- Ergodicity and the Estimation of Markov Decision Processes
Abstract: I create a class of dynamic discrete choice estimators that exploit Markov chain ergodicity. The empirical likelihood of a Markov decision process depends only on the differences in the value function. And whereas the value function converges, with Bellman contractions, at the rate of cash flow discounting, the value function differences converge at the rate of cash flow discounting times the rate of Markov chain mixing (the subdominant eigenvalue of the state transition matrix). With this strong convergence result, I make Rust's (1987) nested fixed point (NFXP) estimator 200 times faster in problems with more than 2,000 states and Aguirregabiria and Mira's (2002) nested pseudo-likelihood (NPL) estimator 10 times faster in problems with more than 10,000 states. The refined estimators can also handle problems without discounting. I show that optimal policies are similar under discount factors 0.99 and 1.01, which indicates that (i) misspecifying the discount factor does not meaningfully bias the utility estimates, and (ii) small perturbations in the discount factor near one are not well-identified, despite having unbounded effects on the value function.
- Information Transmission and the Bullwhip Effect: An Empirical Investigation with Haim Mendelson
Management Science May 2012, p. 860-875.
Abstract: The bullwhip effect is the amplification of demand variability along a supply chain: a company bullwhips if it purchases from suppliers more variably than it sells to customers. Such bullwhips (amplifications of demand variability) can lead to mismatches between demand and production, and hence to lower supply chain efficiency. We investigate the bullwhip effect in a sample of 4,689 public U.S. companies over 1974-2008. Overall, about two thirds of firms bullwhip. The sample's mean and median bullwhips, both significantly positive, respectively measure 15.8% and 6.7% of total demand variability. Put another way, the mean quarterly standard deviation of upstream orders exceeds that of demand by $20 million. We decompose the bullwhip by information transmission lead time. Estimating the bullwhip's information-lead-time components with a two-stage estimator, we find that demand signals firms observe with more than three quarters' notice drive 30% of the bullwhip, and those firms observe with less than one quarter's notice drive 51%. From 1974-94 to 1995-2008, our sample's mean bullwhip dropped by a third.
- Production Smoothing and the Bullwhip Effect with Haim Mendelson
MSOM Spring 2015, p. 208-220.
Abstract: This work distinguishes between two related concepts---the bullwhip effect and production smoothing. These phenomena appear antithetical because they share opposing empirical tests: production variability exceeding sales variability for bullwhip, and vice versa for smoothing. But this is a false dichotomy. We differentiate between the two with a new production smoothing measure, which estimates how much more volatile production would be absent production volatility costs. We apply this metric to an automotive manufacturing sample comprising 162 car models. We find 75% of our sample smooths production by at least 5%, despite the fact that 99% exhibits the bullwhip effect; indeed, we estimate both a strong bullwhip (on average, production is 220% as variable as sales) and a strong degree of smoothing (on average, production would be 22% more variable without deliberate stabilization). We find firms smooth both production variability and production uncertainty. We measure production smoothing with a structural econometric production scheduling model, based on the Generalized Order-Up-To Policy.
- Multitasking, Multi-Armed Bandits, and the Italian Judiciary with Decio Coviello, Andrea Ichino, and Nicola Persico
Forthcoming at MSOM
Abstract: We model how a judge schedules cases as a multi-armed bandit problem. The model indicates that a first-in-first-out (FIFO) scheduling policy is optimal when the case completion hazard rate function is monotonic. But there are two ways to implement FIFO in this context: at the hearing level or at the case level. Our model indicates that the former policy, prioritizing the oldest hearing, is optimal when the case completion hazard rate function decreases, and the latter policy, prioritizing the oldest case, is optimal when the case completion hazard rate function increases. This result convinced six judges of the Roman Labor Court of Appeals---a court that exhibits increasing hazard rates---to switch from hearing-level FIFO to case-level FIFO. Tracking these judges for eight years, we estimate that our intervention decreased the average case duration by 12% and the probability of a decision being appealed to the Italian supreme court by 3.8%, relative to a 44-judge control sample.
- Auto Recalls: A Game of Chicken with Ahmet Colak
Abstract: We model a manufacturer's and regulator's joint recall decisions as an asymmetric dynamic discrete choice game. We estimate our model with a data set comprising 14,124 recalls and 976,062 defect reports. The agents use these reports to learn component quality, trading off between a fixed recall cost and a variable liability cost. Both agents perceive a recall to be less costly when initiated by the other. Hence, initiating auto recalls is a game of chicken: The agents want faulty products off the road but hold out for the other to act, increasing the average product's recall time by 1.81 years.
- Decoupling the Supply Chain with a Dynamic Discrete Choice Inventory Model with Oliver Yao, Jiazhen Huo, and Yongrui Duan
Abstract: Most supply chain works suppose retailers can credibly communicate costs to suppliers. But honest cost disclosure can be untenable because stores can shift the inventory burden upstream by inflating marginal costs (e.g., they can reduce stockout rates by exaggerating the goodwill lost to unsatisfied demand). So suppliers may not receive true cost estimates, preventing them from instituting optimal inventory policies. We develop an empirical means to resolve this supply chain ``cheap talk'' problem---to compel the supplier and retailer to coordinate optimally, even when the latter is dishonest. Rather than ask a retailer for its private costs, we estimate them directly with a dynamic discrete choice inventory model. We illustrate this approach with a 5,320-SKU, 1,371-day sample from a Chinese supermarket. We conclude the distribution center stocking out of the median product costs the store the equivalent of .03 shipments, .51 lost sales, or 37 days of storage.