- Email: [email protected]
Pass-through of motor gasoline taxes: Efficiency and efficacy of environmental taxes
Energy Policy 125 (2019) 207–215
Contents lists available at ScienceDirect
Energy Policy journal homepage: www.elsevier.com/locate/enpol
Pass-through of motor gasoline taxes: Efficiency and efficacy of environmental taxes
T
Robert K. Kaufmann Department of Earth and Environment, Boston University, Boston, USA
ARTICLE INFO
ABSTRACT
Keywords: Tax incidence Environmental taxes Environmental policy Motor gasoline prices Oil supply chain
To investigate the efficacy and efficiency of environmental taxes, I analyze the rate at which taxes on motor gasoline are passed to consumers by estimating two cointegrating vector autoregression models for each of six states. For state models that specify the retail price of motor gasoline without taxes, exclusion tests suggest that taxes on motor gasoline are not passed to consumers on a one-for-one basis. For state models that specify the retail price of motor gasoline including taxes, results indicate that taxes are passed to wholesale prices in Florida and Massachusetts on a one-for-one basis and are passed to retail prices with a ‘mark-up’ in Florida, Massachusetts, New York, and Ohio, and are not fully passed through in Washington. State-specific rates of passthrough differ from results suggested by theory and fixed effects estimators, which may be biased by the presence of nonstationary data and the assumption that the rate of pass through is the same across states. Rates of pass through greater than one transfer $12.2 billion from consumers to retailers in FL, $2.3 billion in MA, and $19.2 billion in NY during the sample period, which represent 10.7%, 6.0%, and 23.9% of total expenditures on regular motor gasoline.
1. Introduction Are taxes that seek to ameliorate environmental externalities effective and/or are they efficient? These outcomes depend on taxes being passed to consumers on a one-for-one basis. Taxes are not efficient if retail prices increase more (or less) than taxes. Consumer surplus is transferred to retailers if prices rise more than taxes. Conversely producer surplus is transferred to consumers if prices rise less than taxes. Both transfers also reduce economic efficiency by reducing total social welfare. Similarly, an optimal tax is not effective if it is not passed to consumers on a one-for-for basis. An optimal tax generates too much abatement if retail prices increase by more than the tax. Conversely, an optimal tax generates too little abatement if it is not fully passed to consumers. Too much and too little abatement is not effective because the marginal cost of abatement is greater than or less than respectively, the marginal damage of environmental degradation. In a perfectly competitive market, the rate at which industry-wide changes in costs are passed to consumers depends on the elasticity of demand relative to supply (RBB Economics, 2014). Based on this hypothesis, the rate at which a Federal tax is passed to consumers can be ) , in which is the supply elasticity and is approximated by /( the demand elasticity (Chouinard and Perloff, 2004). Demand elasticities for many fuels are inelastic whereas supply elasticities are
relatively elastic (Labandiera and Lopez-Otero, 2015). Under these conditions, theory suggests that a competitive market will cause consumers to pay a relatively large fraction of a tax on motor gasoline. Consistent with theory, a limited body of empirical research indicates that taxes on motor gasoline are largely passed on to consumers. Much of this research analyzes panels that specify monthly observations of retail prices for motor gasoline as the dependent variable. Results indicate that the coefficient associated with taxes on motor gasoline generally are not statistically different from one (or slightly less than one) (Chouinard and Perloff, 2004; Alm and Skidmore, 2009; Marion and Muehlegger, 2011; Bello and Contin-Pilart, 2012; Stolper, 2016; Li and Muehlegger, 2014). A second approach uses changes in motor gasoline taxes as natural experiments. Before and after comparisons suggest that most of a tax is passed to consumers; a higher percentage of a tax increase is passed to consumers than a tax reduction (Doyle and Samphantharak, 2008; Silvia and Taylor, 2014). The empirical consensus that taxes on motor gasoline are largely passed to consumers may be misleading because previous efforts ignore the possibility of heterogeneous effects, the presence of nonstationary variables, and system dynamics. Previous efforts to estimate the rate at which taxes on motor gasoline are passed to consumers analyze variations over time within individuals using the fixed effects estimator. This estimator allows the intercept to vary among individuals. Such an
E-mail address: [email protected]. https://doi.org/10.1016/j.enpol.2018.10.045 Received 18 May 2018; Received in revised form 31 August 2018; Accepted 24 October 2018 0301-4215/ © 2018 Elsevier Ltd. All rights reserved.
Energy Policy 125 (2019) 207–215
R.K. Kaufmann
intercept captures the time-invariant effects of unobservable variables that vary across individuals. But this estimator forces the regression coefficients associated with the independent variables to be the same across individuals (i.e. homogeneous effects). That is, the effect of a tax change (or a change in the wholesale price of motor gasoline) is assumed to be the same across individuals. The assumption of homogeneous effects is not tested by previous efforts, although techniques are available to do so (Hsiao, 1986). If this assumption is violated and the relation between taxes on and prices for motor gasoline (and other variables) varies across individuals, dynamic models will generate inconsistent and potentially misleading estimates of the long-run effects (Pesaran and Smith, 1995). Similarly, Robertson and Symons (1992) find that incorrectly imposing homogeneity on panels in the presence of dynamics bias the estimates for the regression coefficients. Furthermore, panel models used by previous analyses do not separate long- and short-run effects and so do not explicitly represent the rate at which taxes on motor gasoline are ultimately passed to consumers. For example, Marion and Muehlegger (2011) estimate a model in first differences (e.g. x t = xt x t 1). But taking first differences eliminates long-run relations among nonstationary variables (Juselius, 2006). As such, Marion and Muehlegger (2005) cannot evaluate the rate at which taxes on motor gasoline are passed to consumers in the long-run. Similarly, long- and short-run relations are not represented explicitly in before and after comparisons in which one state changes its tax while surrounding states do not. These comparisons depend on the unstated assumption that the rate at which retail prices adjust to changes in taxes (and other independent variables) is the same across states that do and do not change taxes. Equally important, previous efforts to estimate the rate at which taxes on motor gasoline are passed to consumers from panel data do not account for the presence of stochastic trends in the time series. As described in Section 3, most of the variables included in the state models of motor gasoline prices are nonstationary. Although spurious regressions are less problematic in analyses of panel data than analyses of a single individual (Kao, 1999), problems remain. The fixed effects estimate for coefficients associated with independent variables converge ,N towards their true value as T , but their standard error diverges from its true value (Kao, 1999). Under these conditions, inferences about the regression coefficient are wrong with a probability that goes to one. This failure affects the conclusions about pass-through rates because the null hypothesis of complete pass-through is evaluated ˆ with a statistic ( 1 ) that tests the null hypothesis that the regression
(p. 102).” To do so, I estimate a cointegrated vector autoregression (CVAR) model for each of six states for which the requisite data are available. The CVAR model alleviates many of the difficulties associated with previous efforts; it explicitly represents long-run relations and market dynamics and uses statistical procedures to separate weakly exogenous variables from endogenous variables. Furthermore, the CVAR model is designed to analyze relations among nonstationary time series, which allows it to avoid spurious regressions and generate reliable diagnostic statistics. Results indicate that taxes are not fully passed to consumers; in most states analyzed here, retail prices rise more than taxes. State-specific rates of pass-through that differ from one-for-one undermine the efficacy and efficiency of environmental taxes. These results and the methods used to obtain them are described in five sections. The second section describes the data analyzed, the CVAR model, and the advantages of this model relative to previous approaches. The results of the CVAR models are described in the third section. Section four discusses these results relative to the existing consensus that taxes on motor gasoline are passed to consumers on a one-to-one basis. Section 5 concludes with a brief discussion of the monetary transfers from consumers to producers in states where prices rise faster than taxes and a plea for more attention to the rate at which environmental taxes are passed to consumers. 2. Methodology 2.1. Data Rather than focus on assumed changes thought to affect demand (e.g. income, speed limits, etc.), I compile observations on upstream sectors of the oil market that are related to the retail price of motor gasoline (Kaufmann and Laskowski, 2005; Marion and Muehlegger, 2011); wholesale prices for motor gasoline (Whole), inventories of motor gasoline (Stock), refinery utilization rates (Refine), and the price of crude oil (PCrude). The price of motor gasoline for resale is used to measure wholesale prices (https://www.eia.gov/dnav/pet/pet_pri_ refmg_dcu_SMA_m.htm). One measure of the retail price for motor gasoline is the sale price of motor gasoline through retail outlets excluding taxes (https://www.eia.gov/dnav/pet/pet_pri_allmg_d_SOH_PTC_dpgal_ m.htm). These data are available for all fifty states, but observations stop in February 2011. Retail prices for motor gasoline including taxes are available through the present, but these data start in 2000 or later (https://www.eia.gov/dnav/pet/pet_pri_gnd_dcus_nus_w.htm). Furthermore, observations are available for only nine states. Of these, state taxes on motor gasoline do not change after 2000 in Texas and Colorado (Federal taxes are constant during this period) therefore, these states are excluded from the sample. California is excluded from the sample because state taxes on motor gasoline are levied both as a percentage of price and a flat rate. Based on the data, the sample includes observations for six states; Florida, Massachusetts, Minnesota, New York, Ohio, and Washington. These states account for 12.5% of US sales of motor gasoline in 2016 and are located in three (of five) PADD regions. As such, they should be representative. Furthermore, it is unlikely that the availability of data has ‘chosen’ the only six states that have pass through rates that do not equal one. Nonetheless, I recognize that the results reported here cannot be generalized to the remaining 44 states. For each state, I collect retail prices for and inventories of the largest selling form of regular gasoline, either conventional or all formulations (Supplemental Material Table A-1). The form is chosen based on the availability of data and proportion of sales. Focusing on a single grade and form of gasoline is critical because there can be significant changes in the types of gasoline purchased over the sample period. Furthermore, these changes may be affected by taxes on motor gasoline. Higher taxes may encourage consumers to switch from more expensive premium and/or midgrade gasolines to less expensive regular, which would lower the average price across grades. Changes in the average price due
se ˆ
coefficient associated with taxes ( ˆ ) is equal to one. This test will not be accurate if nonstationary data cause the standard error to diverge from its true value. Even if the time series are stationary, problems remain if the autocorrelation coefficient for independent variables is not zero. Under these conditions, the fixed effects estimator generates an inconsistent estimate for the average long-run effect of the independent variable (Pesaran and Smith, 1995). And this inconsistency does not disappear if variations in the effect of independent variables are the only source of heterogeneity (Pesaran and Smith, 1995). Finally, previous efforts assume that retail prices for motor gasoline are endogenous while taxes on motor gasoline (and other variables specified on the right-hand side of the equation) are exogenous. But assumptions about exogeneity are not tested. Without such information, incorrectly specifying an endogenous variable on the right-hand side causes simultaneous equation bias, which causes parameter estimates to be biased and inconsistent. To assess the degree to which these potential difficulties affect the conclusion that taxes on motor gasoline are passed to consumers on a one-for-one basis, I follow the suggestion offered by Pesaran and Smith (1995) “The lesson for applied work is that when large T panels are available, the individual micro relations should be estimated separately 208
Energy Policy 125 (2019) 207–215
R.K. Kaufmann
Fig. 1. State taxes on motor gasoline. The evolution of taxes on motor gasoline in Florida (orange), Massachusetts (black), Minnesota (blue), New York (purple), Ohio (orange), and Washington (green).
