NBER WORKING PAPER SERIES EMPIRICAL ESTIMATES FOR ENVIRONMENTAL POLICY MAKING IN A SECOND-BEST SETTING. Sarah E. West Roberton C.

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1 NBER WORKING PAPER SERIES EMPIRICAL ESTIMATES FOR ENVIRONMENTAL POLICY MAKING IN A SECOND-BEST SETTING Sara E. West Roberton C. Williams III Working Paper ttp:// NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massacusetts Avenue Cambridge, MA February 2004 For teir elpful comments and suggestions, we tank Don Fullerton, Eban Goodstein, Larry Goulder, Micael Greenstone, Dan Hamermes, Sulamit Kan, Gib Metcalf, Ian Parry, Raymond Robertson, Dan Slesnick, Steve Trejo, Frank Wolak, Ann Wolverton, Pete Wilcoxen, and seminar participants at te Brookings Institution, te NBER Environmental Economics Working Group, te Universities of California (Berkeley), Maryland, Minnesota, Texas, and Virginia, Syracuse University, te Soutern Economics Association, and te U.S. Environmental Protection Agency. For teir excellent researc assistance, we tank Cris Lyddy, Trey Miller, and Jim Sallee. Te views expressed erein are tose of te autors and not necessarily tose of te National Bureau of Economic Researc by Sara E. West and Roberton C. Williams III. All rigts reserved. Sort sections of text, not to exceed two paragraps, may be quoted witout explicit permission provided tat full credit, including notice, is given to te source.

2 Empirical Estimates for Environmental Policy Making in a Second-Best Setting Sara E. West and Roberton C. Williams III NBER Working Paper No February 2004 JEL No. H21, H23, Q5 ABSTRACT Tis study estimates parameters necessary to calculate te optimal second-best gasoline tax, most notably te cross-price elasticity between gasoline and leisure. Prior work indicates tat in a secondbest setting wit distortionary income taxes, bot te cost of environmental regulation and te optimal environmental tax rate depend crucially on te cross-price elasticity between a polluting good and leisure. However, no prior study on second-best environmental regulation as estimated tis elasticity. Using ouseold data, we find tat gasoline is a relative complement to leisure, and tus tat te optimal gasoline tax is significantly iger tan marginal damages te opposite of te result suggested by te prior literature. Following tis approac to estimate cross-price elasticities wit leisure for oter major polluting goods could strongly influence estimates of optimal environmental taxes. Sara E. West Department of Economics Macalester College 1600 Grand Avenue St. Paul, MN wests@macalester.edu Roberton C. Williams III Department of Economics University of Texas at Austin Austin, TX and NBER rwilliam@eco.utexas.edu

3 I. Introduction Growing concern about global warming and continuing struggles wit local pollution and congestion ave led to increased attention to regulations designed to correct tese externalities. Economists ave played an important role in determining te optimal design of tese regulations. Pigou (1938) sowed tat pollution taxes sould be set equal to marginal damage te level tat fully internalizes an externality. But te presence of pre-existing distortionary taxes canges tis conclusion. Tullock (1967) first suggested tat pollution taxes ave an additional benefit besides improving te environment: te revenue from pollution taxes can replace revenue from preexisting distortionary taxes, tus reducing te deadweigt loss from tose taxes. Tis as since been termed te revenue-recycling effect. Subsequent work pointed out te tax-interaction effect, wic arises wen te pollution tax affects te equilibrium quantity of anoter taxed good, suc as labor. 1 A tax on te average consumption good leads to a fall in labor supply, because it lowers te real wage. In an economy wit a pre-existing income tax, te marginal social benefit of labor exceeds its marginal social cost, and tus tat fall in labor supply produces a welfare loss. Te more substitutable te polluting good is for leisure, te larger te fall in labor supply, and tus te larger te loss. However, if te polluting good is a complement to leisure, ten te pollution tax will increase labor supply, and tis effect will actually yield a welfare gain. Te tax-interaction effect tus depends crucially on te cross-price elasticity between leisure and te polluting good, as does te optimal pollution tax rate. But, wile prior analytical work allows tis elasticity to take on any value, it as never been estimated; indeed, te extensive literature on second-best environmental regulation is almost exclusively teoretical and numerical, wit virtually no empirical work. 2 Tus, to calculate te tax-interaction effect for a particular 1 Tis literature is far too extensive to provide a compreensive summary ere, but important papers include Sandmo (1975), Bovenberg and De Mooij (1994), Bovenberg and van der Ploeg (1994), Parry (1995), Goulder (1995), Bovenberg and Goulder (1996 and 1997), Goulder et al. (1999), Parry et al. (1999), and Fullerton and Metcalf (2001). Tese general-equilibrium effects are also important in a variety of non-environmental contexts. For examples, see Browning (1997) on te welfare cost of monopoly, Goulder and Williams (2003) on te excess burden of commodity taxes, Parry (1999) on agricultural policy, and Williams (1999) on trade policy. 2 An exception is Jorgenson and Wilcoxen (1993), wic uses empirical estimates to parameterize a computable general equilibrium model tat is ten used to study te costs of reducing carbon emissions. However, tat paper assumed a separable utility function wic, as discussed below, implies tat te cross-price elasticity wit leisure is determined by te expenditure elasticity for te polluting good. 1

