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Journal of the Air Pollution Control Association Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/uawm16

Mortality and Air Pollution: Revisited a

Ben-Chieh Liu & Eden Siu-hung Yu

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Midwest Research Institute Published online: 13 Mar 2012.

To cite this article: Ben-Chieh Liu & Eden Siu-hung Yu (1976) Mortality and Air Pollution: Revisited, Journal of the Air Pollution Control Association, 26:10, 968-971, DOI: 10.1080/00022470.1976.10470346 To link to this article: http://dx.doi.org/10.1080/00022470.1976.10470346

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Mortality and Air Pollution: Revisited

Ben-Chieh Liu and Eden Siu-hung Yu Midwest Research Institute

This paper represents an exploratory effort to estimate a physical nonlinear function between excess mortality rates and the SO2 concentration with both considerations over econometric problems such as multicollinearity and heteroscedasticity (the residuals of regression analysis), and the threshold levels. Through a recursive and stepwise adjustment procedure, the average physical mortality function was generalized with much more complete specifications. That is, the generalized average mortality model includes not only the demographic, socioeconomic, and climatological determinants but also air pollution variable. The average pollution damage function developed in this study with observations from relevant SMSA's which have pollution concentrations exceeding the threshold level represents an important departure from the prior studies in which sample observations were selected regardless of the SO2 concentration level.

Empirical analyses in the area of air pollution and human health by Lave and Seskin,1-2 Jaksch and Stoevener,3 and R. K. and M. Koshal,4 among others, have confirmed the existence of a close association between health and air pollution. The ordinary least square linear or log-linear regression method has been conventionally employed to quantify the 968

damaging effect of air pollution on mortality. The major difficulties often encountered in estimating such a physical damage function involves the problems regarding errors in variables, nonnormality, heteroscedasticity, and multicollinearity among air pollution and other explanatory socioeconomic, demographic, and climatological variables, and the lack of knowledge regarding the shape of the function which depicts the relationship between air pollution and health.5 Lave and Seskin,1 in a well-known article, noted possible specification errors in the empirical estimates of mortality and air pollution relation. This observation has been verified by Smith6 in a recent article. The Ramsey tests were utilized with data on the mortality rates and suspended particulates for 50 SMSA's. His findings indicate that the errors in specification concerning nonnormality and heteroscedasticity constitute serious problems in estimation. Perhaps due to the lack of data and information, very few dose response relationships between mortality rate and air pollution were constructed. While the effect of climatological variables was not investigated in the cited Lave and Seskin study, the Koshal study ignored all socioeconomic and demographic factors affecting mortality rates. Despite the fact that the specification errors were observed by Lave and Seskin, those econometric problems have been by and large empirically assumed away in the prior studies. While the aforementioned multicollinearity problem between air pollution and other independent variables in the damage function makes it difficult, if not impossible, to disentangle their influences so as to obtain reasonably precise estimates of their separate independent effects on mortality, Journal of the Air Pollution Control Association

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the presence of the heteroscedasticity problem, violating one of the assumptions used in the normal linear regression model, i.e., the disturbances were independently distributed with constant variance, renders the ordinary least squares estimates inefficient.7-8 The purpose of this paper is twofold. First, it attempts to develop a step-wise regression model for circumventing the heteroscedasticity and multicollinearity problems which were well recognized by the authors. Second, the step-wise regression model is then utilized for estimating a generalized average physical damage function relating mortality to air pollution, demographic, socioeconomic, and climatological variables. The estimated damage function presented in this paper is hoped to be informative and useful in predicting possible benefits resulting from air pollution abatement programs in U.S. metropolitan areas individually. At the outset, it should be noted that there are three features in the physical damage function derived in this paper which distinguish our study from those of Lave-Seskin and Koshal. First, a nonlinear physical damage function between mortality and SO2 alone is constructed and only the residual rather than gross mortality rate for each observation is utilized in estimating the physical damage function. Second, threshold levels for mortality and SO2 are explicitly taken into account. Third, all four sets of variables—demographic, socioeconomic, climatic, and air pollution—are included in the average physical damage function for explaining variations in the mortality rate. The plan of this paper which represents an exploratory stepwise regression effort to estimate an average air pollution damage function for the 40 U. S. metropolitan areas follows: the methodology and derivation of a nonlinear physical damage function for depicting the effect of SO2 on mortality are discussed; then the development of the overall predictive model for the nation is provided. A Nonlinear Physical Damage Function

