Panel Data Model with Stationary and Nonstationary Regressors and Error Terms

In this book, we say a model or parameter is identifiable if it can be estimated consistently. If the parameter is not identifiable, then consistent estimators cannot exist. Before we discuss estimation, it is important to establish that they are identifiable. Here we follow Canay and Shaikh (2017)’s general notion of identifiability of a parameter in a semi-parametric setting. Let P denote the true distribution of the observed data X. Let P = {Pθ : θ ∈ Θ} denote a model for the distribution of the observed data X. We assume that the model is correctly specified, i.e., P ∈ P, where there is some θ ∈ Θ such that Pθ = P. We are interested in θ or some functions of f of θ. Suppose it is known that the distribution of the observed data is P ∈ P. Since the model is correctly specified by assumption, it is known a priori that there exists some θ ∈ Θ such that Pθ = P. But we cannot distinguish any θ ∈ Θ from any other θ∗ ∈ Θ such that Pθ∗ = P . Thus, from knowledge of P alone, all we can say is that θ ∈ Θ0 (P), whereΘ0(P)={ θ∈Θ:Pθ=P }…