Synthetic Data and Differential Privacy in Economic Research

Data privacy is an important topic today, especially when collecting information about individuals and businesses. In the U.S., a valuable database called the Longitudinal Business Database (LBD) holds employment and payroll information for all U.S. businesses, dating back to 1976. Researchers often want to use this data to study economic trends, but the sensitive nature of this information means that privacy protections must be put in place.

One way to protect this information is by creating synthetic data, which is a fake dataset that mimics the real one but does not contain any real individual information. This allows researchers to conduct their work without risking someone’s privacy. However, not all synthetic data is created equally, and some methods do not provide solid privacy guarantees.

Differential Privacy (DP) is a strong method used to ensure that individual data remains protected while still allowing researchers to use it. This paper discusses the creation of synthetic data using differential privacy, focusing on heavy-tailed data, which often appears in economic studies, like income data.

#Why Synthetic Data?

Synthetic data can be made to look similar to real data without revealing any real information about individuals or companies. This is particularly useful when the original data is sensitive and cannot be shared openly. Traditional methods to protect data often fail to provide the same level of utility for researchers. This is where synthetic data comes into play, providing a balance between privacy and usability.

The concept of synthetic data allows researchers to conduct exploratory analysis while they wait for approval to access the more sensitive real dataset. By using synthetic data, they can test their methods and refine their analyses without compromising individual privacy.

#The Challenge of Heavy-Tailed Data

Heavy-tailed data refers to data distributions where extreme values or outliers are more common than in normal distributions. Income data is a typical example of heavy-tailed data, as there are often individuals with very high incomes compared to the average.

When generating synthetic data from heavy-tailed distributions, it is crucial to maintain the essential characteristics of the data, particularly the tail ends. This is a challenging task, as extreme values contain significant information but also raise privacy concerns.

If too much noise is added in the process of making the data private, the results may not accurately reflect the original dataset. On the other hand, if too little noise is added, the risk of revealing sensitive information increases. This delicate balance is essential for creating effective synthetic datasets.

#Differential Privacy Explained

Differential privacy offers a mathematical approach to measure and protect privacy when sharing data. It allows researchers to analyze data without being able to identify any single individual's data. The idea is that any change to a single individual’s data will have a minimal impact on the overall result, making it hard to determine if any one individual’s information has been included.

This method assigns a privacy budget to each database query, controlling how much privacy is lost with each analysis. A smaller privacy budget results in more noise being added to the data, which enhances privacy but may reduce the dataset's usefulness.

#Using K-Norm Gradient Mechanism

We propose using the K-Norm Gradient (KNG) mechanism in the context of differential privacy to generate synthetic data. KNG focuses on minimizing the amount of noise while still ensuring that the privacy of individual data is protected. This approach allows the generation of synthetic heavy-tailed data effectively.

By using quantile regression with KNG, we can estimate various quantiles of the data-the values below which a certain percentage of data falls. This technique is particularly useful for dealing with heavy-tailed data, helping to incorporate the characteristics of extreme values while maintaining privacy.

#Stepwise and Sandwich Methods

To improve how KNG works further, we propose two new methods: Stepwise KNG and Sandwich KNG. The Stepwise KNG approach estimates quantiles in a sequence, ensuring that each estimate can utilize the information from previously estimated points. This helps stabilize the estimates and leads to better performance with the privacy budget.

The Sandwich KNG method builds upon the Stepwise approach by allowing for additional flexibility in how privacy budgets are allocated among various quantiles. By ensuring that critical quantiles receive more privacy budget, we can enhance the overall utility of the synthetic data produced.

#Simulations to Test Methods

To evaluate the effectiveness of these new methods, we conducted simulations comparing traditional KNG with the Stepwise and Sandwich KNG mechanisms. We generated synthetic datasets using a known number of quantiles and measured how closely the synthetic data resembled the original data.

The results indicated that both the Stepwise and Sandwich methods provide better data utility than the traditional KNG approach. This means that researchers can derive more useful insights from synthetic datasets without compromising individual privacy.

#Application to SynLBD

We applied our methods to the Synthetic Longitudinal Business Database (SynLBD) to see how well they perform in practice. The SynLBD is a synthetic version of the LBD, and we aimed to create a new DP synthetic dataset using our methods.

We synthesized various employment variables for different years and industries, ensuring that our methods retained the critical characteristics of the original data. By doing so, we maintained the trends and relationships essential for further economic research.

Through this application, we found that our methods effectively preserved the trends over time while allowing researchers to access useful synthetic datasets. This is crucial for fields like economics, where understanding employment trends can inform policy decisions and business strategies.

#Evaluating Data Quality

To ensure the utility of the synthetic data, we compare it to the original data through various performance measures. General utility focuses on how closely the synthetic data matches the original data distribution, while specific utility examines the accuracy of statistical analyses performed using the synthetic data.

We utilized several utility measures in our evaluation, including the propensity score mean-squared error and the k-marginal test. These assessments help gauge how well the synthetic data can support research findings.

Our results show that our methods provide synthetic datasets with a reasonable level of utility, allowing researchers to carry out analyses similar to those they could perform with the original data.

#Privacy Considerations

While the generation of synthetic data is beneficial, it is essential to consider the trade-off between privacy and data utility. The methods we developed focus on maximizing data usability while ensuring that individual privacy is never compromised.

The key to effective synthetic data generation lies in finding the right balance between noise addition and the preservation of essential data characteristics. Our proposed methods help achieve this balance, making them suitable for various research applications.

#Future Directions

As we move forward in this area of research, there are several exciting opportunities to explore. One potential avenue is to develop more refined utility measures explicitly designed for differential privacy synthetic data. These measures could provide more standardized ways to evaluate the quality of synthetic datasets, making comparisons easier and more meaningful.

Additionally, we can investigate methods to address the bias introduced by privacy mechanisms during regression analyses. Finding a way to correct for this bias would enhance the usability of the synthetic data.

Finally, automating the tuning of certain parameters in our methods could significantly improve their efficiency. By developing systems that can adjust parameters dynamically based on the characteristics of the data, we can streamline the process of generating synthetic datasets.

#Conclusion

In summary, the development and application of synthetic data using differential privacy are critical for protecting individual privacy while allowing researchers to access valuable datasets. Our proposed methods-Stepwise KNG and Sandwich KNG-offer innovative solutions for generating synthetic heavy-tailed data with robust privacy guarantees.

Through simulations and real-world applications, we demonstrated the effectiveness of these methods. The ability to analyze sensitive data without compromising privacy can lead to significant advancements in various fields, especially economics.

As the discussion around data privacy continues to grow, leveraging techniques like those outlined in this work will be essential for responsible and insightful research. By ensuring that synthetic datasets remain both useful and secure, we can advance our understanding of complex issues while respecting individual privacy rights.