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Air pollution and hospital admissions
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Journal of Environmental Economics and Management 49 (2005) 116–131 www.elsevier.com/locate/jeem
Air pollution and hospital admissions an ARMAX modelling approach David Maddison Institute of Economics, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark Received 17 June 2003; received in revised form 9 February 2004 Available online 19 June 2004
Abstract Using daily data this paper analyses the time-series relationship between hospital admissions and air pollution in London. In doing so it addresses an important issue not dealt with in the existing empirical literature: Are hospital admissions truly additional or merely advanced by air pollution? If it could be shown that the hospital admissions are only advanced by air pollution rather than additional then it would be incorrect to attribute the cost to air pollution. The evidence presented indicates that a 1 percent reduction in the currently prevailing levels of PM10 in London would in the long-run result in a statistically significant 0.14 percent reduction in the number of respiratory hospital admissions. By contrast one cannot reject the hypothesis that cardiovascular hospital admissions are simply brought forward and accordingly their cost should not be attributed to air pollution. r 2004 Elsevier Inc. All rights reserved. Keywords: Cost–benefit analysis; Air pollution; Hospital admissions
1. Introduction A significant number of dose response functions estimated on time-series data have identified particulate matter and other air pollutants too as being statistically related to a range of ill-health Tel.: +45-6550-3270; fax: +45-6615-8790
E-mail address: [email protected] (D. Maddison). 0095-0696/$ - see front matter r 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jeem.2004.04.001
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effects. For examples of such studies published by economists see [7,9,23,25,26] for mortality; [28] for hospital admissions; [1,17] for acute respiratory symptoms and [13] for work loss days. Many more such studies have been published in the epidemiological literature although recently the statistical software used by a significant number of these studies has been shown to contain a programming error as well as an inappropriately lax default criterion for declaring convergence [14].1,2 Amongst other things these studies have been widely used to value the external costs of power generation facilities, where typically the health effects of air pollution dominate. The procedure involves using atmospheric dispersion models to calculate the change in ambient concentrations of air pollution associated with an additional kilowatt-hour of electricity. Dose–response functions are then used to predict the changed incidence of ill-health amongst the population. In the final step economic values are attached to these health impacts. Good examples of such studies include [10,30]. Krupnick and Burtraw [16] provide an excellent review of these and other studies complete with discussion about the treatment afforded to the effect of air pollution on health. Ostro and Chestnut [24] have also used these studies for the purposes of quantifying the health benefits of attaining national standards for particulate matter in the United States whilst Olsthoorn et al. [22] conducted a similar analysis for the European Union. For an example of a study using dose–response studies to determine the external costs of road transport see [36]. But despite the fact that these time-series studies of air pollution have been widely used their results require very careful interpretation. Such interpretation has frequently been lacking. For a chastening review of the ‘inappropriate’ use of these studies by economists written by a distinguished group of epidemiologists see [20]. One reason why the available evidence is inappropriate for the use to which it has been put arises because of the way in which air pollution variables are typically entered into the statistical regression model. Standard practice in the statistical modelling of the relationship between daily mortality or hospital admission counts and ambient levels of air pollution is to include controls for autonomous trends, seasonal cycles, meteorological variables, day of the week effects and contemporaneous, once or twice lagged values for air pollution in the regression equation. Often it seems that the single most significant lag is selected as for example is explicitly stated in [15]. Clearly such models estimate only the short-run impact of air pollution. They do not for example, account for the possibility that a high number of hospital admissions on 1 day might be followed by an offsetting reduction in the number of hospital admissions spread over the following weeks and months. The importance of this point to the conduct of policy should be obvious. If air pollution precipitates hospital admissions that have merely been borrowed from the future then the cost of these admissions should not be attributed to air pollution unless they are advanced to such a degree that time discounting becomes an issue. Only if these hospital admissions would never
1
Good examples of such studies include [31,34] for mortality and [5,37] for hospital admissions. The effect of correcting this programming error and adopting a stricter convergence criterion seems not to alter the qualitative conclusion that air pollution and in particular particulate matter are linked to ill-health. It does however seem to reduce the significance of effect. As the Health Effects Institute notes, the moral of this tale is that it is dangerous to rely on a single approach or software package. 2
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otherwise have occurred is it appropriate to attribute the cost to air pollution. But by relying on studies that yield information only about the short-run effects of air pollution researchers have often implicitly assumed that all hospital admissions are additional. Whilst there is now a much clearer realisation of the fact that the deaths identified by studies focussing on the short term might have been advanced by only a few weeks or months, the fact that potentially the same problem applies to hospital admissions, work loss days and surgery attendances and a range of other health impacts is perhaps less widely appreciated. Recognising the importance of this point a number of researchers [32,33,39] have sought to provide what they refer to as ‘harvesting resistant’ estimates of the health effects of air pollution. Taking the last of these as an example, the approach involves analysing the relationship between 15 day moving averages of air pollution and mortality counts and hospital admissions. The paper’s author Schwartz argues that if air pollution involves only short-term harvesting of less than 15 days then no relationship should be present. In fact, statistically significant relationships are observed even when 60 day moving averages are present which appears to reject the hypothesis of short-term harvesting. The limitation of this approach is that it is capable of estimating only the interim rather than the long-run impact of air pollution. Adopting an alternative approach Zanobetti et al. [38] uses polynomial lags to explore the short-term mortality displacement issue. Although the authors find no evidence of short-term harvesting the method of polynomial lags suffers from the defect that it is necessary to specify a finite endpoint prior to estimation. Simply assuming a maximum lag length is hazardous; the technique will generally distribute the effects of over the entire lag whether this is appropriate or not. And critically the technique has extreme difficulty in capturing any long-tailed distribution of a type that might be expected in epidemiological time-series studies. These features make the polynomial lags technique unsuitable for use in epidemiological time-series studies. Partly because of these shortcomings the polynomial technique has seen relatively few recent applications in the field of econometrics either. And once again the technique is capable of estimating only the interim rather than the long-run impact of air pollution. A more realistic regression model would seek to approximate the infinite distributed lag effects of air pollution on hospital admissions. Summing these lag coefficients would then provide an estimate of the long-run impact of air pollution on hospital admissions net of any cases brought forward. It is even possible that such a strategy might reveal that the health impacts of air pollution are larger than suggested by models that focus on the short-run effect if there is a long time lag between exposure to air pollution and admission to hospital. A second problem arises in that the existing literature is also largely characterised by regression models including one or at most two air pollutants. Given the correlation between different air pollutants, single-pollutant models risk explaining what are essentially the same adverse health events several times over. A strategy of relying on single-pollutant models also frustrates any attempt to determine which air pollutants are responsible for the empirically observed health impacts. Neither the fact that some pollutants may not themselves be harmful to human health but serve as markers for other pollutants, nor the fact that ambient concentrations recorded by monitors may be a poor representation of individuals’ exposure, nor the fact that some air pollutants are precursors of others obviously justifies the almost complete reliance on single-pollutant models. The only way of dealing with the problem of multicollinearity between different air pollutants is to combine the results obtained from different
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sites using meta-analytical techniques.3 For an example of a study adopting a multiple-pollutant approach see [9]. The use of single-pollutant models has nevertheless been defended in the literature. One of the most eminent epidemiologists Schwartz has for example remarked: ‘‘One occasionally sees studies that have fitted regression models using four or even more collinear pollutants in the same regressiony Given the non-trivial correlation of the pollutant variables and the relatively low explanatory power of air pollution for mortality or hospital admissions such procedures risk letting the noise in the data choose the pollutant’’.4 Even if impacts cannot be reliably attributed to particular pollutants, given that most air pollution emanates from the same set of sources it would still be interesting to know the health effects of a simultaneous reduction in all forms of air pollution. The purpose of this paper is to present an alternative approach to modelling air pollution doseresponse relationships. The approach uses a statistical technique familiar to economists and is intended to address some of the deficiencies of the existing studies that make their results difficult to interpret from a policy perspective. Whilst this approach could be used to analyse a variety of health endpoints such as mortality counts and surgery attendances here it is demonstrated in the context of a study linking air pollution and cause-specific hospital admissions in London.5 Using an ARMAX modelling approach the paper estimates the infinite lag effects of air pollution on hospital admissions enabling it to distinguish the short-run effects of air pollution from the more relevant long-run effects. This distinction is shown to be empirically important for one major category of hospital admissions regularly linked to air pollution in the epidemiological literature. These results are shown to hold irrespective of whether one includes only particulate matter in the regression or whether one includes only those pollutants remaining after a process of stepwise elimination. The same results also obtain in a multiple pollutant model containing six different air pollutants and two rival measures of particulates. The remainder of the paper describes the empirical implementation of the technique. Section 2 discusses the data used to estimate the model along with the econometric methods involved. Section 3 analyses the data and compares the results obtained with those from the only other proposed method for producing harvesting resistant estimates of air pollution. Section 4 concludes with ideas for further applications of the technique.
2. Empirical analysis Daily counts of hospital admissions were taken from Greater London from the start of 1992 to the end of 1994, a period of some 1096 days. Hospital admissions are classified by cause and these include the broad categories of respiratory disease (RES) and cardiovascular disease (CARD). Maximum temperatures (TMAX), minimum temperatures (TMIN) and relative humidity 3
It may be that the main explanation for the prevalence of single-pollutant models is the difficulty of publishing a paper in which none of the pollutant variables are individually significant because they are multi-collinear. 4 This quote is taken from Schwartz et al. [35, p. 9]. 5 The effect of air pollution on life expectancy can also be examined within the context of a prospective cohort study e.g. [29]. This approach is advantageous in that it also accounts for the chronic mortality impacts of air pollution. Unfortunately, the data requirements of such studies are onerous and there are correspondingly very few of them.
