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The Big Data revolution is challenging the state-of-the-art statistical andeconometric techniques not only for the computational burden connected with thehigh volume and speed which data are generated, but even more for the varietyof sources through which data are collected (Arbia, 2021). This paperconcentrates specifically on this last aspect. Common examples of nontraditional Big Data sources are represented by crowdsourcing (data voluntarilycollected by individuals) and web scraping (data extracted from websites andreshaped in a structured dataset). A common characteristic to theseunconventional data collections is the lack of any precise statistical sampledesign, a situation described in statistics as 'convenience sampling'. As it iswell known, in these conditions no probabilistic inference is possible. Toovercome this problem, Arbia et al. (2018) proposed the use of a special formof post-stratification (termed 'post-sampling'), with which data aremanipulated prior their use in an inferential context. In this paper wegeneralize this approach using the same idea to estimate a Spatial Lag Model(SLM). We start showing through a Monte Carlo study that using data collectedwithout a proper design, parameters' estimates can be biased. Secondly, wepropose a post sampling strategy to tackle this problem. We show that theproposed strategy indeed achieves a bias-reduction, but at the price of aconcomitant increase in the variance of the estimators. We thus suggest anMSE-correction operational strategy. The paper also contains a formalderivation of the increase in variance implied by the post-sampling procedureand concludes with an empirical application of the method in the estimation ofa hedonic price model in the city of Milan using web scraped data.

On Spatial Lag Models estimated using crowdsourcing, web-scraping or other unconventionally collected data