A Catch-Curve Approach to Product Cohort Mortality: Estimating Discard and Export Rates from Observational Data Without Stock Registers

Every year, billions of electrical devices—refrigerators, washing machines, and coffee makers—reach the end of their useful lives. Some are scrapped locally, while others vanish across borders, often ending up in informal recycling streams that go uncounted. For policymakers trying to build a circular economy, where materials are kept in use as long as possible, this lack of data is a blind spot. We know how many new machines are sold, but we rarely know how long they actually last before being thrown away or shipped abroad. Without this knowledge, it is impossible to tell if a new law helping people repair their toasters is actually working, or to understand exactly how much electronic waste is leaving a country without a trace.

To fill this gap, a researcher at Ostfalia University of Applied Sciences in Germany has adapted a method long used by fisheries biologists to study fish populations. In the ocean, scientists estimate how many fish are dying by counting how many are caught at different ages. If they see fewer older fish than expected, they can calculate the rate at which the population is disappearing, even without knowing exactly how many fish were born. This paper applies that same logic to consumer products. Instead of fish, the "catch" consists of old appliances found at recycling centers. By counting how many machines of different ages arrive for disposal, the researcher can reconstruct the life story of a product cohort, estimating when they are discarded and when they are exported, all without needing access to private sales records or government stock registers.

The study began by testing this new approach against a known reality. The researcher used detailed, publicly available data on six types of household appliances in Norway, where the true history of every product's life was already mapped out by other scientists. This provided a perfect control group to see if the new method could find the truth. The results were striking. A method that looks at a single snapshot in time—counting all the old fridges and washing machines in a recycling center on one specific day—proved unreliable. It often got the trend completely wrong, suggesting that machines were living longer when they were actually dying sooner, or vice versa. This happened because the snapshot mixed up machines from different sales years, confusing the age of the product with the volume of sales in those years.

However, a different approach worked with near-perfect accuracy. Instead of a single snapshot, this method tracks the same group of products over time, like following a specific class of students from graduation year to graduation year. By observing the same batch of appliances as they age from one year to the next, the researcher could isolate the true rate at which they were being discarded. This "cohort-diagonal" method recovered the exact trend of product lifespans for all six appliances tested, with errors so small they were almost negligible. It proved that by watching products age in real-time at recycling points, one can accurately measure how long they last without ever needing to know how many were originally sold.

The research also tackled a second, more complex puzzle: separating the products that are thrown away locally from those that are exported. In the ocean, scientists distinguish between fish that die of natural causes and those caught by fishermen. Similarly, this study treats domestic scrapping as one type of loss and cross-border export as another. The math shows that you cannot figure out the exact split between these two just by counting total losses; you need an independent piece of information, like a specific record of how many machines are being deregistered locally, to solve the equation. While the study did not solve this split for every product, it provided the first formal framework to do so, turning a vague "export gap" into a measurable, age-specific problem.

Perhaps the most practical innovation is a new way to measure the success of repair initiatives. The researcher introduced a simple ratio: the number of broken items brought in for repair compared to the number brought in for disposal. If more people are bringing in a specific type of appliance to be fixed than to be thrown away, it signals a strong willingness to keep products alive. This "repair-to-discard" ratio offers a direct, observable signal of whether policies like the European Union's Right to Repair directive are changing consumer behavior. Unlike previous methods that had to guess at repair rates based on complex models, this ratio can be counted directly at community repair cafes and recycling centers.

Looking ahead, the researcher proposes a four-year field survey in Germany to put these methods to work in the real world. The plan involves visiting recycling centers and repair cafes to count the age of discarded and repaired items for four specific categories: refrigerators, washing machines, vacuum cleaners, and coffee makers. The goal is to see if the repair ratio shifts after new laws come into effect, providing a clear, data-driven answer to whether these policies are working. However, the study is careful to note that while the method works beautifully when applied to theoretical data, applying it to real-world counts of discarded items requires a final, untested correction to account for how product failure rates naturally change as they get older. Until that correction is validated, the field survey will provide raw, valuable counts of what is being thrown away and repaired, but the precise calculation of lifespan trends will remain a work in progress.

The ultimate value of this work lies in its ability to turn the invisible into the visible. By borrowing a tool from the ocean and applying it to our kitchens and living rooms, the research offers a way to see the hidden life cycle of our possessions. It shows that we do not need perfect sales records to understand how long our products last; we only need to watch them carefully as they arrive at the end of their journey. This shift from guessing to observing could fundamentally change how we design policies for a circular economy, ensuring that efforts to extend the life of our devices are based on what is actually happening, not just on what we assume is happening.