Vocational versus General Upper Secondary Education and Earnings

Eskil Heinesen; Elise Stenholt Lange

doi:10.3368/jhr.0221-11497R2

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Figure 1
Marginal Treatment Effects on Earnings of Completing Vocational Instead of General Education ($1,000)
Notes: The two upper panels show MTEs on earnings at age 28 and the two lower panels show MTEs on predicted earnings at age 40. The MTEs are evaluated at the sample means of covariates. The order of the polynomials in the propensity score is two for earnings at age 28; for predicted earnings at age 40, the order is one for males and three for females. The confidence intervals are bootstrapped.
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Figure 2
The Relation between ATT and ATE, and Estimates of Potential Outcomes, by Unobserved Resistance to Treatment—Outcome: Predicted Earnings at Age 40 ($1,000).
Notes: In the two upper panels the MTE curve is evaluated at the overall means of the covariates as in Figure 1, whereas the MTE(ATT) curve is evaluated at the means of the treatment group. These panels also show the ATT weights (on the right vertical axis) by the unobserved resistance to treatment, and the overall ATE and ATT effects are shown as horizontal lines. The ATT is above the ATE both because the observed characteristics of the treatment group differ from those of the control group and because individuals with lower unobserved resistance to treatment (and therefore higher probability of being treated) receive a higher weight in the estimation of the ATT. In the two lower panels, all graphs are evaluated at the overall means of the covariates. These panels again show the MTE curve and the overall ATE (the horizontal line) and, in addition, the potential outcomes by unobserved resistance to treatment (measured on at the right vertical axis).

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Table 1

Outcomes by Gender and Type of Completed Upper Secondary Education

	Males		Females		All
	General	Vocational	General	Vocational	All
Main Outcomes
Earnings age 28 ($1,000)	47.117	50.023	40.251	31.248	43.167
Earnings age 40 ($1,000)	84.910	65.439	64.863	42.293	68.210
Additional Outcomes at Age 28
Employed	0.812	0.877	0.802	0.759	0.815
Wage earner	0.787	0.836	0.791	0.739	0.793
Self‐employed	0.025	0.041	0.011	0.020	0.022
Student	0.097	0.041	0.086	0.065	0.078
Not in employment or education	0.091	0.082	0.112	0.177	0.107
Unemployed	0.047	0.031	0.050	0.059	0.046
Not in labor force	0.044	0.051	0.062	0.118	0.061
Post‐secondary degree	0.718	0.127	0.805	0.111	0.565
University degree (BA/MA/PhD)	0.421	0.010	0.388	0.007	0.278
Years of education (YOE)	15.992	14.431	16.278	13.859	15.550
YOE if no post‐secondary degree	13.348	14.161	13.433	13.568	13.741
YOE if post‐secondary degree	17.032	16.275	16.967	16.195	16.942
Parent by age 28	0.266	0.425	0.433	0.632	0.405
For Wage Earners at Age 28
Hours per month	143.147	153.309	140.295	138.761	143.749
Hourly wage ($)	30.331	30.764	28.075	24.812	28.966
N	46,779	32,291	63,928	18,434	161,432

Notes: If a student completed both a general and a vocational upper secondary education program before age 25, they are categorized by their first completed program. Labor market status is measured at the end of November in the year in which the person was 28 years of age at the beginning of the year. Post‐secondary degrees include professionally oriented degrees and degrees from research‐based universities. Years of education (YOE) is the standard number of years needed to complete the highest degree attained at age 28 (including ten years of primary and lower secondary school). Working hours are per month (with standard full time being 160 hours). Working hours and the hourly wage rate are only available for wage earners.

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Table 2

Selected Covariates by Completed Upper Secondary Education

	General	Vocational	Total
Male	0.423	0.637	0.490
Parents separated at age 14	0.253	0.333	0.279
Father vocational education	0.393	0.510	0.430
Father higher education	0.124	0.016	0.090
Father unemployed	0.018	0.022	0.019
Father disability pension	0.023	0.036	0.027
Father not in work force	0.045	0.057	0.049
Log income father	4.094	3.925	4.041
Father conviction at age 0–13	0.088	0.145	0.106
Test score math, Grade 9	8.435	7.038	8.020
Test score Danish, Grade 9	8.685	7.209	8.245
Test score English, Grade 9	8.999	7.230	8.509
Test score science, Grade 9	8.418	7.224	8.096
No Grade 9 test scores	0.021	0.072	0.037
N	110,707	50,725	161,432

Notes: If a student completed both a general and a vocational upper secondary education program before age 25, they are categorized by their first completed program. This table shows only selected covariates; Online Appendix Table A5 includes all covariates. The standard deviations in the distributions of test scores are 1.5, 1.2, 1.8, and 1.6 for math, Danish, English, and science, respectively.

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Table 3

Observations (Percent) by Distance to General and Vocational Upper Secondary Schools

Distance to General Schools	Distance to Vocational Schools
	0–5 km	5–10 km	10–15 km	15–20	20+ km	Total
0–5 km	14.05	19.10	3.55	1.93	1.82	40.45
5–10 km	0.38	7.18	7.51	4.10	3.76	22.92
10–15 km	0.01	0.52	4.45	5.74	6.08	16.79
15–20 km	0.00	0.01	0.20	3.59	8.49	12.29
20+ km	0.00	0.00	0.00	0.15	7.39	7.54
Total	14.43	26.80	15.71	15.51	27.55	100.00

Notes: Weighted average distance to general schools (rows) and vocational schools (columns). Weights are based on the number of students starting on each main type (track) of general and vocational programs, respectively.

