IV with MA errors

[MikeK]

Dear Tom,

I would like to estimate a nonlinear IV model with a moving average error structure. I played with different frml configurations but I didn't succeed. Is it possible to estimate such a model with nlls oder nlsystem?

Thank you for your help.

Best regards,
Mike

[TomDoan]

It should be. It would require the use of a Recursive FRML. Can you show me what the model looks like?

[MikeK]

Dear Tom,

Thank you for your quick reply. The model is a standard Taylor rule (I know I could estimate it in a linear way but I don't want to for several reasons):
i(t) = (1-rho_i)*(mu + gamma_pi*pi(t) + gamma_y*Ygap(t)) + rho_i*i(t-1) + u(t), whereas u(t) = lambda*u(t-1) + epsilon(t).

My first idea was indeed to start with recursive frmls but I don’t see the trick. I tried

Code: Select all

set u = 0
frml cfrml1 i = (u = lambda*u{1} + epsilon), ((1-rhoi)*(mu + gamma_pi*pi + gamma_y*Ygap) + rhoi*i{1}) + u

and

Code: Select all

declare real u
frml cfrml1 i = (u = epsilon + lambda*%if(t==start,0,u)), ((1-rhoi)*(mu + gamma_pi*pi + gamma_y*Ygap) + rhoi*i{1}) + u

but lambda cannot be estimated in both cases.

Best,
Mike

[TomDoan]

That's an AR(1) error process, not MA(1). Is that what you want?

[MikeK]

Yes, you are right. I would like to estimate a Taylor rule with an AR(1) term (interest rate smoothing) and AR(1) errors.

[TomDoan]

First of all, you can't use I as a series name (it's a reserved name). I've replaced it with IR below. A model with AR(1) errors is done by quasi-differencing the entire regression to eliminate the AR part.

frml basef = (1-rhoi)*(mu + gamma_pi*pi + gamma_y*Ygap) + rhoi*ir{1}
frml taylorar1 = lambda*ir{1}+basef{0}-lambda*basef{1}
nlls(frml=taylorar1,instruments,other options) ir

Note that the identification of RHOI vs LAMBDA depends crucially on whether the (mu + gamma_pi*pi + gamma_y*Ygap) is non-zero (significantly)-- rho_i and lambda aren't identified by lagged IR terms.