Testing for the onset of fertility decline: an illustration with the case of Egypt.

Zaky, Hassan ; Wong, Rebeca ; Sirageldin, Ismail 等

This paper describes and illustrates how the economic household production model can be taken as a frame of reference to test the stage of the fertility transition for a given society. Egypt during the 1970s and early 1980s is taken as the setting to illustrate the test. Egyptian fertility trends from the mid-1960s to the early 1980s puzzled demographers and social scientists. It was not known if Egypt was at the onset of a sustainable fertility decline by the early 1980s. The illustration exercise shows that the Egyptian household fertility behaviour during this period fits poorly with the model specification corresponding to a post-transition society. We find that fertility by the end of the 1970s was not endogenous to other household decisions, and conclude that a sustained decline in fertility was unlikely without this endogeneity. These results agree with previous literature on the fertility transition in Egypt. The paper concludes with limitations of the empirical test presented, laying emphasis on the lessons learned to examine the stage of the fertility transition in any society. The conclusions also highlight the importance of considering the stage of the transition in order to specify fertility models appropriately.

INTRODUCTION

The economic household production model assumes that households maximise utility under resource constraints-mostly time and income, and given a set of preferences. In essence, the household production model assumes that people behave rationally; that reproductive behaviour in particular is economically rationale within biological, psychological, and normative bounds. Individuals and households respond to price signals and allocate their activities and resources within these set bounds. The premise is the ability of the household to assign its life-cycle time resource among three ends: activities that increase the household members' market wage (that is, human capital), market production, and non-market production including leisure. Accordingly, the model implies simultaneous decisions on fertility and other demographic and economic factors such as contraceptive use and female labour force participation.

Applications of the model include those in developed- as well as developing-country settings [DeTray (1974); Khan (1979); Michael (1974)]. As [Easterlin (1975), p. 55] writes, "economics has clarified causal inter-relations, for example, few economists would speak of lower fertility 'causing' higher female labour force participation, or vice versa, but would view both magnitudes as simultaneously determined by other factors". It is argued, however, that one of the shortcomings of the household production model is that the outcome decisions modelled--such as fertility, contraceptive use, and female labour force participation--may not be a matter of choice for households in some societies. (1) Specially in pre-transition societies, many of these decisions present limited choices. The trade-off between fertility and other alternatives for time allocation by household members may be highly limited. Hence, in this context, the predictions of the household production model may not apply to all settings.

In the present paper, we argue that essentially three types of societies exist. One is of stable high fertility where households do not perceive a trade-off among the. various fertility-related household outcomes. The second society implies a post-transitional stage, where the household calculus of interdependent choices covers a wide range of economic and demographic behaviour. The third is a transitional society. It is our thesis that we could use the household production model as a frame of reference to test the stage of the fertility transition for a given society. If fertility as well as other decisions on the allocation of resources are simultaneous, then the society is in a post-transition stage. Alternatively, if the society is at the pre-transition stage, fertility decisions are made mainly in the perceived context of mortality restrictions and their biological consequences. The third type is context-specific, where some, but not all, household decisions are perceived under allocative control. In this sense, the weakness of the household production model mentioned above can yield useful statements on modelling fertility decisions for a given society: the conceptualisation of fertility models is different if the particular society under study is either in pre- or post-transition stage.

Egypt during the 1970s and early 1980s can be taken as the setting to perform the test. Egyptian fertility trends from the mid-1960s to the early 1980s have puzzled demographers and social scientists. The main puzzle is the steady decline in the crude birth rate between 1964 and 1972, followed by a steady rise through the early 1980s. Several factors can account for this reversal of trend. These include the presence of difficult economic and social factors, such as the absence of husbands and reduced incomes during the inter-war period, from 1967 to 1973. Such explanations, although fitting conceptually with the general prediction of the household production framework, lack an adequate explanation for the full phenomenon. Bucht and El-Badry (1986) illustrated that the bulk of change in the crude birth rate could be due to the change in the age structure resulting from historical mortality and fertility experiences.

