the impact of economic, technological and demographic factors on aggregate births

The Impact of Economic, Technological and Demographic Factors on Aggregate BirthsAuthor(s): Yiannis P. Venieris, Frederick D. Sebold and Richard D. HarperSource: The Review of Economics and Statistics, Vol. 55, No. 4 (Nov., 1973), pp. 493-497Published by: The MIT PressStable URL: http://www.jstor.org/stable/1925673 .

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THE IMPACT OF ECONOMIC, TECHNOLOGICAL AND DEMOGRAPHIC FACTORS ON AGGREGATE BIRTHS

Yiannis P. Venieris, Frederick D. Sebold, Richard D. Harper

Introduction

HIS study is an econometric investigation T of the economic and demographic deter-

minants of aggregate births in the post-war history of the United States. Prior studies have focused on the endogenous character of demographic variables; but, unfortunately, with the partial exception of Gary Becker (1960) they have failed to recognize the dynamic flavor of the problem. Indeed, issues associated with adjustment, timing, interaction between flows and stocks and depreciation rates are for the most part ignored.

On the other hand, the existing econometric effort does not lend its support to a unique hypothesis in regard to the qualitative charac- teristics of the relation of births with various economic variables. Indeed, Richard and Nancy Ruggles' (1960) study of cross-section data failed to reveal a unique relationship between size of family and socio-economic status; the same problem but on a different plane has appeared in studies of time series by Becker (1960),Thomas (1960, 1927) and others (Kirk (1960), Silver (1965)) who have produced conflicting results between cyclical and secular association of fertility and business economic activity. This apparent inconsistency has gen- erated some doubts concerning Becker's hypothesis that children can be treated as a class of consumer durables and that a traditional demand function can be used to explain births' behavior.

From the above considerations it is therefore desirable that further progress be sought in the development of econometric models which integrate the dynamic aspects of both demographic and economic mechanisms. This is the intention of the present study. To this end we shall make use of a model of simultaneous equations which will allow us to consider, in a systematic fashion, the questions of timing,

adjustment process, and the interaction of flows and stocks.

The Model

The purpose of this section is to present a model which will account for the behavior of births. We begin then with an identity relating the flows, i.e., births (B), deaths (D) and the net change in population (AP) at time t:'

B (t) _ D (t) + AP(t). (1)

Furthermore, we assume that during period t, 1/nlth of the existing population plus an equal or smaller fraction 1/Mth of newly-born babies die,2 i.e.:

D(t) = (l/m) B(t) +(lln) P(t- 1). (2) The second behavioral equation of the model relates the change in population to the difference between the desired and actual stock of population:

APP(t) -x [PD(t) - P(t-1)] 0 - X - 1 (3) where X is the coefficient of adjustment. The constant X measures the fraction of the adjustment the society makes towards equating its actual and desired level of population (pD)

during any time period. On the other hand, the desired stock of population is based on decision-making and reflects the preferences of the individual family units. Consequently, it carries no connotation of planning or a socially optimum population-- unless the behavior of families leads naturally to such an optimum level of this stock variable. In addition, we further assume that:

I

pD (t) = aj Zi (t- vj) (4) j=0

where Z? - 1 and the rest of the Z1's are to be specified later. The coefficients of the explanatory variables in equation (4) denote the

Received for publication September 11, 1972. Revision accepted for publication May 1, 1973.

'During our sampling period, the United States did not experience any serious immigration flows. Accordingly, this term is missing from equation (1).

2 The term 1//m is defined to be the death rate of newly-born babies (of age one month or less), and 1 /n is defined to be the death rate of the rest of the population.

[493 ]



494 THE REVIEW OF ECONOMICS AND STATISTICS

long-run effects of the independent variables on the desired stock of population. Finally, the system can be closed by an identity relating the flows with the stocks, i.e.:

P (t) _= P (t -1) + AP (t). (5) Given the linear structure (1)-(5), we can

derive the reduced form of the variable B: I

B (t) = ajA, [ml (m - 1) ] {Zi (t -vj) j=0

-[(n-l)/n] Zi(t-Vj-1)} + (1-A) B(t-1). (6)

Next we must specify the explanatory variables of equation (6). First, to test the Becker hypothesis, we assume that the desired stock of population is a function of permanent real median family income, which is defined by

K

YP (t) = 1 ku Yl) Y(t- k). (7) k=O

The advantage of the use of a "permanent" variant of income is that it takes into account a stream of past income experience. Although several values of ,u and K were considered to construct alternative series on permanent income, the resulted estimates of the birth equation were relatively unaffected by the choice of these parameters. To economize on space, all results presented in the next section were obtained under the assumption that ,u = .1 and K = 16.

