Improving air quality in California's San Joaquin Valley: The role of vehicle heterogeneity in optimal emissions abatement

Journal of Environmental Economics and Management 63 (2012) 169–186

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Journal of Environmental Economics and Management journal homepage: www.elsevier.com/locate/jeem

Improving air quality in California’s San Joaquin Valley: The role of vehicle heterogeneity in optimal emissions abatement Pierre Me´rel a,n, Emily Wimberger b a b

Department of Agricultural and Resource Economics, UC Davis, 1 Shields Avenue, Davis, CA 95616, United States Bren School of Environmental Science & Management, UC Santa Barbara, 2400 Bren Hall, Santa Barbara, CA 93106, United States

a r t i c l e i n f o

abstract

Article history: Received 24 February 2011 Available online 12 November 2011

We exploit cross-sectional repair cost and emissions data to estimate an abatement cost schedule for vehicles participating in a program in California’s San Joaquin Valley to reduce tailpipe emissions. We find that 1995 and older model year vehicles have a lower marginal abatement cost than newer vehicles across all emissions levels. Since older vehicles are also significantly more polluting, an optimal allocation of emissions-related repair funds should target these vehicles. Total emissions reductions could be improved by an estimated 20% if the program has to shift from the actual flat $500 voucher to the first-best vehicle-specific voucher scheme. A two-tier voucher based on vehicle model year would yield a 15% decrease in emissions over the flat voucher, achieving three fourths of the remaining potential abatement. We also use our estimated abatement cost schedule to provide a measure of the foregone emissions reductions for this fleet due to the current structure of the California Smog Check program. Optimally redistributing the total expenditure required to bring each vehicle to California Smog Check standards could further reduce emissions by an estimated 19–31%. & 2011 Elsevier Inc. All rights reserved.

Keywords: Vehicle emissions abatement Marginal abatement cost Cost effectiveness Smog Check program Latent class analysis

1. Introduction California’s San Joaquin Valley (SJV) has the nation’s highest levels of ground-level ozone. It exceeded the 8 h National Ambient Air Quality Standard (NAAQS) more days from 2003 through 2007 than any other area in the United States and has been classified as an ‘‘extreme nonattainment’’ area by the United States Environmental Protection Agency [5]. High levels of ground-level ozone can lead to respiratory problems; according to the National Academy of Sciences, ‘‘short-term exposure to ambient ozone is likely to contribute to premature deaths’’ [10]. Failure to meet the ground-level ozone NAAQS has been estimated to cost the SJV $32.64 million in health costs each year [7]. Motor vehicles’ tailpipe emissions are the largest single source of ozone forming pollutants nationwide, creating 56% of all nitrous oxides (NOx) and 45% of all volatile organic compounds (VOC) that react with sunlight to form ground-level ozone [14]. On-road vehicles are also responsible for 59% of all carbon monoxide (CO) emissions [13]. Exposure to high concentrations of CO inhibits the blood’s ability to transport oxygen and can result in nausea, angina, and even death [12]. In California, regulators monitor vehicle emissions by subjecting vehicles to biennial testing known as the Smog Check program. This program requires vehicles to pass a three-part inspection (emissions test, visual test, and functional test) in order to be registered or sold within California. The functional and visual tests ensure that all emissions-related components and

n

Corresponding author. Fax: þ 1 530 752 5614. E-mail address: [email protected] (P. Me´rel).

0095-0696/$ - see front matter & 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.jeem.2011.10.004

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systems are operational while the emissions test measures the concentration of pollutants emitted from the vehicle’s tailpipe. Though some flexibility exists as to the scope and modalities of the emissions test, for the majority of the state the program requires vehicles to comply with emissions cutpoints for hydrocarbons (HC, a type of VOC), CO and NOx.1 Regulatory cutpoints for each of the monitored pollutants are based on vehicle characteristics, typically model year and weight.2 For the majority of vehicles in the SJV, biennial inspections using the Acceleration Simulation Mode (ASM) emissions test for HC, CO and NOx are required for vehicles that are at least six years old. Inspections are also required upon the sale of vehicles that are at least four years old.3 But increases in population and miles driven are exacerbating the plight of regulators to bring the area in line with federal NAAQS. From 1990 to 2005, the population of the SJV grew by 37%, while the average of miles driven annually increased by 70% [5]. Yet another factor to contribute to the consistently high levels of air pollution in the SJV may be that some vehicles are driven without being in compliance with California Smog Check standards. Since a Smog Check certificate (received upon passing the inspection) is required for vehicle registration, non-compliant vehicles are also unregistered, which makes quantifying this phenomenon difficult. Even if non-compliance is rare, it may have a significant impact on air quality as these vehicles may have extremely high emissions levels.4 Valley Clean Air Now (Valley CAN) is a non-profit advocacy group involved in the reduction of vehicle tailpipe emissions in the SJV through their Tune In and Tune Up program (TI&TU). TI&TU events target vehicle owners that cannot afford to pay for emissions-related repairs and drive their vehicles regardless of registration status or compliance with the California Smog Check program.5 According to Valley CAN’s website, the TI&TU program is6 A car clean up outreach effort to help eliminate mobile source pollutants generated by older, ‘‘out of tune’’ cars in the San Joaquin Valley. It is well known that the Valley is home to a large number of older cars, many of which do not have current smog certificates. At a typical TI&TU event, Valley CAN identifies vehicles with high tailpipe emissions using a two-speed idle (TSI) test, and gives owners a $500 voucher for emissions-related testing and repairs at a Valley CAN-sanctioned gold shield repair shop.7 From 2005 through 2009, Valley CAN held 10 TI&TU events throughout the SJV, passing out over 2,000 vouchers and markedly reducing the tailpipe emissions of treated vehicles [9]. Fifteen more events are scheduled through 2011 and 2012. The primary goal of this article is to evaluate the cost-effectiveness of Valley CAN’s TI&TU program. To this end, we first use cross-sectional data on emissions-related repair costs and emissions abatement for a sample of vehicles participating in two recent TI&TU events held in Bakersfield, CA to estimate an emissions abatement cost schedule. The abatement cost schedule is specified as a parameterized latent class model where, conditional on initial and final emissions levels, abatement cost is allowed to vary according to vehicle model year and weight. We find that 1995 and older model year vehicles have a lower abatement cost than newer vehicles across all relevant emissions levels. We then use the estimated abatement cost schedule to evaluate the cost-effectiveness of Valley CAN’s current emissions reduction program. Formally, we model Valley CAN’s objective as the maximization of expected emissions reductions among an exogenous fleet of vehicles, under a fixed budget (expectations being taken with respect to class probabilities). Our optimization problem is therefore dual to the classical approach to cost-effectiveness that consists of minimizing the cost of abatement under a fixed pollution reduction target. Just as the solution to this latter cost-minimization program is characterized by the equality of marginal abatement costs across all participating firms, the solution to our maximization program is characterized by the equality of expected marginal abatement (from an additional dollar) across all treated vehicles. As such, the resulting allocation is cost-effective, in the sense that the corresponding level of expected emissions reductions cannot be achieved at a lower cost than the initially assumed budget. Using the vehicle fleet from Valley CAN’s events in Bakersfield, CA, we find that total expected emissions reductions could be improved by an estimated 20% if the program were to shift from the current flat $500 voucher to the optimal vehicle-specific voucher scheme. A two-tier voucher scheme based on vehicle model year alone would allow to realize most of this additional abatement potential. This finding seems robust to various behavioral assumptions regarding the extent to which voucher funds are redeemed as well as the willingness of vehicle owners to contribute financially to repairs. 1 Areas that are compliant with NAAQS or have low population densities are subjected to a less comprehensive inspection measuring only HC and CO. In some remote areas vehicles are only required to be inspected when sold. 2 As of March 31, 2010, emissions cutpoints are make-, model year- and model-specific. 3 In rural areas of the SJV with low population the two-speed idle (TSI) test may be used to measure vehicle emissions. 4 This fact is confirmed by our data on tailpipe emissions in Bakersfield, CA. Among 270 vehicles tested, emissions ranged from 8 lbs/10,000 miles to 2800 lbs/10,000 miles. 5 There is reason to believe that Valley CAN is successful at targeting vehicles that would not have undergone emissions-related repairs in the absence of a subsidy. Among the 270 vehicles participating in the 2009 Valley CAN event in Bakersfield, CA for which we have data, 80% did not have current registration status; 88% of those failed the Smog Check inspection. 6 Accessed on July 20, 2011. 7 Gold shield stations are a subset of high quality stations, authorized to test and conduct emissions-related repairs on all vehicles in California.