4 policy, prior studies ave needed to impose strong assumptions on te form of te utility function. Most assume tat te utility function is omotetic and is weakly separable between leisure and consumption, implying tat all goods are average leisure substitutes. In tis case, te tax-interaction effect yields a welfare loss tat exceeds te gain from revenue recycling, and tus te optimal pollution tax is less tan marginal damage. 3 Tese assumptions greatly simplify te analysis, but are igly unlikely to old in practice; empirical studies tat estimate te joint demand for goods and leisure decisively reject separability. 4 Tis issue is not unique to environmental taxes: te effect of tis cross-elasticity on te optimal tax is te same for a non-polluting good. But even for tis broader class of goods, tere are very few empirical studies tat estimate optimal taxes and, to our knowledge, none of tose studies use micro data. Tis paper estimates te cross-price elasticity between gasoline and leisure and uses tat estimate to calculate te optimal second-best gasoline tax. We use data from te 1996 troug 1998 Consumer Expenditure Surveys, merged wit data from te American Cambers of Commerce Researcers Association (ACCRA) cost of living index and te National Bureau of Economic Researc s (NBER) TAXSIM model. Tis gives us detailed ouseold-level data on labor supply, taxes, and prices and quantities consumed of gasoline and oter goods. Most commonly used functional forms impose separability, omoteticity, or bot; te linear expenditure system (LES), for example, imposes additive separability, wile a constant elasticity of substitution (CES) utility function is bot separable and omotetic. We resolve tis issue by using te Almost Ideal Demand System (AIDS) derived by Deaton and Muellbauer (1980). Te AIDS gives a first-order approximation to any demand system, satisfies te axioms 3 A few studies (e.g., Parry and Small, 2002 and Ballard, Goddeeris, and Kim, 2000) relax te assumption of omoteticity, but maintain separability, wic implies tat te cross-price elasticity is determined by te expenditure elasticity for te polluting good; luxuries are relative leisure substitutes (implying a lower optimal tax), wile necessities are relative leisure substitutes (implying a iger optimal tax). 4 Separability as been tested and rejected in many studies; see, for example, Abbott and Asenfelter (1976), Barnett (1979), Blundell and Walker (1982), and Browning and Megir (1991). But no prior study offers estimates of te cross-price elasticity between leisure and a polluting good. Te closest is Diewert and Lawrence (1996), wic uses macro-level data from New Zealand to estimate te cross-price elasticity between motor veicles and leisure, but does not consider gasoline or miles driven. 2

5 of coice, is simple to estimate, and does not impose eiter separability or omoteticity. We find tat te optimal second-best gasoline tax is rougly 35% above marginal external damage. In contrast, prior work suggests tat second-best optimal pollution taxes are typically less tan marginal external damage. Te difference arises because we find tat gasoline is more complementary to leisure tan is te average good, wic leads to a substantially iger optimal tax rate. One possible explanation for tis result is tat driving is a relatively time-intensive good, and time-intensive goods tend to be leisure complements, as suggested by Becker (1965). Anoter possible explanation is tat te demand for leisure driving is muc more elastic tan te demand for commuting. In eiter case, our results suggest tat te widely used assumptions of separability and omoteticity are not merely convenient simplifications, but can substantially affect policy conclusions. Peraps more importantly, we sow tat tese effects can be estimated, and provide a teoretical and empirical framework for doing so. Te next section of tis paper develops a simple teoretical model and derives an expression for te optimal second-best environmental tax. Subsequent sections describe te empirical model, data, estimation results, and te implied optimal environmental tax. Te final section presents conclusions and suggests directions for future researc. II. A Teoretical Model Tis section presents a simple teoretical model and uses it to derive an expression for te optimal second-best environmental tax. Tis model is similar to tose used in te prior literature, but, unlike most earlier work, does not assume tat leisure is separable, tat te utility function is omotetic, or tat te polluting good is an average substitute for leisure. It also differs from prior models in tat it allows for multiple ouseolds (and te possibility of multiple individuals in a ouseold), rater tan a representative agent. 5 5 Recent papers tat use a similar model, but assume omoteticity and separability in deriving optimal taxes include Goulder et al. (1999), Parry et al. (1999), and Williams (2001). Parry and Small (2002) and Ballard et al. (2000) relax te assumption of omoteticity, but maintain separability. Kim (2002) provides a teoretical model tat derives an expression for te optimal pollution tax witout imposing separability or omoteticity, but does not include any empirical estimates using tat expression. All of tese papers assume a representative agent. As is briefly discussed in te next section, te aggregate demands in our system do not equal te demand of a representative ouseold. Tus, we need to allow for multiple ouseolds in tis teoretical model. Wile tis model could also be used to study distributional effects, we do not consider tat issue in tis paper. 3

6 Eac ouseold in te economy consumes a dirty consumption good (D), a clean good (C), and a government-provided public good (G). Te utility function for ouseold is (1) U ( l,c, D,G) φ ( D), were U is continuous and quasi-concave and te function φ represents te disutility from an externality associated wit te economy-wide total consumption of te dirty good. 6 Te elements l i of te vector l represent ours of leisure for eac of te adults in te ouseold. Te time constraint for individual i is (2) L = L i + l i, were L is te time endowment and L i is ours worked. Te ouseold budget constraint is (3) p C C + p D D = Y I + w i L i, i were w is te after-tax wage, I is after-tax non-labor income, and Y is total after-tax income, wic equals total expenditure. Te consumer price of te dirty good ( p D ) is given by (4) p D = p D + τ D, were p D is te producer price and τ D is a unit tax on te dirty good. Te clean good is untaxed, and tus its producer price ( p C ) and consumer price ( p C ) are equal. 7 Te after-tax wage is (5) w i = w i τ i L, were w is te pre-tax wage and τ L is te marginal tax per unit of labor. After-tax non-labor income is given by (6) I = I T, were I is pre-tax non-labor income, and T is a lump-sum tax or transfer. 8 6 We assume tat te damage from te externality appears only as an additively separable term in utility. If damages were to enter in some oter form, tat could also affect labor supply and tus generate a second-best welfare effect. See Bovenberg and van der Ploeg (1994), Espinosa and Smit (2001), and Williams (2002 and 2003) for furter discussion on tis point. Te present paper focuses on weter te polluting good is separable in utility, and tus ignores te question of weter damages are separable. 7 Assuming tat te clean good is untaxed leads to no loss of generality, because any tax system tat taxes te clean good can be renormalized as a system wit a iger income tax and no clean good tax (see, for example, Fullerton 1997). Williams (2001) sows tat tis renormalization does not affect te ratio of te optimal environmental tax to marginal damages. 8 Note tat τ L and T could represent a linear tax system or a (ouseold-specific) local linear approximation to a nonlinear tax system. 4