Second, we assume that pD is also a function of the employment of married women (E,,w). This variable is included in the regression to pick up the influence of minor variations in business activity. By its very nature, Em,w is extremely sensitive to short-run changes in economic conditions. One of the advantages of its use is that it is relatively uncorrelated with the permanent income, and thus allows more efficient estimates of the regression coefficients than would an alternative indicator.

Third, we shall assume that pD is related to the stock of families of child-bearing age. Two measures of this variable will be employed: the total stock of families (F) and a stream of values for the number of newly-married couples (M). Later, when we specify these variables in first-difference form, the change in the stock of families will be approximated by the level of marriages. The algebraic speci-

fication of the model will present only the second version, but empirical estimates will be given for both.

Fourth, we shall include a rough measure 3

of the use of oral contraceptives (C). The inclusion of this variable is part of an attempt to standardize for the technological and social changes of recent years. We shall return to this point later.

Insofar as the timing of births may depend on the timing of marriages, but this timing varies across couples, several lagged values of these marriage variables will be included in the birth equation. Thus, including the specific regressors in the birth equation, we have:

B(t) h0bo + bh {Yl(t-vl) -[(n-l)/n] YP(t-vj-1)j

+ b2 {Emw(t-V2)

- [(n-1)/n] Emw(t-V2- 1)) + b3 {C(t-v3) - [(n-l)/n] C(t-V3-1))

I

+ hb {M(t-9-v1) j=4

- [ (n-l)/n] M(t-10-vj) }

+ (1-A,)B(t-l) + u(t) (8) where the residual u has been added and the relationship between the two sets of constants is bj = ajXm(m-1) -1, (j = 1, 2, ... .J).

The constants of equation (8) denote the short-run effects of the explanatory variables on current births.

Estimates and Estimation Procedure The above equation is estimated through the

use of aggregate monthly data for the United States for the period 1956-1967. Estimation is simplified through the use of extraneous information in regard to the actual values of n and m. Indeed, demographic statistics over our sample period reveal values of n and m of 100 and 55, respectively. Thus, the corre- sponding monthly death rates are approximately equal to 0.0008 and 0.0015, respectively. It follows then that the explanatory variables may be used in terms of their first differences as opposed to weighted differences. Assuming then

'The basic data series was an annual estimate of oral- contraceptive sales. Insofar as the annual series followed a geometric time rate, a geometric time trend was fitted to the scatter and the monthly computed values derived from that were used in our birth equation.



DETERMINANTS OF AGGREGATE BIRTHS 495

that (n-1) /n (m-1) /m -1, equation (8) collapses into:

B(t) = 3o + bi AYP(t-v1) + b2 AEmw(t-V2) J

+ b3AC(t-v3) + bj AM(t-9-vj) j=4

+ (1-A)B(t-1) + u(t). (9) The constant term, bo, in equation (8), dif-

fers from the one included in equation (9), 8I3. The latter coefficient is introduced into the first difference equation to pick up any trends in the level of the dependent variable.

Both versions of the birth equation were estimated using monthly data for the period 1956-1967, and the results are presented in table 1. According to these two versions, the influence of permanent income is negative and significant. This result is quite inconsistent with the Becker hypothesis and with the empirical evidence of Kirk (1960), Silver (1965) and others. In terms of Becker's analysis, our estimates suggest that the income-elasticity of the quantity of children is negative, rather than positive. This could mean, as has been sug- gested by Okun, that "for most of the income range, the quality income-elasticity may be so high that it contributes to a negative quantity elasticity of demand (1960, p. 237). However, before we can claim that we have offered any reasonable evidence of a negative income-elasticity, it is necessary to consider the Becker objections to such time-series results. Becker rationalizes the observed secular relation between income and fertility on the basis of de- clining child mortality, rising cost of children and increasing contraceptive knowledge.