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In the last part of the article, we further exploit our estimated abatement cost schedule to provide a measure of the foregone emissions reductions for our vehicle fleet due to the current structure of the California Smog Check program. Optimally redistributing the expected repair expenditures required to bring each vehicle to Smog Check program standards is expected to further reduce emissions by an estimated 19–31%. Alternatively, aggregate abatement due to compliance with standards could be achieved at less than 60% of current expected repair costs under a scheme that equates the expected marginal abatement cost of repaired vehicles. Overall, our results demonstrate the role of vehicle heterogeneity in optimal abatement policy, and suggest the existence of sizeable improvements in emissions reductions from directing emissions-related repair funds towards older model year vehicles.

2. Data set Our data comes from Valley CAN and concerns two recent TI&TU events held in Bakersfield, CA in 2006 and 2009. For each vehicle, the data set includes vehicle-specific characteristics (model year, odometer reading, vehicle make, vehicle model, and test weight). For vehicles that were successfully repaired to California Smog Check program standards the data set includes pre-repair (hereafter initial) and post-repair (hereafter final) emissions levels measured according to the ASM procedure. For other vehicles, the data set includes only pre-repair ASM emissions readings.8 For all vehicles the total repair cost is converted to 2009 US dollars.9 Total repair cost includes the amount of the voucher that is redeemed as well as any additional repair funds provided by the vehicle owner.10 Since the TI&TU program vouchers are redeemable solely for emissions-related repairs, we assume that all incurred repair expenditures contribute to emissions reductions. Pre- and post-repair emissions levels are converted from ASM readings to Federal Test Procedure (FTP) emissions rates in order to yield one single measure of emissions. Emissions readings for HC, NOx and CO are converted to pounds per 10,000 miles of driving using equations outlined in the Carl Moyer Program guidelines and developed by the California Bureau of Automotive Repair [3].11 The FTP measures for NOx, CO, and HC are then combined, producing an aggregate measure of a vehicle’s emissions by weight. Arguably, such an aggregation rule is not ideal. CO typically represents the largest contribution by weight, about 88% in our sample, while HC and NOx contribute 7% and 5%, respectively. Yet, the toxicity of CO is arguably lower than that of the other two pollutants.12 This raises concerns when using an abatement cost based on pounds of emissions for cost-benefit analysis, as large reductions in CO may be less critical than small reductions in the other two pollutants. Yet, removing CO from the emissions measure raises obvious problems since some repairs are incurred to reduce non-compliant CO levels, and thus our repair cost includes the cost of CO reduction. Hence, in what follows we estimate two abatement cost schedules: one where the three pollutants are aggregated with identical weights, and one where CO is removed while HC and NOx have identical weights. These two aggregation rules represent polar assumptions regarding the contribution of CO to overall ‘‘meaningful emissions.’’ As it happens, results based on these alternative measures turn out to be qualitatively similar, and the policy experiments based on the two estimated schedules lead to identical conclusions. Therefore, we believe our results to be robust to a wide range of assumptions regarding the toxicity of CO relative to that of HC and NOx. In the following sections, we refer to two distinct subsets of our data. Vehicles from the 2006 and 2009 TI&TU events for which pre- and post-repair emissions levels are available are used to construct the marginal abatement cost schedule and are referred to as the ‘‘calibration sample’’. The subset of vehicles in the calibration sample is denoted Sc; the number of vehicles in Sc is Nc ¼235. All subsequent counterfactual policy experiments are conducted on the subset of vehicles from the 2006 and 2009 TI&TU events for which pre-repair emissions data is available (irrespective of whether post-repair data is available). We refer to this subset as the ‘‘policy sample’’, Sp, and Np ¼411. Table 1 details vehicle characteristics and emissions-related repair costs for the policy and the calibration samples. The ranges of model year, weight and initial emissions levels are comparable between the two samples, as well as their means and standard deviations. In Fig. 1, the model year distribution of the policy sample is compared to the distribution of vehicles with current registration status in Bakersfield, CA as of April 7, 2009, ten days after the 2009 TI&TU event. The 667,271 vehicles with current registration status have a mean model year of 1997.59 and a standard deviation of 9.34, while the policy sample has a mean of 1992.18 and standard deviation of 5.95. Thus, our policy sample is clearly older than vehicles legally on the road around the time of the 2009 TI&TU event. 8 ASM emissions readings are recorded at 15 and 25 mph for HC, CO, and NOx and passing the emissions test component of the Smog Check inspection requires vehicles to have emissions levels below the cutpoints for all six readings. 9 We use the ‘‘all items’’ Consumer Price Index (CPI) for the United States obtained from the Organization for Economic Co-operation and Development [11] as our measure of inflation. 10 For the 2006 event repairs were conducted at one repair station. For the 2009 event, vehicle owners had a choice among three pre-approved repair stations. 11 The Carl Moyer Program provides grants to reduce mobile source NOx and VOC emissions throughout California. The program identifies a costeffectiveness threshold of $16,000 per weighted ton of emissions, which is regarded as the California standard of cost-effective emissions reductions [2]. 12 It is difficult to meaningfully compare the toxicity of the three pollutants as their adverse effects are targeted at different organs. Yet, maximum allowed concentrations for NOx and ozone in NAAQS are much lower than that for CO, suggesting a higher toxicity for HC and NOx than for CO.

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Table 1 Summary statistics. Calibration sample (Nc ¼235)

Model year Weight (lbs) Initial HC–NOx–CO (lbs/10,000 miles) Initial HC–NOx (lbs/10,000 miles) Final HC–NOx–CO (lbs/10,000 miles) Final HC–NOx (lbs/10,000 miles) Repair cost ($)

Mean

Std. dev.

Min

Max

1991.64 3471.40 498.70 59.03 185.00 29.18 527.33

5.57 671.65 629.39 51.10 183.77 24.70 195.45

1977 2000 13.77 2.19 12.34 2.38 155.22

2003 6000 3401.99 417.14 1143.42 134.11 1100.00

Policy sample (Np ¼ 411)

Model year Weight (lbs) Initial HC–NOx–CO (lbs/10,000 miles) Initial HC–NOx (lbs/10,000 miles)

Mean

Std. dev.

Min

Max

1992.18 3485.97 463.64 54.13

5.95 711.36 645.13 50.03

1976 2000 8.28 0.92

2004 6000 4431.44 417.14

Fig. 1. Registered vehicles as of April 7, 2009 and policy sample vehicles.

