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Examining Production Efficiency in Higher Education: The Utility of Stochastic Frontier Analysis

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Book cover Higher Education: Handbook of Theory and Research

Part of the book series: Higher Education: Handbook of Theory and Research ((HATR,volume 31))

Abstract

Production frontier analysis and the technical efficiency of production are conceptual tools that can provide insight into the production efficiency of colleges and universities. This chapter provides an overview of the theoretical and conceptual underpinnings of stochastic frontier analysis (SFA) and its application to degree production efficiency in higher education. The theoretical background, conceptual basis, statistical properties, and application of different types of SFA models that are used to generate measures of production efficiency are discussed. True fixed-effects (TFE), true random-effects (TRE), random parameter (RP), and latent class (LC) are among the SFA models introduced and discussed. Using cross-sectional and panel data and various models, this chapter demonstrates how SFA can be employed to examine bachelor’s degree productivity of master’s comprehensive universities. Differences in estimates of the technical efficiency of degree production across TFE, TRE, RP, and LC models of SFA, with different distributional assumptions of technical efficiency are discussed. The chapter also provides an example of the utility of a SFA model and how it is used to rank institutions based on their technical efficiency of degree production. It concludes with recommendations for future applications of SFA models in higher education.

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Notes

  1. 1.

    Greene (2003) -->also proposed a gamma-normal distribution -->, which has not been used extensively in the stochastic frontier analysis literature.

  2. 2.

    If there is a competitive higher education, then the inputs (e.g., instructional faculty and educational technology) factors are paid their marginal product.

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Authors and Affiliations

  1. Higher Education, Student Affairs, and International Education Policy (HESI), University of Maryland, 3209 Benjamin Building, College Park, Maryland, 20742, USA

    Marvin A. Titus

  2. Department of Education, UCLA, 3101D Moore Hall, 951521, Los Angeles, CA, 90095, USA

    Kevin Eagan

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  1. Marvin A. Titus
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Correspondence to Marvin A. Titus .

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Editors and Affiliations

  1. College of Education, The University of Iowa, IOWA CITY, Iowa, USA

    Michael B. Paulsen

Appendices

Appendices

9.1.1 Appendix A : Stata Syntax

*create quadratic and interaction terms for the translog models.

gen lgraddeg2=lgraddeg*lgraddeg

gen lgraddeglugrad=lgraddeg*lugrad

gen lgraddeglgrad=lgraddeg*lgrad

gen lgraddeglresh=lgraddeg*lresh

gen lgraddegleandg=lgraddeg*leandg

gen lgraddeglftfac=lgraddeg*lftfac

gen lgraddeglptfac=lgraddeg*lptfac

gen lgraddeglfacsal=lgraddeg*lfacsal

gen lugrad2=lugrad*lugrad

gen lugradlgrad=lugrad*lgrad

gen lugradlresh=lugrad*lresh

gen lugradleandg=lugrad*leandg

gen lugradlftfac=lugrad*lftfac

gen lugradlptfac=lugrad*lptfac

gen lugradlfacsal=lugrad*lfacsal

gen lgrad2=lgrad*lgrad

gen lgradlresh=lgrad*lresh

gen lgradleandg=lgrad*leandg

gen lgradlftfac=lgrad*lftfac

gen lgradlptfac=lgrad*lptfac

gen lgradlfacsal=lgrad*lfacsal

gen lresh2=lresh*lresh

gen lreshleandg=lresh*leandg

gen lreshlftfac=lresh*lftfac

gen lreshlptfac=lresh*lptfac

gen lreshlfacsal=lresh*lfacsal

gen leandg2=leandg*leandg

gen leandglftfac=leandg*lftfac

gen leandglptfac=leandg*lptfac

gen leandglfacsal=leandg*lfacsal

gen lftfac2=lftfac*lftfac

gen lftfaclptfac=lftfac*lptfac

gen lftfaclfacsal=lftfac*lfacsal

gen lptfac2=lptfac*lptfac

gen lptfaclfacsal=lptfac*lfacsal

gen lfacsal2=lfacsal*lfacsal

*stochastic frontier analysis of cross-sectional data with different error distributions (Cobb-Douglas functional form); use “predict” command to generate efficiency score.

