Disappointing Welfare Impact of Indirect Pigouvian Taxation

The Disappointing Welfare Impact of Indirect Pigouvian Taxation: Evidence from Transportation Abstract A basic tenet of economics is that when consumers or firms don’t face the true social cost of their actions, market outcomes are inefficient. In the case of negative externalities, Pigouvian taxes are one way to correct this market failure, where the optimal tax leads agents to internalize the true cost of their actions. A practical complication, however, is that the level of externality nearly always varies across economic agents and directly taxing the externality may be infeasible. In such cases, policy often taxes a product correlated with the externality. For example, instead of taxing vehicle emissions directly, policy makers may tax gasoline even though per-gallon emissions vary across vehicles. This paper estimates the implications of this approach within the personal transportation market. We have three general empirical results. First, we show that vehicle emissions are positively correlated with vehicle elasticities for miles traveled with respect to fuel prices (in absolute value)—i.e. dirtier vehicles respond more to fuel prices. This correlation substantially increases the optimal second-best uniform gasoline tax. Second, and perhaps more importantly, we show that a uniform tax performs very poorly in eliminating deadweight loss associated with vehicle emissions; in many years in our sample over 75 percent of the deadweight loss remains under the optimal second-best gasoline tax. Substantial improvements to market efficiency require differentiating based on vehicle type, for example vintage. Finally, there is a more positive result: because of the positive correlation between emissions and elasticities, the health benefits from a given gasoline tax increase by roughly 90 percent, compared to what one would expect if emissions and elasticities were uncorrelated. 1 Introduction A basic tenet of economics is that when consumers or firms do not face the true social cost of their actions, market outcomes are inefficient. In the case of externalities, Pigouvian taxes are one way to correct this market failure, and the optimal tax or subsidy leads agents to internalize the true cost of their actions. A practical complication, however, is that the level of externality nearly always varies across economic agents and directly taxing the externality may be infeasible. In such cases, policy often taxes or subsidizes a product correlated with the externality. For example, instead of taxing vehicle emissions directly, policy makers may tax gasoline even though per-gallon emissions vary across vehicles. Similarly, a uniform alcohol or tobacco tax is imposed as a means of reducing the negative externalities associated with their use even though externalities may vary by person or alcohol type. Or, in the case of positive externalities associated with research and development activities, policy might subsidize R&D uniformly across firms. In this paper, we address two related questions. The first is what is the size of the optimal uniform tax rate for gasoline. The second is to what extent of the market inefficiency that remains once this tax is imposed. As to the first question, an obvious starting point for the optimal tax is to set a tax equal to the average of the externality. Diamond (1973), however, shows that the correct tax is based on the joint distribution of agent-specific externalities and demand elasticities. We estimate this joint distribution and calculate how the two taxes differ.1 The second question we address has received very little attention in the literature, but is perhaps even more important. Under the optimal uniform Pigouvian tax, deadweight loss will remain, with some agents under-taxed and others over-taxed. The greater the heterogeneity, the greater the deadweight loss that will remain. Understanding the efficiency gains of agentspecific Pigouvian taxes relative to their uniform counterparts is a valuable input in the costbenefit analysis of policy makers. The larger is the remaining deadweight loss, the greater the payoffs from taxing individuals differentially. Using the framework in Diamond (1973), we analytically solve for the deadweight loss that remains. We then estimate the deadweight 1 Parry and Small (2005) calculate the optimal tax based on average emissions given that the correlation between emissions and price responsiveness, as far as we are aware, has not been estimated. 1 loss that remains in our empirical setting. Our empirical setting is the personal transportation market between 1998 and 2008. We show three things. First, we observe substantial variation in vehicle-level emissions (externalities) in the lightduty vehicle market and that this variation is correlated with the vehicle-specific elasticity of miles driven to gasoline prices. Dirtier vehicles are more price responsive. Using detailed vehicle-specific data on miles driven, we show that that the positive correlation between emissions and elasticities (in absolute value) hold for all three criteria pollutant emissions for which we have data: carbon monoxide, hydrocarbons, and nitrogen oxides, as well as for vehicle weight and greenhouse gases.2 We find that the average “two-year” elasticity of miles traveled is -0.15 across all vehicles, but the the differences across vehicle types is substantial. The elasticity for the dirtiest quartile of vehicles with respect to nitrogen oxides is -0.29. The second, third and fourth quartile elasticities are -0.16, -0.06, and 0.04, respectively. Similar variation exists for carbon monoxide and hydrocarbons. This correlation drives a wedge between the optimal uniform Pigouvian tax associated with emissions and what we call the “naive” tax which is based on average externalities. This increase is substantial, on the order of 50 percent in each of the years of our sample (1998 to 2008). Second, and we argue more importantly, even when instituting the optimal uniform Pigouvian tax, the uniform tax performs very poorly in eliminating deadweight loss. Across our sample (1998 to 2008), we estimate that the optimal uniform Pigouvian tax, a gasoline tax in this case, eliminates only 30 percent of the deadweight loss associated with these pollutants. During the second half of our sample 75 percent of the deadweight loss remains under the optimal uniform tax. We investigate ways to improve upon this. We find that allowing gasoline taxes to be county specific leads to a small improvement, increasing the amount of deadweight loss eliminated by less than 5 percentage points. We find moderate benefits from “homogenizing” the fleet, potentially through vehicle retirement (“Cash-for-Clunkers) programs; scrapping the dirtiest 10 percent of vehicles reduces the deadweight loss that remains 2 Criteria air pollutants are the only air pollutants for which the Administrator of the U.S. Environmental Protection Agency has established national air quality standards defining allowable ambient air concentrations. Congress has focused regulatory attention on these pollutants (i.e., carbon monoxide, lead, nitrogen dioxide, ozone, particulate matter, and sulfur dioxide) because they endanger public health and they are widespread throughout the U.S.. 2 by 14 percentage points. Only when taxes vary by vehicle type, e.g., vehicle’s age, do we see a majority of the amount of deadweight loss eliminated. Finally, there is some good news. We show that the positive correlation that we document between emissions and the miles-driven elasticity (with respect to gasoline prices) implies that health benefits from a given gasoline tax are larger than would be suggested by ignoring this correlation. We estimate that across our sample, the health benefits of a gasoline tax, per gallon of gasoline reduced, increase by 90 percent once one accounts for the the heterogeneity that we document. We also investigate several sources of the heterogeneity to the response of gasoline prices on miles traveled. At the most general level, we show that while the age of the vehicle contributes to our results—older vehicles respond more to changes in gasoline prices—this does not explain all or even most of the heterogeneity. There are at least two additional sources of criteria pollutant-related heterogeneity in the response of changes in gasoline prices. For one, low income consumers may both own dirtier vehicles and be more responsive to changes in gasoline prices. Second, the heterogeneity may come from within-household shifts in vehicle miles traveled, for example if a household has one newer and one older vehicle. As gasoline prices increase, they may shift miles away from the older vehicle and to the newer vehicle. Because age is, on average, correlated with both fuel economy and criteria pollutant emissions, this would lead to our result. Our data can speak to this. We find that while there is evidence of both a within household effect and an income effect; but, a significant amount of variation persists once these are accounted for. We also estimate how the hazard rate of scrapping a vehicle varies with criteria pollutant emissions. Here, the evidence is more mixed. We find little variation in scrappage across emission levels within the same age. However, we find that increases in gasoline prices changes the age distribution; older vehicles are scrapped sooner while middle-aged vehicles stay on the road longer. Since older vehicles have higher levels of emissions, this too increases the optimal uniform tax, but has a much smaller effect than the VMT variation. An obvious concern is that our empirical results are only applicable to California. However, in appendix D we present evidence that provided the heterogeneity is somewhat similar to what we observe in California, the environmental benefits may be larger for other states. The paper proceeds as follows. Section 2 draws on Diamond (1973) to derive the optimal 3 uniform gasoline tax and the amount of deadweight loss that remains. Section 3 discusses the empirical setting. The data are discussed in Section 4. Section 5 provides graphical support for the empirical results. Sections 6 and 7 present empirical models and results on miles driven and scrappage. Section 8 estimates the empirically the optimal uniform tax and estimates welfare effects, and Section 9 presents the results from our policy simulation. Finally, Section 10 concludes the paper. 