3. Abatement cost schedules Let us index each vehicle by j, j ¼ 1, . . . ,Nc , and denote by C j ðeij ,efj Þ the cost of reaching the emissions level efj, given an initial level eij. Thus, Cj represents the abatement cost function of vehicle j. For efj oeij , the cost of reducing the emissions of vehicle j from eij to efj is C j ðeij ,efj Þ ¼ 

Z

efj

eij

cj ðEÞ dE,

where cj ðEÞ represents the marginal abatement cost of vehicle j at the emissions level E. We assume that the marginal abatement cost cj is a decreasing function of E, that is, it is more and more costly to reduce emissions by one unit as emissions are being reduced. 3.1. Latent class model To empirically estimate the marginal abatement cost schedule for our vehicle fleet, we need to impose some structure on the set of marginal cost functions. Because we observe at most one point on the marginal cost schedule for each vehicle, we cannot estimate a model where each vehicle would have its own marginal abatement cost curve. Instead, we assume an underlying class structure for marginal abatement cost functions, so that vehicles have different probabilities pk of belonging to each abatement cost class k¼1,y,K based on a vector of vehicle characteristics zj. This approach has the additional advantage of enabling us to infer the marginal abatement cost of vehicles for which post-repair emissions data are not available, provided we can observe zj.

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Fig. 2. Marginal abatement cost for the calibration sample. Note: for each vehicle, the marginal abatement cost is assumed to be equal to aj at the emission point em j . Top panel, HC–NOx–CO; Bottom panel, HC–NOx.

Denoting by g k ð:Þ the marginal abatement cost function for vehicles in class k, we can write: cj ðEÞ ¼

K X

pk ðzj Þg k ðEÞ:

k¼1

We parameterize the class probabilities pk using the multinomial logit specification: expðc0k zj Þ pk ðzj Þ ¼ PK , 0 l ¼ 1 expðcl zj Þ

ð1Þ

where the vector zj includes a constant, the weight and the model year of the vehicle.13 The vector ck is a vector of unknown parameters, and we set c1 ¼ 0 as a normalization. We further parameterize the marginal abatement cost functions gk as follows: g k ðEÞ ¼ expðak þ bk logðEÞÞ,

ð2Þ

where bk o0. This functional form dictates that the marginal abatement cost curves gk are convex, that is, the marginal cost of abatement increases at an increasing rate as the emissions level is reduced. The choice of functional form in (2) can be motivated by the observed average abatement costs for vehicles in the calibration sample Sc. Denote by yj the observed emissions-related repair cost of vehicle j. Assuming that the marginal abatement cost curves cj are differentiable, the mean value theorem implies that the average abatement cost aj ¼ yj =ðeij efj Þ must equal the marginal abatement cost at a point lying strictly between the initial and final emissions levels. Fig. 2 plots the marginal abatement costs for the vehicles in the calibration sample, assuming that for each vehicle this marginal f i abatement cost is equal to aj when evaluated at the midpoint between eij and efj, em j ¼ ðej þ ej Þ=2. The figure clearly suggests 13 Although the odometer reading is available, we chose not to include it in the probability parameterization due to the propensity of older model year vehicles to have 5-digit odometers. Odometers of older model year vehicles may have rolled over multiple times, rendering the readings highly inaccurate.

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that the relationship between emissions levels and marginal abatement cost is non-linear, and instead should be modeled using a convex function. Given the marginal cost specification in (2), the total abatement cost to decrease the emissions of vehicle j from eij to efj conditional on vehicle j being in class k can be calculated as Gk ðeij ,efj Þ ¼

expðak Þ i 1 þ bk ½ðej Þ ðefj Þ1 þ bk   f j ðak , bk Þ: 1þ bk

ð3Þ

We estimate the latent class model using the observations on ðyj ,eij ,efj Þ for vehicles in the calibration subsample. To this end, we specify the distribution of the repair cost yj conditional on being in class k as a normal random variable: yj 9k  N ½f j ðak , bk Þ, s2k ,

ð4Þ

where the mean fj is defined in (3) and the yj 9k are assumed to be independent. Given (1) and (4), the log-likelihood function can be written as 0 1 ! Nc K X ðyj f j ðak , bk ÞÞ2 C expðc0k zj Þ 1 BX qffiffiffiffiffiffiffiffiffiffiffiffi exp  ð5Þ log@ Lða, b, r, cÞ ¼ A: PK 0 2s2k 2ps2 j¼1 l ¼ 1 expðcl zj Þ k¼1 k

We first obtain an estimate of the parameter vector ða, b, r, cÞ using the E-M algorithm [6]. This estimate is then used as a starting value for the direct non-linear maximum likelihood estimation of (5), implemented using the Newton–Raphson method. The covariance matrix of the estimates is derived using White’s sandwich estimate [15]. 3.2. Model selection We estimate model (5) with either one, two, or three classes. The optimal number of classes can be selected using the AIC or BIC criteria, as suggested for instance in Cameron and Trivedi [4].14 For small sample sizes, a corrected AIC criterion (crAIC) is preferable [1]. As the selection criterion, we therefore use the corrected AIC, as defined in Hynnes et al. [8]:   2ðJ þ 1ÞðJ þ 2Þ crAIC ¼ 2L þ 2 þ J, NJ2 where N is the sample size and J is the number of estimated parameters. Whether or not CO is included in our measure of vehicle emissions, the crAIC leads us to select the model with two classes over models with one or three classes. We therefore present results for the two-class models. Results for the one-class specification are reported in Appendix A. They do not differ much from those derived for the preferred two-class model, though the magnitude of the abatement gain from moving from the flat voucher to the optimal voucher is automatically reduced, due to reduced heterogeneity in abatement cost relative to the two-class model.15 3.3. Results The estimation results are reported in Table 2. Interestingly, results are qualitatively close for the two pollutant aggregation rules. All estimated intercept and slope coefficients are significant at the 1% level. A Wald test of the pairwise equality of intercept and slope coefficients between classes rejects the null hypothesis at the 1% level of significance, further justifying the use of the two-class model over the one-class model. For the two aggregation rules, the reported multinomial logit (MNL) coefficients are extremely large, reflecting complete separation of observations between classes. Technically, the MNL coefficients all go to infinity. Here, we report the coefficients corresponding to the point estimate where the convergence criterion for our maximum likelihood algorithm is met. Only the signs and relative magnitudes of the reported coefficients are meaningful, as they dictate the allocation of vehicles between classes. Complete separation of observations implies that all vehicles in the calibration sample have an ex ante probability of being in a given class of either zero or one. Although the MNL coefficients are not identified, it is possible to test whether the included covariates (weight and model year) are jointly statistically significant, by running a likelihood ratio test between the estimated model and a restricted model with g1 ¼ g2 ¼ 0, that is, the non-parameterized variant of our latent class model. The likelihood ratio test leads us to clearly reject the restricted model at the 1% level of significance. The likelihood ratio test of the null hypothesis that g2 ¼ 0 rejects the restricted model at the 1% level of significance, indicating that model year is very significant. The likelihood ratio test of the null hypothesis that g1 ¼ 0 rejects the restricted model at the 10% level of significance in the HC–NOx–CO model, and fails to reject the null in the HC–NOx model. These results imply that the main separation between classes occurs along the model year characteristic. 14 Of course, one may have a prior on the number of cost classes, based on technical knowledge of emissions-related repair procedures. However, there is no guarantee that the econometrically obtained classification will match the prior. Here, we prefer to let the data select the number of classes and reveal how vehicle characteristics determine class probabilities. 15 Results for the three-class specification are not presented, as the third class turned out to be a class of outliers with very few vehicles in it.

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Table 2 Abatement cost estimates. HC–NOx–CO

HC–NOx

Cost coeff.

MNL coeff.

Cost coeff.

MNL coeff.

