Consistent Evidence on Duration Dependence of Price Changes

Research Question. 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?

Methodology. 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.

Interest Rates and Inflation

Reconciling the consensus view that raising short rates fights inflation with the quantity-theoretic evidence that inflation and interest rates move together with money growth in the long run, this paper builds a segmented-markets exchange economy that can do both. In the model, all agents share the same preferences and constant endowment, but only a fraction λ (“traders”) participate in the bond market where open-market operations occur, while “non-traders” never do; this segmentation, adapted from Grossman-Weiss/Rotemberg-style models, generates a genuine short-run liquidity effect – an open-market bond purchase lowers the nominal interest rate by an amount proportional to a coefficient φ that depends on the degree of segmentation – while the underlying equation of exchange still ties long-run inflation to money growth exactly as the quantity theory predicts. Introducing velocity shocks and working through a sequence of policy examples, the paper shows that a money-growth rule that can be conditioned on the contemporaneous velocity shock can hit an announced inflation target exactly, for any shock process, whereas Taylor-type interest-rate feedback rules, though they use exactly the same information, generically cannot do as well: because they tie the interest rate to a base rate determined by long-run (Fisherian) considerations outside the policymaker’s control, “committing to a Taylor rule amounts to tying the hands of the monetary authority in a way that can only limit its effectiveness” at controlling inflation. The paper’s headline conclusion is a “qualified affirmative answer” to whether interest-rate policy can be rationalized within an essentially quantity-theoretic framework: yes, once markets are segmented enough to generate a liquidity effect, but the specific practice of following a Taylor rule for inflation control alone cannot be justified as better than direct money-growth management, and must instead be rationalized by some other policy objective, such as smoothing real interest rates in the presence of endowment risk that segmented markets prevent agents from pooling.

Fernando Alvarez | Macro Paper Warehouse

Consistent Evidence on Duration Dependence of Price Changes

Interest Rates and Inflation