estimate only the impact of infrastructure, without controlling for the other blocks of IC variables, we might get different signs on certain coefficients because of the omitted variables problem (Escribano and Guasch, 2008).

Another econometric problem we have to face when estimating the parameters of the INF and IC variables—either from the two-step or single-step procedure—is the possible endogeneity of some of these variables. That is, many INF or IC variables are likely to be determined simultaneously along with any TFP measure. With these productivity equations, the traditional instrumental variable (IV) approach is difficult to implement, given that we only have information for one year, and therefore we cannot use the natural instruments for inputs, such as those provided by their own lags. As an alternative correction for the endogeneity of the INF and IC variables, we use the region-industry-size

> 12 Notice that the demeaned TFP concept of equation (4.3b) corresponds to the observable part of the fixed effects equation (4.1c).

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