* LIMITED INFORMATION MAXIMUM LIKELIHOOD * This example was proposed by Professor Ray Byron of Bond University * in Australia. SHAZAM computes Two-Stage Least Squares estimation of a * single equation in a simultaneous equation model with the 2SLS command as * described in the chapter TWO-STAGE LEAST SQUARES AND SYSTEMS OF EQUATIONS. * An alternative estimation method is Limited Information Maximum Likelihood * (LIML). * See Amemiya [1985, Section 7.3.2] for further information on LIML and * the notation used in this example. * The method shown in this procedure can be also be used to compute * k-Class estimates by selecting a desired value of k. SET NOECHO PROC LIML * If you do not want the PROC commands to print during the EXEC phase * then SET NODOECHO here, only do this after the PROC is working properly. SET NODOECHO * ************************************************************* * INPUTS REQUIRED: EXOG, RHSEXOG RHSENDOG ENDOG * ************************************************************* * To keep Proc variables distinct from others append the _ symbol * This is not required but it eliminates confusion * * Define X as all exogenous variables in system COPY [EXOG] X_ / TROW=1,\$N * Define X1 as right-hand-side exogenous variables COPY [RHSEXOG] X1_ / TROW=1,\$N * Define Y1 as all right-hand-side endogenous variables COPY [RHSENDOG] Y1_ / TROW=1,\$N * Define Y as all endogenous variables in equation COPY [ENDOG] Y_ / TROW=1,\$N * Define the Left hand side endogenous variable COPY [LHS] Y2_ / TROW=1,\$N * ************************************************************* * Define Z as all right-hand-side variables, exogenous first MATRIX Z_= X1_ | Y1_ * Compute the M matrices for X and X1 GEN1 ROWS_=\$ROWS GEN1 COLS_=\$COLS MATRIX M_=IDEN(ROWS_)-X_*INV(X_'X_)*X_' MATRIX M1_=IDEN(ROWS_)-X1_*INV(X1_'X1_)*X1_' * Compute W and W1 MATRIX W_=Y_'M_*Y_ MATRIX W1_=Y_'M1_*Y_ * Get the eigenvalues from the W1 and INV(W) matrix computations MATRIX LAMBDA_=EIGVAL(W1_*INV(W_)) PRINT LAMBDA_ * Get the minimum eigenvalue and use it for k STAT LAMBDA_ / MIN=K_ PRINT K_ * Note that k-class estimation can be done by choosing * a different value of k MATRIX ALPHA_=INV(Z_'(IDEN(ROWS_)-K_*M_)*Z_) * Z_'(IDEN(ROWS_)-K_*M_)*Y2_ * Now print the LIML coefficients * The order is: CONSTANT PLAG P WGWP ATITLE_: The estimated coefficient vector is: PRINT ATITLE_ / NONAME PRINT ALPHA_ / NONAME * Get the residuals and variance MATRIX E_=Y2_-Z_*ALPHA_ * Print SIGMA**2 using 17 Degrees of freedom MATRIX SIG2_=E_'E_/(ROWS_-COLS_) ATITLE_: The estimated value of SIGMA-SQUARED is: PRINT ATITLE_ / NONAME PRINT SIG2_ / NONAME * Get the Covariance matrix MATRIX V_=SIG2_*INV(Z_'(IDEN(ROWS_)-K_*M_)*Z_) ATITLE_: COVARIANCE MATRIX OF COEFFICIENTS PRINT ATITLE_ / NONAME PRINT V_ / NONAME * Get the standard errors MATRIX SE_=SQRT(DIAG(V_)) PRINT SE_ * Now delete all the PROC variables DELETE / ALL_ SET DOECHO PROCEND * THE PROC is over, turn echo back on again SET ECHO