Using Wasserstein Generative Adversarial Networks for the Design of Monte Carlo Simulations (1909.02210v3)

Abstract: When researchers develop new econometric methods it is common practice to compare the performance of the new methods to those of existing methods in Monte Carlo studies. The credibility of such Monte Carlo studies is often limited because of the freedom the researcher has in choosing the design. In recent years a new class of generative models emerged in the machine learning literature, termed Generative Adversarial Networks (GANs) that can be used to systematically generate artificial data that closely mimics real economic datasets, while limiting the degrees of freedom for the researcher and optionally satisfying privacy guarantees with respect to their training data. In addition if an applied researcher is concerned with the performance of a particular statistical method on a specific data set (beyond its theoretical properties in large samples), she may wish to assess the performance, e.g., the coverage rate of confidence intervals or the bias of the estimator, using simulated data which resembles her setting. Tol illustrate these methods we apply Wasserstein GANs (WGANs) to compare a number of different estimators for average treatment effects under unconfoundedness in three distinct settings (corresponding to three real data sets) and present a methodology for assessing the robustness of the results. In this example, we find that (i) there is not one estimator that outperforms the others in all three settings, so researchers should tailor their analytic approach to a given setting, and (ii) systematic simulation studies can be helpful for selecting among competing methods in this situation.

• The paper introduces a novel approach using WGANs to generate realistic simulation data for robust econometric analyses.
• It employs the Wasserstein distance to stabilize GAN training, effectively replacing traditional data-generation methods.
• Simulation experiments on benchmark datasets demonstrate that doubly robust estimators provide consistent treatment effect estimates.

Using Wasserstein Generative Adversarial Networks for the Design of Monte Carlo Simulations

The paper by Susan Athey, Guido W. Imbens, Jonas Metzger, and Evan Munro introduces a novel approach to leveraging Generative Adversarial Networks (GANs), specifically Wasserstein GANs (WGANs), in the design of Monte Carlo simulations for econometric analysis. This work is grounded in the context of econometrics where causal inference is a central focus, and it proposes a method to enhance the credibility of simulation studies by closely mimicking the intricacies of real data.

Context and Motivation

Econometric methodologies often rely on simulation studies to evaluate the performance of new estimators. However, a limitation arises due to the discretion researchers have in choosing the data-generating processes, leading to concerns about the relevance or real-world robustness of these evaluations. The authors address these concerns by proposing the use of GANs, an advanced machine learning framework, to generate datasets that mirror real-world examples more accurately, thus reducing researcher bias.

Methodology

The paper focuses on WGANs due to their theoretical stability and ability to measure distance between distributions using the Wasserstein metric. The GAN framework involves two neural networks: the generator, which creates data samples, and the discriminator (or critic, in the case of WGANs), which evaluates how similar these samples are to actual data.

1. GAN Framework Overview:
   • Generator: A neural network that produces synthetic data by transforming random noise.
   • Discriminator/Critic: A neural network that differentiates between real and generated data, guiding the generator's learning process.
2. WGANs: They optimize the Earth-Mover distance (Wasserstein distance), which provides more stable training dynamics compared to the original GAN framework. The authors employ a penalty method rather than weight clipping to enforce the Lipschitz constraint required by the WGAN framework.
3. Implementation: To showcase the method, the authors apply it to the estimation of average treatment effects using the classic Lalonde-Dehejia-Wahba dataset—a benchmark in the program evaluation literature. They address challenges such as the generation of treatment effects conditional on covariates, using Conditional GANs (CGANs).

Empirical Strategy

The empirical strategy involves three samples derived from the Lalonde-Dehejia-Wahba data: experimental, CPS, and PSID samples. The generated data is compared against actual data to test how well various estimators perform in terms of bias, root mean square error (RMSE), and coverage of confidence intervals.

1. Outcome Models: Techniques like linear models, random forests, and neural networks are used to estimate conditional outcome means.
2. Propensity Score Models: Propensity scores are assessed using logistic regression, random forests, and neural networks.
3. Doubly Robust Methods: These combine both outcome models and propensity scores for more reliable estimation of treatment effects.

Results and Implications

The authors report that no single estimator universally outperforms others across all settings, highlighting the importance of context-specific approaches. The doubly robust estimators generally perform well across various conditions, corroborating their theoretical appeal.

• Robustness: Simulation results were consistent across different subsamples and model architectures, indicating robustness in the WGAN-generated datasets.
• ATE Estimation: The generated datasets allow for accurate estimation of Average Treatment Effects (ATE), providing a realistic baseline against which various econometric estimators can be tested.

Future Directions and Applications in AI

This paper not only enhances the methodological toolkit for econometric analysis but also opens pathways for more credible simulations in other fields using AI. The intersection of machine learning and econometrics highlighted in this paper suggests further exploration into using AI-based models for causal inference and other econometric challenges.

By integrating machine learning techniques into econometric methodologies, this research exemplifies a significant shift towards more nuanced and realistic data generation processes, fostering a more reliable assessment of econometric models.