The term "physical damage function" is generally referred to as the functional relationship between the level of physical damage of a particular pollution receptor and the concentration levels of a specific pollutant(s) holding certain relevant demographic, socioeconomic, and climatic variables constant. Conceivably, a physical damage function is more or less allied to a dose-effect function or stimulus-response function. Although medical research thus far has been of little help in identifying the exact causal-effect relationship between mortality and air pollution, the dose-response relationship between human health damage and air pollution described by Buechley9 and Leung, et al.10 seems to be plausible. Utilizing the dose-response relationship between human health damage and air pollution developed by Buechley and Leung, et al., the physical damage function relating SO2 to mortality (MR) in the present study is hence postulated by the following two equations. In (MR - C) = a - 6/SO2

(1)

C = /(PAGE, PYAP, PC0L, PWOP; SUN, RHM, DTS; U) (2) This semi-logarithmic function form of Eq. (1) displays a long flat "s" relationship between the mortality rate (MR) and the SO2 concentration. In estimating such a physical damage function it is assumed that only the residuals rather than the gross mortality rates, i.e. (MR — C) were relevant. Thus, only the residual mortality rates computed from Eq. (2) are related to SO2. By controlling or eliminating the effects on the mortality rate of other major socioeconomic, demographic, and October 1976

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climatological factors prior to the establishment of a physical damage function, the multicollinearity problem and the violation in homoscedasticity of the disturbances may be alleviated. Eq. (2) describes the relationship between the conventional mortality rate (C) and its socioeconomic, demographic, and climatological determinants such as the percentage of population greater than 65 years old (PAGE), percentage of population with income above poverty level (PYAP), percentage of persons 25 or older completed 4 year college (PC0L), percentage of white to total population (PWOP), possible annual sunshine days (SUN), relative humidity (RHM), number of days with thunderstorm (DTS), and U is the conventional disturbance term. It is recognized that many of the determinants of mortality are difficult to quantify, and data are not readily available for some of the variables.* The 1970 data for the above mentioned variables for 40 SMSA's which have SO2 level >25 Mg/m3 between 1968 and 1970 were taken from a comprehensive quality of life study for U. S. SMSA's recently completed by Liu.11 The concentration level of 25 ixg/m3 is considered to be the threshold level in that it is the maximum allowable level for viable human health.^ The real physical damage function for SO2 embodying the effect of the threshold level of 25 Mg/m3 is then specified as follows: (MR - C) = EXP [a - 6/(SO2 - 25)] ( } MRNET = EXP [a - 6/(SO2 - 25)] ° r where C is the computed value from Eq. (2). The methodological procedures for estimating the postulated physical damage function between mortality rate and SO2 are summarized as follows: 1. A linear multivariate regression model expressed by Eq. (2) was utilized for estimating the effects of the socioeconomic, demographic, and climatological factors excluding SO2 on the conventional mortality rate, C, in deaths per 10,000. 2. Subtract the computed values of C, or C from the observed gross mortality rates and then regress the residual, or MRNET, on SO2 as depicted by Eq. (3). It should be noted that the nonlinear physical damage function is expressed in an exponential form, the MRNET takes logarithm value and the SO2 has reciprocal transformation when the lease squares regression is performed.* The regression results for Eq. (2) and (3) are shown as follows: C = 229.6 + 741.8 PAGE - 119.7 PYAP (50.5) (96.4) (62.8) 0.12 PC0L - 76.6 PWP0 (0.04) (21.6) 0.54 SUN + 0.23 RHM - 0.04 DTS (0.24)' (0.22) (0.07) 2 R = 0.82 (4) MRNET = EXP (0.377 - 0.24/(SO2 - 25)) (0.201) (0.66) R2 = 0.04 (5)

* Lave and Seskin1 and R. K. and M. Koshal4 have estimated such a damage function with a portion of the explanatory variables included in their studies. Several estimation problems have been discussed in some detail by Lave and Seskin.1'2 t The level 25 ^g/m3 was chosen as the threshold for SO2 on the basis that it is the level prevailing in the rural areas where virtually no pollution is observed. * Since (MR-C) may take both positive or negative values, and the logarithm of a negative number is undefined, the negative residuals were restricted in the estimation.

