I wish to acknowledge the debt this study owes to Professors Robert Higgs, Stanley Engennan, Douglass North, Ralph Andreano, and the Editor of this Journal. All read this material in one or another of its several forms and provided many useful suggestions as well as much encouragement. I would also like to thank Bryan Shipman for his generous assistance in computer programming. Any remaining errors are solely my own.

¹ United States Census, 1880, Vol. 12; Mortality and Vital Statistics, pp. cxliv–cxlv; and Glover, James W., Untied States Life Tables, 1890, 1901, 1910, and 1901–1910 (Washington: U.S.G.P.O., 1921), p. 170Google Scholar and p.186. The figure for Boston males in 1880 is for whites only, all others are for all males.

² See McKeown, Thomas and Record, R. G., “Reasons for the Decline of Mortality in England and Wales during the Nineteenth Century,” Population Studies, XVI (November 1962)Google Scholar; and Meeker, Edward, “The Improving Health of the United States, 1850–1915,” Explorations in Economic History, IX (Summer 1972).Google Scholar

³ Winslow, C. E. A., The Evolution and Significance of the Modem Public Health Campaign (New Haven: Yale University Press, 1923), p. 38Google Scholar. The discovery in the 1880's that several diseases were water borne appears to have strongly affected the interest in both filtering water and in providing initially pure supplies of water. Cosgrove claims that most American cities were lacking sanitary sewers in 1880, but that nearly all urban dwellers were served by them by 1907. While he asserts that a severe outbreak of Yellow Fever in Memphis in 1879 awakened interest in the sanitary problems of American cities, certainly the increasing wealth and size of these cities must have contributed to their new willingness to install sewers. In addition, the findings of the Citizens’ Association of New York (published in the late 1860's) likely served as an important impetus of the American sanitation movement as did the reported success of the sanitation movement in Europe, which was well under way by the 1870's. See Cosgrove, J. J., History of Sanitation (Pittsburgh: Standard Sanitary Mfg. Co., 1909), pp. 87–88Google Scholar. See also Martin, Edgar W., The Standard of Living in 1860: American Consumption Levels on the Eve of the Civil War (Chicago: University of Chicago Press, 1942)Google Scholar, Chapter VIII.

⁴ The methodology used in this paper is adapted from Griliches, Zvi, “Research Costs and Social Returns: Hybrid Corn and Related Innovations,” Journal of Political Economy, LXVI (October 1958).Google Scholar The included areas are those of at least 2500 population lying within Connecticut, Maine, Massachusetts, Michigan, New Hampshire, New Jersey, New York, Rhode Island, Vermont, and the District of Columbia. The 1900 United States Registration Area, sometimes referred to as the Original Registration States, is abbreviated ORS.

⁵ An improvement in a person's health (an increment to his stock of health capital) has both monetary (or market) and non-monetary (or non-market) components. The former consist of reductions in work time lost/year, additions to the number of work years lived, and increments to the marginal productivity of workers; the latter consist of reductions in the disutility from the pain associated with being sick, reductions in the uncertainty pertaining to ill health, etc. Only the market components will be measured here, and one of these, the addition to MPP, will be ignored. Furthermore, the reduction in time lost to being sick will apply to non-work time as well—but this will not be measured. This omission is especially important in that some segments of the population which received large reductions in sick days/year have low labor force participation rates. In the case of reductions in infant mortality there is an additional unmeasured benefit in the form of fewer “wasted pregnancies.” See Arrow, Kenneth, “Uncertainty and the Economics of Medical Care,” American Economic Review, LIII (December 1963);Google ScholarGrossman, Michael, “On the Concept of Health Capital and the Demand for Health,” Journal of Political Economy, LXXX (March/ April 1972);Google ScholarMushkin, Selma, “Health as an Investment,” Journal of Political Economy, LXX Part 2 (October 1962)Google Scholar; and Weisbrod, Burton, Economics of Public Health (Philadelphia: University of Pennsylvania Press, 1961).Google Scholar

⁶ Sewers were often built so as to serve as both storm and sanitary sewers, with the former requiring a larger diameter system than the latter. Therefore, by counting the entire expenditures for sewer construction we are overstating the capital outlays made solely for health purposes. See Baker, M. N., ed., Manual of American Water Works, 1897 (New York: The Engineering News Publishing Company, 1897)Google Scholar. In addition, filtered water was superior to unfiltered water in certain industrial uses, and had publicly filtered water not been provided, additional industrial water filtration plants would have been built. Indeed, some of the pioneering research into the mechanical filtration of water was done by a New England paper making firm. Therefore, by limiting ourselves to the health benefits from both sewers and water filtration systems we are understanding the total benefits from these systems. See Baker, M. N., The Quest for Pure Water, (New York: American Water Works Association, Inc., 1948).Google Scholar

⁷ These diseases and disease groups are Tuberculosis, Scarlet Fever, Malarial Fevers, Measles, Diarrheal Disorders and Dysentery, Typhoid and Enteric Fevers, Diptheria and Croup, and Smallpox.

⁸ These calculations require data on age, sex, and disease specific mortality for cities within the ORS. For 1910, disease and age specific data are available for several individual cities; the procedure used is to take the disease totals by age groups for that, group of cities within the ORS (Mortality Statistics, 1910 (Washington: U.S.G.P.O., 1913), Table 9). The numbers are not sex specific and their age divisions differ from those of the data on labor force participation rates. In order to obtain sex specific death rates by ages conforming to the LFPR age breakdowns, the city disease totals are interpolated according to the disease totals for all registration states (Mortality Statistics, 1910, Table 7). Population data for computing rates are taken from the same source.Google ScholarPubMed

For 1880 the urban mortality figures are not presented by individual cities, but rather. as totals for several cities lying within certain “Grand Groups,” these being relatively homogeneous areas geographically. A further problem is that not all cities within the Grand Groups had death registration. Grand Groups I and II contained 11 of the 19 cities used for 1910; they contained only one city without death registration (New Haven); and of the 16 cities, only 2 were outside of the ORS. All other Grand Groups contained a substantial proportion of cities either without death registration or outside of the ORS, or both. For this reason the cities in Grand Groups I and II are chosen as the sample for 1880. For 1880 the population of specific cities was given only as totals. The age and sex distributions of Massachusetts and Rhode Island are used for interpolation, these states being largely urban. All distribution of benefits for the thirty year period assumes this age distribution. (Source for 1880, United States Census: 1880, Vols. I and XI.) The 1880 cities are Raltimore, Boston, Brooklyn, Cambridge, Camden, Fall River, Jersey City, Lawrence, Lowell, Lynn, Newark, New Haven, New York, Providence, Washington, D.C., and Wilmington. For 1910 the cities are Albany, Boston, Bridgeport, Buffalo, Cambridge, Detroit, Fall River, Grand Rapids, Jersey City, Lowell, Newark, New Haven, New York, Paterson, Providence, Rochester, Syracuse, Washington, D.C., and Worcester.

⁹ Negatives are not counted. The overwhelming importance of tuberculosis renders this assumption unimportant. The rationale for adopting it is simply that counting negatives implies the unjustifiable conclusion that some of the outlays for health resulted in worsened health.

¹⁰ All data on labor force participation rates as well as all income and wage data used in this study are taken from Kuznets, Simon and others, Population Redistribution and Economic Growth: The United States, 1870–1950, (3 Vols.) (Philadelphia: American Philosophical Society, 1957–1964.) The data for LFPR, income per capita, and wages are adjusted so as to be appropriate for urban areas. This adjustment is described in an Appendix to this paper. The LFPR's are assumed to remain constant for the thirty-year period; The weekly wage rates are derived by subtracting property income per capita from personal income per capita and dividing the remainder by the overall LFPR (both figures adjusted as described in the Appendix). This calculation is performed for 1880, 1900, and 1920. Values for intermediate years are interpolated logarithmically. The Appendix is available upon request from the author.Google Scholar

¹¹ It is assumed that both the costs and the benefits for year k were realized on the first day of the year k + 1 and valued using year k + 1 incomes. The calculations show the gains made from 1880 through 1909 and are shown in the tables as being for the years 1881 to 1910, as these are the years in which the gains were actually received.

¹² In the case of reductions in work time lost the wage rate is the appropriate measure of the amount people would be willing to pay for a given unit of that aspect of a health improvement, and thus the problem of two indices does not arise.

¹³ Picking the “optional life expectancy” actually consists of picking a stream of annual survival probabilities. This process is rather like Grossman's optimal rate of depreciation of the individual's stock of health capital. See Grossman, “On the Concept of Health Capital and the.Demand for Health.” It should be noted that because people value life for more than just the opportunity it affords them for consumption that any measure of willingness to pay for an extension to one's life expectancy based only on estimates of income received must underestimate the value actually placed on that extension.

¹⁴ The series is truncated at age 80 due to data limitations. Inasmuch as the proportion of the population over 80 was less than one percent of the total, the omission is likely an unimportant one.

¹⁵ Weisbrod, Burton, “The Valuation.of Human Capital,” The Journal of Political Economy, LXIX (October 1961), 425–436.CrossRefGoogle Scholar

¹⁶ The population distribution, K _aj, is assumed to remain constant throughout the period 1880–1910, and the distribution is further assumed to be identical to that found in Rhode Island and Massachusetts in 1880. Holding the population distribution constant vastly simplifies computations. However, to hold it constant assumes that the population was stable. The population was not stable—fertility and mortality declined. These declines can be expected to lead to the average age of the population increasing. Furthermore, this period was characterized by rapid migration to the cities. Because ages of migrants tend to be clustered in the middle years of the distribution, immigration will also lead to an increased average age for the population. In fact, the number of persons under 16 in the assumed 1910 urban ORS population exceeds that in the actual 1910 urban ORS population by 3.6 percent. In terms of the numbers in the population, the overstatement of persons under 16 will be offset by an understatement of persons 16 and over; however, in terms of the estimate of the benefits from increased life expectancy, the overstatement of benefits going to those under 16 will not be offset by a like understatement of benefits going to those 16 and over. The reason is that a disproportionate fraction of the benefits go to those in the younger age groups. On the other hand, the number of persons of working age (10 and over) in the assumed 1910 population is less than that in the actual 1910 population. I calculated that in 1910 the actual labor force exceeded the assumed one by five percent. Thus the benefits due to reduced absenteeism will be understated due the assumption of a constant age distribution. (The “catching up” benefits going to newborns will be unaffected by the age distribution assumption because the number of recipients is calculated by applying birth rates to the total population figures.)

In order to compute an estimate of the possible bias which might arise from the assumption of a constant age distribution, I recomputed the annual benefits for both the absenteeism series, and the increments to life expectancy going to the public at large series. The computations are based on the, following two assumptions: (1) The relative understatement of the size of the labor force.increased linearly from zero percent in 1881 to five percent in 1910 (an assumption used only in the computation of the new absenteeism stream); (2) The relative overstatement of the population increased linearly from zero percent in 1881 to 3.6 percent in 1910. (The 3.6 percent figure, the amount by which me assumed number of persons under 16 exceeds the actual number of persons under 16 in 1910, is used because the number.of persons in the actual population in 1910 generally falls short of the number in the assumed population for ages under 16, and generally exceeds the number in the assumed population for ages 16 and over. For the age groups 0–5, 0–9, and 0–15, the relative overstatement is largest for the group 0–15.) The use of the 3.6 percent figure can be given two interpretations. Either the entire population was overcounted by that amount in 1910 (it actually was not overcounted at all) or that all benefits from increased life expectancey accrued solely to individuals under 16 (they did not). With either interpretation the assumption stacks the test in favor of an upwards bias due to the use of the fixed population age distribution assumption. The rate of return estimated using the new benefit streams for the income per capita series was less than one-tenth of a percentage point smaller than that estimated using the constant age distribution. The rate of return using the wage series was less than one percentage point higher than that estimated with the constant age distribution. That the differences in the rates of return are so slight is because the two age distributions differ little. The reason that they differ so little is because the age distribution in Rhode Island and Massachusetts in 1880 had a rather high average age. For example, the assumed age distribution has 48.7 percent of the population under 25, the distribution for the entire United States in 1880 has 58.2 percent under 25. A further factor in the small differences comes from the assumption of a flat age-income profile. Because the total wage bill is thus assumed insensitive to changes in the age distribution, changes in benefits due to changes in the age distribution are avoided.

The assumed and actual (1910) age distributions are as follows: for males ages 0–4, 5–9, 10–14, 16–24, 24–44, 45–64, and over 64 the assumed fractions are 0.051, 0.049, 0.046, 0.093, 0.142, 0.078, and 0.024; The actual (1910) figures are 0.052, 0.045, 0.043, 0.097, 0.172, 0.073, and 0.015; For females the assumed fractions are 0.050, 0.048, 0.046, 0.104, 0.157, 0.084, and 0.030; the actual figures are 0.051, 0.045, 0.044, 0.106, 0.166,0.073, and 0.019.

¹⁷ The data on wage rates, labor force participation rates, and population are the same as those used in the preceding section. The income per capita data are based on the personal income per capita series in Kuznets, Population, Vol. II, p. 185. Again, the figures are adjusted so as to make them appropriate to urban areas (see the Appendix). The income figures are for 1880, 1900, and 1920—values for intervening years are interpolated logarithmically. The population figure used for any given year is the population of the urban areas within the ORS. This figure is the appropriate one because the nature of both infectious disease transmission and the public health projects themselves make it difficult for cities to withhold the benefits from public health from their citizens.

¹⁸ The 1880 life expectancy figures are based on life tables for Boston (whites), Brooklyn ( whites), New York City (based on three years experience, total population), and Washington, D. C. For Washington there are two tables, one each for whites and non-whites. A weighted average is computed to obtain a figure for the total population; the weights are the proportions of the total population white and non-white. The 1880 life tables are in abridged form. from age 5 upwards. To obtain life expectancy for each age it is assumed that life expectancy changes linearly between 5 year intervals. (Source: United States Census: 1880, Vol. XII, pp. cxliv–cxlv.) The 1910 life expectancy figures for each sex are based on a weighted average of two tables: the white male (female) population living in the ORS in places of 10,000 and over; the Negro males (females) living in the ORS. The weights are the proportion of all males (females) black and the proportion of all males (females) white—assuming that all blacks in the ORS lived in places of 10,000 and above and that the total population consisted only of blacks and whites. (Source: Bureau of the Census, United States Life Tables, 1910 (Washington: U.S.G.P.O., 1916), pp. 25–29Google Scholar, 38–41.) (Blacks in the region made up of New England, the Middle Atlantic states, and the East and West North Central states were 77 percent urban in 1910.) United States Bureau of the Census, Negro Population, 1790–1915, (Washington, D.C.: U.S.G.P.O., 1918, p. 90.)Google Scholar

¹⁹ The following procedure was used. I found the pair of Model West life tables which bounded each of the four Me expectancies at birth. (The model life table levels begin Me expectancy at birth equal to 20 and then increases at 2½ year intervals.) I then used linear interpolation to determine the appropriate survival probabilities, that is, the ones lying the same relative distance between the pairs of model life survival rates as the estimated life expectancy at birth lay between the pairs of Model West life expectancy at birth. The model life tables are abridged—survival rates are given for five-year intervals. In order to obtain one-year intervals I used two schemes. For ages 0–9, I pro-rated the survival rates using the distribution of survival rates in Glover's 1910 life tables. For ages 10 and over, I pro-rated them according to the scheme . See Coale, Ansley and Demeny, Paul, Regional Model Life Tables and Stable Populations, (Princeton: Princeton University Press, 1964).Google ScholarPubMed

²⁰ The values of are used to determine the values of . In this project we are interested in the increase in life expectancy which took place during the thirty-year period 1880–1910. Because it is assumed that the changes took place in a linear fashion, the annual change in , used in this study, is defined as follows:

²¹ The use of the model life tables may impart a bias on the estimated rates of return. It is unlikely that such a bias would be large, however, as the model life tables were adjusted so as to yield life expectancies at birth identical to those of the actual tables they replaced. Thus any differences in rates of return estimated with model life tables instead of the actual historical life tables would have to come from differences in the distribution of survival probabilities within the tables. A check on two important survival rates, from birth to ages 5 and 10, suggests that the direction of the bias on the estimated rate of return is a downwards one in both 1880 and 1910. In 1880 the model life survival rates exceeded the ones in the historical tables. The probability of surviving to age 5 for males in the actual life table for 1880 is 0.64; that in the model life table is 0.69. For females the actual figure for 1880 is 0.67; the model life figure is 0.69. The 1880 probabilities of surviving to age 10 for males for the actual and model life tables are 0.63 and 0.66. For females the figures are 0.66 and 0.67. In 1910 the model Me survival rates lay below the ones in the actual hie tables. The 1910 probabilities of surviving to age 5 for males for the actual and model life tables are 0.81 and 0.80. For females the figures are 0.83 and 0.82. The figures for survival to age 10 for the actual and model life tables for males in 1910 are 0.79 and 0.78. The figures for females are 0.82 and 0.80. (The source of the data for the model life tables and for the 1910 life tables is described above. The 1880 figures are from United States Census: 1880, Vol. XII, pp. 773–785.)

It is to be noted that in computing additions to life expectancy only the increment for that year is counted as that year's benefit. This is in contrast to the reduction in weeks lost, where the total reduction in absenteeism since 1880 is counted as that year's benefit. In an analogy to physical capital, one might think on the increase in longevity as increasing the durability of the capital stock; the reduced absenteeism can be thought of as reduced “down time” per year.

²² Ideally this benefit ought to be received by the infants on the day of their birth. However, in order to simplify computations, these benefits are assigned to them on the first day of the calendar year following their birth. Thus, on the first day of 1882, all individuals receive-their share of the increment to life expectancy realized during the year 1881. In addition, all infants bom during 1881 receive the present value of the increment to life expectancy at birth realized during the year 1880. (Assigning the “catching up” benefits at the end of the year of birth instead of at birth results in the infants’ benefits being calculated with an income that is overstated by roughly six months worth of economic growth. However, the benefits are cumulated forward six months less. Because the rate at which they are cumulated forward exceeds the rate of economic growth, the bias on the estimated rate of return earned on the cumulated investment in public health is biased downwards.) The expressions used for estimating the “catching up” benefits in the income per capita series () and the wage series () are given below, where k takes on a value of 1 in 1881, 30 in 1910, and B_k is the birth rate in year k.

In order to estimate births it is first necessary to determine the birth rate appropriate for the urban areas within the ORS. An indirect estimating procedure is required because births were not regularly registered until sometime after the period under consideration. Coale and Zelnick have estimated birthrates for the United States for 1850–1960. However, for several reasons, the birthrate in the urban ORS was likely lower than that for the United States. In order to estimate a rate appropriate to the urban ORS, I first adjusted the Coale and Zelnick birth rates for the United States in 1880, 1890, 1900, and 1910 by the relative amount by which the ORS weighted average ratio of children aged 5–9 to women aged 20–49 for 1870–1910 differed from the same ratio for the United States for the same period. (The ratio of children 5–9 to women 20–49 is used because Okun's work suggests that this ratio, for data unadjusted for undercount, comes the closest to the true fertility ratio.) I used the figures so determined for the base crude birth rates (CBR's) for the ORS for each of the four decade end points. In order to determine the proper rate for the urban ORS I then substituted the weighted average of the above defined child woman ratio for rural areas divided by the urban child woman ratio for the ratio of the rural birth rate (CBR^r) to the urban birth rate (CBR_u) in the following expression:

where α is the fraction of the population living in rural areas. I computed CBR_u for each of the four years (1880, 1890, 1900, and 1910). To estimate birth rates for each year I assumed that the birth rate declined linearly. See Coale, Ansley and Zelnick, Melvin, New Estimates of Fertility and Population in the United States (Princeton: Princeton University Press, 1963), p. 22Google Scholar. The source for the child women ratios was Okun, Bernard, Trends in Birth Rates in the United States Since 1870 (Baltimore: The Johns Hopkins Press, 1958), pp. 36–37Google Scholar, 94–95.

²³ Because of sanitary problems associated with a crowded environment, urban areas were characteristically less healthy than rural ones. These problems are the very ones the sanitation movement sought to correct. However, to anticipate findings presented in the final section of the paper, the rate at which health improved was higher in the urban areas than in the rural ones.

It should be noted that, because all individuals in the population in year k are assigned the present value of health improvements realized during the interval from year k − 1 to year k, immigrants who entered the population during year k − 1 will be attributed benefits in excess of those they actually received. While they received, on average, only one half of the benefits earned during the year they entered the population, they are assigned the entire year's benefit. (This argument does not apply to newborns. While infants receive a benefit for the year in which they are born which is, on average, one half of one year's worth of improvement too large, they receive a “catching up” benefit which is, on average, one half of one year's improvement too small.) If it is assumed that the entire increase in the population between year k − 1 and year k was due to immigration, the estimated total benefits will be biased upwards by 1.5 percent. The impact of this overstatement of benefits on the estimate of the rate of return to public health will be smaller than 1.5 percent because the estimated costs of providing public health will be overstated by the same relative amount.

²⁴ A problem exists in that some of the urban population of the ORS may not have provided with public health by 1910. Two possible errors may arise: (a) attributing health improvements to public health which are in fact due to something else; and (b) assigning to people benefits from improved health which they did not actually receive. With regard to the former, the health improvements estimated in developing the absenteeism stream are based on a sample of cities all of which report some public health expenditures by 1910, and all of which had sewers by then. See U.S. Bureau of the Census, Financial Statistics of Cities Having a Population of Over 30,000: 1910 (Washington: U.S.G.P.O., 1913.)Google Scholar The improvements in life expectancy are calculated from a sample in which 80 percent of the population lived in cities of at least 30,000 which reported spending money on public health, including sewers. Some of the remaining 20 percent were provided with public health, but lived in cities too small to be included in the Financial Statistics of Cities Having a Population of Over 30,000. Furthermore, some smaller cities lying on the periphery of a large city may have been able to take advantage of the public health services of the larger city. Thus it is likely that well over 80 percent of the sample on which the 1910 life tables are based were provided with some forms of public health. On the other hand, some of the improvement in health in the sample cities was due to sources other than public health. An attempt to sort out that fraction of the benefits from improved health which is attributable to public health is made at the conclusion of the paper.

The problem of assigning to people benefits from improved health which they did not receive stems from an inability to determine accurately that fraction of people living in cities of less than 30,000 which were not provided with public health by 1910. Because several cities under 30,000 did have some public health by 1910, it would be incorrect to eliminate them all from the study. See, for example, Baker, M. N., ed., The Manual of American Water Works, 1897 (New York: The Engineering News Publishing Company, 1897.)Google Scholar Because both costs and benefits are estimated first on a per capita basis (using samples which, with the exception of the gains in life expectancy mentioned above, are limited to those cities with public health) and then multiplied by total population to obtain the total benefits and costs in any given year, at the first approximation the relative overstatement of benefits due to an overstatement of population will be offset by the same relative overstatement of costs.

²⁵ United States Census, 1890: Social Statistics of Cities, p. 31. As a check, the replacement costs of sewers as reported for cities in 1910 were summed for those cities in the ORS and divided by the population of the reporting cities. This computation yielded a figure of $26.58 in 1929 dollars, lending confidence to the estimate. See Financial Statistics of Cities Having, a Population of Over 30,000: 1910, pp. 188–190.

²⁶ The assumption of no sewers in 1880 and one hundred percent complete sewering of towns by 1910 is based on Cosgrove, J. J., History of Sanitation (Pittsburgh: Standard Sanitary Mfg. Co., 1909), pp. 87–88Google Scholar. The assumption is extreme. Many places had sewers in 1880, but it would be impossible to estimate how many people were served by them at that«time. Furthermore, not all places of 2500 or more had them in 1910.

²⁷ Financial Statistics of Cities Having a Population of Over 30,000: 1910, pp. 134–143.

²⁸ Whipple confirms these suspicions. Using his figures it was calculated that the average daily consumption of water in Albany, Binghamton, and Watertown was 162 gallons per person. See Whipple, George C., Typhoid Fever, Its Causation, Transmission and Prevention (New York: John Wiley and Sons, 1908), pp. 279–280Google Scholar. The implicit consumption derived above was 270 gallons per day per person.

²⁹ Financial Statistics of Cities Having a Population of Over 30,000: 1910, pp. 134–143.

³⁰ As noted in footnote 24, the existence of cities with no public health means that benefits as well as costs have been assigned to too many people. The fraction of the urban population of the ORS for which no expenditures on health conservation were made is likely small. All cities in the ORS in the Financial Statistics of Cities Having a Population of Over 30,000: 1910 reported having made expenditures for health conservation. Fully 72 percent of the urban ORS lived in cities of over 30,000. It is likely that many urban places too small to appear in the Financial Statistics of Cities devoted resources to health conservation. In addition, small urban places located on the outskirts of large cities likely benefited from the expenditures made for health conservation by the larger cities, even if they themselves did not make such expenditures. (For example, the reduction of the incidence of smallpox in a large city will reduce the likelihood of its being contracted in the suburbs of that city.) The population used in the study is one in which unincorporated places have been netted out—a move which ought to help to minimize the inclusion of places for which no municipal expenditures for health were made. Again, it ought to be pointed out that the per capita costs are estimated using populations where it has been verified that all people were provided with the form or public health in question.

From the standpoint of sorting out those improvements in health which are due to public health in general, it is not necessary that all cities had all forms of public health. The computations are based on averages for the above mentioned sample of cities within the ORS. The filtration of water in Washington, D.C., will reduce average mortality for all of the urban ORS; This point would not be valid, of course, if one were attempting to measure the rate of return on the investment in a single public health project.

³¹ U. S. Bureau of the Census, Historical Statistics of the United States, Colonial Times to 1957 (Washington: U.S.G.P.O., 1960), p. 656Google Scholar, Series X 330–342.

³² This treatment of future costs and benefits, which assumes that total costs and total benefits (as opposed to costs and benefits per capita) will remain at 1910 levels, imparts a downwards bias on the estimated rates of return. On the benefits side, even if health remains at 1910 levels (as assumed) growth of either income per capita or population will lead to total benefits increasing. The rate of growth of total benefits is the sum of the rates of growth of population and income per capita. (Some allowance may need to be made to account for changes in the birth rate and/or the age distribution of the population.) During the decade 1900–10, the population of the urban areas in the ORS grew at about three percent per year, income per capita and wages at slightly less than one percent per year (0.9 percent and 0.8 percent respectively).

On the cost side, the impact of population growth on total outlays per capita depends on the elasticities or expenditures per capita for each of the five categories of public health expenditure with regards to population. The elasticities for all but one of these expenditures are estimated with cross section data. Data limitations do not permit the estimation of the elasticity of water filtration maintenance cost per capita with regards to total population. The elasticities estimated for sewer maintenance and sewer construction costs per capital do not significantly differ from zero. On the other hand, the elasticities for health conservation and water filtration system construction expenditure per capita are significantly positive, and equal to 0.24 and 0.25 respectively. The elasticity of total expenditure per capita with regards to population is determined by summing each of the individual elasticities multiplied by its relative share of total expenditures. Assuming for the moment that the population elasticity of water filtration system maintenance expenditures per capita is zero, and using the 1910 relative shares, the elasticity of total expenditures per capita with regards to population is 0.09. Inasmuch as population grew at three percent during the decade 1900–10, public health outlay on a per capita basis would be expected to grow at 0.27 percent per year. This rate of growth is swamped by the rate of growth of income. Indeed, the population elasticity of water filtration maintenance expenditures per capita would have to equal 10 in order for costs to have grown more quickly than benefits. In view of the elasticity of sewer maintenance, it seems unlikely that the water filtration maintenance elasticity would ever be that high. It is therefore concluded that the treatment of future costs and benefits used here places a downwards bias on the estimated-rate of return. (The regression results are found in an Appendix which follows the paper.)

³³ Griliches, “Research Costs,” p. 245.

³⁴ For the relationship between water filtration and mortality from both typhoid fever and diarrheal diseases, see Whippel, Typhoid Fever, Chapters 10 and 12. The impact of sewers is harder to determine because their construction takes place over a long period of time. Thus it is impossible to obtain figures on mortality for cities before and after the installation of sewers in which all else has remained unchanged. A rough view of the impact of these two public health measures can be seen in the mortality figures for Chicago. During the five-year period 1868–73 (excluding 1871), a period in which Chicago's sewage system was not completed, mortality for the two disease groups stood at 311 per 100,000. During the five-year period 1915–1920 (excluding 1918), a period long after Chicago's renowned sewage system had been completed, mortality from the same two disease groups was 124 per 100,000. See Hoffman, Frederick L., “American Mortality Progress During the Last Half Century,” in Ravenel, Mazyck P., ed., A Half Century of Public Health (New York: American Public Health Association, 1921), pp. 110–111Google Scholar. (The exclusions are Hoffman's.)

³⁵ Hoffman shows malaria mortality at 15 per 100,000 in Chicago for 1868–73, and at less than one per 100,000 for 1915–20. (See Hoffman, “American Mortality Progress.”) That others in the eight disease groups used in this study may have been affected by public health measures can be seen in Charles North, “Milk and Its Relation to Public Health,” in Ravenel, ed., A Half Century of Public Health. He states that the pasteurization of milk (the enforcement of which has been within the domain of many boards of public health) had an important influence on the reduction in the incidence of both scarlet fever and diptheria. On the other hand, it should be pointed out that McKeown and Record have shown that the.reduction in TB mortality which took place during this time period was. due almost entirely to improvements in the level of living, especially to improvements in diet. (See McKeown and Record, “Reasons for the Decline of Mortality in England and Wales during the Nineteenth Cntury.”)

³⁶ Based on data contained in the Appendix.

³⁷ United States Census: 1800, Vol. 11, and Mortality Statistics, 1910.

³⁸ The closest case to a controlled experiment is Whipple's examination of Troy and Albany, New York. Both cities are on the Hudson, ana at any point in time they can be expected to share roughly the same climate and standard of living. During the five years prior to 1899, Troy had average death rates somewhat below those for Albany. In 1899 Albany began to filter its water supply; the Troy water supply remained unaltered. Based on a comparison of the average, death rates for the two cities during the five-year period beginning with the year 1900, it appears that the entire reduction in Albany s typhoid death rate, as well as over two-thirds of the reduction in the death rates for both the diarrheal disease group and for children under 5, is attributable to Albany's improved water supply. (Whipple, Typhoid Fever, pp. 276–277.)

In addition to being based on a rather small sample, Whipple's study does not provide any information on the trend of mortality which might have maintained in the absence of both water filtration and sewers. Hoffman presents information on the trend of crude death rates (CDR'S) for the four cities, Boston, New York, New Orleans, and Philadelphia, for the one hundred years beginning with 1814. His study provides data for a period of time long enough to include several decades in which almost no public health improvements were made. During the first fifty years the standard of living rose, but there was little sewer construction, and no filtration of water. Mortality in the four cities actually rose during this period: The average CDR for the first 25 years is 28.1; that for the second 25 years is 30.2. During the following 25 year period there was some sewer construction, but very little water filtration. The average death rate fell to 25.7. Sewer systems in these four cities were completed during the final 25 years, and at least part of the water supplies in three of the cities were filtered. The average death for this period was 18.9. Of the decline in mortality between the last two quarter centuries, a decline in mortality from stomach and intestinal disorders, typhoid and typhus, and smallpox account for twenty-five percent.

³⁹ In 1880, the disease and age specific mortality data are directly divisible into two parts, one for fifty large cities, and the other for the remainder of the population. The smallest city in the 1880 urban sample had a population of 38,000. In 1910 the minimum size city for which age and disease specific death rate data are available is 100,000. Thus the. “rural” sample in both years is not strictly rural, and in 1910 it contains people living in some rather large cities. It might be expected that the larger cities would be less healthy than the smaller ones; however, the correlation between city size and mortality is actually rather small. I regressed the CDR's for all ORS cities of at least 25,000 population for 1910 against their populations, and obtained the following results (with population in 100,000 s).

⁴⁰ The filtration plant built in Lawrence, Massachusetts, in 1893 resulted in a 79 percent reduction in typhoid fever mortality. See Johnson, George A., “The Typhoid Toll,” Journal of the American Water Works Association, III (June 1916), 306.Google Scholar

⁴¹ Historical Statistics of the United States, p. 656. It must be stressed at this point that the use of income per capita as a measure of the utility derived from improved survival probabilities may well be less than ideal. Placing values on the increased life expectancy of infants is especially tricky. From the standpoint of increased lifetime labor productivity due to increased life expectancy, the use of income per capita clearly overstates the benefits from improved survival in the younger ages and understates it for those in the labor force. It should be noted that Series B shows that when the benefits are limited solely to labor force participants (including future participants properly discounted), the rate of return so estimated exceeds the market of return.

⁴² The estimated rates are not only lower than the rates actually received, but they are likely considerably below the rates which households perceived that they were receiving at the time. The rate of return which households thought they were getting depends on what they, considered to be the benefits from public health, on what they considered to be the benefits of improved health from other sources, and on what they considered to be their own personal investment in their health capital. In the case of personal investments in the stock of health capital a problem arises: some of the expenditure on goods having the potential of adding to a household's stock of health capital is considered consumption by the household and some is considered an investment in its state of health. Minimum expenditures on food from the standpoint of maintaining and improving levels of health may be fafless than the actual outlays—the household considering that most of the actual outlay is purely consumption. That only a small fraction of additional expenditures on food during the period under consideration were the result of a conscious effort to add to the stock of health capital appears especially likely in that the information available to households on the relationship between diets and health was nearly nonexistent. For example, that vitamins were necessary for normal nutrition was not known until 1915. (See Charles E. North, “Milk and Its Relation to Public Health,” p. 261.) There was no knowledge of a clear connection between TB mortality and diet prior to World War I. (See McKeown and Record, “Reasons for the Decline of Mortality in England and Wales in the Nineteenth Century,” pp. 114–116.) This last point is especially important as a declining incidence of TB accounted for a large share of the health improvements realized 1880–1910. Given the general lack of knowledge about the role nutrition played in improving health, it is probable that little of the additional expenditures made for food during the period 1880–1910 were made for the express purpose of improving health. The result is that households likely perceived that they were receiving a higher rate of return on what they considered to be their total (household and public) investment in their health than the rate which they actually received on their actual investment.

⁴³ Whipple, Typhoid Fever, p. 285.