JOURNAL OF RESEARCH IN NATIONAL DEVELOPMENT VOLUME 8 NO 1, JUNE, 2010
FERTILITY BEHAVIOR OF HOUSEHOLDS AND NIGERIA’S POPULATION POLICIES
Njiforti Peter and Hamzat Soliu
Department of Economics, Ahmadu Bello University, Zaria
Email: njifortica@yahoo.com
Abstract Keywords: Fertility, population, household, family size 
Introduction
Mainstream economists, during the last forty years of the last millennium, view socioeconomic phenomenon like crime, rising human number, prostitution e.t.c strictly as a choice problem Glaeser(1999). They therefore explain them through a choice paradigm developed by Gary Becker (1960). Policy makers and bureaucrats especially in developing countries like Nigeria have, since then, based several policies on the premises over which the choicetheoretic approach is laid.
Like many other policy prescriptions (e.g Structural Adjustment Programme(SAP)) adopted from international development partners (World Bank,USAID,DFID and IMF ), there are indication that Nigeria’s population policies the first in 1988 targeted 4 children per family and the second in 2004 targeted 2% growth rate were founded on Becker styled choice theoretic model made popular by these institutions .
The first evidence is that the policies are follow up to SAP and Poverty Reduction Strategic Papers(PRPS) prescribed to Nigeria by World Bank. The second is that the US Agency for International Development (USAID) provided US $67 million of the US $100 million allocated for family planning programme in the implementation of the policy (Mazzocco, 1988).The third is that the policies aligned strongly with neoliberal policies advocated by these institutions because they hold (in common) most of the underlying assumptions of an economic man.
Meanwhile, these population policies have not successfully (in terms of their respective targets) checked the rate of rising human number in Nigeria (RedOrbit,2004). It follows that if the implementations process of the policies are ineffective, then the theoretical conception underlying the policies are ab initio not valid. This is in line with Garba’s (2003) assertion that “economic policy action and economic policy successin terms of stated goalsare contingent on the knowledge embodied in the economic doctrine from which policy predictions derive”
This paper is therefore written to assess the validity or otherwise of the theoretical construct underlying the policies with the view of explaining rising human number in Nigeria. To achieve this, the authors, raised a metaphysical(issue of existence) question with regard to demand function for children.
Other than this introductory section, there are other five sections in this paper. The second section review literature and opens the gap in literature. Section three discusses the theoretical framework of the paper. Section four and five respectively discusses the methodology and the results of analysis. We summarize our discussions and conclude in section six
Literature review
When applied to children, the theory of demand holds that demand for children is a function of prices of goods/ services used in raising children, child services to parents and parents income ceteris paribus Schultz (1973).This position is a product of economists’ view of children as durable goods (i.e basic form of human capital) whose production in the household is a function of parents’ time allocated between market and nonmarket activities. Each household is therefore assumed to make choice regarding the number of children that will maximize its utility from the productive activity of children bearing and other market activities. With little qualifications, economists like Willis (1973) ,De Tray(1973),Becker(1973) and many others characterized demand for children or tradeoff between quality and quantity of children in the above manner.
However, these neoclassical theories of fertility have one common fundamental problem: imposition of the assumption of the existence of utility function and hence demand for children. By this assumption people are presumed to have convex preferenceorderings for family sizes and that their choices are transitive and consistent. It is possible, however, for behavior in the real world to be at odds with these axioms (Spengler, 1966). If it does, there would be shift in people’s preferences and perceptions and this would make nonsense of the notion of a demand function of the usual sort (Earl, 1983).
Shone (1975) offered a full exposition of the assumed axioms in the choice theoretic paradigm and Kahnemann and Tversky (1979) applied it through a money related goods to test whether the usual demand function really holds. Several attempts have also been made to validate the theory of demand through axioms of choice by using other ‘goods/services’. For example, in an attempts to find out whether people’s behavior is consistent with the model of utility maximization, utility and demand function, Choi, Fisman and Gale (2005) used financial securities as goods and the Generalized Axioms of Revealed Preference(GARP) as the normative rule of choice was put to test.
In a recent study Chen, Lakshminarayanan and Santos (2006) used capuchin monkeys to show that decision makings rules are basic to all animals. The researchers introduced fiat currency to the monkeys and teach them how to exchange it for food. The conclusion is that rational behavior is not unique to human being.
Other than purely economic factors , some other studies have attempted to explain fertility behavior of people through religion(Tanturri and Mencarini,2008), religiousness( Westoff and Frejka (2007) ,intrafamily ties(Alesina and Giuliano,2007), kingship ties (Smith ,2004) , values ( McQuillan ,2004), child mortality (Benefo and Schultz,1996)and other ethnoregional factors.