The analysis of Bucht and El-Badry questioned significant changes in the fertility behaviour during the three decades following World War II. Based on the 1980 Egyptian Fertility Survey, recent attempts to examine demographic responses to modernisation did not give a clear picture of the Egyptian demographic transition [Hallouda, Farid and Cochrane (1988)]. For example, husband's and wife's education were non-significant in models of the determinants of demand for children [Cochrane, Khan and Osheba (1988)]. However, in the analysis of the determinants of contraceptive use, female education opportunities were significant while the analysis ".. demonstrated convincingly that measures of female employment show [ed] no net effects on use" [El-Deeb and Casterline (1988), p. 569]. Easterlin, Crimmins and Osheba (1988) illustrated the importance of motivation in determining fertility regulation, while income "added surprisingly little" to the analysis of the impact of modernisation on the motivation for fertility control [Easterlin, Crimmins, Ahmed and Soliman (1988), p. 671]. Analyses of age at marriage and age difference among spouses found contradictions, leading [Sokona and Casterline (1988), p. 129] to conclude that "our understanding of the determinants of the age difference is poorly developed". In their analysis of the determinants of birth interval length, [Trussell, Vaughan and Farid (1988), p. 152] emphasised the importance of the biological determinants in Egypt. Their analysis "... found that female education [was] not a significant determinant of the risk of pregnancy; this (lack of significance) is almost surely due to the effects of biological factors." Other findings on infant and child mortality illustrate the lack of consistent behavioural patterns [for example, Callum and Cleland (1988); Eid and Casterline (1988)].

It is evident from this brief survey that whether Egypt had been at the onset of a sustainable fertility decline by the early 1980s was unknown. The purpose of the present paper is to illustrate that it is possible to test if this was the case, using the approach described. First, the paper will present the specification of alternative models according to the stage of fertility transition (post-transition and pre-transition). Next, we describe the data set available to perform the test. We present the estimation techniques in the following section, followed by the empirical findings. At the end, we provide the discussion and conclusions.

It is worth mentioning that the main purpose of this paper is not to add new knowledge to the subject of fertility transition in Egypt. Rather, the purpose is to illustrate, with the case of Egypt, how the predictions of the household production model can be used to test empirically the stage of the fertility transition in a given society.

MODEL SPECIFICATION

Our approach is to examine fertility as a long-term decision, instead of using a sequential decision-making approach. We condense a couple's life cycle to one period; changes occurring during the life cycle are ignored for the present investigation. Accordingly, our focus is on couples who completed their desired family size by the end of the 1970s. Hence, we study fertility from a completed-family-size perspective, and we associate this variable with lifetime variables as well, such as indicators of wealth and lifetime income, attained education, ever-use of contraception, cumulative deaths, and ever-employment of the woman. We use the household production model as our frame of reference, and model a series of household-demand functions. We present below the empirical specifications of the two models, post- and pre-transition. Other specifications are presented in Zaky (1989).

Post-Transition: Model I

For the transition from high to low fertility to become sustainable, the relationship among a significant set of family size decisions becomes integrated, re-enforcing, and simultaneously determined in a behavioural context. These family size decisions include fertility, contraceptive use, child mortality, female labour force, and income. Families are assumed to control their resource allocation decisions, subject to basic resource constraints. Under such household production regime, it is assumed that family size variables are choice variables, fertility being one of them. This approach has long been recognised in the economic demography literature [Cochrane, Khan and Osheba (1988); Khan and Sirageldin (1975); Sirageldin et al. (1976); Schultz (1978)]. Studies have concluded that fertility determination should be estimated within a system of simultaneous equations. Hence, the post-transition specification considers that a group of family decisions are endogenous to the fertility decision. In our analysis, these family decisions are: contraceptive use, child mortality, female labour force, and income. The exogenous variables in our models include variables both at the household and community levels, capturing aspects of the opportunity cost of time, relative prices, social norms, and household preferences. A brief elaboration of the choice variables follows.

The decisions on income are assume as endogenous to the fertility decision [Mueller and Short (1983)], since husbands may work longer hours and increase their earnings as a response to more children. Also at the post-transition stage, decisions on fertility are made simultaneously with those on the allocation of time towards market activities by women. Hence, female labour force is endogenous to fertility decisions [Lee and Bulatao (1983); Schultz (1978)]. Child mortality is an important determinant of the supply of children [Bongaarts and Menken (1983)]. And it has been recognised as simultaneously related to fertility, where the effect of fertility on mortality is mainly biological, while the effect of mortality on fertility is assumed as behavioural. Decisions on the use of contraception are assumed to be made in the context of fertility decisions as well [DeGraff (1991); Easterlin and Crimmins (1982)]. An excess of number of children in relation to the desired number would motivate the use of contraception.

