snapshot

Examples/GMM/TwoStepGMM.m

@@ -1,3 +1,4 @@
+%%
 NerloveData = importdata('NerloveData.m');
 n = size(NerloveData,1);
 y = log(NerloveData(:,2));
@@ -8,6 +9,7 @@
 %% this block shows that start values can be important, even for this simple problem
 %% in the past, Matlab would not get the correct answer here, though Octave does. I'm
 %% not sure of the current behavior of Matlab
+%% Note April 2024: now Octave has copied Matlab's incorrect result! Bug for bug compatibility!
 W = eye(k);
 thetastart = zeros(k,1);
 options = optimset('TolX',1e-15,'TolFun',1e-12);
@@ -33,7 +35,7 @@
 omega = ms'*ms/n;
 fprintf('estimated covariance of moments\n');
 omega
-W = inv(omega);  
+W = inv(omega);
 thetastart = x\y; % this give OLS coefficients
 [thetahat, obj] = fminunc(@(theta) moments(theta, y, x)'*W*moments(theta, y, x), thetastart);
 fprintf('GMM results, optimal weight matrix\n');

Examples/GMM/moments.m

@@ -1,8 +1,9 @@
 % moments for OLS estimation
 function [m, ms] = moments(theta, y, x)
     e = y - x*theta;
+    n = size(y,1);
     k = size(theta,1);
-    m = x'*e;
+    m = x'*e/n;
     if nargout > 1
         ms = x.*repmat(e,1,k);
     end    

PracticalSummaries/16-GMM.jl

@@ -19,7 +19,7 @@ mleresults(model, β⁰);                               # but won't overflow
 ## GMM
 using Econometrics
 moments1 = β -> x.*(y - λ(β))
-gmmresults(moments1, β⁰);
+βhat, objv, V, D, W, convergence = gmmresults(moments1, β⁰);
 # note that the GMM estimator is identical to the ML estimator. You should
 # be able to prove that result analytically, by showing that the moment conditions
 # are the same as the ML score vector. Because this GMM estimator is
@@ -29,7 +29,7 @@ gmmresults(moments1, β⁰);
 ## Trying a different GMM estimator, based on E(y)=λ, so E(y/λ)=1.
 using Econometrics
 moments2 = β -> x.* (y./λ(β) .- 1.0) 
-gmmresults(moments2, β⁰);
+βhat, objv, V, D, W, convergence = gmmresults(moments2, β⁰);
 
 
 ## Try out overidentified GMM estimator, using both sets of moments
@@ -47,11 +47,6 @@ m = moments3(βhat) # the moment contributions, evaluated at estimate
 ## let's see how the Hansen-Sargan test can detect 
 # incorrect moments
 η = 0.01 # if this is different from zero, moments4, and, thus moments5, will not be valid
-moments4 = β -> x.* (y./λ(β) .- 1.0 .+ η)
-moments5 = β -> [moments1(β) moments4(β)]
-gmmresults(moments5, β⁰);
+moments4 = β -> moments3(β) .+ η
+βhat, objv, V, D, W, convergence = gmmresults(moments4, β⁰);
 
-## Yet another version, using conditional mean = conditional variance
-using Econometrics, ForwardDiff
-moments6 = β -> x.*((y - λ(β)) .^2.0 - λ(β))
-βhat, objv, V, D, W, convergence = gmmresults(moments6, β⁰);