With regard to the first of these points, we need only consider the time span covered by our sample (1956-1967), and note that child mortality was practically constant over this period.4 Thus, the decline in birth rates could not have been due to medical advances alone. The second rationalization probably does not "explain" our results, either, in that we have standardized for a substantial part of the change in the cost of children over the period. To begin, we contend that the most relevant

single measure of the real cost of having children is the cost-of-living price index. Although the initial expense of child-bearing is substantial, it is rather small relative to the "main- tenance" of the child through the first 18 or 20 years. In addition, the bundle of goods provided for the child is likely to be very sim- ilar to that consumed by the parents (1960, p. 235). Given the nature of the cost-of-living index as a good proxy for the cost-of-children, its inclusion in the equation should standardize for this influence. If one assumes that money illusion is absent, our deflation of money income by the cost-of-living index accomplishes this standardization. The third rationalization offered by Becker - the increasing influence of contraception - is a much more relevant one in the context of this study. We have attempted to standardize for the growing use of contraception in two ways. First, we use as an explanatory variable the use of oral contraception. Second, the distributed-lag equation is specified with a constant term (,80) which should pick

TABLE 1. - ESTIMATES OF BIRTH EQUATION, WITH MARRIAGES AS AN EXPLANATORY VARIABLE

Version la Version lb

Estimated Estimated Coefficient Coefficient

Variable (t value) Variable (t value)

Constant Constant Term 143,732.38 Term 127,943.69

B(t-1) .59349 B(t-1) .36775 (10.700) (4.389)

A Yp(t - 10) - 566.56128 A Yp(t - 10) -1082.79501 (3.236) (4.833)

XEmw (t - 10) 112.56491 AEm, (t - 10) 147.29790 (2.388) (2.514)

AM(t - 9) .26144 M(t-9) .20964 (7.768) (4.796)

AM(t - 13) .28110 M(t-13) .35492 (8.890) (9.884)

AM(t - 14) .25904 M(t - 14) .16335 (8.447) (3.553)

AM(t - 15) .22107 M(t-15) .04897 (6.586) (1.214)

AM(t - 16) .33258 (11.483)

AC(t-9) - 92.73692 AC(t-9) -220.75409 (5.226) (8.094)

R2 .906 R2 .854 F 138.608 F 96.057 D.W. 1.97906 D.W. 2.07923

'The annual death rate for newborn children varied from 0.01875 in 1956 to 0.01651 in 1967, but did not follow a secular trend over that entire period. It seems unlikely that this variation is responsible for the estimated negative relationship between income and births.



496 THE REVIEW OF ECONOMICS AND STATISTICS

up at least part of the remaining trend. Thus, it does not appear that this rationalization ex- plains our results. More specifically, income and births do seem to exhibit a strong negative relation over our sample period - even aside from any indirect influence of income on contraceptive knowledge and use. Adding to this conclusion our earlier comments on the standardization for change in the cost of equal- quality children and the decrease in child mortality rates, our results do not support the Becker hypothesis.

Turning back to the regression results in table 1, we find that the employment of married women adds little to the equation; its coefficient is positive, but insignificant. Several lagged values of the marriage variables (M and AM) were used in order to investigate the lag structure involved in the relationship between births and marriages.5 In analyzing several versions not presented here, it was found that the effect of marriages (specified as either levels or first differences) declined in an approximately geometric fashion from a nine- through-twelve period lag; then, marriages lagged thirteen periods exerted an exceptionally strong influence. When the level of. marriages was used, this influence declined rather rapidly for values further in the past; when the first difference of marriages was used, the influence declined slightly through a lag of fifteen months, then peaked again at a lag of sixteen months, then declined geometrically. In order to take advantage of the consistent shape of the lag structures and to economize on the number of past values to be included, the lagged values exhibiting approximately geometrically declin- ing influence were omitted. The result of this procedure is that the influence of the excluded past values of marriages is forced to decline geometrically. Using the restricted estimation technique described above, the estimates de-

picted in table 1 were obtained. It appears that the response of births to variations in marriages is strong and fairly rapid. In version la (using AM) all of the coefficients on marriages are positive and highly significant. In version lb (using M) the coefficients on the level of marriages lagged nine and thirteen months are positive and significant.

The estimated equations presented in table 1 included variables standardizing for the flow of marriages. While their inclusion allowed us to focus on the direct effect of income on births, it could also introduce a statistical problem into the estimation. More specifically, if income and marriages are strongly related, the inclusion of both variables in the regression model would result in multicollinearity. To avoid this problem, the basic equation was respecified without the marriage variables. Given this modified specification, the coefficient on income will now represent the net impact of a change in permanent income operating on births both directly and indirectly (through its effects on marriages). The estimates of the revised model are presented in table 2. As should be expected, the coefficient on income is slightly less significant than it was in the

previous estimates; however, it retains its negative sign and is significant at the 0.05 level. This result suggests that even the net effect of variations in income is the opposite of that proposed by Becker.

