Econometrics with Privacy Preservation

Many data are sensitive in areas such as finance, economics, and other social sciences. We propose an ER (encryption and recovery) algorithm that allows a central administration to do statistical inference based on the encrypted data, while still preserving each party’s privacy even for a colluding majority in the presence of cyber attack. We demonstrate the applications of our algorithm to linear regression, logistic regression, maximum likelihood estimation, the method of moments, and estimation of empirical distributions. Moreover, our algorithm can help to address another practically significant issue—privacy preservation for distributed statistical inference when data are allocated to different parties who are unwilling to share their own data with others. Finally, we provide two extensions of the applications of our algorithm, including the combination of our algorithm and Fourier transforms and the development of a modified root-finding method for recovering quantiles with privacy preservation.