这是一份liverpool利物浦大学ECON223的成功案例
Let $\left{q_{i t}\right}$ be a balanced panel ${ }^{22}$ of $N$ time-series with $T$ observations which are generated by
$$
\Delta q_{i t}=\delta_{i} t+\beta_{i} q_{i t-1}+u_{i t}
$$
where $-2<\beta_{i} \leq 0$, and $u_{i t}$ has the error-components representation
$$
u_{i t}=\alpha_{i}+\theta_{t}+\epsilon_{i t}
$$
$\alpha_{i}$ is an individual-specific effect, $\theta_{t}$ is a single factor common time effect, and $\epsilon_{i t}$ is a stationary but possibly serially correlated idiosyncratic effect that is independent across individuals. For each individual $i, \epsilon_{i t}$ has the Wold moving-average representation
$$
\epsilon_{i t}=\sum_{j=0}^{\infty} \theta_{i j} \epsilon_{i t-j}+u_{i t}
$$
ECON223/ ECON224 COURSE NOTES ：
The Im, Pesaran and Shin test as well as the Maddala-Wu test (discussed below) relax the homogeneity restrictions under the alternative hypothesis. Here, the null hypothesis
$$
H_{0}: \beta_{1}=\cdots=\beta_{N}=\beta=0,
$$
is tested against the alternative
$$
H_{A}: \beta_{1}<0 \cup \beta_{2}<0 \cdots \cup \beta \beta_{N}<0 .
$$
The alternative hypothesis is not $H_{0}$, which is less restrictive than the Levin-Lin alternative hypothesis.
