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This paper studies an asymptotic framework for conducting inference on parameters of the form φ(θ 0 ), where φ is a known directionally differentiable function and θ 0 is estimated byθ n . In these settings, the asymptotic distribution of the plug-in estimator φ(θ n ) can be readily derived employing existing extensions to the Delta method. We show, however, that (full) differentiability of φ is a necessary and sufficient condition for bootstrap consistency whenever the limiting distribution ofθ n is Gaussian. An alternative resampling scheme is proposed which remains consistent when the bootstrap fails, and is shown to provide local size control under restrictions on the directional derivative of φ. We illustrate the utility of our results by developing a test of whether a Hilbert space valued parameter belongs to a convex seta setting that includes moment inequality problems, tests of random utility models, and certain tests of shape restrictions as special cases (e.g. tests of monotonicity of the pricing kernel or of parametric conditional quantile model specifications).

As consumers spend more time on their mobile devices, a focal retailer's natural approach is to target potential customers in close proximity to its own location. Yet focal (own) location targeting may cannibalize profits on infra-marginal sales. This study demonstrates the effectiveness of competitive locational targeting, the practice of promoting to consumers near a competitor's location. The analysis is based on a randomized field experiment in which mobile promotions were sent to customers at three similar shopping areas (competitive, focal, and benchmark locations). The results show that competitive locational targeting can take advantage of heightened demand that a focal retailer would not otherwise capture. Competitive locational targeting produced increasing returns to promotional discount depth, whereas targeting the focal location produced decreasing returns to deep discounts, indicating saturation effects and profit cannibalization. These findings are important for marketers, who can use competitive locational targeting to generate incremental sales without cannibalizing profits. While the experiment focuses on the effects of unilateral promotions, it represents the first step in understanding the competitive implications of mobile marketing technologies.

T his research examines the effects of hyper-contextual targeting with physical crowdedness on consumer responses to mobile ads. It relies on rich field data from one of the world's largest telecom providers who can gauge physical crowdedness in real-time in terms of the number of active mobile users in subway trains. The telecom provider randomly sent targeted mobile ads to individual users, measured purchase rates, and surveyed purchasers and nonpurchasers. Based on a sample of 14,972 mobile phone users, the results suggest that, counterintuitively, commuters in crowded subway trains are about twice as likely to respond to a mobile offer by making a purchase vis-à-vis those in noncrowded trains. On average, the purchase rates measured 2.1% with fewer than two people per square meter, and increased to 4.3% with five people per square meter, after controlling for peak and off-peak times, weekdays and weekends, mobile use behaviors, and randomly sending mobile ads to users. The effects are robust to exploiting sudden variations in crowdedness induced by unanticipated train delays underground and street closures aboveground. Follow-up surveys provide insights into the causal mechanism driving this result. A plausible explanation is mobile immersion: As increased crowding invades one's physical space, people adaptively turn inwards and become more susceptible to mobile ads. Because crowding is often associated with negative emotions such as anxiety and risk-avoidance, the findings reveal an intriguing, positive aspect of crowding: Mobile ads can be a welcome relief in a crowded subway environment. The findings have economic significance because people living in cities commute 48 minutes each way on average, and global mobile ad spending is projected to exceed $100 billion. Marketers may consider the crowdedness of a consumer's environment as a new way to boost the effectiveness of hyper-contextual mobile advertising.Data, as supplemental material, are available at http://dx.