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POOL

The POOL command can be used to combine cross section and time series data under certain model specifications and conditions. Pooled Cross-Section Time Series data (aka Panel Data) takes the form of N cross-sectional units (a cross-sectional unit is, for example, a household, an industry or a region) with T(i) observations for cross-section i, i = 1, . . . , N. This command provides methods for dealing with Cross-Section Heteroskedasticity and Time-wise Autoregression. Lagrange Multiplier Tests and Standard Errors corrections are available.

In general, the format is:

POOL depvar indeps / options NC=

The available options are:

OPTION DESCRIPTION
anova Prints the ANalysis Of VAriance tables and the F-statistic for the test that all coefficients are zero. In some restricted models, the F-test from an ANOVA table is invalid. In these cases the F-statistic will not be printed, but may be obtained with the TEST command. Model Selection Tests are also printed.
ar1 Transform the observations to correct for AR(1) errors, but do not allow for cross-section heteroskedasticity. When this option is specified the SAME, CORCOEF and HETCOV options are also available.
beg= Specifies the BEGinning observation to be used in estimation. This option overrides the SAMPLE command and defaults to the sample range in effect.
blup The predicted values are adjusted using information obtained from previous period residuals according to the transformation specified by the P matrix. This option is not effective in forecasts using the GLS coefficients.
coef= Saves the estimated coefficients, the RHO vector, and the square root of the diagonal elements of the PHI matrix in the variable specified.
conv= Specifies a convergence criterion to stop the iterative procedure when the ITER= option is used. The default is 0.001.
corcoef Estimates the autoregressive parameters rho(i) using the correlation coefficient form. This method confines the estimate of rho(i) to the interval [ 1,+1].
cov= Saves the COVariance matrix of coefficients in the variable specified.
csindex= Specifies a variable that contains the cross-section identifier for each observation. The cross-section identifier must be a positive number. The NCROSS= option must also be specified. If the CSINDEX= option is not specified then the estimation assumes balanced panels.
dlag Used to compute Durbin's h statistic when there is a LAGged Dependent variable. DN Uses a divisor of N instead of N-K for SIGMA**2. The lagged dependent variable must be the first listed independent variable when this option is used. The h statistic is useful since the Durbin-Watson statistic may not be valid in such situations. Durbin's h statistic cannot always be computed since the square root of a negative number may be required. In such cases, the h statistic will neither be computed nor printed. It is essential to remember that when lagged variables have been generated a SAMPLE command must be included to delete the beginning observations.
dn Uses a divisor of T(i) instead of T(i)-K , i = 1, . . . , N when calculating the PHI matrix. That is, no degrees of freedom correction is considered in the estimation of error variances.
dump DUMPS large amounts of output mainly useful to SHAZAM Consultants
end= Specifies the ENDing observation to be used in estimation. This option overrides the SAMPLE command and defaults to the sample range in effect.
fixed Estimates a fixed effects model. This model assumes that the intercept varies across cross-sections.
full Estimates the FULL cross-sectionally correlated and time-wise autoregressive model. This option is not available with the CSINDEX= option. If the FULL option is not specified then the model assumptions are cross-sectional heteroskedasticity with cross-sectional independence. The UT or BLUP options are recommended as the transformed residuals in the FULL model are sensitive to order of the cross-sections and have no useful interpretation. The FULL option is not available when N > T (when there are a large number of cross-sections but the number of time series is few). When N > T the estimated error covariance matrix PHI is singular and SHAZAM will terminate with the message MATRIX IS NOT POSITIVE DEFINITE.
gf Prints Goodness of Fit tests for normality of residuals. Coefficients of skewness and excess kurtosis and the Jarque-Bera test for normality of the residuals are also computed.
hetcov For pooled OLS estimation, calculate a panel-corrected covariance matrix of the coefficient estimates and report the panel-corrected standard errors. If the AR1 option is also specified then the estimation considers AR(1) errors for each cross-section.
iter= Specifies the maximum number of iterations if an iterative procedure is desired. If this option is not specified then one iteration is done.