2 Optimal Uniform Taxes In this section, we derive the optimal uniform tax in the presence of heterogeneity in the externality, following closely the model of Diamond (1973). We reiterate that the optimal uniform Pigouvian tax is second best since heterogeneity would imply taxing different agents differently. Consumer h derives utility (indirectly, of course) from her gasoline purchases, αh , but is also affected by the gasoline consumption of others, α−h . We assume single-car households and discuss the robustness of these results after the formal model. Consumer h’s utility can be written as: U h (α1 , α2 , ..., αh , ..., αn ) + µh (1) We assume utility is monotone in own consumption: ∂U h ≥ 0. ∂αh (2) Consumers choose gasoline consumption to maximize utility. Formally we model this as a quasi-linear utility function, given as: max αh U h (α1 , α2 , ..., αh , ..., αn ) + µh , (3) s.t. (p + τ )αh + µh = mh . (4) Where p is the price and τ the tax per gallon. Assuming an interior solution, we have: ∂U h = (p + τ ). ∂αh 4 (5) This yields demand curves, given by: αh∗ = αh (p + τ ) . (6) The optimal uniform Pigouvian tax will maximize social welfare, or the sum of utilities: W (τ ) = X U h [α1∗ , ..., αh∗ , ...αn∗ ] − p X h αh∗ + X h mh . (7) h The first-order condition for the optimal uniform Pigouvian tax is given as: X X ∂U h W 0 (τ ) = ∂αi i h αi0 − p X αh0 = 0. (8) h We can rewrite this as follows: W 0 (τ ) = X X ∂U h h 0 ⇒ W (τ ) = ∂αi i6=h αi0 + h X X ∂U h h i6=h X ∂U h ∂αi αi0 + ∂αh X αh0 − p X αh0 = 0, (9) h αh0  h h ∂U −p ∂αh From the consumers’ first-order conditions, we have: ∂U h ∂αh  = 0. (10) − p = τ . We can plug this in to the social planner’s first-order condition to get: W 0 (τ ) = X X ∂U h h i6=h ∂αi αi0 + τ X αh0 = 0. (11) h Solving for the second-best tax yields: ∗ τ = − ∂U h 0 i6=h ∂αi αi P 0 . h αh P P h (12) The optimal uniform Pigouvian tax becomes a weighted average of the vehicles’ externalities where the weights are the derivative of the externality with respect to the tax. There are a few things to notice. First, the relative size of the optimal uniform Pigouvian tax and the naive tax is unclear. The more price responsive are dirtier agents, or vehicles in our case, the closer the tax will be to the marginal externality of these vehicles. However, if clean vehicles are more sensitive than dirty vehicles, then the marginal externality is closer to the externality of the clean vehicles. 5 As an intuitive example, imagine the case where there are only two vehicle types. The first emits little pollution, while the second is dirtier. Also imagine the clean vehicles are completely price insensitive, while the dirty vehicles are price sensitive. The naive Pigouvian tax would tax based on the average emissions of the two vehicle types. However, the marginal emission is the emission rate of the dirty vehicles; the clean cars are driven regardless of the tax level. In this case, we can achieve first best by setting the tax rate at the externality rate of the dirty vehicle. There is no distortion to owners of the clean vehicles since their demand is completely inelastic, so we can completely internalize the externality to those driving the dirty vehicles. The formula above implies this. Second, as Diamond explicitly discusses, there is no requirement that all of the αh0 s must be negative, although the optimal second-best tax loses the interpretation as a weighted average. Indeed, if households hold multiple vehicles, it is conceivable that miles traveled is shifted from the low mileage vehicle to the high mileage vehicle. This also implies that the second-best tax can be negative. For example, suppose the dirty vehicles had a positive miles-traveled elasticity, while clean vehicles were very price sensitive. In this case, it may be optimal for policy to subsidize gasoline. The trade-off being more miles from the cleaner vehicles, but fewer miles traveled by the dirty ones. We will find, however, that the potential for positive elasticities will drive the second-best tax upward; it can then exceed the negative externality of the dirtiest vehicles. Finally, the elasticity of the negative externality with respect to the price also accounts for any changes on the extensive margin. That is, if the gasoline tax increases the scrappage rate of some vehicles, then the relevant derivative of the externality with respect to price is the expected change in miles driven, not the change in miles driven, conditional on survival. The presence of heterogeneity also implies that the uniform tax will not achieve the first best outcome. In short, the uniform tax will under-tax high externality agents and over-tax low externality agents. 2.1 Extensions to Diamond (1973) Diamond (1973) does not analyze the amount of deadweight loss remaining in the presence of a uniform Pigouvian tax applied to a market with heterogenous externalities. Suppose the drivers are homogenous in their demand for miles driven, but vehicles differ 6 in terms of emissions. In particular, each consumer has a demand for miles drive given as: m = β0 − β1 dpm(pg + τ ). (13) If the distribution of the externality per mile, E, is log normal, with probability density function of: 1 ϕ(Ei ) = p 2 exp Ei 2σE  −(Ei − µE )2 2σE2  . (14) Given these assumptions, the deadweight loss absent any market intervention will be given as: Z D= 0 ∞ (Ei )2 ϕ(Ei )dEi 2β1 1 E[Ei2 ] 2β1 1 2µE +2σE2 = e . 2β1 = (15) Since the level of externality is uncorrelated with the slope of demand, the optimal uniform Pigouvian tax will be the average emissions across all vehicles. This is given as: 2 E = τ = eµE +σE /2 . The deadweight loss associated with all vehicles is given as: Z ∞ (τ − Ei )2 D(τ ) = ϕ(Ei )dEi 2β1 0 1 = E[τ 2 − 2τ Ei + Ei2 ] 2β1 1 2 = (τ − 2τ E[Ei ] + E[Ei2 ]) 2β1 2 σE 1 2 2 = (τ − 2τ eµE + 2 + e2µE +2σE ) 2β1 2 σE 1 2 = (τ − 2τ eµE + 2 ) + D 2β1 2 e2µE +σE =D− . 2β1 (16) (17) The ratio of the deadweight loss that remains with the deadweight loss absent the tax is 7 therefore: 2 R= D− e2µE +σE 2β1 D 2 e2µE +σE 2 = 1 − 2µ +2σ2 = 1 − e−σE . e E E (18) With the externality uncorrelated with demand for miles driven, the remaining deadweight loss from a uniform tax depends only on the shape parameter of the externality distribution. The larger is σE2 , the wider and more skewed will be the distribution of the externality, causing the uniform tax to “overshoot” the optimal quantity of miles for more vehicles. If the demand for miles driven is not homogeneous, and in fact is correlated with externalities per mile, the calculation changes. For ease of calculation, define Bi = 1 , βi and assume that Bi is distributed lognormal with parameters µB and σB2 . Define ρ as the dependence parameter of the bivariate lognormal distribution (the correlation coefficient of ln E and ln B). The optimal tax is: P Ei βi τ = P βi P 1 E i βi = N1 P βi N E[Ei βi ] = E[ B1i ] ∗ = eµE + = eµE + 2 σE 2 (19) −µB + 2 σB 2 e−µB + σ2 B 2 2 σE 2 eρσE σB +ρσE σB As we would expect, the optimal tax does not depend on the scale of the elasticity distribution, only extent to which externalities are correlated with elasticities. The deadweight loss with no gasoline tax is: Z ∞ Z D= 0 0 ∞  (Ei )2 Bi ϕ(Ei )dEi ϕB (Bi )dBi 2 1 = E[Ei2 Bi ] 2 2 σB 1 2 = e2µE +2σE +µB + 2 +2ρσE σB . 2 8 (20) The deadweight loss with the optimal uniform tax is:  Z ∞ Z ∞ (τ − Ei )2 Bi ∗ D(τ ) = ϕ(Ei )dEi ϕB (Bi )dBi 2 0 0 1 = E[τ 2 Bi − 2τ Ei Bi + Ei2 Bi ] 2 1 = (τ 2 E[Bi ] − 2τ E[Ei Bi ] + E[Ei2 Bi ]) 2 2 σ2 σ2 σB 1 2 µB + σB2 2 µ + 2E +µB + 2B +ρσE σB 2 − 2τ e E = (τ e + e2µE +2σE +µB + 2 +2ρσE σB ) 2 2 2 σB σB 1 2 2 = e2µE +σE +µB + 2 +2ρσE σB − e2µE +σE +µB + 2 +2ρσE σB + D 2 2 σB 1 2 = D − e2µE +σE +µB + 2 +2ρσE σB , 2 (21) while the deadweight loss with the naive tax, equal to the average externality level is: 2 2 σB σB 1 2 2 D(τnaive ) = D − (2e2µE +σE +µB + 2 +ρσE σB − e2µE +σE +µB + 2 ). 2 (22) Then the ratios of the remaining deadweight loss after a tax to the original deadweight loss will be: 2 R(τ ∗ ) = 1 − e2µE +σE +µB + 2 2 σB 2 e2µE +2σE +µB + +2ρσE σB σ2 B 2 +2ρσE σB 2 = 1 − e−σE , 2 R(τnaive ) = 1 − 2e2µE +σE +µB + (23) 2 σB 2 2 ρσE σB e2µE +2σE +µB + 2 − e2µ+σE +µB + σ2 B 2 2 σB 2 +2ρσE σB 2 = 1 − e−σE (2e−ρσE σB − e−2ρσE σB ). (24) As we would expect, the optimal tax correctly accounts for the the correlation between the externality and demand responses, and thus the remaining deadweight loss depends only on the variance and skewness of the externality distribution. However, in the presence of correlation the “naive” tax reduces less of the deadweight loss from the externality, reducing it by a proportion related to the degree of correlation and the spread of the two distributions. The term in parentheses in (24) is strictly less than 1, and strictly greater than zero if ρ > 0, but may be negative if ρ < 0 and the shape parameters are sufficiently high. In Section 8, we will show that σE2 is such that R(τ ∗ ) is surprisingly large, and that while 9 R(τnaive ) is measurably larger, it is not much larger. 