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Table 1 Descriptive statistics Variables (units)
Mean
Std. dev.
Minimum
Maximum
RES CARD HOL SCHOOL TMAX (1C) TMIN (1C) HUMID (%) BS (mg/m3) NO2 (mg/m3) SO2 (ppb) O3 (ppb) CO (mg/m3) PM10 (mg/m3)
150.85 172.43 0.02 0.23 14.9 8.8 70.58 13.06 33.63 8.77 17.24 1.28 28.84
43.67 32.81 0.14 0.42 5.62 4.69 10.85 8.45 10.64 4.53 11.49 0.78 14.24
66 72 0 0 2.0 4.6 41.00 1.70 12.40 2.30 0.45 0.40 6.80
318 259 1 1 31.7 21.5 97.00 72.90 133.70 42.00 79.90 7.90 131.97
(HUMID) were from Holborn in Central London. Measures of 24-h averages for Black Smoke (BS) and SO2 in were taken from 5 sites. Measures of 24-h averages for NO2 and 8-h averages for CO were taken from three sites whilst measures of 8-h averages for O3 were taken from two sites. A measure of 24-h average PM10 was obtained from only one site in Central London. Despite the relatively large geographic area the records taken from different pollution monitors were all highly correlated with one another. For all pollutants a single index was formed taking the mean of all non-missing observations. Missing observations were interpolated using zero-order regression methods. Six dummy variables (MON, TUE, WED, etc.) were included for day of the week effects. The variable HOL accounts for statutory holidays whereas the variable SCHOOL accounts for school holidays. The data are described in Tables 1 and 2. Note that whilst it is customary to provide a simple correlation matrix for the pollution variables simple correlation matrices tend to understate the extent to which the pollution variables are as a group multicollinear with one another. Note that these data have already been analysed by Atkinson et al. [4] using techniques typical of those encountered in the epidemiological literature.6 The time-series properties of the log RES and log CARD have been investigated using two alternative test procedures. The Phillips–Perron test [27] is used to test the null hypothesis that there exists a unit root present in the data. The Kwiatkowski–Phillips–Schmidt–Shin test [18] by contrast tests the null hypothesis of stationarity. Both tests assume the presence of a time trend. For either category of hospital admission the Phillips–Perron tests are able to reject the null hypothesis of a unit root.7 The Kwiatkowski–Phillips–Schmidt–Shin tests on the other hand
6
I am grateful to Ross Anderson and Richard Atkinson for providing me with this data. The Phillips–Perron test statistics ZðrÞ were 225.09 and 631.40 for the Log RES and Log CARD variables respectively with a one percent critical value of 29.50. The ZðtÞ test statistics were 11.48 and 25.01 with a one percent critical value of 3.96. 7
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Table 2 The pollutant correlation matrix
BS SO2 NO2 O3 CO PM10
BS
SO2
NO2
O3
CO
PM10
1.00 0.67 0.55 0.39 0.79 0.59
1.00 0.67 0.10 0.64 0.74
1.00 0.18 0.50 0.72
1.00 0.40 0.00
1.00 0.48
1.00
cannot reject the null hypothesis of stationarity.8 It was therefore deemed unnecessary to firstdifference these variables prior to analysing them. Traditional analyses of mortality counts and hospital-admissions usually remove autonomous and seasonal trends before subjecting the data to regression analysis. Frequently they use the locally weighted least squares smoothing (LOWESS) technique developed by Cleveland [6] for this purpose.9 In this analysis the effects of autonomous trends, epidemics and seasonal effects are accounted for by including high-order Chebyshev time polynomials among the explanatory variables (e.g. see [12]). Where n is the number of time periods and t is time, a Chebyshev time polynomial of order k is defined by: pffiffiffi 2 cos½kpðt 0:5Þ=n: CHEBYSHEVkt ¼ The degree of control afforded by Chebyshev time polynomials of up to and including order 20 is virtually identical to that obtained using the LOWESS technique with the bandwidth set at 120 days, the value most often chosen in other epidemiological studies. The regression equation presented below uses the ARMAX modelling technique to approximate an infinite distributed-lag on meteorological variables, pollution variables, statutory holidays and school holidays in the presence of serial correlation. It is the ability of the ARMAX modelling technique to approximate infinite distributed lags that makes the use of this technique advantageous in this context. For a comprehensive discussion of the ARMAX model see [11]. Note that L is the lag operator and that the maximum lag length for the dependent and independent variables is sufficient to capture quite complicated lag patterns. Longer lag lengths were investigated but resulted in convergence problems indicating perhaps the redundancy of introducing additional parameters in to the regression model. It is assumed that the error term e is normally distributed and estimates of the parameters y12 ; a; d120 ; b139 and g12 are obtained using maximum likelihood procedures.10 The model for cardiovascular admissions is of course 8
The Kwiatowski–Phillips–Schmidt–Shin test statistics were 0.138 and 0.139 for the Log RES and Log CARD variables, respectively, with a five percent critical value of 0.146. 9 There are many different ways of controlling for seasonal effects, autonomous trends and epidemics. Some researchers prefer to regress daily mortality on sine and cosine terms of differing frequencies. Others use a monthly dummy variable approach that in effect fits a histogram to the data. Yet more use non-linear splines. 10 In many empirical analyses the number of deaths or hospital admissions is assumed distributed as a Poisson variable. In this analysis the daily number of hospital admissions is typically so large and there is probably no discernible difference in the results from modeling hospital admissions as a lognormal variable.
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analogous. ð1 þ y1 L þ y2 L2 Þ logðRESÞ ¼ a þ
k¼20 X
dk CHEBYSHEVkt þ ðb1 þ b2 L þ b3 L2 ÞTMAXt
k¼1 2
þ ðb4 þ b5 L þ b6 L ÞTMINt þ ðb7 þ b8 L þ b9 L2 ÞHUMIDt þ ðb10 þ b11 L þ b12 L2 ÞBSt þ ðb13 þ b14 L þ b15 L2 ÞNO2t þ ðb16 þ b17 L þ b18 L2 ÞSO2t þ ðb19 þ b20 L þ b21 L2 ÞO3t þ ðb22 þ b23 L þ b24 L2 ÞCOt þ ðb25 þ b26 L þ b27 L2 ÞPM10t þ ðb28 þ b29 L þ b30 L2 ÞHOLt þ ðb31 þ b32 L þ b33 L2 ÞSCHOOLt þ b34 MONt þ b35 TUEt þ b36 WEDt þ b37 THUt þ b38 FRIt þ b39 SATt þ ð1 þ g1 L þ g2 L2 Þet : If the coefficients on same day and lagged pollutant concentrations are statistically significant this indicates that at least one pollutant has short-term effects. If these coefficients sum to zero however it indicates that the long-run impact is zero and hence that hospital admissions are simply reallocated through time rather than additional.11 If the lagged values of hospital admissions are statistically significant this points to the presence of infinite lag effects. Note that the model represents the most general of several considered. Given the aforementioned disagreement concerning the merits of single-pollutant models versus multiplepollutant models a number of simpler alternatives were also considered. These include a model in which only PM10 is included on the grounds that it is the pollutant that has most often been linked to adverse health outcomes, as well as a model in which the least significant pollutants are removed using stepwise regression. This process might result in a model in which one or more pollutants are present.12 Note also that the use of maximum and minimum temperature appears preferable to using mean temperature and its squared value. Other researchers have used non-linear splines for meteorological variables although such an approach is not taken here.
3. Results Turning to the results, in the model of respiratory admissions the stepwise elimination procedure selects a model containing only SO2 whilst in the model explaining cardiovascular admissions the procedure selects a model containing only BS. In either case the resulting singlepollutant model cannot be rejected against a more general model including all pollutants. The fact that in neither case is PM10 the single most important pollutant might be because it is measured at only one site compared to the five sites that measure BS and SO2. On the other hand, Moolgavkar
11
The long-run impact of BS on the logarithm of hospital admissions is given by ðb10 þ b11 þ b12 Þ=ð1 þ y1 þ y2 Þ: The formula is analogous for other pollutants. 12 It seems appropriate here to remind the reader about the risks of using stepwise regression for the purposes of model selection given the sequential test procedures employed by the technique.