lininv Used when the dependent variable is LINear, but the independent variables are in INVerse form. This type of model is known as the reciprocal model. This option only affects the calculation of the elasticities. NOTE: This option does not transform the data. The data must be transformed by the user with the appropriate GENR commands or the Data Editor. See the chapter ORDINARY LEAST SQUARES in the SHAZAM Reference Manual.
linlog Used when the dependent variable is LINear, but the independent variables are in LOG form. This option only affects the calculation of the elasticities. NOTE: This option does not transform the data. The data must be transformed by the user with the appropriate GENR commands or the Data Editor. See the chapter ORDINARY LEAST SQUARES in the SHAZAM Reference Manual.
list LISTs and plots the residuals and predicted values of the dependent variable and residual statistics. When LIST is specified RSTAT is automatically turned on.
loginv Used when the dependent variable is in LOG form, and the independent variables are in INVerse form.
loglin Used when the dependent variable is in LOG form, but the independent variables are LINear. This option only affects the calculation of the elasticities. NOTE: This option does not transform the data. The data must be transformed by the user with the appropriate GENR commands or the Data Editor. See the chapter ORDINARY LEAST SQUARES in the SHAZAM Reference Manual.
loglog Used when the dependent variable is in LOG form, and the independent variables are in LOG form. This option only affects the calculation of the elasticities. NOTE: This option does not transform the data. The data must be transformed by the user with the appropriate GENR commands or the Data Editor. See the chapter ORDINARY LEAST SQUARES in the SHAZAM Reference Manual.
max Prints Analysis of Variance Tables, Variance-covariance matrix, Correlation matrix, Residuals, Residual Statistics and Goodness of Fit Test for Normality. This option is equivalent to using the ANOVA, LIST, PCOV, PCOR and GF options. Users should be sure the MAX output is necessary, otherwise unnecessary calculations are required.
mulsigsq Multiplies Covariance Matrix by Sigma**2. This option is the default, but can be turned off with the NOMULSIGSQ option.
ncross= Specifies the number of cross-sectional units in the data. This option is required. With balanced panels, the NTIME= option can be used as a substitute.
noconstant There will be NO CONSTANT (intercept) in the estimated equation. This option is used when the intercept is to be suppressed in the regression or when the user is supplying the intercept. This option should be used with caution as some of the usual output may be invalid. In particular, the usual R^2 is not well defined and could be negative. However, when this option is used, the raw moment R^2 may be of interest. The ANALYSIS OF VARIANCE - FROM MEAN table will not be computed if this option is used.
nomulsigsq When NOMULSIGSQ is specified the estimated covariance matrix will just be X'X inverse. i.e. the complete covariance matrix of the estimated coefficients and is NOt MULtiplied by Sigma-squared.
ntime= With balanced panels, specifies the number of time periods in the data. This option is required if the NCROSS= option is not used. If both NCROSS= and NTIME= are specified, NCROSS= is ignored.
ols Estimation by pooled OLS.
pcor Prints the CORrelation matrix of the estimated coefficients. This should not be confused with a correlation matrix of variables which can be obtained with a STAT command.
pcov Prints the covariance matrix of coefficients. In addition it prints the PHI matrix if NCROSS= is greater than 8. If NCROSS= is less than 8 the PHI matrix is always printed.
predict= Saves the PREDICTed values of the dependent variable in the variable specified.
resid= Saves the values of the RESIDuals from the regression in the variable specified.
restrict Forces linear RESTRICTions into the regression. It tells SHAZAM that RESTRICT commands follow. Restrictions must be linear. This option may not be used with DWPVALUE or METHOD=HH.
rho= Specifies a fixed value of RHO to use. If this is not specified the autoregressive parameters are estimated. When this option is used the SAME option is automatically in effect. This option is commonly used with RHO=0 to suppress the autocorrelation correction so that only the heteroskedastic correction is performed.
rstat Prints Residual Summary STATistics. The output includes the Durbin-Watson statistic and related residual test statistics. It also includes the Runs Test. When the LIST option is specified RSTAT is automatically turned on.
same Forces all values of rho(i) to be equal for each of the cross-sections
stderr= Saves the values of the STanDard ERRors of the coefficients in the variable specified.
tratio= Saves the values of the T-RATIOs in the variable specified.
ut The estimated coefficients will be used with the original data to compute predicted values and residuals that are UnTransformed. Without this option, the residual output and predicted values given are transformed.

The available temporary variables on the POOL command are:

$ANF, $DF, $ERR, $DW, $K, $LLF, $N, $R2, $R2OP, $RAW, $RHO, $SIG2, $SSE, $SSR, $SST, $ZANF, $ZDF, $ZSSR, $ZSST.