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The idea that people suffering from anxiety have a proclivity to consume alcohol to relieve their symptoms is supported by reports showing high comorbidity rates of alcohol and anxiety problems. The authors reviewed relevant epidemiologic surveys, family studies, and field studies and conclude that the relationship between alcohol problems and anxiety appears to be variable among the anxiety disorders. In agoraphobia and social phobia, alcohol problems appear more likely to follow from attempts at self-medication of anxiety symptoms, but panic disorder and generalized anxiety disorder may be more likely to follow from pathological alcohol consumption. Simple phobia does not appear to be related to alcohol problems in any meaningful way.
Kushner et al. (1990) studied this question.