conditional pricing model using GMM

[Yura Kim]

Hi everyone!
I have a question about GMM command of Stata
Following Choi,Hiriki, Takezawa(1998), I utilize the conditional pricing model and pricing error and innovation.
Three equation is as follow:
1.Conditional model: E(R_i,tlomega_t-1)=lamda₀(omega_t-1)+gamma_LMcov(R_i,t,R_LMtㅣomega_t-1)+gamma_WMcov(R_i,t,R_WMtㅣomega_t-1)+gamma_FXcov(R_i,t,R_FXtㅣomega_t-1)
2.pricing error: u_t=-Z_t-1r₀+Z_t-1r_LMR_LM,t+Z_t-1r_WMR_WM,t+Z_t-1r_FXR_FX,t
3.innovation: h_i,t=R_i,t-R_i,tu_t


,where Z is instumental variables. The pricing error should be zero and the expected value of innovations is zero. Choi,Hiriki, Takezawa(1998) used GMM method to the set of equations in pricing error and innovation.So they obtained estimates of r₀,r_LM,r_WM,r_FX. I want to analyze conditional model following them.

I use Hansen(1982)’s GMM method aplying pricing kernel.
So the STATA code I executed is as follows.
[CODE]
.gmm(eq1:rit_a-{a0}-{a1}*cov1-{a2}*cov2-{a3}*cov3)
(eq2:rit_a-{a0}-{a1}*cov1-{a2}*cov2-{a3}*cov3), instruments(eq1:lag1 lag2 lag3 Jandum) instruments(eq2:lag1) winitial(identity)
warning: 359978 missing values returned for equation 1 at initial values
warning: 359978 missing values returned for equation 2 at initial values

Step 1
Iteration 0: GMM criterion Q(b) = 1.9949011
Iteration 1: GMM criterion Q(b) = 1.537e-06
Iteration 2: GMM criterion Q(b) = 1.537e-06

Step 2
Iteration 0: GMM criterion Q(b) = 8.837e-07
Iteration 1: GMM criterion Q(b) = 7.546e-07
Iteration 2: GMM criterion Q(b) = 7.546e-07

GMM estimation

Number of parameters = 4
Number of moments = 7
Initial weight matrix: Identity Number of obs = 575207
GMM weight matrix: Robust

------------------------------------------------------------------------------
| Robust
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
/a0 | -.4532532 .0876545 -5.17 0.000 -.6250529 -.2814535
/a1 | -.0992952 .0192035 -5.17 0.000 -.1369334 -.061657
/a2 | .0293273 .005053 5.80 0.000 .0194235 .039231
/a3 | -64.23148 9.697605 -6.62 0.000 -83.23844 -45.22452
------------------------------------------------------------------------------
Instruments for equation 1: lag1 lag2 lag3 Jandum _cons
Instruments for equation 2: lag1 _cons

. estat overid

Test of overidentifying restriction:

Hansen's J chi2(3) = .434048 (p = 0.9331)



But I'm not sure if this is done right.
I want to analyze all the above three equations.
Any help is highly appreciated.
Thank you for your time.

[Phil Bromiley]

You will increase your chances of a helpful answer by following the faq on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

I don't use GMM, but I don't understand why you would have two equations with precisely the same specifications in the model. I also don't understand exactly how your three equations hang together. It certainly looks like your three equations are a lot more complex than what you have in the GMM statement.

First, it would help if you solve the three equations model so that it looks somewhat like what you intend to estimate in the GMM. It would also help if you use the same notation in both so that we don't have to try to guess the conversion between lambda, gamma, Omega, and a1, a2, a3 and what the cov variables are. This may be obvious to someone who works in GMM but the easier mate you make it for us the more likely you are to get a useful answer.

A full GMM seems like a somewhat challenging estimation for what appears to be your first efforts at Stata.