Theoretical model
The authors modeled demand for children from the primitive concepts of axioms of choice in order to establish the criteria for holding and believing that demand function actually exist.
Assume the following options
A: jth number of children or B: kth number of children
among χ conceivable number of children available to a person within his/her life span.
Choices in the real practical world are associated with some level of uncertainties. The associated uncertainties are assumed to be the prices the agents pay for their respective choices. These uncertainties are, here, characterized as probabilities α and β of being able to raise and give the children University education. Nothing is special about “University Education” used here .It only serve as a common denominator to bring the values underlying the options at par.
We now rephrase the options to indicate their respective associated level of uncertainty as follows::
A*: jth number of children with α probability of raising and giving them University Education
or
B*: kth number of children with β probability of raising and giving them University Education
Referred to as compound probabilities, the probability of choosing to have jth and kth children are respectively given as
α*= μα+(1μ)β(1)
β*=(1μ)α+β(1μ)(2)
The expected value of the options A* and B* are therefore respectively given as
g1= α*A+ (1 α*)B (3)and
g2= β*A+(1 β*)B(4). g1 and g2 are referred to as gambles in the literature(Reny and Jehle(2000).
Given the foregoing, the axioms of rational choice at tested in this paper( axiom of independence ) states that an agent’s preference between two uncertain outcomes should be the same with his/her preference between their prices (i.e pay off). This can simply be represented as follows: for all A, B Є χ
if A is preferred to B then
g1= α*A+(1 α*)B must be preferred to g2=β*A+(1 β*)B
To formalize the idea, for all choices where
A > B and
g1 > g2 , we say the choice is rational.
Also, for all choices where
A>B and
g1 < g2 , we say the choice is irrational.
Methodology
To adequately capture all the parameters of theoretical model, this research is designed around a quasiexperiment where the same sets of respondents are exposed to two different sets of optional stimuli. The first set of stimulus is represented by option A or B (shown above).Here, there is no uncertainty associated the available jth or kth number of children to choose from. The second set of stimulus is represented by option A* or B*(shown above).
In other words, the questions are designed in such a way as to show whether the preference of an agent between two uncertain options would be the same with his preference for their payoff (prices). Should the preference of an agent turn out to be the same with the preference of their payoff, such choice is adjudged rational. Otherwise it would be adjudged irrational.
Nature of data and Sample
Nominal data showing the type of responses (Rational or Irrational) that people make with regard to the number of children they prefer to bear under varying level of uncertainty .
The samples are therefore drawn from Nigerians, male and female, who are willing and able to bear children. We chose a subunit of people in Nigeria students (Post graduate and Undergraduate) in Ahmadu Bello University  as the sampling unit of this study for the following reasons:
 the main preoccupation of the study is to evaluate people’s choice against the suggestions of a normative rule of choice (i.e axioms of rational choice). This normative rule is not contingent on where the response comes from. It is purely mathematical (free of stochastic term) as can be seen in the theoretical model above.
 secondly, we chose students in A.B.U because the student body of the school is a fair representation of households in Nigeria. This is because male students(Post graduate and Undergraduate ) admitted to the school are people whose age is not less than 15 years and the female mostly fall into the age range of 1550 years. Besides, the students not only come from all the regions of Nigeria but they also come from all the socioeconomic strata in Nigeria.
Sample size
The study used the formular for computing sample sizes of sample surveys developed by Yamene(1967)cited in Eboh(2009)to arrive at the sample size of 395 at 5% significant level . The formular says
n= (20)where n is sample size, N is population size and e is the level of precision desired. This formular assume a variability of 50% among the samples. The total population of students in the University is 32,306 and there are 12 faculties in the University M.I.S Unit A.B.U(2008).
This study used two basic instruments to elicit the data used for analysis. The two instruments of data collection for this study are
 Manual. An instructional manual containing sets of simple information and instructions concerning how the questionnaire (the main instrument) should be completed.
 Questionnaire. The question attached as appendix 6 is the main instrument of data collection. The question elicit responses concerning socioeconomic background of respondents as well as responses to some hypothetical choice problems with regard to the number of children people would prefer given some level of uncertainty. A complete set of frequency distribution table for the responses obtained through the questionnaire is shown in appendix A1.
Hypothetical questions are the simplest method of obtaining data from this line of enquiry by which a large number of theoretical choice questions can be investigated Kahneman and Tversky(1979).The authors of this present research also share this view.
Like Kahneman and Tversky’s(1979), the authors also adduced the following reasons for not considering other research designs
 Real choices can be investigated either in the field, by naturalistic or statistical observation of economic behavior or in laboratory.
