# An Analysis of the Supply of Open Government Data
## 3 Material and Methods
### Empirical Analysis  
In this section, we test if political and social institutions such as civil rights, transparency, quality of democracy, and political participation, as well as economic and sociodemographic characteristics at the country level (such as the size of the economy, the efficiency of the government, the demand for Internet services, the median age of the population of a country, and the size of the population), can explain the global variability in the supply of open government data. To test our hypotheses, we used one of the most popular tools in data science and economics: a linear regression analysis. This allowed us to estimate the marginal effect of how changes in independent variables (such as the size of the economy of a country, the sociodemographic characteristics of individuals in a country, civil liberties, and transparency) affect the supply of open government data. In the next model (see Equation (1)), we postulate that cross-country differences in the supply of open government data are associated with political and economic factors that affect the quality of democracy and the incentives of governments to provide open government data:  
\[Od_{i}=\alpha+\beta^{\prime}X+\ \varepsilon_{i} \tag{1}\]  
In Equation (1), the differences in the supply of open government data across countries \(Od_{i}\) for \(i=1,\ldots\)\(I\), where the sub-index distinguishes the different countries in our sample, is explained by a set of \(k\) independent variables contained in the vector \(X\) (such as political participation, the size of the economy, socio-demographic characteristics of households, and indicators of demand for Internet services). The vector \(\beta\prime=[\beta_{1},\beta_{2}\cdot\ldots\beta_{k}\,]\) represents the marginal effect of exogenous changes in \(X_{i}\) in our indicator of the supply of open government data; that is to say, \(\frac{\partial Od_{i}}{\partial X_{i}}=\beta_{i}\). Our model also allowed us to test whether the marginal effect of \(X_{i}\) on open government data was statistically significant or not. Finally, \(\varepsilon_{i}\) is a random error term from our model. To be more specific, the model we tested in our analysis is specified as follows:  
\[ \begin{array}{c}Od_{i}=\alpha+\beta_{1}GdpPP_{i}+\beta_{2}Dem_{i}+\beta_{3} PolPar_{i}+\beta_{4}\mathit{Liberty}_{i}+\beta_{5}Trans_{i}+\beta_{6}Pop_{i}\\ +\beta_{7}Age_{i}+\beta_{8}GovEfficiency_{i}+\beta_{9}IntPen_{i}+\varepsilon_{i} \end{array}  \tag{2}\]  
Hence, in Equation (2), our model tests the postulated determinants of the supply of open government data discussed in Section 2.1 of this paper. Therefore, we were interested in testing whether the supply of open government data is associated with changes in the economic size of the country (see \(GdpPP_{i}\), which is the purchasing power parity of the gross domestic product of a country and affects the demand of open government data and its corresponding supply). The effect of the quality of democracy of a country is defined as \(Dem_{i}\), which is a metric that measures the function, state, and trust of political freedoms and civil liberties through pillars such as political participation of citizens (defined as \(PolPar_{i}\)), civil liberties (defined as \(\mathit{Liberty}_{i}\)), and the transparency of a country's government (see \(Trans_{i}\)). Other determinants in our model are the size of the population (defined as \(Pop_{i}\)) and the sociodemographic characteristics in a country (characterized by the median age of the population of a country, \(Age_{i}\)). Besides that, there is the efficiency of the government (labelled as \(GovEfficiency_{i}\)), which is an index that measures and compares per country the burden of government regulation, legal framework performance, and transparency of public policies, and our indicator of demand for Internet services (defined by \(IntPen_{i}\), or Internet penetration), which is the number of Internet users as a proportion of the population in each country.