Gasoline prices are a major contributor to inflation and have recently exhibited significant volatility.1 Several price series of the U.S. Bureau of Labor Statistics (BLS) track changes in gas prices throughout the supply chain from petroleum extraction to gas stations.2 The role of profits in driving inflation has been a closely followed issue in 2022 and 2023, and some research indicates that profits drove inflation in these years.3 BLS research on other industries, such as the automotive industry, shows that intermediaries in the supply chain can have an impact on consumer pricing, and that the impact of these intermediaries can be identified by examining the implicit statistical relationship between the BLS price indexes for each respective portion of the supply chain.4 The prices and indexes for wholesalers, retailer intermediaries, and final consumers should have statistically strong and economically meaningful relationships in industries in which quality change is low (this occurs with gasoline and other homogenous commodities). This article uses novel statistical methods that simulate the BLS gasoline price measures along the supply chain to demonstrate the internal statistical consistency of these methods, to show the validity of the methods, and to better understand the impact of gas station markups on gasoline inflation.5 Overall, gas station markups had volatile and varying impacts and pressures on gasoline price changes during the COVID-19 pandemic. There were three periods of price changes:
- March 2020 through April 2020, a period of rapid and strong inflationary pressure from gas station markup increases
- May 2020 through January 2021, a period of modest deflationary pressure from gas station markup decreases
- January 2021 through May 2023, a period of modest and steady inflationary impact from gas station markup increases
Theory and industry background
It is possible to simulate BLS price indexes by statistically isolating producer commodity, producer margins, or consumer commodity indexes from each of their respective supply chain counterparts. For example, Kevin M. Camp, Michael Havlin, and Sara Stanley show that the BLS margins index for dealership services in the auto industry can be approximated by the residual between the Producer Price Index (PPI) for completed vehicles and the Consumer Price Index (CPI) for completed vehicles.6 Camp, Havlin, and Stanley show that the residual between commodity indexes for completed vehicles generally tracked the dealership profit-margins index of the PPI. However, it is unclear in Camp, Havlin, and Stanley what is the true statistical relationship between the residual and the official margins index. Additionally, Michael Havlin introduces some additional methods showing that the CPI for completed vehicles can be simulated with an input price index that includes dealership markups.7
Although the methods used in the automotive market worked reasonably well, they are likely to work much better in a homogenous industry. There are several factors that could prevent the margins-simulation method from working perfectly for heterogenous goods like automobiles and other manufactured goods. First, a strong statistical correlation between approximated and official margins indexes may not be possible to simulate because BLS quality adjusts the commodity PPIs and CPIs but does not quality adjust the margins indexes. Gaps between the simulated approximation index and the official margins index could partially represent the isolated quality-adjustment differences between each commodity index and other technical differences. Second, time lags on either side of the retailing intermediaries could prevent a strong correlation between the approximated and the official margins indexes. Finally, one must add the regression residuals to the other regression parameters, namely, the intercept and beta coefficient, to complete the margins-simulation process suggested in Camp, Havlin, and Stanley.8
Industries are excellent test cases for examining the implicit theoretical interdependencies of the commodity and margins indexes in the CPI and PPI. A good test case is an industry that has a high degree of product overlap in the intermediate indexes, does not have a substantial amount of product-quality change, does not have large time lags in the supply chain, and has a high degree of product-flow overlap between supply-chain participants.
Also, industries that produce homogenous commodities, such as gasoline, are excellent test cases for examining the conditions and characteristics that may support the use of the methods developed in Havlin and Camp, Havlin, and Stanley. These methods can be tested with fewer confounding variables (such as quality change, sample-size differences, product-composition differences, and product-flow differences) in analyses of highly homogeneous gasoline indexes with large sample sizes. Nevertheless, technical differences between price-relative calculations, such as those involving geometric means and Laspeyres indexes, may continue to cause differences. Because of assumptions regarding consumer behavior, the CPI uses geometric means that tend to weaken the impact of large changes. Because the PPI does not use geometric means, large price changes may have a larger impact on PPIs than on CPIs. To test the methods developed in Havlin and Camp, Havlin, and Stanley, this article focuses on the CPI for gasoline, the PPI for gasoline, the PPI for automotive fuels and lubricants retailing (PPI for gasoline margins), CPI data on average gasoline prices, and Energy Information Administration (EIA) data on wholesale gasoline prices.
