Schooling opportunities for 5-year-olds: some early origins of high school achievement

Figures & data

Table 1. Descriptive statistics

			All	Male	Female	NZ European	Māori	Asian	Australian	European	Pacific People
NCEA 1	NCEA level 1 achieved (0/1)	Mean	0.890	0.868	0.911	0.920	0.753	0.965	0.890	0.950	0.853
		Standard Deviation	0.313	0.339	0.284	0.271	0.432	0.185	0.312	0.218	0.355
		No. of observations	331,320	163,458	167,862	206,310	58,737	21,867	2,028	14,916	21,471
NCEA 2	NCEA level 2 achieved (0/1)	Mean	0.840	0.809	0.870	0.872	0.673	0.953	0.845	0.919	0.806
		Standard Deviation	0.367	0.393	0.336	0.334	0.469	0.212	0.362	0.273	0.396
		No. of observations	331,320	163,458	167,862	206,310	58,737	21,867	2,028	14,916	21,471
NCEA 3	NCEA level 3 achieved (0/1)	Mean	0.629	0.554	0.702	0.661	0.402	0.879	0.658	0.760	0.570
		Standard Deviation	0.483	0.497	0.457	0.473	0.490	0.327	0.475	0.427	0.495
		No. of observations	331,320	163,458	167,862	206,310	58,737	21,867	2,028	14,916	21,471
UE	University Entrance achieved (0/1)	Mean	0.425	0.356	0.496	0.478	0.185	0.743	0.473	0.589	0.250
		Standard Deviation	0.494	0.479	0.500	0.500	0.388	0.437	0.499	0.492	0.433
		No. of observations	411,765	210,246	201,522	248,667	80,163	24,606	2,511	17,430	31,023
Maximum length of schooling	Maximum length of schooling prior to Year 2 (months)	Mean	7.463	7.461	7.465	7.468	7.461	7.438	7.432	7.449	7.448
		Standard Deviation	1.809	1.807	1.811	1.804	1.820	1.785	1.841	1.828	1.824
		No. of observations	411,765	210,246	201,522	248,670	80,163	24,606	2,511	17,430	31,023
Age	Age at the start of Year 2 (months)	Mean	74.129	74.125	74.133	74.140	74.124	74.086	74.064	74.093	74.094
		Standard Deviation	S	S	S	S	S	S	S	S	S
		No. of observations	411,765	210,246	201,522	248,670	80,163	24,606	2,511	17,430	31,023
Female	Female gender (0/1)	Mean	0.489	-	-	0.488	0.491	0.495	0.484	0.483	0.498
		Standard Deviation	0.500	-	-	0.500	0.500	0.500	0.500	0.500	0.500
		No. of observations	411,765	-	-	248,670	80,163	24,606	2,511	17,430	31,023
Dob y	Year of birth (1988–2001)	Mean	1995	1995	1995	1995	1995	1995	1995	1995	1995
		Standard Deviation	S	S	S	S	S	S	S	S	S
		No. of observations	411,765	210,246	201,522	248,670	80,163	24,606	2,511	17,430	31,023
School decile	School deprivation decile (1–10)	Mean	6.132	6.127	6.137	6.783	4.405	6.873	6.991	7.638	3.803
		Standard Deviation	2.635	2.611	2.660	2.249	2.460	2.584	2.381	2.081	3.483
		No. of observations	389,796	200,721	189,072	234,972	74,925	23,805	2,379	16,578	30,426

Note: Following Stats NZ privacy requirements, all figures have been randomly rounded to base three and values identified with (S) have been supressed.

Figure 1. The relationship between the date of birth and the maximum length of schooling (excluding school holidays and weekends)

Table 2. Test of the exogeneity of the date of birth

	Age	Age	Maximum length of schooling	Maximum length of schooling
Age	–	–	−0.479***	−0.487***
			(0.004)	(0.004)
Age^2/100	–	–	0.672***	0.677***
			(0.003)	(0.003)
Female	0.004	0.011	0.001	0.001
	(0.014)	(0.012)	(0.001)	(0.000)
Ethnicity omitted category: NZ European
Ethnicity: Māori	0.060***	0.005	−0.003***	−0.001
	(0.016)	(0.015)	(0.001)	(0.001)
Ethnicity: Asian	−0.064*	−0.055*	0.000	−0.000
	(0.026)	(0.023)	(0.001)	(0.001)
Ethnicity: Australian	−0.020	−0.071	−0.002	−0.004
	(0.067)	(0.068)	(0.003)	(0.003)
Ethnicity: European	−0.052	−0.053	0.003**	0.002
	(0.032)	(0.031)	(0.001)	(0.001)
Ethnicity: Pacific People	−0.003	−0.020	0.001	0.001
	(0.023)	(0.022)	(0.001)	(0.001)
School decile (1–10)	NO	YES	NO	YES
School fixed effects	YES	NO	YES	NO
Year of birth dummies	YES	NO	YES	NO
Year of birth*region	YES	NO	YES	NO
Number of observations	411,765	411,765	411,765	411,765

Note: Robust standard errors adjusted for clustering at the school level are reported in parentheses. *, **, and *** indicate statistical significance at 95%, 99%, and 99.9% confidence levels respectively.

