108,490 research outputs found
Automatic Debiased Machine Learning of Causal and Structural Effects
Many causal and structural effects depend on regressions. Examples include
average treatment effects, policy effects, average derivatives, regression
decompositions, economic average equivalent variation, and parameters of
economic structural models. The regressions may be high dimensional. Plugging
machine learners into identifying equations can lead to poor inference due to
bias and/or model selection. This paper gives automatic debiasing for
estimating equations and valid asymptotic inference for the estimators of
effects of interest. The debiasing is automatic in that its construction uses
the identifying equations without the full form of the bias correction and is
performed by machine learning. Novel results include convergence rates for
Lasso and Dantzig learners of the bias correction, primitive conditions for
asymptotic inference for important examples, and general conditions for GMM. A
variety of regression learners and identifying equations are covered. Automatic
debiased machine learning (Auto-DML) is applied to estimating the average
treatment effect on the treated for the NSW job training data and to estimating
demand elasticities from Nielsen scanner data while allowing preferences to be
correlated with prices and income
Dynamic Mixture of Finite Mixtures of Factor Analysers with Automatic Inference on the Number of Clusters and Factors
Mixtures of factor analysers (MFA) models represent a popular tool for
finding structure in data, particularly high-dimensional data. While in most
applications the number of clusters, and especially the number of latent
factors within clusters, is mostly fixed in advance, in the recent literature
models with automatic inference on both the number of clusters and latent
factors have been introduced. The automatic inference is usually done by
assigning a nonparametric prior and allowing the number of clusters and factors
to potentially go to infinity. The MCMC estimation is performed via an adaptive
algorithm, in which the parameters associated with the redundant factors are
discarded as the chain moves. While this approach has clear advantages, it also
bears some significant drawbacks. Running a separate factor-analytical model
for each cluster involves matrices of changing dimensions, which can make the
model and programming somewhat cumbersome. In addition, discarding the
parameters associated with the redundant factors could lead to a bias in
estimating cluster covariance matrices. At last, identification remains
problematic for infinite factor models. The current work contributes to the MFA
literature by providing for the automatic inference on the number of clusters
and the number of cluster-specific factors while keeping both cluster and
factor dimensions finite. This allows us to avoid many of the aforementioned
drawbacks of the infinite models. For the automatic inference on the cluster
structure, we employ the dynamic mixture of finite mixtures (MFM) model.
Automatic inference on cluster-specific factors is performed by assigning an
exchangeable shrinkage process (ESP) prior to the columns of the factor loading
matrices. The performance of the model is demonstrated on several benchmark
data sets as well as real data applications
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