Business, Stephen M. Ross School of - Working Papers Series
http://hdl.handle.net/2027.42/35324
2016-07-26T19:53:57ZIdentification with Models and Exogenous Data Variation
http://hdl.handle.net/2027.42/122724
Identification with Models and Exogenous Data Variation
Kahn, R. Jay; Whited, Toni M.
We distinguish between identification and establishing causality. Identification means forming a unique mapping from features of data to quantities that are of interest to economists. Establishing causality is synonymous with finding sources of exogenous variation. These two issues are often confused. However, exogenous variation is only sometimes necessary and never sufficient to identify economically interesting parameters. Instead, even for causal questions identification must rest on an underlying economic model. We illustrate these points by examining identification in two recent papers: one causal study relying on an entirely verbal model and one non-causal study relying on a formal mathematical model.
2016-07-01T00:00:00ZOn (Re-Scaled) Multi-Attempt Approximation of Customer Choice Model and its Application to Assortment Optimization
http://hdl.handle.net/2027.42/122455
On (Re-Scaled) Multi-Attempt Approximation of Customer Choice Model and its Application to Assortment Optimization
Chung, Hakjin; Ahn, Hyun-Soo; Jasin, Stefanus
Motivated by the classic exogenous demand model and the recently developed Markov chain model, we propose a new approximation to the general customer choice model based on random utility called multi-attempt model, in which a customer may consider several substitutes before finally deciding to not purchase anything. We show that the approximation error of multi-attempt model decreases exponentially in the number of attempts. However, despite its strong theoretical performance, the empirical performance of multi-attempt model is not satisfactory. This motivates us to construct a modification of multi-attempt model called re-scaled multi-attempt model. We show that re-scaled 2-attempt model is exact when the underlying true choice model is Multinomial Logit (MNL); if, however, the underlying true choice model is not MNL, we show numerically that the approximation quality of re-scaled 2-attempt model is very close to that of Markov chain model. The key feature of our proposed approach is that the resulting approximate choice probability can be explicitly written. From a practical perspective, this allows the decision maker to use off-the-shelf solvers, or borrow existing algorithms from literature, to solve a general assortment optimization problem with a variety of real-world constraints.
2016-06-01T00:00:00ZCapacity Investment with Demand Learning
http://hdl.handle.net/2027.42/122454
Capacity Investment with Demand Learning
Qi, Anyan; Ahn, Hyun-Soo; Sinha, Amitabh
We study a firm’s optimal strategy to adjust its capacity using demand information. The capacity adjustment is costly and often subject to managerial hurdles which sometimes make it difficult to adjust capacity multiple times. In order to clearly analyze the impact of demand learning on the firm’s decision, we study two scenarios. In the first scenario, the firm’s capacity adjustment cost increases significantly with respect to the number of adjustments because of significant managerial hurdles, and resultantly the firm has a single opportunity to adjust capacity (single adjustment scenario). In the second scenario, the capacity adjustment costs do not change with respect to the number of adjustments because of little managerial hurdles, and therefore the firm has multiple opportunities to adjust capacity (multiple adjustment scenario). For both scenarios, we first formulate the problem as a stochastic dynamic program, and then characterize the firm’s optimal policy: when to adjust and by how much. We show that the optimal decision on when and by how much to change the capacity is not monotone in the likelihood of high demand in the single adjustment scenario, while the optimal decision is monotone under mild conditions and the optimal policy is a control band policy in the multiple adjustment scenario. The sharp contrast reflects the impact of demand learning on the firm’s optimal capacity decision. Since computing and implementing the optimal policy is not tractable for general problems, we develop a data-driven heuristic for each scenario. In the single adjustment scenario, we show that a two-step heuristic which explores demand for an appropriately chosen length of time and adjusts the capacity based on the observed demand is asymptotically optimal, and prove the convergence rate. In the multiple adjustment scenario, we also show that a multi-step heuristic under which the firm adjusts its capacity at a predetermined set of periods with exponentially increasing gap between two consecutive decisions is asymptotically optimal and show its convergence rate. We finally apply our heuristics to a numerical study and demonstrate the performance and robustness of the heuristics.
2016-07-01T00:00:00ZA Theory of Multi-Tier Ecolabel Competition
http://hdl.handle.net/2027.42/120918
A Theory of Multi-Tier Ecolabel Competition
Lyon, Thomas P.
We model competing ecolabels sponsored by an industry trade association and an environmental group. For either sponsor in autarky, multi-tier labels are more attractive when there are many producers with high cost of quality, and the cost gap between low-cost and high-cost firms is large. When the two sponsors compete using binary ecolabels, multiple equilibria exist, and either sponsor may oﬀer the more ambitious label; competition may increase environmental protection. When sponsors compete using multi-tier labels, however, there exists a unique equilibrium and competition produces less environmental protection than would the NGO in autarky.
2016-01-01T00:00:00Z