3 Empirical Setting Our empirical setting is California. California implemented its first inspection and maintenance program in 1984 in response to the 1977 Clean Air Act Amendments. The initial incarnation of the Smog Check program relied purely on a decentralized system of privately run, state-licensed inspection stations, and was plagued by cheating and lax inspections. Although the agreement between California and the federal EPA promised reductions in hydrocarbon and carbon monoxide emissions of more the 25 percent, estimates of actual reductions of the early Smog Check Program range from zero to half that amount (Glazer, Klein, and Lave (1995)). The 1990 Clean Air Act Amendments required states to implement an enhanced inspection and maintenance program in areas with serious to extreme non-attainment of ozone limits. Several of California’s urban areas fell into this category, and in 1994, a redesigned inspection program was passed by California’s legislature after reaching a compromise with the EPA. The program was updated in 1997 to address consumer complaints, and fully implemented by 1998. Among other improvements, California’s new program introduced a system of centralized “Test-Only” stations and an electronic transmission system for inspection reports.3 Today, more than a million Smog Checks take place each month. An automobile appears in the data for a number of reasons. First, vehicles that are older than four years old must pass a smog check within 90 days of any change in ownership. Second, in parts of the state (details below) an emissions inspection is required every other year as a pre-requisite for renewing the registration on a vehicle that is six years old or older. Third, a test is required if a vehicle moves from out-of-state. Vehicles which fail an inspection must be repaired and receive another inspection before they can be registered and driven in the state. There is also a group of exempt vehicles. These are: vehicles of 1975 model-year or older, hybrid and electric vehicles, motorcycles, diesel powered vehicles, and large trucks powered by natural gas. Since 1998, the state has been divided into three inspection regimes (recently expanded 3 For more detailed background see http://www.arb.ca.gov/msprog/smogcheck/july00/if.pdf. 10 to four), the boundaries of which roughly correspond to the jurisdiction of the regional Air Quality Management Districts. “Enhanced” regions, designated because they fail to meet state or federal standards for carbon monoxide (CO) and ozone, fall under the most restrictive regime. All of the state’s major urban centers are in Enhanced areas, including the greater Los Angeles, San Francisco, and San Diego metropolitan areas. Vehicles registered to an address in an Enhanced area must pass a biennial Smog Check in order to be registered, and they must take the more rigorous Acceleration Simulation Mode (ASM) test. The ASM test involves the use of a dynamometer, and allows for measurement of NOx emissions. In addition, a randomly selected two percent sample of all vehicles in these areas is directed to have their Smog Checks at Test-Only stations, which are not allowed to make repairs.4 Vehicles which match a “High Emitter Profile” are also directed to Test-Only stations, as are vehicles which are flagged as “gross polluters” (this occurs when a vehicle fails an inspection with twice the legal limit of one or more pollutant in its emissions). More recently some “Partial-Enhanced” areas have been added, where a biennial ASM test is required, but no vehicles are directed to Test-Only stations. Areas with poor air quality that does not exceed legal limits fall under the Basic regime. Cars in a Basic area must have biennial Smog Checks as part of registration, but they are allowed to take the simpler Two Speed Idle (TSI) test, and no vehicles are directed to TestOnly stations. The least restrictive regime, consisting of rural mountain and desert counties in the east and north of the state, is known as the Change of Ownership area. As the name suggests, inspections in these areas are only required upon change of ownership; no biennial Smog Check is required. 3.1 Automobiles, Criteria Pollutants, and Health The tests report the emissions of three criteria pollutant: Nitrogen oxides, hydrocarbon, and carbon monoxide. All three of these pollutants are a direct consequences of the combustion process within either gasoline or diesel engines. Both NOx and HCs are precursors to groundlevel ozone, but, as with CO, have been shown to have negative health effects individually.5 4 Other vehicles can be taken to Test-Only stations as well if the owner chooses, although they must get repairs elsewhere if they fail. 5 CO has also been shown to speed up the smog-formation process. For early work on this, see Westberg, Cohen, and Wilson (1971). 11 While numerous studies have found links between the exposure of either smog or these three pollutants directly and health outcomes, the direct mechanisms are still uncertain. These pollutants, as well as smog, may directly impact vital organs or indirectly cause trauma. For example, CO can bind to hemoglobin, thereby decreasing the amount of oxygen in the bloodstream. High levels of carbon monoxide have also been linked to heart and respiratory problems. NOx reacts with other compounds to create nitrate aerosols, which are fine-particle particulate matter (PM). PM has been shown to irritate lung tissue, lowers lung capacity and hinders long term-lung development. Extremely small PM can be absorbed through the lung tissue and cause damage on the cellular level. On its own, HC can interfere with oxygen intake and irritate lungs. Ground-level ozone is a known lung irritant, has been associated with lowered lung capacity, and can exacerbate existing prior heart problems as well as lung problems such as asthma or allergies. 4 Data We bring together a number of large data sets. First, we have the universe of smog checks from 1996 to 2010 from California’s Bureau of Automotive Repair (BAR). These data report the location of the test, the vehicle’s VIN, odometer reading, the reason for the test, and test results. We decode the VIN to obtain the vehicles’ make, model, engine, and transmission. Using this, we match the vehicles to EPA data on fuel economy. Because the VIN decoding only holds for vehicles made after 1981, our data are restricted to these models. We also restrict our sample to 1998 and beyond given the large changes that occurred in the Smog Check program in 1997. This yields roughly 120 million observations. The Smog Check data report two measurements each nitrogen oxides and hydrocarbons in terms of parts per million and carbon monoxide levels as a percentage of the exhaust, taken under two engine speeds. As we are interested in the quantity of emissions, the more relevant metric is a vehicles emissions per mile. We convert the smog check reading into emissions per mile using conversion equations developed by Sierra Research for California Air Resources Board for Morrow and Runkle (2005), an evaluation of the Smog Check program. The conversion equations are functions of both measurements of all three pollutants, vehicle weight, model year, and truck status. 12 We also estimate scrappage decisions. For this we use data reported to CARFAX Inc. for 32 million of the vehicles in the BAR data. These data contain the date and location of the last record reported to CARFAX. This includes registrations, emissions inspections, repairs, import/export records and accidents. At times we use information about the household. For a subsample of our BAR data, we are able to match vehicles to given households using data come from confidential Department of Motor Vehicle records that track the registered address of the vehicle. We use this information to aggregate up to addresses, the stock of vehicles registered. Appendix A discusses how this is done. These data are from 2000 to 2008. Finally, we use gasoline prices from EIA’s weekly California average price series to construct average prices between Smog Check. Table 1 reports means and standard deviations of the main variables used in our analysis, as well as these summary statistics split by vehicle vintage and 1998 and 2008. The average fuel economy of vehicles in our sample is 23.5 MPG, with fuel economy falling over our sample. The change in the average dollar per mile has been dramatic, more than doubling over our sample. The dramatic decrease in vehicle emissions is also clear in the data, with per-mile emissions of hydrocarbon, CO, and NOx falling considerable from 1998 to 2008. The tightening of standards has also meant that more vehicles fail the smog check late in the sample, although some of this is driven by the aging vehicle fleet. 5 Preliminary Evidence One of the main driving forces behind our empirical results is whether vehicle elasticities, both in terms of their intensive and extensive margins, vary systematically with the magnitude of their externalities. In this section, we present evidence that significant variation exists in terms of vehicle externalities within a year, across years, and even within the same vehicle type (make, model, model year, etc.) within a year. Further, simple statistics, such as the average miles traveled by vehicle type, suggest that elasticities are correlated with externalities.6 Figure 1 plots the distributions of NOx , HCs, and CO emissions in 1998, 2004, and 2010. The distribution of criteria pollutant emissions tends to be right-skewed in any given year, 6 We are not the first to document the large variation across vehicles in emissions. See, for example, Kahn (1996). Instead, the contribution is in finding a link between elasticities and emissions. 