Combining convex regression with the regression discontinuity design: Effectiveness of e-scooter providers during the Covid-19 lockdown

The efficiency literature has only recently begun to address endogeneity and causal inference in frontier estimation. Most previous studies combine efficiency analysis with causal inferences using a two-stage estimation strategy, hence not properly addressing correlation between efficiency and treatment. This paper proposes a one-stage approach that combines a semi-nonparametric estimator subject to shape-constraints with the quasi-experimental regression discontinuity design. The proposed method enables joint estimation of the impacts of contextual factors and a non-parametric production frontier. Building on recent methodological developments within the literature on regression discontinuity design, the current paper develops strategies for estimation, bandwidth selection and inference for both average and heterogenous treatment effects. The novel methodology is applied for analyzing the reopening of Norway after lockdown using the Regression Discontinuity in Time design, considering both average and firm-specific treatment effects. Empirical analysis of the novel e-scooter markets in the cities Oslo and Drammen indicates that while the average performance of e-scooter providers was unaffected by the reopening of Norway during the Covid-19 pandemic, operators are heterogenous with regards to both effectiveness and responsiveness. While the empirical analyses provide mixed evidence that lockdown policies affect transport operator performance, they offer important insights into the benefits of accommodating heterogenous policy impacts in assessment of diverse and volatile industries.