cointegrating relation for motor gasoline prices). But as described in Section 3, results indicate that all of the CVAR models contain one or more cointegrating relations that include taxes on motor gasoline and its retail price. This implies that either there is no change in the point of taxation in individual states or such changes have no statistically measurable effect on the stationarity of cointegrating relations that represent the long-run equilibrium for motor gasoline prices. To make price variables directly comparable, observations for the price of crude oil, motor gasoline, and taxes on motor gasoline are converted to US dollars per gallon and deflated by monthly values of the U.S. city average for all items (CUUR0000SA0) that is obtained from the Bureau of Labor Statistics (https://data.bls.gov/cgi-bin/ surveymost?cu). To eliminate the effects of inverting matrices with elements that differ greatly in size (due to different units of measure), the time series for inventories of motor gasoline and refinery utilization rates are standardized as follows:
to changes in the types of gasoline purchased would obfuscate the effects of motor gasoline taxes on motor gasoline prices. Changes in the types of motor gasoline purchased over time are ignored by previous efforts that use panel techniques. I use monthly observations on refinery inventories of motor gasoline by type for each Petroleum Administration Defense District (PADD) because state level data are not available (https://www.eia.gov/dnav/ pet/pet_stoc_ref_dc_r10_mbbl_m.htm). Refinery utilization rates also are available only by PADD (https://www.eia.gov/dnav/pet/pet_pnp_unc_ dcu_nus_m.htm). Finally, the price of crude oil is measured by the average price paid by refiners (https://www.eia.gov/dnav/pet/pet_pri_ rac2_dcu_nus_m.htm). Monthly data for the Federal and state tax on motor gasoline are available by state from the Federal Highway Administration (https:// www.fhwa.dot.gov/policyinformation/motorfuelhwy_trustfund.cfm). These data are expressed in cents per gallon. Because the Federal tax does not change over the sample period, I sum Federal and state taxes (Tax). State taxes represent the charge that is levied as a dollar amount per volume of motor fuel (Fig. 1). Previous research indicates that the point at which taxes on diesel fuel are collected affects the rate at which the tax is passed to consumers (Kupzczuk et al., 2016). Unfortunately, there is no consistent set of data to identify the point in the supply chain at which taxes on motor gasoline are collected. Data on the point of collection are available through 2008 from Highway Taxes and Fees: How They Are Collected and Distributed,” published by the Federal Highway Administration (https://www.fhwa. dot.gov/policyinformation/motorfuel/hwytaxes/2008/mf101.cfm). Between 2001 and 2008, there is no change in the point of taxation in any of the six states analyzed (Supplemental Material Table A-2). Data are available for 2012 from the FTA Motor Fuel Tax Uniformity Committee ECommerce Subcommittee Survey and 2016 from the Federation of Tax Administrators (https://www.taxadmin.org/assets/docs/MotorFuel/ 201609%20Motor%20Fuel%20Tax%20Information%20by%20Stat %20Book.pdf), but the categories used to describe the point of taxation are not consistent with the categories used between 2000 and 2008 (Supplemental Material Table A-2). As such, it is not possible to determine whether there is a change in the point at which taxes on motor gasoline are collected. If such changes affect the rate at which taxes on motor gasoline are passed to consumers, such changes would disrupt long-run cointegrating relations (i.e. results would indicate that there no long-run
xt =
(yt
y) (1)
Var (y )
in which yt is the value (in original units), y¯ is the average value over the sample period, and Var(y) is the variance over the sample period. 2.2. Statistical methodology Short- and long-run relations among prices for wholesale and the largest selling retail grade of motor gasoline (with and without taxes), taxes on motor gasoline, prices of crude oil, refinery utilization rates, and inventories of motor gasoline are quantified by estimating a cointegrating vector autoregression (CVAR) model1 for each of six states. The general form of the CVAR model is given by:
x t = A0 wt + A1 wt
1
+
1
xt
1
+
(x t 1 wt 1) + k 0 +
M+
t
(2) in which xt is a vector of (p) endogenous variables whose behavior is being modeled, wt is a vector of weakly exogenous variables, k0 is a vector of constant terms, M is a vector of eleven monthly dummy variables (Jan-Nov), A0, A1 , 1, , and are matrices of regression 1
209
Models are estimated using CATS for RATS (Dennis et al., 2005).
Energy Policy 125 (2019) 207–215
R.K. Kaufmann
coefficients, is the first difference operator ( x t = xt x t 1) , and is Niid (0, ) . When the time series are nonstationary, the long-run matrix can be formulated as:
=
disrupts the stationarity of the cointegrating relation if taxes on and prices for motor gasoline do not change on a one-for-one basis, which will cause the test on the overidentified restrictions to reject the null hypothesis that there is no change in the number of stationary relations.
(3)
2.4. Simulating the long-run effect of taxes on motor gasoline prices
in which is a p × r matrix of adjustment coefficients (also known as loadings), is an r × p matrix of cointegration coefficients that define stationary deviations from long-run equilibrium relations, and r is the number of long-run cointegrating relations (Juselius, 2006). The number of cointegrating relations present is determined using the likelihood based trace test (Johansen, 1996). Once the rank of the CVAR model is determined, I test restrictions that evaluate whether individual variables are stationary, weakly exogenous, or can be excluded from cointegration space. Variables found to be weakly exogenous are moved from the x vector to the w vector in Eq. (2). For each of six states, the CVAR model is estimated with two sets of data. One set uses the real price of motor gasoline without taxes. For this model, I test restrictions that exclude real taxes on motor gasoline from cointegration space by making all elements of β that are associated with taxes equal to zero. If taxes on motor gasoline prices are passed to consumers on a one-for-one basis, there will be no long-run relation between taxes and the price of motor gasoline without taxes. Under these conditions, test statistics will fail to reject restrictions that eliminate taxes from cointegration space. The second CVAR model for each of six states specifies the real price of motor gasoline that includes taxes. These data are used to generate an overidentified model. The direct long-run equilibrium relation between taxes and prices is given by the element of associated with taxes in a cointegrating relation that; (1) incudes taxes and the wholesale and/or retail price of motor gasoline and (2) disequilibrium in this cointegrating relation loads into the equation for wholesale and/ or retail prices in a way that moves price towards equilibrium at the rate given by the element of the matrix in Eq. (3). In addition to this adjustment towards equilibrium, other short-run effects are given by the elements of the A0, A1 , 1,and , matrices (Eq. (2)).
Beyond a direct long-run relation between taxes on and prices for motor gasoline, which is given by the element of associated with Tax in a cointegrating relation for Whole or Retail, the total long-run effects of a change in taxes on motor gasoline is quantified by simulating the overidentified models to two equilibria. The first equilibrium holds the weakly exogenous variables at their sample mean ( x ). The mean value of the tax is increased by one cent (x + 0.01) and the model is simulated to a second equilibrium. The difference between the two equilibrium prices represents the total long-run effect of a one cent tax increase on the wholesale or retail price for motor gasoline. Indirect effects are the difference between the total effect and the value of associated with taxes in the cointergating relation for the wholesale or retail price of motor gasoline. 3. Results For models that specify the retail price of motor gasoline without taxes, test statistics reject the null hypothesis that each of the time series is stationary (Supplemental Material Table A-3). For each state, the CVAR models contains one or more cointegrating relations (Supplemental Material Table A-4). For all states other than Ohio (and retail prices in NY), tests reject the null hypothesis that the wholesale or retail (excluding taxes) price for motor gasoline is weakly exogenous (i.e. prices respond to disequilibrium in the long-run cointegrating relations). To evaluate whether there is a long-run relation between retail prices for motor gasoline (without taxes) and taxes on motor gasoline, I test restrictions that eliminate taxes from cointegration space. Tests of these restrictions fail to reject the null hypothesis that the tax on motor gasoline can be excluded from cointegration space for only one state, Florida (Supplemental Material Table A-3). In all other states, tests reject the hypothesis that taxes on motor gasoline can be excluded from cointegration space (Supplemental Material Table A-3). This indicates that there is a long-run stationary relation among taxes, wholesale prices, and retail prices (without taxes). This interpretation requires a caveat. Test statistics reject the null hypothesis that the wholesale or retail price of motor gasoline is weakly exogenous in CVAR models for Ohio and New York (Supplemental Material Table A-3). Rejecting this null hypothesis indicates wholesale or retail prices adjust to disequilibrium in the long-run relation among taxes and wholesale and/or retail prices for motor gasoline. In the other five states, the failure to reject the null hypothesis that the wholesale or retail price of motor gasoline is weakly exogenous implies that these prices are unaffected by disequilibrium in the cointegrating relations. Nonetheless, the inability to exclude taxes on motor gasoline, wholesale prices for motor gasoline, and retail prices for motor gasoline (without taxes) from cointegration space implies that the retail price of motor gasoline, which excludes taxes, shares a stochastic trend with taxes on motor gasoline (and wholesale prices). These long-run relations (regardless of adjustment to equilibrium) imply that taxes on motor gasoline have a long-run relation with retail (or wholesale) prices. For models that specify the price of motor gasoline including taxes, test statistics reject the null hypothesis that each of the time series are stationary, except refinery utilization rates in Minnesota (Supplemental Material Table A-5). These nonstationary variables share stochastic trends, as indicated by the presence of either three or four cointegrating relations (Supplemental Material Table A-6). For all states, tests reject the null hypothesis that the wholesale and retail price of motor gasoline
2.3. Advantages of the CVAR model Many of the difficulties with the fixed effects estimate for the relation between taxes on and prices for motor gasoline that are described in Section I can be alleviated by estimating a cointegrated vector autoregression (CVAR) model for individual states. To alleviate concerns about simultaneous equation bias, I test the null hypothesis that a variable y is weakly exogenous by imposing restrictions on the elements of (Eq. (3)) that eliminates a response by variable y to disequilibrium in all cointegrating relations. Rejecting these restrictions indicates that variable y responds to disequilibrium in one or more long-run cointegrating relations (i.e. the variable is not weakly exogenous). Under these conditions, variable y is endogenous and is included in the x matrix (Eq. (2)). Failure to reject this restriction means that variable y is weakly exogenous and is included in the w matrix (Eq. (2)). Because the CVAR model is designed to analyze relations among nonstationary variables, the diagnostic statistics can be used reliably to interpret the results. After imposing over-identifying restrictions on the cointegrating relations, the standard errors associated with the eleˆ ments of the matrix can be used reliably to calculate a t statistic ( 1 ) SE ˆ
that can be used to test the null hypothesis that the element of the cointergating relation for motor gasoline prices that is associated with taxes equals one. I supplement this test by imposing an additional restriction on the cointergating relation for gasoline price that make the element of associated with taxes equal to (but with the opposite sign) the element of associated with the price of motor gasoline. This restriction 210
Energy Policy 125 (2019) 207–215
R.K. Kaufmann
Fig. 2. Wholesale prices for motor gasoline. Predicted versus observed wholesale prices for motor gasoline in Florida (blue), Massachusetts (red), Minnesota (black), New York (orange), Ohio (green), and Washington (blue).