7 Eac of te tree goods is produced under perfect competition wit constant returns to scale. We assume tat non-labor income is derived from ownersip of a fixed factor tat is a perfect substitute for labor. 9 Tese assumptions imply tat te pre-tax wage and all producer prices are exogenously fixed and tat te aggregate production constraint is (7) I + w i L i = p G G + [ p C C + p D D ], i were p G is te producer price of te public good. Te government s budget constraint is (8) τ D D + τ i L L i + T = p G G. i Te level of te public good is assumed to be fixed, wit any cange in revenue from te dirty good tax offset by adjusting τ L and T, following (9) τ i L = ˆ τ i L + τ Y w i i ( ˆ τ L ) and Τ = T ˆ + τ Y ( I T ˆ ), i were ˆ τ L and T ˆ are constant, and τ Y adjusts to old government revenue constant as τ D varies. Equation (9) implies tat te reduction in ouseold s taxes from a decrease in τ Y will be proportional to Y. Tis could represent adjusting a broad-based consumption tax, renormalized as an income tax, or could represent an income tax cut tat is proportional to after-tax income. 10 Eac ouseold maximizes utility (1) subject to its time constraint (2) and budget constraint (3), taking as given prices, tax rates, te level of te public good, and te level of pollution. Tis yields te first-order conditions (10) U C = p C λ ; U D = p D λ ; U l i = w i λ, were λ is te marginal utility of after-tax income. Togeter wit te constraints given 9 Tis assumption is clearly unrealistic, but it provides a simple way to introduce non-labor income into te model. For a similar model in wic te fixed factor is not a perfect substitute for labor, see Williams (2002). Bovenberg and Goulder (1996) provide a model wit non-labor income derived from capital, but it is muc more complex tan te model used ere, and terefore cannot be solved analytically. 10 We coose tis approac for adjusting te income tax because it implies tat raising te dirty good tax and lowering te income tax will not sift te tax burden from labor to non-labor income or vice-versa. In tis model, a tax on non-labor income is nondistortionary, because we represent non-labor income as lump-sum. But in te real world, taxes on non-labor income are distortionary, and tus we do not want te model s results to be driven by te effect of sifting te tax burden onto or off of non-labor income. Te results would be similar if te added revenue were used to purcase more of te public good, as long as te level of te public good is close to te optimum. 5

8 previously, tese implicitly define te (uncompensated) demand functions (11) C ( p C, p D,w,I ); D ( p C, p D,w,I ); l i ( p C, p D,w,I ). To derive an expression for te aggregate cange in utility from a cange in te tax on te dirty good, we take te total derivative of utility (1) wit respect to τ D, sum over ouseolds, substitute in te first-order conditions (10), subtract te total derivatives wit respect to τ D of te time constraint (2) and aggregate production constraint (7), and rearrange terms. Tis gives (12) 1 du = ( τ λ D τ P ) dd i dl i τ L, dτ D dτ D i dτ D were τ P is te Pigouvian tax, equal to te dollar value of marginal external damage per unit of D 1 (13) τ P = φ λ D. Expression (12) equals te cange in deadweigt loss in te two distorted markets: te distortion in te dirty good market ( τ D τ P ) times te cange in dirty good consumption, plus te distortion in te labor market ( τ L ) times te cange in labor supply. Note tat tis is a pure efficiency measure; distributional issues, wile important, are beyond te scope of tis paper. Te total derivatives in (12) include not only te effect of te increase in te dirty good tax, but also te effect of te resulting income tax cut. Tis makes little difference for te dirty good, were te effect of te income tax cange will be tiny relative to te effect of te dirty good tax, but will be muc more important for labor supply. Tus, it is useful to rewrite te term for te labor market in (12) in terms of l p D rater tan dl dp D. To do tis, we first define η, wic is te marginal cost of public funds (MCPF). As sown in Appendix 1, η is given by (14) η = Y Y i l i + τ L I I l i + w j w j i j. Tis is te marginal cost to ouseolds of raising government revenue via te income tax; tus, it is te ratio of te loss to ouseolds to te revenue raised for a marginal increase in tis tax Tis definition of te MCPF is non-environmental in tat it omits te effects of canges in environmental quality and canges in revenue from te environmental tax resulting from a cange in te income tax. Tis expression for te MCPF and tose typically used in te prior literature differ sligtly because of differences in model assumptions. Tey are equivalent for te special case of tis model tat matces te typical assumptions in te prior literature: only one ouseold, only one individual in tat ouseold, and no non-labor income. 6

