Perfect competition, urbanization, and tax incidence in the retail gasoline market.

Alm, James ; Sennoga, Edward ; Skidmore, Mark 等

I. INTRODUCTION

In applied tax incidence studies, it is typically assumed that prices respond one-for-one to changes in sales and excise taxes (Chernick and Reschovsky 1997; Pechman 1985; Shepard 1976; State of Wisconsin Department of Revenue 2004; Wiese, Rose, and Schluter 1995; Zupnick 1975). Is this assumption reasonable? Despite the fundamental role of tax incidence in the study of public finance, there is surprisingly little empirical analysis that sheds light on who bears the burden of taxes. In this article, we examine the incidence of state gasoline excise taxes using monthly price data for all 50 states in the United States over the period 1984-1999. Our estimation results generally indicate full shifting of gasoline taxes to the final consumer, with changes in gasoline taxes fully reflected in the tax-inclusive gasoline price almost instantly. We also find that the incidence of excise taxes depends on the competitiveness of retail gasoline markets (e.g., urban vs. rural markets). Gasoline markets in urban states typically exhibit full shifting, but those in rural states demonstrate somewhat less than full shifting.

Although the issue of sales and excise tax incidence has received considerable attention over the years, most research has focused on tax incidence theory, and the standard conclusion of much of this theoretical analysis is that consumers bear the full burden of any sales and excise taxes. (1) Based primarily on this theoretical foundation, most applied incidence studies assume that sales and excise taxes are fully reflected in consumer prices, and the distribution of tax burdens across income classes necessarily reflects this assumption. However, actual empirical testing of this assumption of full forward shifting has been surprisingly sparse. (2) In important recent research, Poterba (1996) and Besley and Rosen (1999) have conducted empirical analyses of the incidence of excise taxes. Poterba (1996) uses city-specific clothing and personal care price data covering the 1947-1977 and the 1925-1939 periods to examine the degree to which state and local retail sales taxes are shifted to consumers, with two data sets based on Bureau of Labor Statistics (BLS) city-specific consumer price indices. Using these BLS data on tax-inclusive prices, Poterba (1996) constructs quarterly price indices for each of 28 Standard Metropolitan Statistical Areas (SMSAs). Many of these 28 SMSAs experienced significant changes in sales tax rates, and Poterba (1996) uses these tax "shocks" to determine the incidence of sales taxes. His estimation results are somewhat variable, but in general he finds for the postwar period that taxes are fully shifted to consumers; in some cases, he finds limited evidence of overshifting, although it is never possible to reject the null hypothesis that prices rise "point-for-point" with the changes in the tax, and he also finds that full shifting typically (though not always) occurs in the first quarter of the tax change. Poterba (1996) also examines tax incidence for individual SMSAs during the Depression era, and his results indicate significant differences across metropolitan areas in the degree of tax shifting. For example, prices on women's clothing in Chicago show significant overshifting, but Atlanta shows negative shifting, a result that does not seem plausible.

Besley and Rosen (1999) also examine the incidence of sales taxes using price data for 12 narrowly defined commodities in 155 different U.S. cities, using quarterly price data for the period 1982-1990 issued by the American Chamber of Commerce Researchers Association (ACCRA). (3) They not only find full shifting for a number of commodities but also find overshifting for more than half the products, a result they attribute to imperfect competition in the retail sector.

While this recent empirical research has significantly expanded our understanding of the actual nature of sales and excise tax incidence, we believe that our work here on gasoline excise taxes makes several contributions to the empirical literature. First, we examine regular unleaded gasoline, and so we are able to focus exclusively on a narrowly defined commodity that has not changed significantly over time in its characteristics. (4) Second, it is important in empirical incidence work to obtain reliable cost data for use as a key control variable, and one limitation of some previous work is that reliable cost data may have been difficult to obtain. With the retail gasoline market, the single most important cost variable is the wholesale price of gasoline, and we are able to obtain information on its cost (as well as other cost information). Third, pricing data used in previous studies came almost exclusively from urban markets, which are likely to be more competitive than rural areas. Our gasoline pricing data are statewide weighted averages and are generated from both urban and rural markets. These data are therefore likely to provide a more representative picture of tax incidence across an entire state. Fourth and relatedly, these data allow us to examine urban and rural gasoline tax incidence separately, in order to test whether more competitive (e.g., urbanized) states yield findings similar to less competitive (e.g., rural) states. Fifth, we use monthly data on gasoline prices, rather than the quarterly price information of Poterba (1996) and Besley and Rosen (1999). The use of monthly data may allow for a more accurate assessment of the length of time required for a complete price response. Finally, we have a number of tax reductions during the period of analysis, so that we can use these episodes of tax reductions to identify whether prices respond asymmetrically to tax changes.

In general, we find consistent evidence of full shifting of gasoline taxes to the final consumer, with changes in gasoline taxes fully reflected in the tax-inclusive gasoline price almost instantly, a result consistent with a retail gasoline market in which firms are perfectly competitive and produce at constant cost. In addition, although we find that gasoline retail prices demonstrate asymmetric responses to changes in gasoline wholesale prices, we do not find such behavior with respect to gasoline excise taxes, perhaps due to the institutions by which taxes are collected and under which wholesale and retail gasoline firms operate. We also examine whether incidence depends somewhat on the competitiveness of retail gasoline markets, as measured by the degree of urbanization of the gasoline market. Consistent with this alternative perspective, our empirical estimates show that gasoline markets in urban states exhibit full shifting, but those in rural states demonstrate somewhat less than full shifting.

[FIGURE 1 OMITTED]

In the following sections, we first present a brief overview of state taxation of gasoline. We then discuss a standard theoretical analysis of excise tax incidence, as well as a novel application of a spatial price discrimination model of tax incidence. We then present our empirical approach, followed by our empirical estimates of retail price reactions to changes in taxes. The final section discusses implications and concludes.

II. THE PRACTICE OF STATE GASOLINE TAX POLICY

Gasoline taxes have changed considerably over time. (5) Figure 1 presents the distribution of taxes in nominal cents per gallon by state in 1984-1999, a period that spans our empirical analysis. In 1984, the average state tax in nominal terms was 11.9 cents/gallon; by 1999, the average state tax had increased to 20.1 cents/ gallon. In real terms, the tax increase has obviously not been as large as indicated in Figure 1, but presenting the data in nominal terms demonstrates that there are many policy-driven tax changes over the period of analysis from which we can generate estimates of tax incidence. It is noteworthy that of the 202 policy-driven tax changes during the period of analysis, 24 were tax reductions, which provides an opportunity to examine whether prices respond asymmetrically to tax increases versus tax decreases. The tax changes were distributed fairly uniformly over this period. We observe 45 tax changes during the 1984-1987 period, 82 changes between 1988 and 1991, 50 changes from 1992 to 1995, and 45 changes during the 1996-1999 period. (6)

The exact procedure by which the state gasoline excise taxes are administered varies across the states. In 42 states (plus the District of Columbia), the tax is administered by a department of revenue or of taxation; in most remaining states, there is a separate transportation or motor vehicles department that is responsible for the administration. Similarly, the agent that collects the gasoline tax (of the "point of taxation") also varies across the states. In many states, it is the gasoline distributor that collects the excise tax; in a smaller number of states, the tax is collected by the retail gasoline station, and several other states collect the tax either on a "first-sale" basis, in which the importer of the gasoline pays the tax upon receipt, or on a "first-import" basis with the tax collected by the agent responsible when the gasoline first comes into the state.

