This paper argues that an important influence on boys’ decisions to stay on into post-compulsory education is the attainment of maths grades that differ from expected.Bivariate probit; post-compulsory education; choice under uncertainty

Don J. Webber

English

Research Papers in Economics

1 
 
Grade surprise and choice at 16 
 
 
 
Don J. Webber 
 
Department of Economics, Auckland University of Technology, Auckland, NZ 
 
 
 
 
 
Abstract 
This paper argues that an important influence on boys’ decisions to stay on 
into post-compulsory education is the attainment of maths grades that differ 
from expected. 
 
 
 
 
 
 
 
 
 
 
 
 
Keywords: Bivariate probit; post-compulsory education; choice under uncertainty 
 
JEL Classification: I21; C35 
 
Corresponding Author: Don J. Webber, Department of Economics, Auckland University of 
Technology, Auckland, New Zealand. E-mail: Don.Webber@aut.ac.nz 
 
 2 
 
1.   Introduction 
 
Standard education investment models attributable to Becker (1962) and Heckman (1976) 
view the individual as maximising discounted lifetime income streams through education 
choice. Individuals calculate the reward for different education pathways and choose the 
pathway that maximises utility. Since Willis and Rosen (1979) and Henderson et al. (1978) 
discussed the issues of education, self-selection and peer groups, many studies have presented 
investigations into the influences of various forces on enhancing education participation. 
Motivations for participation in post-compulsory education vary by gender, and Webber and 
Walton (2006) show that peer groups are stronger for males. Many studies focus on the UK 
youth labour market (e.g. Pissarides, 1981; Rice, 1987; Micklewright, 1989) and Feinstein 
and Symons (1999) and McIntosh (2001) are not alone when they find that the most 
important variable explaining the decision to stay on into post-compulsory education is prior 
educational attainment. The purpose of this paper is to identify whether the attainment of 
higher (or lower) grades than expected affects the decision to stay on into post-compulsory 
education for boys. 
 
2.  Data 
 
Data are drawn from the Bradford Youth Cohort Study
1 that were collected at the school 
level by the Policy Research Institute (at Leeds Metropolitan University). At the centre of the 
work is an administered questionnaire that was distributed in class time with students 
completing them under teacher supervision and corresponds to a student cohort who were 
                                                           
1   The study collected no measure of parental educational or financial background. We attempt to control for 
these effects by including two variables that capture the income levels and inequality within the student’s 4-
digit postcode residential area. 3 
 
going to complete their compulsory school in 1998.
2 The students were asked to respond to a 
subsequent questionnaire which was distributed one year later after they had completed their 
compulsory education.
3 
Two sets of variables are at the centre of this empirical study. The first set 
corresponds to intentions and realisations of the decision to stay on into post-compulsory 
education. These data are summarised in Figure 1; the accompanying Chi
2 statistic indicates 
that there is a statistically significant relationship between these intentions and realisations. 
The second important set of variables corresponds to ability. The data set includes the 
expected and realised grades for maths and English language. Students were informed of the 
grade that they should expect to receive, which was based on their results of mock exams, but 
they did not have to write this grade on the questionnaire if they believed that they would get 
a different final grade. Grades are measured on an ordered scale from “A” (=7) to “G” (=1), 
and “U” (=0). The differences between the expected and actual grades are grades surprises; if 
a student expected grade “C” but actually received grade “B” then the error would be +1. 
Grade surprises are summarised in Table 1. Overall there appears to be limited systematic 
bias in grade surprises, as shown in Table 2, although of note is the 3:1 ratio of negative to 
positive grade surprise for maths. 
 
3.   Results 
 
Table 3 presents the results of a bivariate probit estimation with clustering at the school level 
where the dependent variables are whether the students intends to stay on and whether the 
                                                           
2   More recent data are not available for variables that are at the core of this study. Although changes have 
occurred in the UK post-compulsory education market over the last decade (see Thomas and Webber, 2009, 
for a brief review) the data set remains one of the most detailed and useful for this study. 
3   Students who were in post-compulsory education were interviewed in class, while those who left education 
were sent the questionnaire by post. There was attrition in the response rate for the second questionnaire, 
with those who left education being less likely to return completed questionnaires, suggesting a possible bias 
towards those in education. 4 
 