TABLE 2. - ESTIMATES OF BIRTH EQUATION, WITHOUT MARRIAGES AS AN EXPLANATORY VARIABLE

Estimated Coefficient

Variable (t value)

Constant Term 167099.7

B(t-1) .53086 (7.550)

AYp(t-10) -720.77295 (2.329)

AEmw (t-10) 104.01506 (1.270)

AC(t-9) -95.33177

(3.743)

R2 .674 F 72.397 D.W. 2.08802

'Notice that the lag structure in these equations involves past values of marriages (either M or AM) with subscripts t- Vj for Vj - 9. Thus, we have deliberately ignored the more recent values (v < 9). The reason for such an omission is not that one does not observe births occurring after, say, five or six months of marriages; on the contrary, in some age brackets of mothers a sizeable percentage of first births occur within seven or eight months of the date of marriage. However, should we have included these shorter lags in the above equations we would have encountered an unfortunate problem of simultaneity. Our treatment avoids this.



DETERMINANTS OF AGGREGATE BIRTHS 497

Summary

Our estimates point strongly to the existence of a negative relationship between aggregate births and permanent income, and thus con- flict with Becker's hypothesis. There are un- doubtedly several possible rationalizations for this inconsistency. First, in terms of Becker's analysis, the income-elasticity of the quantity of children may be negative - even though total expenditures on children may be positively related to income. In order for this to be true, it would be necessary that the income-elasticity of child quality be higher than the income-elasticity of total expenditures on children. An- other (related) rationalization has to do with the nature of children as consumption goods. Although we do not object to this characteriza- tion, it would appear that some important modifications of this view need to be made. Most consumption-goods tend either to increase leisure time or to enhance the enjoyment of leisure time. As an example, durable goods such as dishwashers, vacuum cleaners, etc., re- lease families from some of the nonremunera- tive tasks of daily living. Thus, as income increases, the increasing marginal utility of leisure would tend to reinforce the desire to purchase time-saving devices. Other goods, such as automobiles, recreational equipment, etc., tend to augment the enjoyment of leisure time; thus, as income increases, some of the increment of income is likely to be spent on such items (in order that leisure can be used to its best advantage). In fact, it is difficult to think of any good traditionally viewed as a consumption good which does not fall into one of these categories. Children, however, may constitute an exception. No one would argue that, in a highly-urbanized economy, the in- creased "consumption" of children increases leisure time - on the contrary, the larger the

family, the less time is available to the decision-makers (parents) for leisure. One could argue that enjoyment of a given amount of leisure time increases as family size grows; however, this tendency may be offset by the negative relation between children and leisure time. If so, we might expect that increases in income, by increasing the marginal utility of leisure, actually tend to discourage conception. Thus, if one were to make no allowances for quality differences, children could be catego- rized as "inferior" goods.

REFERENCES

Becker, G. S., "An Economic Analysis of Fertility," in Demographic and Economic Change in Developed Countries (Princeton: Bureau of Economic Re- search, 1960).

Duesenberry, J. S., "An Economic Analysis of Fer- tility: Comment," in Demographic and Economic Change in Developed Countries (Princeton: Bureau of Economic Research, 1960).

Kirk, D., "The Influence of Business Cycles on Mar- riages and Birth Rates," in Demographic and Eco- nomic Change in Developed Countries (Princeton: Bureau of Economic Research, 1960).

Nerlove, M., "The Market for Durable Goods: Com- ment," Econometrica, XXIX (Jan. 1961).

Okun, B., "An Economic Analysis of Fertility: Com- ment," in Demographic and Economic Change in Developed Countries (Princeton: Bureau of Eco- nomic Research, 1960).

Ruggles, R., and N. Ruggles, "Differential Fertility in United States Census Data," in Demographic and Economic Change in Developed Countries (Prince- ton: Bureau of Economic Research, 1960).

Silver, M., "Birth, Marriages and Business Cycles in the United States," Journal of Political Economy, LXXIII (June 19-65), 237-255.

Thomas, D. S., "The Influence of Business Cycles on Marriages and Birth Rates: Comment," in De- mographic and Economic Change in Developed Countries (Princeton: Bureau of Economic Re- search, 1960).

, Social Aspects of the Business Cycle (New York: Knopf, 1927).



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