**Information Transmission and the Bullwhip Effect: An Empirical Investigation ** with Haim Mendelson *Management Science* May 2012, p. 860-875.

Online supplement

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

Abstract: This work distinguishes between two concepts that have often been confounded---the bullwhip effect and production smoothing. These phenomena appear antithetical, sharing opposing empirical tests: production variability exceeding sales variability for bullwhip, and vice versa for smoothing. But this is a false dichotomy. We differentiate between these two ideas with a new ``Bullwhip-Corrected Production Smoothing Metric" (BCPSM), 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 65% smooth production by at least 10% the variance of demand, despite the fact that 99% exhibit the bullwhip effect. Indeed, we estimate both the bullwhip effect (we find production 220% as variable as sales) and production smoothing (we find production would be 11% more variable without deliberate production stabilization). We develop our smoothing measure from a structural econometric production scheduling model, based on the Generalized Order-Up-To Policy.