Academic rank, socioeconomic rank, and educational outcomes: longitudinal evidence from Chile

Figures & data

Figure 1. Distribution of students across class-rank percentiles, by GPA (pct) and SES index (Std). Note: This figure shows SES index and GPA scores variation by rank. GPA and SES index are de-meaned by class-cohort.

Figure 2. Local polynomial fit of the outcomes by GPA and SES Class-rank percentile.

Figure 3. Rank dependent on test score distribution, taken from Murphy and Weinhardt (2020, 2078).

Table 1 . Class academic rank balance tests.

	Class rank
	GPA Rank		SES Rank
Outcome	(1)	(2)	(3)	N
Sex (Male = 1)	−0.010*	0.004	0.009**	1,092,584
	(0.006)	(0.007)	(0.004)
Ethnicity (Indigenous parent = 1)	0.001	0.004	0.005	676,087
	(0.004)	(0.006)	(0.004)
Parents have higher education	0.002	−0.002		907,368
	(0.005)	(0.006)
High parental income	0.008**	−0.002		710,979
	(0.003)	(0.004)
SES index quartile	0.002	−0.005		1,092,584
	(0.004)	(0.005)
Adjustments
Achievement (pct)^3	X
Achievement (pct)^3 × class achievement mean quartile	X
SES index, std.		X

Notes: Robust standard errors in parentheses. This table shows the coefficient of academic rank on each characteristic as outcome variable, after linear estimation adjusting for achievement (percentilized SIMCE and GPA) polynomials or SES index (standardized), and class-cohort fixed effects. Standard errors are clustered at class-cohort level. High parental income refers to those above CLP$1,000,000 in the year each student took SIMCE. Balance is also achieved when interacting quadratic achievement with class mean quartile (results not shown, available upon request).

*p<0.1; **p<0.05; ***p<0.01.

Figure 4. Class-level academic and SES Rank coefficients (probability difference), estimated with fully adjusted linear probability model. 95% confidence intervals shown in error bars. Note: Bars show academic and socioeconomic rank coefficient, which reflect the difference in probability of achieving the outcome between the highest and the lowest ranked student in each class.

Table 2. Summary of academic and SES class-rank coefficient after linear probability estimations.

Outcome	M0	M1	M2	M3	N
Completes secondary education					1,092,584
GPA Rank	0.045***	0.044***		0.045***
	(0.005)	(0.005)		(0.005)
SES Rank			0.058***	0.034***
			(0.003)	(0.003)
HE enrollment					1,092,584
GPA Rank	0.046***	0.039***		0.040***
	(0.006)	(0.006)		(0.006)
SES Rank			0.086***	0.066***
			(0.004)	(0.004)
HE enrollment: Academic (ref: Vocational)					813,099
GPA Rank	0.054***	0.043***		0.044***
	(0.007)	(0.007)		(0.007)
SES Rank			0.042***	0.023***
			(0.005)	(0.004)
HE enrollment: STEM (ref: non-STEM subject)					814,872
GPA Rank	0.047***	0.045***		0.045***
	(0.008)	−0.008		−0.008
SES Rank			0.022***	0.014***
			−0.005	−0.005
Completes higher education					814,872
GPA Rank	0.043***	0.059***		0.059***
	(0.008)	−0.008		−0.008
SES Rank			0.047***	0.036***
			−0.005	−0.005
Adjustments
Class-cohort fixed effects	X	X	X	X
GPA*Class-mean GPA quartile	X	X
SIMCE*Class-mean SIMCE quartile		X		X
SES Index			X	X
Sex				X

Note: Robust standard errors in parentheses. Standard errors clustered at the class-year level. Achievement refers to GPA and SIMCE standardized scores, using the polynomial that was most appropriate based on their distribution (See appendix Figures A4 and A5).

*p<0.1; **p<0.05; ***p<0.01.

Table 3 . Summary of academic school-rank coefficient after linear probability estimations.