Fig. 3. Retail prices for motor gasoline. Predicted versus observed retail prices for motor gasoline in Florida (blue), Massachusetts (red), Minnesota (black), New York (orange), Ohio (green), and Washington (blue).
is weakly exogenous (Supplemental Material Table A-5). In all states, tests fail to reject the null hypothesis that the price of crude oil is weakly exogenous (Supplemental Material Table A-5). For states other than New York and Florida (and inventories in MN), tests reject the null hypothesis that inventories of motor gasoline and/or refinery utilization rates are weakly exogenous (Supplemental Material Table A-5). Tests fail to reject the null hypothesis that taxes on motor gasoline are weakly exogenous in all states, except Minnesota (Supplemental Material Table A-5). For states other than Ohio and Washington, the matrix is full rank; the number of cointegrating relations equals the number of endogenous variables. This result indicates that the stochastic movements
of the endogenous variables in the x vector are fully accounted for by the stochastic movements of the weakly exogenous variables in the w vector2 (Juselius, 2006). Consistent with this interpretation, CVAR models are able to simulate wholesale and retail (including taxes) prices for motor gasoline based on the observed values for the weakly exogenous variables (Figs. 2 and 3). As such, these models should accurately represent the long-run effect of a change in taxes on the wholesale and retail price for motor gasoline.
2
211
For each state, weakly exogenous variables are bolded in Table 1.
Energy Policy 125 (2019) 207–215
R.K. Kaufmann
Fig. 4. Rates of direct and total pass through of taxes on motor gasoline prices. The direct (striped) and total (solid) long-run effect of a $0.01 per gallon increase in taxes on motor gasoline on the wholesale (black) and retail (red) price for motor gasoline.
and New York ( ˆ = 2.257, t = 5.82, p < 0.00001). Point estimates greater than one (in absolute terms) imply that retail prices (including taxes) rise 41–126% more than the tax. These results are confirmed by rejecting a restriction that tests whether the number of cointegrating relations remains the same when I equalize the coefficients associated with retail prices and taxes in Florida ( 2 (1) = 8.58, p < 0.01), Massachusetts ( 2 (1) = 8.93, p < 0.01), Minnesota ( 2 (1) = 3.60, p > 0.057 ), and New York ( 2 (1) = 14.93, p < 0.001). Taxes do not appear in the long-run cointegrating relation for the retail price of motor gasoline in Ohio and Washington. The long-run relation between taxes and retail prices in Minnesota is clouded by results that indicate taxes on motor gasoline are not weakly exogenous (Supplemental Material, Table A-5). The third cointegrating relation (CR#3 in Table 1) indicates that taxes on motor gasoline rise when retail prices for motor gasoline are below their long-run equilibrium (i.e. taxes rise when motor gasoline prices are low). Because of this bi-directional adjustment, it does not make sense to assume that taxes are exogenous and evaluate the rate at which taxes are passed to retail prices. Such bi-directional relations are ignored by previous analyses. Beyond the direct long-run relation, taxes on motor gasoline may be related to upstream sectors of the supply chain and these upstream changes may affect wholesale and/or retail prices. In the CVAR model for Florida, CR #3 indicates that inventories of motor gasoline adjust to a long-run equilibrium that is implied by their positive long-run relation with taxes. And CR#1 indicates that retail prices adjust towards a long-run equilibrium that is implied by their positive long-run relation with inventories (and other variables). In Florida and Massachusetts, where there is a long-run relation between taxes and wholesale prices, simulations indicate that the total effects of taxes on wholesale prices are not much different than the direct effects, which implies the indirect effects are small (Fig. 4). Conversely, the indirect effects of taxes on wholesale prices tend to be large in New York, where the CVAR model does not identify a long-run relation between wholesale prices and taxes. Finally, taxes have little or no effect on wholesale prices in Ohio and Washington. In Florida and Massachusetts, the direct effects of taxes on retail prices are amplified by indirect effects. In Florida, the indirect effects of taxes via inventories described previously raise the total effect of a one cent tax by 1.7 cents such that retail prices rise by 3.5 cents per gallon.
4. Discussion 4.1. Pass through rates The need to include taxes in the cointegrating relation that includes the price for motor gasoline without taxes suggests two possible longrun effects. If taxes are not fully passed to consumers, a tax on motor gasoline prices would reduce the pre-tax price of motor gasoline, which would create a negative long-run relation between taxes on motor gasoline and the retail price of motor gasoline without taxes. Conversely, the pre-tax price of motor gasoline would be positively related to taxes if taxes raise the pre-tax price of motor gasoline. The sign and magnitude of the effect of taxes is quantified by models that specify the price of motor gasoline which includes taxes. These models indicate that taxes on motor gasoline are not passed to consumers on a one-for-one basis; in four states (FL, MA, NY, and OH) retail prices rise more than taxes; in one state (WA) retail prices rise less than taxes (Fig. 4). The direct long-run equilibrium effect of taxes on prices is represented by the element of that is associated with taxes in a cointegrating relation that includes the price of gasoline and loads into the equation for the price of motor gasoline in a way that moves price towards the long-run equilibrium implied by the cointegrating relation. These criteria are satisfied by cointegrating relations in Table 1 for wholesale prices in the CVAR models for Florida (CR#2) and Massachusetts (CR#3). The coefficient associated with taxes is not statistically different from −1.0 in the CVAR models for Florida ( ˆ = 1.096, t = 0.60, p > 0.54) and Massachusetts ( ˆ = 0.987, t = 0.08, p > 0.93). The failure to reject this null hypothesis indicates that taxes appear in wholesale prices on a one-for-one basis in Florida and Massachusetts. In the CVAR models for the other four states, taxes on motor gasoline do not appear in the long-run cointegrating relation for wholesale prices. The CVAR models for Florida (CR#1), Massachusetts (CR#2), Minnesota (CR#2), and New York (CR#1) contain a cointegrating relation that represents the long-run equilibrium relation for the retail price of motor gasoline (Table 1). The t statistic strongly rejects the null hypothesis that taxes equal −1.0 in the CVAR model for Florida ( ˆ = 1.789, t = 13.7, p < 0.00001), Massachusetts ( ˆ = 1.408, t = 5.25, p < 0.00001), Minnesota ( ˆ = 2.033, t = 3.22, p < 0.002), 212
Energy Policy 125 (2019) 207–215
R.K. Kaufmann
Table 1 Cointegrating relations in over-identified models for CVAR models that specify the price of gasoline that includes taxes. Retail
Whole
Florida June 2003 – Feb 2017 CR #1 1.000** CR #2 – CR #3 − 11.463*
2 (3)
2 (3)
New York June 2000 – Feb 2017 CR #1 1.000** CR #2 1.000** Ohio June 2003 – Feb 2017 CR #1 – CR #2 – CR #3 1.000
2 (4)
Refinery
Tax
Stock
Constant
– − 1.000** –
− 0.009** – –
− 1.789** − 1.096** − 63.333
− 0.007* – 1.000**
– – 14.053**
– – − 1.000** –
– – – 1.000**
− 57.279** − 1.408** − 0.987** − 56.845**
1.000** – –
18.414** – – 11.237**
= 1.77, p > 0.62 − 1.019** – − 0.694**
– − 1.029** –
– − 0.069* 0.039*
− 1.341** − 2.033** 1.000**
0.011** – –
– – − 0.390**
= 1.08, p > 0.89 – − 1.086**
− 1.110** –
– − 0.009*
− 2.257** –
0.025* –
– − 0.282**
1.000** − 24.75** 0.533**
− 0.032** 1.000** –
− 0.686** – –
– 0.297** –
– 3.312** − 0.201**
– − 0.601** –
– − 0.034** 1.000*
– – –
− 0.076** – − 1.905**
− 0.311** – − 0.964*
= 0.41, p > 0.93 − 1.02** 1.00** 11.965*
Massachusetts June 2003 – Feb 2017 CR #1 25.153** CR #2 1.000** CR #3 – CR #4 – Minnesota June 2000 – Feb 2017 CR #1 1.000** CR #2 1.000** CR #3 0.694**
PCrude
2 (4)
2 (4)
= 2.40, p > 0.66 25.153** − 1.022** 1.000** –
= 2.08, p > 0.72 − 1.000 − 24.75** − 1.551**
Washington June 2003 – Feb 2017 CR #1 1.000** CR #2 − 0.350** CR #3 –
2 (4)
= 3.36, p > 0.50 − 0.984** 1.000** –
Coefficients and test statistics are statistically significantly different from zero at the: **1%, *5%, + 10% level. Values in italics indicate that variable ‘equilibrium adjusts’ to disequilibrium in the cointegrating relation. Values in bold are weakly exogenous and specified in the w vector. Chi squares statistic represent tests of the overidentifying restrictions. Critical values (p = 0.05) for the chi squared distribution Dates refer to the sample period (entire period for which data are available).
In Massachusetts, indirect effects add 1.0 cents per gallon and are associated with long-run relations among taxes, inventories, and refinery utilization rates. In Ohio, taxes have a large indirect effect on retail prices, while taxes have little effect on retail prices in Washington. Repeating the comparison of equilibrium price changes that are simulated using the coefficients from the unidentified model has little effect on the total effect of a tax on retail motor gasoline prices, which indicates the overidentifying restrictions have little effect on the conclusions about rates of pass through (Supplemental Material Table A-7).
