https://macropaperwarehouse.com/authors/katarina-borovickova/Katarína BorovičkováHugo -- gohugo.ioen-ushttps://macropaperwarehouse.com/papers/consistent-evidence-on-duration-dependence-of-price-changes/https://macropaperwarehouse.com/papers/consistent-evidence-on-duration-dependence-of-price-changes/<p><strong>Research Question.</strong> This paper asks two related questions. First, can one develop a robust, distribution-free estimator for the discrete-time mixed proportional hazard (MPH) model of duration with unobserved heterogeneity? Second, what does that estimator reveal about the shape of the hazard of price changes, the role of heterogeneity in shaping aggregate price dynamics, and the distinction between regular price changes and sales?</p> <p><strong>Methodology.</strong> The authors develop a linear generalized method of moments (GMM) estimator for the discrete-time MPH model, building on identification results in Honoré (1993). The model specifies that the probability a price spell ends at duration t, conditional on surviving to t, equals the product of a product-specific frailty parameter θ (unobserved, fixed over time) and a common baseline hazard bt. The estimator exploits repeated price spells per product via moment conditions that are linear in bt, making estimation and inference straightforward. It accommodates right- and left-censored data, competing risks, and spell-specific observable characteristics, without requiring any parametric assumption on the frailty distribution. The estimator is consistent as the number of products grows, even with a short time dimension. A Hansen-Sargan J-test of overidentifying restrictions and a test of the monotone-average-type prediction are also developed.</p>