Optimal investment to control ‘red air day’ episodes: lessons from Northern Utah, USA

ABSTRACT

We address the issue of optimal investment in ‘preventative capital’ to mitigate episodic, mobile-source air pollution events by calibrating an endogenous-risk model with parameter estimates obtained from a unique dataset related to ‘red air day’ episodes occurring during the winter months in Northern Utah. Our analysis demonstrates that, under a wide range of circumstances, the optimal steady-state level of preventative capital stock – raised through the issuance of a municipal ‘clean air bond’ that provides foundational funding for more aggressive mitigation efforts – can meet the standard for PM2.5 concentrations with positive social net benefits. We estimate benefit-cost ratios ranging between 3.1:1 and 11.3:1, depending upon trip-count elasticity with respect to preventative capital stock. These ratios are clustered in the lower end of the range estimated for the 1990 Clean Air Act Amendments in general.

KEYWORDS:

• Preventative capital
• endogenous risk
• PM_2.5 concentrations
• episodic air pollution

JEL CLASSIFICATIONS:

• D62
• Q53
• Q58

Acknowledgement

The authors would like to thank participants at the 2016 Environmental and Resource Economics Workshop, University of Colorado, Eric Edwards, Sherzod Akhundjanov, Ryan Bosworth, and Man-Keun Kim for feedback on earlier versions of this paper. Any remaining errors are of course the authors’ responsibility.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Pope et al. (2002) provide detailed estimates of the human health costs associated with elevated PM_2.5 concentrations; estimates that corroborated by Utah Department of Environmental Quality (UDEQ) (2016b). See Liu et al. (2014) and Zanobetti and Schwartz (2009) (and references therein) for examples of dose-response studies. Morbidity and mortality estimates for US populations have since been compiled in the US Environmental Protection Agency's (EPA's) Environmental Benefits Mapping and Analysis Program (BenMAP) (EPA 2016a), which is used in this study to estimate health damages incurred by Northern Utah residents during episodic outbreaks.

2 Roughly half of the 6.5 million deaths are in turn attributable to elevated PM_2.5 concentrations, the specific pollutant considered in this study (Apte et al. 2015).

3 The application of Berry et al.’s (2015) framework to the problem of mobile-source episodic air pollution is a natural modeling extension given the measurable interplay between exogenous and endogenous risk factors associated with recurring ‘outbreaks’ of elevated pollution events, which in turn induce similarly measurable impacts on human health. Recently, Moscardini and Caplan’s (2017) seasonal gas tax study and Cropper et al.'s (2014) piloted permit programme have investigated specific market-based solutions to the prolific problem of mobile-source, episodic air pollution. Moscardini and Caplan (2017) find that, on average, a one-percent decrease in county-level trip count results in a 0.75 percent reduction in PM_2.5 concentrations, all else equal. Further, a one-percent increase in gas price is correlated with a 0.31 percent reduction in vehicle trips. The authors estimate substantial seasonal social net benefits associated with this reduction. Cropper et al. (2014) also investigate the use of a market-based policy to control episodic air pollution attributable to vehicle emissions, in their case ground-level ozone concentrations in Washington, DC. According to the authors’ estimates, their proposed permit scheme would remove one million vehicles from the road during high-ozone days, resulting in a corresponding reduction in NO_x emissions of 30 tons per day and generating an estimated $111 million annually in government revenue, even in the face of non-compliance.

4 Hence, prevention in our case means preemptively restraining PM_2.5 concentrations below the NAAQS during the winter season. By comparison, prevention in Berry et al.’s (2015) model refers to the preemption of a possible disease outbreak. It may therefore be more accurate to refer to the type of capital stock we have in mind as ‘precautionary’, as in Polasky, de Zeeuw, and Wagener (2011), rather than ‘preventative’ per se. Lastly, we reiterate that our focus in this paper is on estimating the optimal stock of capital – a capital stock which can then be used to fund a variety of programmes aimed at mitigating mobile-source pollution – not on which particular programme might subsequently be implemented. Programme-by-programme assessment is beyond the scope of this study.

5 The regime-shift literature, which proposes somewhat more complex models to control problems such as climate change, invasive species spread, overfished fisheries, etc., similarly distinguishes between investments in preventative and restorative (or adaptive) capital (Polasky, de Zeeuw, and Wagener 2011; Crepin et al. 2012; Ren and Polasky 2014). However, regime shifts are fundamentally different than episodes, since the former involves either a change in system dynamics or stock collapse with either no return or long-delayed return to the initial regime (i.e., hysteresis), while the latter does not. The ‘substantial reorganisation in system structure, functions and feedbacks that often occurs abruptly and persists over time’ as a result of regime shift (Crepin et al. 2012, page 15) is absent in the episodic problem. Interestingly though, Polasky, de Zeeuw, and Wagener (2011) show that optimal management is preventative in the presence of an endogenous regime shift with changed system dynamics, where ‘endogenous’ in this case refers to the hazard function being conditioned on choice of resource stock.

