# 3 Data and Linear Models of Productivity

We consider the same data as those used by Canning (1999) and Canning and Bennathan (2000). For output we use purchasing power parity<sup>5</sup> GDP per worker (chain index). In both studies, physical capital stocks are constructed using a perpetual inventory method. The initial stock is obtained by assuming a capital-output ratio of 3% in the base year. The ‡ows of investments are taken from the Penn World Tables 6.00. As Canning, we assume a constant depreciation rate of 7% for the private capital. Canning shows that his results are robust to variations in the initial choice of capitaloutput ratio and the depreciation rate. Finally, human capital per worker is taken to be the average years of schooling of the workforce. Given the data availability, the average years of schooling of the workforce is approximated here by the average years of schooling of the total population aged 15 and above<sup>6</sup> , from Barro and Lee (2000). Since these human capital data are available only every ...ve years, Canning proposes to interpolate to give annual data.

We use four infrastructure capital stock variables: the number of telephones, kilowatts of electricity generating capacity and the length of paved roads and the railways line length, both expressed in kilometers. The infrastructure ...gures are the processed data from Canning (1998). The corresponding maximal sample is 1950-1995. As stated by Canning, these physical measures do not re‡ect the quality di¤erences in infrastructure across countries and over time. The e¤ectiveness of infrastructure may depend on its quality both initially and in terms of maintenance. But as noted by Canning, a simple ...xed e¤ect speci...cation allows to capture a part of these cross country quality di¤erences, more precisely the part which is constant over time. Consequently, in all our models, individual ...xed e¤ects are introduced.

The estimation of a threshold model requires the use of a balanced panel. For each speci...cation, i.e. for each type of infrastructure, we select countries (among a total of 146 countries) for which we have a complete data set on the relevant variables over the longest period. The period of estimation is chosen in order to maximize the total number of observations. That is why, as in previous studies, the composition of our panel varies with the type infrastructure considered. For each speci...cation, the sample used and the number of included countries are reported in Table 1. The countries can be divided in four groups: low income countries (LIC), lower middle income countries (LMI), upper middle income countries (UMI) and high income countries (HIC). These groups are based on World Bank de...nitions.

In order to asses the comparability of our data sets to the data sets used in previous studies, we ...rst estimate the augmented production function in linear panel models. As in Calderon and Serven (2004), we propose simple estimators of the equation (2). The results are reported in Table 2. First, we consider a model in which the four infrastructures are simultaneously introduced in the production function. It can be seen

> 5 It is important to note that in Penn World Tables, ”real” means ”PPP converted” instead of ”in constant price”.

> 6 Variable code: TYR15, Barro and Lee (2000), ”International Data on Educational Attainment: Updates and Implications”, Harvard University, February 2000.

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