open "H:\Program Files\gretl\data\ETM\tbrate.gdt"
diff r y
smpl 1950:4 1996:4
# ETM 2.23
ols d_r const infl(-1) d_y(-1) d_r(-1 to -2) --robust
# Get predictions and residuals
series yhat1 = $yhat
series uhat1 = $uhat
# regress predictions on residuals and a constant
ols yhat1 const uhat1
# regress residuals on predictions and a constant
ols uhat1 const yhat1
# 2.24 ETM
ols d_r const d_y(-1) d_r(-1 to -2) --robust
series ehat = $uhat
lags 1; infl
# get residuals for d_r
ols d_r const d_y(-1) d_r(-1 to -2)
genr ehat = $uhat
# get residuals for lagged inflation
ols infl_1 const d_y(-1) d_r(-1 to -2)
genr vhat = $uhat
# Verify FWL
ols ehat vhat
# 2.25 ETM
matrix X = { const infl_1 d_y_1 d_r_1 d_r_2 }
matrix hat = X*inv(X'X)*X'
matrix ht=diag(hat)
series hatt = ht
gnuplot hatt --time-series
# 2.26 ETM 
matrix et = zeros($nobs,1)
matrix et[20,1]=1  # set 20th obs of et to 1
series ett = et    # convert it to a series
list X1 = const infl_1 d_y_1 d_r_1 d_r_2 
# Residuals for full sample
ols d_r X1
genr u_full = $uhat
genr y_full = $yhat

# Run regression omitting obs 20.
ols d_r X1 ett
genr u_omit = $uhat
alpha = $coeff(ett)

genr a1 = u_full/(1-hatt)

smpl 1955:3 1955:3
print "u_omit should be zero, a1 and the coefficient on et should be the same " 
print u_full  u_omit a1 alpha

# 2.27 ETM
# Run regression of omit 1 residuals on the full set residuals
smpl 1950:4 1996:4
ols a1 u_full