Imagine that you are in the process of buying a used car. You are considering a three-year-old Honda Accord, with 42,187 miles, and a five-year-old Toyota Camry, with 67,812 miles.
Now, close your eyes and try to remember the exact mileage of the two cars.
Chances are that you will recall the mileage of the Accord to be 42,000, or even 40,000, and the mileage on the Camry to be 67,000, or even 60,000.
You probably did not pay full attention to all of the digits, and focused only on the left-most one, or perhaps the first two on the left. You would not be the only one doing this. We recently conducted a “recall survey” similar to the example above with 127 students, and found that, while they correctly remembered the first digit of the mileage in more than 90% of cases, only 50% recalled the second digit correctly, and less than 15% recalled the other digits.
In most of the cases, these digits were reported to be zeros. In a number of studies, experimental psychologists have found evidence that this kind of “left-digit” bias in processing numbers is quite common.
The economic implications of simple cognitive shortcuts
Partially processing numbers is just one example of the types of simple cognitive shortcuts that we use every day when processing information, leading to systematic biases in decision making.
- When shopping or bidding online for an item, we might tend to focus on the “direct” price of the item, and not fully consider the shipping and handling costs.
- We might ensure that the carats of the diamond in the engagement ring we buy have the “right” first digit (e.g. 1 carat rather than a slightly less than 1 carat).
- When booking a hotel room, we might pay attention to the listed price, but not consider the price of various add-ons (internet connection, drinks from the room bar, etc.).
- If sales taxes are not reported on price tags, we might not immediately factor them into the full price of an item when deciding whether to buy it.
This inattention can have a large impact on the decisions we make in our lives (DellaVigna and Pollet 2007; Chetty et al. 2009; Finkelstein 2009; Hossain and Morgan 2006; Lee and Malmendier 2011; Englmaier and Schmoller 2008, 2009; Pope 2009; Scott and Yelowitz 2010). In fact, sellers might try to take advantage of these biases and “shroud” some attributes of products so as to influence our purchasing behaviour (Gabaix and Laibson 2006). Or, as frequently noted, they may set prices in order to take advantage of this inattention (Basu 1997, 2006).
But can these biases persist in highly competitive, large-stakes markets when full information is readily available?
Do biases persist?
Consider again the used-car market. Buying a car is a major, costly decision to which people dedicate a fair amount of time. This market is also highly competitive. However, consumer inattention to relevant information persists even in this environment and impacts the market in important ways. In our recent research (Lacetera et al. 2011), we examine a novel dataset on more than 22 million used-car transactions from wholesale auctions in the US. Our analysis shows that sale prices drop discontinuously at 10,000-mile marks. For example, cars with odometer values between 79,900 and 79,999 miles are sold on average for approximately $210 more than cars with odometer values between 80,000 and 80,100 miles, but for only $10 less than cars with odometer readings between 79,800 and 79,899. The size of the discontinuities is similar across each 10,000-mile threshold, consistently on the order of $150 to $200 (Figure 1), and we also find smaller price discontinuities at 1,000-mile thresholds. In auctions held at Canadian locations, we find no price discontinuities at 10,000-mile marks, but we do find price drops at 10,000-kilometre marks – not surprisingly, odometers in Canadian cars report kilometres and not miles.
Figure 1. Average residual sales price within 500-mile bins
Note: The adjusted residual value is obtained by removing make-model-model year-body effects from the sales price.
We show that these finding cannot be accounted for by observable differences in the types of cars that sell right before and right after 10,000-mile thresholds. Using a variety of tests, we also rule out the possibility that differences in unobservable car characteristics before and after 10,000-mile thresholds are driving the effects that we find. We also discuss how odometer tampering and the structure of warranties are not consistent with our findings. Ultimately, we reach the conclusion that these drops in prices are likely driven by the “left-digit bias” in how car buyers process the information about a car’s mileage.
Interestingly, some market participants are clearly savvy and aware of these threshold effects. This can be seen by looking at the number of cars that show up to the market in each mileage bucket. Figure 2 illustrates that there are large volume spikes in cars before 10,000-mile thresholds.
Figure 2. Raw counts within 500-mile bins
The price discontinuities that we find are consistent with a simple model of inattention. Based on the model and the empirical analyses, we set out to “quantify” the amount of inattention. We estimate that approximately 30% of the reduction in value caused by increased mileage on a car occurs discontinuously at these salient mileage thresholds. Finally, a range of evidence – including the volume patterns described above, purchase patterns for experienced versus inexperienced dealers at the auctions, pricing dynamics right before thresholds, and data from an online retail used-car market – are all suggestive that the price discontinuities reflect inattention mostly on the part of the final buyers of used car, and not of the agents (e.g. used-car dealers) who participate at the wholesale auctions. A recent study by Englmaier and Schmoller (2009) is consistent with this conclusion, because they show that the asking prices for used cars in an online market adjust discontinuously to registration-year changes even though there is information available on the website about the exact date of first registration for a car.
Our results suggest that a natural information-processing heuristic can limit the extent to which market participants incorporate even the information they are actively observing, when they are making decisions about high-stakes goods. Because of the size of the car market, this simple heuristic leads to a large amount of mispricing. Our estimates of the difference between observed selling prices and the prices that we would expect under full attention suggests approximately $2.4 billion worth of mispricing due to inattention in our full dataset. Additionally, the supply decisions of hundreds of thousands of cars were affected by this heuristic (e.g., sold right before a 10,000-mile threshold). Although it is likely that these distortions largely result in transfers of wealth between market participants rather than large economic inefficiencies, it is striking that this simple heuristic can so profoundly shape the supply decisions, wholesale prices, and retail prices of a competitive, durable-goods market.
We anticipate that heuristic numeric processing might impact a range of other settings, in particular environments where inferences are made based on continuous quality metrics. Examples include hiring or admissions decisions based on GPAs and test scores, the evaluation of companies based on financial reports (e.g., revenues), the treatment of medical test results, and how the public reacts to government spending programmes.
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