9 As sown in Appendix 1, te last term in (12) can now be rewritten as i dl i dd (15) τ L = ( η 1) D i l i + τ D η τ L. i dτ D dτ D i p D To obtain an expression for te optimum tax on te dirty good, set (12) equal to zero, substitute in (15), and solve. Tis gives (16) τ * D = τ P η + τ i l i L p η 1 D η i D dd. dτ D Te first term in tis expression is te traditional Pigouvian tax divided by te marginal cost of public funds. Tis is te optimal tax wen te dirty good is an average substitute for leisure. Te second term sows te influence of te cross-price elasticity between te dirty good and leisure. Wen te dirty good is a stronger substitute for leisure tan is te average good, tis term is negative and tus decreases te optimal tax on te polluting good. If te dirty good is a weaker leisure substitute tan te average good or is a complement to leisure, tis term is positive and tus increases te optimal tax. Te prior literature typically assumes tat utility is omotetic and tat leisure is separable. Tis greatly simplifies te analysis, because it implies tat te two terms in square brackets in (16) cancel, and terefore tat te optimal tax is just τ P η. Tus, tese assumptions eliminate te need to estimate te cross-price elasticity between te dirty good and leisure. Parry and Small (2002) and Ballard et al. (2000) relax te assumption of omoteticity, but still assume tat leisure is separable in utility. Tis assumption allows te derivative of leisure demand wit respect to te price of te dirty good to be expressed as l i l i (17) p = D D I + ε w j l i DX li Y w j I Lj j, were ε DX is te expenditure elasticity of demand for gasoline. Under tis assumption, a luxury must be a relative substitute for leisure, wile a necessity must be a relative complement to leisure. Tus, tis assumption also makes it possible to calculate te optimal pollution tax witout directly estimating te cross-price elasticity between te dirty good and leisure. 7

10 III. An Empirical Model Te optimal tax on te dirty good in (16) depends on several own-price and cross-price derivatives of demand. In tis section, we first specify te demand system tat we use to estimate tese derivatives. Ten we describe te data, variable derivation, and summary statistics. Finally, we discuss te estimation tecnique and system estimation results. A. Specification of te Demand System We use an Almost Ideal Demand System (AIDS), first derived in Deaton and Muellbauer (1980), defined over gasoline (te dirty good), leisure, and a composite of all oter goods (te clean good). Te advantages of te AIDS are well-known: it provides a first-order approximation to any demand system, satisfies te axioms of coice, and does not assume tat te utility function is separable or omotetic. In teir budget sare form, te AIDS demand equations for gasoline, leisure, and a composite of all oter goods for ouseold are: ( ) (18) s j = α j + γ jk log p k + β j log y P j, k = gasoline, leisure, oter goods; = 1,,H k were α, β, and γ are parameters to be estimated, and y is full income, or total expenditures on gasoline, leisure, and oter goods. 12 P is te price index defined by: (19) logp = α 0 + α j log p j γ jk log p j log p k. j k j Demand teory imposes several restrictions on te parameters of te model, including: (20a) α j =1 (20b) γ jk j j = 0 (20c) β j = 0 (20d) γ jk = γ kj. j Under tese restrictions, (18) represents a system of demand functions tat add up to full income, are omogeneous of degree zero in prices and full income, and satisfy Slutsky symmetry. Use of te price index in (19) requires estimation of a nonlinear system of equations. To simplify estimation, Deaton and Muellbauer (1980) suggests a linear approximation to (19): 12 Please note te sligt cange in notation. Te teory model assigned letters D, l, and C to te goods for consistency wit te prior second-best literature. For compactness, tis section uses subscript j to index goods. Also note tat full income (y ) as defined ere differs from income (Y ) as defined in te teory model, in tat y includes te value of leisure consumed, wile Y does not. 8

11 (21) logp s j log p j. j Tis price index, owever, is not invariant to canges in units of measurement (see Moscini 1995). We terefore normalize prices to obtain te unit-invariant price index ( ) (22) logp s j log p j p j, j were p j is te mean price over all ouseolds. 13 B. Data, Variable Derivation, and Summary Statistics Te 1996 troug 1998 Consumer Expenditure Surveys are te main components of our data. Te CEX Family Interview files include te amount spent by eac ouseold on gasoline, total expenditures, and a wide variety of ouseold income measures, all for te tree monts prior to te CEX interview. For eac ouseold member, te Member Files include usual weekly work ours, occupation, te gross amount of last pay, te duration of te last pay period, and a variety of member income measures. Te CEX is a rotating panel survey. Eac quarter, 20 percent of te sample is rotated out and replaced by new consumer units. We pool observations for ouseolds across quarters. We estimate two demand systems: one for one-adult ouseolds and te oter for twoadult ouseolds wit one adult male and one adult female (were an adult is at least 18 years of age). 14 Eac adult s leisure is treated as a separate good. Tus, te two-adult demand system includes four goods: gasoline, male leisure, female leisure, and a composite of all oter goods. Te twelve quarters in te 1996 troug 1998 Consumer Expenditure Surveys ave 4659 one-adult ouseolds and 5047 two-adult ouseolds under 65 wit complete records of te necessary variables. Eac ouseold appears in te data one to four times, giving a total of 9725 one-adult observations and two-adult observations. Females ead 54 percent of te one-adult 13 Note tat te use of any linear approximation to te price index in (19) implies tat te symmetry restriction (20d) is also an approximation. 14 We exclude ouseolds wit adults over te age of 65. Less tan 5 percent of tose over 65 work, and tus nonlabor income is very important for tis group. We do not realistically model capital income, as discussed in Section II. Tus, excluding tose over 65 likely introduces muc less error tan would including tis group. 9