student did actually stay on. Included as explanatory variables are ethnicity dummies, two 
residential area income measures (one capturing the average income level and the other 
capturing the extent of inequality within the residential area) and a variable capturing the peer 
group effect, which is constructed as the rate of staying on into post-compulsory education of 
other students in the school. Also included are dichotic variables capturing whether the 
student felt advice from particular sources (parents, teachers, careers) is important in forming 
their decision and whether they had work experience. 
  The results confirm a priori expectations as greater staying on rates of peers results in 
a greater likelihood of the student staying on, higher incomes encourage (and/or facilitate) the 
realisation of the staying on decision, and greater proportions of the student’s local residents 
on low incomes encourage students to stay on into post-compulsory education.  
Higher expected grades enhance the intention and realisation of the decision to stay 
on; this effect is much larger for maths than for English. Coefficients for grade surprise 
indicate that doing better (worse) than expected enhances (reduces) the likelihood that the 
student decides to stay on.
4 Two columns of marginal effects presented in Table 4 relate to 
when the student intended to stay on and when the student intended to leave respectively. 
Across all expected grades and almost without exception, positive (negative) grade surprise 
enhances (reduces) the likelihood that the student will stay on and these marginal effects are 
substantially larger for those who intended to leave relative to those who intended to stay on. 
Policy geared towards increasing the proportion of students who stay on into post-
compulsory education should not be blind to grade surprise. Students who do better than 
expected may be more easily coerced into staying on as they may feel that they are better 
academically than they originally thought. Students who do worse than they expect may need 
                                                           
4   Similar grade surprise variables were examined earlier for English language but were not identified as being 
statistically significant. Further research could identify why students appear to take maths more seriously 
than English as an indicator of ability. One suggestion is that understanding maths requires sequential 
learning, which may be less important for other subjects such as English language. 5 
 
to be reminded that their result could have been due to abnormally poor performance by them 
on the day of the exam and may not necessarily mean that they would also do poorly in 
exams at the post-compulsory level. 
 
4.   Conclusion 
 
The results presented above suggest that achieving a maths grade that is better than expected 
can significantly enhance the likelihood that a male student stays on into post-compulsory 
education at the age of 16. The influence of grade surprise on this education decision is 
greater for students who intended to leave than for students to intended to stay on. 
 
 
 
 
References 
 
Becker, GS (1993) Human capital: A theoretical and empirical analysis with special 
reference to education (3
rd edition), University of Chicago Press, Chicago. 
Feinstein, L and Symons, J (1999) “Attainment in secondary school”, Oxford Economic 
Papers 51(2), 300–21 
Heckman, JJ (1976) “A lifecycle model of earnings, learning and consumption”, Journal of 
Political Economy 84(4), s11–44 
Henderson, V, Mieszkowski, P and Sauvageau, Y (1978) “Peer group effects and educational 
production functions”, Journal of Public Economics 10(1), 97–106 
McIntosh, S (2001) “The demand for post-compulsory education in four European 
countries”, Education Economics 9(1), 69-90 
Micklewright, J (1989) “Choice at sixteen”, Economica 56, 25–40.  
Pissarides, CA (1981) “Staying-on at school in England and Wales”, Economica 48(192), 
345–63 
Rice, P. (1987) “The demand for post-compulsory education in the UK and the effects of 
educational maintenance allowances”, Economica 48, 465–76 
Thomas, W and Webber, DJ (2009) “Choice at 16: school, parental and peer group effects”, 
Research in post-compulsory education 14(2), 119-141 
Webber, DJ and Walton, F (2006) “Gender specific peer groups and choice at sixteen”, 
Research in Post-compulsory Education 11(1), 65-84 
Willis, RJ, and Rosen, S (1979) “Education and self-selection”, Journal of Political Economy 
87, 7-36 
 
 6 
 
Figure 1: Probability tree 
Intention
to stay on
Realisation of
decision to stay on
Yes = 91.5% 
Yes = 29.3%
Yes = 88.4%
No = 8.5%
No = 70.7%
No = 11.6%
3.4%
7.5%
8.2%
80.9%
Final
probabilities
 
Notes: Pearson chi
2(1) = 155.470 (P<0.000) 7 
 
Table 1: Descriptive statistics for grade surprise 
  Maths 
surprise 
English 
surprise 
Mean  -0.306  -0.139 
St. Dev  0.785  0.778 
Skewness  -0.075  0.246 
Kurtosis  3.717  4.553 
 
 8 
 
Table 2: English and Maths surprises (%) 
  English surprise   
-3  -2  -1  0  1  2  3  Total 
M
a
t
h
s
 
s
u
r
p
r
i
s
e
  -3  0  0.21  0  0  0  0  0  0.21 
-2  0  0.84  2.73  2.31  0.21  0  0  6.08 
-1  0.21  0.21  11.32  15.09  3.14  0.21  0  30.19 
0  0  0.84  10.48  31.87  7.97  0.63  0.42  52.20 
1  0  0.63  1.26  5.87  2.52  0.21  0  10.48 
2  0  0  0.21  0  0.21  0  0.21  0.63 
3  0  0  0  0  0.21  0  0  0.21 
  Total  0.21  2.73  26.00  55.14  14.26  1.05  0.63  100 
Pearson chi
2(36) = 148.051 (P<0.000) 
Likelihood-ratio chi
2(36) = 70.237 (P=0.001) 
Cramér’s V = 0.227 
Goodman and Kruskal’s gamma = 0.361 (Asymptotic Standard Error = 0.063) 
Kendall’s tau-b = 0.2293 (Asymptotic Standard Error = 0.041) 
McNemar-Bowker = 32.89, df=14 (P=0.003) 
Stewart-Maxwell’s test for marginal homogeneity = 15.96, df=6 (P=0.014) 
 9 
 
