We consider the estimation of treatment effects in settings when multiple treatments are assigned over time and treatments can have a causal effect on future outcomes . We formulate the problem as a linear state space Markov process with a high dimensional state and propose an extension of the double/debiased machine learning framework to estimate the dynamic effects of treatments  . Our method  allows the use of arbitrary machine learning methods to control for the high dimensional state  , subject to a mean square error guarantee, while still allowing parametric estimation and construction of confidence intervals for the dynamic treatment effect parameters of interest. Our method is based on a sequential regression peeling process, which we show can be equivalently interpreted as a Neyman orthogonal moment estimator. This allows us to show root-n asymptotic normality of the estimated causal effects .
We consider the estimation of treatment effects in settings when multiple treatments are assigned over time and treatments can have a causal effect on future outcomes or the state of the treated unit. We propose an extension of the double/debiased machine learning framework to estimate the dynamic effects of treatments , which can be viewed as a Neyman orthogonal (locally robust) cross-fitted version of g-estimation in the dynamic treatment regime . Our method applies to a general class of non-linear dynamic treatment models known as Structural Nested Mean Models and allows the use of machine learning methods to control for potentially high dimensional state variables , subject to a mean square error guarantee, while still allowing parametric estimation and construction of confidence intervals for the structural parameters of interest. These structural parameters can be used for off-policy evaluation of any target dynamic policy at parametric rates, subject to semi-parametric restrictions on the data generating process. Our work is based on a recursive peeling process, typical in g-estimation, and formulates a strongly convex objective at each stage, which allows us to extend the g-estimation framework in multiple directions: i) to provide finite sample guarantees, ii) to estimate non-linear effect heterogeneity with respect to fixed unit characteristics, within arbitrary function spaces, enabling a dynamic analogue of the RLearner algorithm for heterogeneous effects, iii) to allow for high-dimensional sparse parameterizations of the target structural functions, enabling automated model selection via a recursive lasso algorithm. We also provide guarantees for data stemming from a single treated unit over a long horizon and under stationarity conditions .
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. We formulate the problem as a linear state space Markov process with a high dimensional state and
or the state of the treated unit. We
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, which can be viewed as a Neyman orthogonal (locally robust) cross-fitted version of g-estimation in the dynamic treatment regime
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applies to a general class of non-linear dynamic treatment models known as Structural Nested Mean Models and
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arbitrary
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the
potentially
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variables
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dynamic treatment effect
structural
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Our method
These structural parameters can be used for off-policy evaluation of any target dynamic policy at parametric rates, subject to semi-parametric restrictions on the data generating process. Our work
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sequential regression
recursive
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which we show can be equivalently interpreted as a Neyman orthogonal moment estimator. This
typical in g-estimation, and formulates a strongly convex objective at each stage, which
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show root-n asymptotic normality of the estimated causal effects
extend the g-estimation framework in multiple directions: i) to provide finite sample guarantees, ii) to estimate non-linear effect heterogeneity with respect to fixed unit characteristics, within arbitrary function spaces, enabling a dynamic analogue of the RLearner algorithm for heterogeneous effects, iii) to allow for high-dimensional sparse parameterizations of the target structural functions, enabling automated model selection via a recursive lasso algorithm. We also provide guarantees for data stemming from a single treated unit over a long horizon and under stationarity conditions