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Table 4
OLS Results—Effect on Earnings of Completing a Vocational Instead of a General Program ($1,000)
Males Females
Earnings Age 28 Earnings Age 40 Earnings Age 28 Earnings Age 40
Vocational 7.161^*** −5.573^*** −2.713^*** −8.789^***
(0.242) (0.367) (0.214) (0.260)
N 79,070 79,070 82,362 82,362
Notes: The table shows OLS estimates of effects of completing a vocational instead of a general upper secondary education on earnings. If a student completed both a general and a vocational upper secondary education program, they are categorized by their first completed program. The full set of controls is included: 92 municipality dummies, three cohort dummies, and 62 family background and ninth grade test score variables. Online Appendix Table A5 shows the means for the family background and test score controls included. Heteroskedasticity robust standard errors are in parentheses. For predicted earnings at age 40, standard errors are bootstrapped. + p < 0.10, ^*p < 0.05, ^**p < 0.01, ^***p < 0.001.

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Table 5

First‐Stage Logit Models—Decision on Completing Vocational Instead of General Upper Secondary Education, Average Marginal Derivatives

	Male (1)	Male (2)	Female (3)	Female (4)
Distance to vocational education (km)	−0.0004	−0.0004	−0.0007^*	−0.0007^*
Distance to vocational education (km)	(0.0004)	(0.0004)	(0.0003)	(0.0003)
Distance to general education (km)	0.0041^***	0.0042^***	0.0018^***	0.0019^***
	(0.0004)	(0.0004)	(0.0003)	(0.0003)
Cross terms: distance × math score	X		X
All control variables	X	X	X	X
N	79,070	79,070	82,362	82,362
Chi‐squared, exclusion restrictions	281.8	256.8	94.1	49.7
p‐value, exclusion restrictions	6.630e‐58	1.745e‐56	4.214e‐18	1.644e‐11
Degrees of freedom, exclusion restrictions	6	2	6	2
Chi‐squared, cross terms	23.2		45.5
p‐value, cross terms	1.148e‐04		3.066e‐09
Degrees of freedom, cross terms	4		4

Notes: The dependent variable is an indicator for completing a vocational instead of a general upper secondary education. Average marginal derivatives based on the logit model estimates are shown for the two distance measures. For each individual, we calculate the effect of increasing the distance by one unit (1 km), holding all control variables fixed, on the probability of completing vocational instead of general education. In Columns 2 and 4, the exclusion restrictions are the two distance measures. In Columns 1 and 3, they also include cross terms between each distance variable and two control variables, namely the math test score and an indicator variable for missing math test score. The first chi‐square test is for all exclusion restrictions. The second is for the cross terms in Columns 1 and 3 only. The models include all control variables: sociodemographics, test scores, and cohort and municipality dummies. Heteroskedasticity robust standard errors are in parentheses. + p < 0.10, ^*p < 0.05, ^**p < 0.01, ^***p < 0.001.

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Table 6

Effects of Completing Vocational Instead of General Education on Earnings ($1,000)

	Males		Females
	Earnings Age 28(1)	Earnings Age 40(2)	Earnings Age 28(3)	Earnings Age 40(4)
Conventional Treatment Effects
ATE	8.036^***	−8.682^***	−6.739^**	−12.195^***
	(1.393)	(1.053)	(2.066)	(2.656)
ATT	14.946^***	3.701^*	5.131^***	8.138^***
	(1.581)	(1.494)	(1.187)	(1.891)
ATUT	3.254	−17.251^***	−10.189^***	−18.108^***
	(2.137)	(1.409)	(2.632)	(3.384)
Policy‐Relevant Treatment Effects
PRTE: p + 0.01	11.009^***	−6.407^***	1.811	1.009
	(1.616)	(1.099)	(1.628)	(2.683)
PRTE: Distance general +1 km	9.343^***	−5.305^***	0.262	0.141
	(1.182)	(1.124)	(1.213)	(1.708)
PRTEs by Grade 9 math scores
PRTE: p + 0.01, math low	15.150^***	0.785	−0.266	0.565
	(2.033)	(1.139)	(1.442)	(2.070)
PRTE: p + 0.01, math medium	10.618^***	−4.237^***	3.463^*	3.407
	(1.356)	(1.106)	(1.596)	(2.649)
PRTE: p + 0.01, math high	9.796^***	−11.366^***	2.321	0.019
	(2.405)	(1.438)	(2.359)	(4.299)
N	79,070	79,070	82,362	82,362
Order of polynomials in p	2	1	2	3
p‐value, observed heterogeneity	<0.0001	<0.0001	<0.0001	<0.0001
p‐value, unobserved heterogeneity	<0.0001	<0.0001	<0.0001	<0.0001

Notes: The table presents estimation results for MTE models with polynomials in the propensity score as control functions. We report results for a polynomial of order n if the n order terms are significant (for either k₀ or k) and if higher order terms are not significant. The models include all control variables: Sociodemographics, test scores, and cohort and municipality dummies. The test for observed heterogeneity is a test that β₁ – β₀ = 0. The test for unobserved heterogeneity is a test that the coefficients of the polynomial for k are equal to zero. The mean propensity score is 0.408 for males and 0.224 for females. The five PRTEs are effects per net individual shifted for five different policy‐related shifts in the propensity score. The first policy augments the propensity score by one percentage point for all observations. The second policy increases the distance to general schools by 1 km for everyone. This results in an average increase in the propensity score by 0.4 and 0.2 percentage points for males and females, respectively. The last three sets of PRTEs are for policies that increase the propensity score by 0.01, but only for those with low, medium, and high ninth grade math scores, respectively. Bootstrapped standard errors in parentheses. + p < 0.10, ^*p < 0.05, ^**p < 0.01, ^***p < 0.001.