Post-compulsory education pathways and labour market outcomes

Figures & data

Table 1. Possible states and activities in the sequence data.

State	Activity	Label	Percent
1	A-Levels	ALEV	29
2	Apprenticeship/Training	APPR	4
3	Employment	EMPL	20
4	GCSE (when not taken with other qualifications)	GCSE	2
5	Higher Education and Level 4+ Vocational	HE	19
6	Not in Education, Employment, or Training	NEET	8
7	Unknown (activity data missing)	MISS	1
8	Vocational qualifications Below Level 3	VBL3	11
9	Vocational qualifications at Level 3	VL3	7
	TOTAL		100

Table 2. Sequence indel and substitution costs.

Panel A: Indel costs vector
State:	ALEV	APPR	EMPL	GCSE	HE	NEET	MISS	VBL3	VL3
	0.44	0.65	0.51	0.68	0.52	0.61	0.69	0.50	0.63
Panel B: Sequence substitution cost matrix
ALEV	0.00	1.09	0.95	1.12	0.96	1.05	1.13	1.03	1.07
APPR		0.00	1.16	1.33	1.17	1.26	1.34	1.24	1.28
EMPL			0.00	1.19	1.04	1.13	1.20	1.10	1.14
GCSE				0.00	1.20	1.29	1.36	1.27	1.30
HE					0.00	1.14	1.21	1.11	1.15
NEET						0.00	1.30	1.20	1.24
MISS							0.00	1.28	1.31
VBL3								0.00	1.22
VL3									0.00

Figure 1. Full sample sequence index plot.

Figure 2. Full sample sequence distribution plot.

Figure 3. Six-pathway typology sequence index plots – 45-month sequences.

Figure 4. Six-pathway typology modal plot of sequences.

Table 3. Age 25 (Wave 8) labour market outcomes by pathway.

	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
	Income	Income	Income	Wage	Wage	Wage	Empl (logit)	Empl (logit)	Empl (logit)
P1: Employment	−0.022***	−0.083***	−0.017***	−0.188***	−0.156***	−0.055***	−0.011	0.023**	0.027**
	(0.008)	(0.006)	(0.006)	(0.015)	(0.015)	(0.016)	(0.011)	(0.012)	(0.012)
P2: NEET dominated	−0.262***	−0.255***	−0.130***	−0.287***	−0.244***	−0.049	−0.192***	−0.073***	−0.059**
	(0.018)	(0.014)	(0.014)	(0.034)	(0.033)	(0.036)	(0.031)	(0.023)	(0.025)
P3: Below Level 3	−0.142***	−0.141***	−0.036***	−0.274***	−0.230***	−0.073***	−0.090***	−0.027*	−0.024
	(0.013)	(0.010)	(0.009)	(0.020)	(0.019)	(0.021)	(0.019)	(0.016)	(0.018)
P4: Apprenticeship	−0.105***	−0.152***	−0.077***	−0.065**	−0.043	0.067**	0.002	0.024	0.026
	(0.017)	(0.014)	(0.013)	(0.031)	(0.029)	(0.028)	(0.022)	(0.022)	(0.022)
P5: Vocational L3 to HE	−0.088***	−0.059***	−0.006	−0.143***	−0.126***	−0.055***	−0.013	0.004	0.004
	(0.013)	(0.009)	(0.008)	(0.020)	(0.020)	(0.019)	(0.015)	(0.016)	(0.016)
Personal characteristics	No	Yes	Yes	No	Yes	Yes	No	Yes	Yes
Prior attainment	No	No	Yes	No	No	Yes	No	No	Yes
N	4987	4987	4987	3765	3765	3765	4985	4985	4985

1. Columns (1) to (3) show the results of OLS log weekly income equations, columns (4) to (6) show OLS log hourly wage equations – conditional on employment – and columns (7) to (9) show marginal effects from logit models of employment status.

2. Base category is P6: A-Levels to HE.

3. Personal characteristics controls are: gender, ethnicity, Government Office Region where the individual lives at age 25, dummies for receipt of state benefits and for receipt of any on-the-job training. Prior attainment controls are: standardised point scores at ages 11, 14, and 16, dummies for obtaining a grade C or above in GCSE Maths and GCSE English.

4. Standard errors in parentheses: * p < 0.1, ** p < 0.05, *** p < 0.01.

Table 4. Bias-adjusted coefficients based on Oster (2019).

