The MODEL Procedure |

MOMENT Statement |

- MOMENT variables = moment specification ;

*variables* can be one or more endogenous variables.

*moment specification* can have the following four types:

(

*number list*) specifies that the endogenous variable is raised to the power specified by each number in*number list*. For example,moment y = (2 3);

adds the following two equations to be estimated:

eq._moment_1 = y**2 - pred.y**2; eq._moment_2 = y**3 - pred.y**3;

ABS(

*number list*) specifies that the absolute value of the endogenous variable is raised to the power specified by each number in*number list*. For example,moment y = ABS(3);

adds the following equation to be estimated:

eq._moment_2 = abs(y)**3 - abs(pred.y)**3;

LAG

*num*(*number list*) specifies that the endogenous variable is multiplied by the*num*th lag of the endogenous variable, and this product is raised to the power specified by each number in*number list*. For example,moment y = LAG4(3);

adds the following equation to be estimated:

eq._moment_3 = (y*lag4(y))**3 - (pred.y*lag4(pred.y))**3;

ABS_LAG

*num*(*number list*) specifies that the endogenous variable is multiplied by the*num*th lag of the endogenous variable, and the absolute value of this product is raised to the power specified by each number in*number list*. For example,moment y = ABS_LAG4(3);

adds the following equation to be estimated:

eq._moment_4 = abs(y*lag4(y))**3 - abs(pred.y*lag4(pred.y))**3;

The following PROC MODEL statements use the MOMENT statement to generate 24 moments and fit these moments using SMM.

proc model data=_tmpdata list; parms a b .5 s 1; instrument _exog_ / intonly; u = rannor( 10091 ); z = rannor( 97631 ); lsigmasq = xlag(sigmasq,exp(a)); lnsigmasq = a + b * log(lsigmasq) + s * u; sigmasq = exp( lnsigmasq ); y = sqrt(sigmasq) * z; moment y = (2 4) abs(1 3) abs_lag1(1 2) abs_lag2(1 2); moment y = abs_lag3(1 2) abs_lag4(1 2) abs_lag5(1 2) abs_lag6(1 2) abs_lag7(1 2) abs_lag8(1 2) abs_lag9(1 2) abs_lag10(1 2); fit y / gmm npreobs=20 ndraw=10; bound s > 0, 1>b>0; run;

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