Njiforti Peter and Hamzat Soliu
Department of Economics, Ahmadu Bello University, Zaria


 In an attempt to suggest reasons for the ineffectiveness of Nigeria’s population policies, the authors investigated whether or not people tend to obey the theory underlying the policies when they take decision concerning the number of children to bear. Tests of  difference between proportions was used to find out whether the proportion of respondents who chooses their desired family sizes rationally are more than those who choose irrationally as the policies are guided by rationalists paradigm. Choices are classified into rational or irrational through axiom of rational choice. The results show that the difference is significant in favor of people who choose rationally. The conclusion is that the source of the ineffectiveness of Nigeria’s population policies (in terms of its goals) may not be from its underlying theory  but from other sources  like the  implementation of policies .

Keywords: Fertility, population, household, family size


Mainstream economists, during the last forty years of the last millennium, view socio-economic 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 choice-theoretic 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 success-in terms of stated goals-are 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 trade-off 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 preference-orderings 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) ,intra-family ties(Alesina and Giuliano,2007), kingship ties (Smith ,2004)  , values ( McQuillan ,2004), child mortality (Benefo and Schultz,1996)and other  ethno-regional 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
   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+(1-μ)β--------------------------------------------------------(1)
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.

To adequately capture all the parameters of theoretical model, this research is designed around a quasi-experiment 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:

  1. 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.
  2. 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  15-50 years. Besides, the students not only come from all the regions of Nigeria but they also come from all the socio-economic 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

  1. Manual. An instructional manual containing sets of simple information and instructions concerning how the questionnaire (the main instrument) should be completed.
  2.  Questionnaire. The question attached as appendix 6 is the main instrument of data collection. The question elicit responses concerning socio-economic 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

  1. Real choices can be investigated either in the field, by naturalistic or statistical observation of economic behavior or in laboratory.
  2. Field survey can only provide for rather crude tests of qualitative predictions , because probabilities and utilities cannot be measured in such contexts
  3. Even where laboratory experiments can measure probability, it often results into large repetition of very small problem.


  1. People often know how they would behave.
  2. People have no special reason to disguise their true preference
  3. The presence of common and systematic deviation of theory in hypothetical problems provides presumptive evidence against theory.


  1. 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:

  1. 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
  2. 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.
  3. 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.
  4. 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 =  ------------------------------------------
     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 z-score 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 (P-Value) 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)
Sample              Sample size       Total population      Sample proportions
Rational responses   203               398                  0.510050
Irrational responses 127               398                  0.319095

Estimate for p(1) - p(2):  0.190955
95% CI for p(1) - p(2):  (0.123805, 0.258105)
Test for p(1) - p(2) = 0 (vs not = 0):  Z = 5.47  P-Value = 0.000
ξWe vary the probability of occurrences and characterized  low(33%)probability occurrences as extreme condition of uncertainty.

 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  P-Value = 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  P-Value = 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 z-score of the test is 9.62 and P-value 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
95% CI for p(1) - p(2):  (0.268119, 0.395198)
Test for p(1) - p(2) = 0 (vs not = 0):  Z = 9.62  P-Value = 0.000

On whether difference could be responsible for the results shown in table 1-4 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  P-Value = 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 Z-score(-1.93) and P-Value(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  P-Value=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  P-Value = 0.000


Similarly, on whether  geographical region could explain the results of table 1-4 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

A-Test and CI for Two Proportions
Rational Northerner and Rational Southwest
Sample      X      N  Sample p
1         110    187  0.588235
2          61    127  0.480315

Estimate for p(1) - p(2):  0.107920
95% CI for p(1) - p(2):  (-0.00399889, 0.219840)
Test for p(1) - p(2) = 0 (vs not = 0):  Z = 1.88  P-Value = 0.059

B-Test and CI for Two Proportions
Rational South West and Ratiional South East.
Sample                  Sample size Total Population   Sample proportion
Rational South West     110         127                 0.866142
Rational South East     30          78                  0.384615

Estimate for p(1) - p(2):  0.481526
95% CI for p(1) - p(2):  (0.358386, 0.604667)
Test for p(1) - p(2) = 0 (vs not = 0):  Z = 7.19  P-Value = 0.000


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

A-Test and CI for Two Proportions
Sample                                Sample size  Population size Sample proportion
Rational responses by Northerners      112         187             0.598930
Rational responses by South Westerners 62          127             0.488189
Estimate for p(1) - p(2):  0.110742
95% CI for p(1) - p(2):  (-0.00102742, 0.222510)
Test for p(1) - p(2) = 0 (vs not = 0):  Z = 1.94  P-Value = 0.053


B-Test and CI for Two Proportions
Sample                                  Sample size  Population size Sample p
Rational responses by South Westerners  62           187             0.331551
Rational responses by South Easterners  41           78              0.525641
Estimate for p(1) - p(2):  -0.194090
95% CI for p(1) - p(2):  (-0.323831, -0.0643492)
Test for p(1) - p(2) = 0 (vs not = 0):  Z = -2.95  P-Value = 0.003



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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Appendix A1
 Frequency Tables



                                                      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

NORESPON             -.6150      -.4175      1.0000
        N of Cases =       398.0
                                                    N of
Statistics for  
                    Mean   Variance    Std Dev   Variables
      Part 1       3.2663     1.5561     1.2474          2
      Part 2        .7085     1.4866     1.2193          1
      Scale        3.9749      .0800      .2828          3
Correlations   Mean    Minimum    Maximum      Range    Max/Min   Variance
Part 1       -.4300     -.4300     -.4300      .0000     1.0000      .0000
Part 2        .2000      .          .          .          .          .0000
Scale        -.55875     -.6150     -.4175      .1975      .6789      0098