Maximum likelihood estimation of a spatial autoregressive model for origin–destination flow variables

Abstract

We introduce a spatial autoregressive hurdle model for nonnegative origin–destination flows $y_{N,ij}$. The model incorporates a hurdle formulation to elucidate the different data-generating processes for zero and positive flows. Our model specifies three types of spatial influences on flow $y_{N,ij}$ that quantify the impact of third-party characteristics on the flow $y_{N,ij}$: (i) the effect of outflows from origin $j$, (ii) the effect of inflows to destination $i$, and (iii) the effect of flows among third-party units. We account for two-way fixed effects in the model to capture the inherent characteristics of both origins and destinations. We employ maximum likelihood estimation to estimate the model parameters. To address statistical inference issues, we analyze the asymptotic properties of the ML estimator using the spatial near-epoch dependence concept. We confirm the presence of an asymptotic bias that arises from the fixed effects, whose dimensions grow with the sample size. Applying our model to migration flows among U.S. states, we estimate significant spatial influences, particularly from inflows to destinations and outflows from origins. Our findings support the notion that zero and positive flow formations are distinct. Consequently, our proposed model outperforms the spatial autoregressive Tobit specification for origin–destination flows, thus providing a better fit to the data.