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Table 3 The regression model for respiratory hospital admissions Variable
Dependent variable ¼ Log (RES)t Log (RES)t1 Log (RES)t2 TMAXt TMAXt1 TMAXt2 TMINt TMINt1 TMINt2 HUMIDt HUMIDt1 HUMIDt2 BSt BSt1 BSt2 NO2t NO2t1 NO2t2 SO2t SO2t1 SO2t2 O3t O3t1 O3t2 PM10t PM10t1
Model A—all pollutants coefficient (t-statistic)
0.0903 (3.92) 0.850 (39.07) 0.00153 (0.96) 0.00262 (1.61) 0.000884 (0.47) 0.0107 (4.76) 0.000148 (0.09) 0.00858 (4.69) 0.000236 (0.61) 0.000215 (0.75) 0.000127 (0.31) 0.0000628 (0.07) 0.00136 (2.13) 0.000438 (0.50) 0.000117 (0.17) 0.000443 (0.95) 0.000617 (0.93) 0.000486 (0.37) 0.000928 (1.10) 0.000414 (0.34) 0.0000601 (0.11) 0.000510 (1.32) 0.000127 (0.25) 0.000256 (0.53) 0.000798 (2.61)
Model B—PM10 only coefficient (t-statistic)
0.0631 (2.17) 0.835 (29.27) 0.000891 (0.57) 0.00451 (2.98) 0.000382 (0.22) 0.0109 (5.05) 0.000388 (0.24) 0.00935 (5.21) 0.000251 (0.73) 0.000376 (1.36) 0.0000573 (0.15)
Model C—SO2 only coefficient (t-statistic)
0.0625 (2.79) 0.840 (38.48) 0.00124 (0.82) 0.00372 (2.42) 0.000292 (0.17) 0.0115 (5.28) 0.000557 (0.35) 0.00936 (5.32) 0.000339 (0.99) 0.000261 (1.01) 0.000156 (0.42)
0.0000286 (0.03) 0.00296 (5.18) 0.000852 (0.97)
0.000142 (0.46) 0.000877 4.13
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Table 3. (continued ) Variable
PM10t2 COt COt1 COt2 Moving average terms et1 et2 Number of observations Loglikelihood
Model A—all pollutants coefficient (t-statistic) 0.000116 (0.24) 0.00644 (0.73) 0.000836 (0.13) 0.000119 (0.15) 0.343 (7.08) 0.656 (13.52) 1094 926.99
Model B—PM10 only coefficient (t-statistic)
Model C—SO2 only coefficient (t-statistic)
0.000326 (1.04)
0.297 (5.78) 0.629 (12.94) 1094 915.63
0.305 (6.66) 0.636 (14.27) 1094 917.52
Note that the t-statistics are heteroscedasticity consistent. Chebyshev time polynomials of up to and including order 20 are included but the coefficients are not displayed. The variables HOL, SCHOOL and their lags, as well as the dummy variables MON through SAT, are likewise included but their coefficients not shown.
[21] also finds that many air pollutants provides an index of air pollution at least as good as PM10 does in the context of hospital admissions. In Tables 3 and 4 these specifications are presented alongside models containing only PM10 as well as models in which all air pollutants are simultaneously included. It is apparent that once autonomous trends, seasonality and epidemics have been accounted for daily variations in hospital admissions are governed mainly by day of the week effects and to a lesser extent, by meteorological variables. Very few of the pollution variables are individually significant in the multiple-pollutant model which is not surprising given the high degree of multicollinearity. In the single-pollutant models, however, the pollution variables are often highly significant. As a group the lagged values of the dependent variable are also highly significant pointing to the presence of infinite lag effects. The statistical significance of the pollution variables is explored further in Table 5. As in earlier reviews of studies reported in the epidemiological literature such as [2-4,19], in the short term there appears to be a highly significant association between air pollution and both respiratory and cardiovascular hospital admissions. This association remains whether one or many pollutants are included in the regression model. Table 5 also examines the effect of imposing the restriction that the long-run effect of each pollutant included in the model is simultaneously zero.13 This restriction is rejected at the 1 percent level of confidence for respiratory admissions regardless of whether the model contains all 13
The hypothesis that the long run impact of BS on hospital admissions is zero is equivalent to testing:
b10 þ b11 þ b12 ¼ 0: The test is analogous for the other pollutants.
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Table 4 The regression model for cardiovascular hospital admissions Variable
Dependent variable ¼ Log (CARD)t Log (CARD)t1 Log (CARD)t2 TMAXt TMAXt1 TMAXt2 TMINt TMINt1 TMINt2 HUMIDt HUMIDt1 HUMIDt2 BSt BSt1 BSt2 NO2t NO2t1 NO2t2 SO2t SO2t1 SO2t2 O3t O3t1 O3t2 PM10t PM10t1
Model A—all pollutants coefficient (t-statistic)
1.123 (1.07) 0.240 (0.28) 0.00303 (2.06) 0.00270 (0.62) 0.000616 (0.18) 0.00124 (0.66) 0.00280 (0.63) 0.000696 (0.12) 0.0000689 (0.20) 0.000589 (1.16) 0.000391 (0.74) 0.000893 (1.18) 0.00107 (0.89) 0.0000684 (0.08) 0.000699 (1.21) 0.000301 (0.25) 0.000352 (0.40) 0.000575 (0.54) 0.00123 (0.55) 0.00145 (1.40) 0.000695 (1.54) 0.000849 (0.47) 0.000231 (0.14) 0.000363 (1.01) 0.000826 (1.13)
Model B—PM10 only coefficient (t- statistic)
1.195 (3.09) 0.306 (1.00) 0.00242 (1.79) 0.00294 (1.17) 0.00133 (0.75) 0.000326 (0.19) 0.00151 (0.58) 0.000933 (0.38) 0.000403 (1.35) 0.0000902 (0.18) 0.000213 (0.72)
0.000662 (2.84) 0.00105 (2.44)
Model C—BS only coefficient (t- statistic)
1.115 (1.72) 0.233 (0.44) 0.00249 (1.87) 0.00264 (0.96) 0.00131 (0.71) 0.000579 (0.34) 0.00205 (0.75) 0.00117 (0.36) 0.000303 (1.02) 0.000363 (0.71) 0.000326 (1.07) 0.00151 (3.44) 0.00212 (2.50) 0.000700 (1.16)
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Table 4. (continued ) Variable
PM10t2 COt COt1 COt2 Moving average terms et1 et2 Number of observations Loglikelihood
Model A—all pollutants coefficient (t-statistic) 0.000539 (1.04) 0.00818 (0.87) 0.0104 (0.88) 0.00334 (0.51) 1.039 (1.02) 0.203 (0.28) 1094 1161.11
Model B—PM10 only coefficient (t- statistic)
Model C—BS only coefficient (t- statistic)
0.000494 (1.98)
1.104 (2.98) 0.260 (1.07) 1094 1151.08
1.023 (1.63) 0.190 (0.44) 1094 1153.81
Note that the t-statistics are heteroscedasticity consistent. Chebyshev time polynomials of up to and including order 20 are included but the coefficients are not displayed. The variables HOL, SCHOOL and their lags, as well as the dummy variables MON through SAT, are likewise included but their coefficients not shown.
pollutants, only PM10, or only SO2 as the single most important pollutant. For cardiovascular admissions, however, this restriction cannot be rejected, not even at the 10 percent level of confidence. This result is also unaffected by whether the model includes all pollutants, only PM10 or only BS as the single most important air pollutant. The evidence is therefore consistent with the suggestion that cardiovascular admissions are only reallocated through time by air pollution and that a reduction in air pollution would in the long-run only lead to a significant change in the number of respiratory admissions. This is the key result of the paper. Estimates of the long-run elasticity of hospital admissions with respect to air pollution are presented in Table 6.14 The t-statistics presented in this table are heteroscedasticity consistent and obtained using the delta method. In the introduction it was argued that these are the results most relevant to policy and expressing them in terms of elasticities makes it easier to compare the findings for different pollutants. Note that these elasticities vary with pollution concentrations and are all evaluated at sample means. If one takes PM10 on its own as a metric of air pollution then a 1 percent reduction in current concentrations leads to a 0.17 percent reduction in respiratory admissions in London. If on the other hand SO2 is taken as a metric of air pollution then it appears that a 1 percent reduction in air pollution concentrations might reduce admissions by 0.15 percent. Turning to the multiplepollutant model it is remarkable that, even in a model containing no less than six pollutants and their lagged values, the long-run elasticity of respiratory hospital admissions with respect to PM10 14
The hypothesis that the long-run elasticity of hospital admissions with respect to the level of BS is zero is equivalent to testing: ½ðb10 þ b11 þ b12 Þ=1 þ y1 þ y2 BS ¼ 0: The test is analogous for other pollutants.
