这是一份anu澳大利亚国立大学ECON2125作业代写的成功案例

When both lagged endogenous variables and serial correlation in the disturbance term appear, we need to impose additional conditions to identify a model. For instance, consider the following two equation system (Koopmans, Rubin and Leipnik, 1950):
$$
y_{1 t}+\beta_{11} y_{1, t-1}+\beta_{12} y_{2, t-1}=u_{1 t} \beta_{12} y_{1 t}+y_{2 t}=u_{2 t} .
$$
If $\left(u_{1 t}, u_{2 t}\right)$ are serially uncorrelated, $(6)$ is identified. If serial correlation in $\left(u_{1 t} u_{2 t}\right)$ is allowed, then
$$
\begin{array}{r}
y_{1 t}+\beta_{11}^{} y_{1, t-1}+\beta_{12}^{} y_{2, t-1}=u_{1 t}^{} \ \beta_{12} y_{1 t}+y_{2 t}=u_{2 t} \end{array} $$ is observationally equivalent to $(6)$, where $\beta_{11}^{}=\beta_{11}+d \beta_{21}, \beta_{12}^{}=\beta_{12}+d$, and $u_{1 t}^{}=u_{1 t}+d u_{2 t}$.

ECON2125 COURSE NOTES ：

For each person $i$, let $\left(y_{0 i}^{}, y_{1 i}^{}\right)$ denote the potential outcomes in the untreated and treated states, respectively. Then the treatment effect for individual $i$ is
$$
\Delta_{i}=y_{1 i}^{}-y_{0 i}^{}
$$
and the average treatment effect (ATE) is defined as
$$
E\left(\Delta_{i}\right)=E\left(y_{1 i}^{}-y_{0 i}^{}\right) ;
$$
see Heckman and Vytlacil (2001).
Let the treatment status be denoted by the dummy variable $d_{i}$ where $d_{i}=1$ denotes the receipt of treatment and $d_{i}=0$ denotes nonreceipt. The observed data are often in the form
$$
y_{i}=d_{i} y_{1 i}^{}+\left(1-d_{i}\right) y_{0 i^{}}^{} $$ Suppose $y_{1 i}^{}=\mu_{1}\left(\mathbf{x}{i}, u{1 i}\right), \quad y_{0 i}^{}=\mu_{0}\left(\mathbf{x}{i}, u{0 i}\right)$, and $d_{i}^{}=\mu_{D}\left(\mathbf{z}{i}\right)-u{d i}$, where $d_{i}=1$ if $d_{i}^{*} \geq 0$ and 0 otherwise, $\mathbf{x}{i}$ and $\mathbf{z}{i}$ are vectors of observable exogenous variables and $\left(u_{1 i}, u_{0 \dot{b}} u_{d i}\right.$ ) are unobserved random variables. The average treatment effect and the complete structural econometric model can be identified with parametric