Table 3. Effects of the maximum length of schooling on high school achievement

	(1) NCEA 1	(2) NCEA 2	(3) NCEA 3	(4) UE
Maximum length of schooling	0.020***	0.037***	0.039***	0.021***
	(0.003)	(0.004)	(0.004)	(0.004)
% change	2.2%	4.4%	6.2%	4.9%
Age	0.038***	0.039***	0.020	−0.003
	(0.007)	(0.007)	(0.010)	(0.009)
Age^2/100	−0.034***	−0.041***	−0.029***	−0.006
	(0.005)	(0.005)	(0.007)	(0.006)
Marginal effect of age	−0.012	−0.022	−0.023	−0.012
Female	0.049***	0.067***	0.152***	0.138***
	(0.003)	(0.003)	(0.008)	(0.009)
Ethnicity omitted category: NZ European
Ethnicity: Māori	−0.127***	−0.147***	−0.177***	−0.193***
	(0.008)	(0.006)	(0.006)	(0.009)
Ethnicity: Asian	0.017***	0.040***	0.139***	0.181***
	(0.003)	(0.005)	(0.008)	(0.009)
Ethnicity: Australian	−0.031***	−0.030***	−0.011	−0.013
	(0.007)	(0.008)	(0.010)	(0.010)
Ethnicity: European	0.012**	0.023***	0.059***	0.065***
	(0.004)	(0.004)	(0.005)	(0.006)
Ethnicity: Pacific People	−0.050***	−0.050***	−0.090***	−0.187***
	(0.007)	(0.007)	(0.009)	(0.011)
Number of observations	331,320	331,320	331,320	411,765

Note: The marginal effect of age (at the start of Year 2) is calculated as the derivative of the regression equation with respect to age, evaluated at the mean age. All regressions also include school fixed effects, year of birth dummies, and year of birth*region interactions. Robust standard errors adjusted for clustering at the school level are reported in parentheses. ** and *** indicate statistical significance at 99% and 99.9% confidence levels, respectively.

Table 4. Effects of the maximum length of schooling on high school achievement; Year 0 vs. Year 1

	(1) NCEA 1	(2) NCEA 2	(3) NCEA 3	(4) UE
Maximum length of schooling in Years 0 & 1	0.020***	0.037***	0.039***	0.021***
	(0.003)	(0.004)	(0.004)	(0.004)
Maximum length of schooling in Year 0	0.008*	0.014**	0.016**	0.009
	(0.003)	(0.004)	(0.005)	(0.005)
Maximum length of schooling in Year 1	0.031***	0.049***	0.051***	0.029***
	(0.004)	(0.004)	(0.005)	(0.004)

Note: All regressions also include age, gender, and ethnicity controls, school fixed effects, year of birth dummies, and year of birth*region interactions. Robust standard errors adjusted for clustering at the school level are reported in parentheses. *, **, and *** indicate statistical significance at 95%, 99%, and 99.9% confidence levels respectively.

Table 5. Robustness and falsification checks: effects of the maximum length of schooling

		Main model	w/o May & June DOB	1st of each month DOB	15th of each month DOB	Last of each month DOB	Placebo group 1: Migrants & Refugees	Placebo group 2: IFP Students
NCEA 1	Coefficient	0.020***	0.012**	0.014***	0.023***	0.029***	0.002	0.023
	(SE)	(0.003)	(0.003)	(0.003)	(0.003)	(0.003)	(0.010)	(0.016)
	% change	2.2%	1.3%	1.6%	2.6%	3.3%	0.0%	3.9%
NCEA 2	Coefficient	0.037***	0.028***	0.027***	0.039***	0.044***	0.000	0.025
	(SE)	(0.004)	(0.004)	(0.004)	(0.004)	(0.004)	(0.010)	(0.017)
	% change	4.4%	3.3%	3.2%	4.6%	5.2%	0.0%	4.3%
NCEA 3	Coefficient	0.039***	0.034***	0.025***	0.040***	0.045***	−0.001	0.043*
	(SE)	(0.004)	(0.005)	(0.005)	(0.004)	(0.005)	(0.015)	(0.021)
	% change	6.2%	5.4%	4.0%	6.4%	7.2%	−0.1%	8.7%
UE	Coefficient	0.021***	0.022***	0.008	0.022***	0.029***	−0.002	0.053**
	(SE)	(0.004)	(0.004)	(0.005)	(0.004)	(0.004)	(0.015)	(0.020)
	% change	4.9%	5.2%	1.9%	5.2%	6.8%	−0.4%	13.8%
Number of	NCEA	331,320	276,933	331,320	331,320	331,320	27,225	11,997
observations	UE	411,765	344,214	411,765	411,765	411,765	35,010	14,157

