In this guest blog written by #PPSVirtual20 Presenter Mark Garratt, Partner and Co-Founder of in4mation insights, learn about time-varying parameters (TVP) for price elasticity.
TVPs are a method of letting many kinds of measurements change over time. For instance, we usually derive price elasticity from a model that includes 2-3 years of data. But what happens if we have a time like the present moment with COVID-19 when all kinds of metrics may be in flux?
Models that use 2-3 years of data will treat the current moment as a rare outcome – on the tail of the distribution, whereas, in fact, we could well be shifting to a new regime. TVP is a way to let the KPIs that we use evolve with time and to see those evolutions the moment they happen.
Usually when we need to keep track of fast moving KPIs such as trends, price or price gaps, we might shift to three month moving averages or “3MMs.”
The problem with 3MMs, however, is that by shortening the period of the rolling average to get a read on near-term events, we may overfit the recent data resulting in less reliable predictions. There is a direct tradeoff between the near-term accuracy of the estimate and its variance.
Fixing the variance problem by using either a model based on 2-3 years or data or by using a 12-month moving average results in estimates that are more stable but they may now be considered “out of date” because they put too much weight on the past. Dynamic Linear Models (DLMs) were designed to solve the problem of loss of accuracy as the estimate becomes more local in time.
Time-varying parameters (TVP) – deliberately letting the estimate evolve over time - are a natural extension of DLMs.
The aim of TVPs, then, is to achieve a statistically robust read of KPIs in near real time. The model is allowed to “wander” to fit the data, but it can’t wander too far without some persistence in the pattern of change. The example below shows a TVP for price elasticity:
In this case, the blue line (top) shows the change in the price index from Dec 2016 to Feb 2019. Two big price increases happen in December of 2017 and 2018. The gray line (bottom), shows the price elasticity (PE) for a typical product and how it evolves over time. One thing that stands out right away is that the PE curve oscillates in a regular pattern.
This turns out to be tied in with the unique seasonal cycle in this industry. The macro movement, meanwhile, shows a steady increase in absolute PE from Dec 2016 to Dec 2017, reaching a low during the Dec 2017 price increase.
After that, however, the macro trend in PE stabilized for a year until the added shock of the Dec 2018 increase. Why did the price stabilize in 2018? One reason may have been the ramp up in media and consistent new product introductions during this time.
The client learned a lot from these TVPs. Many people in the business did not think that demand was at all elastic. They thought that their protection and masking strategies were flawless. This analysis showed them that they were elastic – not using a single number out of a “black box” model but as a KPI moving over time with the pulse of their business.
They also learned (not shown here) that some markets were more sensitive to price and others not sensitive at all. This enabled them to target their strategies to offset negative response to increased price.
Finally, it led them to understand that their business had “sensitivity cycles.” If they were doing spot A/B tests they might get different responses depending on the time of year.
Mark Garrett is a featured presenter at the Fall Pricing Workshops and Conference Virtual Event!