*exponential error distribution assumption

sfcross lbach lgraddeg lugrad lgrad lresh leandg lftfac lptfac lfacsal hbcu hsi control, dist(e)

predict cdcrosse, jlms

*half-normal error distribution assumption.

sfcross lbach lgraddeg lugrad lgrad lresh leandg lftfac lptfac lfacsal hbcu hsi control, dist(h)

predict cdcrossh, jlms

*truncated-normal error distribution assumption.

sfcross lbach lgraddeg lugrad lgrad lresh leandg lftfac lptfac lfacsal hbcu hsi control, dist(t)

predict cdcrosst, jlms

*Translog functional form for cross-sectional data

*create translog variable list.

global xvar “lgraddeg lugrad lgrad lresh leandg lftfac lptfac lfacsal hbcu hsi control lgraddeg2 lgraddeglugrad lgraddeglgrad lgraddeglresh lgraddegleandg lgraddeglftfac lgraddeglptfac lgraddeglfacsal lugrad2 lugradlgrad lugradlresh lugradleandg lugradlftfac lugradlptfac lugradlfacsal lgrad2 lgradlresh lgradleandg lgradlftfac lgradlptfac lgradlfacsal lresh2 lreshleandg lreshlftfac lreshlptfac lreshlfacsal leandg2 leandglftfac leandglptfac leandglfacsal lftfac2 lftfaclptfac lftfaclfacsal lptfac2 lptfaclfacsal lfacsal2”

*exponential error distribution assumption.

sfcross lbach $xvar, dist(e)

predict tcrosse, jlms

*half-normal error distribution assumption.

sfcross lbach $xvar, dist(h)

predict tcrossh, jlms

*truncated-normal error distribution assumption.

sfcross lbach $xvar, dist(t)

predict tcrosst, jlms

*get descriptive statistics for efficiency scores from SFA for cross-sectional data.

summarize cdcrosse cdcrossh cdcrosst tcrosse tcrossh tcrosst

correlate cdcrosse cdcrossh cdcrosst tcrosse tcrossh tcrosst

*set panel.

xtset unitid academicyear, yearly

*Cobb-Douglas true fixed effects with different error distributional assumptions.

*exponential error distribution assumption.

sfpanel lbach lgraddeg lugrad lgrad lresh leandg lftfac lptfac lfacsal hbcu hsi control, model (tfe) distribution(e) iterate(2000) diff rescale restart(5) tech(nr 100 bfgs 100 bhhh 100 dfp 100)

predict panelcrosstfee, jlms

*half-normal error distribution assumption.

sfpanel lbach lgraddeg lugrad lgrad lresh leandg lftfac lptfac lfacsal hbcu hsi control, model (tfe) distribution(h) iterate(2000) diff rescale restart(5) tech(nr 100 bfgs 100 bhhh 100 dfp 100)

predict panelcrosstfeh, jlms

*truncated normal error distribution assumption.

sfpanel lbach lgraddeg lugrad lgrad lresh leandg lftfac lptfac lfacsal hbcu hsi control, model (tfe) distribution(t) iterate(2000) diff rescale restart(5) tech(nr 100 bfgs 100 bhhh 100 dfp 100)

predict panelcrosstfet, jlms

*Translog true fixed effects with different error distributional assumptions

*exponential error distribution assumption.

sfpanel lbach $xvar, model(tfe) distribution(e) iterate(2000) diff rescale restart(5) tech(nr 100 bfgs 100 bhhh 100 dfp 100)

predict paneltranstfee, jlms

*half-normal error distribution assumption.

sfpanel lbach $xvar, model(tfe) distribution(h) iterate(2000) diff rescale restart(5) tech(nr 100 bfgs 100 bhhh 100 dfp 100)

predict paneltranstfeh, jlms

*truncated-normal error distribution assumption.

sfpanel lbach $xvar, model(tfe) distribution(t) iterate(2000) diff rescale restart(5) tech(nr 100 bfgs 100 bhhh 100 dfp 100)

predict paneltranstfet, jlms

*get descriptive statistics for efficiency scores generated from true fixed effects models.

summarize panelcrosstfee panelcrosstfeh panelcrosstfet paneltranstfee paneltranstfeh paneltranstfet

correlate panelcrosstfee panelcrosstfeh panelcrosstfet paneltranstfee paneltranstfeh paneltranstfet

*Cobb-Doulgas functional form for true random effects models.

*exponential error distribution assumption.

sfpanel lbach lgraddeg lugrad lgrad lresh leandg lftfac lptfac lfacsal hbcu hsi control, model(tre) distribution(e) difficult nsim(250) simtype(genhalton) iterate(2000) diff rescale restart(5) tech(nr 100 bfgs 100 bhhh 100 dfp 100)

predict panelcdtree, jlms

*half-normal error distribution assumption.

sfpanel lbach lgraddeg lugrad lgrad lresh leandg lftfac lptfac lfacsal hbcu hsi control, model(tre) distribution(h) difficult nsim(250) simtype(genhalton) iterate(2000) diff rescale restart(5) tech(nr 100 bfgs 100 bhhh 100 dfp 100)

predict panelcdtreh, jlms

*truncated-normal error distribution assumption.

sfpanel lbach lgraddeg lugrad lgrad lresh leandg lftfac lptfac lfacsal hbcu hsi control, model(tre) distribution(t) difficult nsim(250) simtype(genhalton) iterate(2000) diff rescale restart(5) tech(nr 100 bfgs 100 bhhh 100 dfp 100)

predict panelcdtret, jlms

*Translog functional form for true random effects models.