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The figures in the parentheses are standard errors of the estimates. The estimated coefficients shown in both equations have the correct signs, and many of them are statistically significant at the 1 percent level. The socioeconomic, demographic, and climatological variables in Eq. (4) explains more than 82.0% of the total variations in the conventional mortality rate while SO2 accounts for some 0.4% of that of the residual mortality, in Eq. (5). The nonlinear physical damage function between net mortality and SO2 derived from this stepwise regression technique is characterized by the following features: 1. The nonlinear damage function not only resembles the more plausible dose response relationship between air pollution and mortality rate but also is adjusted with both threshold levels of mortality rate and the SO2 concentration of 25 Mg/m3. 2. For the purpose of predicting and computing the marginal mortality damages due to SO2, this nonlinear equation has the advantage over its counterpart linear equation regarding reliability in prediction and better goodness of fit.* 3. In the presence of multicollinearity and heteroscedasticity, but with little relevant extraneous information, adjustment of the mortality threshold in this nonlinear physical damage function circumvents at least partially some of those econometric problems. The damage function and damage estimates derived from the generalized physical damage function to be developed in the ensuing section can then be utilized to either generalize or approximate the overall average mortality function which can serve as the first cut of the predictive model long being sought for in connection with air pollution abatement. A Generalized Average Physical Damage Function

Although the linear multiple regression modeling of the mortality rate and air pollution by Lave and Seskin or the Koshals represents an important contribution to our understanding of the air pollution mortality relation, their results are still not very satisfactory.^ However, a more complete model of mortality determination including all socioeconomic, demographic and air pollution variables is likely to encounter formidable empirical problems such as multicollinearity and heteroscedasticity as noted earlier. If the true problems and their magnitude are known, appropriate econometric techniques as suggested by Goldberger,8 Johnston,7 Hu,12 among others can be employed. Unfortunately, virtually no such needed information about these problems regarding mortality and its determinants is available. Further, reliable and useful average damage functions on mortality rate and air pollution for the U. S. metropolitan areas are still lacking. To close this gap in the air pollution damage investigation, a generalized average damage function is developed by regressing jointly the sum of the estimated mortality rates from both Eq. (4) and (5) on the four socioeconomic and demographic variables, the three climatological variables, and the SO2- It should be stressed that the results of this generalized average damage function should only be used for prediction purpose and any statistical interpretations would be meaningless. Stated otherwise, this damage function so derived serves to yield more accurate prediction as to what would be

* For instance, a linear regression between the residual mortality rate and the SO2 showed an explanatory power 10 times less than the nonlinear fit. t Among the best regressions, Lave and Seskin1 reported the coefficient of determination {R2) ranging from 0.030 to 0.833 as compared to those ranging from 0.35 to 0.52 as obtained by Koshal.4

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the changes in the mortality rates when one of its determinants varies while others are being kept constant. The function is also useful in evaluating the significance of the changes in the value among the determinants. Based on the data of the 40 SMSA's with SO2 exceeding 25 Mg/m3 between 1968 and the generalized linear regression average damage function is estimated as: CMR = CC + CMRNET = 225.6 + 746.8 PAGE - 110.2 PYAP (3.4) (7.0) (4.2) 0.12 PCOL - 78.3 P W P 0 (0.002) (1.6) 0.56 SUN + 0.21 RHM + 0.03 PTS + (0.02) (0.01) (0.005) 0.003(SO2 - 25) (0.002) R2 = 0.99 (6) Where CMR is the computed mortality rate from the computed conventional mortality rate (CC) and the computed residual mortality rate (CMRNET) from Eq. (4) and (5), respectively. All independent variables on the right hand side of Eq. (6) were defined previously. The superiority of the stepwise regression method developed in this paper for estimating damage function can be greatly comprehended by comparing with Eq. (6) the physical damage function with the actual rather than computed mortality rate as the dependent variable. The regression result for such a physical damage function is summarized as follows: MR = 230.1 + 746.4 PAGE - 119.3 PYAP (51.5) (10.59) (63.9) 0.12 PC0L - 77.7 PWP0 (0.035) (24.3) 0.54 SUN + 0.23 RHM + 0.04 PTS (0.25) (0.22) (0.07) 0.004 (SO2 - 25) (0.033) R2 = 0.82 (7) It is noteworthy that the coefficient of SO2 is negative despite the fact that the simple correlation coefficient between MR and SO2 is positive and equal to 0.13. The negativity of the SO2 coefficient is probably due to multicollinearity and other econometric problems discussed in the text. The stepwise regression method utilized for estimating8 partially overcomes those problems and yields the expected positive coefficient ofSO2. Implications and Concluding Remarks