2
(3) = 7.81,
2
(4) = 9.49.
independent variables is statistically different from zero, either individually or in combination. These results are not definitive, given the very small sample size. Nonetheless, the lack of significance is consistent with previous results (Marion and Muehlegger, 2011). As such, the causes for different rates of pass through are uncertain and should be the focus of future research (Section 5). 4.3. Demonstrating the econometric difficulties with the fixed effects estimator Results that indicate taxes on motor gasoline are not passed to consumers on a one-for-one basis beg the question, why do results generated by CVAR models differ from those generated by fixed effects estimates of panel data? I postulate that differences are caused by the econometric difficulties that are described in Section 1. To test this hypothesis, I follow the methodology used by previous analyses by assembling the monthly observations for the six states into a balanced panel (June 2003-Feb 2017) and by estimating the effect of taxes (and other variables) on retail prices for motor gasoline using Eq. (4):
4.2. Why do pass-through rates vary among states? Results that indicate the rate at which taxes are passed to consumers varies among states beg a explanation. According to Chouinard and Perloff (2004), the rate of pass through to consumers should vary inversely with a state's share of US sales of motor gasoline. Alternatively, rates of pass through may be related to market power; high rates of market power may increase the rate at which taxes are passed to consumers. Marion and Muehlegger (2011) postulate that market power is related to inventory levels and rates of refinery utilization. Low inventories and high rates of utilization increase market power and ultimately the rate at which taxes are passed to consumers. To test these hypotheses, I estimate a simple cross-section regression from a sample of five states (FL,MA, NY, OH, and WA) in which the total effect of taxes on the price of motor gasoline is the dependent variable and the state's share of US gasoline sales, refinery utilization rates, and inventories (days of forward consumption3) are the independent variables. None of the coefficients associated with these
Retaili, t =
i
+
1 Wholei, t
+
2 Tax i, t
+
3 PCrudei, t
11
+
4 Stock i, t
+
5 Utili, t
+
j Mj j =1
+ µi, t
(4)
in which the variables are as defined previously and µ is the regression error. To test whether the s are the same across states (i.e. effects are homogeneous), Eq. (4) is estimated using two assumptions. First, I use the fixed effects estimator to estimate a restricted model (intercepts ( ) vary across states, regression coefficients ( ) are the same across the six states). Second, I use ordinary least squares (OLS) to estimate Eq. (4) for each state individually, which allows all regression coefficients vary across states. The restrictions that make all regression coefficients ( 1 1 11 ) equal across states in the fixed effects estimator are 5,
3
Days of forward consumption is calculated by dividing PADD level data for ending stocks of conventional motor gasoline (https://www.eia.gov/dnav/pet/ PET_STOC_TYP_A_EPM0C_SAE_MBBL_M.htm) by product supplied of conventional motor gasoline (https://www.eia.gov/dnav/pet/pet_cons_psup_dc_nus_ mbbl_m.htm). 213
Energy Policy 125 (2019) 207–215
R.K. Kaufmann
Table 2 Results generated by treating the data for individual states as a panel. Fixed Effects Estimator Variable Whole Tax Taxt−1 PCrude Stock Refinery
Swamy Estimator
Cotemporaneous effects 0.996** (0.017) [0.014] 0.925** (0.1127) [0.17]
With Lags 1.00** (0.017) [0.017] 2.987** (0.527) [0.472] −2.105** (0.523) [0.602] 0.020 (0.017) [0.014] −5.78E–06** (9.18E–07) [1.84E–07] 7.66E–03** (1.23E–03) [1.34E–03]
0.025 (0.0169) [0.013] −6.09E–06** (8.85E-07) [1.71E–06] 7.81E− 03** (1.24E−03) [1.35E− 03]
0.999** (02.34E−02) 0.266 (0.298) 1.82E− 02 (0.0223) 5.18E− 06 (4.92E−06) 9.53E− 03 (1.88E−06)
Coefficients and test statistics are statistically significantly different from zero at the: **1%, *5%, + 10% level. Values in parenthesis are standard errors calculated in the standard method. Values in brackets are standard errors that are robust to arbitrary correlation within groups (Bertrand et al., 2004).
evaluated with the following test statistic (Hsiao, 1986):
w=
(RSSR RSSU )/[(N 1)*K ] RSSU )/[(NT N (K + 1)]
consumers. Conversely, producers benefit in four for the six states analyzed here, where the rate of pass through is greater than one. To approximate these transfers, I modify the CVAR models for the three states (FL, MA, and NY) that indicate a direct long-run relation between retail prices for and taxes on motor gasoline. To represent a pass-through rate of 1.0, I change the coefficient associated with taxes in Tables 1 (−1.789 [FL], −1.408 [MA], and −2.257 [NY]) to −1.0 and use this new value to simulate the retail price of motor gasoline over the sample period. These results represent the retail price for motor gasoline if taxes are passed to consumers on a one-for-one basis. I use these prices to approximate the sums transferred from consumers to producers. This sum is approximated by subtracting the prices simulated by imposing a one-for-one pass through from prices simulated by the CVAR model which uses the estimated coefficient (see Fig. 3) and multiplying this difference by the quantity of regular motor gasoline purchased in the state (https://www.eia.gov/dnav/pet/pet_ cons_prim_a_EPM0_P00_Mgalpd_m.htm). Results indicate that rates of pass through greater than one transfer $12.2 billion from consumers to retailers in FL, $2.3 billion in MA, and $19.2 billion in NY during the sample period. These transfers represent 10.7%, 6.0%, and 23.9% of total expenditures on regular motor gasoline in FL, MA, and NY respectively. In these states, pass-through rates greater than one-for-one cause consumers to over-pay for motor gasoline. Rates of pass through different than one also create difficulties for efforts to internalize environmental externalities using taxes. According to economic theory, the optimal tax occurs when the marginal cost of abatement equals to marginal damage caused by the externality. This optimal tax is the focus of considerable research; much of the policy debate about climate change focuses on the social cost of carbon. But efforts to quantify the optimal tax are nullified by rates of passthrough greater than or less than one. If prices rise more than the optimal tax (as suggested by results for FL, MA, NY, and OH), the marginal costs of abatement are greater than the marginal cost of the environmental damage. Under these conditions, the tax is too large and too much abatement occurs. Conversely, too little abatement occurs if the marginal cost of abatement is less than the marginal cost of environmental damage. This will occur if the optimal tax is not fully passed to consumers, as suggested by the results for Washington. These ineffective outcomes imply that researchers and policy makers cannot assume that the market passes optimal taxes to consumers on a one-for-one basis. Instead, researchers and policy makers must explicitly consider the rate at which a tax is passed to consumers. This greatly complicates efforts to internalize environmental externalities using taxes.
(5)
in which RSSR is the residual sum of squares for the restricted model (fixed effects estimator), RSSRu is the residual sum of squares for the unrestricted model (OLS), N is the number of individuals (six states), T is the number of observations per state (165), and K is the number of regressors (16). The test statistic is evaluated against an F distribution with (N 1)*K and (NT N (K + 1) degrees of freedom in the numerator and denominator respectively. The test statistic F(80,888) = 2.08, strongly rejects (p < 0.0001) the null hypothesis that the regression coefficients are equal across states.4 If the F test is correct and the regression coefficients are not the same across states, assuming that they are equal and estimating Eq. (4) with the fixed effects estimator will bias the results; the point estimate for 2 will be smaller than its true value (Robertson and Symons, 1992). Consistent with this hypothesis, ˆ2 = 0.925 and is not statistically different from one, regardless of how the standard errors are calculated (Table 2). Similar conclusions are reached based on the sum of point estimates (0.88) for the regression coefficients that are associated with the contemporaneous and lagged effect of taxes on retail prices for motor gasoline (Table 2), as done by (Alm and Skidmore, 2009). The bias associated with the fixed effects estimator is confirmed by estimating Eq. (4) as a random coefficient model, in which all coefficients are allowed to vary across states. The point estimate for ˆ2 (0.27) that is generated by an estimator that allows the rate of pass through (and other independent variables) to vary across individuals (Swamy, 1970) is not statistically different from zero (Table 2). This suggests that ˆ varies across states such that the ‘average’ value calculated by the 2 Swamy estimator cannot be distinguished from zero. This does not imply that taxes have no effect on retail prices; rather the effect varies greatly among states, which contradicts the assumption of homogeneity that is implicit in the fixed effects estimator. 5. Conclusion and policy implications The results reported here suggest that taxes on motor gasoline are not passed to consumers on a one-for-one basis. If correct, this result creates difficulties for taxes on motor gasoline in particular and environmental taxes in general. For motor gasoline, pass through rates different than one-for-one transfer surplus between producers and consumers. For environmental taxes in general, the results make it more difficult to achieve environmental goals. Rates of pass through less than one transfer surplus from producers to consumers; conversely surplus is transferred from consumers to producers when the rates of pass through are greater than one. For one state WA, the rate of pass through is less than one, which benefits
Acknowledgements I thank Hillary Waite for help on a preliminary analysis. I also thank two anonymous reviewers, Michael Dougherty, Stephen Hall, Bryant Gross, Jeff Perloff, Samuel Stolper, and participants in the Fall 2017 meeting of Project LINK for their comments on preliminary versions of the manuscript. All mistakes that remain are solely my responsibility.
4 The null hypothesis is rejected more strongly (F(25,957) = 4.30, p < 0.0001) if the equation includes only the oil supply chain variables.
214
Energy Policy 125 (2019) 207–215
R.K. Kaufmann
Appendix A. Supplementary material
Kao, C., 1999. Spurious regression and residual-based tests for cointegration in panel data. J. Econ. 90, 1–44. Kaufmann, R.K., Laskowski, C., 2005. Causes for an asymmetric relation between the price of crude oil and refined petroleum products. Energy Policy 33, 1587–1596. Kupzczuk, W., Marion, J., Muehlegger, E., Slemod, J., 2016. Does tax-collection invariance hold? Evasion and the pass-through of state diesel taxes. Econ. Policy 8 (2), 251–286. Labandiera, X.J.M.Labeaga., Lopez-Otero, X., 2015. A meta analaysis of the price elasticity of energy demand, WP 04/2015 ISSN 2172/8437. Li, S.J. Linn, Muehlegger, E., 2014. Gasoline taxes and consumer behavior. Am. Econ. J.:Econ. Policy 6 (4), 302–341. Marion, J., Muehlegger, E., 2011. Fuel tax indcidence and supply conditions. J. Public Econ. 95, 1202–1212. Pesaran, M.H., Smith, R., 1995. Estimating long-run relationships from dynamic heterogeneous panels. J. Econ. 68, 79–113. RBB Economics, 2014. Cost pass-through; theory measurement, and potential policy implication 〈https://www.gov.uk/government/publications/cost-pass-throughtheory-measurement-and-policy-implications〉. Robertson, D., Symons, J., 1992. Strange properties of panel data estimators. J. Appl. Econ. 7 (2), 175–189. Silvia, L., Taylor, C.T., 2014. Tax pass-through in gasoline and diesel fuel: the 2003 Washington state nickel funding package increase, working paper no. 324, Bureau of Economics, Federal Trade Commission, Washington, DC 20580. Stolper, Samuel, 2016. Who bears the burden of energy taxes? The critical role of passThrough. Harv. Environ. Econ. Program Discuss. 16–70. Swamy, 1970. Efficient inference in a random coefficient regression model. Econometrica 38 (1), 311–324.
Supplementary data associated with this article can be found in the online version at doi:10.1016/j.enpol.2018.10.045. References Alm, J.E. Sennoga, Skidmore, M., 2009. Perfect competition, urbanization, and tax incidence in the retail gasoline market. Econ. Inq. 47 (1), 118–143. Bello, A., Contin-Pilart, I., 2012. Taxes, cost, and demand shifters as determinants in the regional gasoline price formation process: evidence from Spain. Energy Policy 48, 439–448. Bertrand, M., Duflo, E., Mullainathan, S., 2004. How much should we trust differences indifferences estimates? Q. J. Econ. 119 (1), 249–275. Chouinard, H., Perloff, J.M., 2004. Incidence of federal and state gasoline taxes. Econ. Lett. 83, 55–60. Dennis, J.H. Hansen, S.Johansen., Juselius, K., 2005. CATS for RATS, Version 2. Estima, Evanston, IL. Doyle, J.J., Samphantharak, K., 2008. $2.00 gas! Studying the effects of a gas tax moratorium. J. Public Econ. 92, 869–884. Hsiao, C., 1986. Analysis of Panel Data. Cambridge University Press, New York. Johansen, S., 1996. Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Advanced texts in Econometrics. Oxford University Press, Oxford. Juselius, K., 2006. The Cointegrated VAR Model: Methodology and Applications. Advanced texts in Econometrics. Oxford University Press, Oxford.
