Estimation of MRR (1997) model with GMM

[onem]

Tom,

I understand that when a model is just identified, for a given set of instruments, the point estimates don't depend upon the weight matrices.

Keeping the model just identified, when I choose different set of instruments, I get different results. This leads to subjectivity.

I am trying to avoid this subjectivity. If I use moment conditions only and no instrumental variables, then I do not have to worry about the sensitivity of the results to the choice of instruments. I will still keep the model just identified by having the number of moment conditions equal to the number of parameters. I wanted to know if there is a problem related to this.

[TomDoan]

But you are using instrumental variables---just a particular choice of them (1 and R(t) I assume). The terminology dates back to Hansen and Singleton(1982). Any function of R(t) is also available, and since the functions are non-linear it's not clear that the linear instrument is necessarily the best.

[onem]

Hi Tom,
It would be great if I can get your feedback about my program. I just want to make sure that it does not have errors before I begin estimations and writing a paper. Since the number of orthogonality conditions ( corr, cons, ols1, ols2 in nlsystem) is equal to the number of coefficients (4) to be estimated, model is just identified and J-statistic is not produced in the output. These 4 orthogonality conditions are specified in the MRR (1997) paper that I mentioned earlier. Thank you.

Code: Select all

*A=1 if transaction is buyer initiated and A=-1 if trade is seller initiated.
*L1A is last A.
*TrPrice is transaction price and L1TrPrice is last transaction price.
*
set Ret = 100*(TrPrice-L1TrPrice)
*
nonlin(parmset=baseparms) KV TV RV alpha
*
frml eps = Ret-(KV+TV)*A+(KV+RV*TV)*L1A
frml corr = A*L1A-A*A*RV
frml cons = eps-alpha
frml ols1 = eps*A-alpha*A
frml ols2 = eps*L1A-alpha*L1A
*
linreg Ret
# Constant A L1A
*
compute KV=%beta(2)*0.5
compute TV=%beta(2)*0.5
compute RV=0.5
compute alpha = %beta(1)
*
instruments L1A{1}
nlsystem(inst,parmset=baseparms,trace,zudep) / corr cons ols1 ols2
*
........

Non-Linear Optimization, Iteration 0. Function Calls 1.
 Cosine of Angle between Direction and Gradient  0.1535572. Alpha used was 0.000000
 Adjusted squared norm of gradient 12.7565
 Diagnostic measure (0=perfect) 0.0000
 Subiterations 1. Distance scale  1.000000000
Old Function = 9.136313         New Function = 2.254782
New Coefficients:
      0.112662       0.107324       0.296196      -0.001811

Non-Linear Optimization, Iteration 1. Function Calls 2.
 Cosine of Angle between Direction and Gradient  0.9264844. Alpha used was 0.000000
 Adjusted squared norm of gradient 1213.861
 Diagnostic measure (0=perfect) 0.7000
 Subiterations 1. Distance scale  1.000000000
Old Function = 18.281797        New Function = 0.000000
New Coefficients:
      0.121835       0.098151       0.296196      -0.001811

Non-Linear Optimization, Iteration 2. Function Calls 3.
 Cosine of Angle between Direction and Gradient  0.8024985. Alpha used was 0.000000
 Adjusted squared norm of gradient 2.718637e-020
 Diagnostic measure (0=perfect) 0.4200
 Subiterations 1. Distance scale  1.000000000
Old Function = 0.000000         New Function = 0.000000
New Coefficients:
      0.121835       0.098151       0.296196      -0.001811

GMM-Continuously Updated Weight Matrix
Convergence in     2 Iterations. Final criterion was  0.0000000 <=  0.0000100
Usable Observations                      1778678
Skipped/Missing (from 1778680)                 2
Function Value                   4.58938198e-022

    Variable                          Coeff       Std Error      T-Stat      Signif
***************************************************************************************
1.  KV                               0.121835011  0.013608726      8.95271  0.00000000
2.  TV                               0.098150551  0.026015506      3.77277  0.00016144
3.  RV                               0.296196264  0.074459016      3.97798  0.00006950
4.  ALPHA                           -0.001810637  0.001289142     -1.40453  0.16016167

[TomDoan]

CONSTANT isn't in your instrument set? That's usually there at a minimum.

[onem]

Thank you Tom.