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 @@;
      df1 = firm = 1;
      df2 = firm = 2;
      df3 = firm = 3;
      df4 = firm = 4;
      df5 = firm = 5;
      d60 = year = 1960;
      d65 = year = 1965;
      d70 = year = 1970;
       1 1955   5.36598   1.14867  1 1960   6.03787   1.45185

   ... more lines ...   

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 RANTWO option specifies the two-way random-effects error model where the variance components are estimated by the Fuller-Battese method, because the data are balanced and the parameters are efficiently estimated by using the GLS method. The variance components model used by the Fuller-Battese method is

\[  y_{it}=\sum _{k=1}^{K}{X_{itk}{{\bbeta }}_{k}}+v_{i}+e_{t}+{\epsilon }_{it} i=1, {\ldots }, \mi {N} ; t=1, {\ldots }, \mi {T}  \]

The following statements fit this model.

proc sort data=greene;
   by firm year;

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

The TSCSREG procedure output is shown in Figure 34.1. A model description is printed first; it 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.

Figure 34.1: The Variance Components Estimates

The TSCSREG Procedure
Fuller and Battese Variance Components (RanTwo)
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