ML versus IV estimates of spatial SUR models: evidence from the case of Airbnb in Madrid urban area

In recent decades we have seen an increased interest in the use of seemingly unrelated regressions models (SUR) in a spatial context, with compelling case studies in different fields. This upsurge has favoured the development of new and more efficient inference techniques. At present, the user has a basic toolkit to deal with this kind of model, that is, however, in need of improvement. This paper focuses on the question of estimating, quickly and accurately, spatial SUR models. The most popular procedure is maximum likelihood (ML) which guarantees precision at the cost of a high computational burden. This is especially true in cases of large sample size and strong spatial structure. We explore simpler estimation algorithms such as instrumental variables (IV), which expedites calculation at the cost of a certain loss in quality of the estimates. We focus on the importance of sample size and the trade-off between accuracy and speed. To that end, we perform a comprehensive simulation experiment in which we compare ML and IV algorithms, looking for their strengths and weaknesses. The paper includes two applications to the case of Airbnb in the urban area of Madrid. First, we estimate a spatial SUR hedonic model of accommodation prices, using micro-data for three different cross sections à la Anselin, that is, considering temporal correlation plus spatial structure. Then, the data are aggregated by neighbourhoods. We specify a spatial SUR model with two equations (apartments and rooms) also using three cross sections. In both cases, the models are estimated by ML and IV using the spsur R package (Angulo et al. in spSUR: spatial seemingly unrelated regression models. R Package version 1.0.0.3, 2019), with the aim of illustrating its capabilities.