III. ANALYTICAL FRAMEWORK

As noted by Poterba (1996) and Besley and Rosen (1999), the degree of competitiveness is in theory important in determining tax incidence. In the simple case of a perfectly competitive market, the after-tax price of a commodity will increase by precisely the amount of the tax if supply is perfectly elastic (although by less than the amount of the tax if the supply curve slopes upward). (7) However, if markets are not perfectly competitive, then the pattern of excise tax incidence becomes more complicated, anda number of different incidence results are possible. (8) For example, under Bertrand oligopoly with identical firms and constant returns to scale production technology, an excise tax is shifted fully forward to consumers. However, under Cournot-Nash oligopoly, the degree of forward shifting depends on such factors as the elasticity of (inverse) product demand, the relative slopes of the marginal cost and inverse demand functions, and the number of firms. Similarly, under spatial competition, incidence also depends (among other things) on the number of firms, with the amount of shifting to consumers increasing as the number of firms increases (e.g., as the market becomes more competitive); that is, there may well be a difference in gasoline tax incidence between, say, urban and rural gasoline markets. Other models generate a range of possible outcomes, with under- and overshifting to consumers possible in some scenarios depending on such factors as the degree of competition, the extent of firm strategic behavior, the various demand and cost elasticities, the possibility of entry, the use of ad valorem taxes versus unit taxes, homogeneous versus differentiated products, and the like. (9)

Although the retail gasoline market is often considered to be very competitive, several studies indicate that market power may exist in certain submarkets. Increased market concentration has been found to lead to higher energy market prices in general (Borenstein, Cameron, and Shepard 1997; Joskow and Kahn 2000) and within the gasoline market in particular (Borenstein and Shepard 1996). There is also some recent evidence from California showing that the preservation of a competitive market structure enhances price competition in the gasoline market and thereby lowers gasoline prices (Hastings 2004; Verlinda 2004). This work suggests that not all gasoline markets are perfectly competitive. Furthermore, Skidmore, Peltier, and Alm (2004) find that state government antitrust policies playa role in determining the degree of market concentration and competition across states and over time. (10)

As a result, we believe that it is possible, indeed likely, that states differ systematically in the degree of competitiveness in the gasoline market. If so, it is important to explore whether tax incidence also differs in predictable ways across the states that vary in competitiveness. Our empirical framework therefore incorporates both kinds of perspectives--a perfectly competitive retail gasoline market and a retail market in which firms have some market power, as measured by the extent of urbanization (e.g., urban versus rural) in the retail gasoline market.

The next section presents our empirical approach for estimating the incidence of the gasoline tax.

IV. EMPIRICAL FRAMEWORK

A. Methods

We collect monthly price and tax data for all states for the period 1984-1999, which allow us to use variation across the states in the timing of tax changes to investigate how taxes affect average prices in states where the changes occurred. We estimate a within-group model that exploits the panel nature of our data and controls for fixed state and time effects. (11) We also include a full array of control variables, including the state gasoline excise tax, demand-side variables, and supply-side factors, and we estimate a range of alternative specifications to test for the robustness of our results.

The econometric model is as follows. Denote [P.sub.it] as the real monthly weighted average tax inclusive end-user price of unleaded gasoline for state i in period t. We assume that the relationship between the explanatory variables and the price of unleaded gasoline is given by:

(1) [P.sub.it] = [t.sub.it][alpha] + [X.sub.it][beta] + [[mu].sub.i] + [[eta].sub.it] + [[epsilon].sub.it],

(plus a constant term), where [t.sub.it] represents the tax in real cents per gallon in state i at time t, [X.sub.it] is a vector of demand--and supply-side characteristics that determine prices, [[mu].sub.i] and [[eta].sub.t] are fixed state and monthly time effects, [alpha] and [beta] are coefficient vectors, and [[epsilon].sub.it] is a random error term. In several specifications, we also use the log-linear version of this equation.

The fixed-effects model is appropriate for our analysis for two reasons. First, much of the variation in prices is between states rather than within states. Although it would be difficult to specify all the institutional, economic, and demographic characteristics that determine the differences across states in prices, we can capture permanent differences between states with state fixed effects. Similarly, there are many factors that may affect prices over time, and we capture those differences with monthly time effects. Second, the fixed-effects model is a within-group estimator that uses a weighted average of the within- and across-state variation to form the parameter estimates. Therefore, our estimate of the effects of tax changes measures how prices change within the states as taxes change. Having said this, we have also estimated similar specifications with a random-effects model, and our results are unaffected. (12)

Given that our panel consists of 50 states for which we have monthly series over 16 yr, it is likely that the errors are serially correlated. Failure to correct for serial correlation when it exists yields consistent but inefficient estimates of the coefficients and biased standard errors. The Baltagi-Li LM test (Baltagi 1995) for first-order serial correlation in a fixed-effects model shows that we should reject the null hypothesis of no first-order serial correlation. This result implies that we need to correct for the serial dependence in the error terms. In particular, we correct for first-order autocorrelation using the Prais-Winston transformation. (13) Estimation is via ordinary least squares (OLS), but the OLS standard errors are replaced with panel-corrected standard errors that account for the contemporaneous correlation across panels (Beck and Katz 1996). The Prais-Winston transformation yields Durbin-Watson (transformed) statistics that are close to 2, and we therefore do not test for the presence of higher order serial dependence. (14) Further, since the OLS estimation procedure yields consistent and unbiased estimates only when the data are stationary, we also tested for the presence of unit root. The Phillips-Perron unit root test indicates that we should reject the null hypothesis of a unit root at the 99% significance level. (15)

B. Data

Our dependent variable is the inflation-adjusted, monthly tax-inclusive retail price of unleaded gasoline in state i for time period t, measured in cents per gallon (or in its natural log). We obtain information on the retail and wholesale prices for the years 1984-1999 from a report published by the U.S. Energy Information Administration (Petroleum Marketing Monthly). The Petroleum Marketing Monthly reports retail and wholesale prices that are inflation-adjusted weighted averages net of all federal, state, and local sales and excise taxes, and are drawn from a sample of more than 3,500 companies. (16) As discussed below, we collect detailed information on state gasoline taxes. To obtain a measure of the tax-inclusive price (P), we add the retail price obtained from the Petroleum Marketing Monthly and our tax measure together.

We use weighted averages of both the retail and the wholesale prices of gasoline across the entire state, rather than price data from a few selected cities and/or localities, to analyze consumer activity and behavior within a given state as a whole. Along the same lines, we believe that the use of a weighted monthly average gasoline price data over a substantial period of time captures more accurately both the immediate and the long-run impact of gasoline taxes on gasoline retail prices within each state. However, as noted by Skidmore, Peltier, and Alm (2004), one drawback to the use of state-average measures of price is that potential differential effects in submarkets within a given state cannot be captured. Overcoming this limitation is cumbersome, given that it is difficult to obtain consistent disaggregated data for an extended period of time (e.g., data collected and analyzed at the store level for all states).

We include several explanatory variables to measure the variations in the gasoline retail price across states and over time. Our primary regressor is the inflation-adjusted state gasoline tax, measured in real cents per gallon. (17) Our specifications include variants of this gasoline tax variable: the level of the gasoline tax in cents per gallon, the natural logarithm of the gasoline tax, and lagged values of the gasoline tax (in order to account for the fact that changes in the gasoline tax may take time to be fully reflected in gasoline prices).

