Bounded Attention and Attenuated Elasticities

When Shoppers Miss the Price Tag

When shoppers do not pay full attention to price changes, economists using standard models may mistakenly calculate a lower elasticity than what actually exists. This error is not caused by a lack of data or weak mathematical tools. Instead, it stems from a mismatch between how people behave and how models are built. A new study from the Vienna University of Economics and Business investigates this gap. It reveals that traditional methods for measuring consumer sensitivity can be systematically blinded by inattention.

Does the data hide the truth?

The core of the investigation asks a simple question: if consumers only partially perceive price fluctuations, what does a standard economist actually measure? Researchers rely on the "elasticity of substitution"—a metric describing how easily consumers switch from one product to another when prices change. This number is critical for calculating the welfare effects of new products or the impact of global tariffs.

The authors seek to determine if the "structural" elasticity (the true, underlying sensitivity of consumers) can be recovered from market data. Specifically, they look at whether the standard "covariance-based estimator"—a tool used to separate demand patterns from supply-side cost shocks—remains valid. This happens when the demand it measures is filtered through a lens of bounded attention.

The cracks in the rational benchmark

For decades, the workhorse of demand estimation has been the Constant Elasticity of Substitution (CES) model. This model assumes a "rational" market where consumers fully attend to every price change. Under this assumption, researchers observe changes in market shares and prices to pinpoint the elasticity.

However, the authors propose that this assumption ignores cognitive limits. They embed the CES model within a "sparse-max" framework. In this model, consumers anchor their perceptions to a default price and only partially adjust to the true market price. The study uses a log-linear perception rule (where consumers adjust to price changes in percentage terms) to define this behavior. This specific mathematical choice ensures the resulting demand response is a clean, scaled version of the true response.

Testing the illusion of precision

The researchers moved from theory to a controlled simulation of heterogeneous consumer markets. They created a digital environment with 15 different product varieties and up to 5,000 individual consumers. Each consumer had slightly different preferences. Crucially, they varied the "attention weight" ($m$), which represents how much of a price change a consumer actually notices.

The researchers first checked if simulating thousands of diverse consumers matched the behavior of a single "representative" consumer. As shown in, the deviation between the mass market and the individual model converges to a predictable floor.

This confirms their simulation was a reliable proxy for real-world populations.

The experiment involved running the standard Feenstra (1994) estimator on these simulated markets. The goal was to see if the estimator could "see through" the inattention to find the true elasticity ($\sigma_r$). The researchers performed a "panel length sweep." They increased the amount of historical data available to see if more information would eventually solve the problem.

A systematic failure of identification

The results were striking: the estimator does not just struggle with inattention. It consistently converges to the wrong answer. The authors report that the estimator returns an "attenuated" elasticity. This is the true elasticity scaled by the attention weight ($\hat{\sigma} = \sigma_r m$).

In their simulation, where the true elasticity was 15 and the attention weight was 0.5, the estimator returned a median value of 7.5 .

This is not a random error that averages out over time. As demonstrated in, increasing the length of the data panel does not move the estimate toward the truth.

Instead, more data simply makes the researcher more confident in the wrong number. While the "instruments" become stronger and the error bars narrow, the median remains stuck at the attenuated value.

The authors explain this via "observational equivalence." To the math used by the estimator, an inattentive market looks exactly like a perfectly rational market with a lower elasticity. Because the supply-side logic holds true for this lower elasticity, the model accepts it as the truth.

Redefining the bounds of certainty

The implications suggest that many current estimates of consumer sensitivity may be systematic lower bounds. If consumers are even slightly inattentive, the elasticity reported in literature is likely understated. This has consequences for welfare analysis. If we underestimate how much people switch products, we may miscalculate the costs of taxes or tariffs.

The paper does not suggest that the data is useless. Rather, it suggests the data is incomplete. Because the error is a "population identification failure," it cannot be fixed by simply collecting more data. To isolate the structural elasticity, researchers need information outside of simple price and quantity records.

One potential path involves using "attention instruments." These are external events that change how much people notice a price without changing the price itself. For example, the study mentions French regulations requiring supermarkets to flag price changes on shrinking packaging. Such interventions create a natural experiment. Comparing stores with high-salience warnings to those without could help separate the components of the attenuated elasticity.