to higher chances that innovation outcomes are successful in the second equation may also (positively) affect productivity outcomes in the third equation (simultaneity).

There have been two main approaches in the literature on how to solve the model. Crepon et al. (1998) suggest solving the model simultaneously using Asymptotic Least Squares.<sup>10</sup> Meanwhile, Griffith et al. (2006) assume that there are no feedback effects and solve the model sequentially, instrumenting knowledge activities in the innovation equation, and innovation outputs in the productivity equation, to avoid endogeneity.

In the original CDM model, the authors solved the model simultaneously using Asymptotic Least Squares (ALS), a minimum distance estimator.<sup>11</sup> This approach is advantageous when the joint distribution of observed variables does not have a closed form and when numerical integration techniques are computationally burdensome. Consistent estimates are first obtained in each equation via maximum likelihood, and then the structural parameters are obtained by minimizing their distance to the reduced form estimates using the empirical covariance matrix weighting function.

Most subsequent papers have followed a sequential approach, where predicted values of one endogenous variable are entered in the estimations of the other equations, correcting for standard errors by bootstrapping methods and using IV in each stage to account for endogeneity, see Griffith, Huergo, Mairesse, and Peters (2006). One benefit to this approach lies in its ability to take into account measurement issues arising in the nature of survey data. For example, firms that do not report undertaking R&D may in fact still possess knowledge outputs. However, one drawback from this approach is that it does not allow to correlation across the different stages that are captured using a structural methodology. Furthermore, standard errors may be underestimated in the model’s last stage.

Recent advances in numerical simulation techniques have made possible solving of the model by full information maximum likelihood with given distributions for the random part of the model. This approach is able to fully exploit the complex interactions in the data without relying on approximations to functional forms. Mohnen and Hall (2013) discuss the tradeoffs between efficiency and robustness to misspecification. Hall, Lotti, and Mairesse (2009) find similar results comparing estimation, although larger standard errors using simultaneous maximum likelihood of all three stages than the sequential method. One extension they do not consider is to allow correlation between disturbances in the SEM model. The approach we follow is, therefore, to estimate the model simultaneously using the SEM estimator in STATA. For robustness, we also estimate the model sequentially using instruments of innovation inputs and outcomes as in Griffith et al. (2006) and compare the results with the SEM estimates.

# **5. ICT use in a sample of African countries**

## **5.1 The data**

We use data collected by the Enterprise Surveys innovation modules. The survey was implemented mainly in 2014 and has one section regarding ICT use that complements the section on innovation. Overall, the

> 10 This implies solving the knowledge function, innovation equation, and productivity equation simultaneously by maximum likelihood using as initial values the estimates of solving the model sequentially in the first place. 11 Alternatively, the model could be solved by GMM but it has been shown to be less efficient in large samples.

12