To assess the impact of gasoline taxes on gasoline prices, it is necessary to control for other factors that potentially affect gasoline prices. Following Vita (2000) and Skidmore, Peltier, and Alm (2004), we include several demand- and supply-side factors that influence gasoline prices. These include the following: the average annual real retail wage, real per capita income, the total number of vehicles per capita, the total number of licensed drivers per capita, the real resale gasoline price (real wholesale price of unleaded gasoline in cents), the number of heating days in the census region (average heating degree days), and population density. As noted above, we include state and time dummy variables to control for the unobservable, permanent differences across states as well as the factors that affect all prices over time. Finally, following Skidmore, Peltier, and Alm (2004), we include a reformulated gasoline dummy variable. Beginning January 1, 1994, the Clean Air Act Amendments of 1990 required that cleaner burning and more expensive reformulated gasoline be sold in the nine worst "ozone nonattainment" areas; the reformulated gasoline dummy is included to control for this factor. (18) Table 1 gives the definitions and sources of the variables, and Table 2 provides summary statistics on the variables.

On the demand side, Vita (2000) has shown that gasoline demand is influenced by population and population density. An increased population may lead to increased demand for gasoline and thus an increase in price. The effect of population density is ambiguous. More densely populated areas have other alternative transportation modes, leading to a reduction in demand. (19) However, more densely populated areas experience greater traffic congestion and thus more fuel consumption per mile traveled, as well as higher rental values, and these factors suggest that prices may be higher in more densely populated areas. We also include the number of vehicles per capita, the number of drivers per capita, and income per capita to control for changes in gasoline demand.

On the supply side, we include the wholesale gasoline price variable in the retail price regressions to control for changes in the most important input cost for retailers. We also include the real annual retail wage variable to control for changes in wage costs for gasoline retailers. Following Borenstein, Cameron, and Shepard (1997) and Vita (2000), we include average heating degree days as an exogenous determinant of gasoline production costs. (20) Finally, we include the reformulated gasoline dummy to control for the Clean Air Act Amendments of 1990 regulations on ozone nonattainment regions.

As discussed in more detail later, we also categorize states into three groups based on "low," "medium," and "high" urbanicity to determine tax incidence in environments that seem likely to differ in competition. It is important to note that the changing patterns in gasoline taxation within these groupings do not exhibit any systematic geographical patterns--all three categories include states from all regions (New England, Middle Atlantic, South, Midwest, Southwest, and West).

IV. ESTIMATION RESULTS

A. Linear Specifications

Consider first Table 3, which presents the estimation results from a linear model without lags and from a linear model that includes a single lag for both the tax variable and the wholesale price variable. (21) Specification 1 of Table 3 reveals that a 10-cent increase in the inflation-adjusted gasoline tax (rtax) leads to a 9.98-cent increase in the inflation-adjusted retail price of unleaded gasoline, a magnitude that is not significantly different from 1 (e.g., full shifting). This result therefore suggests that there is a one-for-one increase in the tax-inclusive gasoline price from an increase in the gasoline tax, a result consistent with a retail gasoline market in which firms are perfectly competitive and produce at constant cost.

Specification (2) in Table 3 reveals that there is no statistical evidence of lagged responses of tax-inclusive gasoline prices (rtaxl) to changes in the gasoline tax, so that prices shift fully during the first month of the tax change. If we sum the coefficients on the tax variable and on the lagged tax variable, the full effect is 9.92 cents, a result that is again consistent with almost complete forward shifting of a 10-cent increase in the gasoline tax.

The control variables generally have the expected signs, although several coefficients are statistically insignificant and one is contrary to expectations. For instance, a 1-cent increase in the wholesale price of gasoline (resale) raises the tax-inclusive price by eight-tenths of a cent, when a lagged response to the wholesale price (resalel) is included. As expected, increases in real retail wages (rwage) are correlated with higher prices, and more drivers per capita (pcdriv) also lead to higher prices. Somewhat surprisingly, an increase in the average number of heating degree days (heatdays) is negatively correlated with prices. The population density, the number of vehicles per capita (pcveh), real income per capita (rincome), and the reformulated gasoline dummy variable (reformD) are not significant determinants of retail price.

B. Log-Linear Specifications

Specifications (3) and (4) in Table 4 use double log functions, and thus the coefficient estimates are interpreted as elasticities. These specifications indicate that a 10-cent increase in the gasoline tax raises the tax-inclusive gasoline price by 9.93 cents. (22) These results further confirm that gasoline tax changes lead to complete (or nearly complete) forward tax shifting. As in Specifications (1) and (2) in Table 3, the other key explanatory variable, of the wholesale price of gasoline, again exerts a positive and statistically significant impact on the tax-inclusive gasoline price. Further, Specifications (3) and (4) show that gasoline prices in the nine worst ozone nonattainment areas are on average about 1% higher compared to the other states in our sample, as shown by the positive though statistically insignificant coefficient on the reformD variable in both Specifications (3) and (4).

C. Asymmetric Responses

Specifications (5) and (6) in Table 5 test for the asymmetric response of gasoline prices to gasoline tax changes. Here, we test the hypothesis that the tax-inclusive gasoline retail price is more responsive to gasoline excise tax increases than to gasoline tax reductions. Given that previous work shows that retail prices respond asymmetrically to wholesale prices, we also examine whether the tax-inclusive gasoline retail price responds asymmetrically to changes in gasoline wholesale prices.

To test these hypotheses, we construct the variables "ctaxpd" and "cresalepd," which are dummy variables equal to 1 if tax changes (ctaxpd) or wholesale price changes (cresalepd) are positive and equal to 0 otherwise. The existence of an asymmetric response will be reflected by positive and statistically significant coefficients on the "ctaxpd" and "cresalepd" variables. As shown in Specifications (5) and (6) in Table 5, there is no statistical evidence of an asymmetric response of tax-inclusive gasoline prices to changes in gasoline taxes. However, these specifications also reveal that tax-inclusive gasoline prices are more responsive to increases than to decreases in gasoline wholesale prices. This finding is consistent with Borenstein, Cameron, and Shepard (1997), who find that retail gasoline prices respond more quickly to increases than to decreases in crude oil prices.

These results may be due to the institutions by which gasoline taxes are collected and under which wholesale and retail gasoline firms operate. For example, retail gasoline stations are likely to watch wholesale prices on a daily basis and attempt to set prices in accordance with the replacement costs of gasoline, which suggests a quick response to any change in wholesale gasoline prices. However, if there is a competitor with a large inventory of gasoline and if that competitor chooses to keep prices low, then others in the market might not increase retail prices to reflect fully and immediately any change in wholesale prices. Consequently, inventories may provide an opportunity for competitors to hold down retail prices in an effort to generate volume and market share and thereby weaken somewhat the connection between wholesale price changes and subsequent retail prices changes. As for tax payments, gasoline excise taxes are collected in different ways across the states (e.g., from gasoline distributors, from retailers, on a first-sale basis or a first-import basis). Regardless, however, the agent at the point of taxation is responsible for collection and remittance of the excise tax, and this agent is responsible for all the gasoline tax from the time of any increase. There would therefore seem to be no incentive for a lagged response to tax changes by the agent at the point of taxation. (23) Also, tax changes are likely to be known in advance of the effective date, thereby allowing collection agents to plan accordingly; in contrast, wholesale prices may change daily without advance warning.

Specifications (5) and (6) also indicate that a 10-cent increase in the gasoline tax raises the tax-inclusive gasoline price by 9.91 cents, a result that is consistent with almost complete full forward shifting.

D. Urbanicity, Competition, and Prices

The estimation results in Tables 6 and 7 examine whether price reactions are similar in markets with differing levels of competitiveness. Here, we split the states into three equally sized categories based on a constructed measure of urbanicity (e.g., low, medium, and high urbanicity), and we estimate separate regressions on each subsample to examine whether tax shifting differs systematically among these states. Urban areas exhibit a more competitive retail gasoline market, and so urbanized states should experience close to full forward shifting, while rural (and less competitive) states seem likely to experience less than full shifting.