Note: IFP stands for international fee paying. All regressions also include age, gender, and ethnicity controls, school fixed effects, year of birth dummies, and year of birth*region interactions. Robust standard errors adjusted for clustering at the school level are reported in parentheses. *, **, and *** indicate statistical significance at 95%, 99%, and 99.9% confidence levels respectively.

Table 6. Subgroup analysis: effects of the maximum length of schooling

		Main model	Female	Male	NZ European	Māori	Asian	Deciles 1–4	Deciles 5–7	Deciles 8–10
NCEA 1	Coefficient	0.020***	0.018***	0.025***	0.015***	0.056***	−0.002	0.028**	0.025***	0.011**
	(SE)	(0.003)	(0.004)	(0.005)	(0.003)	(0.010)	(0.006)	(0.008)	(0.005)	(0.003)
	% change	2.2%	2.0%	2.9%	1.6%	7.4%	−0.2%	3.4%	2.8%	1.1%
NCEA 2	Coefficient	0.037***	0.027***	0.047***	0.037***	0.060***	0.007	0.034***	0.046***	0.026***
	(SE)	(0.004)	(0.006)	(0.006)	(0.005)	(0.011)	(0.007)	(0.008)	(0.007)	(0.005)
	% change	4.4%	3.1%	5.8%	4.2%	8.9%	0.7%	4.5%	5.4%	2.8%
NCEA 3	Coefficient	0.039***	0.037***	0.041***	0.056***	0.027**	0.010	0.016	0.059***	0.036***
	(SE)	(0.004)	(0.006)	(0.007)	(0.006)	(0.010)	(0.013)	(0.008)	(0.009)	(0.007)
	% change	6.2%	5.3%	7.4%	8.5%	6.7%	1.1%	3.2%	9.8%	4.5%
UE	Coefficient	0.021***	0.020**	0.022***	0.033***	0.022**	0.013	0.011	0.039***	0.014
	(SE)	(0.004)	(0.006)	(0.006)	(0.006)	(0.008)	(0.015)	(0.007)	(0.008)	(0.008)
	% change	4.9%	4.0%	6.2%	6.9%	11.9%	1.7%	4.3%	9.9%	2.2%
Number of observations	NCEA	331,320	167,862	163,458	206,310	58,737	21,867	85,314	110,070	118,959
	UE	411,765	201,522	210,246	248,667	80,163	24,606	115,038	138,180	136,575

Note: All regressions also include age, gender and/or ethnicity controls, school fixed effects, year of birth dummies, and year of birth*region interactions. Robust standard errors adjusted for clustering at the school level are reported in parentheses. *, **, and *** indicate statistical significance at 95%, 99%, and 99.9% confidence levels respectively.

Figure A1. Comparison of two hypothetical students starting school at different times