Class 1

a1

a1

3.30nnn (1.01)  1.23nnn (0.24) 14.94nnn (2.38)

b1

s21

2.37nnn (0.37)  1.10nnn (0.16) 16.92nnn (2.94)

b1

s21

Class 2

a2

2.21nnn (0.33)  1.13nnn (0.06) 8.00nnn (0.86)

b2

s22

Observations: Nc ¼ 235 Log-likelihood:  597.47445 Number of vehicles in class 1: 63 Number of vehicles in class 2: 172 ( Test of H0 :

a1 ¼ a2 b1 ¼ b2

F-statistic: 11.47nnn ( Test of H0 :

g1 ¼ 0 g2 ¼ 0

g0 g1 g2

5.24  105 (—)  0.20 (—)  262.08 (—)

a2

1.40nnn (0.29)  0.95nnn (0.08) 9.36nnn (0.96)

b2

s22

g0 g1 g2

1.09  105 (—)  0.02 (—)  54.35 (—)

Observations: Nc ¼ 235 Log-likelihood:  613.97770 Number of vehicles in class 1: 60 Number of vehicles in class 2: 175 ( Test of H0 :

a1 ¼ a2 b1 ¼ b2

F-statistic: 9.95nnn ( Test of H0 :

g1 ¼ 0 g2 ¼ 0

D-statistic: 25.63nnn

D-statistic: 22.42nnn

Test of H0 : g1 ¼ 0 D-statistic: 3.59n

Test of H0 : g1 ¼ 0 D-statistic: 1.68

Test of H0 : g2 ¼ 0 D-statistic: 12.19nnn

Test of H0 : g2 ¼ 0 D-statistic: 14.32nnn

Note: nnn denotes statistical significance at the 1% level. n denotes statistical significance at the 10% level. The variable yj is measured in hundreds of dollars, eij and efj in lbs/10,000 miles. Vehicle weight is measured in lbs.

The two estimated marginal abatement cost schedules are depicted in Fig. 3. For both aggregation rules, Class 1 has a larger intercept coefficient than Class 2 (a1 4 a2 ), and has a steeper slope (b1 o b2 ). The two curves cross at an extremely high emissions point, so that over the range of emissions in our sample the marginal abatement cost curve for Class 1 lies above that for Class 2. As a result, the cost of bringing a vehicle from an initial emissions level to a lower final emissions level always rises with the probability of being in Class 1. The signs of the MNL coefficients always imply a higher probability of belonging to Class 1 for newer model year and/or heavier vehicles. For both aggregation rules, at the mean value of vehicle weight, 1995 and older model year vehicles are assigned to Class 2 with probability one, while vehicles with model year 1996 and newer are assigned to Class 1 with probability one. A similar reasoning holds for the effect of weight on the class probabilities, though for a given model year the cut-off weight varies slightly between the two aggregation rules, leading to a slightly different assignment of vehicles between classes. The cut-off weights by model year are indicated in Table 3.16 The fact that for both models, the switch between classes at the mean weight of the sample occurs at the 1995 model year could be explained, in part, by the introduction of the second generation of the On-Board Diagnostic System (OBD II). Mandatory for all 1996 and newer model year vehicles, OBD II is incorporated into vehicle computers and monitors all emissions-related vehicle components. The increased technical sophistication of the OBD II sensors and its involvement with vehicle computer systems could very likely result in higher emissions-related repair costs.17 16 Although weight is not statistically significant in the HC–NOx model based on the likelihood ratio test, we left it in the model to keep the parallel with the HC–NOx–CO model. 17 We confirmed the plausibility of this hypothesis with Rocky Carlisle who has over twenty-years of combined experience as an emissions-repair specialist and as the executive officer of the Inspection and Maintenance Review Committee (IMRC), which oversees the California Smog Check program.

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0.30 0.25 g1 g2

gk

0.20 0.15 0.10 0.05

0

200

400

600

800

1000

∋ 1.0

0.8 g1 g2

gk

0.6

0.4

0.2

0

50

100

150

200

250

300

∋ Fig. 3. Estimated marginal abatement cost curves. Note: marginal cost is indicated in hundreds of dollars. Top panel, HC–NOx–CO; Bottom panel, HC–NOx. Table 3 Cut-off weights for class allocation by model year. Model year

HC–NOx–CO

HC–NOx

r 1992 1993 1994 1995 1996 1997 Z 1998

47000 6740 5430 4110 2790 1480 o 1000

412; 000 11,260 8160 5050 1950 0 0

4. Efficiency of the voucher program Within the current structure of the TI&TU program, each vehicle that fails the TSI emissions test at the event is given a flat $500 repair voucher, within the limit of the overall budget.18 However, the marginal abatement cost schedules derived in Section 3 suggest that there could be significant efficiency gains if more voucher funds were directed at vehicles with lower marginal abatement costs. More specifically, aside from weeding out vehicles that do not fail the TSI tailpipe emissions test at the event, the current flat voucher scheme does not exploit the difference in the initial level of vehicle emissions nor the finding of Section 3 that newer and heavier vehicles have higher marginal abatement costs. To illustrate our point, consider first two vehicles in Class 2 with initial HC–NOx–CO emissions levels of 100 lbs and 1000 lbs, respectively. The marginal abatement costs of these vehicles are $5.01 and $0.37, respectively. Based on our estimated Class 2 marginal abatement cost curve, it would take $1000 in repairs to bring the vehicle with initial emissions

18 In practice, Valley CAN advertises that it will award $500 vouchers to the first x vehicles that are found to be out of compliance based on the quick TSI test.

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of 1000 lbs down to the same level of emissions—and thus, here, the same marginal abatement cost—as the vehicle with 100 lbs of initial emissions. Therefore, whereas the TI&TU event would simply allocate $1000 worth of voucher funds equally between these two cars, a voucher scheme aimed at maximizing emission reductions would instead give the entire $1000 to the car with the higher initial emissions. More generally, within the same class, vehicles with higher initial emissions should receive more in voucher funds. Between the two classes, marginal abatement costs also vary for vehicles with the same initial emissions level. Based on the HC–NOx–CO model, a vehicle with an initial emissions level of 200 lbs will have a marginal abatement of $2.29 if it is in Class 2 while it will have a marginal abatement cost of $4.01 if it belongs to Class 1. Hence, for the same initial emissions level, more voucher funds should be allocated to vehicles that have a higher probability of being in Class 2. In what follows, we first derive a measure of efficiency loss in emissions abatement for the TI&TU program under the assumptions that (i) the entire voucher is redeemed and (ii) vehicle owners do not contribute financially to repairs. This approach admittedly ignores the incentives facing vehicles owners when deciding whether to redeem the TI&TU voucher, how much of it to redeem, and whether to contribute financially to emissions-related repairs. These incentives are directly related to owners’ opportunity cost of conducting repairs and their utility from having vehicles in compliance with California Smog Check standards. We address these points subsequently by deriving alternative measures of efficiency loss for the current voucher scheme under two polar cases: one in which vehicle owners only redeem vouchers if the amount is sufficient to bring vehicles to California Smog Check standards, and if so, only redeem the amount necessary to bring vehicles in compliance with the standards (the ‘‘high opportunity cost, low utility’’ scenario); and one in which vehicle owners always supplement voucher funds in order to bring vehicles in compliance with California Smog Check standards, where needed, and allow the repair shop to redeem the entire voucher (the ‘‘low opportunity cost, high utility’’ scenario). Our baseline case where the entire voucher is redeemed and there is no financial contribution from vehicle owners corresponds to a ‘‘low opportunity cost, low utility’’ scenario. The ‘‘high opportunity cost, high utility’’ scenario, treated in Section 5, corresponds to the case where non-compliant vehicles are repaired to Smog Check program standards, but not beyond. In this last scenario, the voucher has no effect on actual emissions reductions and merely represents a windfall gain to recipients. All of our measures are derived under the assumption that emissions repairs for all vehicles are good for 10,000 miles.19 Though this is hardly a satisfactory assumption, data limitations prevent us from using a more precise measurement of repair durability on our fleet of vehicles. Valley CAN adopts the same 10,000 miles repair durability assumption in their reports on emissions abatement. 4.1. Baseline scenario In this subsection, we first derive the increase in emissions reductions that would obtain from the optimal reallocation of voucher funds among vehicles that were awarded a repair-cost voucher at the 2006 and 2009 TI&TU events held in Bakersfield, CA and subsequently attempted to redeem it at an approved repair facility (vehicle subset Sp). We then investigate the effect of Valley CAN’s budget on the efficiency loss in emissions reductions from the current flat voucher scheme. Finally, we investigate the abatement efficiency of a two-tier voucher scheme that does not require Valley CAN to know the exact initial emissions levels of vehicles at the time of the TI&TU event. 4.1.1. Optimal allocation Denote by V the total budget of Valley CAN and by N the number of vehicles eligible for a repair voucher. Both V and the set of eligible vehicles are assumed to be exogenous. The results from estimation of the abatement cost schedule imply that the allocation of vehicles between the two classes is deterministic, and therefore we assume that Valley CAN knows the functions C j ðeij ,efj Þ with certainty. Valley CAN distributes individualized vouchers of value vj, solving the problem: 8 i f > > > C j ðej ,ej Þ rvj , N < X f N X ð6Þ ðeij ej Þ s:t: max f > vj r V: e r ei > j j j ¼ 1 > : v Z0 j¼1

