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1、Econometric Analysis of Panel Data,William Greene Department of Economics Stern School of Business,Econometric Analysis of Panel Data,21. Stochastic Frontier Models And Efficiency Measurement,Applications,Banking Accounting Firms, Insurance Firms Health Care: Hospitals, Nursing Homes Higher Educatio
2、n Fishing Sports: Hockey, Baseball World Health Organization World Health Industries: Railroads, Farming, Several hundred applications in print since 2000,Neoclassical Production,Technical Efficiency,Technical Inefficiency,= Production parameters, “i” = firm i.,Regression Basis,Maintaining the Theor
3、y,One Sided Residuals, ui 0.,Other Possible Distributions,Normal vs. Exponential Models,Estimating Inefficiency,Dual Cost Function,Application: Electricity Data,Sample = 123 Electricity Generating Firms, Data from 1970 Variable Mean Std. Dev. Description = FIRM 62.000 35.651 Firm number, 1,123 COST
4、48.467 64.064 Total cost OUTPUT 9501.1 12512. Total generation in KWH CAPITAL .14397 .19558 K = Capital share * Cost / PK LABOR .00074 .00099 L = Labor share * Cost / PL FUEL 1.0047 1.2867 F = Fuel share * Cost / PL LPRICE 7988.6 1252.8 PL = Average labor price LSHARE .14286 .056310 Labor share in t
5、otal cost CPRICE 72.895 9.5163 PK = Capital price CSHARE .22776 .06010 Capital share in total cost FPRICE 30.807 7.9282 PF = Fuel price in cents ber BTU FSHARE .62938 .08619 Fuel share in total cost LOGC_PF -.38339 1.5385 Log (Cost/PF) LOGQ 8.1795 1.8299 Log output LOGQSQ 35.113 13.095 Log (Q)2,OLS
6、Cost Function,+-+ | Ordinary least squares regression | | Residuals Sum of squares = 2.443509 | | Standard error of e = .1439017 | | Fit R-squared = .9915380 | | Diagnostic Log likelihood = 66.47364 | +-+ |Variable | Coefficient | Standard Error |t-ratio |P|T|t | Mean of X| +-+-+-+-+-+-+Constant -7.
7、29402077 .34427692 -21.186 .0000LOGQ .39090935 .03698792 10.569 .0000 8.17947153LOGPL_PF .26078497 .06810921 3.829 .0002 5.58088278LOGPK_PF .07478746 .06164533 1.213 .2275 .88666047LOGQSQ .06241301 .00515483 12.108 .0000 35.1125267,ML Cost Function,+-+ | Maximum Likelihood Estimates | | Log likeliho
8、od function 66.86502 | | Variances: Sigma-squared(v)= .01185 | | Sigma-squared(u)= .02233 | | Sigma(v) = .10884 | | Sigma(u) = .14944 | | Sigma = Sqr(s2(u)+s2(v)= .18488 | +-+ |Variable | Coefficient | Standard Error |b/St.Er.|P|Z|z | Mean of X| +-+-+-+-+-+-+Primary Index Equation for ModelConstant
9、-7.49421176 .32997411 -22.712 .0000LOGQ .41097893 .03599288 11.418 .0000 8.17947153LOGPL_PF .26058898 .06554430 3.976 .0001 5.58088278LOGPK_PF .05531289 .06001748 .922 .3567 .88666047LOGQSQ .06058236 .00493666 12.272 .0000 35.1125267Variance parameters for compound errorLambda 1.37311716 .29711056 4
10、.622 .0000Sigma .18487506 .00110120 167.884 .0000,Estimated Efficiencies,Firms Ranked by Output,Panel Data Applications,Ui is the effect Fixed (OLS) or random effect (ML) Is inefficiency fixed over time?True fixed and random effects Is inefficiency time varying? Where does heterogeneity show up in t
11、he model?,Health Care Systems,WHO Was Interested in Broad Goals of a Health System,They Created a Measure COMP = Composite Index,“In order to assess overall efficiency, the first step was to combine the individual attainments on all five goals of the health system into a single number, which we call
12、 the composite index. The composite index is a weighted average of the five component goals specified above. First, country attainment on all five indicators (i.e., health, health inequality, responsiveness-level, responsiveness-distribution, and fair-financing) were rescaled restricting them to the
13、 0,1 interval. Then the following weights were used to construct the overall composite measure: 25% for health (DALE), 25% for health inequality, 12.5% for the level of responsiveness, 12.5% for the distribution of responsiveness, and 25% for fairness in financing. These weights are based on a survey carried out by WHO to elicit stated preferences of individuals in their relative valuations of the goals of the health system.”(From the World Health Organization Technical Report),