Table A1. Highest attainment variable – classification table

Code	Description	Frequency (%)	NCEA-Equivalent Measure
0	No Formal Attainment	2.18	NCEA not achieved
10	1–13 credits at level 1	1.11	NCEA not achieved
13	Other level 1 NQF Qualification	0.16	NCEA level 1 achieved
14	NCEA level 1 not further defined	0.00	NCEA level 1 achieved
15	NCEA level 1 achieved	3.47	NCEA level 1 achieved
16	NCEA level 1 with merit	0.18	NCEA level 1 achieved
17	NCEA level 1 with excellence	0.01	NCEA level 1 achieved
20	1–13 credits at level 2	0.36	NCEA not achieved†
24	NCEA level 2 not further defined	0.00	NCEA level 2 achieved
25	NCEA level 2 achieved	15.77	NCEA level 2 achieved
26	NCEA level 2 with merit	0.62	NCEA level 2 achieved
27	NCEA level 2 with excellence	0.11	NCEA level 2 achieved
30	1–13 credits at level 3	0.13	NCEA level 1 achieved†
33	Other level 3 NQF Qualification	0.49	NCEA level 3 achieved
34	NCEA level 3 not further defined	0.00	NCEA level 3 achieved
35	NCEA level 3 achieved	30.27	NCEA level 3 achieved
36	NCEA level 3 with merit	12.23	NCEA level 3 achieved
37	NCEA level 3 with excellence	4.65	NCEA level 3 achieved
4	Other level 2 NQF Qualification	0.30	NCEA level 2 achieved
40	3+ NZ Scholarships subjects	0.49	NCEA level 3 achieved
43	National certificate at level 4	0.09	NCEA level 3 achieved
51	14–39 credits at any level without level 1 literacy and numeracy credits	2.68	NCEA not achieved
52	14–39 credits at any level including level 1 literacy and numeracy credits	0.31	NCEA not achieved
53	40+ credits at any level without level 1 literacy and numeracy credits	2.21	NCEA not achieved
54	40+ credits at any level including level 1 literacy and numeracy credits	1.83	–
55	30+ credits at level 2 or above	6.34	–
56	30+ credits at level 3 or above	11.37	–
60	International Baccalaureate Year 11	0.00	NCEA level 1 achieved
61	International Baccalaureate Year 12	0.01	NCEA level 2 achieved
62	International Baccalaureate Year 13	0.49	NCEA level 3 achieved
70	Cambridge International Exams Year 11	0.04	NCEA level 1 achieved
71	Cambridge International Exams Year 12	0.16	NCEA level 2 achieved
72	Cambridge International Exams Year 13	1.87	NCEA level 3 achieved
80	Accelerated Christian Education Year 11	0.02	NCEA level 1 achieved
81	Accelerated Christian Education Year 12	0.01	NCEA level 2 achieved
82	Accelerated Christian Education Year 13	0.02	NCEA level 3 achieved
90	Other Overseas Awards Year 11	0.00	NCEA level 1 achieved
91	Other Overseas Awards Year 12	0.00	NCEA level 2 achieved
92	Other Overseas Awards Year 13	0.00	NCEA level 3 achieved

† Students in New Zealand high schools can earn a limited number of higher-level NCEA credits without achieving the previous level. This includes credits for non-academic accomplishments. For example, obtaining a restricted driver licence counts towards NCEA level 2, even if the student has not achieved NCEA level 1.

Table A2. Effects of gender and ethnicity on high school achievement; further test of the exogeneity of the date of birth

	(1a) NCEA 1	(1b) NCEA 1	(2a) NCEA 2	(2b) NCEA 2	(3a) NCEA 3	(3b) NCEA 3	(4a) UE	(4b) UE
Maximum length of schooling	0.020***	–	0.037***	–	0.039***	–	0.021***	–
	(0.003)		(0.004)		(0.004)		(0.004)
Age	0.038***	–	0.039***	–	0.020	–	−0.003	–
	(0.007)		(0.007)		(0.010)		(0.009)
Age^2/100	−0.034***	–	−0.041***	–	−0.029***	–	−0.006	–
	(0.005)		(0.005)		(0.007)		(0.006)
Female	0.049***	0.049***	0.067***	0.067***	0.152***	0.152***	0.138***	0.138***
	(0.003)	(0.003)	(0.003)	(0.003)	(0.008)	(0.008)	(0.009)	(0.009)
Ethnicity omitted category: NZ European
Ethnicity: Māori	−0.127***	−0.127***	−0.147***	−0.147***	−0.177***	−0.178***	−0.193***	−0.193***
	(0.008)	(0.008)	(0.006)	(0.006)	(0.006)	(0.006)	(0.009)	(0.009)
Ethnicity: Asian	0.017***	0.017***	0.040***	0.040***	0.139***	0.140***	0.181***	0.181***
	(0.003)	(0.003)	(0.005)	(0.005)	(0.008)	(0.008)	(0.009)	(0.009)
Ethnicity: Australian	−0.031***	−0.031***	−0.030***	−0.030***	−0.011	−0.011	−0.013	−0.013
	(0.007)	(0.007)	(0.008)	(0.008)	(0.010)	(0.010)	(0.010)	(0.010)
Ethnicity: European	0.012**	0.012**	0.023***	0.023***	0.059***	0.060***	0.065***	0.065***
	(0.004)	(0.004)	(0.004)	(0.004)	(0.005)	(0.006)	(0.006)	(0.006)
Ethnicity: Pacific People	−0.050***	−0.051***	−0.050***	−0.050***	−0.090***	−0.090***	−0.187***	−0.187***
	(0.007)	(0.007)	(0.007)	(0.007)	(0.009)	(0.009)	(0.011)	(0.011)
Number of observations	331,320	331,320	331,320	331,320	331,320	331,320	411,765	411,765

Note: All regressions also include school fixed effects, year of birth dummies, and year of birth*region interactions. Robust standard errors adjusted for clustering at the school level are reported in parentheses. ** and *** indicate statistical significance at 99% and 99.9% confidence levels, respectively.