Question: Consider observations (left(Y_{i t}, X_{i t} ight)) from the linear panel data model [ Y_{i t}=X_{i t} beta_{1}+alpha_{i}+lambda_{i} t+u_{i t} ] where (t=1, ldots, T

Consider observations $\left(Y_{i t}, X_{i t}\right)$ from the linear panel data model

\[ Y_{i t}=X_{i t} \beta_{1}+\alpha_{i}+\lambda_{i} t+u_{i t} \]

where $t=1, \ldots, T ; i=1, \ldots, n ;$ and $\alpha_{i}+\lambda_{i} t$ is an unobserved entity-specific time trend. How would you estimate $\beta_{1}$ ?

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