More specifically, we create a measure of "urbanicity" to proxy the level of market competition in the retail gasoline market. Our data are sorted in ascending order according to the proportion of the population residing in urban areas. We then group the states into three categories defined as low-, medium-, and high-urbanicity states. The cut-offs for the proportion in urban areas are chosen to classify approximately one-third of the states in each category and are specified as 32.2%-63.2% for the low-urbanicity category, 64.9%-74.1% for the medium-urbanicity category, and 76.4%-92.6% for the high-urbanicity category. (24) States in these groupings do not exhibit any systematic geographical patterns; that is, all three categories include states from all regions (e.g., New England, Middle Atlantic, South, Midwest, Southwest, and West).

As shown in Specification (7) in Table 6, the low-urbanicity states exhibit marginally less than full shifting. For every 10-cent increase in taxes, retail prices increase by 9.49 and 9.69 cents in the low- and high-urbanicity states, results that are statistically different than full shifting at the 99% confidence level. In contrast, the medium-urbanicity regression (Specification (8)) reveals overshifting.

In Table 7, we present three additional specifications that examine both the timing and the asymmetry of the price response in the low-, medium-, and high-urbanicity states. In the medium- and high-urbanicity states, we observe a full price response in 2 mo; however, in the low-urbanicity states, the price response is immediate. In fact, in both low- and medium-urbanicity states, the price response in the first month is less than full shifting, but in the second month, prices rise to reflect full shifting. In contrast, the high-urbanicity states appear to exhibit greater than full shifting in the first month, and then, in the second month, prices tend to fall. Also, for the medium- and high-urbanicity states, we find evidence of an asymmetric response to a tax change, but we find no such response for the low-urbanicity states.

Interestingly, for the medium-urbanicity states, prices respond more quickly to tax increases than to tax decreases, but the opposite is true for high-urbanicity states.

VI. CONCLUSIONS

So who bears the burden of gasoline excise taxes? We find strong and consistent evidence of full shifting of gasoline taxes to the final consumer. We also find that changes in gasoline taxes are reflected almost instantly in the tax-inclusive gasoline price, whereas gasoline retail prices exhibit a more gradual response to changes in gasoline wholesale prices. Additionally, although gasoline retail prices depict asymmetric responses to changes in gasoline wholesale prices, we find little evidence that such behavior of retail prices is reflected with respect to changes in gasoline excise taxes. Finally, our estimation results indicate that tax shifting depends in part on the degree of competition in a state, with less than full shifting in more rural (and so less competitive) states.

ABBREVIATIONS

ACCRA: American Chamber of Commerce Researchers Association

BLS: Bureau of Labor Statistics

OLS: Ordinary Least Squares

SMSAs: Standard Metropolitan Statistical Areas

APPENDIX

The OLS procedure yields consistent but inefficient parameter estimates. One may also correct for serial dependence using a first-difference estimation procedure. The first-differenced estimating equation is a linear transformation of the model given in Equation (1):

[DELTA][P.sub.it] = [DELTA][x.sub.it] [beta] + [DELTA][[eta].sub.t] + [DELTA][[epsilon].sub.it],

where [DELTA][P.sub.it] = [P.sub.it] - [P.sub.it-1], [DELTA][x.sub.it] = [x.sub.it] - [x.sub.i,t-1], [DELTA][[eta].sub.t] = [[eta].sub.t] - [[eta].sub.t-1], and [DELTA][[epsilon].sub.it] = [[epsilon].sub.it] = [[epsilon].sub.it] - [[epsilon].sub.i,t-1]. The first-differencing transformation eliminates the unobserved effect [[mu].sub.i]. The first-difference estimator is in this case the pooled OLS estimator from the regression:

[DELTA][P.sub.it] on [DELTA][x.sub.it] and [DELTA][[eta].sub.t], t = 2, ..., T; i = 1, 2, ..., N.

The first-differenced estimator is unbiased, consistent, and efficient, and the first differences of the errors are serially independent and have constant variance (Wooldridge 2002). Appendix Tables A1-A5 present the results from the first-difference estimator, where the first difference is denoted "D."

TABLE Al
Perfect Competition: First-Difference Linear Specifications

Independent Dependent Variable: First Difference
Variables of Tax-Inclusive Price P

 (1) (2)

Drtax 0.995 (12.05) *** 0.997 (13.13) ***
Drtaxl -0.004 (0.12)
Dresale 0.539 (33.45) *** 0.530 (35.79) ***
Dresalel 0.295 (20.15) ***
Ddensity -0.034 (0.96) -0.078 (2.38) **
Dpcveh -1.238 (0.61) -2.501 (1.36)
Dpcdriv -2.905 (0.85) -3.851 (1.21)
Drincome 0.000 (0.25) -0.000 (0.11)
Dheatdays -0.000 (0.97) -0.000 (0.11)
Drwage 0.000 (1.99) ** 0.000 (2.08) **
DreformD 0.507 (1.18) -0.059 (0.17)
Constant 0.054 (2.07) ** 0.002 (0.08)
Observations 9,550 9,500
Number of states 50 50
[R.sup.2] 0.81 0.83

Notes: All regressions include first-differenced time effects.
Robust t values are given in parentheses. * Significant at 10%;
** significant at 5%; *** significant at 1%.

TABLE A2
Perfect Competition: First-Difference
Log Specifications

 Dependent Variable:
 First Difference of Natural Log
 of Tax-Inclusive Price In P
Independent
Variables (3) (4)

Dlnrtax 0.196 (12.23) *** 0.197 (13.08) ***
Dlnrtaxl 0.001 (0.09)
Dlnresale 0.358 (36.23) *** 0.357 (39.27) ***
Dlnresalel 0.188 (21.92) ***
Dlndensity -0.031 (0.93) -0.055 (1.76) *
Dlnpcveh -0.017 (0.94) -0.024 (1.43)
Dlnpcdriv -0.01 (0.45) -0.013 (0.65)
Dlnrincome -0.042 (0.70) -0.042 (0.84)
Dlnheatdays -0.028 (2.18) ** -0.015 (1.43)
Dlnrwage 0.056 (2.35) ** 0.048 (2.12) **
DreformD 0.008 (1.44) 0.001 (0.26)
Constant -0.000 (1.31) 0.000 (0.74)
Observations 9,550 9,500
Number of states 50 50
[R.sup.2] 0.81 0.83

Notes: All regressions include first-differenced time effects.
Robust t values are given in parentheses. * Significant at 10%;
** significant at 5%; *** significant at 1%.