12 ouseolds. In one adult ouseolds, 78 percent of women and 83 percent of men work. In twoadult ouseolds, 71 percent of women and 88 percent of men work. Full income (y ) equals te amount spent on gasoline, leisure, and all oter goods. Te CEX contains quarterly gasoline expenditure. Since it also contains ours worked per week, we divide quarterly gasoline expenditure by 13 to get weekly gas expenditure. To derive weekly leisure expenditure, we need to specify eac person s time endowment. Te igest number of ours worked in te sample is 90 per week, so we set te weekly time endowment at 90 ours. We ten subtract te number of ours worked per week from 90 to get weekly leisure ours. 15 To obtain te price of leisure (te wage) we first calculate te wage net of tax using state and federal effective tax rates from te NBER s TAXSIM model. 16 Since we do not observe wages for individuals wo do not work, we follow Heckman (1979) to correct for selectivity bias. We explain tis estimation in more detail in Appendix 2. We multiply te selectivity-corrected net wage by te number of ours of leisure per week to obtain weekly leisure expenditure. To calculate weekly spending on oter goods, we first convert te CEX s measure of quarterly total expenditures into weekly total expenditures. Ten we subtract weekly gasoline expenditure from total weekly expenditures to obtain spending on all oter goods. For gas prices and te price of oter goods, we use te ACCRA cost-of-living index. Tis index compiles prices of many separate goods as well as overall price levels for approximately 300 cities in te United States. It is most widely used to calculate differences in overall cost-ofliving across cities. It also lists for eac quarter te average prices of regular, unleaded, nationalbrand gasoline. Since te CEX reports state of residence of eac ouseold, and not city, we average te city prices witin eac state to obtain a state gasoline price and price index for eac 15 Demand system estimates can be sensitive to te coice of time endowment. We terefore experimented wit time endowments of 100 and 112 ours per week. In neiter case do te results cange significantly. 16 Estimates of marginal and average tax rates sould be reasonably accurate given te level of detail in te TAXSIM model, wic incorporates state and federal tax brackets, te earned income tax credit, te cild tax credit, deductibility of state income taxes, and oter important features of te tax code. Some of tese features, suc as credit pase-outs, may cause te marginal tax rate to differ from te statutory marginal rate. Terefore, marginal tax rates are calculated based on a $1000 increase in earned income. For more detail on te TAXSIM model, see Feenberg and Coutts (1993). Tese tax rate estimates, owever, do not include sales taxes or Social Security payroll taxes, and tus will understate te true tax rate. Consequently, our results will tend to understate te importance of second-best effects. 10

13 calendar quarter. Ten we assign a gas price and a price index to eac ouseold based on state of residence and CEX quarter. For ouseolds wose CEX quarters overlap two quarters of price data, we use a weigted average of tose two quarters. We use te ACCRA price index divided by 100 as our price of oter goods. We calculate te price index (P ) using equation (22). Table 1 lists summary statistics for te demand system estimation sample, working ouseolds tat consume gasoline. Bot one- and two-adult ouseolds spend about 2 percent of teir income on gasoline. One-adult ouseolds spend a bit less tan 50 percent of teir total income on leisure and te remainder on oter goods. Two-adult ouseolds spend about 55 percent of teir income on leisure and te remainder on oter goods. Te average selectivitycorrected net wage is $8.31 per our in te one-adult sample, and $11.02 per our for men and $8.60 per our for women in te two-adult sample. 17 C. System Estimation and Results To incorporate te effect tat ouseold and individual specific caracteristics ave on demand, we add a vector of tese caracteristics, c r, to te constant terms in (18) so tat: (23) α j = ζ j 0 + ζ jr c r, j = gasoline, leisure, oter goods r were ζ j 0 and te ζ jr s are parameters to be estimated. Some ouseolds also ave zero expenditure on gasoline. To correct for te selection bias tat may arise, we first estimate a probit on te coice of weter to consume gasoline. From tat probit, we obtain inverse Mills ratios ( R g ) for gasoline (see Appendix 2 for details on tis estimation). Substituting equation (23) into equation (18) and adding R g and error term e j yield te following equations for estimation: (24) s j = ζ j 0 + ζ jr c r + γ jk log p k + β j log y P + θ j R g + e j. r k ( ) We estimate te demand system defined by (24) using working ouseolds tat consume gasoline, separately for one-adult and two-adult ouseolds. We impose te restrictions in (20a- 17 Te wage distribution in our sample closely follows te distribution in te 1997 Current Population Survey. 11

14 d) and drop te equation for oter goods. Eac system includes member and ouseold caracteristics tat may affect gasoline or leisure sares: te members age, age squared, race, sex (in one-adult estimation only), education, and number of cildren. 18 In addition, a wide range of local factors could affect gasoline use or work beavior everyting from availability of public transportation to local urban design to cultural differences. Because many of tese factors are unmeasurable, we include state fixed effects to account for tem. Finally, because gasoline demand varies trougout te year, we include fixed effects for te mont of te CEX interview. Under tis approac, te own-price gas demand elasticity is identified primarily based on differences across states in quarter-to-quarter gas price variation, because cross-state variation is picked up by te state fixed effects and mont-to-mont variation by te mont fixed effects. Te own-price and cross-price labor supply elasticities are identified primarily by cross-section variation in wages witin eac state. 19 Tis requires te implicit assumption tat unobserved ouseold caracteristics are not correlated bot wit wages and wit gasoline consumption or ours worked. Because some regressors may be endogenous, we use instrumental variables tecniques. Te net wage, for example, may be endogenous for two reasons. First, te gross wage is determined by dividing earnings by ours of work, and bot variables may be measured wit error. Tus, ours worked and wage rates may be correlated. Second, te marginal income tax rate depends on income. We terefore use te mean net wage by occupation by state, calculated separately for men and for women, to instrument for te net wage. 20 Te real income term ln(y /P ) may also be endogenous, because it is a function of 18 Note tat te probits used to correct for selectivity bias include at least one variable not included in demand system estimation. West (2004) uses a similar data set to estimate te demand for veicle miles traveled and finds tat accounting for veicle type results in less elastic demand. We do not account for veicle type in tis paper. Te more inelastic is demand for gasoline, te farter te optimal tax will be from te standard second-best result. 19 It migt terefore seem tat we estimate long run labor supply elasticities and sort run gas demand elasticties. But since te coefficients in te demand system are estimated jointly, none of our elasticities is strictly sort-run or long-run. 20 Observations for workers in two occupation categories (farming, forestry, fising, and groundskeeping is te first and te armed forces te second) are spread very tinly across states. For workers wit tese occupations, we instrument for net wage wit te national mean net wages by occupation rater tan te state level means. 12