Pre-Transition: Model II

In traditional societies with relatively high fertility rates, fertility is only partly controlled, and dominated by factors external to the family decision process. These factors can be norms, culture, and biological constraints. In such regimes, the family decisions on fertility (family size, contraception, child mortality, female employment, and income) have not reached the stage of being family choice variables. They can be considered as ascribed decisions, and hence knowledge on fertility can be gained by a simple approach where only fertility and mortality are outcome variables. Hence, for the pre-transition stage, the empirical specification would be a system of two equations, one for fertility and one for mortality. As mentioned earlier, fertility decisions are made mainly in the perceived context of mortality restrictions and the biological consequences. In this stage, fertility and mortality are closely inter-related through biological factors.

DATA SET

We use the Egyptian Fertility Survey (EFS), conducted in 1980 by CAPMAS [CAPMAS (1983)]. Questionnaires were completed for 8,788 ever-married women. A second phase of the EFS included a sub-sample of about one-third of the households interviewed in the first phase, covering a sample of 2,532 households. This second phase of the survey included an economic, a husband's, and community (for rural areas only) questionnaires. The data we use includes information from both phases. We also note that our data set is cross-sectional, failing to provide any time-sequence of events, especially among the endogenous variables. Hence, we are confined to a study of association rather than causation.

Our sub-sample of analysis includes ever-married women between 35 and 49 years of age. We use this age group to get women with completed family size. We restrict the analysis to those couples who, by virtue of the wife's age, will have a low probability of having any more children. This group of couples, however, may include women who want more children. Accordingly, we further limit the analysis to those women who are fecund, in union, exposed to the risk of conception, and do not desire additional children. This definition of our sample may imply a possible selection bias in our estimates. Our sub-sample includes 518 ever-married women who satisfy the previous conditions. In this group of women, as is shown in Table A1 in the Appendix, women have an average of 6.7 children ever-born, and have experienced 1.5 child deaths per woman. Ever-use of contraception is 71 percent, while only 18 percent of the women had ever-worked since marriage. Forty-seven percent of the women live in rural areas, they have an average of 2 years of education, and 82 percent have never been employed while in union. Their average age is 40 years and 48 years for the husbands. Appendix I presents a list of the variables used in our analysis.

METHODS OF ESTIMATION

Model I

The specification of the model for fertility decisions under the post-transition regime represents a system of simultaneous equations. The specification corresponds to the one discussed in Khan and Sirageldin (1975). The model considers five variables as endogenous and includes 17 exogenous variables, as follows:

(1) Fertility Equation

CEB = f1 (EUSE, CHDD, WEMP, FAMC, AGR, RES, PNRM, MACH, PRES, AGEW, YSIN, WBML, HEMP, YWUC, YHUC).

(2) Contraceptive Equation

EUSE = f2 (CEB, CHDD, WEMP, FAMC, AGR, WATE, ELEC, TRAN, PRES, AGEW, AGEH, WBML, HEMP, YWUC, YHUC).

(3) Mortality Equation

CHDD = f2 (CEB, WEMP, FAMC, AGR, PNRM, WATE, ELEC, MACH, TRAN, PRES, YSIN, HMIG, HEMP, YWUC, YHUC).

(4) Female Labour Force Participation Equation

WEMP = f4 (CEB, CHDD, FAMC, AGR, MACH, TRAN, PRES, AGEW, AGEH, HMIG, WBML, HEMP, YWUC, YHUC).

(5) Income Equation

FAMC = f5 (CEB, WEMP, AGR, RES, PNRM, WATE, ELEC, MACH, TRAN, PRES, AGEH, HMIG, HEMP, YWUC, YHUC).

The definition of variables is given in Appendix I.

The five endogenous variables include two count variables, children ever born and child deaths; two dichotomous variables, ever use of contraception and female ever employment; and a continuous variable, the lifetime income proxy.

Model II

The specification of the model for fertility decisions under the pre-transition regime is given by a system of two equations as follows:

(6) Fertility Equation

CEB = f1 (CHDD, AGR, RES, PNRM, MACH, PRES, AGEW, YSIN, WBML, HEMP, YWUC, YHUC, EUSE, WEMP, FAMC).

(7) Mortality Equation

CHDD = f2 (CEB, AGR, PNRM, WATE, ELEC, MACH, TRAN, PRES, YSIN, HMIG, HEMP, YWUC, YHUC, WEMP, FAMC).

