Estimation of Conditional Random Coefficient Models using Machine Learning Techniques
利用机器学习估计条件随机系数模型AI 解读 ↓
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利用机器学习估计条件随机系数模型
- 研究问题
- 如何在高维控制变量条件下估计随机系数密度，从而区分连续处理偏效应中的可观测与不可观测异质性？
- 方法与思路
- 作者提出两阶段筛估计：先将条件随机系数密度近似为筛展开，再用机器学习及适当样本拆分估计条件期望形式的系数。
- 材料陈述的贡献
- 摘要称推导了密度估计的 L₂ 收敛率，并以随机森林模拟和经济实验应用展示方法；应用中识别出两类投资组合选择行为。
- 阅读关注点
- 应核对条件密度的识别依据、筛维数和样本拆分规则、逆问题病态性对速率的影响，以及行为类型划分的不确定性。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要未列识别条件和完整收敛率，行为类型结果依赖所用模型与实验数据。
原文摘要
Nonparametric random coefficient (RC)-density estimation has mostly been considered in the marginal density case under strict independence of RCs and covariates. This paper deals with the estimation of RC-densities conditional on a (large-dimensional) set of control variables using machine learning techniques. The conditional RC-density allows to disentangle observable from unobservable heterogeneity in partial effects of continuous treatments adding to a growing literature on heterogeneous effect estimation using machine learning. %It is also informative of the conditional potential outcome distribution. This paper proposes a two-stage sieve estimation procedure. First a closed-form sieve approximation of the conditional RC density is derived where each sieve coefficient can be expressed as conditional expectation function varying with controls. Second, sieve coefficients are estimated with generic machine learning procedures and under appropriate sample splitting rules. The $L_2$-convergence rate of the conditional RC-density estimator is derived. The rate is slower by a factor then typical rates of mean regression machine learning estimators which is due to the ill-posedness of the RC density estimation problem. The performance and applicability of the estimator is illustrated using random forest algorithms over a range of Monte Carlo simulations and with real data from the SOEP-IS. Here behavioral heterogeneity in an economic experiment on portfolio choice is studied. The method reveals two types of behavior in the population, one type complying with economic theory and one not. The assignment to types appears largely based on unobservables not available in the data.