j

Substituting vj ¼ C j ðeij ,efj Þ, program (6) can be rewritten as max

efj

N X

r eij j ¼ 1

ðeij efj Þ

s:t:

N X

C j ðeij ,efj Þ rV:

ð7Þ

j¼1

Given the abatement cost schedules derived in Section 3 and available information on model year, test weight and initial emissions levels, we solve program (6) for the subset of vehicles in Sp.20 Since Np ¼411, the assumed budget is 19 20

Our comparisons would still be valid if the duration of repairs differs from 10,000 miles, as long as it is the same for all treated vehicles. All policy experiments are implemented in GAMS.

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Table 4 Optimal voucher distribution. $

0

1–249

250–499

500–749

750–999

1000 þ

HC–NOx–CO Obs. Avg. ei Avg. p1

130 60.17 0.969

29 128.68 0.207

49 188.97 0.041

84 328.91 0.024

56 592.01 0.00

63 1729.54 0.00

HC–NOx Obs. Avg. ei Avg. p1

122 9.75 0.959

31 23.19 0.548

46 29.89 0.043

78 51.12 0.013

69 81.77 0.00

65 143.60 0.00

Note: emissions are in lbs/10,000 miles.

$V ¼205,500. Vehicles are assigned with probability one to one class or the other based on their model year and test weight, according to the cut-offs reported in Table 3. First consider results for the HC–NOx–CO model. Total emissions reductions from the optimal allocation of voucher funds amount to 158,691 lbs/10,000 miles driven, representing an abatement per dollar of 0.77 lbs/10,000 miles. The shadow value of the budget constraint, which represents the additional emissions savings from an extra dollar spent on any of the repaired vehicles, is equal to 0.16 lbs/10,000 miles driven. In comparison, emissions reductions are calculated to be 132,307 lbs/10,000 miles driven for the flat $500 voucher, representing an abatement per dollar of 0.64 lbs/10,000 miles. Therefore, a shift from the current scheme to the optimal voucher would result in additional emissions reductions of 19.9%. Under the optimal voucher, 281 vehicles out of 411 receive repair-cost vouchers. The distribution of vouchers is reported in Table 4 and shows that funds are allocated preferentially towards higher emitting vehicles. Given the fact that older model year vehicles are both more polluting and cheaper to repair, under the optimal allocation repair funds are also allocated preferentially towards older model year vehicles, as shown by the average Class 1 probabilities. Results for the HC–NOx model are qualitatively similar to those derived for the three-pollutant model. Emissions reductions from the optimal voucher scheme amount to 17,013 lbs/10,000 miles, representing a 23.1% improvement over the abatement obtained under the flat voucher (13,819 lbs/10,000 miles). The distribution of voucher funds across vehicles shows a pattern similar to that derived for the three-pollutant model. 4.1.2. Budget effect Program (6) can be solved iteratively for various levels of the total budget V. The magnitude of the efficiency loss between the flat $500 voucher and the optimal voucher depends on the per vehicle repair budget, as shown in Fig. 4. Given the shape of the marginal abatement cost curves, with an unlimited budget there would be virtually no difference between the emissions reductions under the flat and the optimal vouchers. This is because marginal abatement goes to zero as large budgets allow to bring all cars to very small emission levels. As the budget is reduced, however, the magnitude of the difference in emissions reductions increases between the two voucher schemes. Theoretically, as the budget per car approaches zero, the two voucher schemes converge to zero abatement, and thus become arbitrarily close again. Fig. 4 shows that under the current budget per car, there is a sizeable difference in abatement between the two schemes. It also shows that if the budget per car were to decrease, the efficiency loss from the flat voucher would increase, both in absolute and relative terms, over a wide range of budget scenarios. 4.1.3. Allocations based on vehicle characteristics The optimal voucher allocation derived above implicitly assumes that Valley CAN has perfect knowledge of the initial emissions level of each vehicle (as well as the abatement cost schedule). In practice, the TSI emissions readings recorded at the TI&TU event do not perfectly predict the ASM emissions readings at the repair shop. For the 203 vehicles out of 411 policy sample vehicles for which TSI event emissions data is available, the R-squared from the regression of initial, prerepair, ASM emissions readings on TSI event emissions readings is only 0.267.21 Results in Table 4 suggest that the class probabilities—determined by model year and test weight—are highly correlated with initial emissions levels. Therefore, we analyze the efficiency of a simple two-tier voucher scheme where voucher amounts are determined based on vehicle model year, a variable that is easily observed at the time of the TI&TU event. Holding the budget at $500 per vehicle, we search for the cut-off model year defining the two tiers, as well as the tier amounts, that yield the highest emissions reductions for the policy sample. For the three-pollutant model, we find the optimal two-tier voucher to be such that the entire budget is split evenly between all 1994 and older model year vehicles, resulting in a voucher amount of $842.20. No voucher is given to 1995 21

The missing TSI readings were the combined result of TSI equipment malfunctions, user error, and untestable vehicles.

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Fig. 4. Effect of the budget on emissions abatement. Top panel, HC–NOx–CO; Bottom panel, HC–NOx.

Table 5 Initial emissions by model year. Model year

1976–1980 1981–1985 1986–1990 1991–1995 1996–2000 2001–2004

Obs.

13 50 90 123 110 25

HC–NOx–CO

HC–NOx

Mean

Std. dev.

Mean

Std. dev.