The specification of the system of equations for both models implies identification; the number of exogenous variables excluded from each equation in the model is at least as great as the number of endogenous variables included minus one. For both Models I and II, we estimate the structural forms of the equations in a simultaneous system. We use tobit regression techniques for the fertility and mortality equations, probit for the contraceptive-use and employment equations, (2) and least squares for the income equation using a two-stage estimation procedure. (3) After presenting the two-stage estimates of the structural forms for Models I and II, we also present the single-equation estimates for the fertility equation in Model II. The latter, a single-equation specification, assumes that all explanatory variables are exogenous to fertility in the pre-transition stage.

EMPIRICAL RESULTS

Model I

Table 1 shows the parameter estimates of the structural form of the five-equation system. Column 1 presents the estimates for the fertility equation, which included all the other endogenous variables (fertility, mortality, female labour force, and income). The results show no evidence of a significant relationship between the endogenous variables included in this equation and fertility. However, longer duration of marriage, ownership of residence, and higher crowdedness are associated with more children ever born. We note that women who are older and with more education have lower fertility.

Column 2 of Table 1 shows the results for ever-use of contraception, with a specification including four endogenous factors as explanatory variables (fertility, mortality, female labour force, and income). The estimates reflect that the availability of water and electricity increase the probability of ever-using a contraceptive method. Among the endogenous variables included in this equation, children ever born, woman's employment, and income are not significant, whereas child mortality is positively related to contraceptive use.

The results for the mortality equation are given in Column 3 of Table 1. This equation includes three endogenous variables (fertility, female employment, and income). The results show that the availability of a machine in the household and higher crowdedness are negatively related to child mortality, while longer duration of marriage leads to more child deaths, as expected. Surprisingly, no endogenous variables are significant.

For the labour force participation equation, the results are given in Column 4 of Table 1. Explanatory variables in this equation include three endogenous variables (fertility, mortality, and income). The results suggest that wife's education and employment before marriage are significant determinants of female employment among these women. No significant endogenous variables are found, except for child mortality. More child deaths decrease the likelihood of women to ever-work, agreeing with a priori expectations.

Column 5 of Table 1 shows the results for the income equation. This equation includes the endogenous variables corresponding to fertility and labour force participation. Higher income is associated with higher husband's age, more education of both spouses, residence in urban areas, availability of a means of transport, and ownership of agricultural land. A higher number of children ever born is associated with lower income.

Model II

The model includes a system of two equation: one for fertility and one for mortality, and each is contained in the other equation. In Egypt, a traditional society with relatively high fertility rates, we would expect the effect of fertility on mortality, which is mainly biological in nature, to be positive. The effect of mortality on fertility, which is mainly behavioural in nature, is expected to be positive. The estimation results shown in the first two columns of Table 2 reflect no significant effects from mortality on fertility, or vice versa.

The third column of Table 2 shows the results of the single-equation estimation procedure for the fertility equation. This single-equation approach considers all explanatory variables as exogenous to fertility. The results show that ever-use of contraception, family income, and child mortality are positively related to completed fertility. This is in line with other empirical work [Schultz (1976)].

The relationship between fertility and female employment (WEMP) appears as non-significant in the results of Model I and Model II. To a certain extent, this result is expected as female employment in its "formal" definition in rural Egypt is rare. Female labour participation is mainly confined to the family's farm and this participation is unrelated to fertility behaviour. The positive association between ever-use of contraception and completed fertility supports the idea that contraception in Egypt is mainly used to stop having more children rather than to space births.

The positive association between income and fertility supports the hypothesis that more children may pressure families to work more and earn more [Mueller and Short (1983)].

DISCUSSION AND CONCLUSIONS

We examine the correlates of family size decisions in Egypt, using data on women who completed their desired family size by the end of the 1970s. We find that family size decisions had not yet reached the stage of being fully controlled within the family's allocative decisions. The perception of the household as utility maximiser may be correct, but many of the essential parameters in household production decisions are exogenous to fertility behaviour. Income, female work, and ever-use of contraception are not perceived as under the control of the household decision-maker(s), especially as part of their family size behaviour.

The Egyptian household fertility behaviour during this period cannot be represented adequately by a simultaneous system of equations. A single-equation model performs better in representing our expectations and in identifying the determinants of fertility.

Often, conceptual differences between Model I (post-transition) and Model II (pre-transition) are detected. All endogenous variables included in the fertility equation in Model I are insignificant, while the same ones are significant (except for female employment) with the expected signs in the single-equation approach of Model II.

