1. L9: SDF 1 Lecture 9: C-CAPM and GMM Estimation GMM Overview Applying GMM Note: a benefit of GMM approach is this approach generates consistent parameters.

2. L9: SDF 2 Estimating SDF -- GMM

3. L9: SDF 3 Estimating SDF – Second Stage

4. L9: SDF 4 Implementing GMM

5. L9: SDF 5 GMM Example

6. L12: SDF 6 GMM Example (2)

7. L9: SDF 7 GMM Example (3)

8. L9: SDF 8 Program GMM using SAS /* N=5, 7 instruments */ proc model data=gmm; parms beta 1.0 gamma 1.0; endogenous cons0 cons1; exogenous r1 r2 r3 r4 r5; instruments lrm1 lrm2 lrm3 lrm4 lrm5 lrm6; eq.m1=1-(1+r0)*(beta*(cons0/cons1)**(-gamma); fit m1-m6/gmm kernel=(parzen, 1,0); ods output EstSummaryStats=parms; run;

9. L9: SDF 9 More on Hypothesis Testing Testing J linear Restrictions We can base a test of H0 on the Wald criterion: The chi-squared statistic is not usable when σ2 is unknown. As an alternative, we have the following F statistic

10. L9: SDF 10 Examples of J Restrictions Each row of R is a single linear restriction on the coefficient vector.

11. L9: SDF 11 More Examples