[Part 7] 1/68 Stochastic FrontierModels Panel Data Stochastic Frontier Models William Greene Stern School of Business New York University 0Introduction 1Efficiency Measurement 2Frontier Functions 3Stochastic Frontiers 4Production and Cost 5Heterogeneity 6Model Extensions 7Panel Data 8Applications

[Part 7] 2/68 Stochastic FrontierModels Panel Data Main Issues in Panel Data Modeling  Issues Capturing time invariant effects Dealing with time variation in inefficiency Separating heterogeneity from Inefficiency Examining technical change and total factor productivity growth  Contrasts – Panel Data vs. Cross Section

[Part 7] 3/68 Stochastic FrontierModels Panel Data Technical Change  Technical Change LnOutput it = f(x it,z i,,t) + v it - u it. LnCost it = c(x it,z i,,t) + v it + u it. Independent of other factors, TC =  f(..)/  t Change in output not explained by change in factors or environment – shift in production or cost function  Time shift the goal function. Lny it =  x it +  z i +  t + v it - u it.

[Part 7] 4/68 Stochastic FrontierModels Panel Data 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?

[Part 7] 5/68 Stochastic FrontierModels Panel Data The Cross Section Departure Point: 1977

[Part 7] 6/68 Stochastic FrontierModels Panel Data A 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

[Part 7] 7/68 Stochastic FrontierModels Panel Data The Panel Data Models Appear: 1981 Time fixed

[Part 7] 8/68 Stochastic FrontierModels Panel Data Estimating Technical Efficiency

[Part 7] 9/68 Stochastic FrontierModels Panel Data Stochastic Frontiers with a Rayleigh Distribution Gholamreza Hajargasht, Department of Economics, University of Melbourne, 2013

[Part 7] 10/68 Stochastic FrontierModels Panel Data Rayleigh vs. Half Normal Swiss Railway Data Rayleigh Half Normal

[Part 7] 11/68 Stochastic FrontierModels Panel Data Reinterpreting the Within Estimator: 1984 Time fixed

[Part 7] 12/68 Stochastic FrontierModels Panel Data Schmidt and Sickles FE Model lny it =  + β ’ x it + a i + v it estimated by least squares (‘within’)

[Part 7] 13/68 Stochastic FrontierModels Panel Data Misgivings About Time Fixed Inefficiency: 1990-

[Part 7] 14/68 Stochastic FrontierModels Panel Data Battese and Coelli Models

[Part 7] 15/68 Stochastic FrontierModels Panel Data Variations on Battese and Coelli  (There are many)  Farsi, M. JPA, 30,2, 2008.

[Part 7] 16/68 Stochastic FrontierModels Panel Data Time Invariant Heterogeneity

[Part 7] 17/68 Stochastic FrontierModels Panel Data Observable Heterogeneity

[Part 7] 18/68 Stochastic FrontierModels Panel Data Are the time varying inefficiency models more like time fixed or freely time varying?

[Part 7] 19/68 Stochastic FrontierModels Panel Data

[Part 7] 20/68 Stochastic FrontierModels Panel Data Greene, W., Distinguishing Between Heterogeneity and Inefficiency: Stochastic Frontier Analysis of the World Health Organization’s Panel Data on National Health Care Systems, Health Economics, 13, 2004, pp

[Part 7] 21/68 Stochastic FrontierModels Panel Data True Random and Fixed Effects: 2004 Time varying Time fixed

[Part 7] 22/68 Stochastic FrontierModels Panel Data The True RE Model is an RP Model

[Part 7] 23/68 Stochastic FrontierModels Panel Data Skepticism About Time Varying Inefficiency Models: Greene (2004)  

[Part 7] 24/68 Stochastic FrontierModels Panel Data Estimation of TFE and TRE Models: 2004

[Part 7] 25/68 Stochastic FrontierModels Panel Data A True FE Model

[Part 7] 26/68 Stochastic FrontierModels Panel Data 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

[Part 7] 27/68 Stochastic FrontierModels Panel Data

[Part 7] 28/68 Stochastic FrontierModels Panel Data

[Part 7] 29/68 Stochastic FrontierModels Panel Data TRE SF Model for 247 Spanish Dairy Farms

[Part 7] 30/68 Stochastic FrontierModels Panel Data Moving Heterogeneity Out of Inefficiency World Health Organization study of life expectancy (DALE) and composite health care delivery (COMP)

[Part 7] 31/68 Stochastic FrontierModels Panel Data

[Part 7] 32/68 Stochastic FrontierModels Panel Data

[Part 7] 33/68 Stochastic FrontierModels Panel Data

[Part 7] 34/68 Stochastic FrontierModels Panel Data A Stochastic Frontier Model with Short- Run and Long-Run Inefficiency: Colombi, R., Kumbhakar, S., Martini, G., Vittadini, G. University of Bergamo, WP, 2011

[Part 7] 35/68 Stochastic FrontierModels Panel Data

[Part 7] 36/68 Stochastic FrontierModels Panel Data Tsionas, G. and Kumbhakar, S. Firm Heterogeneity, Persistent and Transient Technical Inefficiency: A Generalized True Random Effects Model Journal of Applied Econometrics. Published online, November, Forthcoming. Extremely involved Bayesian MCMC procedure. Efficiency components estimated by data augmentation.