To the extent that the coverage of the EFS data is sufficient for our purposes, that we can capture the main factors by proxy variables, and that we restrict the analysis to women with completed fertility, we can draw guarded conclusions from the analyses.

In conclusion, we have argued that it is possible to test the stage of the transition for a given society, and have illustrated this point for Egypt. We find that in Egypt, given the data set used and the time frame the data represents, fertility by the end of the 1970s was not endogenous to other household decisions. Accordingly, we do not expect a dramatic decline in fertility without this endogeneity. The findings support the general conclusions of Bucht and El-Badry (1986) and Trussell et al. 0988) about the importance of the biological determinants of fertility. The predictions of the economic model of household production to model fertility do not apply to Egypt during the period of our analysis. This is probably because there were limitations to the choices offered to households: the economic costs of fertility were not perceived fully by the households as under their allocative control.

It seems that traditional roles within and between generations continued to be deeply rooted in the Egyptian society through the 1970s [Tuma (1988)]. But this conclusion requires another test to assess if the events of the late 1970s and the 1980s would lead to change.

Given the limitations of the data set we used, and the possible questions on the adequacy of some of the measures to capture the concepts stipulated by the theoretical models, we interpret our results with extreme caution. We repeat, however, that the main purpose of the empirical exercise in this paper was not to add new knowledge on fertility in Egypt, but rather to illustrate the use of empirical tests to identify the stage of the transition for a given society.

We also conclude that the specification of fertility models, specially for developing countries, should focus on more details of other outcome variables. As has been previously argued in the literature, the specification should vary according to the stage of the fertility transition in the given society. Also, the exogeneity of outcomes (such as contraceptive use and female labour force participation) can be better specified, as can the role of the determinants of these outcomes in the fertility model. If for example, contraceptive use is exogenous to fertility, then the price of contraception would not be an effective constraint for the household fertility decisions.

Appendix I

DEFINITION OF VARIABLES

CEB : Total number of live births.

EUSE : Dummy variable with a value 1 if the wife has ever used a contraception method and zero otherwise.

CHDD : Total number of child deaths under five years of age.

WEMP: Dummy variable with a value 1 if the wife has ever worked while in union and zero otherwise.

FAMC : Current monthly family expenditure in Egyptian Pound (L. E.).

CUSE : Dummy variable with a value 1 if the wife is currently using a contraception method and zero otherwise.

AGR : Dummy variable with a value 1 if the family owns an agricultural land and zero otherwise.

RES : Dummy variable with a value 1 if the family owns their current residence and zero otherwise.

PNRM : Number of persons per room in the residence.

WATE : Dummy variable with a value 1 if the source of drinking water is a faucet located in the residence or outside the residence but inside structure and zero otherwise.

ELEC : Dummy variable with a value 1 if there is electricity in the residence and zero otherwise.

MACH: Dummy variable with a value 1 if there is a radio set, or television, or gas stove, or water heater, or telephone, or sewing machine, or refrigerator in the residence and zero otherwise.

TRAN : Dummy variable with a value 1 if there is a bicycle, or a motorcycle, or a car in the residence and zero otherwise.

PRES : Dummy variable with a value 1 if the current place of residence is urban and zero otherwise.

AGEW: Wife's age in completed years.

AGWG: Wife's age at first marriage.

YSIN : Years in union.

AGEH : Husband's age in completed years.

HMIG : Dummy variable with a value 1 if the place of birth of husband is different from PRES or whether the husband is working abroad and zero otherwise.

WBML: Dummy variable with a value 1 if the wife was working before marriage and zero otherwise.

HEMP : Dummy variable with a value 1 if the occupation of husband is professional, or clerical, or sales, or skilled labour and zero otherwise.

YWUC: Education of wife in years.

YHUC : Education of husband in years.

