Expectation of the Variable Squared and Squared expectation

Dynare help (legacy posts)
1

Hello,

Does anyone know how to make difference in Dynare between entry of expectation of the forward-looking variable squared E(X[size=85]t+1[/size]^2) ] and squared expectation of that forward-looking variable (E(X[size=85]t+1[/size]))^2 ]?

E(X[size=85]t+1[/size]^2) in Dynare should be written as follows: X(+1)^2
But what about (E(X[size=85]t+1[/size]))^2,how should that be written in Dynare?

Please help

2

See:
[Expected value of a power)

3

Thank you for your answear,

I have an additional question:

I want to calculate variance [variance=E(X^2) - (E(X))^2] using the difference between (E_t(X_t+1)^2) and (E_t(X_t+1))^2 and I understand that I need to use at least 2. order Taylor approximation to have the difference between (E_t(X_t+1)^2) and (E_t(X_t+1))^2 different from zero. However, I am concerned with steady state values of these 2 expectations. Understanding that in steady state all the variables become constant, it seems logical that the steady state values of the (E_t(X_t+1)^2) and (E_t(X_t+1))^2 will be equal ( both will become X^2).

Am I correct in my thinking?

Please help

4

Hi,
I am not sure I get your question and confused by your notation using conditional and unconditional expectations. In the deterministic steady state, obviously there is no difference as there are no shocks. This is the problem of Devereux/Sutherlands indeterminate steady state in models with portfolio choice.