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Table 5 Testing the short- and long-run effects of air pollution on hospital admissions
Only PM10 included
Short run effects of air pollution
Long run effects of air pollution
Respiratory admissions
Cardiovascular admissions
Respiratory admissions
Cardiovascular admissions
w2 ð3Þ ¼ 23:72 ðp ¼ 0:000Þ
w2 ð3Þ ¼ 8:84 ðp ¼ 0:032Þ w2 ð3Þ ¼ 12:33 ðp ¼ 0:006Þ
w2 ð1Þ ¼ 21:45 ðp ¼ 0:000Þ
w2 ð1Þ ¼ 1:65 ðp ¼ 0:199Þ w2 ð1Þ ¼ 0:18 ðp ¼ 0:670Þ
Only BS included Only SO2 included All pollutants included
w2 ð3Þ ¼ 27:11 ðp ¼ 0:000Þ w2 ð18Þ ¼ 54:91 ðp ¼ 0:000Þ
w2ð1Þ ¼ 17:30 ðp ¼ 0:000Þ w2 ð6Þ ¼ 25:44 ðp ¼ 0:000Þ
w2 ð18Þ ¼ 33:66 ðp ¼ 0:014Þ
w2 ð6Þ ¼ 1:94 ðp ¼ 0:925Þ
Table 6 The long-run elasticity of hospital admissions with respect to air pollution (t-statistics are in parentheses) Pollutant
PM10 BS NO2 SO2 CO O3 All pollutants
Respiratory admissions Model A— all pollutants
Model B— PM10 only
0.140 (2.10) 0.094 (1.48) 0.165 (1.52) 0.050 (0.53) 0.024 (0.37) 0.032 (0.62) 0.205 (2.36)
0.170 (4.59)
Cardiovascular admissions Model C— SO2 only
Model A— all pollutants
Model B— PM10 only 0.028 (1.47)
0.151 (3.98)
0.019 (0.37) 0.027 (0.56) 0.013 (0.20) 0.027 (0.84) 0.012 (0.32) 0.011 (0.28) 0.007 (0.10)
Model C— BS only
0.010 (0.53)
is still statistically significant at the 5 percent level. It appears that, holding all other pollutant concentrations constant, a 1 percent reduction in PM10 concentrations might reduce hospital admissions by 0.14 percent. The elasticity of respiratory admissions with respect to air pollution in general is obtained by summing the individual elasticities obtained from the multiple-pollutant model. This measure is also significantly different from zero and suggests that a 1 percent reduction in air pollution might cut respiratory hospital admissions by 0.20 percent. It is also quite clear that in order to avoid double counting, the respiratory admissions identified by the singlepollutant models should not be added together. Expressing the results for the effects of PM10 taken from the multiple-pollutant model on respiratory admissions in terms of a relative risk ratio of 1.62 per 100 mg/m3 it is apparent that the
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effect of PM10 is far more pronounced than suggested by the review of existing studies conducted by Atkinson et al. [3] in which point estimates of the relative risk ratio vary from 1.10 to 1.24 per 100 mg/m3. This could indicate that air pollution continues to have a significant effect on daily respiratory hospital admissions beyond the 1- or 2- day time frame normally considered by conventional studies. However, bear in mind, the estimate presented in this study is not very precisely determined. Turning to the model of cardiovascular admissions consistent with the results shown in Table 5 none of the long-run elasticities are statistically significant. It is difficult to compare these results with those from Schwartz [33], the only other attempt to estimate the long-run effect of air pollution on hospital admissions. Firstly, that paper analyses hospital admissions for heart disease, chronic obstructive pulmonary disease and pneumonia rather than the more general categories of respiratory and cardiovascular admissions dealt with here. Secondly, the paper uses only PM10 as a measure of air pollution. Nonetheless, there are some similarities in that the impact of air pollution on chronic obstructive pulmonary disease admissions becomes more rather than less apparent as the time frame of analysis is extended. And although the author finds that the health impacts of air pollution on heart disease admissions are not diminished even up to a period of 60 days this is not necessarily inconsistent with the inability of this paper to reject the hypothesis that cardiovascular admissions are in the long-run all advanced. Whilst it is possible to use the results of the multiple-pollutant study to determine the number of hospital admissions in London attributable to particular forms of air pollution, the results of any single study are generally too uncertain to base benefit estimates on. In this respect anyway this study is no different from the rest.15 Benefit estimates are better based on meta-analysis. But such meta-analyses should be careful to include only long-run estimates from multiple-pollutant studies such as this one. Given the number of hospital admissions presented in Table 1 and the long-run elasticities in Table 6 the reader can easily calculate point estimates of the number of hospital admissions attributable to air pollution in London. For example, judging by the multiplepollutant model a 1 percent reduction in PM10 would avoid altogether 77 respiratory hospital admissions annually in London although a wide confidence interval is attached to this point estimate. It furthermore appears that current ambient concentrations of PM10 might be responsible for 13 percent of respiratory hospital admissions in London. The purely financial costs to a National Health Service hospital of an average emergency respiratory admission were recently estimated to be £1400 in 1996/7 prices [8]. One can only speculate on how these findings would alter published benefit estimates since this paper contains but a single study considering only two health endpoints. Clearly, there is a need for further studies employing techniques capable of distinguishing between the long- and shortrun impacts, and perhaps a reanalysis of the existing data. But until such studies are undertaken and their results subjected to meta-analysis it might be prudent to avoid including reduced cardiovascular hospital admissions as a benefit of improved air quality. Analysts should also continue to resist the temptation to sum reductions in hospital admissions suggested by singlepollutant studies. 15
Obviously, the impressive t-statistics for the single pollutant PM10 and SO2 models presented in Table 8 provide a misleading sense of the uncertainty surrounding the impacts of these two pollutants based as they are on prior assumption and sequential hypothesis testing.
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4. Conclusions This paper has noted that much if not all of the existing epidemiological literature deals exclusively with the very short-term impacts of air pollution on hospital admissions. At the same time reliance on single-pollutant models means that it is unclear whether the health impacts associated with different pollutants are additive or not. Both of these shortcomings have severe implications for the task of estimating the cost of air pollution. Noting the deficiencies of alternative techniques, this paper has used the ARMAX modelling strategy to approximate the entire distributed lag impact of changes in the level of air pollution on hospital admissions. Irrespective of whether one or many pollutants are included in the regression model it is seen that in the long-run air pollution in London results in a significant change in the number of hospital admissions from respiratory disease. Increase in admissions from cardiovascular disease on the other hand appear to be borrowed from future time periods and consequently their cost should not be attributed to air pollution. Although this paper has dealt exclusively with hospital admissions it would be interesting to apply the same methodology to counts of other adverse health events linked to air pollution by studies focussing on the very short term. There must be room for doubt about whether some of these events might not have occurred anyway.
Acknowledgments The author thanks the journal editor and two anonymous referees for their constructive comments. Any remaining errors are the responsibility of the author.
References [1] A. Alberini, A. Krupnick, Air quality and episodes of acute respiratory illness in Taiwan cities: evidence from survey data, J. Urban Econ. 44 (1998) 68–92. [2] H. Anderson, R. Atkinson, Association between ambient particles and daily admissions for cardiovascular diseases systematic review, Report to the Department of Health, Department of Public Health Sciences, St. Georges Hospital Medical School, London, 2001. [3] R. Atkinson, H. Anderson, J. Sunyer, J. Ayres, M. Baccini, J. Vonk, A. Boumghar, F. Forastiere, B. Forsberg, G. Touloumi, J. Schwartz, K. Koutsouyanni, Acute effects of particulate air pollution on respiratory admissions, Amer. J. Respir. Crit. Care Med. 164 (2001) 1860–1866. [4] R. Atkinson, S. Bremner, R. Anderson, D. Strachan, J. Bland, A. Ponce de Leon, Short-term associations between emergency hospital admissions for respiratory and cardiovascular disease and outdoor air pollution in London, Arch. Environ. Health 54 (1999) 398–411. [5] R. Burnett, R. Dales, D. Krewski, R. Vincent, T. Dann, J. Brook, Associations between ambient particulate sulfate and admissions to Ontario hospitals for cardiac and respiratory diseases, Amer. J. Epidemiol. 142 (1995) 23–35. [6] W. Cleveland, Robust locally weighted regression and smoothing scatterplots, J. Amer. Stat. Assoc. 74 (1979) 829–836. [7] M. Cropper, N. Simon, A. Alberini, S. Arora, P. Sharma, The health benefits of air pollution control in Delhi, Amer. J. Agr. Econ. 79 (1997) 1625–1629.