This paper represents an exploratory attempt to estimate a nonlinear physical damage function between excess mortality rates and the SO2 concentration with both considerations of circumventing certain econometric problems such as multicollinearity and heteroscedasticity, and of the effects of the threshold levels. Through a recursive, stepwise adjustment procedure the average physical mortality function was generalized with much more complete specifications. That is, the generalized average mortality model includes not only the demographic, socioeconomic, and climatological determinants but also air pollution variable. The stepwise regresJournal of the Air Pollution Control Association

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sion model developed here represents a constructive response to the call recently made by Lave and Seskin1 and Ferris13 in connection with the urgent need to improve on the existing studies in the area of air pollution and human health. The average SO2 damage functions developed in this study with observations from relevant SMSA's which have pollutant concentrations exceeding the threshold level represents a meaningful departure from the prior studies in which all SMSA's are included as sample observations regardless of the level of SO2 concentration. The availability of average or marginal damages is instrumental in determining the optimal national or regional pollution control strategies. However, the current problem seems far more complex than the question of balancing the benefits to polluters against damages inflicted on the receptors. The issues are pressing and not yet well specified. The basic difficulty in applying the recent research findings to estimate accurately the air pollution damage cost stems from our ignorance about the populations at risk to air pollution. Few attempts have been made to identify who suffers, to what extent, from which sources, and in what regions. At this moment, updating and expansion of the available crude estimates, which are generally restricted to certain regions, are urgently needed.

4. R. R. Koshal and M. Koshal, "Air pollution and the respiratory disease mortality in the United States—a quantitative study," Social Indicator Res. 1: 263 (1974). 5. Lester B. Lave, "Air Pollution Damage: Some Difficulties in Estimating the Value of Abatement," in Allen V. Kneese and Blair T. Boker, eds., Environmental Quality Analysis, Johns Hopkins Press for Resources for the Future, Baltimore, 1972. pp. 213242. 6. V. Kerry Smith, Mortality-air pollution relationships: a comment," J. Amer. Statistical Assoc. 70: 341 (1975). 7. J. Johnston, Econometric Methods, McGraw-Hill Book Company, New York, 1963. 8. Arthur S. Goldberger, Econometric Theory, John Wiley & Sons, Inc., New York, 1974. 9. R. W. Buechley, "SO2 levels and perturbations in mortality," Arch. Environ. Health 27:137 (1971). 10. Steve Leung, Elliot Goldstein and Norman Dalkey, "Human Health Damage from Mobile Source Air Pollution," California Air Resources Board, Sacramento, CA, July 1974. 11. Ben-chieh Liu, Quality of Life Indicators in U. S. Metropolitan Areas 1970, Praeger Publishers, New York, 1976. 12. Teh-Wei Hu, Econometrics, University Park Press, Baltimore, 1973. 13. B. J. Ferris, Jr., "Tests to assess effects of low levels of air pollutants on human health," Arch. Environ. Health 21: 553 (1970).

Acknowledgments

The research underlying this paper is partially financed through a contract from the U. S. Environmental Protection Agency to Midwest Research Institute (No. 69-01-2968). The authors benefited from comments made on an earlier version of this paper by Drs. John Jaksch, Fred Abel, Donald Gillette, William Watson and V. Kerry Smith. The opinions expressed in this paper are those of the authors. They do not necessarily reflect the opinions of the sponsoring agency and MRI. References 1. Lester B. Lave and E. P. Seskin, "An analysis of the association between U. S. mortality and air pollution," J. Amer. Statistical Assoc. 68: 284 (1973). 2. Lester B. Lave and E. P. Seskin, "Air pollution and human health," Science 169: 723 (1970). 3. John Jaksch and Herbert Stoevener, "Outpatient Medical Costs Related to Air Pollution in the Portland, Oregon Area," Washington Environmental Research Center, U. S. Environmental Protection Agency, July 1974.

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Dr. Liu and Dr. Yu are, respectively, the principal and associate economists with Midwest Research Institute, 425 Volker Boulevard, Kansas City, MO 64110. Dr. Liu also teaches at the University of Missouri, Kansas City.

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Mortality and air pollution: revisited.

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