The Use of Machine Learning in Treatment Effect Estimation
3.6 Conclusion
3 The Use of Machine Learning in Treatment Effect Estimation 105
hyperpr = 1
mage<15
6.4[101.1], (2%) mage≥19
−221.7[9.94](64%) −120.1[19.2], (27%) mage<22
85.2[60.1], (3%) −163.0[54.5], (3%) yes no
yes no
yes no
yes no
Fig. 3.1:A causal tree for the effect of smoking on birth weight (first time black mothers).
Notes: standard errors are in brackets and the percentages in parenthesis denote share of group in the sample. The total number of observations is𝑁=157,989 and the covariates used are𝑋1, except for the polynomial and interaction terms. To obtain a simpler model, we choose the pruning parameter using the 1SE-rule rather than the minimum cross-validated MSE.
negative with age (compare the two largest leaves on the𝑚 𝑎𝑔 𝑒≥28 and𝑚 𝑎𝑔 𝑒 <28 branches). Hypertension appears again as a potentially relevant variable, but the share of young women affected by this problem is small. We also note that the results are obtained over a subsample of𝑁=150,000 and robustness checks show sensitivity to the choice of the subsample. Nonetheless, the age pattern is qualitatively stable.
The preceding results illustrate both the strengths and weaknesses of using a causal tree for heterogeneity analysis. On the one hand, letting the data speak for itself is philosophically attractive and can certainly be useful. On the other hand, the estimation results may appear to be too complex or arbitrary and can be challenging to interpret. This problem is exacerbated by the fact that trees grown on different subsamples can show different patterns — suggesting that in practice it is prudent to construct a causal forest, i.e., use the average of multiple trees.
this literature is that machine learning can be fruitfully applied for this purpose if the nuisance functions enter the second stage estimating equations (more precisely, moment conditions) in a way that satisfies an orthogonality condition. This condition ensures that the parameter of interest is consistently estimable despite the selection and approximation errors introduced by the first stage machine learning procedure.
Inference in the second stage can then proceed as usual. In practice a cross-fitting procedure is recommended, which involves splitting the sample between the first and second stages.
In applications of thecausal tree or forestmethodology, the parameter of interest is the full dimensional conditional average treatment effect (CATE) function, i.e., the focus is on treatment effect heterogeneity. The method permits near automatic and data-driven discovery of this function, and if the selected approximation is re-estimated on an independent subsample (the ‘honest approach’) then inference about group-specific effects can proceed as usual. Another strand of the heterogeneity literature estimates the projection of the CATE function on a given, pre-specified coordinate to facilitate presentation and interpretation. This can be accomplished by an extension of the DML framework where in the first stage the nuisance functions are estimated by an ML method and in the second stage a traditional nonparametric estimator is used (e.g., kernel-based or series regression).
In our empirical application (the effects of maternal smoking during pregnancy on the baby’s birthweight) we illustrate the use of the DML estimator as well as causal trees. While the results confirm previous findings in the literature, they also highlight some limitations of these methods. In particular, with the number of observations orders of magnitude larger than the number of covariates, and the covariates not being very strong predictors of the treatment, DML virtually coincides with OLS and even the naive (direct) Lasso estimator. The causal tree approach successfully uncovers important patterns in treatment effect heterogeneity but also some that seem somewhat incidental and/or less straightforward to interpret. This suggests that in practice a causal forest should be used unless the computational cost is prohibitive.
In sum, machine learning methods, while geared toward prediction tasks in themselves, can be used to enhance treatment effect estimation in various ways. This is an active research area in econometrics at the moment, with a promise to supply exciting theoretical developments and a large number of empirical applications for years to come.
Acknowledgements We thank Qingliang Fan for his help in collecting literature. We are also grateful to Alice Kuegler, Henrika Langen and the editors for their constructive comments, which led to noticeable improvements in the exposition. The usual disclaimer applies.
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Chapter 4
Forecasting with Machine Learning Methods
Marcelo C. Medeiros
AbstractThis chapter surveys the use of supervised Machine Learning (ML) models to forecast time-series data. Our focus is on covariance stationary dependent data when a large set of predictors is available and the target variable is a scalar. We start by defining the forecasting scheme setup as well as different approaches to compare forecasts generated by different models/methods. More specifically, we review three important techniques to compare forecasts: the Diebold-Mariano (DM) and the Li-Liao-Quaedvlieg tests, and the Model Confidence Set (MCS) approach.
Second, we discuss several linear and nonlinear commonly used ML models. Among linear models, we focus on factor (principal component)-based regressions, ensemble methods (bagging and complete subset regression), and the combination of factor models and penalized regression. With respect to nonlinear models, we pay special attention to neural networks and autoenconders. Third, we discuss some hybrid models where linear and nonlinear alternatives are combined.
Marcelo C. MedeirosB
Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil, e-mail: mcm@econ.puc-rio.br
111