15 individual-specific sares tat are also dependent variables. We instrument for tis term, using a price index obtained by replacing te individual-specific sares in (22) wit te sample mean sares. 21 Gasoline prices may also be endogenous. In te absence of a good instrument for statelevel gas prices, owever, we do not control for tis potential endogeneity. 22 Since te equations in (24) are functions of te same explanatory variables, we expect error terms among te equations to be correlated. We terefore estimate te demand system using tree-stage least squares (3SLS). Tis enables us to impose te cross-equation restrictions in equations (20a-d), use instrumental variables to obtain consistent estimates, and use generalized least squares to account for te error correlation structure across equations. 23 Tables 2 and 3 present te system estimation results along wit standard errors based on 1500 replications of a nonparametric bootstrap. Eac bootstrap replication recomputes te Heckman-corrected wage and te inverse Mills ratios from te discrete coice of weter to consume gasoline, as well as te regression coefficients. Tus, te standard error estimates incorporate variation in te estimated selectivity-corrected wages and inverse Mills ratios. Because observations for te same ouseold for multiple quarters are not independent, we cluster observations by ouseold in generating eac bootstrap sample. In te one-adult sample, te gasoline sare decreases wit te wage rate. It is iger for blacks, males, and tose wit less education or more cildren. Te leisure sare decreases wit te wage and te price of te oter good, and increases wit te price of gas. It is lower for blacks and tose wit less education or more cildren. Te two-adult estimates generally mirror te oneadult estimates, toug te magnitudes differ. Te sare of leisure (for eiter adult) increases wit 21 We also estimate our system using te real income term calculated using tis alternative index (keeping te wage instrument but wit no price instrument), wic does not noticeably affect any of te results. Using estimates from running te demand system wit no instruments watsoever also does not noticeably affect te results. 22 Because we include state fixed effects, state-level gas tax rates are poor instruments for gas prices; in our sample, tey explain only about 1 percent of te variation in gas prices. 23 In principle, te full econometric model, including all discrete and continuous coices, migt be estimated using maximum likeliood, but tis would be difficult to implement. Since censoring occurs in bot gasoline and leisure demand, and for eiter or bot te male and female in two-adult ouseolds, we would need to evaluate multiple integrals in te likeliood function. Furtermore, suc a procedure would probably be too computationally intensive to be practical, given tat we need to bootstrap standard errors for our elasticity and optimal tax estimates. 13

16 is or er wage and decreases wit te wage of te oter adult in te ouseold. Tables 4 and 5 present elasticities for te one-adult and two-adult samples, respectively, along wit bias-corrected bootstrap confidence intervals. Tese elasticities are calculated separately for eac ouseold and ten aggregated, rater tan being calculated for a representative ouseold. 24 Compensated own-price gas and oter good demand elasticities are negative, and compensated own-wage labor elasticities are positive. Gasoline own-price elasticity estimates are rougly 0.75 for one-adult ouseolds and for two-adult ouseolds, wic fall in te span of estimates reported in gas demand surveys. 25 For one-adult ouseolds, te compensated and uncompensated labor supply elasticities are 0.35 and 0.04, respectively. For two-adult ouseolds, compensated own-wage labor supply elasticities are 0.19 for men and 0.34 for women, wile uncompensated elasticities are 0.06 and Tese fall into te range reported in te survey by Fucs et al. (1998). Compensated crosswage labor elasticities are insignificantly positive, wile uncompensated elasticities are negative; men and women respond to increases in teir partner s wage by working less. Te oter important elasticity in equation (16) is te uncompensated cross-price elasticity of labor wit respect to te price of gasoline. A positive value for tis elasticity raises te optimal gas tax, because in tis case an increase in te price of gasoline increases labor supply and generates a second-best welfare gain. A negative value reverses tis effect, lowering te optimal tax. Te prior literature as implicitly assumed a sligtly negative value for tis elasticity, as a result of assuming separability and omogeneity. In contrast, we find tat tis elasticity is positive for one-adult ouseolds and for bot genders in two-adult ouseolds, toug it is significant only for men in two-adult ouseolds (an elasticity of 0.013). Tis implies a iger optimal gas tax rate tan as been suggested by prior work. One possible explanation for tis result is tat a iger gas price leads to a reduction in 24 In many cases, aggregate demand elasticities under te AIDS are equal to te elasticity for a representative ouseold, but tat property does not old wen some ouseolds are at a corner solution, as is te case ere. Tus, it is necessary to aggregate individual ouseold elasticities. Appendix 1 provides equations for te ouseold demand elasticities in terms of te estimated parameters and for elasticity aggregation. 25 See Dal and Sterner (1991) or Espey (1996). 14