	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
	Income	Income	Income	Wage	Wage	Wage	Empl (LPM)	Empl (LPM)	Empl (LPM)
		$\delta =0.5$	$\delta =1$		$\delta =0.5$	$\delta =1$		$\delta =0.5$	$\delta =1$
		$R_{max}=1.3\tilde{R}$	$R_{max}=1.3\tilde{R}$		$R_{max}=1.3\tilde{R}$	$R_{max}=1.3\tilde{R}$		$R_{max}=1.3\tilde{R}$	$R_{max}=1.3\tilde{R}$
P1: Employment	−0.017***	−0.048***	−0.084***	−0.055***	−0.047***	−0.036	0.029**	0.030**	0.030**
	(0.006)	[0.007]	[0.009]	(0.016)	[0.018]	[0.025]	(0.013)	[0.014]	[0.015]
P2: NEET	−0.130***	−0.138***	−0.147***	−0.049	−0.049	−0.049	−0.091***	−0.078**	−0.063*
	(0.014)	[0.015]	[0.017]	(0.036)	[0.037]	[0.040]	(0.030)	[0.031]	[0.034]
P3: Below Level 3	−0.036***	−0.048***	−0.062***	−0.073***	−0.069***	−0.064**	−0.031	−0.027	−0.023
	(0.009)	[0.011]	[0.013]	(0.021)	[0.025]	[0.027]	(0.020)	[0.021]	[0.022]
P4: Apprenticeship	−0.077***	−0.094***	−0.111***	0.067**	0.061**	0.053	0.028	0.026	0.024
	(0.013)	[0.014]	[0.014]	(0.028)	[0.029]	[0.033]	(0.022)	[0.023]	[0.025]
P5: Vocational L3 to HE	−0.006	−0.003	0.000	−0.055***	−0.066***	−0.079***	0.003	0.000	−0.003
	(0.008)	[0.009]	[0.010]	(0.019)	[0.020]	[0.023]	(0.015)	[0.016]	[0.017]
Personal characteristics	Yes			Yes			Yes
Prior attainment	Yes			Yes			Yes
R^2	0.617			0.214			0.102
N	4987	4987	4987	3765	3765	3765	4985	4985	4985

1. See Table 3. For convenience, columns (1), (4) and (7) are the corresponding estimates from Table 3 with the exception that those for the employment probabilities in column (7) are from a LPM specification rather than a logit specification. However, they are very similar to the marginal effects presented in Table 3, column (7).

2. Each coefficient in columns (2) & (3), (5) & (6) and (8) & (9) is the Oster bias-corrected estimate of the pathway coefficient from separate regressions in which each pathway is considered as a separate treatment effect.

3. Standard errors in parentheses: * p < 0.1, ** p < 0.05, *** p < 0.01.

4. Bootstrapped standard errors, based on 1000 replications, are in square brackets.

Table 5. Characteristics influencing pathway choice: Multinomial logit marginal effect estimates.