The regression model from Camp, Havlin, and Stanley suggests how the error term ϵt, plus the model intercept β0, and plus the beta coefficient β1 of a regression model fitted on the index levels Gasoline CPIt and Gasoline PPIt should estimate the PPI for gasoline margins for each month after rebasing to the same index levels.9 The gasoline margins PPI short-term price relative can also be simulated by inflating the CPI data on average gasoline prices by the CPI for gasoline each month and then subtracting from that figure the EIA data on wholesale gasoline prices inflated each month by the PPI for gasoline. These short-term price relatives can then be used to reconstruct the PPI for gasoline margins. (See appendix.)
Furthermore, Havlin demonstrates that the interdependencies of the PPI for a particular good and the PPI margin for that good should closely correlate—if not equal—the CPI for that same good. The gasoline input price index including markups is a weighted composite of the PPI for gasoline and the PPI for gasoline margins (demonstrated in the appendix). This index is conceptually similar to the composite input price indexes demonstrated by Jayson Pollock and Jonathan C. Weinhagen.10 Also, the gasoline input price index including markups is an application of the model used by Havlin.
The accuracy of the gasoline input price index including markups can be determined by regressing the index against the CPI for gasoline. This method is demonstrated by Don A. Fast and Susan E. Fleck.11 In this regression, because margins are explicitly incorporated into the model with a weighted-interaction term, the residual term between the CPI for gasoline and the gasoline input price index including markups should equal the cumulative impact of technical differences between the PPI for gasoline and the CPI for gasoline (this equality is similar to geometric means and sample-frame differences).
Both Fast and Fleck and Don Fast, Susan E. Fleck, and Dominic A. Smith provide a useful roadmap for assessing the performance of indexes designed to simulate official government statistics.12 Various test statistics are used by these researchers to assess the performance of simulations of margins and commodity indexes described above and shown below. The correlation coefficient, beta coefficients, and p-values from regressions on the percent changes of indexes (short-term price relatives) are used to assess short-term correlations. Longer term correlations are tested by graphical analysis of the index levels (long-term price relatives).
Data analysis and results
A comparison of the commodity and margins indexes in the gasoline industry shows their implicit relationships. These relationships are alluded to by Camp et al. and demonstrated by Havlin.13 Chart 1 shows that the PPI for gasoline margins increases when the PPI for gasoline falls at a faster rate than the CPI for gasoline. Similarly, when the PPI for gasoline rises at a faster rate than the CPI for gasoline, then the PPI for gasoline margins increases. For example, because of pandemic-related volatility, producer gas prices fell by 64.9 percent from January 2020 through April 2020, while consumer prices only fell by 25.6 percent. As a result of producer prices falling 153.6 percent more than consumer prices, the PPI for gasoline margins increased by 88.4 percent over the same period. Similarly, from April 2020 through July 2020, consumer prices increased by 15.1 percent while producer prices increased by 115.0 percent; as a result, the PPI for gasoline margins decreased by 28.3 percent over the same period.
Chart 2 and table 1 show the results of different methods for simulating the gasoline margins PPI. The first method, an enhancement of Camp, Havlin, and Stanley’s method, adds the residual of an ordinary least squares (OLS) model between the index levels of the PPI for gasoline and the CPI for gasoline to the intercept and the beta coefficient of the model and is then rebased. The intercept and beta coefficient represent the average gas station markup, and the residual represents deviations from that markup. Adding the three parameters together provides an index estimate of the markup. The second method, first demonstrated by Havlin,14 takes the CPI data for the average price of gasoline (starting from May 2019) and the EIA wholesale price (starting from May 2019) and then inflates each series by the CPI and PPI monthly percent changes for gasoline. Next, this sum is subtracted from the inflated difference for each month to create an index.15 Graphically, the results for the two methods are nearly identical, so observing both their levels in chart 2 is not possible without the use of dashes. Two very different methods yielding nearly identical results (both graphically and statistically correlated with the PPI for gasoline margins) demonstrate the effectiveness of the simulation methods. While graphical analysis is useful, statistical analysis is also important for evaluating the effectiveness of the simulation methods because nonstationarity in index levels can overstate the impact of outlier short-term changes.16
Table 1. Margins correlations| Method/parameter | Correlation coefficient | Beta of STR OLS | P-value of beta STR OLS | RSME |
|---|
Method 1: sum of regression parameters | 0.70 | 0.89 | 0.00 | 0.09 |
|---|
Method 2: inflating average prices | 0.70 | 0.90 | 0.00 | 0.09 |
|---|
Table 1 shows the test statistics used to compare the simulated indexes with the official PPI for gasoline margins. The results of the comparisons show that the performance metrics far exceed what some economists characterize as a “good” fit.17 BLS economists classified a number of simulated BLS indexes by using various statistical thresholds.18 The results of creating a price index by summing the parameters of the OLS model with the CPI and PPI commodity indexes exceed the statistical thresholds used to determine “good” fits established in the academic literature. The theoretical analysis discussed above, the graphical results in chart 2, and the test statistics in table 1 provide robust evidence demonstrating the internal consistency of the BLS measures. Also, these analyses show that BLS price indexes can be simulated with the algebraic and statistical methods used in this article.