Table A1
Descriptive Statistics of the Main Variables
Ever-married Women Ages, 35-49 (a)

Explanatory
Variables and Mean Standard
Expected Signs (a) Deviation

Children Ever Born 6.75 (2.51)
Ever Use of Contraception 0.71 (0.45)
Current Use of Contraception 0.48 (0.50)
Child Deaths 1.51 (1.63)
Female Employment 0.18 (0.38)
Monthly Family Expenditure 54.35 (41.70)
Ownership of Agricultural Land 0.23 (0.42)
Ownership of Current Residence 0.60 (0.49)
Number of Persons per Room 2.59 (1.41)
Availability of Water 0.49 (0.50)
Availability of Electricity 0.74 (0.44)
Availability of Durable Goods 0.82 (0.39)
Availability of Means of Transport 0.18 (0.34)
Place of Residence 0.53 (0.50)
Wife's Age in Years 39.88 (3.81)
Wife's Age at Marriage in Years 17.27 (4.02)
Years in Union 22.15 (5.15)
Husband's Age in Years 48.12 (7.27)
Husband's Migration History 0.24 (0.42)
Pre-marriage Wife's Employment 0.14 (0.35)
Husband's Employment 0.50 (0.50)
Wife's Education in Years 2.30 (3.74)
Husband's Education in Years 3.91 (5.20)
Sample Size N 518

(a) The sample includes women who are ever-married, aged 35-49
years, fecund, in union, exposed, and do not desire additional
children.

Authors' Note: We appreciate the comments made by the referees and have addressed their concerns in preparing the final version of the paper.

REFERENCES

Amemiya, T. (1974) Multivariate Regression and Simultaneous Equation Models when the Dependent Variables are Truncated Normal. Econometrica 42:6 999-1012.

Bongaarts, J., and J. Menken (1983) The Supply of Children: A Critical Essay. In A. Bulatao and R. D. Lee (eds) Determinants of Fertility in Developing Countries. (Volume 1.) New York: Academic Press pp. 27-60.

Bucht, B., and M. A. El-Badry (1986) Reflections on Recent Levels and Trends of Fertility and Mortality in Egypt. Population Studies 40:101-113.

Callum, C., and J. Cleland (1988) The Effect of Birthspacing on Infant and Child Mortality. In A. M. Hallouda et al. (eds) Demographic Responses to Modernization. Cairo: CAPMAS pp. 215-238.

CAPMAS (1983) The Egyptian Fertility Survey 1980. Cairo: Central Agency for Public Mobilisation and Statistics in Egypt.

Cochrane, S., M. A. Khan and I. Osheba (1988) The Determinants of the Demand for Children among Husbands and Wives. In A. M. Hallouda et al. (eds) Demographic Responses to Modernization. Cairo: CAPMAS pp. 353-385.

DeTray, D. N. (1974) Child Quality and the Demand for Children. In Theodore W. Schultz (ed) Economics of the Family. Chicago: The University of Chicago Press.

DeGraff, D. S. (1991) Increasing Contraceptive Use in Bangladesh; The Role of Demand and Supply Factors. Demography 28:1 February 65-81.

Duesenberry, J. S. (1969) Comment. In Demography of Economic Change in Developed Countries. New York: NBER pp. 31.

Easterlin, R. A. (1975) An Economic Framework for Fertility Analysis. Studies in Family Planning 6: 54--63.

Easterlin, R. A., and E. M. Crimmins (1982) An Exploratory Study of the "Synthesis Framework" of Fertility Determination with World Fertility Survey Data. The Hague, Netherlands: International Statistical Institute.

Easterlin, R. A., E. M. Crimmins and I. T. Osheba (1988) Determinants of Fertility Control. In A. M. Hallouda et al. (eds) Demographic Responses to Modernization. Cairo: CAPMAS pp. 609-644.

Easterlin, R. A., E. M. Crimmins, M. A. Ahmed and S. M. Soliman (1988) The Impact of Modernization on the Motivation for Fertility Control. In A. M. Hallouda et al. (eds) Demographic Responses to Modernization. Cairo: CAPMAS pp. 645-673.

Eid, I., and J. B. Casterline (1988) Differentials in Infant and Child Mortality. In A. M. Hallouda et al. (eds) Demographic Responses to Modernization. Cairo: CAPMAS pp. 179-214.

El-Deeb, B., and J. B. Casterline (1988) Determinants of Contraceptive Use. In A. M. Hallouda et al. (eds) Demographic Responses to Modernization. Cairo: CAPMAS pp. 527-573.

Hallouda, A. M., S. Farid and S. H. Cochrane (eds) (1988) Demographic Responses to Modernization. Cairo: CAPMAS.

Khan, A. (1979) Relevance of Human Capital Theory to Fertility Research: Comparative Findings for Bangladesh and Pakistan. In I. Sirageldin (ed) Research in Human Capital and Development. (Volume 1.) Greenwich, Connecticut: JAI Press Inc. pp. 3-43.

