Differential privacy is an emerging topic in Economics that has just recently started to gain more attention. In my thesis, I am trying to answer can econometric estimates be preserved when estimation is performed on differentially private synthetic data? While most current approaches to differential privacy in causal inference focus on making specific estimators differentially private, my approach will make synthetic data that is differentially private, so any estimator can be applied to this synthetic data. I will do this using generative adversarial networks (GANs). In doing so, I will also explore other differentially private methods for econometric estimators, as well as explore ways to achieve consistent standard errors when reporting these estimators.