*exponential error distribution assumption.

sfpanel lbach $xvar, model(tre) distribution(e) difficult nsim(250) simtype(genhalton) iterate(2000) diff rescale restart(5) tech(nr 100 bfgs 100 bhhh 100 dfp 100)

predict paneltranstree, jlms

*half-normal error distribution assumption.

sfpanel lbach $xvar, model(tre) distribution(h) difficult nsim(250) simtype(genhalton) iterate(2000) diff rescale restart(5) tech(nr 100 bfgs 100 bhhh 100 dfp 100)

predict paneltranstreh, jlms

*truncated-normal error distribution assumption.

sfpanel lbach $xvar, model(tre) distribution(t) difficult nsim(250) simtype(genhalton) iterate(2000) diff rescale restart(5) tech(nr 100 bfgs 100 bhhh 100 dfp 100)

predict paneltranstret, jlms

*Get descriptive statistics for efficiency scores for the true random effects models.

summarize panelcdtree panelcdtreh panelcdtret paneltranstree paneltranstreh paneltranstret

correlate panelcdtree panelcdtreh panelcdtret paneltranstree paneltranstreh paneltranstret

9.1.2 Appendix B: Limdep Syntax

*set panel.

SETPANEL; Group = unitid; Pds = grpti $

*run frontier model with to get start values for RPM Cobb-Douglass model.

FRONTIER;Lhs=lbach

 ;Rhs=one,lgraddeg, lugrad, lgrad, lresh, leandg, lftfac, lptfac, lfacsal, hbcu, hsi, control

 ;MODEL=E$

*run RPM Cobb-Douglas model (exponential).

FRONTIER;Lhs=lbach

 ;Rhs=one,lgraddeg, lugrad, lgrad, lresh, leandg, lftfac, lptfac, lfacsal, hbcu, hsi, control

 ;Heteroscadasticity

 ;Means

 ;RPM

 ;Maxit=1000

 ;Halton;Pts=250

 ;Str=GRPTI

 ;Eff=RPMCDE

 ;Fcn=one(n),lgraddeg(n), lugrad(n), lgrad(n), lresh(n), leandg(n), lftfac(n), lptfac(n), lfacsal(n), HBCU(n), HSI(n), control(n)

 ;Model = E

 ;Panel$

FRONTIER;Lhs=lbach

 ;Rhs=one,lgraddeg, lugrad, lgrad, lresh, leandg, lftfac, lptfac, lfacsal, hbcu, hsi, control

 ;MODEL=H$

*run RPM Cobb-Douglas model (half-normal).

FRONTIER;Lhs=lbach

 ;Rhs=one, lgraddeg, lugrad, lgrad, lresh, leandg, lftfac, lptfac, lfacsal, hbcu, hsi, control

 ;Heteroscadasticity

 ;Means

 ;RPM

 ;Maxit=1000

 ;Halton;Pts=250

 ;Str=GRPTI

 ;Eff=RPMCDH

 ;Fcn=one(n),lgraddeg(n), lugrad(n), lgrad(n), lresh(n), leandg(n), lftfac(n), lptfac(n), lfacsal(n), HBCU(n), HSI(n), control(n)

 ;Model = H

 ;Panel$

FRONTIER;Lhs=lbach

 ;Rhs=one,lgraddeg, lugrad, lgrad, lresh, leandg, lftfac, lptfac, lfacsal, hbcu, hsi, control

 ;MODEL=T$

*run RPM Cobb-Douglas model (truncated normal).

FRONTIER;Lhs=lbach

 ;Rhs=one,lgraddeg, lugrad, lgrad, lresh, leandg, lftfac, lptfac, lfacsal, hbcu, hsi, control

 ;Heteroscadasticity

 ;Means

 ;RPM

 ;Maxit=1000

 ;Halton;Pts=250

 ;Str=GRPTI

 ;Eff=RPMCDT

 ;Fcn=one(n),lgraddeg(n), lugrad(n), lgrad(n), lresh(n), leandg(n), lftfac(n), lptfac(n), lfacsal(n), HBCU(n), HSI(n), control(n)

 ;Model = T

 ;Panel$

*Run translog stochastic frontier model to get start values (exponential).

