Managing Urban Deer

Conflicts are emerging between humans and wildlife populations adaptable to the high density of humans found in urban and suburban areas. In response to these threats, animal control programs are typically designed with the objective of establishing and maintaining a stable population. This article challenges this view by studying the management of urban deer in Irondequoit, NY. Pulsing controls can be more efficient than steady-state regimes under a wide range of conditions in both deterministic and stochastic environments, but potential gains can be dissipated by management constraints. The effect of citizen opposition to lethal control methods is also investigated.     

An Empirical Model of Advertising Dynamics

This paper develops a model of dynamic advertising competition, and applies it to the problem of optimal advertising scheduling through time. In many industries we observe advertising “pulsing”, whereby firms systematically switch advertising on and off at a high-frequency. Hence, we observe periods of zero and non-zero advertising, as opposed to a steady level of positive advertising. Previous research has rationalized pulsing through two features of the sale response function: an S-shaped response to advertising, and long-run effects of current advertising on demand. Despite considerable evidence for advertising carry-over, existing evidence for non-convexities in the shape of the sales-response to advertising has been limited and, often, mixed. We show how both features can be included in a discrete choice based demand system and estimated using a simple partial maximum likelihood estimator. The demand estimates are then taken to the supply side, where we simulate the outcome of a dynamic game using the Markov perfect equilibrium (MPE) concept. Our objective is not to test for the specific game generating observed advertising levels. Rather, we wish to verify whether the use of pulsing (on and off) can be justified as an equilibrium advertising practice. We solve for the equilibrium using numerical dynamic programming methods. The flexibility provided by the numerical solution method allows us to improve on the existing literature, which typically considers only two competitors, and places strong restrictions on the demand models for which the supply side policies can be obtained. We estimate the demand model using data from the Frozen Entree product category. We find evidence for a threshold effect, which is qualitatively similar to the aforementioned S-shaped advertising response. We also show that the threshold is robust to functional form assumptions for the marginal impact of advertising on demand. Our estimates, which are obtained without imposing any supply side restrictions, imply that firms should indeed pulse in equilibrium. Predicted advertising in the MPE is higher, on average, than observed advertising. On average, the optimal advertising policies yield a moderate profit improvement over the profits under observed advertising.JEL Classification: L11, L66, M30 M37 R12