TABLE A3
Perfect Competition: First-Difference Linear and Log
Asymmetric Response Specifications

Dependent Variable:
First Difference of
Tax-Inclusive Price P (5)

Drtax 0.851 (6.61) ***
Drtaxl 0.143 (1.05)
Dctaxpd 0.156 (1.01)
Dresale 0.448 (24.71) ***
Dresalel 0.382 (19.33) ***
Dcresalepd 0.181 (6.78) ***
Ddensity -0.087 (2.73) ***
Dpcveh -2.853 (1.57)
Dpcdriv -4.307 (1.39)
Drincome -0.000 (0.00)
Dheatdays 0.000 (0.65)
Drwage 0.000 (1.98) **
DreformD -0.045 (0.13)
Constant -0.005 (0.19)
Observations 9,500
Number of states 50
[R.sup.2] 0.84

Dependent Variable:
First Difference of Natural
Log of Tax-Inclusive Price In P (6)

Dlnrtax 0.202 (5.27) ***
Dlnrtaxl -0.004 (0.11)
Dclntaxpd -0.009 (0.19)
Dlnresale 0.304 (27.61) ***
Dlnresalel 0.247 (20.93) ***
Dclnresalepd 0.121 (7.53) ***
Dlndensity -0.061 (1.98) **
Dlnpcveh -0.026 (1.56)
Dlnpcdriv -0.016 (0.79)
Dlnrincome -0.037 (0.75)
Dlnheatdays -0.007 (0.67)
Dlnrwage 0.045 (2.02) **
DreformD 0.001 (0.38)
Constant 0.000 (0.50)
Observations 9,500
Number of states 50
[R.sup.2] 0.83

Notes: All regressions include first-differenced time effects.
Robust t values are given in parentheses. * Significant at 10%;
** significant at 5%; *** significant at 1%.

TABLE A4
Urbanicity: First-Difference Linear Specifications

 Dependent Variable: First Difference
 of Tax-Inclusive Price P

Variables (7) Low Urbanicity (8) Medium Urbanicity

Drtax 0.876 (13.20) ** 1.008 (14.63) **
Dresale 0.439 (18.25) ** 0.534 (17.78) **
Ddensity -0.110 (2.65) ** -0.055 (0.71)
Dpcveh -6.014 (2.49) * -0.429 (0.09)
Dpcdriv -0.913 (0.33) -11.660 (l.ll)
Drincome -0.000 (1.00) -0.000 (0.55)
Dheatdays 0.001 (2.39) * -0.001 (2.07) *
Drwage 0.000 (1.51) 0.000 (1.67)
DreformD 0.196 (0.25)
Constant 0.055 (1.56) 0.109 (1.60)
Observations 3,247 3,247
Number of states 17 17
[R.sup.2] 0.86 0.81

 Dependent Variable:
 First Difference of
 Tax-Inclusive Price P

Variables (9) High Urbanicity

Drtax 1.096 (6.62) **
Dresale 0.590 (20.45) **
Ddensity 0.002 (0.03)
Dpcveh 4.112 (0.86)
Dpcdriv -2.765 (0.40)
Drincome 0.000 (0.64)
Dheatdays -0.000 (0.47)
Drwage -0.000 (0.10)
DreformD -0.463 (0.59)
Constant 0.015
Observations 3,056
Number of states 16
[R.sup.2] 0.80

Notes: All regressions include first-differenced time effects.
Robust t values are given in parentheses. * Significant at 10%;
** significant at 5%; *** significant at 1%.

TABLE A5
Urbanicity: First-Difference Linear Asymmetric Response
Specifications

 Dependent Variable:
 First Difference of Tax-Inclusive
 Price P

Variables (10) Low Urbanicity (11) Medium Urbanicity

Dtax 1.046 (4.87) *** 0.566 (2.86) ***
Drtaxl -0.281 (1.35) 0.515 (2.58) **
Dctaxpd -0.143 (0.61) 0.501 (2.14) **
Dresale 0.368 (16.82) *** 0.436 (12.49) ***
Dresalel 0.335 (14.40) *** 0.402 (10.04) ***
Dcresalepd 0.166 (4.74) *** 0.214 (4.48) ***
Ddensity -0.131 (3.31) *** -0.126 (1.73) *
Dpcveh -6.373 (3.17) *** -1.779 (0.43)
Dpcdriv -1.579 (0.62) -16.206 (1.88) *
Drincome -0.000 (1.47) -0.000 (0.79)
Dheatdays 0.001 (3.28) *** -0.000 (1.30)
Drwage 0.000 (1.43) 0.000 (1.48)
DreformD -0.766 (1.40)
Constant 0.009 (0.28) 0.010 (0.49)
Observations 3,230 3,230
Number of states 17 17
[R.sup.2] 0.88 0.84

 Dependent Variable:
 First Difference of
 Tax-Inclusive Price P

Variables (12) High Urbanicity

Dtax 1.194 (9.16) ***
Drtaxl -0.056 (0.37)
Dctaxpd -0.123 (0.70)
Dresale 0.502 (15.45) ***
Dresalel 0.383 (10.84) ***
Dcresalepd 0.140 (2.85) ***
Ddensity -0.059 (1.01)
Dpcveh 2.151 (0.62)
Dpcdriv 0.693 (0.11)
Drincome 0.000 (0.85)
Dheatdays 0.000 (0.41)
Drwage 0.000 (0.27)
DreformD -0.551 (0.87)
Constant -0.0O6 (0.07)
Observations 3,040
Number of states 16
[R.sup.2] 0.83

Notes: All regressions include first-differenced time effects.
Robust t values are given in parentheses. * Significant at 10%;
** significant at 5%; *** significant at 1%.

REFERENCES

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Bulow, J., and P. Pfleiderer. "A Note on the Effect of Cost Changes on Prices." Journal of Political Economy, 91, 1983, 183-5.

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Katz, M., and H. Rosen. "Tax Analysis in an Oligopoly Model." Public Finance Quarterly, 13(1), 1985, 3-21.

Kay, J. A., and M. J. Keen. "How Should Commodities Be Taxed?" European Economic Review, 23, 1983, 339-58.

Kotlikoff, L. J., and L. H. Summers. "Tax Incidence," in Handbook of Public Economics, Vol. II, edited by A. J. Auerbach and M. S. Feldstein. Amsterdam, The Netherlands: Elsevier Publishing Co., 1987, 1043-1092.

McLure, C. E. Jr.. "General Equilibrium Incidence Analysis." Journal of Public Economics, 4, 1975, 125-61.

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Shepard, L. "The Short-run Incidence of a Gasoline Rebate Plan." Journal of Economic Issues, 10(2), 1976, 169-78.

Sidhu, N. "The Effects of Changes in Sales Tax Rates on Retail Prices." Proceedings of the Sixty-Fourth Annual Conference on Taxation, 1971, 720-33.

Skidmore, M., J. Peltier, and J. Alm. "Do Motor Fuel Sales-below-cost Laws Reduce Prices?" Journal of Urban Economics, 57, 2004, 189-211.

State of Wisconsin Department of Revenue. Wisconsin Tax Incidence Study. Madison, WI. 2004.

Stern, N. "The Effects of Taxation, Price Control and Government Contracts in Oligopoly." Journal of Public Economics, 32, 1987, 133-58.

Sumner, D. "Measurement of Monopoly Behavior: An Application to the Cigarette Industry." Journal of Political Economy, 89, 1981, 1010-1019.

Sullivan, D. "Testing Hypotheses about Firm Behavior in the Cigarette Industry." Journal of Political Economy, 93, 1985, 586-99.

United States Federal Highway Administration. Highway Statistics. Washington DC: Government Printing Office, 1980-2002.

Verlinda, J. A. "Price-Response Asymmetry and Spatial Differentiation in Local Retail Gasoline Markets." University of California-Irvine Working Paper, 2004.

Vita, M. "Regulatory Restrictions on Vertical Integration and Control: The Competitive Impact of Gasoline Divorcement Policies." Journal of Regulatory Economics, 18, 2000, 217-33.

Wiese, A., A. Rose, and G. Schluter. "Motor-Fuel Taxes and Household Welfare: An Applied General Equilibrium Analysis." Land Economics, 71, 1995, 229-43.

Woodard, F., and H. Spiegelman. "Effects of the 1965 Excise Tax Reduction upon Prices of Automotive Replacement Parts." National Tax Journal, 20(2), 1967, 250-8.

