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Instrumental variable estimation of the autoregressive coefficient in ARMA(1,1) model

Consider ARMA(1,1)

$y_t=by_{t-1}+u_t$

$u_t=ae_{t-1}+e_t$

$var(e_t)=\sigma^2$$\text{Var}(e_t)=\sigma^2$

Why is $y_{t-1}$ is endogenous and why there is there an endogenity problem?

How can I provide an instrumental variable (for example $y_{t-2}$  )and such that this variable holds for conditionssatisfies the conditions of validity and relevance?

This(This is not homework. I just try to understand this topic. Thank you.  )

Instrumental variable in ARMA model

Consider ARMA(1,1)

$y_t=by_{t-1}+u_t$

$u_t=ae_{t-1}+e_t$

$var(e_t)=\sigma^2$

Why $y_{t-1}$ is endogenous and why there is endogenity problem?

How can I provide instrumental variable (for example $y_{t-2}$  )and this variable holds for conditions of validity and relevance?

This is not homework. I just try to understand this topic. Thank you.  

Instrumental variable estimation of the autoregressive coefficient in ARMA(1,1) model

Consider ARMA(1,1)

$y_t=by_{t-1}+u_t$

$u_t=ae_{t-1}+e_t$

$\text{Var}(e_t)=\sigma^2$

Why is $y_{t-1}$ endogenous and why is there an endogenity problem?

How can I provide an instrumental variable (for example $y_{t-2}$) such that this variable satisfies the conditions of validity and relevance?

(This is not homework. I just try to understand this topic. Thank you.)

3 added 24 characters in body
source | link

Consider ARMA(1,1)

$y_t=by_{t-1}+u_t$

$u_t=ae_{t-1}+e_t$

$var(e_t)=\sigma^2$

Why $y_{t-1}$ is endogenous and why there is endogenity problem?

How can I provide instrumental variable and(for example $y_{t-2}$ )and this variable holds for conditions of validity and relevance?

This is not homework. I just try to understand this topic. Thank you.

Consider ARMA(1,1)

$y_t=by_{t-1}+u_t$

$u_t=ae_{t-1}+e_t$

$var(e_t)=\sigma^2$

Why $y_{t-1}$ is endogenous and why there is endogenity problem?

How can I provide instrumental variable and this variable holds for conditions of validity and relevance?

This is not homework. I just try to understand this topic. Thank you.

Consider ARMA(1,1)

$y_t=by_{t-1}+u_t$

$u_t=ae_{t-1}+e_t$

$var(e_t)=\sigma^2$

Why $y_{t-1}$ is endogenous and why there is endogenity problem?

How can I provide instrumental variable (for example $y_{t-2}$ )and this variable holds for conditions of validity and relevance?

This is not homework. I just try to understand this topic. Thank you.

2 added 4 characters in body
source | link

Consider ARARMA(1,1)

$y_t=by_{t-1}+u_t$

$u_t=ae_{t-1}+e_t$

$var(e_t)=\sigma^2$

Why $y_{t-1}$ is endogenous and why there is endogenity problem?

How can I provide instrumental variable and this variable holds for conditions of validity and relevance?

This is not homework. I just try to understand this topic. Thank you.

Consider AR(1)

$y_t=by_{t-1}+u_t$

$u_t=ae_{t-1}+e_t$

$var(e_t)=\sigma^2$

Why $y_{t-1}$ is endogenous and why there is endogenity problem?

How can I provide instrumental variable and this variable holds for conditions of validity and relevance?

This is not homework. I just try to understand this topic. Thank you.

Consider ARMA(1,1)

$y_t=by_{t-1}+u_t$

$u_t=ae_{t-1}+e_t$

$var(e_t)=\sigma^2$

Why $y_{t-1}$ is endogenous and why there is endogenity problem?

How can I provide instrumental variable and this variable holds for conditions of validity and relevance?

This is not homework. I just try to understand this topic. Thank you.

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