13 with a standard deviation equal to roughly one to three times the mean, depending on the pollutant. This implies that there are a vehicles on the road that are quite “dirty” relative to the mean vehicle. Over time, the distribution has shifted to the left, as vehicles have been getting cleaner, but the range still remains. Table 2 reports the means and standard deviations across all vehicles receiving smog checks in a given year. From 1998 to 2008 the average emissions of NOx , HCs, and CO fell between 65 and 85 percent. However, the standard deviations, relative to the means, have increased over time. This is especially true for CO, where the standard deviation is over 4 times the mean at the end of the sample. This variation is not only driven by the fact that different types of vehicles are on the road in a given year, but also variation within the same vehicle type, defined as a make, model, model-year, engine, number of doors, and drivetrain combination. To see this, Figure 2 plots the distributions of emissions for the most popular vehicle/year in our sample, the 2001 4-door Toyota Corolla in 2009. The vertical red line is at the mean of the distribution. Here, again, we see that even within the same vehicle-type in the same year, the distribution is wide and right skewed. The distribution of hydrocarbons is less skewed, but the standard deviation is 25 percent of the mean. Carbon monoxide is also less skewed, and has a standard deviation that is 36 percent of the mean. Across all years and vehicles, the mean emission rate of a given vehicle in a given year, on average, is roughly four times the standard deviation for all three pollutants (Table 2). To understand how the distribution within a given vehicle changes over time, Figure 3 plots the distribution of the 1995 3.8L, front-wheel drive, Ford Windstar in 1999, 2001, 2004, and 2007.7 These figures suggest that over time the distributions shift to the right, become more symmetric, and the standard deviation grows considerably, relative to the mean. Across all vehicles, the ratio of the mean emission rate of NOx and the standard deviation of NOx has increased from 3.16 in 1998 to 4.53 in 2010. For hydrocarbons, this has increased from 3.59 to 5.51; and, has increased from 3.95 to 5.72 for CO. These distributions demonstrate that there is significant variation in emissions across vehicles and within vehicle type, and thus significant scope for meaningful emissions-correlated 7 We chose this vehicle because the 1995 3.8L, front-wheel drive, Ford Windstar in 1999 is the second most popular entry in our data and it is old enough that we can track it over four 2-year periods. 14 variation in elasticities along those lines. We next present suggestive evidence that this is the case. To do this, we categorize vehicles into four groups, based on the four quartiles of a given pollutant within a given year. We then plot how the log of daily miles driven has changed over our sample—a period where gasoline prices increased from roughly $1.35 to $3.20. Figure 4 and 5 foreshadow our results on the intensive margin. Figure 4 plots the median of daily miles traveled across our sample split up by the emissions quartile of the vehicle. While the dirtiest quartile begins at a slightly lower daily-VMT, it appears to drop much further than the other quartiles. Indeed, the there is a general trend of monotonicity across the four emissions. To see this more clearly, Figure 5 rescales the median VMT in 1998 and plots the average of the log of VMT over time by quartiles of each pollutant. For each pollutant, the log change in bottom-quartile vehicles is larger than the first quartile, with the other two quartiles often exhibiting monotonic changes in miles driven. 6 Vehicle Miles Traveled Decisions Our first set of empirical models estimates how vehicle miles traveled (VMT) decisions are affected by changes in gasoline prices, and how this elasticity varies with vehicle characteristics. Our empirical approach mirrors Figures 4 to 5. For each vehicle receiving a biennial smog check, we calculate average daily miles driven and the average gasoline price during the roughly two years between smog checks. We will then allow the elasticity to vary based on the emissions of the vehicle. We begin by estimating: ln(V M Tijgt ) = β ln(DP Mijgt ) + γDtruck + ωtime + µt + µj + µg + µv + igt (25) where i indexes vehicles, j vehicle-types, g geographic locations, t time, and v vehicle age, or vintage. DP Mijgt is the average dollars per mile of the vehicle between smog checks, Dtruck is an indicator for whether the vehicle is a truck, and time is a time trend.8 Table 3 shows our basic results. Model 1 controls only for year and vintage fixed effects, with zip-code level demographic characteristics, and indicates and elasticity of -0.265. Simply including make fixed effects in model 2 reduces this to -0.117. Model 3 also includes make 8 Our dollars per mile variable uses the standard assumption that 45 percent of a vehicle miles driven are in the city and 55 percent are on the highway, along with the vehicles EPA fuel economy ratings. 15 fixed effects but interacts log dollars per mile with within-calendar year quartiles of nitrogen oxide emissions and controls for the quartiles as well. The dirtiest quartile of vehicles has an elasticity of -0.189 in this specification, while the cleanest has an elasticity of only -0.037. Model 4 adds VIN-prefix fixed effects, essentially make/model/model year/drivetrain/engine fixed effects with no interactions, and model 5 adds vehicle fixed effects. With vehicle fixed effects, our mean elasticity estimate is -0.147. We begin the analysis by including year, vintage, and zip code fixed effects. We then progressively include finer vehicle-type fixed effects by including make, then make/model/modelyear/engine, and ending with individual vehicle fixed effects. We also differentiate the influence of gasoline prices by vehicle attributes related to the magnitude of their negative externalities—criteria pollutants, CO2 emissions, and weight. We do this in two ways. First, we split vehicles up by the quartile the vehicle falls into with respect to the within-year emissions of nitrogen oxides (NOx ), hydrocarbons (HC), and carbon monoxide (CO), fuel economy (CO2 ), and weight. Second, we include a linear interaction of the percentiles of these variables and the log of gasoline prices. Below we investigate, in a semi-parametric way, the actual functional form of this relationship. Tables 3 shows our results, focusing on nitrogen oxides. Moving from Models 1 to 5 illustrates the importance of controlling for vehicle-type fixed effects. Initially, the average elasticity falls from -0.265 to -0.117 when including fixed make effects, but then rises when including finer detailed vehicle fixed effects. Our final specification includes individual vehicle fixed effects yielding an average elasticity of -0.147.9 In models 6 and 7 we examine heterogeneity with vehicle fixed effects. Model 6 includes interactions with quartiles of nitrogen oxides, as in model 3. The DPM-elasticity for the cleanest vehicles, quartile one, is positive at 0.041, while the DPM-elasticity for the dirtiest vehicles is twice the average elacticity at -0.288. To put these numbers in context, the average per-mile NOx emissions of a quartile one vehicle is 0.163 grams, while the average per-mile NOx emissions of a quartile four vehicle is 1.68 grams. Model 7 assumes the relationship is linear in centiles of NOx and finds that each percentile increase in the per-mile NOx emission rate is associated with a change in the elasticity of .001, from a base of essentially zero. This heterogeneity is also robust to allowing 9 This is larger than that found in Hughes, Knittel, and Sperling (2008) reflecting the longer run nature of our elasticity. 16 our other covariates to vary with NOx quartiles, and to employing a log-linear specification with the level of dollars miles as the variable of interest; see appendix Tables A.23 and A.24. We find similar patterns across the other externalities. Table 4 gives the DPM elasticities by quartile for each of the five externalities. There is slightly more heterogeneity over hydrocarbon and carbon monoxide emissions than over nitrogen oxides, with the dirtiest quartiles around -0.31 and the cleanest around -0.5. For CO2 the cleanest vehicles are those with the highest fuel economy, and here we see the least fuel-efficient vehicles having an elasticity of -0.188, compared to -0.108. We observe some heterogeneity over weight as well, although it is smaller than the other externalities. We next investigate the functional forms of these relationships in a semi-parametric way. For each externality, we define vehicles by their percentile of that externality. We then estimate equation 25 with separate elasticities for vehicles falling in the zero to first percentile, first to second, etc. Figure 6 plots a LOWESS smoothed line through these 100 separate elasticity estimates. For the three criteria pollutants, we find that the relationship is quite linear with the elasticity being positive for the cleanest 10 percent of vehicles. The dirtiest vehicles have elasticities that are roughly 0.4. For fuel economy, the relationship is fairly linear from the 60th percentile onwards, but begins steeply and flattens out from the 20th percentile to the 40th. The elasticity of the lowest fuel economy vehicles is nearly 0.6. To put these numbers into context across the different years, the average fuel economy of the 20th percentile is 18.7, while the average for the 40th percentile is 21.75. The variation in elasticities across weight is not monotonic. The relationship begins by increasing until roughly the 20th percentile, and then falls more or less linearly thereafter. The elasticity of the heaviest vehicles is roughly 0.3. Note that the roughly-linear relationship between criteria pollutant emissions and the elasticity is not due to “over smoothing”. Figure 7 plots the LOWESS smoothed lines for hydrocarbons under different bandwidths. The top left figure simply reports the 100 elasticities. There is some evidence that the relationship is not monotonic early on, but from the 5th percentile on, the relationship appears monotonic. Doing this exercise for the other criteria pollutants yields similar results. 