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[8] Department of Health, Economic Appraisal of the Health Effects of Air Pollution, The Stationery Office, London, 1999. [9] G. Eskeland, Air pollution requires multipollutant analysis: the case of Santiago Chile, Amer. J. Agr. Econ. 79 (1997) 1636–1641. [10] European Commission, ExternE: Externalities of Energy, Vols. 16, Office for Official Publications of the European Community, Luxembourg, 1995. [11] J. Hamilton, Time Series Analysis, Princeton University Press, Princeton, NJ, 1994. [12] R. Hamming, Numerical Methods for Scientists and Engineers, McGraw-Hill, New York, 1973. [13] A. Hansen, H. Selte, Air pollution and sick leaves: a case study using air pollution data from Oslo, Environ. Resour. Econ. 16 (2000) 31–50. [14] Health Effects Institute, Revised Analyses of Time-series Studies of Air Pollution and Health, Health Effects Institute, Boston, MA, 2003. [15] K. Katsouyanni, J. Schwartz, C. Spix, G. Touloumi, D. Zmirou, A. Zanobetti, B. Wojtyniak, J. Vonk, A. Tobias, A. Ponka, S. Medina, L. Bacharova, H. Anderson, Short term effects of air pollution on health. A European approach using epidemiologic time series data: the APHEA protocol, J. Epidemiol. Community Health 50 (1996) 12–18. [16] A. Krupnick, D. Burtraw, The social costs of electricity. Do the numbers add up?, Resour. Energy Econ. 18 (1996) 423–466. [17] A. Krupnick, W. Harrington, B. Ostro, Ambient ozone and acute health effects: evidence from daily data, J. Environ. Econ. M. 18 (1990) 1–18. [18] D. Kwiatkowski, P. Phillips, P. Schmidt, Y. Shin, Testing the null hypothesis of stationarity against the alternative of a unit root, J. Econometrics 54 (1992) 159–178. [19] A. Le Tertre, S. Medina, E. Samoli, B. Forsberg, P. Michelozzi, A. Boumghar, J. Vonk, A. Bellini, R. Atkinson, J. Ayres, J. Sunyer, J. Schwartz, K. Katsouyanni, Short-term effects of particular air pollution on cardiovascular diseases in eight European cities, J. Epidemiol. Community Health 56 (2002) 773–779. [20] A. McMichael, H. Anderson, B. Brunekreef, A. Cohen, Inappropriate use of daily mortality analyses to estimate longer-term mortality effects of air pollution, Int. J. Epidemiol. 27 (1998) 450–453. [21] S. Moolgavkar, Air pollution and hospital admission for diseases of the circulatory system in three US metropolitan areas, J. Air Waste Manage. 50 (2000) 1199–1206. [22] X. Olsthoorn, M. Amann, A. Bartonova, J. Clench-Aas, J. Cofala, K. Dorland, C. Guerriero, J. Henriksen, H. Jansen, S. Larssen, Cost benefit analysis of European air quality targets for sulphur dioxide, nitrogen dioxide and fine and suspended particulate matter in cities, Environ. Resour. Econ. 14 (1999) 333–351. [23] B. Ostro, R. Broadwin, M. Lipsett, Coarse and fine particles and daily mortality in the Coachella valley, California: a follow-up study, J. Expo. Anal. Environ. Epidemiol. 10 (2000) 412–419. [24] B. Ostro, L. Chestnut, Assessing the health benefits of reducing particulate matter air pollution in the United States, Environ. Res. 76 (1998) 94–106. [25] B. Ostro, L. Chestnut, N. Vichit-Vadakan, A. Laixuthai, The impact of particulate matter on daily mortality in Bangkok, Thailand, J. Air Waste Manage. 49 (1999) 100–107. [26] B. Ostro, J. Sanchez, C. Aranda, G. Eskeland, Air pollution and mortality: results from a study of Santiago, Chile, J. Expo. Anal. Environ. Epidemiol. 6 (1996) 97–114. [27] P. Phillips, P. Perron, Testing for a unit root in time series regression, Biometrika 75 (1988) 335–346. [28] C. Pope, Respiratory hospital admissions associated with PM10 pollution in Utah, Salt Lake, and Cache valleys, Arch. Environ. Health 46 (1991) 90–97. [29] C. Pope, M. Thun, M. Namboodiri, D. Dockery, J. Evans, F. Speizer, C. Heath, Particulate air pollution as a predictor of mortality in a prospective study of US adults, Amer. J. Resp. Crit. Care Med. 151 (1995) 669–674. [30] R. Rowe, C. Lang, L. Chestnut, D. Latimer, D. Rae, D. Bernow, D. White, New York State Environmental Externalities Cost Study, Empire State Electricity Energy Research Corporation, Oceana Publications, New York, 1995. [31] J. Schwartz, Total suspended particulate matter and daily mortality in Cincinnati, Ohio, Environ. Health Perspect. 102 (1994) 186–189. [32] J. Schwartz, Harvesting and long term exposure effects in the relationship between air pollution and mortality, Amer. J. Epidemiol. 151 (2000) 440–448.
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[33] J. Schwartz, Is there harvesting in the association of airborne particles with daily deaths and hospital admissions?, Epidemiology 12 (2001) 55–61. [34] J. Schwartz, D. Dockery, Increased mortality in Philadelphia associated with daily air pollution concentration, Amer. Rev. Respir. Dis. 145 (1992) 600–604. [35] J. Schwartz, C. Spix, G. Touloumi, L. Bacharova, T. Barumamdzadeh, A. Le Tertre, A. Piekarski, A. Ponce De Leon, A. Ponka, G. Rossi, M. Saez, J. Schouten, Methodological issues in studies of air pollution and daily counts of deaths or hospital admissions, J. Epidemiol. Community Health 50 (1996) 3–11. [36] K. Small, C. Kazimi, On the costs of air pollution from motor vehicles, J. Transp. Econ. Policy 29 (1995) 7–32. [37] G. Thurston, P. Kinney, K. Ito, M. Lippmann, A multi-year study of air pollution and respiratory hospital admissions in three New York state metropolitan areas: results for 1988 and 1989 summers, J. Expo. Anal. Environ. Epidemiol. 2 (1992) 429–450. [38] A. Zanobetti, J. Schwartz, E. Samoli, A. Gryparis, G. Touloumi, R. Atkinson, A. Le Tertre, J. Bobros, M. Celko, A. Goren, N. Forsberg, P. Michelozzi, D. Rabczenko, E. Ruiz, K. Katsouyanni, The temporal pattern of mortality responses to air pollution, Epidemiology 13 (2002) 87–93. [39] S. Zeger, F. Dominici, J. Samet, Harvesting-resistant estimates of air pollution effects on mortality, Epidemiology 10 (1999) 171–176.
Journal of Environmental Economics and Management 49 (2005) 116–131 www.elsevier.com/locate/jeem
Air pollution and hospital admissions an ARMAX modelling approach David Maddison Institute of Economics, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark Received 17 June 2003; received in revised form 9 February 2004 Available online 19 June 2004
Abstract Using daily data this paper analyses the time-series relationship between hospital admissions and air pollution in London. In doing so it addresses an important issue not dealt with in the existing empirical literature: Are hospital admissions truly additional or merely advanced by air pollution? If it could be shown that the hospital admissions are only advanced by air pollution rather than additional then it would be incorrect to attribute the cost to air pollution. The evidence presented indicates that a 1 percent reduction in the currently prevailing levels of PM10 in London would in the long-run result in a statistically significant 0.14 percent reduction in the number of respiratory hospital admissions. By contrast one cannot reject the hypothesis that cardiovascular hospital admissions are simply brought forward and accordingly their cost should not be attributed to air pollution. r 2004 Elsevier Inc. All rights reserved. Keywords: Cost–benefit analysis; Air pollution; Hospital admissions
1. Introduction A significant number of dose response functions estimated on time-series data have identified particulate matter and other air pollutants too as being statistically related to a range of ill-health Tel.: +45-6550-3270; fax: +45-6615-8790
E-mail address: [email protected] (D. Maddison). 0095-0696/$ - see front matter r 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jeem.2004.04.001
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effects. For examples of such studies published by economists see [7,9,23,25,26] for mortality; [28] for hospital admissions; [1,17] for acute respiratory symptoms and [13] for work loss days. Many more such studies have been published in the epidemiological literature although recently the statistical software used by a significant number of these studies has been shown to contain a programming error as well as an inappropriately lax default criterion for declaring convergence [14].1,2 Amongst other things these studies have been widely used to value the external costs of power generation facilities, where typically the health effects of air pollution dominate. The procedure involves using atmospheric dispersion models to calculate the change in ambient concentrations of air pollution associated with an additional kilowatt-hour of electricity. Dose–response functions are then used to predict the changed incidence of ill-health amongst the population. In the final step economic values are attached to these health impacts. Good examples of such studies include [10,30]. Krupnick and Burtraw [16] provide an excellent review of these and other studies complete with discussion about the treatment afforded to the effect of air pollution on health. Ostro and Chestnut [24] have also used these studies for the purposes of quantifying the health benefits of attaining national standards for particulate matter in the United States whilst Olsthoorn et al. [22] conducted a similar analysis for the European Union. For an example of a study using dose–response studies to determine the external costs of road transport see [36]. But despite the fact that these time-series studies of air pollution have been widely used their results require very careful interpretation. Such interpretation has frequently been lacking. For a chastening review of the ‘inappropriate’ use of these studies by economists written by a distinguished group of epidemiologists see [20]. One reason why the available evidence is inappropriate for the use to which it has been put arises because of the way in which air pollution variables are typically entered into the statistical regression model. Standard practice in the statistical modelling of the relationship between daily mortality or hospital admission counts and ambient levels of air pollution is to include controls for autonomous trends, seasonal cycles, meteorological variables, day of the week effects and contemporaneous, once or twice lagged values for air pollution in the regression equation. Often it seems that the single most significant lag is selected as for example is explicitly stated in [15]. Clearly such models estimate only the short-run impact of air pollution. They do not for example, account for the possibility that a high number of hospital admissions on 1 day might be followed by an offsetting reduction in the number of hospital admissions spread over the following weeks and months. The importance of this point to the conduct of policy should be obvious. If air pollution precipitates hospital admissions that have merely been borrowed from the future then the cost of these admissions should not be attributed to air pollution unless they are advanced to such a degree that time discounting becomes an issue. Only if these hospital admissions would never
1
Good examples of such studies include [31,34] for mortality and [5,37] for hospital admissions. The effect of correcting this programming error and adopting a stricter convergence criterion seems not to alter the qualitative conclusion that air pollution and in particular particulate matter are linked to ill-health. It does however seem to reduce the significance of effect. As the Health Effects Institute notes, the moral of this tale is that it is dangerous to rely on a single approach or software package. 2