Table 3: Coefficients estimates 
  Intention to stay on 
into post-compulsory 
education 
Actual participating in 
post-compulsory 
education 
         
Constant  -7.769  (3.205)**  -8.835  (3.101)*** 
         
Caribbean  0.348  (0.272)  0.391  (0.244) 
Indian  0.106  (0.523)  0.422  (0.505) 
Other  0.172  (0.370)  0.861  (0.444)* 
White  Control variable 
         
Average income in residential area 
postcode   0.119  (0.106)  0.194  (0.091)** 
Proportion of residents in postcode area 
with income less than ₤10,000 per annum  0.048  (0.045)  0.073  (0.042)* 
         
Peer group effect  2.392  (0.911)***  2.071  (0.693)*** 
Parents advice is important  -0.064  (0.141)  -0.082  (0.143) 
Teachers advice is important  0.541  (0.193)***  0.311  (0.212) 
Careers advice is important  -0.289  (0.223)  -0.254  (0.172) 
Work experience  0.210  (0.186)  0.063  (0.211) 
       
Expected maths result  0.454  (0.101)**  0.263  (0.093)*** 
Expected English language result  0.153  (0.085)***  0.138  (0.075)* 
       
Maths surprise +ve ‘B’    5.332  (0.683)*** 
Maths surprise +ve ‘C’    0.054  (0.286) 
Maths surprise +ve ‘D’    0.637  (0.236)*** 
Maths surprise +ve ‘E’    0.442  (0.399) 
Maths surprise +ve ‘F’    5.009  (0.691)*** 
Maths surprise +ve ‘G’    5.199  (0.713)*** 
Maths surprise +ve ‘U’    2.656  (0.367)*** 
         
Maths surprise -ve ‘A’    -5.511  (0.284)*** 
Maths surprise -ve ‘B’    -0.233  (0.119)** 
Maths surprise -ve ‘C’    -0.287  (0.131)** 
Maths surprise -ve ‘D’    -0.561  (0.239)** 
Maths surprise -ve ‘E’    0.129  (0.324) 
         
n  477 
Log pseudo likelihood  -252.817 
rho  0.806 (0.061) 
Notes: Standard errors are in parentheses; ***, ** and * represent statistical confidence at the 1%, 5% and 10% 
levels. Rho suggests strong positive correlation between regressions (chi
2(1)=40.809, p<0.000). 
 
 10 
 
Table 4: Marginal effects 
  Participating in post-
compulsory education 
given the student intended 
to stay on 
Participating in post-
compulsory education 
given the student 
intended to leave 
         
Caribbean  0.009  (0.007)  0.083  (0.134) 
Indian  0.011  (0.006)*  0.172  (0.089)* 
Other  0.015  (0.005)***  0.300  (0.094)*** 
White  Control variable 
         
Average income in residential postcode   0.006  (0.003)**  0.063  (0.039) 
Proportion of residents in postcode with 
income less than ₤10,000pa 
0.002  (0.001)*  0.023  (0.016) 
         
Peer group effect  0.046  (0.037)  0.245  (0.446) 
Parents advice   -0.002  (0.005)  -0.021  (0.069) 
Teachers advice   0.003  (0.008)  -0.033  (0.107) 
Careers advice   -0.006  (0.007)  -0.032  (0.088) 
Work experience  -0.002  (0.008)  -0.043  (0.098) 
         
Expected maths result  0.003  (0.004)  -0.026  (0.051) 
Expected English language result  0.003  (0.003)  0.019  (0.037) 
         
Mathsurprise +ve @ grade ‘B’  0.022  (0.006)***  0.447  (0.066)*** 
Mathsurprise +ve @ grade ‘C’  0.002  (0.011)  0.030  (0.155) 
Mathsurprise +ve @ grade ‘D’  0.029  (0.012)**  0.354  (0.138)** 
Mathsurprise +ve @ grade ‘E’  0.011  (0.005)**  0.203  (0.142) 
Mathsurprise +ve @ grade ‘F’  0.228  (0.064)***  2.781  (0.265)*** 
Mathsurprise +ve @ grade ‘G’  0.014  (0.004)***  0.363  (0.064)*** 
Mathsurprise +ve @ grade ‘U’  0.121  (0.033)***  1.475  (0.129)*** 
         
Mathsurprise -ve @ grade ‘A’  -0.251  (0.049)***  -3.060  (0.471)*** 
Mathsurprise -ve @ grade ‘B’  -0.011  (0.006)*  -0.129  (0.062)** 
Mathsurprise -ve @ grade ‘C’  -0.013  (0.006)**  -0.159  (0.085)* 
Mathsurprise -ve @ grade ‘D’  -0.026  (0.012)**  -0.311  (0.143)** 
Mathsurprise -ve @ grade ‘E’  0.006  (0.015)  0.071  (0.179) 
 

Grade surprise and choice at 16

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