  The U.S. Census Longitudinal Business Database (LBD) product contains
employment and payroll information of all U.S. establishments and firms dating
back to 1976 and is an invaluable resource for economic research. However, the
sensitive information in LBD requires confidentiality measures that the U.S.
Census in part addressed by releasing a synthetic version (SynLBD) of the data
to protect firms' privacy while ensuring its usability for research activities,
but without provable privacy guarantees. In this paper, we propose using the
framework of differential privacy (DP) that offers strong provable privacy
protection against arbitrary adversaries to generate synthetic heavy-tailed
data with a formal privacy guarantee while preserving high levels of utility.
We propose using the K-Norm Gradient Mechanism (KNG) with quantile regression
for DP synthetic data generation. The proposed methodology offers the
flexibility of the well-known exponential mechanism while adding less noise. We
propose implementing KNG in a stepwise and sandwich order, such that new
quantile estimation relies on previously sampled quantiles, to more efficiently
use the privacy-loss budget. Generating synthetic heavy-tailed data with a
formal privacy guarantee while preserving high levels of utility is a
challenging problem for data curators and researchers. However, we show that
the proposed methods can achieve better data utility relative to the original
KNG at the same privacy-loss budget through a simulation study and an
application to the Synthetic Longitudinal Business Database.
