Neural Networks Solve a Fifty Year Old Problem in Economics
A new method borrows the mathematical engine of AI—the ReLU function—to make complex economic estimations faster, easier, and interpretable.
Economists have long struggled with the computational difficulty of predicting discrete choices—simple "yes or no" decisions like whether a person buys a house or enters the labor force. Since the 1970s, the "maximum score estimator" has been the standard tool for analyzing these choices when the data is messy or the underlying probability distributions are unknown. However, this method relies on "indicator functions"—mathematical switches that snap from zero to one. These rigid switches make the math "nonsmooth," meaning standard computer algorithms struggle to find the best solutions, often requiring fragile and slow search methods.
Research by Xiaohong Chen, Wayne Yuan Gao, and Likang Wen proposes a solution derived from the cutting edge of artificial intelligence. They replace the rigid indicator function with the "Rectified Linear Unit" (ReLU)—the fundamental mathematical building block of modern Deep Neural Networks (DNNs). Unlike the old method, the ReLU function is continuous and possesses a specific type of smoothness that allows computers to use gradient-based optimization.
“In practice, RMS can be optimized using off-the-shelf routines from machine learning, avoiding the fragile, combinatorial searches often required for discontinuous maximum score criteria.”
This shift offers two major advantages. First, it drastically improves statistical performance. The researchers demonstrate that this new "ReLU-based Maximum Score" (RMS) estimator converges on the correct answer faster than the traditional method. Second, and perhaps more importantly for practitioners, it bridges the gap between econometrics and machine learning. Because the RMS estimator functions like a layer in a neural network, economists can now estimate complex structural parameters using powerful, off-the-shelf AI software like PyTorch or TensorFlow.
The implications extend beyond simple binary choices. The authors show that this method can handle "multi-index" problems—complex scenarios where outcomes are determined by multiple interacting factors, such as consumers choosing between products based on both utility and awareness. By integrating these economic structures into neural networks, the research offers a way to utilize the flexibility of AI while retaining the interpretability of economic theory.