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Suppose we want to estimate a total effect with covariate adjustment in alinear structural equation model. We have a causal graph to decide whatcovariates to adjust for, but are uncertain about the graph. Here, we propose atesting procedure, that exploits the fact that there are multiple validadjustment sets for the target total effect in the causal graph, to perform arobustness check on the graph. If the test rejects, it is a strong indicationthat we should not rely on the graph. We discuss what mistakes in the graph ourtesting procedure can detect and which ones it cannot and develop twostrategies on how to select a list of valid adjustment sets for the procedure.We also connect our result to the related econometrics literature oncoefficient stability tests.

A Robustness Test for Estimating Total Effects with Covariate Adjustment