Lee, L. F. (1981) Simultaneous Equations Models with Discrete and Censored Dependent Variables. In C. F. Manski and D. McFadden (eds) Structural Analysis of Discrete Data with Econometric Applications. Cambridge: MIT Press pp. 346-364.

Lee, R. D., and R. A. Bulatao (1983) The Demand for Children: A Critical Essay. In R. A. Bulatao and R. D. Lee (eds) Determinants of Fertility in Developing Countries. (Volume 1.) New York: Academic Press pp. 233-287.

Michael, R. T. (1974) Education and the Derived Demand for Children. In Theodore W. Schultz (ed) Economics of the Family. Chicago: The University of Chicago Press.

Mueller, E., and K. Short (1983) Effects of Income and Wealth on the Demand for Children. In R. A. Bulatao and R. D. Lee (eds) Determinants of Fertility in Developing Countries. (Volume 1.) New York: Academic Press pp. 590-642.

Nelson, F., and F. Olson (1978) Specification and Estimation of a Simultaneous Equation Model with Limited Dependent Variables. International Economic Review 19:3 695-709.

Schultz, T. P. (1976) Determinants of Fertility: A Microeconomic Model of Choice. In A. J. Coale (ed) Economic Factors in Population Growth. London: Macmillan.

Schultz, T. P. (1978) The Influence of Fertility on Labor Supply of Married Women: Simultaneous Equation Estimates. Research in Labor Economics 2: 273-351.

Sokona, O., and J. B. Casterline (1988) Socio-economic Differentials in Age at Marriage. In A. M. Hallouda et al. (eds) Demographic Responses to Modernization. Cairo: CAPMAS pp. 101-132.

Trussell, J., B. Vaughan and S. Farid (1988) Determinants of Birth Interval Length. In A. M. Hallouda et al. (eds) Demographic Responses to Modernization. Cairo: CAPMAS pp. 133-158.

Tuma, E. H. (1988) Institutional Obstacles to Development: The Case of Egypt. World Development 16:10 1185-1198.

(1) Duesenberry (1969) provided an early critique of the household production model.

(2) In censored, truncated, and qualitative endogenous variables, the assumption is that the non-observed variables are continuous and with a normal distribution. For dichotomous observed variables, we use probit estimation techniques, while for polychotomous observed variables, we use tobit techniques.

(3) The procedure, when applied with tobit and probit techniques, is analogous to the two-stage least squares, and yields consistent and asymptotically normal parameter estimates. It has been suggested and applied, for example, by Amemiya (1974); Lee (1981); Nelson and Olson (1978).

Hassan Zaky is associated with the Department of Statistics, Faculty of Economics and Political Science, Cairo University, Giza, Egypt: Rebeca Wong is Assistant Professor and Ismail Sirageldin is Professor in the Department of Population Dynamics, The Johns Hopkins University, 615 N. Wolfe Street, Baltimore, MD 21205, USA.

Table 1
Estimates for Structural Form Parameters of Model 1
Ever-married Women Ages 35-49
Egyptian Fertility Survey, 1980

 Dependent Variable
Explanatory
Variables and (1) (2)
Expected Fertility Contraception
Signs * (CEB) (EUSE)

Constant 3.466 *** -1.402 -0.548 -1.512
AGR + 0.319 -0.268 0.019 -0.494
RES + 0.949 *** -0.261
PNRM + 0.252 *** -0.083
WATE 0.750 ** -0.295
ELEC 0.611 *** -0.219
MACH ? -0.543 * -0.326
TRAN 0.164 -0.749
PRES - -0.324 -0.297 0.136 -0.311
AGEW ? -0.056 * -0.034 -0.019 -0.031
YSIN + 0.218 *** -0.035
AGEH ? -0.003 -0.022
HMIG ?
WBML ? -0.585 -0.821 -0.294 -0.825
HEMP ? 0.178 -0.241 0.088 -0.261
YWUC - -0.113 * -0.066 0.011 -0.097
YHUC - -0.061 -0.040 -0.019 -0.073
CEB (b) 2.550 -2.944
EUSE (b) + 0.829 -0.726
CHDD (b) + -0.603 -0.891 1.069 * -0.608
WEMP (b) ? 1.158 -1.461 0.084 -1.252
FAMC (b) + 0.002 -0.012 0.012 -0.029