1571.07 1421.23 638.99 263.02 76.99 29.63

847.77 948.98 524.23 143.72 45.76 26.50

134.18 125.05 77.94 45.46 13.67 5.58

42.67 56.28 30.83 31.72 8.00 5.30

and newer model year vehicles. This allocation rule reflects the facts that newer vehicles tend to have lower initial emissions, as is made clear in Table 5, and are more costly to repair across all emissions levels. Under this optimal two-tier voucher, the average post-repair emissions level for 1994 and older model year vehicles is predicted to be about 84 lbs/10,000 miles. The 1995 and newer vehicles would remain at an average emissions level of 93 lbs/10,000 miles driven. Therefore, the overall effect of the two-tier voucher is to bring older model year vehicles down to the average emission level of newer model year vehicles. This two-tier voucher allocation based solely on model year is predicted to abate HC–NOx–CO emissions for our fleet by 151,103 lbs/10,000 miles driven, representing an abatement per dollar of 0.74 lbs/10,000 miles, compared to 0.77 for the optimal voucher. Thus, a substantial portion of the remaining abatement potential can be realized by shifting from the flat voucher to the two-tier voucher. Such a move would allow a 14.2% improvement over the abatement achieved under the flat voucher. Results for the HC–NOx model are in line with these findings. The optimal two-tier voucher is such that all voucher funds are split between 1995 and older model year vehicles, resulting in a $744.60 voucher. The corresponding abatement,

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taking only HC and NOx into consideration, would amount to 16,092 lbs/10,000 miles driven, representing a 16.4% additional abatement over the flat voucher. Under this scheme, 1995 and older vehicles are brought down to an emissions level of about 13 lbs/10,000 miles, while 1996 and newer vehicles remain at an average of 12 lbs/10,000 miles. Again, the effect of the two-tier voucher would be to bring the older model year vehicles to a level of emissions comparable to that of newer vehicles. Therefore, whether or not CO is considered, a simple voucher scheme based on model year alone would seem to represent an easily implementable alternative to the current flat voucher, that would result in emissions reductions not far from those obtained under the optimal vehicle-specific voucher scheme. We note that the calculated voucher amounts for older model year vehicles remain very reasonable. In particular, they seem much too low to start considering using the voucher to encourage scrappage of older model year vehicles as an alternative policy to the current repair subsidy scheme. 4.2. Alternative scenarios We now present comparisons among the flat $500 voucher scheme, the optimal voucher allocation derived in Section 4.1.1 and the two-tier voucher allocation presented in 4.1.3, under alternative assumptions regarding the financial participation of vehicle owners and the exhaustion of voucher funds. Under these new assumptions, the voucher scheme of subsection 4.1.1—which was derived assuming that every voucher dollar was spent on repairs, and that no funds would be added by vehicle owners—is no longer ‘‘optimal’’, in the sense that it does not take into account the behavioral response of vehicle owners. Nonetheless, we continue to refer to it as the ‘‘optimal’’ voucher. Results for the HC–NOx model are in line with those for the three-pollutant model. Though not explicitly discussed below, they are included in the results (Table 7). 4.2.1. Passing emissions thresholds The extent of voucher redemption, as well as the incentives of vehicle owners to supplement voucher funds, is directly related to the Smog Check passing emissions thresholds, which determine the compliance cost given initial emissions and vehicle class. Because this variable is not directly observed, we need to estimate it. An estimate could be constructed by simply aggregating the Smog Check regulatory cutpoints for each of the three monitored pollutants (having converted them to pounds/10,000 miles equivalent). However, we believe that such an estimate could only be a poor indicator of the vehicle-specific compliant level of aggregate emissions, for at least two reasons. First, it would not capture the fact that a vehicle may fail the inspection due to subpar visual and functional inspections, even with passing emissions levels. In fact, a substantial share of vehicles in our policy sample that failed the initial Smog Check did so not because of excessive emissions levels, but because of one or both of these additional inspections. When repairs are conducted on such vehicles to bring them into compliance, these repairs typically improve overall emissions as well, so that, in effect, the passing emissions level may be significantly lower than that dictated by simply adding up the regulatory thresholds. Another reason to be wary of an estimate of passing emissions purely based on regulatory thresholds is that even when vehicles fail the Smog Check inspection due to excessive emission levels, they do not necessarily exceed cutpoints for all three gases. Yet, when vehicles are repaired to bring the non-compliant emissions levels within the standard, their emission levels for the compliant gases will typically be reduced as well. Consequently, the actual passing level of aggregate emissions for a given vehicle may be well below that inferred from the regulatory thresholds. As such, using regulatory cutpoints would almost systematically lead to underestimating the compliance cost.22 We therefore propose to use observed, post-repair emissions levels for vehicles that were successfully repaired to Smog Check standards as a basis for inference of the passing level of emissions.23 The California Smog Check standards to which vehicles participating in the two TI&TU events were repaired is model year- and vehicle weight-specific—such that vehicles with the same model year and the same weight face the same ASM emissions thresholds—and thus the same ‘‘target’’ emissions. To obtain meaningful estimates of passing emissions levels from observed post-repair emissions we thus regress (the log of) post-repair ASM emissions on model year and weight for vehicles in Sc that were successfully repaired.24 The results are displayed in Table 6 and show that almost 80% of the observed variation in the post-repair ASM emissions can be explained by vehicle model year and weight, regardless of the aggregation rule. We subsequently use 22 Yet another, perhaps less critical reason not to use regulatory cutpoints as the basis for inferring passing emissions levels is the fact that due to the discrete nature of repairs and abatement, repair stations mechanically have to ‘‘overshoot’’ in order to bring vehicles within the compliance region (they cannot ‘‘stop’’ repairs exactly at the emissions cutpoint). This concern is somewhat mitigated by our proposed estimate. 23 One could argue that this solution suffers inevitably from another type of bias: the fact that observed final emissions levels in fact represent a lower bound to the emissions levels that would technically be required to pass the Smog Check, because repair stations may have an incentive to redeem as much of the voucher as possible, irrespective of the standards. If so, compliant emissions level estimates based on observed post-repair emissions may be too low. At the same time, if overshooting by repair stations was prevalent, one could argue that this behavioral feature of the repair technology should be fully accounted for in the actual cost of passing the Smog Check inspection. 24 Two vehicles in Sc were not repaired to Smog Check standards. As an alternative specification, we regressed post-repair ASM emissions on model year and weight. Since the R-squared was higher for the logarithmic specification, we selected it for subsequent analysis.

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Table 6 Regression of post-repair emissions on vehicle model year and weight.

Intercept Model year Weight Observations R-squared Note:

nnn

(resp.

HC–NOx–CO

HC–NOx

logðefj Þ

logðefj Þ

294.7591nnn (9.7316)  0.1458nnn (0.0049) 0.0001nn (0.0000) 233 0.7948

283.7983nnn (9.4318)  0.1413nnn (0.0047) 0.0002nnn (0.0000) 233 0.7974

nn

) denotes statistical significance at the 1% (resp. 5%) level.

Table 7 Abatement efficiency under various behavioral scenarios. Voucher

Abatement per dollar (lbs/10,000 miles) Low opp. cost, low utility

High opp. cost, low utility

Low opp. cost, high utility

HC–NOx–CO Optimal Two-tier Flat

0.772 0.735 (95.2%) 0.644 (83.4%)

1.301 1.173 (90.1%) 0.714 (54.9%)

0.201 0.185 (91.8%) 0.098 (48.6%)

HC–NOx Optimal Two-tier Flat

0.083 0.078 (94.6%) 0.067 (81.2%)

0.113 0.099 (87.6%) 0.077 (68.5%)

0.033 0.029 (89.2%) 0.018 (56.3%)

Note: Percentage relative to the optimal voucher is indicated in brackets.

these regression coefficients to construct our predicted passing emissions level for each vehicle in the policy sample. This predicted passing level is then used to compare the performance of the three voucher schemes under the alternative behavioral scenarios.