Outcome	M0	M1	M2	M3	N
Completes secondary education					1,092,584
GPA Rank	0.070***	0.078***		0.077***
	(0.011)	(0.011)		(0.011)
SES Rank			0.075***	0.043***
			(0.004)	(0.003)
HE enrollment					1,092,584
GPA Rank	−0.004	0.016*		0.018*
	(0.011)	(0.01)		(0.009)
SES Rank			0.102***	0.077***
			(0.004)	(0.004)
HE enrollment: Academic (ref: Vocational)					813,099
GPA Rank	0.010	0.021**		0.023**
	(0.012)	(0.01)		(0.01)
SES Rank			0.044***	0.024***
			(0.005)	(0.005)
HE enrollment: STEM (ref: non-STEM subject)					814,872
GPA Rank	0.104***	0.090***		0.092***
	(0.013)	(0.013)		(0.013)
SES Rank			0.031***	0.021***
			(0.005)	(0.005)
Completes Higher Education					814,872
GPA Rank	0.019	0.058***		0.051***
	(0.014)	(0.013)		(0.013)
SES Rank			0.055***	0.041***
			(0.006)	(0.005)
Adjustments
School-cohort fixed effects	X	X	X	X
GPA*School-mean GPA quartile	X	X
SIMCE*School-mean SIMCE quartile		X		X
SES Index			X	X
Sex				X

Notes: Robust standard errors in parentheses. Standard errors clustered at the school-year level. Achievement refers to GPA and SIMCE standardized scores, using the polynomial that was most appropriate based on their distribution (See appendix Figures A4 and A5).

*p<0.1; **p<0.05; ***p<0.01.

Figure 5. Predicted probabilities for class-level academic and SES Rank ventiles, estimated after fully adjusted linear probability model. Note: 95% confidence intervals shown in error bars.

Figure 6. Academic and SES Rank coefficients at class and school level after estimating the fully adjusted model, by sex. Note: 95% confidence intervals shown in error bars.

Figure 7. Academic and SES Rank coefficients at class and school level after estimating the fully adjusted model, by school type. Note: Note: 95% confidence intervals shown in error bars.

Table 4. Robustness checks: Academic and socioeconomic rank coefficients after adjustment for different functional forms of achievement in Model 3.

Outcome	Achievement (pct)	Achievement (pct)^2	Achievement (pct)^3	Achievement Deciles	Achievement ventiles
Completes secondary education
GPA rank	0.161***	0.045***	0.064***	0.228***	0.112***
	(0.005)	(0.005)	(0.005)	(0.005)	(0.005)
SES rank	0.035***	0.034***	0.032***	0.034***	0.032***
	(0.003)	(0.003)	(0.003)	(0.003)	(0.003)
HE enrollment
GPA rank	0.063***	0.033***	0.040***	0.109***	0.065***
	(0.004)	(0.005)	(0.006)	(0.005)	(0.005)
SES rank	0.067***	0.066***	0.066***	0.066***	0.066***
	(0.004)	(0.004)	(0.004)	(0.004)	(0.004)
HE enrollment: Academic (ref: Vocational)
GPA rank	−0.012**	0.044***	0.055***	0.095***	0.068***
	(0.005)	(0.007)	(0.007)	(0.006)	(0.007)
SES rank	0.022***	0.023***	0.023***	0.023***	0.023***
	(0.004)	(0.004)	(0.004)	(0.004)	(0.004)
HE enrollment: STEM (ref: non-STEM subject)
GPA rank	0.153***	0.051***	0.045***	0.134***	0.068***
	(0.006)	(0.008)	(0.008)	(0.007)	(0.008)
SES rank	0.014***	0.014***	0.014***	0.014***	0.013***
	(0.005)	(0.005)	(0.005)	(0.005)	(0.005)
Completes higher education
GPA rank	0.068***	0.055***	0.059***	0.114***	0.073***
	(0.006)	(0.008)	(0.008)	(0.007)	(0.008)
SES rank	0.037***	0.036***	0.036***	0.036***	0.036***
	(0.005)	(0.005)	(0.005)	(0.005)	(0.005)
Adjustments
Class-cohort fixed effects	X	X	X	X	X
Achievement*Class-mean quartile Achievement	X	X	X	X	X
Sex	X	X	X	X	X
SES Index	X	X	X	X	X
SES Index Rank	X	X	X	X	X

Notes: Robust standard errors in parentheses. Standard errors clustered at class-year level for class-rank estimates. Model 2 is adjusted for academic achievement, class-cohorts fixed effects. Sex, socioeconomic status, socioeconomic rank.

*p<0.1; **p<0.05; ***p<0.01.

Murphy, Richard, and Felix Weinhardt. 2020. “Top of the Class: The Importance of Ordinal Rank.” The Review of Economic Studies 87 (6): 2777–2826. https://doi.org/10.1093/restud/rdaa020.

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Data availability statement

This paper uses data from the Chilean Education Minister that can be accessed online at http://datos.mineduc.cl/ and https://informacionestadistica.agenciaeducacion.cl/.