A matrix exponential approach to spatial panel data models: An application to carbon emissions

The estimation of matrix exponential spatial panel data models with entity and time fixed effects is considered under both homoskedastic and heteroskedastic error terms. Under the assumption of homoskedasticity, a quasi-maximum likelihood estimator (QMLE) formulated from the partial likelihood functions is proposed. In the case of heteroskedasticity, an M-estimator derived from the adjusted quasi score functions obtained from the partial likelihood functions is suggested. The large sample properties of the proposed estimators are established under certain assumptions. Through Monte Carlo simulations, the proposed estimators are shown to exhibit good finite sample properties. In an empirical application, the relationship between carbon emissions and economic activity is investigated using state-level data from the United States.