 Field survey can only provide for rather crude tests of qualitative predictions , because probabilities and utilities cannot be measured in such contexts
 Even where laboratory experiments can measure probability, it often results into large repetition of very small problem.
Assumptions:
 People often know how they would behave.
 People have no special reason to disguise their true preference
 The presence of common and systematic deviation of theory in hypothetical problems provides presumptive evidence against theory.
Limitations:
 Reliance on hypothetical choice could raise questions regarding validity and generalization. The author is aware of this. Hence the documentation of the assumptions above. Also, as indicated above other available methods also suffer from severe drawback.
Methods of analysis
By way of testing the hypothesis of this study (which says the proportion of households’ whose fertility behavior is rational is not significantly higher than those whose fertility behavior is irrational) , we obtained a 5 and 10% statistical test of difference between the proportion of rational and irrational (with regard to the number of children people prefer to bear) responses. The results of this test will serve as a mark for validating the theoretical construct underlying the targets of Nigeria’s population policies.
To further shed light on the results obtained in the above test, we obtained the following relevant test of significant different between proportions to show whether variations in the choice of respondents can be explained by gender, geographical region, or religion:
 A 5 and 10% statistical tests of the difference between the proportion of male respondents who chose the number of children they desire rationally against other male who chose irrationally
 A 5 and 10% statistical tests of the difference between the proportion of female who chose the number of children they desire rationally against other female who chose irrationally.
 A 5 and 10% statistical tests of the difference between the proportion of male who chose the number of children they desire to rationally against female who chose irrationally.
 A 5 and 10% statistical tests of the difference between the proportion of Northern respondents who chose the number of children they prefer irrationally against their Southwest and Southeast counterpart
The test statistic for the difference between the proportion of rational and irrational responses from all respondents is given by Z1. Similar statistics by gender and region of respondents are respectively given by Z2 and Z3 below.
Z1= 
Z2 = 
Z3=
where
n1, and n2 are respectively the number of Rational and Irrational choices by respondents/gender/geographic region. is the proportion of rational respondents/male and is the proportion of irrational respondents/male or female as the case may be.
P= .
This Z value is compared with the critical value from the zscore table.
Results and discussion
A test of statistical difference between the proportion of people whose responses are rational (51%)(with regard to decision to bear no child, one or two children) and those whose response are irrational(31.9%) show that there exist significant difference at 5 and 10% significance level. The responses of 203 respondents are rational and those of 127 are irrational. 67 people did not respond to the choice question. Shown in table 1 below, the computed z statistics of the difference between the proportion of rational respondents and irrational respondents is 5.47 and the probability value (PValue) is 0.000.
Table1. Test of difference of proportions between rational responses and irrational response with regard to zero, one or two children. Under an extreme condition of uncertaintyξ
Test and Confidence Interval for Two Proportions (Rational and Irrational Choices) Estimate for p(1)  p(2): 0.190955 
The conclusions reached from the result obtained in table 2 below when the circumstances surrounding the choice problem is made less uncertain is not different from the conclusions reached from the results of table 1 above.
Table 2 .Test of difference of proportions between rational responses and irrational responses with regard to zero, one or two children under a less condition of uncertainty
Test and Confidence Interval for Two Proportions (Rational and Irrational Choices) Sample Sample size Total population Sample proportion Rational responses1 193 398 0.484925 Irrational response 130 398 0.326633 Estimate for p(1)  p(2): 0.158291 95% CI for p(1)  p(2): (0.0909590, 0.225624) Test for p(1)  p(2) = 0 (vs not = 0): Z = 4.55 PValue = 0.000 λWe vary the probability of occurrences and characterized high(above 60%)probability occurrences as extreme condition of uncertainty. 
We also vary the number of children ( the jth and kth) involve in the choice questions. With regard to the decision problem involving choice between three or four children, there are 242 and 93 people whose choices are respectively rational and irrational. The results of the test shown in table 3 says there is significant difference between them at 5 and 10% significance level.
Table 3.
Table 3.Test of difference of proportion between rational responses and irrational responses type with regard to three or four children
Test and Confidence Interval for Two Proportions(Rational and Irrational Choices) Sample Sample size Total population Sample proportions Rational responses 242 398 0.608040 Irrational responses 93 398 0.233668 Estimate for p(1)  p(2): 0.374372 95% CI for p(1)  p(2): (0.310900, 0.437844) Test for p(1)  p(2) = 0 (vs not = 0): Z = 10.70 PValue = 0.000 
For choices between three or six children, there are 219 and 87 rational and irrational choices respectively. As can be observed in table 4 below where the zscore of the test is 9.62 and Pvalue of 0.000, we conclude that there is significant difference between these proportions. So we reject the null hypothesis which says there is no significant difference between the proportions.