17 6.1 The Source of the Heterogeneity While the optimal uniform Pigouvian tax is not affected by the mechanism behind the heterogeneity, it is of independent interest to investigate the mechanism. We investigate three sources, which are not necessarily independent of each other. First, it may be driven entirely through a vintage effect. That is, older vehicles are both more responsive to changes in gasoline prices and have higher emissions. Second, it might be driven by differences in the incomes of consumers that drive dirtier versus cleaner vehicles.10 Third, it may result from households shifting which of their vehicles are driven in the face of rising gasoline prices. To investigate whether it is simply a vintage effect, we redefine the quartiles based on the distribution of emissions within vintage and calendar year bins. We split vehicles into three age categories: 4 to 9 years old, 10 to 15 years old, and 16 to 27 years old. Table 5 reports the results for heterogeneity over NOx emissions.11 These results suggest that while vintage is a factor in the externality-based heterogeneity, it is not the only source or even the most important source. While middle aged and older vehicles are more elastic than new vehicles on average, within age bin there is still substantial heterogeneity. For new vehicles, the difference between the dirtiest and cleanest quartiles is two thirds of the range for the whole sample. Middle-aged vehicles have three quarters as much range, and the oldest vehicles, 16 years and older, have a range nearly as large as for the whole sample. For a sub-sample of our smog check vehicles, we are able to group them into households. This grouping comes from access to California Department of Motor Vehicles (DMV) data. A number of steps are undertaken to “clean” the address entries in the DMV records. These are discussed in Appendix A. Ultimately, however, the subsample of vehicles that we are able to match likely draw more heavily from households residing in single-family homes. Given this selection and the fact that the sample period differs from our base specification, it is not surprising that we find average elasticities that differ from those presented above. The results from this sample are presented in Table 6. For this sample, we construct two additional variables meant to capture the household stock of vehicles. The variable “Higher MPG in HH” equals one if there is another vehicle in the household that has a higher MPG 10 West (2005) also documents a positive correlation between income and emissions. She does not separately estimate elasticities, however. 11 Results for the other four externality types are quite similar. 18 rating than the vehicle at question. Likewise, the variable “lower MPG in HH” equals one if there is another vehicle in the household that has a lower MPG rating than the vehicle at question. If household shift usage from low MPG vehicles to high MPG vehicles, we would expect “Higher MPG in HH” to be negative and “Lower MPG in HH” to be positive. The results suggest that this is a mechanism, but not the only one. If there is a vehicle with higher fuel economy in the household, the elasticity is larger, while if there is a vehicle with a lower MPG, the elasticity is smaller. Column 2 of Table 6 adds these variables to our base specification. The point estimates suggest that a vehicle in the highest fuel economy quartile belonging to a household that also has a lower fuel economy vehicle has an elasticity that is more than a third lower. We cannot reject the null hypothesis that the sum of the interactions with quartile 4 and “Higher MPG in HH” is zero.12 For this same sample of vehicles, we also use the Census-tract information to categorize owners into income quartiles. We interact these quartiles with the log of dollars per mile to see if differences in elasticities exist. Column 3 of Table 6 adds these interaction terms. There is little evidence that higher income consumers are less elastic, the emissions quartile effects persist; vehicles in the bottom quartile remain nearly three times more sensitive even after accounting for income differences. Our smog check data report the zip code of the testing station the vehicle visited. For our more general sample, we can also use this information to construct measures of income. Table 7 compares these results with the DMV data. We find similar differences in the elasticities, despite the smaller average elasticity. 7 Scrappage Decisions Our next set of empirical models examine how vehicle owners’ decisions to scrap their vehicles are affected by gasoline prices. Again we will also examine how this effect varies over emissions profiles. We determine whether a vehicle has been scrapped using the data from CARFAX Inc. We 12 The sum of the two vehicle-stock variables is positive, but because lower fuel efficient vehicles are driven more earlier in the sample, the elasticities are not comparable in terms of what they imply for total miles driven. 19 begin by assuming that a vehicle has been scrapped if more than a year has passed between the last record reported to CARFAX and the date when CARFAX produced our data extract (October 1, 2010). However, we treat a vehicle as being censored if the last record reported to CARFAX was not in California, or if more than a year and a half passed between the last Smog Check in our data and that last record. As well, to avoid treating late registrations as scrappage, we treat all vehicles with Smog Checks after 2008 as censored. Finally, to be sure we are dealing with scrapping decisions and not accidents or other events, we only examine vehicles which are at least 10 years old. Some modifications to our data are necessary. To focus on the long-run response to gasoline prices, our model is specified in discrete time, denominated in years. Where vehicles have more than one Smog Check per calendar year, we use the last Smog Check in that year. Also, since it is generally unlikely that a vehicle is scrapped at the same time as its last Smog Check, we create an additional observation for scrapped vehicles either one year after the last Smog Check, or 6 months after the last CARFAX record, whichever is later. For these created observations, odometer is imputed based on the average VMT between the last two Smog Checks, and all other variables take their values from the vehicle’s last Smog Check. An exception is if a vehicle fails the last Smog Check in our data. In this case, we assume the vehicle was scrapped by the end of that year. Because many scrapping decisions will not take place until after our data ends, a hazard model is needed to deal with right censoring. Let Tjivg be the year in which vehicle i, of vehicle type j, vintage v, and geography g is scrapped. Assuming proportional hazards, our basic model is: Pr[t < Tijvg < t + 1|T > t] = h0jv (t) · exp{βxDP Migt + γDf ailit + ψGigt + αXit }, where DP Migt is defined as before, Df ailit is a dummy equal to one if the vehicle failed a Smog Check any time during year t, G is a vector of demographic variables, determined by the location of the Smog Check, X is a vector of vehicle characteristics, including a dummy for truck and a 6th-order polynomial in odometer, and h0ijv (t) is the baseline hazard rate, which varies by time but not the other covariates. In some specifications, we will allow each vehicle type and vintage to have its own baseline hazard rate. 20 We estimate this model using semi-parametric Cox proportional hazards regressions, leaving the baseline hazard unspecified. We report exponentiated coefficients, which may be interpreted as hazard ratios. For instance, a 1 unit increase in DPM will multiply the hazard rate by exp{β}, or increase it by (exp{β} − 1) percent. In practice, we scale the coefficients on DPM for a 5-cent change, corresponding to a $1.00 increase in gasoline prices for a vehicle with fuel economy of 20 miles per gallon. Tables 8 and 9 show the results of our hazard analysis. Models 1 and 2 of table 8 assign all vehicles to the same baseline hazard function. Model 1 allows the effect of gasoline prices to vary by whether or not a vehicle failed a Smog Check. Model 2 also allows the effect of gasoline prices to vary by quartiles of NOx as well.13 Models 3 and 4 are similar, but stratify the baseline hazard function, allowing each VIN prefix to have its own baseline hazard function. Model 5 allows the effect of gasoline prices to vary both by externality quartile and age group, separating vehicles 10 to 15 years old from vehicles 16 years and older. Models 1 and 2 indicate that increases