6 It is important to point out that these ratios do not account for any potential co-benefits associated with the control of other air pollutant concentrations in Northern Utah to which mobile sources contribute, such as summertime ground level ozone (UDEQ 2019; UDH 2019). Estimating the extent of these co-benefits is beyond the scope of this particular study.

7 Logan is Northern Utah's largest city. In 2009, Logan's population consisted of 46,000 people residing in 16,000 households (U.S. Census Bureau 2016). The population of Northern Utah is roughly 150,000. See Moscardini and Caplan (2017) for a detailed explanation of Northern Utah's winter inversion phenomenon.

8 Utah residents concur that air quality is an insistent social concern. According to Envision Utah (2014, 2013), Utah residents believe that mitigation of poor air quality should be the state's second highest priority, tied with funding of public education and only slightly behind management of water resources. Survey results indicate that, inter alia, over 60 percent of respondents believe air quality negatively impacts their lives, over 90 percent believe good air quality is integral in maintaining good health, and almost 80 percent believe air quality has worsened in the Greater Wasatch and Northern Utah regions over the past 20 years. Further, residents identify changes in how they transport themselves (i.e., changes in the extent to which they contribute mobile-source emissions), e.g., telecommuting, ridesharing, use of public transportation, reduced idling and unnecessary driving, as being the most beneficial approaches to improving air quality. Roughly 65 percent of respondents report that they would likely reduce the use of their vehicles if a tax increased the per-gallon price of gasoline by $1.00; 32 percent indicating that they would be very likely to do so (Envision Utah 2013, 2014).

9 PM_2.5 concentrations, vehicle trip counts, and the weather variables used in this study are reported by their various sources on an hourly basis. For the analyses we have created daily averages from the hourly data.

10 Specifically, 40,538 is the average daily trip count across our entire dataset based on the ATRs reporting the largest trip counts per day. We chose the largest reported daily trip count rather than the average across all ATRs because even the former measure is likely an underestimate of daily trips taken in the valley. This is due to the fact no one ATR is capable of recording all daily trips taken in the county. We were precluded from adding daily trips across all ATRs because of potential double-counting errors. It is important to bear in mind that even though our measure of daily trip counts is thus an underestimate in absolute terms, the measure exhibits no bias in relative terms across days. This fact is crucial for our analysis since it is the variability in trip count across days that we are interested in measuring in order to estimate trip count's marginal effect on the variability in daily PM_2.5 concentrations. 

11 We have chosen not to jointly estimate an underlying structural model linking determination of the region's steady-state background risk with its hazard function for two reasons. First, our underlying theoretical framework portrays background risk as an exogenous process. Thus, as in Berry et al. (2015), this risk factor is assumed to affect the hazard function exogenously, rather than as a joint determinant per se. Second, the probit and survival models estimated in this section are ‘un-nested’, in the sense that the categorical variable being determined in the former equation (whether or not a red air day has occurred) is not an endogenously determined explanatory variable in the latter equation (which itself determines the number of days until a red air day episode commences). As a result, any error correlation across these two equations potentially affects the efficiency of each equations’ estimated coefficients not their accuracy. 

12 We ran a host of other specifications for this model, including different sets of explanatory variables. We also tested for causal effects (endogeneity) associated with the TEMP, HUMIDITY, and HUMWIND weather variables, even though we know of no theory to suggest that PM_2.5 concentrations partially determine these weather conditions. Results for these specifications were qualitatively similar to those reported in Table 3, particularly with respect to the estimation of $R^{ss}$, which is the key value being estimated in these regressions. Results for these models are available from the authors upon request. We used STATA version 14.1 for our regression analyses.

13 We also ran the model in Table 3 without LagPM_2.5 as a regressor in order to assess the impact on the remaining regressors’ coefficient estimates (as a test of LagPM_2.5's potential endogeneity) and standard errors (as a test of potential serial autocorrelation). The results were qualitatively very similar. Further, the estimate for $R^{ss}$ was 15.8 percent, also very similar to the 16 percent estimate from the model including LagPM_2.5. Lastly, we do not consider TC as an omitted variable from this model because it is uncorrelated with the remaining variables. As we discuss in Section 4.2, TC can instead be instrumented with either a weekday dummy or a series of day-of-the-week dummies. 

14 Slight breezes stimulate the evaporation of water, leading to increases in humidity. Thus, we expected HUMWIND to exhibit a negative relationship with PM2.5. WIND was included in an earlier specification and found to be statistically insignificant.

15 Because multiple red air day episodes typically occur in Northern Utah during the inversion season, we consider each episode as a special case and format the data accordingly (which is discussed in more detail below). Hence, the wording ‘given no such outbreak has occurred prior to day $t$’ should, in a more technical sense, read ‘given no such outbreak has occurred prior to day $t$ since the previous episode’. The episodes must be independently distributed in order to warrant such a statement, which in our case is evidenced by the statistically significant role that the weather variables (which are themselves exogenously determined) play in determining the start and finish of any given episode, as well as the episode's duration and intensity. Hence, in our case survival is tracked between successive episodes during a given inversion season. As an example of what we mean by ‘successive episodes’, suppose the first episode in a given inversion season does not begin until day 20 and then lasts until day 23. Then the period during which no outbreak has occurred for the first episode (i.e., the first episode's survival period) is days 1 to 19. If the second episode then begins on day 31, the associated survival period for the second episode is then days 24 to 30.

