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The U.S. military spends roughly $100 million annually to place advertisements to promote enlistments. Army data for 1981 to 1984 exhibit substantial cross-sectional and times series variation in advertising intensities, which enables estimation of advertising effects separately for four media (television, radio, magazines, and newspapers) using a functional form allowing media-specific, S-shaped response functions and relatively flexible, media-specific lag structures. We find that army advertising was very productive in producing enlistments; response functions for television, radio, and magazines are consistent with widespread advertising practice; lag patterns differ substantially over media; and the army's allocation of spending across media was nearly optimal.
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Dertouzos et al. (2006) studied this question.
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