这是一份nottingham诺丁汉大学ECON1044作业代写的成功案例

For ease of exposition, we assume that there are no time-specific effects, that is, $\lambda_{t}=0$ for all $t$ and $u_{i t}$ are independently, identically distributed (i.i.d) across $i$ and over $t$. Stack an individual’s $T$ time series observations of $\left(y_{i t}, x_{i t}^{\prime}\right)$ into a vector and a matrix, may alternatively be written as
$$
{\underset{\sim}{i}}{i}=X{i} \underset{\sim}{\beta}+\underset{\sim}{e} \alpha_{i}+{\underset{\sim}{i}}{i}, \quad i=1, \ldots, N, $$ vector of 1’s. Let $Q$ be a $T \times T$ matrix satisfying the condition that $Q e=0$. Pre-multiplying by $Q$ yields $$ Q y{\sim i}=Q X_{i} \beta \underset{\sim}{\beta}+Q u_{i}, \quad i=1, \ldots, N .
$$

ECON1044 COURSE NOTES ：

$$
y_{i t}^{}={\underset{\sim}{\beta}}^{\prime} x_{i t}+\alpha_{i}+u_{i t}, $$ and $$ y_{i t}= \begin{cases}1, & \text { if } y_{i t}^{}>0 \ 0, & \text { if } y_{i t}^{*} \leq 0\end{cases}
$$
where $u_{i t}$ is independently, identically distributed with density function $f\left(u_{i t}\right)$. Let
$$
y_{i t}=E\left(y_{i t} \mid x_{i t}, \alpha_{i}\right)+\varepsilon_{i t},
$$
then
Since $\alpha_{i}$ affects $E\left(y_{i t} \mid x_{i t}, \alpha_{i}\right)$ nonlinearly, $\alpha_{i}$ remains after taking successive difference of $y_{i t}$
The likelihood function conditional on $x_{i}$ and $\alpha_{i}$ takes the form,
$$
\prod_{i=1}^{N} \prod_{t=1}^{T}\left[F\left(-\beta_{\sim}^{\prime} x_{i t}-\alpha_{i}\right)\right]^{1-y_{i t}}\left[1-F\left(-\beta_{\sim}^{\prime} x_{i t}-\alpha_{i}\right)\right]^{y_{i t}} \text {. }
$$