17 leisure driving tat is substantially greater tan te reduction in work-related driving (primarily commuting). Parry and Small (2002) note tat commuting makes up less tan alf of all veicle miles traveled in te US, and it is reasonable to tink tat te demand for leisure driving would be more elastic tan te demand for work-related driving. A more sopisticated argument is tat driving is a relatively time-intensive activity (at te margin, once ouseolds ave incurred te fixed cost of buying a car). Becker s (1965) model of time use suggests tat time-intensive goods are complements to leisure (or, more precisely, to non-market time). Tis result is sensitive to te inclusion of state fixed effects: dropping te state fixed effects switces te sign on te elasticity of labor supply wit respect to te gas price from positive (meaning gas and leisure are complements) to negative (gas and leisure are substitutes). Tis suggests tat unobserved state-level variables are quite important. In contrast, dropping mont fixed effects as little effect on te results. IV. Optimal Tax Calculations Tis section calculates te optimal second-best gasoline tax rate and compares it to te rates implied by te two formulas from te prior literature: one tat assumes separability and omoteticity, and one tat assumes only separability. Our data set provides values for most of te variables in te formulas for te optimal tax rate (16) and te marginal cost of public funds (14), wile te estimates from te previous section allow us to calculate all of te necessary derivatives of demand. 26 Te only additional parameter value needed is te marginal external damage from gasoline. We take tis value from Parry and Small (2002), wo estimate marginal damages at 83 cents per gallon in year 2000 dollars, a figure tat incorporates pollution, congestion and accident externalities. To make tis number 26 We assume tat te derivatives of demand at te optimum are te same as tose present in te status quo (wic are wat we estimated). In addition, equation (16) depends on te total derivative of gasoline demand wit respect to te gas tax. Tis derivative is neiter strictly uncompensated (because te total derivative includes te effect of reducing te income tax) nor strictly compensated (because te income tax cut does not fully compensate for te increased gas tax). However, as long as te tax rates are relatively small, tis total derivative will be very close to te compensated derivative, and tus we use tat value. Finally, for consistency wit te model in Section II, were te externality was associated exclusively wit a final good, we assume tat te tax is imposed only on consumer use of gasoline, not on gasoline used as an intermediate good. Parry and Small (2002) note tat intermediate use of gasoline is only a very small sare of te total, so tis seems like a reasonable assumption. 15

18 consistent wit te rest of our data, we use te CPI to deflate it, yielding an estimate of 77 cents in 1997 dollars, wic we assume remains constant as te gas tax rate canges. Substituting te appropriate values into equation (14) yields estimates for te MCPF of 1.01 in te one-adult sample, 1.03 in te two-adult sample, and 1.02 in te full sample. Tese estimates are somewat lower tan te values for te MCPF used by te prior literature, for two reasons. First, our estimate of te uncompensated labor supply elasticity is sligtly lower tan te prior literature ad assumed. Second, marginal tax rates in our data are somewat lower tan wat te prior literature as assumed (at least partly because, as noted previously, our tax rate data include only income taxes, omitting sales taxes and payroll taxes). For comparison, Goulder et al. (1999) and Parry et al. (1999) assume an uncompensated labor supply elasticity of 0.15 and a tax rate of 40%, wic togeter imply an MCPF of Te now-standard formula from te prior literature, wic assumes tat utility is omotetic and separable, states tat te optimal second-best tax is equal to marginal damages divided by te marginal cost of public funds (MCPF). Tis would imply a gas tax of $0.76 per gallon in te one-adult sample, $0.75 in te two-adult sample, and $0.75 for te full sample. Relaxing te assumption of omoteticity but keeping separability gives a somewat iger optimal tax, as in Parry and Small (2002). Substituting (17) and te appropriate parameter values into (16) yields an optimal tax of $0.87 for te one-adult sample, $1.01 for te two-adult sample, and $0.93 for te full sample all significantly above marginal damages. Because gasoline is a necessity, equation (17) implies tat it is a relative leisure complement. Tus, increasing te gasoline tax decreases labor supply by less tan an equivalent increase in te tax on oter goods, implying a smaller loss from te tax interaction effect and a iger optimal tax rate. Relaxing bot separability and omoteticity gives te optimal tax formula from equation (16). Wen we substitute te appropriate parameter estimates into (16), we get a second-best optimal gasoline tax of $0.82 in te one-adult sample, $1.30 in te two-adult sample, and $1.04 per gallon for te full sample. Te difference between tis rate and marginal damages is statistically significant at te 95% level for eiter te two-adult sample or te full sample, as is te difference between tis rate and te optimal tax assuming bot separability and 16

19 omoteticity. Te difference from te optimal tax assuming only separability is significant at te 90% level. Our estimates suggest tat increasing te gasoline tax will actually increase labor supply, wic implies tat te tax-interaction effect will actually generate a welfare gain, rater tan te loss suggested by te prior literature. Tus, te optimal tax rate is iger. Te difference between te optimal second-best tax and marginal external damage a difference of 27 cents per gallon (35% of marginal damages) for te full sample is not enormous, but is quite important. And tis difference as te opposite sign from wat te prior literature as suggested. Tat literature as certainly noted te teoretical possibility tat te optimal tax may exceed marginal damage, for exactly te reasons found ere, but gave no clear indication of ow likely suc an outcome migt be or of ow large te difference would be. Comparing te impact of including second-best effects wit and witout assuming separability and omoteticity demonstrates te importance of tese assumptions. Given tese point estimates, te difference caused by relaxing te assumptions of separability and omoteticity (a rise from $0.75 to $1.04 in te optimal tax) is more tan ten times as large as te difference caused by incorporating second-best effects in te first place ($0.77 to $0.75) te difference tat as been te primary focus of te literature tus far. Finally, we consider weter raising te gas tax would yield a double dividend : tat is, if it would produce a welfare gain even if marginal external damage were zero. Substituting a value of zero for τ P in (16) yields an estimated optimal tax of $0.28. Tis suggests te existence of a double dividend from raising te gas tax above zero, but not from raising it above te average rate in our sample ($0.34). However, te 95% confidence interval for te optimal tax in tis case runs from $0.11 to $0.72, so we cannot reject te ypotesis tat raising te gas tax would yield a double dividend or, to put it differently, tat te optimal gas tax would exceed te current rate even if tere were no externalities associated wit gasoline use. V. Conclusions Tis paper estimates a complete consumer demand system witout imposing separability or omoteticity, and applies tose estimates togeter wit a simple teoretical model to 17