Table 4. Test of difference of proportions between rational responses and irrational responses with regard to three or six children
Test and Confidence Interval for Two Proportions(Rational and Irrational Choices) Sample Sample size Total population Sample proportions Rational responses 219 398 0.550251 Irrational responses 87 398 0.218593 Estimate for p(1)  p(2): 0.331658 
On whether difference could be responsible for the results shown in table 14 above, we results of the tests of significance different between proportion of rational and irrational respondents by gender. The results show that there is not significant difference between the proportion of male whose responses are rational (with regard to the choice of zero, one or two children)to their female counterpart(see table 5 below) at 5 and 10% level of significance.
Table 5.Test of difference of proportion between rational responses by to rational females with regard to zero,one or two children
. Test and Confidence Interval for Two Proportions Sample Sample size Total population Sample proportion Rationnal responses by male 120 253 0.474308 Rational responses by female 73 145 0.503448 Estimate for p(1)  p(2): 0.0291400 95% CI for p(1)  p(2): (0.131163, 0.0728834) Test for p(1)  p(2) = 0 (vs not = 0): Z = 0.56 PValue = 0.576 
However, when the choice is between three children on one hand and six on the other, the difference between the proportions of male whose choice is rational is significantly higher than those of their female counterparts. These results could respectively be found in table 6 and 7 below. re (see panel C of table 33 in appendix 3 for the Zscore(1.93) and PValue(0.054) ).
Table 6.Tests of difference of proportion between rational responses of males to females with regard to choices concerning three or four children
Confidence Interval for Two Proportions Sample Sample size Total population Sample p Rational responses by male 154 253 0.608696 Rational responses by female 55 253 0.217391 Estimate for p(1)  p(2): 0.391304 95% CI for p(1)  p(2): (0.312566, 0.470043) Test for p(1)  p(2) = 0 (vs not = 0): Z=8.94 PValue=0.000 
Table7.Tests of difference of proportion between rational responses of males to females with regard to choices concerning three or six children
Test and Confidence Interval for Two Proportions Sample Sample size Total population Sample proportion Rational responses of male 130 253 0.513834 Irrational responses of male 58 253 0.229249 Estimate for p(1)  p(2): 0.284585 95% CI for p(1)  p(2): (0.204112, 0.365058) Test for p(1)  p(2) = 0 (vs not = 0): Z = 6.62 PValue = 0.000 
Similarly, on whether geographical region could explain the results of table 14 above, the results obtained from the tests of significance different between proportion of rational (with regard to choice involving zero, one or two children; three or six children) respondents by geographical region show that people who hail from northern Nigeria more often than not make more rational choices (relative to others from other parts of the country) regardless of the level of uncertainty associated with the choices(see tables 8 and 9 below).
Table 8. Tests of difference of proportion with regard to choices concerning zero,one or two children by geographical region 

ATest and CI for Two Proportions Estimate for p(1)  p(2): 0.107920 

BTest and CI for Two Proportions Estimate for p(1)  p(2): 0.481526 

Table 9. Tests of difference of proportion with regard to choices concerning three or six gepgrphical region 

ATest and CI for Two Proportions


BTest and CI for Two Proportions 
Conclusions
In line with the objective of the study, the findings from the research show that regardless of the category of rate of birth or degree of uncertainty associated with choice concerning children number, people who make rational choices are significantly more than those who do not.
By way of shedding light on the above findings, the study show that males are generally more rational when they make choices concerning the number of children they prefer to bear than their female counterpart. Also, there are always more male whose choices are rational than those whose choices are irrational.
Also, the study also found out that Nigerians who hail from the North (of whatever religion)tend to make more rational choices than their Southwest and Southeast counterpart. In this study, people’s orientation is also found not to be independent of their rationality when they make choices concerning the number of children to bear. Religion is a strong factor that usually influences people’s choice in any choice circumstances and whatever the rate of child birth involved in the choice circumstances.
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Westoff, F.C& Frejka,T. (2007) “Religiousness and Fertility Among European Muslims. Population and Development Review 33(4)http://cepa.newschool.edu/het/essays/uncert/vnmaxioms.htm
Appendices
Appendix A1
Frequency Tables
APPENDIX A2
RESULTS OF RELIABILITY TEST
R E L I A B I L I T Y A N A L Y S I S  S C A L E (S P L I T)
Correlation Matrix RATIONAL IRRATION NORESPON RATIONAL CHOICES 1.0000 