in gasoline prices actually decrease scrapping on average, with the cleanest vehicles seeing the largest decreases. The effect is diminished once unobserved heterogeneity among vehicle types is controlled for, but is still statistically significant. However, the true heterogeneity in the effect of gasoline prices on hazard seems to be over age groups. Model 5 shows that when the cost of driving a mile increases by 5 cents, the hazard of scrappage decreases by about 23% for vehicles between 10 and 15 years old, while it increases by around 3% for vehicles age 16 and older, with little variation across NOx quartiles within age groups. This suggests that when gasoline prices rise, very old cars are scrapped, increasing demand for moderately old cars and thus reducing the chance that they are scrapped. Table 9 presents the quartile by age by dollars per mile interactions for each of the 5 externality dimensions. Hydrocarbons and carbon monoxide have the identical pattern to NOx , with no heterogeneity within age-group. With fuel economy and vehicle weight, there is within-age heterogeneity, although the form is counter-intuitive. The heaviest and least fuel efficient vehicles are relatively less likely to be scrapped when gasoline prices increase than the lightest and most fuel efficient. That is, while all 10–15 year old vehicles are less likely 13 Quartiles in these models are calculated by year among only vehicles 10 years and older. 21 to be scrapped, the decrease in hazard rate is larger for heavy, gas-guzzling vehicles. For vehicles 16 years and older, the heaviest quartile is less likely to be scrapped when gasoline prices increase, even though the lightest (and middle quartiles) are more likely. As the model stratifies by VIN prefix, this cannot be simply that more durable vehicles have lower fuel economy. In summary, increases in the cost of driving a mile over the long term increase the chance that old vehicles are scrapped, while middle aged vehicles are scrapped less, perhaps because of increased demand. Although vehicle age is highly correlated with emissions of criteria pollutants, there is little variation in the response to gasoline prices across emissions rates within age groups. 8 Efficiency of Uniform Pigouvian Taxes In this section, we consider the efficiency of using a uniform Pigouvian tax to abate the externalities caused by driving, specifically those resulting from emissions of NOx , HCs and CO. We will begin by calculating both the “naive” and optimal second-best Pigouvian tax, and then compare the remaining dead weight loss left over from these second-best taxes to the optimal outcome obtained by a vehicle specific tax. 8.1 Optimal Uniform Pigouvian Tax We calculate the “naive” Pigouvian tax per gallon of gasoline as the simple average of the externality per gallon caused by all vehicles on the road in California in a particular year. We value the externalities imposed by NOx and HCs using the marginal damages calculated by Muller and Mendelsohn (2009), based on the county each vehicle has its Smog Check in.14 For CO, we use the median marginal damage estimate from Matthews and Lave (2000). Let the marginal damage per gram of pollutant p in county c be θcp , with emissions rate in grams per mile by vehicle i of pi . Then the externality per mile of vehicle i, Ei is: N Ox CO · N · C Ei = θhc · hi c + θcHC · H i Oxc + θ i Oc . i C +θ 14 Note: The values used in this paper differ from those used in the published version of Muller and Mendelsohn (2009). The published values were calculated using incorrect baseline mortality numbers that were too low for older age groups. Using corrected mortality data increases the marginal damages substantially. We are grateful to Nicholas Muller for providing updated values, and to Joel Wiles for bringing this to our attention. 22 The naive tax in year y will then be simply y τnaive N 1 X Ei = y N i=1 M P Gi Following the results of Diamond (1973) in Section 2 we calculate the second best optimal Pigouvian tax, taking into account the heterogeneity in both the levels of the externality and the responsiveness to gasoline prices. We estimate a regression similar to equation 25, but allowing the elasticity of VMT with respect to dollars per mile vary over all our dimensions of heterogeneity. For more details, see appendix C. Let the group-specific elasticity for vehicle i be εqi , where q indexes cells by HC emissions, NOx emissions, CO emissions, MPG, weight and age, with the externalities again in quartiles by year. Further, let the average price per gallon and the quantity of gasoline consumed per year in gallons in year y be Piy and Qyi , respectively. Then the optimal tax in year y based on the marginal externality will be y τmarginal ∗ ∂U h 0 i6=h ∂αi αi P 0 , h αh − P P −εqi Qyi 15 · y. Pi =τ = h with αi0 = Table 10 shows the taxes based on the average and marginal externalities for each year from 1998–2008. The average externality is 61.2 cents per gallon of gasoline consumed in 1998, while the marginal externality is 86 cents, 39% higher. The ratio of the average and marginal tax increases even as the level of the externalities declines over time. From 2002 on, the marginal tax is at least 50% larger than the naive tax in each year. 8.2 Welfare with Uniform Taxes We have shown that because of the correlation between elasticities and externality rates, the optimal uniform Piguovian tax is much higher than the “naive” tax calculated as the average of per-gallon externalities. We now turn to the question of how much the optimal tax improves welfare beyond what is achieved by the “naive” tax. We note again that even the optimal uniform tax is still a second-best policy. Because of the heterogeneity in externality 15 We also weight vehicles based on the number of vehicles of that age and class appear in the fleet as a whole; see appendix C. 23 levels, the most polluting vehicles will be taxed by less than their external costs to society, leaving remaining dead weight loss. Vehicles which are cleaner than the weighted average will be taxed too much, overshooting the optimal quantity of consumption and creating more deadweight loss—potentially more than those vehicle contributed prior to the tax. In each of the following analyses, we compare the remaining deadweight loss resulting from the local pollution externality with each tax to the deadweight loss without any additional tax. 8.2.1 Simulation Results We can begin by approximating the ratios of deadweight loss with and without tax using our data to simulate the change in miles driven and thus in gasoline consumption from a tax. Let milesyi be the actual average miles per day traveled by vehicle i between its last Smog Check ˆ y (τ ) be the miles per day that a vehicle and the current one, observed in year y, and let miles i would travel if the average price of gasoline were raised by a tax of τ which is fully passed through to consumers. We approximate DWL has a triangle, such that the ratio of interest is: y P r(τ ) = 1 i 2 ·| 1 i 2 P ˆ milesyi −miles i (τ ) | · | MEPiGi M P Gi ˆ y ( Ei ) milesy −miles ·| i i M P Gi M P Gi |· − τ| Ei M P Gi The fully optimal tax would have a ratio of 0, while a tax that actually increased the deadweight loss from gasoline consumption would be greater than 1. Table 11 shows these ratios for various taxes. The first two columns show ratios for a statewide tax based on the average and marginal externalities, respectively, of all vehicles in California in each year. The deadweight loss from the uniform naive tax averages 72.8% of the deadweight loss with no additional tax over the sample period, and rises over time as the fleet becomes cleaner. The uniform marginal tax is little better, averaging 69.8% of the deadweight loss with no tax during our sample period. The remaining columns of Table 11 allows the tax to vary so that it is uniform by groups, but not uniform over the entire state. The marginal damages from Muller and Mendelsohn (2009) vary substantially at the county level16 , both due to baseline emissions levels and the 16 We discuss this further in Section D. 24 population exposed to harmful emissions. As such, a county-specific tax on emissions might be expected to target externality levels more precisely. The third and fourth columns of Table 11 shows the deadweight loss ratios for an average and marginal tax computed this way, and it turns out there is relatively little improvement. The average ratios over our sample are 0.684 for and average tax and 0.653 for a marginal tax. Since emissions rates are highly correlated with vintage, another approach would be to tax the average or marginal externality rate by age. The fifth and sixth columns of the table show this, and here we see a substantial improvement: 0.342 for the naive tax and 0.34 for a marginal tax. Combining these and having the tax vary by both vintage and location, shown in the last two columns, reduces the ratios to 0.276 and 0.274, respectively. This analysis shows two striking results. First, a uniform Pigouvian tax does a terrible job of addressing the market failure from the pollution externality. The dirtiest vehicles are not taxed enough, and many clean vehicles are over taxed. This is true even when the uniform tax is calculated taking heterogeneity into account. The roughly 50% increase in the tax level from a marginal tax correctly abates more emissions from the dirtiest vehicles, but also over-taxes the cleanest vehicles by a larger amount. This is still an improvement over the naive tax, but not by much. The number of vehicles for which the uniform tax overshoots is striking. Table 12 shows