High Frequency Evidence on the
Demand For Gasoline
Laurence Levin - Visa Decision Sciences
Matthew S. Lewis - The Ohio State University
Frank A. Wolak - Stanford University
Why do we care about gasoline demand?
• Understanding the elasticity of gasoline demand is
crucial for:
– Predicting gasoline price volatility and its impact on consumers
• Determining the impact of supply disruptions
• Evaluating policies intended to ease the impacts of shocks
– Evaluating policies that target negative externalities of vehicle
use and pollution
• Studies on a variety of topics often use (or replicate)
estimates from this literature:
– macroeconomic, automobile usage, public transit,
environmental, public finance and policy analysis
Existing Evidence on Demand Elasticity
• Nearly all studies utilize highly aggregated data
– Monthly, quarterly, or annual
– National time-series or state-level panel
• Difficult to capture response of consumers in a given
location on a given day
– Highly aggregated models require strong assumptions about the
nature of demand over time or across location
– Unobserved demand factors likely to result in incorrect estimates
• Studies have produced a wide range of estimates
Contributions of Our Analysis
• We utilize data on daily city-level gasoline expenditures
and prices from 243 U.S. cities
– Measures consumption at the point of sale
– Offers higher frequency and greater geographic detail
– Can avoid aggregation and better control for unobserved factors
• Primary Contributions:
1.
2.
3.
Provide a more robust estimate of demand elasticity
Demonstrate the importance of aggregation bias
Derive and decompose the different sources of bias that arise
in more aggregate models
Findings
• Our estimates of the price elasticity of gasoline demand
range from -.27 to -.38
• This is substantially more elastic than other studies have
estimated for recent years:
– Hughes, Knittel & Sperling (2008):
– Park & Zhao (2010) approximately:
– Small and Van Dender (2007):
-.03 to -.07
-.05 to -.10
-.07
• Note: Estimates using data from the 1970’s & 80’s are
closer to ours, however, our analysis suggests these
may also have been biased downward or the
correlations generating bias may have strengthened.
Findings
• Aggregating our data and estimating models similar to
previous studies reveals that estimated elasticities tend
to increase with the degree of aggregation
• A decomposition is derived to identify three different
sources of bias that can result from aggregation
• The decomposition is applied to our data to estimate the
magnitudes of each bias component at different levels of
aggregation
Data
• Sample period Feb. 1, 2006 to Dec. 30, 2009
• 243 U.S. metropolitan areas
• Gasoline expenditures from Visa card users:
– Total daily gasoline expenditures at metropolitan level
– Total daily number of cardholder transactions at gas stations in
each metropolitan area
– Total number of active cardholders in each area (by month)
• Daily city average retail prices:
– Prices reported by AAA based on data constructed by OPIS
• Station prices collected using fleet cards and direct feeds
Advantages of high-frequency panel data
• Daily city-level observations:
– Reveal how demand responds to fluctuations in the
prices consumers actually pay
• Using panel data models:
– Can compare how demand in different cities responds
to different price changes while controlling for national
macroeconomic factors
Prices fluctuate independently across cities
Demand also varies across cities
Empirical Model
1. Basic log-log static demand model:
ln 𝑄𝑗𝑑 = α𝑗 + λ𝑑 + β ln 𝑝𝑗𝑑 + ε𝑗𝑑
Qjd = per capita demand in city j on day d
pjd = average gasoline price in city j on day d
Advantages
– Similar to models used in previous studies
– Easy to examine the impacts of data aggregation
Empirical Model
2. Individual purchase model:
– Separates gasoline usage from purchase
– Demand 𝑑𝑗𝑑 for each customer in city j on day d:
ln 𝑑𝑗𝑑 = α𝑗 + λ𝑑 + β ln 𝑝𝑗𝑑 + ε𝑗𝑑
– Probability 𝜌𝑗𝑑 that consumer purchases is allowed to
vary across cities j and days d:
𝜌𝑗𝑑 = 𝛾𝑗 + 𝛿𝑑
Empirical Model
2. Individual purchase model (cont.)
– Likelihood of purchase linked to demand:
𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑑𝑒𝑚𝑎𝑛𝑑𝑒𝑑𝑗𝑑
𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑑𝑗𝑑 =
𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝑝𝑟𝑜𝑏 𝑜𝑓 𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑗𝑑
– Customer model is aggregated to the MSA level:
ln 𝑄𝑗𝑑 = α𝑗 + λ𝑑 + β ln 𝑝𝑗𝑑 + ln 𝑛𝑗𝑑 − ln 𝜌𝑗𝑑 + ε𝑗𝑑
Qjd = per capita demand in city j on day d
pjd = average gasoline price in city j on day d
njd = number of purchase transactions in city j on day d
𝜌jd = predicted probability of purchase in city j on day d
Estimates of Demand Model
Note: coefficients on ln(pricejd) represent estimates of the elasticity of
gasoline demand with respect to price
Estimates from Alternative Specifications
Interpretation and Response Horizon
• Our estimates are significantly more elastic than
those from studies using more highly
aggregated data
• Does using daily data generate an estimate of
response over a shorter time horizon?
– No!
– Regardless of observation frequency, the estimated
price coefficient captures the average demand
response over the entire duration of the price change
Prices fluctuate independently across cities
Examining Immediate Demand Response
• Unlike other studies we can separately examine
if consumers respond differently in the days
immediately following a price change.
• Approach: Include lagged prices in the demand
(and purchase probability) equations.
• Findings:
– Purchase probability responds very strongly within the
first day or two days, but little impact after a few days
– Demand responds immediately and persists for the
duration of the price change
Estimated Response Following a Sustained Price Change
Estimates from Disaggregate and Aggregate Models
Possible Sources of Aggregation Bias
• Differences in demand response across regions
– If price response actually differs across cities, then 𝛽 represents
a weighted average of these 𝛽𝑐s. Aggregation can change the
weights of this average in undesired ways.
• Aggregate models require stronger econometric
assumptions
– In disaggregated model OLS only requires pcd to be uncorrelated
with εcd. In aggregated model, each pcd must be uncorrelated
with all the unobserved shocks in the days and cities being
aggregated. (Main source of bias in aggregated panel models.)
• Harder to control for unobserved demand
changes in time-series models
– Can no longer use time-period fixed effects
(Main source of bias in time-series models.)
Implications for Studies Using Aggregate Data
• Significant bias can arise, likely resulting in
substantially less elastic demand estimates
– particularly when using time series models
• Likelihood of specific types of heterogeneity and
correlation in an empirical setting can be used
as indicators of potential bias
– to help explain different findings obtained by various
existing studies
– to guide empirical design and interpretation in future
work
Example: Elasticity of Demand to Gasoline Taxes
• Several recent studies have suggested that demand may
be more responsive to changes in gasoline tax than to
changes in gasoline price
– Li, Linn and Muehlegger (2014)
– Rivers and Schaufele (2015)
– Davis and Kilian (2011)
• Evidence interpreted to suggest that taxes changes may
be more salient to consumers
• Our findings suggest an alternative explanation:
– State tax changes are uniform and simultaneous within each state
– May exhibit less correlation with βc or with ε’s in other cities or days
Conclusions
• Gasoline demand more responsive to price in
the short-run than aggregate studies suggest
• Demand elasticity may be more responsive over
longer-run as well
– Channels through which consumers respond in shortrun are also relevant in the long-run
• miles driven, public transit usage, carpooling, multi-vehicle
households choosing to drive more efficient vehicles, etc.
– Same data aggregation issues may impact long-run
elasticity estimates
General Policy Implications
• Responses to temporary price fluctuations
– Supply disruptions have a smaller impact on price
– Policies intended to reduce price volatility (SPR?) will
be less necessary and less effective
• Responses to sustained price changes
– Fuel/carbon taxes or cap-and-trade programs are
more likely to be effective
– Necessary tax levels or expected permit prices are
likely to be much lower