	P1	P2	P3	P4	P5	P6
	Employment	NEET dominated	Below L3	Apprenticeship	Voc L3 to HE	A-Levels to HE
Male	−0.006	−0.004	−0.037***	0.028***	0.023***	−0.003
	(0.010)	(0.006)	(0.008)	(0.006)	(0.008)	(0.010)
Non-White	−0.093***	−0.021**	−0.005	−0.028***	0.042***	0.105***
	(0.016)	(0.010)	(0.011)	(0.009)	(0.010)	(0.013)
SEN	−0.015	−0.002	0.016*	0.001	−0.004	0.003
	(0.013)	(0.008)	(0.009)	(0.006)	(0.011)	(0.014)
FSM	−0.056***	0.002	0.009	−0.013	0.007	0.051***
	(0.018)	(0.009)	(0.011)	(0.010)	(0.012)	(0.018)
IMD	−0.001	0.001***	0.001*	−0.000	0.000	−0.001**
	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)
Likely to apply to Uni (at age 14)	−0.052***	−0.003	−0.014*	−0.020***	−0.002	0.091***
	(0.011)	(0.007)	(0.009)	(0.005)	(0.010)	(0.013)
Risk factors	0.020***	0.005***	−0.004	0.002	0.001	−0.025***
	(0.003)	(0.002)	(0.003)	(0.001)	(0.003)	(0.004)
Advised FTE – Parent	−0.030***	−0.028***	0.030***	−0.019***	0.018**	0.028**
	(0.011)	(0.007)	(0.009)	(0.005)	(0.009)	(0.011)
Advised FTE – Sibling	−0.008	0.003	0.001	−0.001	−0.004	0.009
	(0.013)	(0.009)	(0.011)	(0.007)	(0.009)	(0.012)
Advised FTE – Other family	−0.030**	0.011	0.006	0.017**	0.012	−0.016
	(0.014)	(0.010)	(0.011)	(0.007)	(0.009)	(0.013)
Advised FTE – Friends	0.012	−0.015**	−0.004	−0.002	0.009	−0.001
	(0.010)	(0.007)	(0.008)	(0.005)	(0.008)	(0.010)
Advised FTE – Career advisor	−0.003	−0.011	0.001	−0.003	0.011	0.005
	(0.011)	(0.008)	(0.009)	(0.006)	(0.008)	(0.010)
Advised FTE – Teacher	0.006	−0.011	−0.004	−0.008	−0.004	0.021**
	(0.010)	(0.007)	(0.008)	(0.005)	(0.007)	(0.009)
Parents Evening – 1 Parent	0.003	0.016**	0.002	0.005	−0.013*	−0.013
	(0.010)	(0.007)	(0.008)	(0.005)	(0.008)	(0.010)
Parents Evening – 0 Parent	0.021	0.017*	−0.005	−0.002	−0.006	−0.024
	(0.019)	(0.010)	(0.013)	(0.010)	(0.015)	(0.022)
Parent Aspiration – Apprenticeship	0.068***	−0.004	0.008	0.029***	−0.002	−0.099***
	(0.014)	(0.008)	(0.011)	(0.006)	(0.014)	(0.021)
Parent Aspiration – Work	0.063	−0.003	−0.024	−0.003	0.030	−0.064
	(0.044)	(0.016)	(0.031)	(0.023)	(0.040)	(0.071)
Parent Aspiration – Other	0.079*	0.043*	−0.043	−0.030	−0.055	0.006
	(0.041)	(0.023)	(0.049)	(0.031)	(0.048)	(0.044)
School 5 A*-C % (2004)	−0.000	−0.000	−0.001***	0.000	−0.001***	0.002***
	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)
School FSM % (2004)	−0.001	0.000	−0.000	0.001	−0.001*	0.001**
	(0.001)	(0.000)	(0.000)	(0.000)	(0.000)	(0.001)
School Non-White % (2004)	−0.000	−0.000**	−0.000	−0.000	−0.000	0.001***
	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)
School KS3-KS4 value added	−0.008	0.013***	0.013***	0.002	0.001	−0.020***
	(0.007)	(0.004)	(0.005)	(0.003)	(0.005)	(0.007)
A*-C English	−0.014	−0.005	−0.035***	−0.003	−0.006	0.063***
	(0.015)	(0.012)	(0.012)	(0.007)	(0.011)	(0.016)
A*-C Maths	0.001	−0.020*	−0.014	−0.006	−0.006	0.045***
	(0.015)	(0.011)	(0.013)	(0.008)	(0.012)	(0.016)
KS4 point score (Std)	−0.012	−0.042***	−0.002	0.004	0.038***	0.014
	(0.019)	(0.013)	(0.015)	(0.009)	(0.013)	(0.019)
No of A*-A GCSEs	−0.011***	−0.000	0.002	−0.012***	−0.003	0.023***
	(0.004)	(0.005)	(0.004)	(0.003)	(0.002)	(0.003)
No of B-C GCSEs	−0.005	−0.004	−0.008***	0.000	−0.006**	0.023***
	(0.003)	(0.003)	(0.003)	(0.002)	(0.002)	(0.003)
No of D-G GCSEs	0.007*	0.002	0.003	0.001	0.002	−0.016***
	(0.004)	(0.003)	(0.003)	(0.002)	(0.003)	(0.005)
N	8046	8046	8046	8046	8046	8046

1. Standard errors in parentheses.

2. * p < 0.1, ** p < 0.05, *** p< 0.01.

Table 6. Assessment of prediction accuracy.