Wooldridge, J. M. Econometric Analysis of Cross Section and Panel Data. Cambridge, MA: The MIT Press, 2002.

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Alm: Professor and Dean, Andrew Young School of Policy Studies, Georgia State University, Campus Box 3992, Atlanta, GA 30302-3992. Phone 404-413-0093, Fax 404-413-0004, E-mail [email protected].

Sennoga: Professor, Department of Economic Policy and Planning, Faculty of Economics and Management, Makerere University, P.O. Box 7062, Kampala, Uganda. Phone +256-41-4-530115, E-mail [email protected].

Skidmore: Professor and Morris Chair in State and Local Government Finance and Policy, Department of Agricultural Economics, Michigan State University, East Lansing, Michigan 48824-1039. Phone 517-353-9172, Fax 517-432-1800, E-mail [email protected].

doi: 10.1111/j.1465-7295.2008.00164.x

Online Early publication August 21, 2008

(1.) For example, see Brown (1939), Due (1942), Rolph (1952), Musgrave (1959), and Bishop (1968). For more general analyses of the theory of tax incidence, see Harberger (1962), Mieszkowski (1967), McLure (1975), Kotlikoff and Summers (1987), and Fullerton and Metcalf (2002).

(2.) For some examples of early empirical research on the incidence of sales and excise taxes, see Due (1954), Brownlee and Perry (1967), Woodard and Spiegelman (1967), and Sidhu (1971). For comprehensive discussions of this early work, see Poterba (1996) and Besley and Rosen (1999).

(3.) The ACCRA price information was originally gathered from establishments and neighborhoods used by a "mid-management executive household." Comparisons indicate that the ACCRA price index is similar to the BLS price index, generating a correlation of .715.

(4.) For example, Poterba (1996) examines price reactions of "women's and girls' clothing," "men's and boys" clothing," and "personal care items." Besley and Rosen (1996) examine more specific commodities such as bananas, Crisco, eggs, and shampoo.

(5.) See the Federation of Tax Administrators for a useful discussion of state gasoline taxation, at http://www.taxadmin.org/ fta/mf/rate/ssi. Also, the U.S. Department of Energy has an overview of the gasoline market in "A Primer on Gasoline Prices" (DOE/EIA-X040-2-01) at http://www.eia.doe.gov/pub/oil_gas/petroleum/ analysis_publications/primer_on_gasoline_prices/html/petbro.html.

(6.) Eight states apply the general sales tax to the purchase of gasoline (California, Georgia, Illinois, Indiana, Louisiana, Michigan, Mississippi, and New York). However, since sales tax rates in these states changed little over the period of analysis, we do not focus on this tax in our analysis.

(7.) For example, suppose that a perfectly competitive market has a demand curve defined by [P = a - bQ] and a supply curve defined by [P = c + dQ], where a, b, c, and d are positive parameters. The imposition of a specific excise tax t changes the supply curve to [P = c + t + dQ], where the price P is interpreted as the gross-of-tax price paid by consumers. Solving these equations gives P = (ad + bc + bt)/(b + d). The tax therefore raises the gross-of-tax price paid by consumers and lowers the net-of-tax price received by producers; that is, [partial derivative]P/[partial derivative]t = b/(b + d), and the incidence is in general split between consumers and producers depending on the slopes (and the elasticities) of the demand and supply curves. The incidence will fall completely on consumers (e.g., [partial derivative]P/[partial derivative]t = 1) in the special cases that b equals infinity or d equals 0; the former case implies that demand is perfectly inelastic, and the latter case implies that supply is perfectly elastic. Consequently, although in the short run the incidence is likely to be split between consumers and producers, it also seems likely that, as the elasticity of supply increases with an increase in the time horizon, the relative burden on consumers will increase in the long run in perfectly competitive markets. Indeed, if in the long run supply becomes perfectly elastic, then the burden of the gasoline excise tax will fall completely on the consumers. Other, more complicated scenarios also generally imply that consumers are likely to bear the bulk of the tax burden.

(8.) For example, see the theoretical analyses of Greenhut and Greenhut (1975); Salop (1979); Kay and Keen (1983); Katz and Rosen (1985); Stern (1987); and Anderson, de Palma, and Kreider (2001); and the empirical work of Sidhu (1971); Poterba (1996); and Besley and Rosen (1999); see also Sumner (1981), Bulow and Pfleiderer (1983), and Sullivan (1985). For a recent review of the entire tax incidence literature, including the results when markets are not perfectly competitive, see Fullerton and Metcalf (2002).

(9.) Again, see Fullerton and Metcalf (2002) for a survey of much of this literature.

(10.) Skidmore, Peltier, and Alm (2004) show that the adoption of a motor fuel sales-below-cost law (or a minimum mark-up law) by a state enhances the competitiveness of the retail gasoline market.

(11.) State fixed effects capture any permanent differences across states (e.g., laws banning self-service, divorcement, transportation costs) not otherwise captured by other explanatory variables. Similarly, the time effects capture any variation in prices over time that affects the whole country (e.g., changes in national environmental standards, federal excise taxes, crude oil prices).

(12.) Hsiao (1986) presents an excellent discussion of panel data estimation procedures.

(13.) See Greene (2000) for a detailed discussion of the Prais-Winston transformation.

(14.) The first-difference approach was also used to correct for serial correlation, and the estimation results are nearly identical. We rely on the results from the Prais-Winston transformation due to the case of interpretation. See also Bharghava, Franzini, and Narendranathan (1982) for methods to due with serial correlation.

(15.) We also tested for the presence of unit root using the modified and augmented Dickey-Fuller unit root tests, and these tests also show that we should reject the null hypothesis of unit root at the 99% level of significance. Absence of unit roots implies that the Prais-Winston transformation yields consistent, unbiased, and efficient estimates. Our conclusions are therefore based on the Prais-Winston estimates, but we also estimated all our specifications using the first-difference approach. A discussion of the first-difference estimation approach and regression results are presented in Appendix. We note that results from the first-difference estimation approach are largely similar to those obtained using the Prais-Winston transformation.

(16.) For a more detailed discussion of the price data, see http://www.eia.doe.gov/oil_as/petroleum/data_publications/ petroleum_marketing_monthly/pmm.html.

(17.) In principle, we might also include the federal gasoline excise tax. However, since the federal tax is the same for all states at any given time, the time effects control for this. Since we cannot include both the time effects and the federal tax simultaneously, we choose to include only the time effects. Our tax measure also includes local taxes that are consistently applied statewide but not location-specific taxes. Including local excise and sales taxes imposed on gasoline is difficult to incorporate into a statewide analysis. However, the estimated coefficient on the state tax variable is only biased by this omission if changes in state taxes are systematically correlated with changes in local taxes.

(18.) These areas are Baltimore, Chicago, Hartford, Houston, Los Angeles, Milwaukee, New York, Philadelphia, and San Diego. Also, Sacramento was added later.

(19.) Note that increased population density may lead via the supply side to reduced wholesale transport costs.

(20.) Transportation and production costs of gasoline are affected by the demand for jointly produced products such as home heating oil, which has a demand that is weather determined. Gasoline is a by-product of the production of home heating oil so that gasoline and home heating oil are complements in production but substitutes in transportation. The expected sign on this variable is indeterminate.

(21.) Changes in the gasoline taxes may not be instantaneously reflected in the tax-inclusive gasoline price. We include the lag of the gasoline tax to account for this effect; additional lags beyond l mo provide no additional information to the regression.