215
Contents lists available at ScienceDirect
Energy Policy journal homepage: www.elsevier.com/locate/enpol
Pass-through of motor gasoline taxes: Efficiency and efficacy of environmental taxes
T
Robert K. Kaufmann Department of Earth and Environment, Boston University, Boston, USA
ARTICLE INFO
ABSTRACT
Keywords: Tax incidence Environmental taxes Environmental policy Motor gasoline prices Oil supply chain
To investigate the efficacy and efficiency of environmental taxes, I analyze the rate at which taxes on motor gasoline are passed to consumers by estimating two cointegrating vector autoregression models for each of six states. For state models that specify the retail price of motor gasoline without taxes, exclusion tests suggest that taxes on motor gasoline are not passed to consumers on a one-for-one basis. For state models that specify the retail price of motor gasoline including taxes, results indicate that taxes are passed to wholesale prices in Florida and Massachusetts on a one-for-one basis and are passed to retail prices with a ‘mark-up’ in Florida, Massachusetts, New York, and Ohio, and are not fully passed through in Washington. State-specific rates of passthrough differ from results suggested by theory and fixed effects estimators, which may be biased by the presence of nonstationary data and the assumption that the rate of pass through is the same across states. Rates of pass through greater than one transfer $12.2 billion from consumers to retailers in FL, $2.3 billion in MA, and $19.2 billion in NY during the sample period, which represent 10.7%, 6.0%, and 23.9% of total expenditures on regular motor gasoline.
1. Introduction Are taxes that seek to ameliorate environmental externalities effective and/or are they efficient? These outcomes depend on taxes being passed to consumers on a one-for-one basis. Taxes are not efficient if retail prices increase more (or less) than taxes. Consumer surplus is transferred to retailers if prices rise more than taxes. Conversely producer surplus is transferred to consumers if prices rise less than taxes. Both transfers also reduce economic efficiency by reducing total social welfare. Similarly, an optimal tax is not effective if it is not passed to consumers on a one-for-for basis. An optimal tax generates too much abatement if retail prices increase by more than the tax. Conversely, an optimal tax generates too little abatement if it is not fully passed to consumers. Too much and too little abatement is not effective because the marginal cost of abatement is greater than or less than respectively, the marginal damage of environmental degradation. In a perfectly competitive market, the rate at which industry-wide changes in costs are passed to consumers depends on the elasticity of demand relative to supply (RBB Economics, 2014). Based on this hypothesis, the rate at which a Federal tax is passed to consumers can be ) , in which is the supply elasticity and is approximated by /( the demand elasticity (Chouinard and Perloff, 2004). Demand elasticities for many fuels are inelastic whereas supply elasticities are
relatively elastic (Labandiera and Lopez-Otero, 2015). Under these conditions, theory suggests that a competitive market will cause consumers to pay a relatively large fraction of a tax on motor gasoline. Consistent with theory, a limited body of empirical research indicates that taxes on motor gasoline are largely passed on to consumers. Much of this research analyzes panels that specify monthly observations of retail prices for motor gasoline as the dependent variable. Results indicate that the coefficient associated with taxes on motor gasoline generally are not statistically different from one (or slightly less than one) (Chouinard and Perloff, 2004; Alm and Skidmore, 2009; Marion and Muehlegger, 2011; Bello and Contin-Pilart, 2012; Stolper, 2016; Li and Muehlegger, 2014). A second approach uses changes in motor gasoline taxes as natural experiments. Before and after comparisons suggest that most of a tax is passed to consumers; a higher percentage of a tax increase is passed to consumers than a tax reduction (Doyle and Samphantharak, 2008; Silvia and Taylor, 2014). The empirical consensus that taxes on motor gasoline are largely passed to consumers may be misleading because previous efforts ignore the possibility of heterogeneous effects, the presence of nonstationary variables, and system dynamics. Previous efforts to estimate the rate at which taxes on motor gasoline are passed to consumers analyze variations over time within individuals using the fixed effects estimator. This estimator allows the intercept to vary among individuals. Such an
E-mail address: [email protected]. https://doi.org/10.1016/j.enpol.2018.10.045 Received 18 May 2018; Received in revised form 31 August 2018; Accepted 24 October 2018 0301-4215/ © 2018 Elsevier Ltd. All rights reserved.
Energy Policy 125 (2019) 207–215
R.K. Kaufmann
intercept captures the time-invariant effects of unobservable variables that vary across individuals. But this estimator forces the regression coefficients associated with the independent variables to be the same across individuals (i.e. homogeneous effects). That is, the effect of a tax change (or a change in the wholesale price of motor gasoline) is assumed to be the same across individuals. The assumption of homogeneous effects is not tested by previous efforts, although techniques are available to do so (Hsiao, 1986). If this assumption is violated and the relation between taxes on and prices for motor gasoline (and other variables) varies across individuals, dynamic models will generate inconsistent and potentially misleading estimates of the long-run effects (Pesaran and Smith, 1995). Similarly, Robertson and Symons (1992) find that incorrectly imposing homogeneity on panels in the presence of dynamics bias the estimates for the regression coefficients. Furthermore, panel models used by previous analyses do not separate long- and short-run effects and so do not explicitly represent the rate at which taxes on motor gasoline are ultimately passed to consumers. For example, Marion and Muehlegger (2011) estimate a model in first differences (e.g. x t = xt x t 1). But taking first differences eliminates long-run relations among nonstationary variables (Juselius, 2006). As such, Marion and Muehlegger (2005) cannot evaluate the rate at which taxes on motor gasoline are passed to consumers in the long-run. Similarly, long- and short-run relations are not represented explicitly in before and after comparisons in which one state changes its tax while surrounding states do not. These comparisons depend on the unstated assumption that the rate at which retail prices adjust to changes in taxes (and other independent variables) is the same across states that do and do not change taxes. Equally important, previous efforts to estimate the rate at which taxes on motor gasoline are passed to consumers from panel data do not account for the presence of stochastic trends in the time series. As described in Section 3, most of the variables included in the state models of motor gasoline prices are nonstationary. Although spurious regressions are less problematic in analyses of panel data than analyses of a single individual (Kao, 1999), problems remain. The fixed effects estimate for coefficients associated with independent variables converge ,N towards their true value as T , but their standard error diverges from its true value (Kao, 1999). Under these conditions, inferences about the regression coefficient are wrong with a probability that goes to one. This failure affects the conclusions about pass-through rates because the null hypothesis of complete pass-through is evaluated ˆ with a statistic ( 1 ) that tests the null hypothesis that the regression
(p. 102).” To do so, I estimate a cointegrated vector autoregression (CVAR) model for each of six states for which the requisite data are available. The CVAR model alleviates many of the difficulties associated with previous efforts; it explicitly represents long-run relations and market dynamics and uses statistical procedures to separate weakly exogenous variables from endogenous variables. Furthermore, the CVAR model is designed to analyze relations among nonstationary time series, which allows it to avoid spurious regressions and generate reliable diagnostic statistics. Results indicate that taxes are not fully passed to consumers; in most states analyzed here, retail prices rise more than taxes. State-specific rates of pass-through that differ from one-for-one undermine the efficacy and efficiency of environmental taxes. These results and the methods used to obtain them are described in five sections. The second section describes the data analyzed, the CVAR model, and the advantages of this model relative to previous approaches. The results of the CVAR models are described in the third section. Section four discusses these results relative to the existing consensus that taxes on motor gasoline are passed to consumers on a one-to-one basis. Section 5 concludes with a brief discussion of the monetary transfers from consumers to producers in states where prices rise faster than taxes and a plea for more attention to the rate at which environmental taxes are passed to consumers. 2. Methodology 2.1. Data Rather than focus on assumed changes thought to affect demand (e.g. income, speed limits, etc.), I compile observations on upstream sectors of the oil market that are related to the retail price of motor gasoline (Kaufmann and Laskowski, 2005; Marion and Muehlegger, 2011); wholesale prices for motor gasoline (Whole), inventories of motor gasoline (Stock), refinery utilization rates (Refine), and the price of crude oil (PCrude). The price of motor gasoline for resale is used to measure wholesale prices (https://www.eia.gov/dnav/pet/pet_pri_ refmg_dcu_SMA_m.htm). One measure of the retail price for motor gasoline is the sale price of motor gasoline through retail outlets excluding taxes (https://www.eia.gov/dnav/pet/pet_pri_allmg_d_SOH_PTC_dpgal_ m.htm). These data are available for all fifty states, but observations stop in February 2011. Retail prices for motor gasoline including taxes are available through the present, but these data start in 2000 or later (https://www.eia.gov/dnav/pet/pet_pri_gnd_dcus_nus_w.htm). Furthermore, observations are available for only nine states. Of these, state taxes on motor gasoline do not change after 2000 in Texas and Colorado (Federal taxes are constant during this period) therefore, these states are excluded from the sample. California is excluded from the sample because state taxes on motor gasoline are levied both as a percentage of price and a flat rate. Based on the data, the sample includes observations for six states; Florida, Massachusetts, Minnesota, New York, Ohio, and Washington. These states account for 12.5% of US sales of motor gasoline in 2016 and are located in three (of five) PADD regions. As such, they should be representative. Furthermore, it is unlikely that the availability of data has ‘chosen’ the only six states that have pass through rates that do not equal one. Nonetheless, I recognize that the results reported here cannot be generalized to the remaining 44 states. For each state, I collect retail prices for and inventories of the largest selling form of regular gasoline, either conventional or all formulations (Supplemental Material Table A-1). The form is chosen based on the availability of data and proportion of sales. Focusing on a single grade and form of gasoline is critical because there can be significant changes in the types of gasoline purchased over the sample period. Furthermore, these changes may be affected by taxes on motor gasoline. Higher taxes may encourage consumers to switch from more expensive premium and/or midgrade gasolines to less expensive regular, which would lower the average price across grades. Changes in the average price due
se ˆ
coefficient associated with taxes ( ˆ ) is equal to one. This test will not be accurate if nonstationary data cause the standard error to diverge from its true value. Even if the time series are stationary, problems remain if the autocorrelation coefficient for independent variables is not zero. Under these conditions, the fixed effects estimator generates an inconsistent estimate for the average long-run effect of the independent variable (Pesaran and Smith, 1995). And this inconsistency does not disappear if variations in the effect of independent variables are the only source of heterogeneity (Pesaran and Smith, 1995). Finally, previous efforts assume that retail prices for motor gasoline are endogenous while taxes on motor gasoline (and other variables specified on the right-hand side of the equation) are exogenous. But assumptions about exogeneity are not tested. Without such information, incorrectly specifying an endogenous variable on the right-hand side causes simultaneous equation bias, which causes parameter estimates to be biased and inconsistent. To assess the degree to which these potential difficulties affect the conclusion that taxes on motor gasoline are passed to consumers on a one-for-one basis, I follow the suggestion offered by Pesaran and Smith (1995) “The lesson for applied work is that when large T panels are available, the individual micro relations should be estimated separately 208
Energy Policy 125 (2019) 207–215
R.K. Kaufmann
Fig. 1. State taxes on motor gasoline. The evolution of taxes on motor gasoline in Florida (orange), Massachusetts (black), Minnesota (blue), New York (purple), Ohio (orange), and Washington (green).
