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

2. Session 7
Panel Data

3. Main Issues in Panel Data Modeling
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)

17. Observable Heterogeneity

18. Heteroscedasticity

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

20. Parameter Heterogeneity in Banks

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

22. 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.

23. Time Variation in Random Effects Battese and Coelli

24. Battese and Coelli Models

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

26. A Distance Function Approach

27. Kriese Study of Municipalities