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otherwise have occurred is it appropriate to attribute the cost to air pollution. But by relying on studies that yield information only about the short-run effects of air pollution researchers have often implicitly assumed that all hospital admissions are additional. Whilst there is now a much clearer realisation of the fact that the deaths identified by studies focussing on the short term might have been advanced by only a few weeks or months, the fact that potentially the same problem applies to hospital admissions, work loss days and surgery attendances and a range of other health impacts is perhaps less widely appreciated. Recognising the importance of this point a number of researchers [32,33,39] have sought to provide what they refer to as ‘harvesting resistant’ estimates of the health effects of air pollution. Taking the last of these as an example, the approach involves analysing the relationship between 15 day moving averages of air pollution and mortality counts and hospital admissions. The paper’s author Schwartz argues that if air pollution involves only short-term harvesting of less than 15 days then no relationship should be present. In fact, statistically significant relationships are observed even when 60 day moving averages are present which appears to reject the hypothesis of short-term harvesting. The limitation of this approach is that it is capable of estimating only the interim rather than the long-run impact of air pollution. Adopting an alternative approach Zanobetti et al. [38] uses polynomial lags to explore the short-term mortality displacement issue. Although the authors find no evidence of short-term harvesting the method of polynomial lags suffers from the defect that it is necessary to specify a finite endpoint prior to estimation. Simply assuming a maximum lag length is hazardous; the technique will generally distribute the effects of over the entire lag whether this is appropriate or not. And critically the technique has extreme difficulty in capturing any long-tailed distribution of a type that might be expected in epidemiological time-series studies. These features make the polynomial lags technique unsuitable for use in epidemiological time-series studies. Partly because of these shortcomings the polynomial technique has seen relatively few recent applications in the field of econometrics either. And once again the technique is capable of estimating only the interim rather than the long-run impact of air pollution. A more realistic regression model would seek to approximate the infinite distributed lag effects of air pollution on hospital admissions. Summing these lag coefficients would then provide an estimate of the long-run impact of air pollution on hospital admissions net of any cases brought forward. It is even possible that such a strategy might reveal that the health impacts of air pollution are larger than suggested by models that focus on the short-run effect if there is a long time lag between exposure to air pollution and admission to hospital. A second problem arises in that the existing literature is also largely characterised by regression models including one or at most two air pollutants. Given the correlation between different air pollutants, single-pollutant models risk explaining what are essentially the same adverse health events several times over. A strategy of relying on single-pollutant models also frustrates any attempt to determine which air pollutants are responsible for the empirically observed health impacts. Neither the fact that some pollutants may not themselves be harmful to human health but serve as markers for other pollutants, nor the fact that ambient concentrations recorded by monitors may be a poor representation of individuals’ exposure, nor the fact that some air pollutants are precursors of others obviously justifies the almost complete reliance on single-pollutant models. The only way of dealing with the problem of multicollinearity between different air pollutants is to combine the results obtained from different
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sites using meta-analytical techniques.3 For an example of a study adopting a multiple-pollutant approach see [9]. The use of single-pollutant models has nevertheless been defended in the literature. One of the most eminent epidemiologists Schwartz has for example remarked: ‘‘One occasionally sees studies that have fitted regression models using four or even more collinear pollutants in the same regressiony Given the non-trivial correlation of the pollutant variables and the relatively low explanatory power of air pollution for mortality or hospital admissions such procedures risk letting the noise in the data choose the pollutant’’.4 Even if impacts cannot be reliably attributed to particular pollutants, given that most air pollution emanates from the same set of sources it would still be interesting to know the health effects of a simultaneous reduction in all forms of air pollution. The purpose of this paper is to present an alternative approach to modelling air pollution doseresponse relationships. The approach uses a statistical technique familiar to economists and is intended to address some of the deficiencies of the existing studies that make their results difficult to interpret from a policy perspective. Whilst this approach could be used to analyse a variety of health endpoints such as mortality counts and surgery attendances here it is demonstrated in the context of a study linking air pollution and cause-specific hospital admissions in London.5 Using an ARMAX modelling approach the paper estimates the infinite lag effects of air pollution on hospital admissions enabling it to distinguish the short-run effects of air pollution from the more relevant long-run effects. This distinction is shown to be empirically important for one major category of hospital admissions regularly linked to air pollution in the epidemiological literature. These results are shown to hold irrespective of whether one includes only particulate matter in the regression or whether one includes only those pollutants remaining after a process of stepwise elimination. The same results also obtain in a multiple pollutant model containing six different air pollutants and two rival measures of particulates. The remainder of the paper describes the empirical implementation of the technique. Section 2 discusses the data used to estimate the model along with the econometric methods involved. Section 3 analyses the data and compares the results obtained with those from the only other proposed method for producing harvesting resistant estimates of air pollution. Section 4 concludes with ideas for further applications of the technique.
2. Empirical analysis Daily counts of hospital admissions were taken from Greater London from the start of 1992 to the end of 1994, a period of some 1096 days. Hospital admissions are classified by cause and these include the broad categories of respiratory disease (RES) and cardiovascular disease (CARD). Maximum temperatures (TMAX), minimum temperatures (TMIN) and relative humidity 3
It may be that the main explanation for the prevalence of single-pollutant models is the difficulty of publishing a paper in which none of the pollutant variables are individually significant because they are multi-collinear. 4 This quote is taken from Schwartz et al. [35, p. 9]. 5 The effect of air pollution on life expectancy can also be examined within the context of a prospective cohort study e.g. [29]. This approach is advantageous in that it also accounts for the chronic mortality impacts of air pollution. Unfortunately, the data requirements of such studies are onerous and there are correspondingly very few of them.
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Table 1 Descriptive statistics Variables (units)
Mean
Std. dev.
Minimum
Maximum
RES CARD HOL SCHOOL TMAX (1C) TMIN (1C) HUMID (%) BS (mg/m3) NO2 (mg/m3) SO2 (ppb) O3 (ppb) CO (mg/m3) PM10 (mg/m3)
150.85 172.43 0.02 0.23 14.9 8.8 70.58 13.06 33.63 8.77 17.24 1.28 28.84
43.67 32.81 0.14 0.42 5.62 4.69 10.85 8.45 10.64 4.53 11.49 0.78 14.24
66 72 0 0 2.0 4.6 41.00 1.70 12.40 2.30 0.45 0.40 6.80
318 259 1 1 31.7 21.5 97.00 72.90 133.70 42.00 79.90 7.90 131.97
(HUMID) were from Holborn in Central London. Measures of 24-h averages for Black Smoke (BS) and SO2 in were taken from 5 sites. Measures of 24-h averages for NO2 and 8-h averages for CO were taken from three sites whilst measures of 8-h averages for O3 were taken from two sites. A measure of 24-h average PM10 was obtained from only one site in Central London. Despite the relatively large geographic area the records taken from different pollution monitors were all highly correlated with one another. For all pollutants a single index was formed taking the mean of all non-missing observations. Missing observations were interpolated using zero-order regression methods. Six dummy variables (MON, TUE, WED, etc.) were included for day of the week effects. The variable HOL accounts for statutory holidays whereas the variable SCHOOL accounts for school holidays. The data are described in Tables 1 and 2. Note that whilst it is customary to provide a simple correlation matrix for the pollution variables simple correlation matrices tend to understate the extent to which the pollution variables are as a group multicollinear with one another. Note that these data have already been analysed by Atkinson et al. [4] using techniques typical of those encountered in the epidemiological literature.6 The time-series properties of the log RES and log CARD have been investigated using two alternative test procedures. The Phillips–Perron test [27] is used to test the null hypothesis that there exists a unit root present in the data. The Kwiatkowski–Phillips–Schmidt–Shin test [18] by contrast tests the null hypothesis of stationarity. Both tests assume the presence of a time trend. For either category of hospital admission the Phillips–Perron tests are able to reject the null hypothesis of a unit root.7 The Kwiatkowski–Phillips–Schmidt–Shin tests on the other hand
6
I am grateful to Ross Anderson and Richard Atkinson for providing me with this data. The Phillips–Perron test statistics ZðrÞ were 225.09 and 631.40 for the Log RES and Log CARD variables respectively with a one percent critical value of 29.50. The ZðtÞ test statistics were 11.48 and 25.01 with a one percent critical value of 3.96. 7
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Table 2 The pollutant correlation matrix
BS SO2 NO2 O3 CO PM10
BS
SO2
NO2
O3
CO
PM10
1.00 0.67 0.55 0.39 0.79 0.59
1.00 0.67 0.10 0.64 0.74
1.00 0.18 0.50 0.72
1.00 0.40 0.00
1.00 0.48
1.00
cannot reject the null hypothesis of stationarity.8 It was therefore deemed unnecessary to firstdifference these variables prior to analysing them. Traditional analyses of mortality counts and hospital-admissions usually remove autonomous and seasonal trends before subjecting the data to regression analysis. Frequently they use the locally weighted least squares smoothing (LOWESS) technique developed by Cleveland [6] for this purpose.9 In this analysis the effects of autonomous trends, epidemics and seasonal effects are accounted for by including high-order Chebyshev time polynomials among the explanatory variables (e.g. see [12]). Where n is the number of time periods and t is time, a Chebyshev time polynomial of order k is defined by: pffiffiffi 2 cos½kpðt 0:5Þ=n: CHEBYSHEVkt ¼ The degree of control afforded by Chebyshev time polynomials of up to and including order 20 is virtually identical to that obtained using the LOWESS technique with the bandwidth set at 120 days, the value most often chosen in other epidemiological studies. The regression equation presented below uses the ARMAX modelling technique to approximate an infinite distributed-lag on meteorological variables, pollution variables, statutory holidays and school holidays in the presence of serial correlation. It is the ability of the ARMAX modelling technique to approximate infinite distributed lags that makes the use of this technique advantageous in this context. For a comprehensive discussion of the ARMAX model see [11]. Note that L is the lag operator and that the maximum lag length for the dependent and independent variables is sufficient to capture quite complicated lag patterns. Longer lag lengths were investigated but resulted in convergence problems indicating perhaps the redundancy of introducing additional parameters in to the regression model. It is assumed that the error term e is normally distributed and estimates of the parameters y12 ; a; d120 ; b139 and g12 are obtained using maximum likelihood procedures.10 The model for cardiovascular admissions is of course 8
The Kwiatowski–Phillips–Schmidt–Shin test statistics were 0.138 and 0.139 for the Log RES and Log CARD variables, respectively, with a five percent critical value of 0.146. 9 There are many different ways of controlling for seasonal effects, autonomous trends and epidemics. Some researchers prefer to regress daily mortality on sine and cosine terms of differing frequencies. Others use a monthly dummy variable approach that in effect fits a histogram to the data. Yet more use non-linear splines. 10 In many empirical analyses the number of deaths or hospital admissions is assumed distributed as a Poisson variable. In this analysis the daily number of hospital admissions is typically so large and there is probably no discernible difference in the results from modeling hospital admissions as a lognormal variable.
