Blaming the exogenous environment? Conditional efficiency estimation with continuous and discrete exogenous variables

De Witte, Kristof and Mika, Kortelainen (2009): Blaming the exogenous environment? Conditional efficiency estimation with continuous and discrete exogenous variables.

Abstract

This paper proposes a fully nonparametric framework to estimate relative efficiency of entities while accounting for a mixed set of continuous and discrete (both ordered and unordered) exogenous variables. Using robust partial frontier techniques, the probabilistic and conditional characterization of the production process, as well as insights from the recent developments in nonparametric econometrics, we present a generalized approach for conditional efficiency measurement. To do so, we utilize a tailored mixed kernel function with a data-driven bandwidth selection. So far only descriptive analysis for studying the effect of heterogeneity in conditional efficiency estimation has been suggested. We show how to use and interpret nonparametric bootstrap-based significance tests in a generalized conditional efficiency framework. This allows us to study statistical significance of continuous and discrete exogenous variables on production process. The proposed approach is illustrated using simulated examples as well as a sample of British pupils from the OECD Pisa data set. The results of the empirical application show that several exogenous discrete factors have a statistically significant effect on the educational process.

• Item Type: MPRA Paper
• Language: English
• Keywords: Nonparametric estimation, Conditional efficiency measures, Exogenous factors, Generalized kernel function, Education
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General; I - Health, Education, and Welfare > I2 - Education and Research Institutions > I21 - Analysis of Education; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C25 - Discrete Regression and Qualitative Choice Models ; Discrete Regressors ; Proportions ; Probabilities

References

Aitchison, J. and C.B.B. Aitken (1976). Multivariate Binary Discrimination by Kernel Method. Biometrika 63, 413-420.

Badin, L., C. Daraio and L. Simar (2008). Optimal Bandwidth Selection for Conditional Efficiency Measures: A Data-Driven Approach. Discussion Paper 0828, Institut de Statistique, UCL.

Blass Staub, R. and G. da Silva e Souza (2007). A Probabilistic Approach for Assessing the Significance of Contextual Variables in Nonparametric Frontier Models: an Application for Brazilian Banks. Working Paper Series 150, Central Bank of Brazil, Research Department.

Bonaccorsi, A., C. Daraio and L. Simar (2007a). Efficiency and Productivity in European Universities. Exploring Trade-Offs in the Strategic Profile. In Bonaccorsi, A. and C. Daraio (eds.). Universities and Strategic Knowledge Creation. Specialization and Performance in Europe. Specialization and Performance in Europe. Edward Elgar PRIME Collection.

Bonaccorsi, A., C. Daraio, T. Räty and L. Simar (2007b). Efficiency and University Size: Discipline-Wise Evidence From the European Universities. In: Hyvinvointipalvelujen Tuottavuus: Tuloksia opintien varrelta, VATT Publications, Helsinki, Finland.

Bonaccorsi, A. and C. Daraio (2007c). Measuring Knowledge Spillover Effects via Conditional Nonparametric Analysis. Paper presented at the Workshop on Agglomeration and Growth in Knowledge-based Societies in Kiel, Germany, April 20-21.

Bonaccorsi A. and C. Daraio (2008). The Differentiation of the Strategic Profile of Higher Education Institutions. New Positioning Indicators Based on Microdata. Scientometrics 74 (1), 15-37.

Bonaccorsi, A., C. Daraio and L. Simar (2006). Advanced Indicators of Productivity of Universities, An Application of Robust Nonparametric Methods to Italian Data. Scientometrics 66 (2), 389-410.

Bound, J., C. Brown and N. Mathiowetz (2001). Measurement Error in Survey Data. In Heckman J. and E. Leamer (Ed.), Handbook of Econometrics 5. Elsevier. Broekel, T. (2008). From Average to the Frontier: A Nonparametric Frontier Approach to the Analysis of Externalities and Regional Innovation Performance. Papers in Evolutionary Economic Geography 08.04.

Broekel, T. and A. Meder (2008). The Bright and Dark Side of Cooperation for Regional Innovation Performance. Jena Economic Research Papers in Economics 2008-053.

Cazals, C., J.P. Florens and L. Simar (2002). Nonparametric Frontier Estimation: A Robust Approach. Journal of Econometrics 106 (1), 1-25.

Cazals, C, P. Dudley, J.-P. Florens, S. Patel and F. Rodriguez (2008). Delivery Offices Cost Frontier: A Robust Non Parametric Approach with Exogenous Variables. The Review of Network Economics 7 (2), 294-308.

Charnes, A., W.W. Cooper and E. Rhodes (1978). Measuring Efficiency of Decision-Making Units. European Journal of Operational Research 2 (6), 428-449.

Cherchye, L., K. De Witte, E. Ooghe and I. Nicaise (2007). Equity and Efficiency in Private and Public Education: A Nonparametric Comparison. CES Discussion Paper Series DPS 07.25.

