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Econometrics Procedures
 

DEEPCAUSAL Procedure

Missing Values

Treatment Variable

The input treatment variable cannot have missing values. If the input treatment variable has missing values, PROC DEEPCAUSAL terminates with an error.

Outcome Variable

In the DNN training stage of the outcome model, the missing outcome values are replaced by imputed values. For more information, see the TARGETMISSING= option. In the inference stage, the observations that have missing outcome values have missing values for residuals and any estimates that need residuals.

Covariate

In the DNN training stage of the propensity score model or the outcome model, the missing covariate values are replaced by imputed values. For more information, see the MISSING= option. In the inference stage, the observations that have missing covariates are ignored. However, the probability mass function (PMF) of the treatment variable (normal upper P normal r left-parenthesis t equals 0 right-parenthesis or normal upper P normal r left-parenthesis t equals 1 right-parenthesis) considers all observations. As mentioned in the section Treatment Variable, each observation has a nonmissing treatment variable, and that value is used for calculating the PMF of the treatment variable.

Parameter of Interest

For any parameter of interest, psi left-parenthesis y Subscript i Baseline comma bold x Subscript i Baseline comma t Subscript i Baseline comma ModifyingAbove alpha With caret left-parenthesis bold x Subscript i Superscript left-parenthesis 2 right-parenthesis Baseline right-parenthesis comma ModifyingAbove beta With caret left-parenthesis bold x Subscript i Superscript left-parenthesis 2 right-parenthesis Baseline right-parenthesis comma normal upper Lamda left-parenthesis bold x Subscript i Baseline right-parenthesis comma t Superscript asterisk Baseline right-parenthesis is assigned a missing value if any component of it is missing, except for the following two subpopulation parameters of interest:

  • rho Subscript 0 comma 0: If t Subscript i Baseline equals 1, then psi Subscript 0 comma 0 Baseline left-parenthesis y Subscript i Baseline comma bold x Subscript i Baseline comma t Subscript i Baseline comma ModifyingAbove alpha With caret left-parenthesis bold x Subscript i Superscript left-parenthesis 2 right-parenthesis Baseline right-parenthesis comma ModifyingAbove beta With caret left-parenthesis bold x Subscript i Superscript left-parenthesis 2 right-parenthesis Baseline right-parenthesis comma normal upper Lamda left-parenthesis bold x Subscript i Baseline right-parenthesis comma t Superscript asterisk Baseline right-parenthesis equals 0 always holds no matter whether any component of it is missing for i equals 1 comma ellipsis comma n, where n is the number of observations in the input data table.

  • rho Subscript 1 comma 1: If t Subscript i Baseline equals 0, then psi Subscript 1 comma 1 Baseline left-parenthesis y Subscript i Baseline comma bold x Subscript i Baseline comma t Subscript i Baseline comma ModifyingAbove alpha With caret left-parenthesis bold x Subscript i Superscript left-parenthesis 2 right-parenthesis Baseline right-parenthesis comma ModifyingAbove beta With caret left-parenthesis bold x Subscript i Superscript left-parenthesis 2 right-parenthesis Baseline right-parenthesis comma normal upper Lamda left-parenthesis bold x Subscript i Baseline right-parenthesis comma t Superscript asterisk Baseline right-parenthesis equals 0 always holds no matter whether any component of it is missing for i equals 1 comma ellipsis comma n, where n is the number of observations in the input data table.

Last updated: July 09, 2026