[Part 7] 37/68 Stochastic FrontierModels Panel Data Kumbhakar, Lien, Hardaker Technical Efficiency in Competing Panel Data Models: A Study of Norwegian Grain Farming, JPA, Published online, September, Three steps based on GLS: (1) RE/FGLS to estimate ( ,  ) (2) Decompose time varying residuals using MoM and SF. (3) Decompose estimates of time invariant residuals.

[Part 7] 38/68 Stochastic FrontierModels Panel Data

[Part 7] 39/68 Stochastic FrontierModels Panel Data Estimating Efficiency in the CSN Model

[Part 7] 40/68 Stochastic FrontierModels Panel Data 247 Farms, 6 years. 100 Halton draws. Computation time: 35 seconds including computing efficiencies.

[Part 7] 41/68 Stochastic FrontierModels Panel Data Estimated efficiency for farms 1-10 of 247.

[Part 7] 42/68 Stochastic FrontierModels Panel Data

[Part 7] 43/68 Stochastic FrontierModels Panel Data Cost Efficiency of Swiss Railway Companies: Model Specification C = f ( Y 1, Y 2, P L, P C, P E, N, DA ) 43 C = Total costs Y 1 = Passenger-km Y 2 = Freight ton-km P L = Price of labor (wage per FTE) P C = Price of capital (capital costs / total number of seats) P E = Price of electricity N = Network length DA = Dummy variable for companies also operating alpine lines

[Part 7] 44/68 Stochastic FrontierModels Panel Data Data  50 railway companies, Period 1985 to 1997  Unbalanced panel with number of periods (Ti) varying from 1 to 13 and with 45 companies with 12 or 13 years, resulting in 605 observations  Data source: Swiss federal transport office  Data set available at  Data set used in: Farsi, Filippini, Greene (2005), Efficiency and measurement in network industries: application to the Swiss railway companies, Journal of Regulatory Economics 44

[Part 7] 45/68 Stochastic FrontierModels Panel Data Model Specifications: Special Cases and Extensions  Pitt and Lee  True Random Effects  Extended True Random Effects  Mundlak correction for the REM, group means of time varying variables  Extended True Random Effects with Heteroscedasticity in v it :  v,it =  v exp(  ’z it )

[Part 7] 46/68 Stochastic FrontierModels Panel Data Efficiency Estimates 46 TRE Models Move Heterogeneity Out of the Inefficiency Estimate

[Part 7] 47/68 Stochastic FrontierModels Panel Data 2. Cost Efficiency of Norwegian Electricity Distribution Companies: Model Specification C = f ( Y, CU, NL, P L, P C ) 47 C = Total costs of the distribution activity Y = Output (total energy delivered in kWh) CU = Number of customers NL = Network length in km P L = Price of labor (wage per FTE) P C = Price of capital (capital costs / transformer capacity)

[Part 7] 48/68 Stochastic FrontierModels Panel Data Data  111 Norwegian electricity distribution utilities  Period 1998 – 2002  Balanced panel with 555 observations  Data source: Norwegian electricity regulatory authority (Unpublished) 48

[Part 7] 49/68 Stochastic FrontierModels Panel Data Mundlak Specification Suggests e i or w i may be correlated with the inputs.

[Part 7] 50/68 Stochastic FrontierModels Panel Data Efficiency Estimates 50

[Part 7] 51/68 Stochastic FrontierModels Panel Data Appendix A: Implementation  Customized version of NLOGIT 5/LIMDEP 10.  Both instructions exist in current version. Modifications were:  For the generalized TRE, allow the random constant term in the TRE model to have a second random component that has a half normal distribution.  For the selection model, allow products of groups of observations to appear as the contribution to the simulated log likelihood  Now available from the author as an update to LIMDEP or NLOGIT. To be released with the next version.

[Part 7] 52/68 Stochastic FrontierModels Panel Data

[Part 7] 53/68 Stochastic FrontierModels Panel Data DISTANCE FUNCTION

[Part 7] 54/68 Stochastic FrontierModels Panel Data A Distance Function Approach

[Part 7] 55/68 Stochastic FrontierModels Panel Data Kriese Study of Municipalities

[Part 7] 56/68 Stochastic FrontierModels Panel Data

[Part 7] 57/68 Stochastic FrontierModels Panel Data

[Part 7] 58/68 Stochastic FrontierModels Panel Data

[Part 7] 59/68 Stochastic FrontierModels Panel Data

[Part 7] 60/68 Stochastic FrontierModels Panel Data

[Part 7] 61/68 Stochastic FrontierModels Panel Data

[Part 7] 62/68 Stochastic FrontierModels Panel Data

[Part 7] 63/68 Stochastic FrontierModels Panel Data TOTAL FACTOR PRODUCTIVITY

[Part 7] 64/68 Stochastic FrontierModels Panel Data Factor Productivity Growth  Change in output attributable to change in factors, holding the technology constant  Malmquist index of change in technical efficiency  TE(t+1|t) = technical efficiency in period t+1 based on factor usage in period t+1 in comparison to firms using factors and producing output in period t.  Index measures the change in productivity

[Part 7] 65/68 Stochastic FrontierModels Panel Data TFP measurement using DEA

[Part 7] 66/68 Stochastic FrontierModels Panel Data

[Part 7] 67/68 Stochastic FrontierModels Panel Data Total Factor Productivity Growth Spanish Dairy Farms

[Part 7] 68/68 Stochastic FrontierModels Panel Data Malmquist Index of Factor Productivity Growth Spanish Dairy Farms