# A Statistical Analysis of Industrial Penetration and Internet Intensity in Taiwan +
## 3 [PERSON] Sample Selection Model  
Manufacturing firms may make decisions to use the internet and to purchase raw materials and components online simultaneously, possibly leading to sample selection bias. Some enterprises that purchase online are a subset of manufacturing firms, forming a non-randomly selected sample from manufacturing firms. Therefore, observations on the amount of internet purchases taken and the corresponding firm-specific characteristics, are available only for those who use the internet to purchase raw materials and components. Therefore, a manufacturing firm that uses the internet to purchase raw materials and components online has a different preference structure from that of a non-user. In order to draw appropriate conclusions about the larger population of all manufacturing firms in Taiwan, and not just the subpopulation of manufacturing firms from which the firm reports the internet purchase data are taken, the [25] [PERSON] (1979) two-stage estimation procedure for a continuous decision variable can be used to incorporate the amount of internet purchases and the decision to have joint internet purchases ([26] [PERSON] 1974; [25,27] [PERSON] 1976, 1979; [28] [PERSON], 1981). This method assumes that the decisions to use the internet and purchase raw materials online are made simultaneously (that is, the error terms of the two equations are correlated). It is assumed that a zero observation represents the decision not to use the internet to purchase materials, so no individual firm is observed at the standard corner solution, namely a special solution to an agent's maximization problem, in which the quantity of one of the arguments in the maximized function is zero. Therefore, the demand curve for the internet purchaser is established only for manufacturing firms that have reports of internet purchases online. All non-users are assumed to not want to use the internet purchase mechanism, so firms that do not use the internet will not influence the demand curve for purchases online ([29] [PERSON] and [PERSON], 1992). In order to correct the problem of sample selection bias, this paper uses the [PERSON] selection model ([24] [PERSON] 1974; [23,25] [PERSON] 1976, 1979; [28] [PERSON], 2003), which assumes that there exists an underlying regression relationship, as given below:  
Regression equation:  
\[ \begin{array}{rl}y_{i}=x_{i}^{\prime}\beta+u_{yi},&i=1,\;2,\ldots,n\\ u_{yi}\sim\mathrm{N}\Big{(}0,\sigma_{y}^{2}\Big{)}\end{array}  \tag{1}\]  
where \(x_{i}^{\prime}\) is a vector of explanatory variables for each \(i\), and \(u_{yi}\) is the error term for observation \(i\). However, the dependent variable, \(y_{i}\), is not always observed. Rather, the dependent variable for observation \(i\) is observed if \(\omega_{i}^{\prime}\gamma+u_{zi}>0\), as (\(\omega_{i}^{\prime}\)) is the vector of variables that determines whether the dependent variable, \(y_{i}\), is observed or unobserved (that is, selected or not selected). The selection equation is given as follows:  
Selection equation:  
\[ \begin{array}{rl}z_{i}^{*}\;=\;\omega_{i}^{\prime}\gamma+u_{zi},&i=1,\;2, \ldots,n\\ u_{zi}\sim\mathrm{N}(0,\;1)\\ corr(u_{yi},u_{zi})=\rho\end{array}  \tag{2}\]  
When \(\rho\
eq 0\), Ordinary Least Squares (OLS) estimation applied to Equation (1) yields biased estimates. As \(z_{i}^{*}\) is latent, it is more convenient to specify a binary variable, \(z_{i}\), that identifies the observations for which the dependent is observed (\(z_{i}^{*}\
eq 0\)) or not observed (\(z_{i}^{*}=0\)). Therefore, the selection mechanism and regression model is reformulated as follows:  
Selection mechanism:  
\[ \begin{array}{rl}z_{i}=\omega_{i}^{\prime}\gamma+u_{zi}=1,&\text{if}\;z_{i}^ {*}>0\\ z_{i}=\omega_{i}^{\prime}\gamma+u_{zi}=\;0,&\text{otherwise}\\ \text{prob}(z_{i}=1|\omega_{i})=\Phi\big{(}\omega_{i}^{\prime}\gamma\big{)}& \text{and}\end{array}  \tag{3}\]  
where \(\Phi(\cdot)\) is the standard normal cdf (cumulative distribution function). Regression (or observation) equation:  
\[