It is also possible to simulate the CPI for gasoline by using the PPI for gasoline and the PPI for gasoline margins. The gasoline input price index including markups, introduced in this article, has a higher correlation with the official CPI than with the PPI for gasoline. The OLS regression can be viewed as a model with a variably weighted interaction term as the independent variable and the CPI as the dependent variable. The weights in the gasoline input price index including markups are defined as the margin in the prior period, and the initial margin is assumed to be 6.7 percent.19 Chart 3 graphically compares the CPI for gasoline and the PPI for gasoline with the gasoline input price index including markups.
Table 2 shows the test statistics used to compare the gasoline input price index including markups with the CPI for gasoline. The correlation statistic for the gasoline input price index including markups is appreciably higher than the correlation statistic for the official PPI for gasoline. These correlation statistics exceed the threshold that BLS-domain-hosted articles consider are “good” fits.20 The theoretical analysis discussed above, the graphical results in chart 3, and the test statistics in table 2 provide robust evidence demonstrating the internal consistency of these BLS measures. Again, these results show that BLS price indexes can be simulated with the algebraic and statistical methods used in this article.
Table 2. Correlation with CPI| Correlation with CPI for gasoline | Correlation coefficient | Beta of STR OLS | P-value of STR OLS | RMSE |
|---|
Gasoline input price index including markups | 0.94 | 0.82 | 0.00 | 0.02 |
|---|
PPI for gasoline | 0.79 | 0.35 | 0.00 | 0.04 |
|---|
Overall, the results of this article show that, because margins were not constant, gas stations had inflationary and deflationary roles in gas-price changes over the 3-year study period. All three of the index methods, that for the official PPI for gasoline margins and those for the two simulations, show the same trends in price changes of gasoline margins. Gas station margins contributed substantially to inflationary pressures early in the pandemic, from January 2020 through April 2020, but then contributed substantially to deflationary pressures from April 2020 through July 2020. More noteworthy, there had been a steady but modest inflationary impact from gas station margins from January 2021 through May 2023. This result can be observed in the steady increase of all three simulated gas station margins. All three margins exhibited similar volatility and similar trends.
Overview and discussion
The models suggested by Camp, Havlin, and Stanley and by Havlin work well when applied to the homogenous and timely gasoline indexes.21 The results documented in this article demonstrate the internal consistency of the simulated indexes and show that index simulation and estimation methods may be applied to other homogeneous industries. Researchers may try this approach in simulating price changes in other industries, attempt a vector autoregression, or even attempt a simulation of hypothetical margins indexes based on multidecade commodity indexes that predate the official margins indexes published by BLS. These results are of interest to the general public because they help explain how gas prices at the pump may be affected by gas station profits. Over the past 3 years, the impact of gas station margins on gasoline prices has been volatile. This impact of gas station margins was sometimes inflationary and at other times deflationary.
Appendix
Margin simulation method 1:
,
where β0 and β1 capture the average gas station markup over time period t, and ϵt represents upward or downward deviations from the average markup. Therefore, in time t,
.
Margin simulation method 2:
where AGTPt–1 and AGTPt–2 are the average gasoline transaction prices in, respectively, periods t–1 and t–2; AGWPt–1 and AGWPt–2 are the average EIA wholesale-gasoline prices in, respectively, periods t–1 and t–2; CPI STR Gt and CPI STR Gt–1 are the CPI short-term price relatives (STRs) for gasoline in, respectively, periods t and t–1; and PPT STR Gt and PPI STR Gt–1 are the PPI STRs for gasoline in, respectively, periods t and t–1.
The values of AGTPt–i and AGWPt–i are calculated as follows:
The initial base-period values AGTP and AGWP are calculated as follows:
The values of WT and Wt are calculated as follows:
The initial base-period value W is calculated as follows:
The Gasoline CPIt is calculated as follows:
,
where β0 and β1 represent the average difference between the indexes in period t, and ϵt represents deviations from that average. Because profit margins have now been controlled for, the average difference arguably represents the cumulative technical difference between the PPI and CPI measurement methods.
United States Department of Labor