20 calculate te second-best optimal tax on gasoline. Contrary to te prior literature, wic suggests tat optimal environmental taxes are less tan marginal external damage, we find tat te optimal tax substantially exceeds marginal damage. Te difference arises because gasoline is more complementary to leisure tan is te average good, wile typical assumptions in te prior literature imply tat te polluting good is an average substitute for leisure. Tis result as important implications bot for policy and for future researc. One obvious implication is tat te efficiency gain from increasing te gas tax would be even larger tan a first-best analysis would indicate. However, given te necessary simplifications in te model (most notably tat it ignores capital), some caution sould be exercised in drawing policy conclusions from tis result. Peraps more importantly, te practical relevance of any result on optimal gasoline taxes is limited by political constraints; te existing tax in te U.S. is far below wat almost any economic analysis would indicate as te optimum. Our result also as implications for te general problem of setting environmental taxes in a second-best world. Some readers may be tempted to use our results to support setting oter environmental taxes at levels above marginal damages. Tis conclusion does not necessarily follow, given tat oter polluting goods are used for very different purposes tan is gasoline. But our result does sow tat te case in wic tax-interaction effects cause te optimal tax to exceed marginal damages is relevant in practice, not merely a teoretical possibility. Tis indicates far more uncertainty about te influence of second-best effects on environmental policy tan prior work as suggested, and it sows tat te widely used separability and omoteticity assumptions are not merely convenient simplifications; tey can ave large effects on te results. Peraps more importantly, we sow tat it is possible to estimate empirically te influence of tese assumptions on te second-best optimal environmental tax, and we provide te necessary empirical and teoretical framework to do so. Tis approac can be fruitfully applied not only to oter polluting goods, but also to non-polluting goods, to yield better estimates of optimal tax rates and of te deadweigt losses from taxes on tese goods. 18

21 References Abbott, Micael and Orley Asenfelter, Labour Supply, Commodity Demand and te Allocation of Time. Review of Economic Studies 43: Ballard, Carles, Jon Goddeeris and Sang-Kyum Kim, Non Homotetic Preferences and te Non-Environmental Effects of Environmental Taxes. Working Paper. Barnett, William A., Te Joint Allocation of Leisure and Goods Expenditure. Econometrica 47: Becker, Gary, A Teory of te Allocation of Time. Te Economic Journal 75: Blundell, Ricard and Ian Walker, Modelling te Joint Determination of Houseold Labour Supplies and Commodity Demands. Te Economic Journal 92: Bovenberg, A. Lans and Ruud A. de Mooij, Environmental Levies and Distortionary Taxation. American Economic Review 85: Bovenberg, A. Lans and Lawrence H. Goulder, Optimal Environmental Taxation in te Presence of Oter Taxes: General Equilibrium Analyses. American Economic Review 96: Bovenberg, A. Lans and Lawrence H. Goulder, Costs of Environmentally Motivated Taxes in te Presence of Oter Taxes: General Equilibrium Analyses. National Tax Journal L(1): Bovenberg, A. Lans and Frederick van der Ploeg, Green policies and public finance in a small open economy. Scandinavian Journal of Economics 96: Browning, Edgar, A Neglected Welfare Cost of Monopoly And Most Oter Product Market Distortions. Journal of Public Economics 66: Browning, Martin and Costas Megir, Te Effects of Male and Female Labor Supply on Commodity Demands. Econometrica 59: Dal, Carol, and Tomas Sterner, Analyzing Gasoline Demand Elasticities: A Survey. Energy Economics 13: Deaton, Angus and Jon Muellbauer, An Almost Ideal Demand System. American Economic Review 70: Diewert, W. Erwin, and Denis A. Lawrence, Te deadweigt costs of taxation in New Zealand. Canadian Journal of Economics 29:S659-S

22 Espey, Molly, Explaining te Variation in Elasticity Estimates of Gasoline Demand in te United States: A Meta-Analysis. Te Energy Journal 17: Espinosa, J. Andrès and V. Kerry Smit, Environmental Levies wit Non-Separable Damages. working paper, Nort Carolina State University. Feenberg, Daniel and Elisabet Coutts, An Introduction to te TAXSIM Model. Journal of Policy Analysis and Management 12: Fucs, Victor R., Alan B. Krueger and James M. Poterba, Economists Views about Parameters, Values and Policies: Survey Results in Labor and Public Economics. Journal of Economic Literature 36: Fullerton, Don, Environmental Levies and Distortionary Taxes: Comment. American Economic Review 87: Fullerton, Don and Gilbert Metcalf, Environmental Controls, Scarcity Rents, and Pre- Existing Distortions. Journal of Public Economics 80: Goulder, Lawrence, Environmental Taxation and te Double Dividend: A Reader s Guide. International Tax and Public Finance 2: Goulder, Lawrence H., Ian W. H. Parry, Roberton C. Williams III, and Dallas Burtraw, Te Cost-Effectiveness of Alternative Instruments for Environmental Protection in a Second-Best Setting. Journal of Public Economics, 72: Goulder, Lawrence H. and Roberton C. Williams III, Te Substantial Bias from Ignoring General Equilibrium Effects in Estimating Excess Burden, and a Practical Solution. Journal of Political Economy 111: Heckman, James, Sample Selection Bias as Specification Error. Econometrica 47: Heien, Dale and Caty Wessels, Demand System Estimation wit Microdata: A Censored Regression Approac. Journal of Business and Economic Statistics 8: Jorgenson, Dale W. and Peter J. Wilcoxen, Reducing U.S. Carbon Emissions: An Econometric General Equilibrium Assessment. Resource and Energy Economics 15:7-26. Kim, Seung-Rae, "Optimal Environmental Regulation in te Presence of Oter Taxes: Te Role of Non-separable Preferences and Tecnology." Contributions to Economic Analysis & Policy: Vol. 1: No. 1, Article 4. Moscini, Giancarlo, Units of Measurement and te Stone Index in Demand System Estimation. American Journal of Agricultural Economics 77: