Birthweight productivity of prenatal care.

1. Introduction

This paper investigates the health of newborns, using the approach of Mark Rosenzweig and Paul Schultz (1982, 1983). They acknowledged the influence of population heterogeneity in unobserved characteristics on child health and the possible influence on parental behavior. The heterogenous characteristic in question is the innate level of health stock or health endowment. I extend their work by incorporating the number of visits and a visits delay interaction term into the measure of prenatal care and including measures of maternal anthropometry in the birthweight production equation. In addition, I include maternal education in the birthweight equation to test the Rosenzweig and Schultz hypothesis that education influences birthweight exclusively through input demand. The goal of this paper is to obtain consistent estimates of the prenatal care parameters in the birthweight production function that can then be used to assess the effectiveness of prenatal care in reducing the incidence of low-weight births.

Section 2 of this paper discusses the development of the model. Section 3 discusses the data set and estimation method. Section 4 discusses the results of the regressions. Section 5 summarizes the main conclusions and mentions some policy implications.

2. Analytical Framework

Rosenzweig and Schultz (1982, 1983) investigated the role of parental behaviors in the production of birthweight and the determination of the fetal growth rate. They correctly reasoned that parental expectations about the child's "health endowment" can influence parental behavior. For example, if a woman's previous children were full term and normal weight, she may not feel the need to start prenatal care as early for subsequent children as for the first child. Because the child's health endowment is unobserved and also affects his or her birthweight, an ordinary least squares regression of birthweight on parental inputs will yield inconsistent coefficients.

In their model, Rosenzweig and Schultz use parental behaviors (prenatal care delay, maternal smoking, maternal age, and parity) as almost exclusive explanators of birthweight and fetal growth. Only the mother's race, metropolitan residence (Standard Metropolitan Statistical Area [SMSA]), and the SMSA size are nonbehavioral variables. Epidemiological research (Kelly et al. 1996) indicates that maternal anthropometric characteristics have a strong influence on birthweight. In particular, the mother's height is seen as a limiting factor of fetal growth (Institute of Medicine 1985).

I assume that maternal anthropometry is an important determinant of birthweight and fetal growth and have included the mother's height, prepregnancy weight, pregnancy weight gain (adjusted for gestation),(1) and the mother's own birthweight in the birthweight equation. I estimate the following equation where the x variables are the noncare variables including the maternal anthropometry variables. (The exponent a takes on the values 0, 2, and 0.5.)

b = [[Delta].sub.1]x + [[Delta].sub.2]m + [[Delta].sub.3]n + [[Delta].sub.4](n/m) + [[Delta].sub.5][m.sup.a] + [[Delta].sub.6][n.sup.a] + e (1)

The Rosenzweig and Schultz framework is further expanded by giving prenatal care two measures. The first, m, is the time interval, in weeks, between the last normal menstrual period and the first prenatal care visit. The second, n, the standardized number of prenatal care visits, is the observed number of visits adjusted for the length of the pregnancy. Gestation is controlled for by comparing the observed number of visits a mother made to the number recommended by the American College of Obstetrics and Gynecology (ACOG), for the length of her pregnancy.(2) The standardized number of visits (the number of visits a mother would have made in a full-term pregnancy) is calculated by multiplying the recommended number of visits associated with a full-term pregnancy (15) by the proportion of recommended visits made (the observed number of visits divided by the recommended number of visits for that gestation).(3) This dual continuous variable method of measuring prenatal care is preferable to a single categorical index because it allows identification of the independent effects of delay and visits on birthweight.

Except for Warner (1995), there has not been any empirical research focusing on whether subsequent frequent visits can compensate for extended delay in initiating prenatal care, or whether early initiation of prenatal care needs frequent follow-up visits to be beneficial. I again include an interaction term, the n/m variable, in the birthweight production equation to measure the degree of substitution or complementarity, if any exists. It is constructed to increase or decrease as prenatal care use increases or decreases, respectively. A positive coefficient in the birthweight regression would indicate complementarity, a negative one substitution, and an insignificant coefficient would indicate neutrality. With regard to policy, substitution implies an either/or option: start prenatal care early or visit the obstetrician often. Complementarity implies the lack of options: start prenatal care early and visit the obstetrician often.

The marginal birthweight product of a prenatal care variable will be composed of a direct, independent effect measured by its own coefficients and an indirect effect dependent on the levels of the prenatal care variables and the coefficient on the interaction term, as follows:

[Delta]b/[Delta]m = [[Delta].sub.2] + [[Delta].sub.4](-n/[m.sup.2]) + a[[Delta].sub.5][m.sup.a-1] (2)

[Delta]b/[Delta]n = [[Delta].sub.3] + [[Delta].sub.4](1/m) + a[[Delta].sub.6][n.sup.a-1] (3)

As previously stated, using the observed values of prenatal care will yield inconsistent coefficients due to the correlation between prenatal care use and unobserved factors such as the health endowment. A variable that is correlated with prenatal care use but uncorrelated with the unobserved health endowment is needed, and such a variable is provided by the first stage of the two-stage least squares method of estimation, a regression of observed prenatal care on an appropriate set of instrumental variables. These are reduced form prenatal care demand equations and have been reported by Rosenzweig and Schultz (1982, 1983), Joyce (1994), and Warner (1995). The prenatal care instruments are the traditional demand determinants: measures of income and availability. The variables used to measure income are household income, source of income, parental education, and method of financing prenatal care. The variables that measure availability are descriptors of the health infrastructure of the state of residence of the mother. The number of physicians, registered nurses, and hospital beds and the amount of expenditures on health and hospitals, all per capita at the state level, are the variables I use to describe the health infrastructure producing the prenatal care available for a mother to receive. I also include state environmental expenditures per capita to capture any effects that air and water quality may have on prenatal care utilization. The state tax on cigarettes is included to capture any effect public policy toward smoking has on prenatal care utilization. Other variables included as prenatal care demand determinants are parental education, number of children in the household, work status (raises the mother's price of time), and urban residence (medical facilities and physicians are concentrated in cities). A mother's marital status and cohabitation status are included because care provided by a husband or relatives may substitute for some purchased care. Attendance at birthing classes and participation in the Women's, Infants', and Children's program (WIC) may also influence prenatal care utilization through greater contact with health professionals. Foreign maternal birth is included because some cultures view pregnancy and childbirth as a normal condition of womanhood that does not require the intensive intervention of medical professionals. Pregnancy wantedness is included because mothers may demand less care for an unwanted pregnancy.

The determination of observed birthweight has two paths: the rate per unit time at which the fetus grows (fetal growth rate) and the amount of time spent in the uterus (gestation). If all observations had the same gestation, comparing birthweights would be equivalent to comparing fetal growth rates. Comparing observed birthweights having different gestations will confound fetal growth rate with gestation. Rosenzweig and Schultz estimate birthweight as a function of gestation and normalize it by dividing observed weight by predicted weight. The normalized value indicates the degree to which the newborn is small (index [less than] 1), appropriate (index = 1), or large (index [greater than] 1) for gestational age.(4)

Like Rosenzweig and Schultz, I standardize birthweight so that it is comparable across gestations. The methodology I have chosen for controlling for gestation is similar to the Rosenzweig and Schultz method in that it involves the estimation of a birthweight/gestation function. It differs in that this function will not be used to compare observed birthweight to predicted birthweight but rather to calculate the predicted fetal weight gain over the remaining period from observed gestation to term delivery.(5) This predicted weight gain is then added to observed birthweight. My method makes the resulting birthweight value and its underlying fetal growth rate a weighted average of two values: observed birthweight at the individual level and observed birthweight at the sample level. The weights are observed gestation and remaining gestation to term. For births that are close to term, this adjustment will be very small and will have an extremely limited impact on the regression estimates. Appreciable adjustments will occur with preterm infants. It is this group that will have underlying fetal growth rates that are possibly the most different from fetal growth rates measured at term. For extremely preterm births, the adjustment may amount to half of the standardized birthweight. A danger is that, for infants both very preterm and small for gestational age, the standardization adjustment may comprise a larger proportion of the standardized birthweight than observed birthweight. In these cases, the sample fetal growth rate dominates the individual fetal growth rate, leading to an overstatement of the average fetal growth rate for that observation. The number of these cases is sufficiently low so as to not substantially affect the population regression estimates.

Rosenzweig and Schultz argue that maternal education is not directly related to birthweight production, affecting birthweight entirely through health input demand. They state that "Education would not, however, appear empirically to affect marginal products of the production inputs as long as all of the inputs which varied across families were suitably taken into account" (Rosenzweig and Schultz 1982, p. 59). In other words, education will not have a significant coefficient unless some input is omitted from the production equation. Given that there are several production inputs that are unobservable or unmeasurable, it seems that at least a test of their claim is warranted. Epidemiological evidence suggests that maternal education is strongly related to birthweight production and fetal growth (Institute of Medicine 1985; Hulsey et al. 1991; Nordstrom and Cnattingius 1996). Women with higher levels of education consistently have lower low birthweight odds ratios than women with lower levels of education. I assume that the mother's education significantly affects nonmarket production, which includes the production inputs of good nutrition and a stress-free environment. The father's education is excluded from the birthweight production equation because men's education traditionally has been, and still is, very market oriented.

Not every pregnancy results in a live birth. Pregnancies can resolve into miscarriages, stillbirths, or abortions, in addition to live births. Abortions can be problematic to birthweight estimation because of the control a mother exercises in an abortion decision. Mothers can select themselves out of the population by aborting. In the event abortion is correlated with any of the birthweight determinants, then this selection effect will bias the results of a birthweight estimation. Grossman and Joyce (1990) investigated the selection effect of pregnancy resolution on birthweight and found evidence of favorable selection regarding abortion. Unaborted infants were born heavier than aborted infants would have been. This effect was especially strong for blacks.

Becoming pregnant is another selection mechanism. The availability of and degree of competence in the use of birth control methods affect who becomes pregnant and when, and therefore who is eligible to be drawn into the research sample. If access to birth control is correlated with city residence and income, and competence in its use correlated with education, then educated women with high incomes living in metropolitan areas may be becoming pregnant and delivering babies at more opportune times than women without these characteristics. The data for this paper are not rich enough to investigate these selection issues. However, to the extent that the ability to time a pregnancy according to one's desires is correlated with education, pregnancy selection may manifest itself as positive coefficients on the higher education variables.

What I suspect may be a greater problem than the general existence of pregnancy selection effects is whether these effects differ systematically between population subgroups. The Reagan presidency brought limitations and reversals to some liberal social policies of the 1970s. For example, federal funding for abortion clinics was reduced. More recent Republican control of Congress has sustained that trend. In 1994, the states provided almost all of the public funding for abortions (Sollom, Gold, and Saul 1996). Funding for the national family planning program under Title X decreased 43% in real terms during Republican control of the White House (1981-1991), with the number of clinics participating in the program declining 19% during the same period (Anonymous 1994, p. 33). More importantly, there is a racial difference and income gradient in who uses Title X family planning services. In 1991, black women, who made up 13.4% of women of childbearing age, made up 23.0% of the women served, and 64.6% of those served had incomes at or below the federal poverty level (Anonymous 1994, pp. 32-3). These factors manifest themselves in this paper through black mothers reporting a larger proportion of mistimed pregnancies than white mothers. Wantedness, in the context of the above discussion, manifests the consequences of the decision to become pregnant or not, or to abort or not, and therefore may capture their selection effects. A finding of this paper is that pregnancy wantedness has no effect on birthweight, after controlling for other inputs. The selection effects that I cannot control for may have only a minimal direct impact on birthweight.

3. Data and Estimation

The data come from the National Maternal and Infant Health Survey (NMIHS) of 1988 (U.S. Department of Health and Human Services 1992). This is a sample of all conception outcomes (live birth, fetal death, infant death) occurring in 1988 in 48 states and the District of Columbia (Montana and South Dakota declined to participate in the survey). The survey was intended to explore the causes of poor birth outcomes, so low-weight births and minority births were oversampled. Weights for obtaining population estimates are available and used in the regressions and means. The NMIHS data were supplemented by data on the state of maternal residence from the State and Metropolitan Area Data Book 1991. These area data were mostly for 1988, the cigarette tax was from 1989, and the population data were from 1990. Singleton births to non-Hispanic Black (4158 observations) and non-Hispanic White (4344 observations) women aged at least 21 years comprise the universe.

Teenagers are excluded from the analysis because any behavioral differences between teenage and adult mothers and their impact on birthweight production are better examined separately from the general examination of prenatal care and birthweight. An adolescent's level of education and marital status may be significantly correlated with the state of pregnancy. This issue of endogeneity of education and marital status is curtailed by excluding adolescents from the analysis. To reduce the inclusion of incorrectly recorded data, gestation less than 20 or more than 45 weeks and birthweights below 400 grams or above 6000 grams were excluded.

The National Center for Health Statistics (NCHS), which conducted the survey, imputed values for those observations with incomplete data. The imputation method was to find another complete observation with the most similar maternal characteristics and use that observation's value for the missing one. Some imputation rates exceeded 5%.(6) Two such variables, household income and working mother, are identifying instruments, and their high imputation rates slightly reduce the strength of identification. The state level variables, having only 48 data points, are also limited in their identifying power.

The birthweight equation (1) is estimated by the 2SLS method. The birthweight equation is identified by excluding the method of financing prenatal care, household income, source of income, father's education, and the state level variables. Since simultaneous estimation requires identifying instruments, a test of the validity of those instruments should be performed to ensure that they are truly uncorrelated with the health endowment. I use the Hausman method to test the validity of the instruments. The residuals of the birthweight equation are regressed on the instruments (Hausman 1983, p. 433). The test statistic value is the product of the sample size and the unadjusted coefficient of determination. Exceeding the critical value is a rejection of the null hypothesis that the instruments are independent of the health endowment. It follows a chi-squared distribution with degrees of freedom equal to the number of overidentifying instruments (the number of excluded exogenous variables less the number of included endogenous variables).

The original empirical specification was rejected due to the correlation of some instruments with the health endowment. The Hausman test provides little theoretical guidance on possible remedial measures after rejecting an instrument set. The ad hoc amendments I made were to exclude from the set those instruments that had significant coefficients in the residual regression. For whites, these variables were self-payment of prenatal care, urban residence, and Hispanic father. For blacks, these variables were father has undergraduate degree only, father's age, other category for source of income, other category for prenatal care payment, white father, and Hispanic father. An advantage to this action is that the birthweight equations remain directly comparable across the races. A disadvantage is that the two samples have different instrument sets, which raises questions such as why a father's characteristics are so much more correlated with birthweight in the black sample than they are in the white sample. These amendments lessen the number of strong identifying variables in each regression. The identification task falls heavily on father's education, father's age, number of children, cohabitation, source of income, and the state level variables in the white regression, and on cohabitants, number of children, and the state level variables in the black regression. The end result, the lack of a strongly identified birthweight equation, is a serious weakness for this paper.(7)

[TABULAR DATA FOR TABLE 1 OMITTED]

Rosenzweig and Schultz estimate their birthweight production equation with mother's age, parity, and smoking during pregnancy as endogenous to parental decision on the level of inputs to birthweight production and with good reason.(8) The decision to smoke during pregnancy can be related to the state of pregnancy in addition to the number of cigarettes smoked being related to health status. Reproductive health, like general health, depreciates over time. Age, also correlated with time, is therefore correlated with the level of reproductive health. Parity is related to the level of reproductive health through selection. Women with lower levels of reproductive health who experience difficulty conceiving and/or carrying the pregnancy to term, may voluntarily or involuntarily cease childbearing before reaching a high parity.(9) I test the endogeneity of these variables and marital status. The results of those tests are presented in Tables 1 and 2. Exogeneity is not rejected for any variable in either the black or white sample. The empirical model will have only prenatal care as endogenous.

Another aspect of the birthweight model is the specification for prenatal care. Rosenzweig and Schultz (1982) estimated three specifications from the generalized Leontief-Diewert form: linear, square root, and square root with interactions. At issue is the productivity of prenatal care. Since there is an upper bound to birthweight and fetal growth imposed by maternal anthropometry, the marginal product of prenatal care must be decreasing at high levels of care utilization. I use linear, linear with interaction, quadratic, and square root forms to explore this issue.

In keeping with most of the literature (Rosenzweig and Schultz 1982; Lewit 1983; Corman, Joyce, and Grossman 1987; Grossman and Joyce 1990; Joyce 1994; Warner 1995), [TABULAR DATA FOR TABLE 2 OMITTED] I use an additive form for the birthweight equation. There has not been extensive discussion of the alternatives to an additive birthweight production function such as a Cobb-Douglas, translog, or a hybrid functional form. Rosenzweig and Schultz (1983) did estimate translog and Cobb-Douglas forms. Their translog equation yielded an insignificant delay coefficient with the incorrect sign and very few significant interaction coefficients. They rejected the translog specification in favor of the Cobb-Douglas. In addition, the smoking variable, the number of cigarettes smoked per day, was set at one for nonsmokers to achieve a defined log of smoking variable. They acknowledge the weakness of this adjustment due to nonsmokers comprising 66% of the sample. Their test showed the smoking coefficient to be sensitive to the choice of nonsmoking value, but they did not find a change in the significance of the coefficient (Rosenzweig and Schultz 1983, note 9).

The translog form is extremely popular in empirical production research due to the fewer number of assumptions imposed on the data and to its duality properties. Two reservations I have concerning its use in birthweight research are related to the log of birthweight as a dependent variable. In such equations, the coefficients measure the relative rather than the absolute change in the dependent variable due to a change in the independent variable. The absolute change in birthweight increases as the base birthweight (the birthweight determined by the intercept and the other variables) increases. This puts an implicit focus on high birthweights, whereas the problems policy wants to address are with low birthweights. Many variables in birthweight production functions are categorical, such as marital status or race. The relative change aspect of their coefficients means that categorical differences between otherwise identical mothers will be more pronounced, in an absolute sense, at higher base birthweights than at lower base birthweights. Theories predicting or explaining why a, say, racial birthweight difference should be greater at 3500 grams than at 2500 grams of base birthweight do not currently exist and need to be developed to evaluate the alternative functional forms.

Rosenzweig and Schultz included interactions between all endogenous variables. I include only an interaction between amount of care delay and number of care visits. A specification that included interactions between parity and delay and visits yielded insignificant coefficients both individually and jointly. Due to the oversampling of low-weight births, the regressions performed in this analysis were by weighted least squares to obtain consistent population estimates.

4. Results(10)

The birthweight equations have few unexpected results (Tables 3, 4). None of the coefficients on the mother's education variables are significant in the black regression. In the white regression, only the coefficients on the mother who has attended college but not graduated and the mother who has an undergraduate degree are consistently significant. The magnitudes are quite modest; 100 grams is barely 3% of mean birthweight. Since the higher education coefficients can also reflect pregnancy selection, these results taken together strongly suggest that the mother's education has little direct effect on birthweight, supporting Rosenzweig and Schultz's assertion.

The degree of wantedness of the infant does not have a significant effect on birthweight. This result contradicts those of other researchers such as Joyce and Grossman (1990). Their findings are that higher degrees of wantedness are associated with higher birthweight. The coefficient on smoking during pregnancy, as expected, is negative and significant. Unexpected is the significant negative coefficient on smoking before pregnancy in the white regression. Even more unexpected is that it is of greater magnitude than the smoking during pregnancy coefficient.

The coefficient on parity is positive and significant in all regressions. This result is consistent with the finding that first births are at higher risk of low birthweight (Institute of Medicine 1985). The coefficient on mother's age is negative and significant in most regressions of both samples. This result is consistent with epidemiological findings (Institute of Medicine 1985). An unexpected result is the large magnitude of the age coefficient for blacks compared to whites; it is double. The notion that birthweight production declines faster with age for black women than for white women is not new. It is the core of the weathering hypothesis posited by Geronimus and Bound (1990) as an explanation for observed racial differences in birth outcomes.

The maternal anthropometry variables, comprising height, prepregnancy weight, weight gain during pregnancy, and mother's birthweight, all have positive coefficients and are highly significant in all regressions. This result is consistent with other research on this issue (Cawley, McKeown, and Record 1954; Kramer 1987; Kelly et al. 1996) and is important because height and mother's birthweight are determined well before traditional child-bearing age. Since these variables, apart from weight gain, are determined prior to conception, these results imply that some inputs to birthweight production are generated over a time continuum that at least spans the mother's entire life. Because a mother's prepregnancy weight can be determined much closer to conception than height, it does not carry long-term implications. Still, its coefficient indicates that nutritional adequacy before conception has an important impact on later reproductive performance. In addition to height representing a physical constraint on the infant's potential size [TABULAR DATA FOR TABLE 3 OMITTED] at birth, it also represents, in part, the state of nutritional adequacy in childhood and genetic endowment. Its coefficient indicates that hereditary factors and nutritional factors in a girl's childhood and adolescence affect her reproductive performance in adulthood. A mother's own birthweight can be interpreted as a proxy for her health endowment. Its coefficient indicates that mothers pass some of their own health endowment on to their children. The number of generations in which a mother can affect the health endowments of her progeny is subject to speculation. At a minimum, though, a woman's current health influences her grandchildren's birth outcomes. One consequence of this result is that the determination of infant health cannot be conceptualized as a one-period event.

Taken together, these three variables strongly suggest that birthweight production is the result of both short- and long-term factors that may not necessarily operate in the same direction. Short-term factors, such as prenatal care adequacy or smoking cessation, reinforce or counteract long-term factors, such as mother's height and mother's birthweight. The relative impacts of these factors on birthweight production give an indication of which time frame is dominating. The endowment aspect of these results is not well suited to policy intervention, but the childhood nutrition aspect is. My findings imply that current childhood nutrition programs (WIC, school lunch) will have a favorable impact on birthweight when the girls become adult mothers.

The racial differences in the anthropometric coefficients are also of note. The white coefficients are larger than the black ones. White mothers are more efficient than are black mothers, almost twice as efficient for height and own birthweight, in converting their anthropometric characteristics into infant birthweight. Only in the mother's prepregnancy weight do blacks compare favorably to whites. Given the time frames of these variables, my interpretation is that this productivity difference is a manifestation of the more favorable social and economic environment that white girls grow up in compared to that for black girls.

Other variables are marital status, birthing classes, and stable residence, whose coefficients are insignificant in all regressions in both samples. The coefficient on number of months receiving WIC supplements is negative in both samples, significantly so in the black sample. Maternal foreign birth coefficient is positive and significant in the black regression, but negative and insignificant in the white regression. This finding of a birthweight advantage for foreign-born blacks is consistent with other research (Ventura and Taffel 1985; Cabral et al. 1990) and merits further investigation.

The main result concerning the prenatal care variables is that prenatal care delay does not seem to have any significant effect on the fetal growth rate for anyone. Prenatal care visits do seem to have a significant effect on the fetal growth rate for both blacks and whites. Multicollinearity, discussed further below, is a serious problem in the quadratic and square root specifications due to the high correlations between the predicted values of the prenatal care variables. [TABULAR DATA FOR TABLE 4 OMITTED] The linear specification adequately captures the general underlying relationship between prenatal care and birthweight. The delay coefficient is insignificant in both samples, while the visits coefficient is significant in both samples. The main implication is that modest reductions in the rate of low birthweight can be realized from prenatal care-based interventions. Regarding substitution versus complementarity of delay and visits, the interaction coefficient is positive in five of six specifications and significant in only one. This suggests neutrality or slight complementarity between delay and visits in contrast to my previous results (Warner 1995), where I obtained an insignificant negative interaction coefficient.

The issue of marginal returns is explored using the different specifications. Unfortunately, the quadratic and square root specifications are not problem free. These two specifications are arguably unidentified in the black sample. Identification is rejected at 5% and even at 1% if income is not counted as an identifying instrument. Multicollinearity is distorting the results for the quadratic and square root specifications in the white sample. The delay coefficients are significant individually but insignificant jointly. Some of the delay and visits coefficients have unexpected signs. The magnitudes of the coefficients yield unreasonable marginal products. These are signs of serious multicollinearity (Greene 1993, p. 267).

Notwithstanding these problems in the complex specifications, the black coefficients suggest decreasing marginal returns to visits and increasing marginal returns to delay (near its mean). In contrast, the white coefficients suggest increasing marginal returns for visits. Delay has decreasing marginal returns in the square root specification but increasing returns in the quadratic specification due to the unexpected negative sign on the delay squared coefficient. Joint tests of significance of the squared or square rooted coefficients with the interaction coefficient (presented in Table 5) are not rejected at 5% for any specification in either sample. Given the multicollinearity, the weak identification, and the significance results, these data do not provide evidence of anything other than constant marginal returns to prenatal care visits.

The results of the Wu tests are presented in Table 6. The null hypothesis of exogeneity is not rejected for delay in any regression. Exogeneity for visits is rejected in all specifications of the black regressions and three of four of the white regressions. The main result here is that endogeneity is more pronounced for visits than it is for delay. Factors that determine the initiation of prenatal care seem unrelated to those that determine birthweight. Women with low health stocks seem to compensate by having more visits rather than by starting care earlier. The results of this paper confirm the Rosenzweig and Schultz hypothesis but reveal the mechanism to be through the number of visits rather than the amount of delay.

The marginal birthweight products are presented in Table 7. Due to methodological differences, few other studies have comparable results. Rosenzweig and Schultz (1982) found a delay productivity of 40 grams per month. This value was determined without holding the number of [TABULAR DATA FOR TABLE 5 OMITTED] visits constant, and includes both black and white observations distinguished by a race dummy. The delay productivity per month, holding visits constant, ranges from 0 to around 80 grams for blacks and -30 grams for whites. It must be borne in mind, however, that no set of the delay coefficients is ever significant, making delay productivity not significantly different from zero. In addition, though Rosenzweig and Schultz briefly discuss the possibility of their identifying variables being correlated with the health endowment, they perform no identification tests. Rosenzweig and Schultz (1983, p. 741) conclude that prenatal care delay affects birthweight through extending gestation and not through increasing the fetal growth rate. Since I have purged birthweight of gestational effects, the appropriate interpretation of their results with regard to mine is that prenatal care delay has zero productivity. Frank et al. (1992) found a significant relationship between the incidence of first trimester care initiation and the incidence of low birthweight at the county level. However, the magnitude of the relationship was very small, with elasticities of - 0.11 for whites and -0.10 for blacks (Frank et al. 1992, p. 638). Using New York City birth certificate data, I found a statistically significant coefficient on delay and a monthly delay productivity of between 25 and 30 grams. The visits coefficient was insignificant, in contrast to these results (Warner 1995). My previous results, however, need a caveat. Birthweight was not adjusted for gestation. The instrument set for the prenatal care variables was less rich than that used for this paper. In particular, several instrumental variables were defined at the health area level (there are 353 health areas in New York City). This correlates the instruments with the geography of New York City. New York's geography is highly segmented by income, race, and housing stock. To the extent that birthweight is correlated with these factors, the instruments used will be invalid. Lastly, I did not test the validity of the instruments in the manner in which I do in this paper. Regardless of whether or not prenatal care delay significantly affects birthweight, the results of this and the previously cited papers strongly suggest that earlier initiation of prenatal care does not substantially increase birthweight in a practical sense. Prenatal care-based interventions into low birthweight reduction may be more effective if focused more on the frequency and content of the visits than on its early initiation.

Table 6. Wu Tests

Variable     Linear     Interaction     Quadratic     square Root

Black

Delay         0.53         0.69            2.42           0.48
Visits       15.54         8.17            6.91          10.45

White

Delay         0.82         0.69            1.71           0.52
Visits        5.95         3.28            3.57           2.12

Critical F (d.f. = 2, [infinity]) 5%: 3.00, 1%: 4.61.

[TABULAR DATA FOR TABLE 7 OMITTED]

The contribution of visits to birthweight production is not unimportant. Using the marginal product of visits from the linear specification and the mean number of adjusted visits, visits yields a total product of 584 grams for blacks and 474 grams for whites, compared to mothers who made no prenatal care visits. This represents 17.7 and 13.4% of mean birthweight for blacks and whites, respectively. Joyce's (1994) results are different from those of this paper. His expected increase in birthweight due to a change in prenatal care adequacy from inadequate to adequate is quite modest, never exceeding 10% of mean birthweight for any race or ethnicity or any set of maternal characteristics. With whites showing the largest birthweight gain due to adequate prenatal care, he doesn't find the same racial difference pattern as I found here.

The results of Corman, Joyce, and Grossman (1987) are consistent with the findings of this paper, though they used data aggregated up to the county level, for the years 1964-1977. They found that the black neonatal mortality rate was more sensitive to input usage than the white neonatal mortality rate. Specifically, prenatal care, through increased birthweight, reduced black mortality by 1.82 deaths per thousand live births but reduced white mortality by only 0.30 deaths per thousand live births (Corman, Joyce, and Grossman 1987, p. 356).

5. Conclusion and Policy Recommendations

The results of this paper identify two main points with regard to prenatal care. It increases birthweight only through visits, not through delay. Delay and visits appear to be neutral in the production of birthweight. These findings were obtained with weakly identified equations and were subject to substantial multicollinearity. Several instruments were rejected, particularly in the black sample, due to correlation with the birthweight disturbance term. The linear specification yields the most reliable prenatal care results, implying constant marginal returns to prenatal care visits. This contrasts with the prediction of decreasing marginal returns. Overall, the prenatal care results are perhaps too weak to form a basis for policy recommendations.

The findings concerning pregnancy wantedness and certain demographic characteristics such as level of education and marital status are that these variables do not directly affect birthweight. Their influence is indirect, most likely through input demand. Another finding of note is that of a birthweight advantage for foreign-born black mothers but none for foreign-born white mothers.

Somewhat unexpectedly, the strongest findings concern the anthropometric variables. Their marginal products (their coefficients) are large relative to those of the prenatal care variables. This implies that strategies for reducing low-weight births on a long-term basis may benefit from a focus on producing more physically robust women. This suggests a tactic of dietary, nutritional, and physical activity interventions directed at girls and adolescents, the next generation of child-bearing women. It also implies that such a long-term intervention will reduce the rate of low birthweight more than will a series of prenatal care-oriented interventions. For the current generation of child-bearing women, however, increased prenatal care use, manifested as more frequent visits, is likely the best tactic.

I am grateful to Mike Grossman, Joe Newhouse, and three anonymous referees for constructive comments on previous versions. Of course, I alone am responsible for all remaining deficiencies.

1 Pregnancy weight gain, like birthweight, is gestation determined in that longer pregnancies provide greater opportunity to gain weight than do shorter pregnancies. Weight gain during pregnancy needs to be adjusted to reflect gestation so that it can be comparable across all observations. Both the Institute of Medicine (IoM) and the American College of Obstetricians and Gynecologists (ACOG) develop pregnancy weight gain guidelines. The most recent one was published in 1990 (Institute of Medicine 1990; American College of Obstetricians and Gynecologists 1993). I control for gestation by comparing observed weight gain to that recommended given the observed gestation and prepregnancy body mass index (BMI). The BMI is a measure designed to yield a standardized measure of body size by scaling one's weight by one's height. The exact calculation is weight in kilograms divided by height squared in meters. According to IoM and ACOG standards, a BMI less than 20 is underweight, 20 through 26 is normal weight, 26 through 29 is overweight, while over 29 is considered obese. Using the midpoints of the weight gain ranges for each prepregnancy weight classification as total weight gain recommendations for a term delivery, I calculate a weekly weight gain rate over the last 28 weeks of a normal 40-week pregnancy. I assume that almost none of the weight gain occurs in the first trimester and attribute zero weight gain to the first 12 weeks. (This assumption is validated by Kramer et al. [1992].) The ratio of observed weight gain to recommended weight gain given gestation and prepregnancy BMI is the percent of the recommended weight gain achieved by the mother. I multiply the total weight gain recommendation by this percent to arrive at adjusted weight gain, the weight a mother would have gained had the pregnancy lasted 40 weeks.

2 ACOG recommends that a pregnant woman visit her obstetrician once every four weeks from conception until week 28, then once every two to three weeks until week 36, and once every week thereafter until birth (American College of Obstetrics and Gynecology 1988). The more frequent two-week interval was used to calculate the recommended visits between weeks 28 and 36.

3 The precise calculation is as follows. A mother delivers after 37 completed weeks of gestation, giving her an ACOG-recommended 12 visits. She actually made 10 visits starting in week 12. The number of gestation-adjusted visits is 15 multiplied by 10/12 to give 12.5 visits. Milton Kotelchuk (1994) has developed a visits measure that adjusts for the timing of the first prenatal care visit as well as the timing of the birth. He reduces the number of ACOG-recommended visits by the number of scheduled visits lost due to initiation of care after the fourth week, in addition to those lost due to delivery before the 40th week. His precise calculation, using the above hypothetical example, is as follows. Since visits should have been made at four and eight weeks, two visits are lost due to starting care at week 12. This yields 10 recommended visits, (15 - 3 - 2). The number of delay-and-gestation-adjusted visits is 15 multiplied by 10/10 to give 15 visits. I reject its use in this paper for several masons. The adjustments for delay and gestation are conceptually asymmetric but are treated equivalently. The opportunity existed to make the visits that were lost due to delay. The opportunity to make visits lost due to the infant's birth does not exist. In essence, the former visits are censored while the latter are truncated. Making the visits variable express both these concepts seriously distorts the quantity aspect of care that it is trying to measure and makes its coefficient uninterpretable. With a delay and gestation adjustment, the visits standard for the entire pregnancy is determined by the number of visits recommended in the interval between initiation of care and delivery. As this interval becomes smaller, that is, for those with long delay, the standard becomes smaller and the adjusted visits larger. For example, a mother who delays care until two weeks before her term delivery is expected to make two care visits during that time. If she makes four, then she has received 200% of the recommended visits, giving 30 adjusted visits for the entire pregnancy. When delay is until a few days before delivery and visits made daily until delivery, adjusted visits can approach 100. In unpublished details of the calculation of his index, Kotelchuk explains that to avoid these extremely large numbers he sets the minimum standard visit to one. This is equivalent to deeming that maximum delay is one week before delivery. Even with this arbitrary action, large visits values are associated with long delay. Because long delay is also associated with lower birthweights, this leads to a correlation between large visits values and lower birthweight. In an exploratory regression using the delay and gestation adjusted visits variable, I obtained a significant negative coefficient that contradicts almost all available evidence relating quantity of prenatal care and birthweight. A weakness of the visits measure is that each visit is assumed to be equivalent in its content or propriety in relation to the stage of gestation. A visit at 14 weeks may have a different content than a visit at 28 weeks, which is not accounted for in this visits measure.

4 As Rosenzweig and Schultz's birthweight/gestation estimates show, and epidemiological evidence also shows (Falkner and Tanner 1978), fetal weight is a cubic function of gestation. The amount of weight gained per week is very small in the first trimester. The rate of growth is highest in the middle trimester. Growth tapers in the third trimester, while the last few weeks of gestation are for maturation, as organs such as the lungs and the liver prepare for independent life support. My point is that the marginal fetal growth rate follows an inverted U-shaped path. The average fetal growth rate as measured at term will be different from the average fetal growth rate measured at some point before term. I believe that the Rosenzweig and Schultz method of removing gestation's effect on birthweight does not remove gestation's effect on the fetal growth rate. For example, the average fetal growth rate implicit in an infant delivered at 32 weeks whose weight is appropriate to gestational age may be greater than that in an infant delivered at 40 weeks whose weight is appropriate to gestational age. The Rosenzweig and Schultz methodology will give each case a normalized birthweight of 1 and will treat the infant's implied fetal growth rates as equal even though they may not be. For fetal growth to be fully comparable across observations, it must be measured at the same gestation for all observations, which Rosenzweig and Schultz did not do.

5 The adjusted birthweight was calculated by adding to the observed birthweight the difference between the predicted birthweight at 40 weeks and the predicted birthweight at the observed gestation. The predicted birthweights were calculated using the equations presented in Appendix Table A3.

6 The high imputation rate variables for Whites are working mother (7.6%), mother's birthweight (12.8%), and household income (10.8%). The high imputation rate variables for Blacks are working mother (13.1%), mother's birthweight (33.5%), father's education (9.4%), Hispanic father (7.8%), and household income (18.9%).

7 To gain some measure of how weak the identification was, I use two critical values for the Hausman statistic. The liberal value has degrees of freedom equal to the sum of the final identifying variables less the number of endogenous variables. The conservative value is the sum of only the "nonredundant" identifying variables (e.g., the care payment dummy variables are counted as one variable; the number of physicians, nurses, and beds per capita is counted as one variable; etc.) less the number of endogenous variables. At the conservative critical values, independence of the instruments is not rejected at a 1% level of significance but is rejected at 5% in the Black regression. If the household income is excluded as a weak identifying instrument due to its high imputation rate, then identification for the black quadratic and square root specifications, but not the linear and interaction specifications, is rejected at 1%.

8 Rosenzweig and Schultz (1982), with a richer data set, were able to estimate a smoking demand function and use predicted smoking values in their birthweight equations. Joyce (1994), using probit, estimated the likelihood of smoking and included the predicted probabilities and a selection correction term in his birthweight equation.

9 For example, a mother who was eclamptic in her first pregnancy (eclampsia is a potentially fatal condition that develops during pregnancy and is characterized by severe hypertension [Stedman's Editorial Committee 1966]) has a risk of recurrence of between 21.9 and 46.8% in her second pregnancy (Niesert 1996). Such a woman may decide to not put herself at risk many more times.

10 The care demand equation results are available from the author upon request. The instruments were not stellar. No [R.sup.2] value exceeded 17%. For Blacks, the [R.sup.2] value for the delay regressions ranges from 11.5-16%, and from 2-12% for the visits regressions. For Whites, the figures were 8-10% for delay and 2-4% for visits. Frank et al. (1992) report delay [R.sup.2] values of 15% for blacks and 13% for Whites, similar in magnitude and pattern to my delay results.

