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Efficiency Measurement

William Greene Stern School of Business New York University. Efficiency Measurement. Session 7. Panel Data. Main Issues in Panel Data Modeling. Issues Capturing Time Invariant Effects Dealing with Time Variation in Inefficiency Separating Heterogeneity from Inefficiency

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Efficiency Measurement

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  1. William Greene Stern School of Business New York University Efficiency Measurement

  2. Session 7 Panel Data

  3. Main Issues in Panel Data Modeling • Issues • Capturing Time Invariant Effects • Dealing with Time Variation in Inefficiency • Separating Heterogeneity from Inefficiency • Contrasts – Panel Data vs. Cross Section

  4. Familiar RE and FE Models • Wisdom from the linear model • FE: y(i,t) = f[x(i,t)] + a(i) + e(i,t) • What does a(i) capture? • Nonorthogonality of a(i) and x(i,t) • The LSDV estimator • RE: y(i,t) = f[x(i,t)] + u(i) + e(i,t) • How does u(i) differ from a(i)? • Generalized least squares and maximum likelihood • What are the time invariant effects?

  5. Frontier Model for Panel Data • y(i,t) = β’x(i,t) – u(i) +v(i,t) • Effects model with time invariant inefficiency • Same dichotomy between FE and RE – correlation with x(i,t). • FE case is completely unlike the assumption in the cross section case

  6. Pitt and Lee RE Model

  7. Estimating Efficiency

  8. Schmidt and Sickles FE Model lnyit=  + β’xit + ai+ vit estimated by least squares (‘within’)

  9. A Problem of Heterogeneity In the “effects” model, u(i) absorbs two sources of variation • Time invariant inefficiency • Time invariant heterogeneity unrelated to inefficiency (Decomposing u(i,t)=u*(i)+u**(i,t) in the presence of v(i,t) is hopeless.)

  10. Time Invariant Heterogeneity

  11. A True RE Model

  12. Kumbhakar et al.(2011) – True True RE yit = b0 + b’xit + (ei0 + eit) - (ui0 + uit) ei0 and eit full normally distributed ui0 and uit half normally distributed (So far, only one application) Colombi, Kumbhakar, Martini, Vittadini, “A Stochastic Frontier with Short Run and Long Run Inefficiency, 2011

  13. A True FE Model

  14. Schmidt et al. (2011) – Results on TFE • Problem of TFE model – incidental parameters problem. • Where is the bias? Estimator of u • Is there a solution? • Not based on OLS • Chen, Schmidt, Wang: MLE for data in group mean deviation form

  15. Moving Heterogeneity Out of Inefficiency World Health Organization study of life expectancy (DALE) and composite health care delivery (COMP)

  16. Observable Heterogeneity

  17. Heteroscedasticity

  18. Unobservable Heterogeneity - RPM Random variation in production functions and inefficiency distributions across firms Continuous variation: Random parameters models Discrete variation: Latent Class models

  19. Parameter Heterogeneity in Banks

  20. Pooled vs. Random Parameters RP model vs. Pooled LC model vs. Pooled Random Parameters vs. Latent Class Model

  21. Time Variation – Early Ideas Kumbhakar and Hjalmarsson (1995) uit = i + ait where ait ~ N+[0,2]. They suggested a two step estimation procedure that begins either with OLS/dummy variables or feasible GLS, and proceeds to a second step analysis to estimate i. Cornwell et al. (1990) propose to accommodate systematic variation in inefficiency, by replacing ai with ait = i0 + i1t + i2t2. Inefficiency is still modeled using uit = max(ait) – ait.

  22. Time Variation in Random EffectsBattese and Coelli

  23. Battese and Coelli Models

  24. Variations on Battese and Coelli • (There are many) • Farsi, M. JPA, 30,2, 2008.

  25. A Distance Function Approach http://www.young-demography.org/docs/08_kriese_efficiency.pdf

  26. Kriese Study of Municipalities

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