Weak Identification in GMM and time series

[Deanna Brown]

Dear

I want to examine the Taylor rule use the GMM estimations, But I read some papers argue that this model has drawback such as weak identifications? How I can check it after I run my GMM models using time series data ??

Any help about the diagnostic tests to tackle this issue and to help me if my regressions are good fit??

[Carlo Lazzaro]

Deanna:
hopefully Sebastian Kripfganz 's previous replies cover the topic you're intrested in.

[Deanna Brown]

Dear @Sebastian Kripfganz I use the gmm commands in STATA to estimate the Taylor rule and my models are exact identification for 4 countries
my questions:
1- What are the postemation tests I can use it after the GMM models for time series data???
2- How I can implement the R square and adjusted R square ?
3- how I can tell to the reader that my model is good fit for my data and the forecast is robust?
4- My model is exact identification how I can test if the instruments are weak or not????
5- I notice that in my linear and non linear estimation using the gmm, once I split my shocks in to positive and negative the inflation gap in becomes significant and negative while in linear is not significant but still negative there is no economic interpretation for this : IS may be there are something wring in my gmm estimation??

My linear estimation in STATA

 gmm ( PolicyRate - {b1}* lag- {b2}* infgapt  -{b3}* outputgap  - {b4}* FEDPolicyRate  - {b5}* shock1  -{b6}* shock2
>   -{b7}* shock3 - {b0}), instruments(  smoothpolicyIR  infgap  outputgap1600   FEDPolicyRate shock1  shock2  shock3  )

Step 1
Iteration 0:   GMM criterion Q(b) =  5.1708628  
Iteration 1:   GMM criterion Q(b) =  2.667e-25  
Iteration 2:   GMM criterion Q(b) =  3.495e-33  

Step 2
Iteration 0:   GMM criterion Q(b) =  1.336e-31  
Iteration 1:   GMM criterion Q(b) =  2.414e-32  

note: model is exactly identified.

GMM estimation 

Number of parameters =   8
Number of moments    =   8
Initial weight matrix: Unadjusted                 Number of obs   =         50
GMM weight matrix:     Robust

------------------------------------------------------------------------------
             |               Robust
             | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         /b1 |   .6518003   .0734278     8.88   0.000     .5078844    .7957161
         /b2 |  -.0155327   .0102887    -1.51   0.131    -.0356981    .0046327
         /b3 |   .5714525    1.07031     0.53   0.593    -1.526316    2.669221
         /b4 |   .3239513   .0806144     4.02   0.000       .16595    .4819527
         /b5 |  -.0636603   .1244655    -0.51   0.609    -.3076082    .1802877
         /b6 |  -.0102865    .043342    -0.24   0.812    -.0952352    .0746622
         /b7 |   .0105484   .0135934     0.78   0.438    -.0160941    .0371909
         /b0 |    .362889   .0731644     4.96   0.000     .2194894    .5062885
------------------------------------------------------------------------------
Instruments for equation 1: smoothpolicyIR infgap outputgap FEDPolicyRate shock1 shock2 shock3 _cons

. 

My non linear models in to split the shocks to positive and negative

. gmm ( PolicyRate - {b1}* smoothpolicyIR  - {b2}* infgap  -{b3}* outputgap  - {b4}* FEDPolicyRate  - {b5}* shock1pos-{b6}*shock1neg -{b7}* shock2pos- {b8}* shock2neg-{b9}* shock3pos-{b10}* shock3neg- {b0}), instruments(  smoothpolicyIR  infgap  outputgap
>    FEDPolicyRate shock1pos shock1neg shock2pos shock2neg shock3pos shock3neg)

Step 1
Iteration 0:   GMM criterion Q(b) =  5.1750049  
Iteration 1:   GMM criterion Q(b) =  3.421e-25  
Iteration 2:   GMM criterion Q(b) =  1.537e-32  

Step 2
Iteration 0:   GMM criterion Q(b) =  4.693e-31  
Iteration 1:   GMM criterion Q(b) =  2.437e-31  

note: model is exactly identified.

GMM estimation 

Number of parameters =  11
Number of moments    =  11
Initial weight matrix: Unadjusted                 Number of obs   =         50
GMM weight matrix:     Robust

------------------------------------------------------------------------------
             |               Robust
             | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         /b1 |   .6794108   .0815899     8.33   0.000     .5194975     .839324
         /b2 |  -.0198003   .0101686    -1.95   0.052    -.0397304    .0001299
         /b3 |   .5905393   1.113342     0.53   0.596     -1.59157    2.772649
         /b4 |   .3292806   .0885114     3.72   0.000     .1558015    .5027597
         /b5 |   .1641691   .2276544     0.72   0.471    -.2820253    .6103635
         /b6 |  -.4526728   .3232403    -1.40   0.161    -1.086212    .1808666
         /b7 |    .055376   .0936189     0.59   0.554    -.1281136    .2388656
         /b8 |  -.2041953   .1606201    -1.27   0.204    -.5190048    .1106143
         /b9 |   .0243778   .0229175     1.06   0.287    -.0205397    .0692953
        /b10 |  -.0413273   .0584144    -0.71   0.479    -.1558174    .0731628
         /b0 |   .4412144   .0964731     4.57   0.000     .2521306    .6302983
------------------------------------------------------------------------------
Instruments for equation 1: smoothpolicyIR infgap outputgap FEDPolicyRate shock1pos shock1neg shock2pos shock2neg
    shock3pos shock3neg _cons 

[Sebastian Kripfganz]

Carlo probably referred to my posts on GMM for dynamic panel models. This is not what we have here. I am afraid I cannot be of help here.