FRONTIER;Lhs=lbach

 ;Rhs= one, lgraddeg, lugrad, lgrad, lresh, leandg, lftfac, lptfac, lfacsal, hbcu, his, control, lgraddeg2, lgraddeglugrad, lgraddeglgrad, lgraddeglresh, lgraddegleandg, lgraddeglftfac, lgraddeglptfac, lgraddeglfacsal, lugrad2, lugradlgrad, lugradlresh, lugradleandg, lugradlftfac, lugradlptfac, lugradlfacsal, lgrad2, lgradlresh, lgradleandg, lgradlftfac, lgradlptfac, lgradlfacsal, lresh2, lreshleandg, lreshlftfac, lreshlptfac, lreshlfacsal, leandg2, leandglftfac, leandglptfac, leandglfacsal, lftfac2, lftfaclptfac, lftfaclfacsal, lptfac2, lptfaclfacsal, lfacsal2

 ;MODEL=E$

*Run translog RPM (exponential).

FRONTIER;Lhs=lbach

 ;Rhs=one, lgraddeg, lugrad, lgrad, lresh, leandg, lftfac, lptfac, lfacsal, hbcu, his, control, lgraddeg2, lgraddeglugrad, lgraddeglgrad, lgraddeglresh, lgraddegleandg, lgraddeglftfac, lgraddeglptfac, lgraddeglfacsal, lugrad2, lugradlgrad, lugradlresh, lugradleandg, lugradlftfac, lugradlptfac, lugradlfacsal, lgrad2, lgradlresh, lgradleandg, lgradlftfac, lgradlptfac, lgradlfacsal, lresh2, lreshleandg, lreshlftfac, lreshlptfac, lreshlfacsal, leandg2, leandglftfac, leandglptfac, leandglfacsal, lftfac2, lftfaclptfac, lftfaclfacsal, lptfac2, lptfaclfacsal, lfacsal2

 ;Heteroscadasticity

 ;Means

 ;RPM

 ;Maxit=1000

 ;Halton;Pts=250

 ;Str=GRPTI

 ;Eff=RPMTE

 ;Fcn= one(n), lgraddeg(n), lugrad(n), lgrad(n), lresh(n), leandg(n), lftfac(n), lptfac(n), lfacsal(n), hbcu(n), hsi(n), control(n), lgraddeg2(n), lgraddeglugrad(n), lgraddeglgrad(n), lgraddeglresh(n), lgraddegleandg(n), lgraddeglftfac(n), lgraddeglptfac(n), lgraddeglfacsal(n), lugrad2(n), lugradlgrad(n), lugradlresh(n), lugradleandg(n), lugradlftfac(n), lugradlptfac(n), lugradlfacsal(n), lgrad2(n), lgradlresh(n), lgradleandg(n), lgradlftfac(n), lgradlptfac(n), lgradlfacsal(n), lresh2(n), lreshleandg(n), lreshlftfac(n), lreshlptfac(n), lreshlfacsal(n), leandg2(n), leandglftfac(n), leandglptfac(n), leandglfacsal(n), lftfac2(n), lftfaclptfac(n), lftfaclfacsal(n), lptfac2(n), lptfaclfacsal(n), lfacsal2(n)

 ;Model = E

 ;Panel$

***LATENT CLASS MODEL.

*set panel.

SETPANEL; Group = unitid; Pds = grpti $

*get initial point estimates using regression.

REGRESS;Lhs = lbach

 ;Rhs = one, lgraDdeg, lugrad, lgrad, lresh, LEANDG, lftfac, lptfac, lfacsal, HBCU, HSI

 ;Str=unitid

 ;Margin

 ;Panel$

*run frontier model to generate start values from LCM.

FRONTIER;Lhs=lbach

 ;Rhs=one,lgraddeg, lugrad, lgrad, LRESH, leandg, LFTFAC, LPTFAC, LFACSAL, HBCU, HSI, CONTROL

 ;Panel$

*run latent class model.

FRONTIER;Lhs=lbach

 ;Rhs=one,lgraddeg, lugrad, lgrad, LRESH, leandg, LFTFAC, LPTFAC, LFACSAL, HBCU, HSI, CONTROL

 ;LCM

 ;MAXIT=1000

 ;Pds=8

 ;Pts=2

 ;Eff = efflccd

 ;Panel$

*compute efficiency term using the inefficiency (u) term.

CREATE; TECHEFFL=EXP(−EFFLCCD)$

*show descriptive statistics for the efficiency score.

KERNEL; LHS=;RHS=TECHEFFL$

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Titus, M.A., Eagan, K. (2016). Examining Production Efficiency in Higher Education: The Utility of Stochastic Frontier Analysis. In: Paulsen, M. (eds) Higher Education: Handbook of Theory and Research. Higher Education: Handbook of Theory and Research, vol 31. Springer, Cham. https://doi.org/10.1007/978-3-319-26829-3_9

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