cointegrating relation for motor gasoline prices). But as described in Section 3, results indicate that all of the CVAR models contain one or more cointegrating relations that include taxes on motor gasoline and its retail price. This implies that either there is no change in the point of taxation in individual states or such changes have no statistically measurable effect on the stationarity of cointegrating relations that represent the long-run equilibrium for motor gasoline prices. To make price variables directly comparable, observations for the price of crude oil, motor gasoline, and taxes on motor gasoline are converted to US dollars per gallon and deflated by monthly values of the U.S. city average for all items (CUUR0000SA0) that is obtained from the Bureau of Labor Statistics (https://data.bls.gov/cgi-bin/ surveymost?cu). To eliminate the effects of inverting matrices with elements that differ greatly in size (due to different units of measure), the time series for inventories of motor gasoline and refinery utilization rates are standardized as follows:
to changes in the types of gasoline purchased would obfuscate the effects of motor gasoline taxes on motor gasoline prices. Changes in the types of motor gasoline purchased over time are ignored by previous efforts that use panel techniques. I use monthly observations on refinery inventories of motor gasoline by type for each Petroleum Administration Defense District (PADD) because state level data are not available (https://www.eia.gov/dnav/ pet/pet_stoc_ref_dc_r10_mbbl_m.htm). Refinery utilization rates also are available only by PADD (https://www.eia.gov/dnav/pet/pet_pnp_unc_ dcu_nus_m.htm). Finally, the price of crude oil is measured by the average price paid by refiners (https://www.eia.gov/dnav/pet/pet_pri_ rac2_dcu_nus_m.htm). Monthly data for the Federal and state tax on motor gasoline are available by state from the Federal Highway Administration (https:// www.fhwa.dot.gov/policyinformation/motorfuelhwy_trustfund.cfm). These data are expressed in cents per gallon. Because the Federal tax does not change over the sample period, I sum Federal and state taxes (Tax). State taxes represent the charge that is levied as a dollar amount per volume of motor fuel (Fig. 1). Previous research indicates that the point at which taxes on diesel fuel are collected affects the rate at which the tax is passed to consumers (Kupzczuk et al., 2016). Unfortunately, there is no consistent set of data to identify the point in the supply chain at which taxes on motor gasoline are collected. Data on the point of collection are available through 2008 from Highway Taxes and Fees: How They Are Collected and Distributed,” published by the Federal Highway Administration (https://www.fhwa. dot.gov/policyinformation/motorfuel/hwytaxes/2008/mf101.cfm). Between 2001 and 2008, there is no change in the point of taxation in any of the six states analyzed (Supplemental Material Table A-2). Data are available for 2012 from the FTA Motor Fuel Tax Uniformity Committee ECommerce Subcommittee Survey and 2016 from the Federation of Tax Administrators (https://www.taxadmin.org/assets/docs/MotorFuel/ 201609%20Motor%20Fuel%20Tax%20Information%20by%20Stat %20Book.pdf), but the categories used to describe the point of taxation are not consistent with the categories used between 2000 and 2008 (Supplemental Material Table A-2). As such, it is not possible to determine whether there is a change in the point at which taxes on motor gasoline are collected. If such changes affect the rate at which taxes on motor gasoline are passed to consumers, such changes would disrupt long-run cointegrating relations (i.e. results would indicate that there no long-run
xt =
(yt
y) (1)
Var (y )
in which yt is the value (in original units), y¯ is the average value over the sample period, and Var(y) is the variance over the sample period. 2.2. Statistical methodology Short- and long-run relations among prices for wholesale and the largest selling retail grade of motor gasoline (with and without taxes), taxes on motor gasoline, prices of crude oil, refinery utilization rates, and inventories of motor gasoline are quantified by estimating a cointegrating vector autoregression (CVAR) model1 for each of six states. The general form of the CVAR model is given by:
x t = A0 wt + A1 wt
1
+
1
xt
1
+
(x t 1 wt 1) + k 0 +
M+
t
(2) in which xt is a vector of (p) endogenous variables whose behavior is being modeled, wt is a vector of weakly exogenous variables, k0 is a vector of constant terms, M is a vector of eleven monthly dummy variables (Jan-Nov), A0, A1 , 1, , and are matrices of regression 1
209
Models are estimated using CATS for RATS (Dennis et al., 2005).
Energy Policy 125 (2019) 207–215
R.K. Kaufmann
coefficients, is the first difference operator ( x t = xt x t 1) , and is Niid (0, ) . When the time series are nonstationary, the long-run matrix can be formulated as:
=
disrupts the stationarity of the cointegrating relation if taxes on and prices for motor gasoline do not change on a one-for-one basis, which will cause the test on the overidentified restrictions to reject the null hypothesis that there is no change in the number of stationary relations.
(3)
2.4. Simulating the long-run effect of taxes on motor gasoline prices
in which is a p × r matrix of adjustment coefficients (also known as loadings), is an r × p matrix of cointegration coefficients that define stationary deviations from long-run equilibrium relations, and r is the number of long-run cointegrating relations (Juselius, 2006). The number of cointegrating relations present is determined using the likelihood based trace test (Johansen, 1996). Once the rank of the CVAR model is determined, I test restrictions that evaluate whether individual variables are stationary, weakly exogenous, or can be excluded from cointegration space. Variables found to be weakly exogenous are moved from the x vector to the w vector in Eq. (2). For each of six states, the CVAR model is estimated with two sets of data. One set uses the real price of motor gasoline without taxes. For this model, I test restrictions that exclude real taxes on motor gasoline from cointegration space by making all elements of β that are associated with taxes equal to zero. If taxes on motor gasoline prices are passed to consumers on a one-for-one basis, there will be no long-run relation between taxes and the price of motor gasoline without taxes. Under these conditions, test statistics will fail to reject restrictions that eliminate taxes from cointegration space. The second CVAR model for each of six states specifies the real price of motor gasoline that includes taxes. These data are used to generate an overidentified model. The direct long-run equilibrium relation between taxes and prices is given by the element of associated with taxes in a cointegrating relation that; (1) incudes taxes and the wholesale and/or retail price of motor gasoline and (2) disequilibrium in this cointegrating relation loads into the equation for wholesale and/ or retail prices in a way that moves price towards equilibrium at the rate given by the element of the matrix in Eq. (3). In addition to this adjustment towards equilibrium, other short-run effects are given by the elements of the A0, A1 , 1,and , matrices (Eq. (2)).
Beyond a direct long-run relation between taxes on and prices for motor gasoline, which is given by the element of associated with Tax in a cointegrating relation for Whole or Retail, the total long-run effects of a change in taxes on motor gasoline is quantified by simulating the overidentified models to two equilibria. The first equilibrium holds the weakly exogenous variables at their sample mean ( x ). The mean value of the tax is increased by one cent (x + 0.01) and the model is simulated to a second equilibrium. The difference between the two equilibrium prices represents the total long-run effect of a one cent tax increase on the wholesale or retail price for motor gasoline. Indirect effects are the difference between the total effect and the value of associated with taxes in the cointergating relation for the wholesale or retail price of motor gasoline. 3. Results For models that specify the retail price of motor gasoline without taxes, test statistics reject the null hypothesis that each of the time series is stationary (Supplemental Material Table A-3). For each state, the CVAR models contains one or more cointegrating relations (Supplemental Material Table A-4). For all states other than Ohio (and retail prices in NY), tests reject the null hypothesis that the wholesale or retail (excluding taxes) price for motor gasoline is weakly exogenous (i.e. prices respond to disequilibrium in the long-run cointegrating relations). To evaluate whether there is a long-run relation between retail prices for motor gasoline (without taxes) and taxes on motor gasoline, I test restrictions that eliminate taxes from cointegration space. Tests of these restrictions fail to reject the null hypothesis that the tax on motor gasoline can be excluded from cointegration space for only one state, Florida (Supplemental Material Table A-3). In all other states, tests reject the hypothesis that taxes on motor gasoline can be excluded from cointegration space (Supplemental Material Table A-3). This indicates that there is a long-run stationary relation among taxes, wholesale prices, and retail prices (without taxes). This interpretation requires a caveat. Test statistics reject the null hypothesis that the wholesale or retail price of motor gasoline is weakly exogenous in CVAR models for Ohio and New York (Supplemental Material Table A-3). Rejecting this null hypothesis indicates wholesale or retail prices adjust to disequilibrium in the long-run relation among taxes and wholesale and/or retail prices for motor gasoline. In the other five states, the failure to reject the null hypothesis that the wholesale or retail price of motor gasoline is weakly exogenous implies that these prices are unaffected by disequilibrium in the cointegrating relations. Nonetheless, the inability to exclude taxes on motor gasoline, wholesale prices for motor gasoline, and retail prices for motor gasoline (without taxes) from cointegration space implies that the retail price of motor gasoline, which excludes taxes, shares a stochastic trend with taxes on motor gasoline (and wholesale prices). These long-run relations (regardless of adjustment to equilibrium) imply that taxes on motor gasoline have a long-run relation with retail (or wholesale) prices. For models that specify the price of motor gasoline including taxes, test statistics reject the null hypothesis that each of the time series are stationary, except refinery utilization rates in Minnesota (Supplemental Material Table A-5). These nonstationary variables share stochastic trends, as indicated by the presence of either three or four cointegrating relations (Supplemental Material Table A-6). For all states, tests reject the null hypothesis that the wholesale and retail price of motor gasoline
2.3. Advantages of the CVAR model Many of the difficulties with the fixed effects estimate for the relation between taxes on and prices for motor gasoline that are described in Section I can be alleviated by estimating a cointegrated vector autoregression (CVAR) model for individual states. To alleviate concerns about simultaneous equation bias, I test the null hypothesis that a variable y is weakly exogenous by imposing restrictions on the elements of (Eq. (3)) that eliminates a response by variable y to disequilibrium in all cointegrating relations. Rejecting these restrictions indicates that variable y responds to disequilibrium in one or more long-run cointegrating relations (i.e. the variable is not weakly exogenous). Under these conditions, variable y is endogenous and is included in the x matrix (Eq. (2)). Failure to reject this restriction means that variable y is weakly exogenous and is included in the w matrix (Eq. (2)). Because the CVAR model is designed to analyze relations among nonstationary variables, the diagnostic statistics can be used reliably to interpret the results. After imposing over-identifying restrictions on the cointegrating relations, the standard errors associated with the eleˆ ments of the matrix can be used reliably to calculate a t statistic ( 1 ) SE ˆ
that can be used to test the null hypothesis that the element of the cointergating relation for motor gasoline prices that is associated with taxes equals one. I supplement this test by imposing an additional restriction on the cointergating relation for gasoline price that make the element of associated with taxes equal to (but with the opposite sign) the element of associated with the price of motor gasoline. This restriction 210
Energy Policy 125 (2019) 207–215
R.K. Kaufmann
Fig. 2. Wholesale prices for motor gasoline. Predicted versus observed wholesale prices for motor gasoline in Florida (blue), Massachusetts (red), Minnesota (black), New York (orange), Ohio (green), and Washington (blue).
Fig. 3. Retail prices for motor gasoline. Predicted versus observed retail prices for motor gasoline in Florida (blue), Massachusetts (red), Minnesota (black), New York (orange), Ohio (green), and Washington (blue).
is weakly exogenous (Supplemental Material Table A-5). In all states, tests fail to reject the null hypothesis that the price of crude oil is weakly exogenous (Supplemental Material Table A-5). For states other than New York and Florida (and inventories in MN), tests reject the null hypothesis that inventories of motor gasoline and/or refinery utilization rates are weakly exogenous (Supplemental Material Table A-5). Tests fail to reject the null hypothesis that taxes on motor gasoline are weakly exogenous in all states, except Minnesota (Supplemental Material Table A-5). For states other than Ohio and Washington, the matrix is full rank; the number of cointegrating relations equals the number of endogenous variables. This result indicates that the stochastic movements
of the endogenous variables in the x vector are fully accounted for by the stochastic movements of the weakly exogenous variables in the w vector2 (Juselius, 2006). Consistent with this interpretation, CVAR models are able to simulate wholesale and retail (including taxes) prices for motor gasoline based on the observed values for the weakly exogenous variables (Figs. 2 and 3). As such, these models should accurately represent the long-run effect of a change in taxes on the wholesale and retail price for motor gasoline.
2
211
For each state, weakly exogenous variables are bolded in Table 1.
Energy Policy 125 (2019) 207–215
R.K. Kaufmann
Fig. 4. Rates of direct and total pass through of taxes on motor gasoline prices. The direct (striped) and total (solid) long-run effect of a $0.01 per gallon increase in taxes on motor gasoline on the wholesale (black) and retail (red) price for motor gasoline.
and New York ( ˆ = 2.257, t = 5.82, p < 0.00001). Point estimates greater than one (in absolute terms) imply that retail prices (including taxes) rise 41–126% more than the tax. These results are confirmed by rejecting a restriction that tests whether the number of cointegrating relations remains the same when I equalize the coefficients associated with retail prices and taxes in Florida ( 2 (1) = 8.58, p < 0.01), Massachusetts ( 2 (1) = 8.93, p < 0.01), Minnesota ( 2 (1) = 3.60, p > 0.057 ), and New York ( 2 (1) = 14.93, p < 0.001). Taxes do not appear in the long-run cointegrating relation for the retail price of motor gasoline in Ohio and Washington. The long-run relation between taxes and retail prices in Minnesota is clouded by results that indicate taxes on motor gasoline are not weakly exogenous (Supplemental Material, Table A-5). The third cointegrating relation (CR#3 in Table 1) indicates that taxes on motor gasoline rise when retail prices for motor gasoline are below their long-run equilibrium (i.e. taxes rise when motor gasoline prices are low). Because of this bi-directional adjustment, it does not make sense to assume that taxes are exogenous and evaluate the rate at which taxes are passed to retail prices. Such bi-directional relations are ignored by previous analyses. Beyond the direct long-run relation, taxes on motor gasoline may be related to upstream sectors of the supply chain and these upstream changes may affect wholesale and/or retail prices. In the CVAR model for Florida, CR #3 indicates that inventories of motor gasoline adjust to a long-run equilibrium that is implied by their positive long-run relation with taxes. And CR#1 indicates that retail prices adjust towards a long-run equilibrium that is implied by their positive long-run relation with inventories (and other variables). In Florida and Massachusetts, where there is a long-run relation between taxes and wholesale prices, simulations indicate that the total effects of taxes on wholesale prices are not much different than the direct effects, which implies the indirect effects are small (Fig. 4). Conversely, the indirect effects of taxes on wholesale prices tend to be large in New York, where the CVAR model does not identify a long-run relation between wholesale prices and taxes. Finally, taxes have little or no effect on wholesale prices in Ohio and Washington. In Florida and Massachusetts, the direct effects of taxes on retail prices are amplified by indirect effects. In Florida, the indirect effects of taxes via inventories described previously raise the total effect of a one cent tax by 1.7 cents such that retail prices rise by 3.5 cents per gallon.
4. Discussion 4.1. Pass through rates The need to include taxes in the cointegrating relation that includes the price for motor gasoline without taxes suggests two possible longrun effects. If taxes are not fully passed to consumers, a tax on motor gasoline prices would reduce the pre-tax price of motor gasoline, which would create a negative long-run relation between taxes on motor gasoline and the retail price of motor gasoline without taxes. Conversely, the pre-tax price of motor gasoline would be positively related to taxes if taxes raise the pre-tax price of motor gasoline. The sign and magnitude of the effect of taxes is quantified by models that specify the price of motor gasoline which includes taxes. These models indicate that taxes on motor gasoline are not passed to consumers on a one-for-one basis; in four states (FL, MA, NY, and OH) retail prices rise more than taxes; in one state (WA) retail prices rise less than taxes (Fig. 4). The direct long-run equilibrium effect of taxes on prices is represented by the element of that is associated with taxes in a cointegrating relation that includes the price of gasoline and loads into the equation for the price of motor gasoline in a way that moves price towards the long-run equilibrium implied by the cointegrating relation. These criteria are satisfied by cointegrating relations in Table 1 for wholesale prices in the CVAR models for Florida (CR#2) and Massachusetts (CR#3). The coefficient associated with taxes is not statistically different from −1.0 in the CVAR models for Florida ( ˆ = 1.096, t = 0.60, p > 0.54) and Massachusetts ( ˆ = 0.987, t = 0.08, p > 0.93). The failure to reject this null hypothesis indicates that taxes appear in wholesale prices on a one-for-one basis in Florida and Massachusetts. In the CVAR models for the other four states, taxes on motor gasoline do not appear in the long-run cointegrating relation for wholesale prices. The CVAR models for Florida (CR#1), Massachusetts (CR#2), Minnesota (CR#2), and New York (CR#1) contain a cointegrating relation that represents the long-run equilibrium relation for the retail price of motor gasoline (Table 1). The t statistic strongly rejects the null hypothesis that taxes equal −1.0 in the CVAR model for Florida ( ˆ = 1.789, t = 13.7, p < 0.00001), Massachusetts ( ˆ = 1.408, t = 5.25, p < 0.00001), Minnesota ( ˆ = 2.033, t = 3.22, p < 0.002), 212
Energy Policy 125 (2019) 207–215
R.K. Kaufmann
Table 1 Cointegrating relations in over-identified models for CVAR models that specify the price of gasoline that includes taxes. Retail
Whole
Florida June 2003 – Feb 2017 CR #1 1.000** CR #2 – CR #3 − 11.463*
2 (3)
2 (3)
New York June 2000 – Feb 2017 CR #1 1.000** CR #2 1.000** Ohio June 2003 – Feb 2017 CR #1 – CR #2 – CR #3 1.000
2 (4)
Refinery
Tax
Stock
Constant
– − 1.000** –
− 0.009** – –
− 1.789** − 1.096** − 63.333
− 0.007* – 1.000**
– – 14.053**
– – − 1.000** –
– – – 1.000**
− 57.279** − 1.408** − 0.987** − 56.845**
1.000** – –
18.414** – – 11.237**
= 1.77, p > 0.62 − 1.019** – − 0.694**
– − 1.029** –
– − 0.069* 0.039*
− 1.341** − 2.033** 1.000**
0.011** – –
– – − 0.390**
= 1.08, p > 0.89 – − 1.086**
− 1.110** –
– − 0.009*
− 2.257** –
0.025* –
– − 0.282**
1.000** − 24.75** 0.533**
− 0.032** 1.000** –
− 0.686** – –
– 0.297** –
– 3.312** − 0.201**
– − 0.601** –
– − 0.034** 1.000*
– – –
− 0.076** – − 1.905**
− 0.311** – − 0.964*
= 0.41, p > 0.93 − 1.02** 1.00** 11.965*
Massachusetts June 2003 – Feb 2017 CR #1 25.153** CR #2 1.000** CR #3 – CR #4 – Minnesota June 2000 – Feb 2017 CR #1 1.000** CR #2 1.000** CR #3 0.694**
PCrude
2 (4)
2 (4)
= 2.40, p > 0.66 25.153** − 1.022** 1.000** –
= 2.08, p > 0.72 − 1.000 − 24.75** − 1.551**
Washington June 2003 – Feb 2017 CR #1 1.000** CR #2 − 0.350** CR #3 –
2 (4)
= 3.36, p > 0.50 − 0.984** 1.000** –
Coefficients and test statistics are statistically significantly different from zero at the: **1%, *5%, + 10% level. Values in italics indicate that variable ‘equilibrium adjusts’ to disequilibrium in the cointegrating relation. Values in bold are weakly exogenous and specified in the w vector. Chi squares statistic represent tests of the overidentifying restrictions. Critical values (p = 0.05) for the chi squared distribution Dates refer to the sample period (entire period for which data are available).
In Massachusetts, indirect effects add 1.0 cents per gallon and are associated with long-run relations among taxes, inventories, and refinery utilization rates. In Ohio, taxes have a large indirect effect on retail prices, while taxes have little effect on retail prices in Washington. Repeating the comparison of equilibrium price changes that are simulated using the coefficients from the unidentified model has little effect on the total effect of a tax on retail motor gasoline prices, which indicates the overidentifying restrictions have little effect on the conclusions about rates of pass through (Supplemental Material Table A-7).
2
(3) = 7.81,
2
(4) = 9.49.