The wantedness variables, the care payment variables, and variables including parental education, income, working mother, cohabitation, marital status, foreign born status, aid to the poor, and number of children had significant coefficients in the Black delay equations; none of the state level variables did. Some state level variables (nurses per capita and environmental expenditures per capita), along with parity, care payment, mother's age, cohabitation, and income had significant coefficients in the Black visits equations, but wantedness, foreign born status, father's education, aid to the poor, and number of children did not. Wantedness, father's education (but not mother's education), income, care payment, cohabitation, parity, marital status, foreign born status, hospital and environmental expenditures had significant coefficients in the White delay equations. The same variables had significant coefficients in the White visits equations, except for wantedness, cohabitation, state expenditures, and foreign born status. Mother's education and physicians per capita also had significant coefficients in the visits equations.

References

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American College of Obstetricians and Gynecologists. 1993. Nutrition during pregnancy; ACOG Technical Bulletin 179. International Journal of Gynecology and Obstetrics 43(1):67-74.

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Corman, Hope, Theodore Joyce, and Michael Grossman. 1987. Birth outcome production functions in the United States. Journal of Human Resources 22(3):339-60.

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Table A1. Description of Variables

Adjusted Birthweight                   The infant's weight, in
                                       grams, at birth, adjusted
                                       for gestation to represent
                                       the weight the infant would
                                       have been had the pregnancy
                                       lasted 40 weeks.

Prenatal Care Delay                    The time, in weeks, from the
                                       last menstrual period to the
                                       first prenatal care visit. If
                                       no visits were made, then
                                       delay equals 40 weeks.

Standardized Prenatal Care Visits      The number of prenatal care
                                       visits that would have been
                                       made had the pregnancy lasted
                                       40 weeks.

Wantedness                             The actual timing of
                                       pregnancy relative to desired
                                       timing. There are four
                                       categories: wanted earlier,
                                       wanted now (the omitted
                                       category), wanted later, and
                                       never wanted.

Prenatal Care Payment                  Indicates that some portion
                                       of prenatal care was paid for
                                       with one of the four
                                       categories: Medicaid or other
                                       government assistance; out of
                                       the pockets of the mother,
                                       father, their parents, or
                                       other relatives; by private
                                       health insurance or HMO plans
                                       (the omitted category); by
                                       the Indian Health Service,
                                       the military, or other
                                       parties.

Foreign Born                           Indicates that the mother was
                                       born outside the 50 states
                                       and the District of Columbia.
                                       Puerto Rico, the U.S. Virgin
                                       Islands, and Guam are
                                       considered foreign for this
                                       paper.

Education                              The highest level of attained
                                       academic education. High
                                       school only is the omitted
                                       category.

Stable Residence                       Indicates that the mother
                                       lived in one place of
                                       residence throughout her
                                       pregnancy.

Household Income                       Total household income from
                                       all sources in thousands of
                                       dollars.

Source of Income                       Indicates that some portion
                                       of household income came from
                                       one of three categories:
                                       salary or wages (the omitted
                                       category); aid to poor (AFDC,
                                       food stamps, housing
                                       assistance, or unemployment
                                       insurance); other (social
                                       security or veterans'
                                       benefits, alimony, child
                                       support, or other source).

Maternal Anthropometry                 Mother's height in meters,
                                       mother's prepregnancy weight
                                       in kilograms, weight gain
                                       adjusted for gestation in
                                       kilograms, mothers
                                       birthweight in grams.

State Level Variables                  The number of physicians per
Physicians per Capita                  100,000 of state population
                                       as of July 1, 1988.

Nurses per Capita                      The number of registered
                                       nurses per 100,000 of state
                                       population as of July 1,
                                       1988.

Hosp. Beds per Capita                  The number of community
                                       hospital beds per 100,000 of
                                       state population as of July
                                       1, 1988.

Health Exp. per Capita                 Millions of dollars of 1988
                                       state expenditures on health
                                       and hospitals per 100,000 of
                                       1990 state population. The
                                       District of Columbia has the
                                       mean of the 50 states.

Environ. Exp. per Capita               Millions of dollars of 1988
                                       state expenditures on the
                                       environment and housing per
                                       100,000 of 1990 state
                                       population. The District of
                                       Columbia has the mean of the
                                       50 states.

Cigarette Tax                          The 1989 cigarette excise tax
                                       in cents per package Hawaii,
                                       which uses a percent of
                                       wholesale price, has the mean
                                       of the other states and the
                                       District of Columbia.

Cohabitants                            Indicates that during most of
                                       her pregnancy the mother
                                       lived with one of the
                                       following: the infant's
                                       father; her parents without
                                       the father present; the
                                       father's parents without the
                                       father present (due to the
                                       small number of observations,
                                       this category is consolidated
                                       with "Other Cohabitants");
                                       alone (the omitted category);
                                       distant or nonrelatives; or
                                       other cohabitants.

Father's Ethnicity                     Indicates that the father was
                                       of black, white, or Hispanic
                                       race or ethnicity. Asian or
                                       American Indian paternal
                                       ancestry is included in the
                                       "other" category.

Number of Children                     The number of children, own
                                       or not, living in the same
                                       household as the mother
                                       during her pregnancy.

Smoking                                The number of cigarettes
                                       smoked per day before or
                                       during pregnancy.

Mother Works                           Indicates that the mother
                                       worked for pay during the
                                       pregnancy.

Birthing Classes                       Indicates that the mother
                                       attended childbirth classes
                                       during the pregnancy.

WIC                                    The number of months of the
                                       pregnancy the mother was
                                       enrolled in the WIC program.

[TABULAR DATA FOR TABLE A2 OMITTED]

[TABULAR DATA FOR TABLE A3 OMITTED]