the proportion of vehicle-years over the 11 years of our sample for which each tax overshoots. Because the distribution of emissions is so strongly right skewed, the naive uniform tax overshoots more than 72% of the time, and the optimal uniform tax by even more. Second, there is enough heterogeneity in the distribution of the per-gallon externality that even a targetted tax that targets broad groups leaves a substantial portion of the deadweight loss. Overshooting is again an issue—when the tax is allowed to vary by county and vintage, only the average tax by county and vintage overshoots for less than 70% of vehicles. The variance and skewness in the distribution of externality per gallon causes a uniform tax to be less efficient than might otherwise be expected. Figure 8 shows this clearly, plotting the kernel density of the externality per gallon in 1998 and 2008, with vertical lines indicating the naive tax and the optimal tax, respectively. The long right tail of the distribution requires that either tax be much higher than the median externality. We next examine how the optimal uniform tax would compare to the optimal vehicle 25 specific tax if the distribution become less skewed. That is, how would a uniform tax perform if the right tail of the distribution—the oldest, dirtiest vehicles—were removed from the road? This could be achieved directly from a “cash for clunkers”-style program, or indirectly through tightening emissions standards in the Smog Check Program. Sandler (Forthcoming) shows that vehicle retirement programs are not a cost-effective way to reduce criteria emissions, and possibly grossly over pay for emissions, but the overall welfare consequences of this sort of scheme may be more favorable if they improve the efficiency of a uniform gasoline tax. Table 13 shows the ratios of the deadweight loss with the optimal Pigouvian tax to the deadweight loss with no tax, with increasing proportions of the top of the externality distribution removed. Removing the top 1% increases the DWL reduction from 30% to 38% of the total with no tax. Scrapping more of the top end of the distribution improves things further. If the most polluting 25% of vehicles were removed from the road and the optimal Pigouvian tax was imposed based on the weighted externality of the remaining 75%, this would remove 58.3% of remaining deadweight loss. Of course, the practical complications of scrapping this large a proportion of the vehicle fleet might make this cost-prohibitive. 8.2.2 Analytical Results We can also calculate the ratio of remaining deadweight loss to the original deadweight loss by calibrating equations (23) and (24) and with the moments in our data. For each year from 1998 to 2008, we separately calculate the parameters of the externality and inverse elasticity distributions by maximum likelihood, assuming that both variables follow a lognormal distribution. Also for each year we calculate ρ, the correlation coefficient for the logs of externality and inverse elasticity. Table 14 shows the sample moments for each year and the ratios for the naive tax τnaive and the optimal uniform tax τ ∗ . The parameters are fairly constant over the sample period, although the shape parameters increase somewhat and the dependence parameter ρ decreases somewhat over time. The fact that this correlation exists actually improves the performance of a uniform tax, since vehicles which are overtaxed also create relatively little deadweight loss. Of course, the optimal uniform tax which takes the variation in elasticities into account performs somewhat better than the naive tax. The analytical results are largely in line with the simulation results in Table 11. With σ 2 around 1.47, the optimal uniform tax can only decrease deadweight loss 26 by 23%. 8.3 Treatment of Other Externalities In the discussion of the previous section, we have assumed that the difference between the socially optimal consumption of gasoline and actual consumption was entirely driven by externalities from local pollution. In practice, there are several other externalities from automobiles, as well as existing federal and state taxes on gasoline. Accounting for the additional externalities from congestion, accidents, infrastructure depreciation and other forms of pollution will make low-polluting vehicles less likely to “overshoot” the optimal quantity due a tax based on the value of the criteria pollution externality, which in turn will improve the deadweight loss ratios. On the other hand, the existing tax will cause a new tax to result in more overshooting. The combined state and federal gasoline tax in California was $0.47 during our sample period. Since most of the funds from these taxes go to highway construction and maintenance, we will assume for simplicity that the existing tax is exactly equal to the congestion, accident and depreciation externality. In essence, we assume that as far as their infrastructure maintenance goal is concerned, the respective governments have “got the price right”. This leaves other forms of pollution, most prominent being the social cost of CO2 emissions and their contribution for global warming. We assume that the carbon externality amounts to $0.30 per gallon and recalculate our deadweight loss ratios as y P r(τ ) = 1 i 2 1 i 2 P ·| ˆ milesyi −miles i (τ ) | · | MEPiGi M P Gi ˆ y ( Ei +0.3) milesyi −miles i MP G ·| i M P Gi + 0.3 − τ | | · ( MEPiGi + 0.3) with taxes still calculated based on the average or weighted average of the local pollution externality only. Table 15 repeats the analysis of Table 11 taking the carbon externality into account. The ratios do improve somewhat. The statewide naive tax now removes 36.6% of the deadweight loss from gasoline consumption, and the marginal tax removes 48.8%. The more targetted taxes again eliminate more deadweight loss, and look similar to the analysis without the GHG externality. The main difference is that the marginal tax has a more substantial advantage here. This is not surprising, since the reason that the marginal tax provides little additional 27 benefit is because it overshoots for so many vehicles, even as it correctly taxes the dirtiest vehicles. Table 16 shows the overshooting rates with the additional buffer of the GHG externality. The county and vintage-specific tax only overshoots about 30% of the time for both the naive and marginal taxes. Our assumption of an additional, untaxed externality changes the analysis for removing the most polluting vehicles as well, shown in Table 17. Because many fewer vehicles overshoot the optimal consumption quantity with a uniform tax, removing the most polluting vehicles has less downside to address, and also reduces the upside of internalizing the largest externalities. The optimal uniform tax is actually less effective with the top 25% of the externality distribution removed. 9 Co-benefits and the Social Cost of Carbon Pricing The positive correlation between emissions and the sensitivity to gasoline prices has a positive effect on the amount of local pollution benefits arising from a given GHG tax. This, in turn, reduces the net social cost of such a policy, and to our knowledge, has been ignored in the discussion surrounding the desirability of carbon tax or cap and trade policy. We calculate the cost of a relatively high tax on CO2 net of the local pollution benefits. Specifically, we use our data to simulate the change in emissions resulting from a $80 tax on CO2 , which translate to a $1 increase in the tax on gasoline.17 This is much higher than permit prices in Europe’s cap and trade program, peaked at $40 per ton of CO2 -equivalent in 2008 and have plummeted since. It is also higher than those permit prices expected in California’s cap and trade program trade which is expected to yield permit prices of roughly $30 per ton of CO2 -equivalent. The Waxman-Markey bill of 2009 expected a similar permit price. We account for both the intensive and extensive margins, as well as all the dimensions of heterogeneity we have documented in Sections 6 and 7. For this simulation, we assume that the tax was imposed in 1998, and use our empirical models to estimate the level of gasoline consumption and emissions from 1998 until 2008, had gasoline prices been $1 greater. 