This projects is a continuation of my research in high-dimensional econometrics models. At the current stage of the project our need for computational resources has increased as explained in the latest activity report. I therefore have increased the requested allocation of computing hours. The current focus is panel models with long time dimensions. The individual time series reveal information about unit heterogeneity. Justifying methods that exploit this information is often theoretically challenging as it requires one to control statistical error simultaneously over a large number of time series. The theory builds on recent advances in high-dimensional statistics for serially correlated data. A substantial contribution of this project is conducing a rich set of simulations. These simulations check that the theoretical predictions about the properties of the new statistical tests developed within this project are both correct and relevant for small and medium sample sizes.