16 As we discuss in Section 4.3, we find some empirical evidence to support our presumed range for elasticity measure $c$. The range of trip-count elasticities adopted for this study represent a range of possible behavioural responses of drivers to different scales of investment in preventative capital. As we also discuss at greater length in Section 4.3, since $N\left(t=0\right)$ is per force a best-guess estimate provided by a county executive officer for this analysis, we sensitise the analysis to alternative values, $N\left(t=0\right)\in \left[\mathrm{\$}500,000,\mathrm{\$}1\mathrm{m}\mathrm{i}\mathrm{l}\mathrm{l}\mathrm{i}\mathrm{o}\mathrm{n}\right]$.

17 Notationally speaking, the post-estimation version of $\mathrm{\Psi }\left(\mathit{X}\left(t\right),R\left(t\right)\right)$ is perhaps best written as $\mathrm{\Psi }\left(\mathit{X}\left(t\right),R\left(t\right);f\left(N\left(t\right)\right)\right)$, where $f\left(N\left(t\right)\right)$, which represents the functional relationship between $N\left(t\right)$ and $TC\left(t\right)$, is decreasing in $N\left(t\right).$

18 The Weibull hazard function exhibits the appealing property of increasing hazard over time for $p>1$.

19 It is important to note that the intervening periods between red air day episodes and the lengths of the episodes themselves each occur independently both within and between years. This is due to the fact that weather conditions, which are necessary for the emergence of the episodes, are exogenously determined. We also considered an alternative specification of the count-data variable, whereby the number of consecutive inversion days (i.e., days in which the Logan-peak temperature exceeds the valley floor temperature (TEMP > 0)) were counted between episodes. However, this approach unfortunately whittled our sample size down to a mere 21 observations. Results based on this count-variable specification are qualitatively similar to those presented in Table 4 and are available from the authors upon request.

20 TC is ‘coarse’ in the sense that it serves as a proxy for vehicle-use decisions that are inherently made at the household level and yet is aggregated at the county level (recall that it is calculated as the total number of vehicle trips per day made in the region). In contrast, each weather variable is a non-aggregated, relatively precise scientific measurement of a meteorological occurrence. 

21 The value$N\left(t=0\right)$ = $1 million represents Cache County Executive M. Lynn Lemon's best estimate, provided through personal communication on June 14, 2016. We have also run separate simulations assuming$N\left(t=0\right)=\mathrm{\$}500,000$, which was Mr. Lemon's lower-bound estimate provided at the time. Results based on this assumption are contained in Appendix Table A1. Note the current preventative capital stock described here is notably different than the types of preventative capital we described in Section 1. This is because the preventative capital described in Section 1 represents what might best be described as investments in what are now considered to be ‘outside-the-box’ technologies and information campaigns that heretofore have been deemed infeasible given current funding levels.

22 We use Matlab version R2016b (9.1.0.441655) 64-bit for our numerical analyses.

23 In other words, we assume an initial red air day PM_2.5 concentration level of 50 µg/m³, which is roughly equal to the mean estimate of the concentration level that occurs in our sample strictly on red air days, i.e., given that the concentration level is no less than 35 µg/m³ per day to begin with. BenMAP requires input of an initial PM_2.5 concentration level in order to generate benefits associated with the reduction in damages from that level. For detailed information on the BenMAP facility visit https://www.epa.gov/benmap.

24 Note that equations (23) and (24) in Berry et al. (2015) are used to derive the expression for $N^{ss}$ used in our simulations.

25 A 5 percent interest rate and 20-year loan term period are assumed for the amortisation exercise.

26 This non-monotonic relationship between trip count elasticity and optimal investment in preventative capital contrasts with Berry et al.'s (2017) finding of a monotonically decreasing effect of prevention effectiveness on optimal investment.

27 The specific curvature conditions assumed for $\mathrm{\Psi }\left(N\left(t\right),R\left(t\right)\right)$ are provided in Section 2.

28 The percentage change in PM_2.5 concentration is calculated as the mean of the sampling distribution of 10,000 sample means, where each sample consists of 90 observations (representing the length of the three-month winter inversion season) randomly drawn from respective normal distributions for each variable used in the ARMAX(1,0,0) equation, where the mean of the variable's distribution is the variable's sample mean.

29 Social net benefit begins to diminish at $c=7.5$.

30 It is important to point out that the reduction in vehicle trips necessary to attain the NAAQS for PM_2.5 concentrations in this model, as well as in Moscardini and Caplan (2017) are not necessarily socially optimal from a purely normative perspective. We estimate the socially optimal vehicle trip count and corresponding PM_2.5 concentration level for Northern Utah in a separate study, Acharya and Caplan (2018b).

 

Additional information

Funding

This study is funded in part by the Utah Agricultural Experiment Station (UTA0-1074 and UTA0-1334).