	(1)	(2)	(3)	(4)	(5)	(6)	(7)
	Constant only	+ Personal	+ Family SES	+ YPattitudes	+ Parents	+ School	+ GCSEs
a. Assessment of prediction accuracy: cross-validation exercise – cumulative
Overall	46.41	47.31	49.19	52.55	52.88	53.38	56.35
	(0.96)	(0.96)	(0.98)	(0.98)	(0.97)	(0.98)	(0.97)
P1: Employment	0.00	17.56	30.52	40.68	40.59	42.51	46.89
	(0.00)	(1.95)	(1.92)	(2.15)	(2.09)	(2.18)	(2.21)
P2: NEET	0.00	0.00	11.54	17.04	17.20	17.63	26.66
	(0.00)	(0.00)	(2.39)	(2.99)	(3.02)	(3.10)	(3.49)
P3: Below L3	0.00	5.17	7.32	11.73	11.38	13.05	24.80
	(0.00)	(1.52)	(1.58)	(1.93)	(1.97)	(2.08)	(2.82)
P4: Apprenticeship	0.00	0.00	0.01	0.33	0.91	1.23	2.60
	(0.00)	(0.00)	(0.11)	(0.62)	(1.06)	(1.27)	(1.72)
P5: Voc L3 + HE	0.00	0.00	0.26	0.29	0.62	0.64	4.77
	(0.00)	(0.04)	(0.34)	(0.37)	(0.53)	(0.51)	(1.35)
P6: A-Level + HE	100.00	92.52	88.44	89.13	89.82	89.52	88.86
	(0.00)	(1.15)	(1.16)	(1.04)	(1.04)	(1.07)	(1.02)
No. of replications	500	500	500	500	500	500	500
b. Assessment of prediction accuracy: cross-validation exercise – Separate
Overall	46.41	47.31	46.62	51.30	49.69	47.70	53.54
	(0.96)	(0.96)	(1.00)	(0.96)	(0.97)	(0.98)	(0.99)
P1: Employment	0.00	17.56	13.33	40.78	24.95	23.63	36.86
	(0.00)	(1.95)	(1.41)	(2.05)	(3.31)	(2.03)	(2.16)
P2: NEET	0.00	0.00	7.27	2.09	1.15	0.20	22.21
	(0.00)	(0.00)	(2.14)	(1.34)	(1.10)	(0.51)	(3.34)
P3: Below L3	0.00	5.17	2.91	3.27	0.01	4.66	23.90
	(0.00)	(1.52)	(1.20)	(1.38)	(0.08)	(1.22)	(2.81)
P4: Apprenticeship	0.00	0.00	0.00	0.00	0.00	0.00	0.00
	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)
P5: Voc L3 + HE	0.00	0.00	0.00	0.00	0.00	0.00	0.75
	(0.00)	(0.04)	(0.03)	(0.00)	(0.00)	(0.00)	(0.59)
P6: A-Level + HE	100.00	92.52	92.59	90.46	95.28	90.63	89.43
	(0.00)	(1.15)	(1.05)	(0.99)	(1.73)	(1.23)	(0.99)
No. of replications	500	500	500	500	500	500	500

1. The sets of covariates are defined as follows:

• Personal characteristics – gender, ethnicity, government office region, special educational needs.

• Family background – free school meals indicator, index of multiple deprivation (IMD), parent occupation, number of parents in household, housing tenure type, home access to computer and/or internet.

• Young person behaviour/attitudes – taking vocational qualifications at school, likelihood of applying to university, advice on continuing in FE from parents, family, siblings, friends, teachers, and careers advisors, and risk factors (a 1–8 scale indicating the number of self-reported risky behaviours engaged in including smoking, drinking, cannabis, graffiti, and shoplifting.)

• Parental attitudes/engagement – number of parents attending parents evening, parents’ aspirations for the young person at age 16.

School characteristics – School proportion of 5 A*-C GCSE attainment, school proportion receiving free school meals, school non-white proportion.

• Test scores/performance – number of GCSEs at A*-A, B-C, and D-G, A*-C GCSE in Maths, A*-C GCSE in English, overall KS4 point score, KS3 and KS2 English and Maths.

2. Standard deviations in parentheses.

Oster, E. 2019. “Unobservable Selection and Coefficient Stability: Theory and Evidence.” Journal of Business Economics and Statistics 37 (2): 187–204. doi:10.1080/07350015.2016.1227711

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