The "MPG Illusion" demonstrates that consumers systematically misjudge fuel savings when evaluating vehicle efficiency in linear distance-per-volume metrics (Miles Per Gallon) compared to inverse volume-per-distance metrics (Liters per 100 kilometers). While existing literature establishes that information framing broadly affects Willingness-To-Pay (WTP), empirical architectures isolating the causal effect of mathematical metric representation—independent of explicit cost translation—remain underdeveloped. This protocol details a rigorous experimental design to isolate the effect of mathematically equivalent representations on objective comprehension and economic valuation. By employing a multi-level measurement hierarchy linking computational benchmarks to a randomized Discrete Choice Experiment (DCE), this study utilizes a Mixed Multinomial Logit (MMNL) framework built on an invariant physical consumption metric. We estimate the Average Treatment Effect (ATE) of metric framing on WTP, formally testing whether the valuation effect is mediated by objective fuel-cost comprehension across a nonlinear efficiency baseline, while strictly controlling for prior metric familiarity.
Consumer vehicle purchasing decisions exhibit persistent anomalies regarding fuel economy valuation. Previous research has established that fuel-economy information presentation can alter stated valuation and that consumers systematically misperceive fuel-cost differences. The present protocol is designed to isolate a narrower causal mechanism: whether alternative mathematical representations of identical physical fuel consumption—MPG versus L/100 km—alter objective comprehension and WTP when cost information, vehicle attributes, and underlying physical efficiency are strictly held constant. We propose the following testable hypotheses:
Larrick & Soll (2008) established the MPG illusion, demonstrating that linear metrics cause systemic undervaluation of fuel savings at low baseline efficiencies and overvaluation at high baselines. Allcott (2011) documented systematic fuel-cost misperceptions, while Allcott & Knittel (2019) tested whether providing additional fuel-economy information changes vehicle purchases and found no statistically or economically significant effect on average fuel economy purchased. Long et al. (2021) experimentally demonstrated that fuel-economy information presentation causally changes valuation; however, their conditions primarily compared MPG against monetary fuel costs and savings rather than purely isolating mathematical representation. Furthermore, recent stated- and revealed-preference evidence (Petrov, Carroll & Denny, 2025) highlights the divergence that can arise between information interventions in hypothetical choice settings and actual effects on observed vehicle purchases.
The functional unit of measurement is the Marginal Willingness-To-Pay (WTP), alongside the objective calculation error (RMSEfuel). Critically, all experimentally displayed efficiency values are generated from a common underlying physical-consumption parameter, qijt, measured internally in L/100km.
The econometric specification uses this invariant physical-consumption measure (qijt) rather than the displayed numerical metric, preventing coefficient-scale differences from being mistaken for framing effects. To ensure the main framing effect is interpretable at a meaningful baseline, physical consumption is mean-centered: qijtc=qijt-q̅.
Measurements are organized according to increasing economic realism and construct breadth, rather than a strict ranking of measurement validity:
Participants are randomized into four information conditions representing the same underlying vehicle and fuel-consumption scenarios. All arms receive identical vehicle attributes, purchase prices, expected mileage, fuel prices, visual prominence, font sizes, and layouts.
A prospective Monte Carlo power analysis will simulate 5,000 synthetic datasets for each candidate sample size using prespecified effect sizes and variance components informed by prior literature, estimating the complete MMNL model in each replication and selecting the smallest sample size achieving at least 0.90 power at α=0.05. Cross-validation employs a K-fold strategy (K=5) partitioned strictly at the respondent level to prevent individual-specific preference leakage.
Parameter estimation relies on an MMNL model where the utility of alternative j in task t for individual i is:
Because qijtc is derived from L/100 km, higher values indicate greater fuel consumption; accordingly, the expected sign of βq is negative. To avoid pathological WTP distributions resulting from a random price coefficient near zero, the model will impose a log-normal sign-constrained distribution on βp,i or be estimated in WTP space. Parameter uncertainty for WTP will be calculated via 10,000 draws from N(β̂,Σ̂).
| Arm | Information Condition | Experimental Purpose |
|---|---|---|
| A | MPG (Linear Baseline) | Control condition representing standard US labeling. |
| B | L/100 km (Inverse Volume-per-Distance) | Isolates the representation effect (ATEB-A) without providing cost data. |
| C | Annual Fuel Cost ($) | High-information benchmark condition (translation effect). |
| D | MPG + Fuel Cost | Determines if the effect is driven by metric substitution or supplementary information. |
This protocol outlines a strictly controlled empirical architecture to determine if the mathematical representation of efficiency alters economic valuation. By enforcing a measurement hierarchy that separates objective comprehension from stated WTP using an invariant and centered underlying physical metric, this methodology rigorously tests whether representing fuel consumption in L/100 km reduces the measured comprehension and valuation distortions associated with MPG framing.