PROCEDURE TOBIT PROBIT

LOG-LIKELIHOOD -1061.2 -225.59
DEGREES OF
 FREEDOM 502 502
N 518 518

 (3) (4)
 Mortality Female Labour
 (CHDD) (WEMP)

Constant -0.736 -0.664 -0.364 -1.560
AGR + 0.249 -0.508 0.553 -0.561
RES +
PNRM + -0.139 * -0.079
WATE -0.251 -0.373
ELEC -0.125 -0.303
MACH ? -0.594 ** -0.297 0.474 * -0.271
TRAN 0.019 -0.725 0.900 -0.865
PRES - 0.214 -0.379 0.396 -0.385
AGEW ? 0.024 -0.036
YSIN + 0.155 *** -0.043
AGEH ? -0.002 -0.025
HMIG ? 0.243 -0.260 0.328 -0.231
WBML ? 1.537 *** -0.275
HEMP ? 0.316 -0.301 -0.256 -0.269
YWUC - 0.010 -0.116 0.225 * -0.126
YHUC - -0.075 -0.076 0.129 -0.090
CEB (b) -3.488 -4.666 -0.499 -1.576
EUSE (b) +
CHDD (b) + -1.467 ** -0.713
WEMP (b) ? 0.544 -0.618
FAMC (b) + -0.016 -0.031 -0.052 -0.037

PROCEDURE TOBIT PROBIT

LOG-LIKELIHOOD -921.98 -119.90
DEGREES OF
 FREEDOM 502 503
N 518 518

 (5)
 Income
 (FAMC)

Constant -8.235 -11.26
AGR + 14.059 *** -3.642
RES + -1.894 -3.594
PNRM + -0.513 -1.103
WATE 3.010 -4.510
ELEC -4.614 -3.832
MACH ? 3.541 -4.160
TRAN 22.355 *** -4.242
PRES - 7.501 * -4.288
AGEW ?
YSIN +
AGEH ? 0.713 *** -0.189
HMIG ? 3.521 -3.227
WBML ?
HEMP ? 4.739 -3.493
YWUC - 3.758 *** -0.571
YHUC - 2.443 *** -0.390
CEB (b) -55.198 ** -22.64
EUSE (b) +
CHDD (b) +
WEMP (b) ? -3.337 -6.763
FAMC (b) +

 LEAST-
PROCEDURE SQUARES

LOG-LIKELIHOOD -2493.0
DEGREES OF
 FREEDOM 502
N 518

Standard errors are in parentheses.

* 0.05 < P value < = 0.10.

** 0.01 < P value < = 0.05.

*** P value < = 0.01.

(a) The expected signs refer to the direction
of the expected effects of endogenous and
exogenous variables on fertility.

(b) Endogenous variable.

Table 2
Estimates for Structural Form Parameters of Model II
Ever-married Women Ages 35-49
Egyptian Fertility Survey, 1980

 Single-
 equation
 Two-equation Model Model
Explanatory
Variables and (1) (2) (3)
Expected Fertility Mortality Fertility
Signs (a) (CEB) (CHDD) (CEB)

Constant 3.948 *** -0.647 2.985 ***
AGR + 0.274 0.024 0.309 *
RES + 0.920 *** 0.878 ***
PNRM + 0.292 *** -0.116 0.328 ***
WATE -0.386
ELEC 0.007
MACH ? -0.412 -0.603 ** -0.138
TRAN -0.345
PRES - -0.349 0.071 -0.251
AGEW ? -0.066 ** -0.060 **
YSIN + 0.219 *** 0.137 *** 0.150 ***
AGEH ?
HMIG ? 0.188
WBML ? 0.178 -0.027
HEMP ? 0.095 0.202 0.014
YWUC - -0.095 *** -0.031 -0.084 ***
YHUC - -0.055 ** -0.107 *** -0.016
EUSE + 0.588 *** 0.714 ***
WEMP ? -0.191 0.006 -0.095
FAMC + 0.003 -0.002 0.004 **
CEB -3.144 (b)
CHDD + -0.737 (b) 0.789 ***

PROCEDURE TOBIT TOBIT TOBIT
LOG-LIKELIHOOD -1058 -923 -939
DEGREES OF
FREEDOM 502 502 502
N 518 518 518

* 0.05 < Pvalue < = 0.10.

** 0.01 < Pvalue < = 0.05.

*** P value < = 0.01.

(a) The expected signs refer to the direction of the
expected effects of endogenous and exogenous variables
on fertility.

(b) Endogenous variables.