17 We assume all of the tax is passed through to consumers. Our implicit assumption is that the supply elasticity is infinite. This is likely a fair assumption in the long-run and for policies that reduce gasoline consumption in the near-term. 28 Appendix C provides details of the steps we take for the simulation. Tables 18, 19, and 20 show the results of our simulation for each year from 1998-2008, and the yearly average over the period. The first two columns shows the total reduction in annual gasoline consumption and CO2 emissions, in millions of gallons and millions of tons, respectively. The next two columns value the deadweight loss from the reduction in gasoline consumption. We approximate deadweight loss as ∆P ·∆Q 2 and adjust for inflation. The next section of the table presents the social benefit resulting from the reduction in NOx , HC, and CO due to the tax. Social benefits are valued using the marginal damages of NOx and HC calculated by Muller and Mendelsohn (2009) and the median CO value from Matthews and Lave (2000). Finally, the last column of the table shows the net cost of abating a ton of carbon dioxide, accounting for the reductions in criteria pollution. Table 18 shows the results of a simulation that does not account for heterogeneity across emissions profiles. The reduction in gasoline consumption declines over time from around 470 million gallons in 1998 down to around 219 in 2008. The reduction in criteria pollutants declines quickly as the fleet becomes cleaner. Nonetheless, the co-benefits of a gasoline tax are substantial, averaging 42% of the deadweight loss over the ten year period. Table 19 adds heterogeneity on the intensive margin, but not the extensive margins. The total change in gasoline consumption is smaller, declining from 272 million gallons in 1998 to 107 million gallons in 2008. This is a result of more fuel efficient vehicles having a higher average VMT. However, the reductions in criteria pollutants are much larger. In 1998 the co-benefits are over 125% of the deadweight loss, and the net cost of abating a ton of carbon is negative until 2001. On average, we estimate that on average benefits of a decrease in local air pollution from a gasoline tax would be about 80% of the change in surplus between 1998 and 2008. Finally, Table 20 adds heterogeneity on the extensive margins of scrappage and new car purchases. The net effect of the extensive margin is a small increase in criteria pollutants, due to the decreased scrappage vehicles 10-15 years old, and a small increase in greenhouse gasoline abatement. The annual reduction in gasoline consumption increases from 272 million gallons in 1998 to 110 million gallons in 2008. The amount and value of the co-benefits is increased compared to the figures in Table 19, but the difference is relatively small. Now over 85% of the deadweight loss is compensated for by the co-benefits. The net cost of the tax is 29 negative until 2002. Consistent with the way smog is formed, the majority the benefits come from reductions in hydrocarbons. As discussed in the next section, most counties in California are “NOx constrained”. In simplest terms this means that local changes in NOx emissions do not reduce smog, but changes in hydrocarbons do. In addition to the precursors to smog, we also find large co-benefits arising from CO reductions. We argue that these results should be viewed as strict lower bounds of the co-benefits for a variety of reasons. First, we have valued the cobenefits from NOx and HCs using the most conservative marginal damages from Muller and Mendelsohn (2009). Muller and Mendelsohn’s estimates depend heavily on the value place upon mortality. Their baseline, used here in Tables 18 to 20, assumes a VSL of $2 million, weighted by remaining years of life, and they acknowledge this may not be the correct value. They also calculate a scenario with mortality valued as in the USEPA model, with a VSL of $6 million, constant over ages. Tables 21 and 22 repeat the simulation without and with heterogeneity from Tables 22 and 20, but value cobenefits as per Muller and Mendelsohn’s USEPA scenario. Now even without heterogeneity the average cobenefits are greater than the deadweight loss, but decline to just over 78% by 2008. With heterogeneity, the cobenefits average more than three times the deadweight loss over the period, and remain twice as large in 2008. There are other reasons why our estimates should be considered a lower bound. First, we have ignored all other negative externalities associated with vehicles; many of these, such as particulate matter, accidents, and congestion externalities, will be strongly correlated with either VMT and the emissions of NOx , HCs, and CO. Second, because of the rules of the Smog Check program many vehicles that emission standards are not required to be tested, leading to their omission in this analysis. Third, a variety of behaviors associated with smog check programs would lead the on-road emissions of vehicles to likely be higher than the tested levels. These include, but are not limited to, fraud, tampering with emissioncontrol technologies between tests, failure to repair emission-control technologies until a test is required, etc. When we account for the heterogeneity in the responses to changes in gasoline prices, we see that the co-benefits from reduced air pollution would substantially ameliorate the costs of an increased gasoline tax. The co-benefits would have been especially substantial in the 30 late 1990s, but persist in more recent years as well, even though the fleet has become cleaner. To put these numbers into context, Greenstone, Kopits, and Wolverton (2011) estimate the social cost of carbon for a variety of assumptions about the discount rate, relationship between emissions and temperatures, and models of economic activity. For 2010, using a 3 percent discount rate, they find an average SCC of $21.40, with a 95th percentile of $64.90. Using a 2.5 percent discount rate, the average SCC is $35.10. Our results suggest that once the co-benefits are accounted for, a $1.00 gasoline tax (i.e., a tax of $80 per ton of CO2 ) would be nearly cost-effective even at the lower of these three numbers and well below the average social cost of capital using a 2.5 percent interest rate.18 The co-benefits vary considerably across counties. This variation comes from variation in the marginal damages, variation in the elasticities, and variation in the heterogeneity across vehicle types. Figure 9 illustrates the first two types of variation. Panels (a) and (b) map the variation in the marginal damages for NOx and HC calculated by Muller and Mendelsohn (2009). While marginal damages for HC are positively correlated with population (correlation coefficient of 0.84), the marginal damage for NOx are negatively correlated with both HC (0.49) and population (0.36). The reason for this has to do with the chemistry of ground-level ozone formation. Ground-level ozone, or smog, is formed in the presence of NOx , HCs, heat, and sunlight. When the ratio of NOx to HCs is not too large or small, the production function of smog, in the presence of sunlight and heat, is similar to that of a Leontiff production function. Therefore, a county can be in a region of the level-set where increasing NOx does not increase smog production because there are not enough HCs to mix with the additional NOx . This is known as NOx constrained. In contrast, a county may have so much HCs such that increasing HC does not lead to more smog. This is known as HC, or VOC, constrained.19 Therefore, the marginal damages of NOx and HC are negatively correlated.20 Given that vehicles emit roughly equal amounts of NOx and HCs, in some respects the average (or total) of marginal damages across NOx and HCs is more telling. Panel (c) maps the absolute value of the elasticity of VMT across counties, calculated 18 Of course, a tax somewhere below this would likely maximize welfare. The chemistry is more complicated than this. In fact, the isoquants of the production process are backward bending in the sense that if there is so much NOx , more NOx actually reduces smog (NO combines with O3 (ozone) to form NO2 and O2 ). This is known as titration. 20 For California the correlation is -0.36. 19 31 by estimating equation 25 and allowing the elasticity to vary by county of Smog Check. The absolute value of demand elasticities tend to be positively correlated with population, although the correlation coefficient is only 0.20. This variation leads to the variation in the co-benefits in panel (d) of Figure 9. The distribution is slightly skewed with a non-population weighted mean of $52.92 per ton of CO2 and median of $37.79; the standard deviation is $63.97. More populated areas have greater co-benefits, on average. Figure 10 shows a scatterplot of the co-benefits across counties versus the log of the counties population.21 Los Angeles is clearly an outlier with benefits of $367.28 per ton of CO2 over our sample, although as noted the median is nearly $38 with 75 percent of counties exceeding average co-benefits of over $15. 10 Conclusions In this paper we show three general empirical results. First, the sensitivity to a given vehicle’s miles traveled to gasoline prices is correlated with the vehicle’s emissions. Dirtier vehicles are more price responsive. This increases the size of the optimal uniform gasoline tax by as much as 50 percent. Second, gasoline taxes are an inefficient policy tool to reduce vehicle emissions. Gasoline taxes are often promoted as a means of reducing vehicle emissions. The optimal policy would differentially tax vehicles based on their emissions, not gasoline consumption. While gasoline consumption and emissions are positively correlated, we show that gasoline taxes are a poor substitute for vehicle-specific Pigouvian taxes. The deadweight loss that remains under the optimal gasoline tax exceeds 75 percent in the second half of our sample, and is above 70 percent across all years. Finally, the correlation we document leads to a positive result. We show that this correlation significantly increases the health benefits associated with gasoline taxes. This final results increases the attractiveness of carbon taxes as a means of reducing greenhouse gas emissions especially when viewed in light of the fact that existing policies used to reduce greenhouse gasoline emissions from transportation—CAFE standards, ethanol subsidies, and the RFS—fail to take advantage of these co-benefits, and can even increase criteria pollutant 21 County names are listed for a random 50 percent of the counties, plus Los Angeles. 32 emissions, because they reduce the marginal cost of an extra mile traveled. Given that previous work that has analyzed the relative efficiency of these policies to gasoline or carbon taxes has ignored the heterogeneity that we document, such policies are less efficient than previous thought. 33 References Busse, Meghan, Christopher R. 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