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analogous. ð1 þ y1 L þ y2 L2 Þ logðRESÞ ¼ a þ
k¼20 X
dk CHEBYSHEVkt þ ðb1 þ b2 L þ b3 L2 ÞTMAXt
k¼1 2
þ ðb4 þ b5 L þ b6 L ÞTMINt þ ðb7 þ b8 L þ b9 L2 ÞHUMIDt þ ðb10 þ b11 L þ b12 L2 ÞBSt þ ðb13 þ b14 L þ b15 L2 ÞNO2t þ ðb16 þ b17 L þ b18 L2 ÞSO2t þ ðb19 þ b20 L þ b21 L2 ÞO3t þ ðb22 þ b23 L þ b24 L2 ÞCOt þ ðb25 þ b26 L þ b27 L2 ÞPM10t þ ðb28 þ b29 L þ b30 L2 ÞHOLt þ ðb31 þ b32 L þ b33 L2 ÞSCHOOLt þ b34 MONt þ b35 TUEt þ b36 WEDt þ b37 THUt þ b38 FRIt þ b39 SATt þ ð1 þ g1 L þ g2 L2 Þet : If the coefficients on same day and lagged pollutant concentrations are statistically significant this indicates that at least one pollutant has short-term effects. If these coefficients sum to zero however it indicates that the long-run impact is zero and hence that hospital admissions are simply reallocated through time rather than additional.11 If the lagged values of hospital admissions are statistically significant this points to the presence of infinite lag effects. Note that the model represents the most general of several considered. Given the aforementioned disagreement concerning the merits of single-pollutant models versus multiplepollutant models a number of simpler alternatives were also considered. These include a model in which only PM10 is included on the grounds that it is the pollutant that has most often been linked to adverse health outcomes, as well as a model in which the least significant pollutants are removed using stepwise regression. This process might result in a model in which one or more pollutants are present.12 Note also that the use of maximum and minimum temperature appears preferable to using mean temperature and its squared value. Other researchers have used non-linear splines for meteorological variables although such an approach is not taken here.
3. Results Turning to the results, in the model of respiratory admissions the stepwise elimination procedure selects a model containing only SO2 whilst in the model explaining cardiovascular admissions the procedure selects a model containing only BS. In either case the resulting singlepollutant model cannot be rejected against a more general model including all pollutants. The fact that in neither case is PM10 the single most important pollutant might be because it is measured at only one site compared to the five sites that measure BS and SO2. On the other hand, Moolgavkar
11
The long-run impact of BS on the logarithm of hospital admissions is given by ðb10 þ b11 þ b12 Þ=ð1 þ y1 þ y2 Þ: The formula is analogous for other pollutants. 12 It seems appropriate here to remind the reader about the risks of using stepwise regression for the purposes of model selection given the sequential test procedures employed by the technique.
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Table 3 The regression model for respiratory hospital admissions Variable
Dependent variable ¼ Log (RES)t Log (RES)t1 Log (RES)t2 TMAXt TMAXt1 TMAXt2 TMINt TMINt1 TMINt2 HUMIDt HUMIDt1 HUMIDt2 BSt BSt1 BSt2 NO2t NO2t1 NO2t2 SO2t SO2t1 SO2t2 O3t O3t1 O3t2 PM10t PM10t1
Model A—all pollutants coefficient (t-statistic)
0.0903 (3.92) 0.850 (39.07) 0.00153 (0.96) 0.00262 (1.61) 0.000884 (0.47) 0.0107 (4.76) 0.000148 (0.09) 0.00858 (4.69) 0.000236 (0.61) 0.000215 (0.75) 0.000127 (0.31) 0.0000628 (0.07) 0.00136 (2.13) 0.000438 (0.50) 0.000117 (0.17) 0.000443 (0.95) 0.000617 (0.93) 0.000486 (0.37) 0.000928 (1.10) 0.000414 (0.34) 0.0000601 (0.11) 0.000510 (1.32) 0.000127 (0.25) 0.000256 (0.53) 0.000798 (2.61)
Model B—PM10 only coefficient (t-statistic)
0.0631 (2.17) 0.835 (29.27) 0.000891 (0.57) 0.00451 (2.98) 0.000382 (0.22) 0.0109 (5.05) 0.000388 (0.24) 0.00935 (5.21) 0.000251 (0.73) 0.000376 (1.36) 0.0000573 (0.15)
Model C—SO2 only coefficient (t-statistic)
0.0625 (2.79) 0.840 (38.48) 0.00124 (0.82) 0.00372 (2.42) 0.000292 (0.17) 0.0115 (5.28) 0.000557 (0.35) 0.00936 (5.32) 0.000339 (0.99) 0.000261 (1.01) 0.000156 (0.42)
0.0000286 (0.03) 0.00296 (5.18) 0.000852 (0.97)
0.000142 (0.46) 0.000877 4.13
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Table 3. (continued ) Variable
PM10t2 COt COt1 COt2 Moving average terms et1 et2 Number of observations Loglikelihood
Model A—all pollutants coefficient (t-statistic) 0.000116 (0.24) 0.00644 (0.73) 0.000836 (0.13) 0.000119 (0.15) 0.343 (7.08) 0.656 (13.52) 1094 926.99
Model B—PM10 only coefficient (t-statistic)
Model C—SO2 only coefficient (t-statistic)
0.000326 (1.04)
0.297 (5.78) 0.629 (12.94) 1094 915.63
0.305 (6.66) 0.636 (14.27) 1094 917.52
Note that the t-statistics are heteroscedasticity consistent. Chebyshev time polynomials of up to and including order 20 are included but the coefficients are not displayed. The variables HOL, SCHOOL and their lags, as well as the dummy variables MON through SAT, are likewise included but their coefficients not shown.
[21] also finds that many air pollutants provides an index of air pollution at least as good as PM10 does in the context of hospital admissions. In Tables 3 and 4 these specifications are presented alongside models containing only PM10 as well as models in which all air pollutants are simultaneously included. It is apparent that once autonomous trends, seasonality and epidemics have been accounted for daily variations in hospital admissions are governed mainly by day of the week effects and to a lesser extent, by meteorological variables. Very few of the pollution variables are individually significant in the multiple-pollutant model which is not surprising given the high degree of multicollinearity. In the single-pollutant models, however, the pollution variables are often highly significant. As a group the lagged values of the dependent variable are also highly significant pointing to the presence of infinite lag effects. The statistical significance of the pollution variables is explored further in Table 5. As in earlier reviews of studies reported in the epidemiological literature such as [2-4,19], in the short term there appears to be a highly significant association between air pollution and both respiratory and cardiovascular hospital admissions. This association remains whether one or many pollutants are included in the regression model. Table 5 also examines the effect of imposing the restriction that the long-run effect of each pollutant included in the model is simultaneously zero.13 This restriction is rejected at the 1 percent level of confidence for respiratory admissions regardless of whether the model contains all 13
The hypothesis that the long run impact of BS on hospital admissions is zero is equivalent to testing:
b10 þ b11 þ b12 ¼ 0: The test is analogous for the other pollutants.
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Table 4 The regression model for cardiovascular hospital admissions Variable
Dependent variable ¼ Log (CARD)t Log (CARD)t1 Log (CARD)t2 TMAXt TMAXt1 TMAXt2 TMINt TMINt1 TMINt2 HUMIDt HUMIDt1 HUMIDt2 BSt BSt1 BSt2 NO2t NO2t1 NO2t2 SO2t SO2t1 SO2t2 O3t O3t1 O3t2 PM10t PM10t1
Model A—all pollutants coefficient (t-statistic)
1.123 (1.07) 0.240 (0.28) 0.00303 (2.06) 0.00270 (0.62) 0.000616 (0.18) 0.00124 (0.66) 0.00280 (0.63) 0.000696 (0.12) 0.0000689 (0.20) 0.000589 (1.16) 0.000391 (0.74) 0.000893 (1.18) 0.00107 (0.89) 0.0000684 (0.08) 0.000699 (1.21) 0.000301 (0.25) 0.000352 (0.40) 0.000575 (0.54) 0.00123 (0.55) 0.00145 (1.40) 0.000695 (1.54) 0.000849 (0.47) 0.000231 (0.14) 0.000363 (1.01) 0.000826 (1.13)
Model B—PM10 only coefficient (t- statistic)
1.195 (3.09) 0.306 (1.00) 0.00242 (1.79) 0.00294 (1.17) 0.00133 (0.75) 0.000326 (0.19) 0.00151 (0.58) 0.000933 (0.38) 0.000403 (1.35) 0.0000902 (0.18) 0.000213 (0.72)
0.000662 (2.84) 0.00105 (2.44)
Model C—BS only coefficient (t- statistic)
1.115 (1.72) 0.233 (0.44) 0.00249 (1.87) 0.00264 (0.96) 0.00131 (0.71) 0.000579 (0.34) 0.00205 (0.75) 0.00117 (0.36) 0.000303 (1.02) 0.000363 (0.71) 0.000326 (1.07) 0.00151 (3.44) 0.00212 (2.50) 0.000700 (1.16)
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Table 4. (continued ) Variable
PM10t2 COt COt1 COt2 Moving average terms et1 et2 Number of observations Loglikelihood
Model A—all pollutants coefficient (t-statistic) 0.000539 (1.04) 0.00818 (0.87) 0.0104 (0.88) 0.00334 (0.51) 1.039 (1.02) 0.203 (0.28) 1094 1161.11
Model B—PM10 only coefficient (t- statistic)
Model C—BS only coefficient (t- statistic)
0.000494 (1.98)
1.104 (2.98) 0.260 (1.07) 1094 1151.08
1.023 (1.63) 0.190 (0.44) 1094 1153.81
Note that the t-statistics are heteroscedasticity consistent. Chebyshev time polynomials of up to and including order 20 are included but the coefficients are not displayed. The variables HOL, SCHOOL and their lags, as well as the dummy variables MON through SAT, are likewise included but their coefficients not shown.
