Monetary policy shock: the timing issue

[elee]

Dear all,

I have a question regarding to the timing of monetary policy shocks. I am using the following Taylor rule in my model:

r_t = rho_r * r_{t-1} + rho_pi * pi_t + rho_x * x_t + e_t

where r_t, pi_t, and x_t are the interest rate, inflation, and output gap. e_t is the monetary policy shock.

If I write the Taylor rule this way, as in most examples posted here, monetary shock e_t will affect the contemporaneous inflation and output gap pi_t and x_t.

Can anyone tell me how to change the Taylor rule if I don't want the shock on r_t to affect pi_t and x_t?

Many thanks!

[jpfeifer]

What is the economic intuition of your request? Any shock at time t will have an impact on the endogenous variables of the model (and via persistence also in the following periods).

[elee]

Dear jpfeifer,

Thanks for your reply! Here is the economic reason of question. Suppose "t" is the first quarter of year 2012. The interest rate of the second quarter is announced at the end of the first quarter, hence is labeled as r_t. I don't want the shock on r_t to affect the consumption of the first quarter, which is denoted as c_t. But as you said, if I use the above Taylor rule, the shock e_t will affect c_t and other endogenous variables of period t.

Best,
Elee

[jpfeifer]

You have to think about the concepts you are modeling. I am not sure your way to think about a monetary policy shock is correct. For consumption, c_t represents the flow of consumption during the whole quarter. For the interest rate, the model equivalent would not be an interest at a point in time, but rather an average during the quarter.
Clarida/Gali/Gertler (2000) for example state:

We use as the interest rate the average Federal Funds rate (FYFF) in the first-month of each quarter