The Worldwide Governance Indicators (WGI) are well-known proxies for institutions and are widely used in many studies across different disciplines. Each of the six WGI is constructed by aggregating several baseline indicators that reflect information about a single latent variable. The method used, however, assumes that the errors associated with the baseline indicators are independent. Here, we extend this method by allowing cluster dependence among those errors. The differences between the original and new estimates of the WGI are statistically significant. We compare the results of two highly cited papers with the ones obtained from our method to illustrate that the new indices can alter their conclusions.