pollutants, only PM10, or only SO2 as the single most important pollutant. For cardiovascular admissions, however, this restriction cannot be rejected, not even at the 10 percent level of confidence. This result is also unaffected by whether the model includes all pollutants, only PM10 or only BS as the single most important air pollutant. The evidence is therefore consistent with the suggestion that cardiovascular admissions are only reallocated through time by air pollution and that a reduction in air pollution would in the long-run only lead to a significant change in the number of respiratory admissions. This is the key result of the paper. Estimates of the long-run elasticity of hospital admissions with respect to air pollution are presented in Table 6.14 The t-statistics presented in this table are heteroscedasticity consistent and obtained using the delta method. In the introduction it was argued that these are the results most relevant to policy and expressing them in terms of elasticities makes it easier to compare the findings for different pollutants. Note that these elasticities vary with pollution concentrations and are all evaluated at sample means. If one takes PM10 on its own as a metric of air pollution then a 1 percent reduction in current concentrations leads to a 0.17 percent reduction in respiratory admissions in London. If on the other hand SO2 is taken as a metric of air pollution then it appears that a 1 percent reduction in air pollution concentrations might reduce admissions by 0.15 percent. Turning to the multiplepollutant model it is remarkable that, even in a model containing no less than six pollutants and their lagged values, the long-run elasticity of respiratory hospital admissions with respect to PM10 14
The hypothesis that the long-run elasticity of hospital admissions with respect to the level of BS is zero is equivalent to testing: ½ðb10 þ b11 þ b12 Þ=1 þ y1 þ y2 BS ¼ 0: The test is analogous for other pollutants.
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Table 5 Testing the short- and long-run effects of air pollution on hospital admissions
Only PM10 included
Short run effects of air pollution
Long run effects of air pollution
Respiratory admissions
Cardiovascular admissions
Respiratory admissions
Cardiovascular admissions
w2 ð3Þ ¼ 23:72 ðp ¼ 0:000Þ
w2 ð3Þ ¼ 8:84 ðp ¼ 0:032Þ w2 ð3Þ ¼ 12:33 ðp ¼ 0:006Þ
w2 ð1Þ ¼ 21:45 ðp ¼ 0:000Þ
w2 ð1Þ ¼ 1:65 ðp ¼ 0:199Þ w2 ð1Þ ¼ 0:18 ðp ¼ 0:670Þ
Only BS included Only SO2 included All pollutants included
w2 ð3Þ ¼ 27:11 ðp ¼ 0:000Þ w2 ð18Þ ¼ 54:91 ðp ¼ 0:000Þ
w2ð1Þ ¼ 17:30 ðp ¼ 0:000Þ w2 ð6Þ ¼ 25:44 ðp ¼ 0:000Þ
w2 ð18Þ ¼ 33:66 ðp ¼ 0:014Þ
w2 ð6Þ ¼ 1:94 ðp ¼ 0:925Þ
Table 6 The long-run elasticity of hospital admissions with respect to air pollution (t-statistics are in parentheses) Pollutant
PM10 BS NO2 SO2 CO O3 All pollutants
Respiratory admissions Model A— all pollutants
Model B— PM10 only
0.140 (2.10) 0.094 (1.48) 0.165 (1.52) 0.050 (0.53) 0.024 (0.37) 0.032 (0.62) 0.205 (2.36)
0.170 (4.59)
Cardiovascular admissions Model C— SO2 only
Model A— all pollutants
Model B— PM10 only 0.028 (1.47)
0.151 (3.98)
0.019 (0.37) 0.027 (0.56) 0.013 (0.20) 0.027 (0.84) 0.012 (0.32) 0.011 (0.28) 0.007 (0.10)
Model C— BS only
0.010 (0.53)
is still statistically significant at the 5 percent level. It appears that, holding all other pollutant concentrations constant, a 1 percent reduction in PM10 concentrations might reduce hospital admissions by 0.14 percent. The elasticity of respiratory admissions with respect to air pollution in general is obtained by summing the individual elasticities obtained from the multiple-pollutant model. This measure is also significantly different from zero and suggests that a 1 percent reduction in air pollution might cut respiratory hospital admissions by 0.20 percent. It is also quite clear that in order to avoid double counting, the respiratory admissions identified by the singlepollutant models should not be added together. Expressing the results for the effects of PM10 taken from the multiple-pollutant model on respiratory admissions in terms of a relative risk ratio of 1.62 per 100 mg/m3 it is apparent that the
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effect of PM10 is far more pronounced than suggested by the review of existing studies conducted by Atkinson et al. [3] in which point estimates of the relative risk ratio vary from 1.10 to 1.24 per 100 mg/m3. This could indicate that air pollution continues to have a significant effect on daily respiratory hospital admissions beyond the 1- or 2- day time frame normally considered by conventional studies. However, bear in mind, the estimate presented in this study is not very precisely determined. Turning to the model of cardiovascular admissions consistent with the results shown in Table 5 none of the long-run elasticities are statistically significant. It is difficult to compare these results with those from Schwartz [33], the only other attempt to estimate the long-run effect of air pollution on hospital admissions. Firstly, that paper analyses hospital admissions for heart disease, chronic obstructive pulmonary disease and pneumonia rather than the more general categories of respiratory and cardiovascular admissions dealt with here. Secondly, the paper uses only PM10 as a measure of air pollution. Nonetheless, there are some similarities in that the impact of air pollution on chronic obstructive pulmonary disease admissions becomes more rather than less apparent as the time frame of analysis is extended. And although the author finds that the health impacts of air pollution on heart disease admissions are not diminished even up to a period of 60 days this is not necessarily inconsistent with the inability of this paper to reject the hypothesis that cardiovascular admissions are in the long-run all advanced. Whilst it is possible to use the results of the multiple-pollutant study to determine the number of hospital admissions in London attributable to particular forms of air pollution, the results of any single study are generally too uncertain to base benefit estimates on. In this respect anyway this study is no different from the rest.15 Benefit estimates are better based on meta-analysis. But such meta-analyses should be careful to include only long-run estimates from multiple-pollutant studies such as this one. Given the number of hospital admissions presented in Table 1 and the long-run elasticities in Table 6 the reader can easily calculate point estimates of the number of hospital admissions attributable to air pollution in London. For example, judging by the multiplepollutant model a 1 percent reduction in PM10 would avoid altogether 77 respiratory hospital admissions annually in London although a wide confidence interval is attached to this point estimate. It furthermore appears that current ambient concentrations of PM10 might be responsible for 13 percent of respiratory hospital admissions in London. The purely financial costs to a National Health Service hospital of an average emergency respiratory admission were recently estimated to be £1400 in 1996/7 prices [8]. One can only speculate on how these findings would alter published benefit estimates since this paper contains but a single study considering only two health endpoints. Clearly, there is a need for further studies employing techniques capable of distinguishing between the long- and shortrun impacts, and perhaps a reanalysis of the existing data. But until such studies are undertaken and their results subjected to meta-analysis it might be prudent to avoid including reduced cardiovascular hospital admissions as a benefit of improved air quality. Analysts should also continue to resist the temptation to sum reductions in hospital admissions suggested by singlepollutant studies. 15
Obviously, the impressive t-statistics for the single pollutant PM10 and SO2 models presented in Table 8 provide a misleading sense of the uncertainty surrounding the impacts of these two pollutants based as they are on prior assumption and sequential hypothesis testing.
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4. Conclusions This paper has noted that much if not all of the existing epidemiological literature deals exclusively with the very short-term impacts of air pollution on hospital admissions. At the same time reliance on single-pollutant models means that it is unclear whether the health impacts associated with different pollutants are additive or not. Both of these shortcomings have severe implications for the task of estimating the cost of air pollution. Noting the deficiencies of alternative techniques, this paper has used the ARMAX modelling strategy to approximate the entire distributed lag impact of changes in the level of air pollution on hospital admissions. Irrespective of whether one or many pollutants are included in the regression model it is seen that in the long-run air pollution in London results in a significant change in the number of hospital admissions from respiratory disease. Increase in admissions from cardiovascular disease on the other hand appear to be borrowed from future time periods and consequently their cost should not be attributed to air pollution. Although this paper has dealt exclusively with hospital admissions it would be interesting to apply the same methodology to counts of other adverse health events linked to air pollution by studies focussing on the very short term. There must be room for doubt about whether some of these events might not have occurred anyway.
Acknowledgments The author thanks the journal editor and two anonymous referees for their constructive comments. Any remaining errors are the responsibility of the author.
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