4 added 23 characters in body

# 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

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

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.

1