4.2.2. High opportunity cost, low utility First, we assume that vehicle owners have a high opportunity cost of undergoing repairs and a low utility from passing the Smog Check inspection. As a result, they only redeem voucher funds if the repair cost necessary to pass the Smog Check lies below the voucher amount (we assume that vehicle owners know vehicle class before making this decision.) In addition, vehicle owners prevent repair stations from redeeming more than necessary to bring their vehicle in compliance with the Smog Check standard. Under this scenario, the $500 flat voucher would result in an abatement of 44,760 lbs/10,000 miles driven, while the optimal voucher allocation would result in the abatement of 114,370 lbs/10,000 miles. Thus, under these behavioral assumptions, the optimal differentiated voucher would more than double the emissions reductions of the flat voucher scheme. By utilizing the two-tier voucher scheme based on model year, the abatement of 103,165 lbs/10,000 miles driven would be realized. Of course, under this behavioral scenario not all voucher funds are redeemed, so the ex post budget differs across voucher schemes. Under the optimal voucher, the ex post budget is calculated to be $87,888, out of an ex ante budget V ¼ $205; 500. Under the flat voucher, the ex post budget would drop to $62,658, while under the two-tier voucher it would be $87,944.25 We can therefore construct meaningful abatement efficiency measures for each voucher based on abatement per Valley CAN dollar spent. These measures are reported in Table 7 and show that, even when accounting for partial voucher redemption, there are significant cost efficiency gains to moving from the flat voucher to the two-tier voucher. 25 The fact that the optimal voucher results in a significant increase in voucher redemption in this scenario reflects the fact that under the optimal voucher, the allocation of funds is more in line with the amounts required to pass the Smog Check, compared to the flat voucher. In particular, under the flat voucher vehicles that would require relatively more expensive repairs are not being repaired as their owners are being deterred by the financial contribution that is required of them.

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4.2.3. Low opportunity cost, high utility We now assume that vehicle owners have a low opportunity cost of undergoing repairs and a high utility from passing the Smog Check inspection. Therefore, they are willing to contribute personal funds in order for their vehicles to pass the Smog Check inspection (we assume that vehicle owners know their vehicle class). Vehicle owners also allow repair shops to conduct repairs beyond the amount required to meet the standard, thereby fully exhausting the voucher. In this scenario, the emissions reductions attributable to the voucher program itself are those realized beyond the passing emissions level, as it is assumed that in the absence of the voucher vehicles owners would comply with the Smog Check program. As such, the magnitude of the emissions reductions attributable to the program is much lower than in the previous scenarios, resulting in lower measures of abatement per dollar. Under these assumptions, the flat $500 voucher would result in a per (Valley CAN) dollar abatement of 0.098 lbs/ 10,000 miles driven. The optimal voucher allocation would result in a per dollar abatement of 0.201 lbs/10,000 miles driven. Under the two-tier voucher, a per dollar abatement of 0.185 lbs/10,000 miles driven would be realized, representing about 92% of the abatement achieved under the optimal voucher, compared to less than 50% for the flat voucher. Table 7 summarizes the abatement per (Valley CAN) dollar achieved by the three voucher allocations under the various behavioral scenarios discussed above, for each of the two pollutant aggregation rules. The table shows that the two-tier allocation based on vehicle model year alone performs reasonably well relative to the optimal allocation in all scenarios. In contrast, the flat voucher always entails sizeable abatement efficiency losses. 5. Abatement efficiency of the California Smog Check program In this section, we provide a measure of the efficiency loss in abatement of the California Smog Check program, by calculating the additional emissions reductions that would result from optimally redistributing the repair funds needed to bring our fleet of vehicles Sp in compliance with California Smog Check standards. Conceptually, bringing our fleet exactly in compliance with the Smog Check standards corresponds to a ‘‘high opportunity cost, high utility’’ scenario where the size of the voucher becomes irrelevant. All results are reported in Table 8. We begin by quantifying the emissions reductions from bringing the 411 policy sample vehicles in compliance with our predicted level of passing emissions. For the three-pollutant model, the resulting aggregate emissions reductions are calculated to be 123,401 lbs/10,000 miles driven, for a total cost of $148,529. Optimally redistributing these funds would

Table 8 Cost effectiveness of the California Smog Check program based on the policy sample.

Compliance cost ($) Abatement due to compliance (lbs/10,000 miles) Abatement per dollar (lbs/10,000 miles) Abatement potential given cost (lbs/10,000 miles) Minimized cost of realized abatement ($)

HC–NOx–CO

HC–NOx

148,529 123,401 0.831 146,939 83,587

143,579 11,310 0.079 14,758 84,411

Table 9 Predicted repair expenditures by model year group. Model year

Obs.

Smog Check standard

Optimal reallocation

Mean ($)

Std. dev. ($)

Mean ($)

Std. dev. ($)

HC–NOx–CO 1976–1979 1980–1984 1985–1989 1990–1994 1995–1999 2000–2004

7 43 90 104 120 47

111.58 378.00 395.78 391.40 386.15 187.87

154.81 206.25 237.06 207.57 333.81 359.28

875.47 955.05 675.01 334.54 48.25 0.00

258.97 258.01 265.08 207.68 127.07 0.00

HC–NOx ways 1976–1979 1980–1984 1985–1989 1990–1994 1995–1999 2000–2004

7 43 90 104 120 47

38.31 217.67 405.98 414.69 372.16 204.80

58.56 168.25 180.41 222.43 308.12 331.45

948.67 820.97 662.27 347.65 48.97 0.00

157.02 156.00 210.94 224.41 157.31 0.00

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result in emissions reductions of 146,939 lbs/10,000 miles driven, representing an additional 19.1% reduction in emissions. The difference in the allocation of repair funds across model year groups between the Smog Check standard and the abatement-maximizing allocation is shown in Table 9. It is apparent that the gains in emissions abatement arise from a reallocation of repair funds from newer model year vehicles towards older model year vehicles, and that pre-1990 model year vehicle owners must consent to a significantly larger repair expenditure. Alternatively, setting aggregate emissions reductions equal to the emissions reductions achieved under the current California Smog Check program standards, total abatement costs could be brought down to $83,587 if funds were allocated optimally so that all repaired vehicles had the same marginal abatement cost. Thus, total repair costs for our fleet of vehicles could be reduced by 43.7% while achieving current abatement under a cost-effective program structure. Results for the HC–NOx model also suggest a large cost inefficiency of the program: the optimal reallocation of repair funds is predicted to further abate HC and NOx by 30.5%, while current abatement could be achieved at 58.8% of the current cost. Though our vehicle fleet may not be a representative of the overall California fleet, the large size of the calculated deadweight loss suggests that there exist sizeable gains to reallocating the burden of emissions reductions towards older model year vehicles. In particular, substantially larger amounts should be spent on pre-1990 vehicles in order to maximize abatement.