(22.) Interpreting the tax coefficient as an elasticity ([epsilon]) and using average values of the tax-inclusive gasoline price (P) and the real gasoline tax per unit of 96.69 and 18.98 cents, respectively, then the impact of the excise tax on price is given by [DELTA]P = [[epsilon]([DELTA]t/t)P]. This equation yields [DELTA]P = 0.993 for Specification (3) in Table 4. A similar estimate is found for Specification (4).

(23.) We thank Robert Bartlett of the Wisconsin Petroleum Marketers and Convenience Store Association for insight into the dynamic pricing behavior of gasoline retailers.

(24.) The low-urbanicity category has 17 states, including Alabama, Arkansas, Georgia, Idaho, Iowa, Kentucky, Maine, Mississippi, Montana, North Carolina, North Dakota, New Hampshire, South Carolina, South Dakota, Tennessee, Vermont, and West Virginia. The medium-urbanicity category also includes 17 states: Alaska, Delaware, Kansas, Indiana, Louisiana, Michigan, Minnesota, Missouri, Nebraska, New Mexico, Ohio, Oklahoma, Oregon, Pennsylvania, Virginia, Wisconsin, and Wyoming. The high-urbanicity category includes 16 states, including Arizona, California, Colorado, Connecticut, Florida, Hawaii, Illinois, Maryland, Massachusetts, Nevada, New Jersey, New York, Rhode Island, Texas, Utah, and Washington.

TABLE 1 Variable Definitions and Sources

Variable Details

Average annual SIC 5541: Gasoline service station, average
 inflation-adjusted annual inflation-adjusted wage per service
 wage per service station employee in the state
 station employee
Drivers per capita Total number of driver licenses divided by
 state population
Heating degree days Heating degree days by Census Division
 (where "heating degree days" are deviations
 from the mean daily temperature below
 65[degrees]F)
Per capita income Inflation-adjusted per capita income
Population Total state population
Population density Total state population divided by state
 land area in square miles
Proportion of Number of drivers between ages 20 and 44
 drivers between divided by total number of drivers in the
 the ages 20 and 44 state
Proportion of Proportion of population over 65 within the
 population over state
 the age of 65
Retail price of Average monthly inflation-adjusted price of
 unleaded gasoline unleaded gasoline sales to end-users net
 of all taxes (where "sales to end-users"
 are sales made directly to the ultimate
 consumer, including bulk customers such
 as agriculture, industry, and utilities,
 as well as residential and commercial
 customers)
State gasoline tax State gasoline tax in inflation-adjusted
 cents per gallon
Vehicles per Total number of vehicles divided by state
 population population
Wholesale price of Average monthly inflation-adjusted price of
 unleaded gasoline unleaded gasoline sales for resale net of
 all taxes (where "sales for resale" are
 those made to purchasers who are other
 than ultimate consumers)

Variable Source

Average annual http://stats.bls.gov/sahome.html
 inflation-adjusted
 wage per service
 station employee
Drivers per capita Federal Highway Administration, Highway
 Statistics, 1980-1999
Heating degree days http://www.eia.doe.gov/emeu/aer/overview.html
Per capita income http://www.bea.doc.gov/bea/regional/data.htm
Population http://www.census.gov/population/
 www/estimates/statepop.html
Population density http://www.census.gov/population/
 www/estimates/statepop.html
Proportion of Federal Highway Administration, Highway
 drivers between Statistics, 1980-1999
 the ages 20 and 44
Proportion of http://www.census.gov/population/
 population over www/estimates/statepop.html
 the age of 65
Retail price of Energy Information Administration,
 unleaded gasoline Petroleum Marketing Monthly, 1984-1999
State gasoline tax Federal Highway Administration, Highway
 Statistics, 1980-1999
Vehicles per Federal Highway Administration, Highway
 population Statistics, 1980-1999
Wholesale price of Energy Information Administration, Petroleum
 unleaded gasoline Marketing Monthly, 1984-1999

TABLE 2 Summary Statistics for All States, 1984-1999

 Standard
Variables Mean Deviation

Weight 1.00 0.01
reformD (reformulated gasoline dummy) 0.05 0.22
crudeprice (crude oil price) 18.23 93.05
euser (real retail price of unleaded 77.71 13.02
 gasoline in cents)
resale (real wholesale price of unleaded 66.11 12.78
 gasoline in cents)
rtax (real state gasoline tax in cents) 18.98 4.69
pop (population in thousands) 5,075.66 5,492.11
rincome (real per capita income in 21,901.70 3,869.38
 dollars)
density (population density) 167.41 231.13
pccveh (vehicles per capita) 0.79 0.12
pcdriv (drivers per capita) 0.68 0.05
rwage (average annual real retail wage 13,946.88 1,734.68
 in dollars)
heatdays (average heating degree days in 4,687.17 1,663.50
 the census region)
lnresale (natural log of resale) 4.17 0.19
Ineuser (natural log of euser) 4.34 0.17
lnrwage (natural log of rwage) 9.41 0.19
Inpop (natural log of pop) 8.05 1.01
lnrincome (natural log of rincome) 9.98 0.17
lndensity (natural log of density) 4.30 1.42
lnpcveh (natural log of pcveh) -0.24 0.14
lnpcdriv (natural log of pcdriv) -0.38 0.08
lnheatdays(natural log of heatdays) 8.38 0.39
lncrudeprice (natural log of crudeprice) 2.81 0.26
raxl(lag of rtax) 18.98 4.69
resalel (lag of resale) 66.04 12.82
lnrtaxl (natural log of rtaxl) 2.91 0.27
lnresalel (natural log of resalel) 4.17 0.19
ctax (rtax - rtaxl) 0.01 0.44
cresale (resale - resalel) -0.05 4.43
clntax (lnrtax - lnrtaxl) 0.00 0.02
clnresale (lnresale - lnresalel) 0.00 0.07
P (tax-inclusive real retail price of 96.69 13.26
 unleaded gasoline in cents)
ln P (naturallog of P) 4.56 0.14
positivedummyl (dummy = 1 if etax > 0) 0.03 0.17
positivedummy2 (Dummy = 1 if cresale > 0) 0.51 0.50
positivedummy3 (Dummy = 1 if clntax > 0) 0.03 0.17
positivedummy4 (Dummy = 1 if clnresale > 0.51 0.50
 0)
ctaxpd (ctax x positivedummyl) 0.04 0.41
cresalepd (cresale x positivedummy1) 1.57 2.69
clntaxpd (clntax x positivedummy1) 0.00 0.02
clnresalepd (clnresale x positivedummy1) 0.02 0.04

TABLE 3 Perfect Competition: Linear Specifications

 Dependent Variable: Tax-Inclusive Price P

Independent Variables (1) (2)

rtax 0.998 (45.48) *** 1.001 (45.86) ***
rtaxl -0.009 (0.81)
resale 0.799 (81.21) *** 0.690 (82.06) ***
resalel 0.127 (21.31) ***
density -0.003 (0.46) -0.003 (0.47)
pcveh -0.619 (0.64) -0.551 (0.58)
pcdriv 5.734 (3.53) *** 5.719 (3.63) ***
rincome 0.000 (0.50) 0.000 (1.12)
heatdays -0.000 (1.79) * -0.000 (1.23)
rwage 0.000 (2.08) ** 0.000 (2.11) **
reformD -0.179 (0.69) -0.120 (0.48)
Constant 30.399 (14.31) *** 19.880 (9.36) ***
Observations 9,600 9,550
Number of states 50 50
[R.sup.2] 0.93 0.93
Durbin-Watson statistic 0.6993 0.6592
 (original)
Durbin-Watson statistic 2.0550 2.0709
 (transformed)

Notes: All regressions include state and time effects.
t Values are given in parentheses. * Significant at 10%;
** significant at 5%; *** significant at 1%.

TABLE 4 Perfect Competition: Log Specifications

 Dependent Variable: Natural Log of
 Tax-Inclusive Price In P

Independent Variables (3) (4)

lnrtax 0.195 (47.32) *** 0.195 (47.51) ***
lnrtaxl -0.002 (0.85)
lnresale 0.553 (79.08) *** 0.450 (80.11) ***
lnresalel 0.079 (19.74) ***
lndensity 0.180 (15.63) *** 0.170 (15.18) ***
lnpcvch 0.065 (7.12) *** 0.063 (7.06) ***
lnpcdriv 0.094 (8.60) *** 0.091 (8.51) ***
lnrincome -0.089 (5.11) *** -0.079 (4.66) ***
lnheatdays -0.014 (1.59) -0.010 (1.18)
lnrwage 0.017 (1.81) * 0.019 (2.05) **
reformD 0.007 (2.55) ** 0.007 (2.81) ***
Constant 2.233 (12.23) *** 1.798 (10.02) ***
Observations 9,600 9,550
Number of states 50 50
[R.sup.2] 0.93 0.94
Durbin-Watson statistic 0.6845 0.6502
 (original)
Durbin-Watson statistic 2.0589 2.0735
 (transformed)

Notes: All regressions include state and time effects.
t Values are given in parentheses. * Significant at 10%;
** significant at 5%; *** significant at 1%.

TABLE 5 Perfect Competition: Linear and Log Asymmetric
Response Specifications

Dependent Variable: (5)
Tax-Inclusive Price P

rtax 0.984 (36.21) ***
rtaxl 0.007 (0.37)
ctaxpd 0.022 (0.65)
resale 0.640 (63.33) ***
resalel 0.182 (21.19) ***
cresalepd 0.108 (8.81) ***
density -0.003 (0.45)
pcveh -0.708 (0.75)
pcdriv 6.006 (3.83) ***
rincome 0.000 (1.40)
heatdays 0.000 (6.97) ***
rwage 0.000 (7.92) ***
reformD -0.108 (0.43)
Constant 18.952 (8.96) ***
Observations 9,550
Number of states 50
[R.sup.2] 0.93
Durbin-Watson statistic (original) 0.6609
Durbin-Watson statistic (transformed) 2.0682

Dependent Variable: Natural Log (6)
of Tax-Inclusive Price In P

Inrtax 0.190 (39.05) ***
lnrtaxl 0.003 (0.86)
clntaxpd 0.007 (1.36)
Inresale 0.418 (62.03) ***
Inresalel 0.117 (19.86) ***
clnresalepd 0.071 (8.65) ***
lndensity 0.166 (14.88) ***
Inpcveh 0.060 (6.77) ***
Inpcdriv 0.092 (8.62) ***
lnrincome -0.075 (4.41) ***
lnheatdays -0.008 (0.96)
lnrwage 0.019 (2.09) **
reformD 0.008 (2.86) ***
Constant 1.730 (9.68) ***
Observations 9,550
Number of states 50
[R.sup.2] 0.94
Durbin-Watson statistic (original) 0.6516
Durbin-Watson statistic (transformed) 2.0708

Notes: All regressions include state and time effects.
t Values are given in parentheses. * Significant at 10%;
** significant at 5%; *** significant at 1%.

TABLE 6 Urbanicity: Linear Specifications

Variables Dependent Variable: Tax-Inclusive Price P

 (7) Low Urbanicity (8) Medium Urbanicity

rtax 0.949 (18.80) *** 1.036 (20.25) ***
resale 0.503 (32.83) *** 0.623 (38.60) ***
density -0.177 (7.07) *** -0.022 (1.02)
pcveh -0.923 (0.52) 16.921 (5.37) ***
pcdriv -8.281 (2.90) *** 20.507 (4.48) ***
rincome 0.000 (1.49) -0.001 (3.09) ***
heatdays 0.002 (5.58) *** -0.000 (0.39)
rwage 0.000 (2.74) *** 0.000 (3.32) ***
reformD -3.446 (4.38) ***
Constant 56.160 (12.93)*** 37.359 (6.11) ***
Observations 3,264 3,264
Number of states 17 17
[R.sup.2] 0.98 0.97
Durbin-Watson 0.5332 0.5786
 statistic
 (original)
Durbin-Watson 1.8352 2.0508
 statistic
 (transformed)

Variables Dependent Variable:
 Tax-Inclusive Price P

 (9) High Urbanicity

rtax 0.969 (20.63) ***
resale 0.664 (46.29) ***
density -0.054 (3.68) ***
pcveh -16.657 (6.15) ***
pcdriv -1.447 (0.32)
rincome 0.000 (2.77) ***
heatdays 0.000 (0.07)
rwage 0.000 (1.45)
reformD -2.020 (4.43) ***
Constant 92.789 (5.69) ***
Observations 3,072
Number of states 16
[R.sup.2] 0.97
Durbin-Watson 0.5336
 statistic
 (original)
Durbin-Watson 1.8559
 statistic
 (transformed)

t Values are given in parentheses. * Significant at 10%;
** significant at 5%; *** significant at 1%.

TABLE 7 Urbanicity Competition: Linear Asymmetric
Response Specifications

 Dependent Variable: Tax-Inclusive Price P

Variables (10) Low Urbanicity (11) Medium Urbanicity

rtax 0.926 (16.64) *** 0.878 (14.11) ***
rtaxl 0.040 (0.61) 0.134 (5.59) ***
ctaxpd 0.034 (0.66) 0.472 (6.79) ***
resale 0.485 (28.89) *** 0.530 (27.91) ***
resalel 0.103 (9.46) *** 0.272 (15.52) ***
cresalepd 0.042 (2.19) ** 0.184 (7.88) ***
density -0.171 (7.15) *** -0.025 (1.23)
pcveh -0.878 (0.52) 13.946 (4.78) ***
pcdriv -7.641 (2.81) *** 18.256 (4.30) ***
rincome 0.000 (1.55) -0.000 (2.74) ***
heatdays 0.002 (5.70) *** 0.000 (0.04)
rwage 0.000 (2.89) *** 0.000 (3.37) ***
reformD -2.568 (3.48) ***
Constant 48.639 (11.46) *** 11.254 (1.33)
Observations 3,247 3,247
Number of states 17 17
[R.sup.2] 0.98 0.97
Durbin-Watson 0.5052 0.5317
 statistic
 (original)
Durbin-Watson 1.8439 2.0625
 statistic
 (transformed)

 Dependent Variable:
 Tax-Inclusive Price P

Variables (12) High Urbanicity

rtax 1.157 (19.24) ***
rtaxl -0.168 (4.01) ***
ctaxpd -0.259 (3.96) ***
resale 0.607 (34.89) ***
resalel 0.187 (12.17) ***
cresalepd 0.091 (4.41) ***
density -0.041 (3.07) ***
pcveh -16.718 (6.66) ***
pcdriv -2.056 (0.50)
rincome 0.001 (3.55) ***
heatdays 0.000 (0.28)
rwage 0.000 (1.26)
reformD -1.689 (4.00) ***
Constant 30.905 (6.91) ***
Observations 3,056
Number of states 16
[R.sup.2] 0.97
Durbin-Watson 0.4835
 statistic
 (original)
Durbin-Watson 1.8716
 statistic
 (transformed)

Notes: All regressions include state and time effects.
t Values are given in parentheses. * Significant at 10%;
** significant at 5%; *** significant at 1%.