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In response to price dispersion across stores and price promotions over time, consumers search across both stores (spatial) and time (temporal), in many retail settings. Yet there is no search model in extant research that jointly endogenizes search in both dimensions. We develop a model of spatiotemporal search that nests a ﬁnite horizon model of spatial search across stores within an inﬁnite horizon model of inter-temporal search. The model is estimated using an iterative procedure that formulates it as a mathematical program with equilibrium constraints (MPEC) embedded within an E-M algorithm to allow estimation of latent class heterogeneity. The empirical analysis uses data on household store visits and purchases in the milk category. In contrast to extant research, we ﬁnd that omitting the temporal dimension underestimates price elasticity. We attribute this diﬀerence to the relative frequency of household stock outs and purchase frequency in the milk category. Further, contrary to the conventional wisdom that promotions increase store switching and reduces store loyalty, we ﬁnd that in the presence of search frictions, price promotions can be a store loyalty-enhancing tool.
Mojir, Navid and Sudhir, K., "Price Search Across Stores and Across Time" (2014). Cowles Foundation Discussion Papers. 2341.