6. Conclusion With its TI&TU program, Valley CAN aims at improving air quality in the San Joaquin Valley by giving vehicle owners financial incentives to undergo emissions-related repairs. In this article, we provided evidence that the efficiency of this program would be improved if Valley CAN could offer more selective vouchers based on the marginal abatement cost of vehicles. By ignoring vehicle heterogeneity and attendant differences in marginal abatement costs, Valley CAN is foregoing an estimated 20% in emissions reductions, relative to current abatement levels. While access to vehicle-specific marginal abatement costs at TI&TU events is unrealistic, reallocating repair vouchers towards older model year vehicles would result in an estimated 15% improvement in emissions reductions compared to current abatement. The existence of sizable efficiency gains from shifting from the current flat voucher to a differentiated voucher seems robust to varying levels of financial participation by vehicle owners and partial redemption of the voucher. Results also seem robust to varying assumptions regarding the toxicity of CO relative to that of NOx and HC. Our abatement measures were calculated assuming that the expected durability of emissions-related repairs is uniform across all vehicles. If, instead, repairs performed on newer model year vehicles can be expected to be more durable, there could be a case for reallocating some of Valley CAN’s budget towards more recent model year vehicles as emissions reductions on these vehicles, though more costly, could last for more miles driven. Although our data set does not allow us to investigate this question in much detail, we were able to track the subsequent Smog Check results of 67 vehicles that were successfully repaired at the 2009 TI&TU Bakersfield event. A simple logistic regression of the subsequent Smog Check outcome on model year (1995 and older vs. 1996 and newer), controlling for the mileage increment, did not show any significance of the age of the vehicle on the probability of passing the inspection.26 Although this seems to indicate no particular effect of model year on repair durability, mileage increment was not statistically significant either. Therefore, we cannot entirely rule out that repairs conducted on newer model year vehicles could, in fact, be more resilient. Yet, we can provide a measure of how large this additional resilience would need to be in order to invalidate our main policy recommendation. Under the current assumption that repair durability is the same across all vehicles, emissions reductions are maximized, under a two-tier voucher, when only 1994 and older model year vehicles receive repair funds. In order to justify spending the first 100 dollars repairing 1995 and newer vehicles (thereby reducing the amount spent on older model year vehicles), we calculated that repairs to these vehicles would have to be 1.8 times as durable in terms of miles driven as those made to 1994 and older vehicles. To justify moving away from the proposed two-tier, model-year based voucher to the current flat voucher scheme, repairs made to 1995 and newer model years would need to be 3.5 times as durable as those made to 1994 and older vehicles.27 Investigating further the issue of repair durability, and how it may affect policy recommendations regarding the optimal allocation of abatement effort, would constitute a natural extension to this study. All of our counterfactual calculations were made assuming that the fleet of vehicles attending the TI&TU event is exogenous. Yet, our marginal abatement cost schedules imply that if Valley CAN can influence the composition of the fleet and increase the number of older model year vehicles participating (for instance, by ex ante restricting participation to 1995 and older model year vehicles) further efficiency gains could be realized. As a general rule, our abatement cost 26 Odometer readings taken at the Smog Check inspection for this small subset of vehicle is obtained through the Vehicle Identification Database (VID) a centralized database of information collected at all Smog Check inspections in California. This information was made available by Jeffrey Williams of the University of California, Davis. 27 These figures were derived for the three-pollutant model. For the NOx–HC model, repair durability factors were 2.6 and 4.1, respectively.

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0.30 0.25

g1

0.20 0.15 0.10 0.05

0

200

400

600

800

1000

∋ 1.0 0.8

g1

0.6 0.4 0.2

0

50

100

150

200

250

300

∋ Fig. 5. Estimated marginal abatement cost curve with one class. Note: marginal cost is indicated in hundreds of dollars. Top panel, HC–NOx–CO; Bottom panel, HC–NOx.

schedules and the observed distribution of initial emissions suggests that Valley CAN should attract as many older model year vehicles as possible to each planned TI&TU event.28 A factor that may undermine the benefits from reallocating repair funds towards older model year vehicles is that a rise in voucher amounts may encourage vehicle owners who would otherwise have paid for repairs to join TI&TU events and enjoy windfall gains from the program. Yet, an increase in voucher amounts may also attract more owners of highemitting vehicles who did not bother to attend when vouchers were lower, thereby reinforcing the benefits from moving toward a differentiated voucher. While it is difficult to predict how these changes in attendance to events would affect the actual benefits from reallocating voucher funds towards older vehicles, we believe these effects to be secondary given that voucher amounts remain reasonable in our proposed two-tier subsidy. We would also expect owners of older model year vehicles to be less likely to undergo repairs in the absence of the voucher, which could mitigate the free-rider problem arising from a more generous subsidy. A related concern with our proposed two-tier subsidy is that it may discourage owners from retiring older model year vehicles, thereby foregoing the environmental benefits associated with vehicle scrappage. Given that the majority of vehicles participating in TI&TU events do not have current registration status, it is not certain that the correct alternative to event participation and subsequent vehicle repairs would be vehicle scrappage, but instead may well be continued vehicle usage. After all, the raison d’ˆetre of the TI&TU program is indeed that a number of vehicles are being driven regardless of compliance with smog check standards in the SJV. To the extent that the program does a good job at targeting drivers that are not diligent enough to—or simply cannot—either put their vehicle in compliance or scrap it, our recommendation to target older model year vehicles stands. Finally, an important insight of this paper is that the current structure of the California Smog Check program may entail significant abatement efficiency losses. Though our fleet of vehicles is not representative of the entire state, and our

28 Theoretically, for a fixed budget emissions reductions are an increasing function of the number of (identical) vehicles repaired, so that Valley CAN should spread their budget among the largest possible number of (identical) vehicles. There are practical limitations to this goal, however, as voucher amounts should remain attractive.

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Table 10 Abatement cost estimates with one class. HC–NOx–CO

a1 b1

s21 Observations: Log likelihood:

nnn

HC–NOx

3.54 (0.32)  1.36nnn (0.06) 10.67nnn (0.95)

2.33nnn (0.22)  1.19nnn (0.07) 11.98nnn (1.08)

Nc ¼ 235  611.65987

Nc ¼ 235  625.18733

Note: *** denotes statistical significance at the 1% level.

Table 11 Main policy results for one-class models. HC–NOx–CO

HC–NOx

Abatement per dollar (lbs/10,000 miles): Optimal Two-tier Flat

0.760 0.734 (96.5%) 0.671 (88.2%)

0.081 0.077 (95.6%) 0.069 (85.3%)

Smog Check analysis: Compliance cost ($) Abatement due to compliance Abatement per dollar Abatement potential given cost Minimized cost of realized abatement ($)

139,888 123,401 0.882 144,162 77,522

138,047 11,310 0.082 14,408 79,879

Note: In both models, the optimal two-tier voucher is such that all repair funds are split evenly between 1995 and older model year vehicles.

calculations ignore any potential heterogeneity in repair durability, the large size of the deadweight loss measure suggests that the current program is likely far from being cost-effective. Of course, cost-effectiveness is not the only goal of the Smog Check program, and equity considerations likely play an important role in explaining its structure. Demanding that older model year vehicles achieve the same emissions levels as newer vehicles would likely constitute an unfair burden on their owners. To alleviate this burden, in lieu of undergoing an inspection and subsequent repair expenses, owners of newer model year vehicles could be charged an additional smog tax on their yearly registration fees.29 This smog tax could then be redistributed towards subsidizing the repair of older model year vehicles to more stringent Smog Check cutpoints.

Acknowledgments We thank, in addition to the Editor and two anonymous referees, Jeffrey Williams, Katrina Jessoe, Aaron Smith, Rocky Carlisle and participants at the inaugural AERE Conference in Seattle for helpful comments. We thank Tom Knox for sharing the Valley CAN data. Appendix A. Results for the one-class model Abatement cost estimates with one class and main policy results for the one-class model are given in Fig. 5 and Tables 10 and 11. References [1] K.P. Burnham, D.R. Anderson, Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, 2nd ed., Springer-Verlag, 2002. [2] California Air Resources Board, The 2008 Carl Moyer Program Guidelines, Sponsored by the California Environmental Protection Agency, 2008. [3] California Bureau of Automotive Repair, California Enhanced I/M Program Evaluation Technical Support Document Part 2. Technical Notes, 2001.

29

Owners of vehicles less than 6 years old are already charged a $20 Smog Abatement Fee upon registration.

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