GOODHART'S LAW AND MACHINE LEARNING: A STRUCTURAL PERSPECTIVE
构建了一个结构性模型，说明当训练数据干净但未来代理人以已知成本操纵协变量时，惩罚回归如何产生古德哈特偏差，并推导出抗操纵的预测算法。
Abstract We develop a simple structural model to illustrate how penalized regressions generate Goodhart bias when training data are clean but covariates are manipulated at known cost by future agents. With quadratic (extremely steep) manipulation costs, bias is proportional to Ridge (Lasso) penalization. If costs depend on absolute or percentage manipulation, the following algorithm yields manipulation‐proof prediction: Within training data, evaluate candidate coefficients at their respective incentive‐compatible manipulation configuration. We derive analytical coefficient adjustments: slopes (intercept) shift downward if costs depend on percentage (absolute) manipulation. Statisticians ignoring manipulation costs select socially suboptimal penalization. Model averaging reduces these manipulation costs.