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The TSCSREG Procedure

Introductory Example

The following example uses the cost function data from Greene (1990) to estimate the variance components model. The variable OUTPUT is the log of output in millions of kilowatt-hours, and COST is the log of cost in millions of dollars. Refer to Greene (1990) for details.


   data greene;
      input firm year output cost @@;
   cards;
        1 1955   5.36598   1.14867  1 1960   6.03787   1.45185
        1 1965   6.37673   1.52257  1 1970   6.93245   1.76627
        2 1955   6.54535   1.35041  2 1960   6.69827   1.71109
        2 1965   7.40245   2.09519  2 1970   7.82644   2.39480
        3 1955   8.07153   2.94628  3 1960   8.47679   3.25967
        3 1965   8.66923   3.47952  3 1970   9.13508   3.71795
        4 1955   8.64259   3.56187  4 1960   8.93748   3.93400
        4 1965   9.23073   4.11161  4 1970   9.52530   4.35523
        5 1955   8.69951   3.50116  5 1960   9.01457   3.68998
        5 1965   9.04594   3.76410  5 1970   9.21074   4.05573
        6 1955   9.37552   4.29114  6 1960   9.65188   4.59356
        6 1965  10.21163   4.93361  6 1970  10.34039   5.25520
   ;
   
   proc sort data=greene;
      by firm year;
   run;

Usually you cannot explicitly specify all the explanatory variables that affect the dependent variable. The omitted or unobservable variables are summarized in the error disturbances. The TSCSREG procedure used with the Fuller-Battese method adds the individual and time-specific random effects to the error disturbances, and the parameters are efficiently estimated using the GLS method. The variance components model used by the Fuller-Battese method is

y_{it}=\sum_{k=1}^K{X_{itk}{{\beta}}_{k}}+v_{i}+e_{t}+{\epsilon}_{it}
\hspace*{1em} i=1, { ... }, N;\hspace*{1em} t=1, { ... }, T

The following statements fit this model. Since the Fuller-Battese is the default method, no options are required.


   proc tscsreg data=greene;
      model cost = output;
      id firm year;
   run;

The TSCSREG procedure output is shown in Figure 20.1. A model description is printed first, which reports the estimation method used and the number of cross sections and time periods. The variance components estimates are printed next. Finally, the table of regression parameter estimates shows the estimates, standard errors, and t-tests.

 
The TSCSREG Procedure
Dependent Variable: cost

Model Description
Estimation Method RanTwo
Number of Cross Sections 6
Time Series Length 4
 
Fit Statistics
SSE 0.3481 DFE 22
MSE 0.0158 Root MSE 0.1258
R-Square 0.8136    
 
Variance Component Estimates
Variance Component for Cross Sections 0.046907
Variance Component for Time Series 0.00906
Variance Component for Error 0.008749
 
Hausman Test for Random Effects
DF m Value Pr > m
1 26.46 <.0001
 
Parameter Estimates
Variable DF Estimate Standard Error t Value Pr > |t|
Intercept 1 -2.99992 0.6478 -4.63 0.0001
output 1 0.746596 0.0762 9.80 <.0001
Figure 20.1: The Variance Components Estimates

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