Daouia, A. and L. Simar (2007). Nonparametric Efficiency Analysis: A Multivariate Conditional Quantile Approach. Journal of Econometrics 140, 375--400.

Daraio, C. and L. Simar (2005). Introducing Environmental Variables in Nonparametric Frontier Models: A Probabilistic Approach. Journal of Productivity Analysis 24 (1), 93--121.

Daraio, C. and L. Simar (2006). A Robust Nonparametric Approach to Evaluate and Explain the Performance of Mutual Funds. European Journal of Operations Research 175 (1), 516-542.

Daraio, C. and L. Simar (2007a). Advanced Robust and Nonparametric Methods in Efficiency Analysis. Methodology and Applications. Series: Studies in Productivity and Efficiency, Springer.

Daraio, C. and L. Simar (2007b). Conditional Nonparametric Frontier Models for Convex and Nonconvex Technologies: A Unifying Approach. Journal of Productivity Analysis 28, 13-32.

Deprins, D., L. Simar and H. Tulkens (1984). Measuring Labor Efficiency in Post Offices. In Marchand M., P. Pestieau and H. Tulkens (eds.), The Performance of Public Enterprises: Concepts and Measurements. Amsterdam, North-Holland. pp. 243-267.

De Witte, K. and E. Dijkgraaf (2009). Mean and Bold? On Separating Merger Economies from Structural Efficiency Gains in the Drinking Water Sector. Journal of the Operational Research Society, forthcoming.

De Witte, K. and M. Kortelainen (2008). Blaming the Exogenous Environment? Conditional Efficiency Estimation with Continuous and Discrete Environmental Variables. CES Discussion Paper Series DPS 08.33.

De Witte, K. and R. Marques (2008). Big and Beautiful? On Non-Parametrically Measuring Scale Economies in Non-Convex Technologies. CES Discussion Paper Series DPS 08.22.

De Witte, K. and D. Saal (2008). The Regulator's Fault? On the Effects of Regulatory Changes on Profits, Productivity and Prices in the Dutch Drinking Water Sector. CES Discussion Paper Series DPS 08.28.

Farrell, M. (1957). The Measurement of Productive Efficiency. Journal of the Royal Statistical Society 120 (3), 253-290.

Fried, H., C.A.K. Lovell and S. Schmidt (2008). The Measurement of Productive Efficiency and Productivity Growth. Oxford University Press, pp. 638.

Hall, P., J.S. Racine and Q. Li (2004). Cross-Validation and The Estimation of Conditional Probability Densities. Journal of the American Statistical Association 99 (468), 1015--1026.

Hampden-Thompson, G. and J. Johnston (2006). Variation in the Relationship between Nonschool Factors and Student Achievement on International Assessments. National Center for Education Statistics: Statistics in Brief, NCES 2006-014.

Hayfield, T. and J.S. Racine (2008). Nonparametric Econometrics: The Np Package. Journal of Statistical Software 27 (5).

Jeong, S., B. Park and L. Simar (2008). Nonparametric Conditional Efficiency Measures: Asymptotic Properties. Annals of Operations Research. Forthcoming. Li, Q. and J.S. Racine (2004). Cross-Validated Local Linear Nonparametric Regression. Statistica Sinica 14(2), 485--512.

Li, Q., and J.S. Racine (2007). Nonparametric Econometrics: Theory and Practice. Princeton University Press.

Li, Q. and J.S. Racine (2008). Nonparametric Estimation of Conditional CDF and Quantile Functions with Mixed Categorical and Continuous Data. Journal of Business and Economic Statistics 26 (4), 423-434.

OECD (2007). PISA 2006 Science Competencies for Tomorrow's World: Vol 1. Paris, Organisation for Economic Co-operation and Development.

Park, B., Simar, L. and C. Weiner (2000). The FDH Estimator for Productivity Efficiency Scores: Asymptotic Properties. Econometric Theory 16, 855-877.

Racine, J.S. (1997). Consistent Significance Testing for Nonparametric Regression. Journal of Business and Economic Statistics 15 (3), 369-379.

Racine, J. S., J. Hart and Q. Li (2006). Testing the Significance of Categorical Predictor Variables in Nonparametric Regression Models. Econometric Reviews 25 (4), 523-544.

Racine, J.S. and Q. Li (2004). Nonparametric Estimation of Regression Functions with both Categorical and Continuous Data. Journal of Econometrics 119 (1), 99--130.

Simar, L. and P. Wilson (2007). Estimation and Inference in Two-Stage, Semi-Parametric Models of Production Processes. Journal of Econometrics 136 (1), 31--64.

Sirin, S.R. (2005). Socioeconomic Status and Academic Achievement: A Meta-Analytic Review of Research. Review of Educational Research 75 (3), 417--453.

Thanassoulis, E. and M. Portela (2002). School Outcomes: Sharing the Responsibility between Pupil and School. Education Economics 10 (2), 183-207.