Estimating a hybrid model with GMM

[Vermeiren]

Hello,

For my thesis I estimatie a hybrid model of the New Keynesian Phillips curve. According to Gali en Gertler (1999) the equation is as follows:

π(t)=λmc(t) + γf E({π(t+1)} + γb π(t-1)

where:

λ≡(1-ω)(1-θ)(1-βθ)/ϕ,
γf≡βθ/ϕ,
γb≡ω/ϕ,

with: ϕ≡θ+ω[1-θ(1-β)].

They estimate this model with GMM and use the following two alternative specifications of the orthogonality conditions as a basis for they GMM estimation:

E(t) {(ϕπ(t) - (1-ω)(1-θ)(1-βθ)s(t) - θβπ(t+1))z(t) }=0

E(t) {(π(t) - (1-ω)(1-θ)(1-βθ)/ϕ s(t)- θβ/ϕ π(t+1))z_t }=0

My question is how i can estimate this model using GMM. When I replace 'ϕ' with its equation 'θ+ω[1-θ(1-β)]' in the specifications i get a error saying that i'm dividing by zero.

Can someone please help me with this?

[startz]

You need to change the initial parameter values so that you don't start at phi=0.

[Vermeiren]

Thank you for your reply

I don't quite understand how to change the initial parameter values.
Do you mean that I must rearrange the three underlying equations?

[startz]

Look at the

Code: Select all

param

command.

[Vermeiren]

Dear sir,

I have tried to change the initial parameter values.
For the equation

gdp_deflator = ((1-c(1))*(1-c(2))*(1-c(3)*c(2))/(c(2)+c(1)*(1-c(2)*(1-c(3)))))*ulc + ((c(3)*c(2))/(c(2)+c(1)*(1-c(2)*(1-c(3)))))*future_inflation

with instruments: 4 lags of inflaton, the ouput gap, long short interest rate spread and the labor income share.

and : c(1) =ω c(2) = θ c(3) = β (I integrate the three specifiactions into the orthogonality condition defined in my previous question)

As you said i tried to change the initial parameter values.
But when i run this i get the error that i have a singular matrix?
What am i doing wrong?

[Vermeiren]

When i estimate the reduced model :

πt=λmc+γf Et {π(t+1)}+γb π(t-1)

with GMM i get estimates for λ, yf and yb.

The main problem i have is that i don't know how i can estimate the deep parameters of the model according the the specifications:

λ≡(1-ω)(1-θ)(1-βθ)/ϕ,
γf≡βθ/ϕ,
γb≡ω/ϕ,

with: ϕ≡θ+ω[1-θ(1-β)].

Thank you in advance

[startz]

Code: Select all

gdp_deflator = ((1-c(1))*(1-c(2))*(1-c(3)*c(2))/(c(2)+c(1)*(1-c(2)*(1-c(3)))))*ulc + ((c(3)*c(2))/(c(2)+c(1)*(1-c(2)*(1-c(3)))))*future_inflation


Shouldn't you have lagged inflation in the equation?

[Vermeiren]

I have thought that to, but in the orthogonality condition defined by Gali en Gertler (see below) they leave the lag inflation out of the equation.

E(t) {(π(t) - (1-ω)(1-θ)(1-βθ)/ϕ s(t)- θβ/ϕ π(t+1))z_t }=0