st: matrix problems

[Dennis Coates <coates@umbc.edu>]

Hi statalisters,

I am trying to program the Chernozhukov-Hansen Wald statistics for 
robust inference with weak instruments with overidentification.  I get 
estimates, compute variance covariance matrices and the various 
adjustments, and then compute the Wald statistic.  The end results are 
Wald statistic values I don't believe (values in the hundreds of 
thousands).  I am running Stata 8, Intercooled.

Z is the matrix of excluded instruments
netY is the value of the variable to be explained minus the value of the 
endogenous explanatory variable multiplied by the value of its 
hypothesized coefficient
V is the residual from the first stage regression
epsilon is the residual from the second stage regression

Here is the code I use to construct the Wald statistic (equation 13 from 
Chernozhukov-Hansen 2005):

matrix sev = (1/(rowsof(Z)))*Z'*netY*V'*Z

matrix see = (1/rowsof(Z))*Z'*epsilon*epsilon'*Z
matrix seeinv = inv(see)

matrix delta = seeinv*Z'*stddevgrgsp - seeinv*sev*seeinv*Z'*netY

matrix Ztild = Z*delta

matrix Wklm = netY'*Ztild*syminv(delta'*see*delta)*Ztild'*netY

*******

The value of Wklm turns out very implausible, so I examined the see, and 
seeinv matrices.  Below is what I got.

. matrix list see

symmetric see[3,3]
                 c1       c2  c3
  r1      195.5102
  r2     27.943648     3.9938963
  r3    -67.939952      -9.71044     23.609187

. matrix list seeinv

symmetric seeinv[3,3]
                 c1   c2   c3
   r1     .00511482
   r2             0             0
   r3             0             0             0

Obviously, the product of see and seeinv does not produce an identity 
matrix.  Using syminv to create the inverse matrix did not resolve matters.

I will appreciate any guidance.

Dennis Coates





--
Dennis Coates
Professor of Economics
UMBC
1000 Hilltop Circle
Baltimore, MD 21250

phone: 410-455-3243

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