independent variables is statistically different from zero, either individually or in combination. These results are not definitive, given the very small sample size. Nonetheless, the lack of significance is consistent with previous results (Marion and Muehlegger, 2011). As such, the causes for different rates of pass through are uncertain and should be the focus of future research (Section 5). 4.3. Demonstrating the econometric difficulties with the fixed effects estimator Results that indicate taxes on motor gasoline are not passed to consumers on a one-for-one basis beg the question, why do results generated by CVAR models differ from those generated by fixed effects estimates of panel data? I postulate that differences are caused by the econometric difficulties that are described in Section 1. To test this hypothesis, I follow the methodology used by previous analyses by assembling the monthly observations for the six states into a balanced panel (June 2003-Feb 2017) and by estimating the effect of taxes (and other variables) on retail prices for motor gasoline using Eq. (4):
4.2. Why do pass-through rates vary among states? Results that indicate the rate at which taxes are passed to consumers varies among states beg a explanation. According to Chouinard and Perloff (2004), the rate of pass through to consumers should vary inversely with a state's share of US sales of motor gasoline. Alternatively, rates of pass through may be related to market power; high rates of market power may increase the rate at which taxes are passed to consumers. Marion and Muehlegger (2011) postulate that market power is related to inventory levels and rates of refinery utilization. Low inventories and high rates of utilization increase market power and ultimately the rate at which taxes are passed to consumers. To test these hypotheses, I estimate a simple cross-section regression from a sample of five states (FL,MA, NY, OH, and WA) in which the total effect of taxes on the price of motor gasoline is the dependent variable and the state's share of US gasoline sales, refinery utilization rates, and inventories (days of forward consumption3) are the independent variables. None of the coefficients associated with these
Retaili, t =
i
+
1 Wholei, t
+
2 Tax i, t
+
3 PCrudei, t
11
+
4 Stock i, t
+
5 Utili, t
+
j Mj j =1
+ µi, t
(4)
in which the variables are as defined previously and µ is the regression error. To test whether the s are the same across states (i.e. effects are homogeneous), Eq. (4) is estimated using two assumptions. First, I use the fixed effects estimator to estimate a restricted model (intercepts ( ) vary across states, regression coefficients ( ) are the same across the six states). Second, I use ordinary least squares (OLS) to estimate Eq. (4) for each state individually, which allows all regression coefficients vary across states. The restrictions that make all regression coefficients ( 1 1 11 ) equal across states in the fixed effects estimator are 5,
3
Days of forward consumption is calculated by dividing PADD level data for ending stocks of conventional motor gasoline (https://www.eia.gov/dnav/pet/ PET_STOC_TYP_A_EPM0C_SAE_MBBL_M.htm) by product supplied of conventional motor gasoline (https://www.eia.gov/dnav/pet/pet_cons_psup_dc_nus_ mbbl_m.htm). 213
Energy Policy 125 (2019) 207–215
R.K. Kaufmann
Table 2 Results generated by treating the data for individual states as a panel. Fixed Effects Estimator Variable Whole Tax Taxt−1 PCrude Stock Refinery
Swamy Estimator
Cotemporaneous effects 0.996** (0.017) [0.014] 0.925** (0.1127) [0.17]
With Lags 1.00** (0.017) [0.017] 2.987** (0.527) [0.472] −2.105** (0.523) [0.602] 0.020 (0.017) [0.014] −5.78E–06** (9.18E–07) [1.84E–07] 7.66E–03** (1.23E–03) [1.34E–03]
0.025 (0.0169) [0.013] −6.09E–06** (8.85E-07) [1.71E–06] 7.81E− 03** (1.24E−03) [1.35E− 03]
0.999** (02.34E−02) 0.266 (0.298) 1.82E− 02 (0.0223) 5.18E− 06 (4.92E−06) 9.53E− 03 (1.88E−06)
Coefficients and test statistics are statistically significantly different from zero at the: **1%, *5%, + 10% level. Values in parenthesis are standard errors calculated in the standard method. Values in brackets are standard errors that are robust to arbitrary correlation within groups (Bertrand et al., 2004).
evaluated with the following test statistic (Hsiao, 1986):
w=
(RSSR RSSU )/[(N 1)*K ] RSSU )/[(NT N (K + 1)]
consumers. Conversely, producers benefit in four for the six states analyzed here, where the rate of pass through is greater than one. To approximate these transfers, I modify the CVAR models for the three states (FL, MA, and NY) that indicate a direct long-run relation between retail prices for and taxes on motor gasoline. To represent a pass-through rate of 1.0, I change the coefficient associated with taxes in Tables 1 (−1.789 [FL], −1.408 [MA], and −2.257 [NY]) to −1.0 and use this new value to simulate the retail price of motor gasoline over the sample period. These results represent the retail price for motor gasoline if taxes are passed to consumers on a one-for-one basis. I use these prices to approximate the sums transferred from consumers to producers. This sum is approximated by subtracting the prices simulated by imposing a one-for-one pass through from prices simulated by the CVAR model which uses the estimated coefficient (see Fig. 3) and multiplying this difference by the quantity of regular motor gasoline purchased in the state (https://www.eia.gov/dnav/pet/pet_ cons_prim_a_EPM0_P00_Mgalpd_m.htm). Results indicate that rates of pass through greater than one transfer $12.2 billion from consumers to retailers in FL, $2.3 billion in MA, and $19.2 billion in NY during the sample period. These transfers represent 10.7%, 6.0%, and 23.9% of total expenditures on regular motor gasoline in FL, MA, and NY respectively. In these states, pass-through rates greater than one-for-one cause consumers to over-pay for motor gasoline. Rates of pass through different than one also create difficulties for efforts to internalize environmental externalities using taxes. According to economic theory, the optimal tax occurs when the marginal cost of abatement equals to marginal damage caused by the externality. This optimal tax is the focus of considerable research; much of the policy debate about climate change focuses on the social cost of carbon. But efforts to quantify the optimal tax are nullified by rates of passthrough greater than or less than one. If prices rise more than the optimal tax (as suggested by results for FL, MA, NY, and OH), the marginal costs of abatement are greater than the marginal cost of the environmental damage. Under these conditions, the tax is too large and too much abatement occurs. Conversely, too little abatement occurs if the marginal cost of abatement is less than the marginal cost of environmental damage. This will occur if the optimal tax is not fully passed to consumers, as suggested by the results for Washington. These ineffective outcomes imply that researchers and policy makers cannot assume that the market passes optimal taxes to consumers on a one-for-one basis. Instead, researchers and policy makers must explicitly consider the rate at which a tax is passed to consumers. This greatly complicates efforts to internalize environmental externalities using taxes.
(5)
in which RSSR is the residual sum of squares for the restricted model (fixed effects estimator), RSSRu is the residual sum of squares for the unrestricted model (OLS), N is the number of individuals (six states), T is the number of observations per state (165), and K is the number of regressors (16). The test statistic is evaluated against an F distribution with (N 1)*K and (NT N (K + 1) degrees of freedom in the numerator and denominator respectively. The test statistic F(80,888) = 2.08, strongly rejects (p < 0.0001) the null hypothesis that the regression coefficients are equal across states.4 If the F test is correct and the regression coefficients are not the same across states, assuming that they are equal and estimating Eq. (4) with the fixed effects estimator will bias the results; the point estimate for 2 will be smaller than its true value (Robertson and Symons, 1992). Consistent with this hypothesis, ˆ2 = 0.925 and is not statistically different from one, regardless of how the standard errors are calculated (Table 2). Similar conclusions are reached based on the sum of point estimates (0.88) for the regression coefficients that are associated with the contemporaneous and lagged effect of taxes on retail prices for motor gasoline (Table 2), as done by (Alm and Skidmore, 2009). The bias associated with the fixed effects estimator is confirmed by estimating Eq. (4) as a random coefficient model, in which all coefficients are allowed to vary across states. The point estimate for ˆ2 (0.27) that is generated by an estimator that allows the rate of pass through (and other independent variables) to vary across individuals (Swamy, 1970) is not statistically different from zero (Table 2). This suggests that ˆ varies across states such that the ‘average’ value calculated by the 2 Swamy estimator cannot be distinguished from zero. This does not imply that taxes have no effect on retail prices; rather the effect varies greatly among states, which contradicts the assumption of homogeneity that is implicit in the fixed effects estimator. 5. Conclusion and policy implications The results reported here suggest that taxes on motor gasoline are not passed to consumers on a one-for-one basis. If correct, this result creates difficulties for taxes on motor gasoline in particular and environmental taxes in general. For motor gasoline, pass through rates different than one-for-one transfer surplus between producers and consumers. For environmental taxes in general, the results make it more difficult to achieve environmental goals. Rates of pass through less than one transfer surplus from producers to consumers; conversely surplus is transferred from consumers to producers when the rates of pass through are greater than one. For one state WA, the rate of pass through is less than one, which benefits
Acknowledgements I thank Hillary Waite for help on a preliminary analysis. I also thank two anonymous reviewers, Michael Dougherty, Stephen Hall, Bryant Gross, Jeff Perloff, Samuel Stolper, and participants in the Fall 2017 meeting of Project LINK for their comments on preliminary versions of the manuscript. All mistakes that remain are solely my responsibility.
4 The null hypothesis is rejected more strongly (F(25,957) = 4.30, p < 0.0001) if the equation includes only the oil supply chain variables.
214
Energy Policy 125 (2019) 207–215
R.K. Kaufmann
Appendix A. Supplementary material
Kao, C., 1999. Spurious regression and residual-based tests for cointegration in panel data. J. Econ. 90, 1–44. Kaufmann, R.K., Laskowski, C., 2005. Causes for an asymmetric relation between the price of crude oil and refined petroleum products. Energy Policy 33, 1587–1596. Kupzczuk, W., Marion, J., Muehlegger, E., Slemod, J., 2016. Does tax-collection invariance hold? Evasion and the pass-through of state diesel taxes. Econ. Policy 8 (2), 251–286. Labandiera, X.J.M.Labeaga., Lopez-Otero, X., 2015. A meta analaysis of the price elasticity of energy demand, WP 04/2015 ISSN 2172/8437. Li, S.J. Linn, Muehlegger, E., 2014. Gasoline taxes and consumer behavior. Am. Econ. J.:Econ. Policy 6 (4), 302–341. Marion, J., Muehlegger, E., 2011. Fuel tax indcidence and supply conditions. J. Public Econ. 95, 1202–1212. Pesaran, M.H., Smith, R., 1995. Estimating long-run relationships from dynamic heterogeneous panels. J. Econ. 68, 79–113. RBB Economics, 2014. Cost pass-through; theory measurement, and potential policy implication 〈https://www.gov.uk/government/publications/cost-pass-throughtheory-measurement-and-policy-implications〉. Robertson, D., Symons, J., 1992. Strange properties of panel data estimators. J. Appl. Econ. 7 (2), 175–189. Silvia, L., Taylor, C.T., 2014. Tax pass-through in gasoline and diesel fuel: the 2003 Washington state nickel funding package increase, working paper no. 324, Bureau of Economics, Federal Trade Commission, Washington, DC 20580. Stolper, Samuel, 2016. Who bears the burden of energy taxes? The critical role of passThrough. Harv. Environ. Econ. Program Discuss. 16–70. Swamy, 1970. Efficient inference in a random coefficient regression model. Econometrica 38 (1), 311–324.
Supplementary data associated with this article can be found in the online version at doi:10.1016/j.enpol.2018.10.045. References Alm, J.E. Sennoga, Skidmore, M., 2009. Perfect competition, urbanization, and tax incidence in the retail gasoline market. Econ. Inq. 47 (1), 118–143. Bello, A., Contin-Pilart, I., 2012. Taxes, cost, and demand shifters as determinants in the regional gasoline price formation process: evidence from Spain. Energy Policy 48, 439–448. Bertrand, M., Duflo, E., Mullainathan, S., 2004. How much should we trust differences indifferences estimates? Q. J. Econ. 119 (1), 249–275. Chouinard, H., Perloff, J.M., 2004. Incidence of federal and state gasoline taxes. Econ. Lett. 83, 55–60. Dennis, J.H. Hansen, S.Johansen., Juselius, K., 2005. CATS for RATS, Version 2. Estima, Evanston, IL. Doyle, J.J., Samphantharak, K., 2008. $2.00 gas! Studying the effects of a gas tax moratorium. J. Public Econ. 92, 869–884. Hsiao, C., 1986. Analysis of Panel Data. Cambridge University Press, New York. Johansen, S., 1996. Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Advanced texts in Econometrics. Oxford University Press, Oxford. Juselius, K., 2006. The Cointegrated VAR Model: Methodology and Applications. Advanced texts in Econometrics. Oxford University Press, Oxford.
215