This article describes sfcross and sfpanel, two new Stata commands for the estimation of cross-sectional and panel-data stochastic frontier models. sfcross extends the capabilities of the frontier command by including addi

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The classical stochastic frontier panel data models provide no mechanism for disentangling individual time-invariant unobserved heterogeneity from inefficiency. Greene (2005a, b) proposed the 'true' fixed-effects specification, which distinguishes these two latent components while allowing for time-variant inefficiency. However, due to the incidental parameters problem, the maximum likelihood estimator proposed by Greene may lead to biased variance estimates. We propose two alternative estimation procedures that, by relying on a first-difference data transformation, achieve consistency when n goes to infinity with fixed T. Furthermore, we extend the approach of Chen et al. (2014) by providing a computationally feasible solution for estimating models in which inefficiency can be heteroskedastic and may follow a first-order autoregressive process. We investigate the finite sample behavior of the proposed estimators through a set of Monte Carlo experiments. Our results show good finite sample properties, especially in small samples. We illustrate the usefulness of the new approach by applying it to the technical efficiency of hospitals.

The classical stochastic frontier panel data models provide no mechanism for disentangling individual time-invariant unobserved heterogeneity from inefficiency. Greene (2005a, b) proposed the 'true' fixed-effects specification, which distinguishes these two latent components while allowing for time-variant inefficiency. However, due to the incidental parameters problem, the maximum likelihood estimator proposed by Greene may lead to biased variance estimates. We propose two alternative estimation procedures that, by relying on a first-difference data transformation, achieve consistency when n goes to infinity with fixed T. Furthermore, we extend the approach of Chen et al. (2014) by providing a computationally feasible solution for estimating models in which inefficiency can be heteroskedastic and may follow a first-order autoregressive process. We investigate the finite sample behavior of the proposed estimators through a set of Monte Carlo experiments. Our results show good finite sample properties, especially in small samples. We illustrate the usefulness of the new approach by applying it to the technical efficiency of hospitals.JEL Classification: C13, C16, C23.

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During the COVID-19 pandemic, several countries have resorted to self-adaptive mechanisms that tailor non-pharmaceutical interventions to local epidemiological and health care indicators. These mechanisms reinforce the mutual influence between containment measures and the evolution of the epidemic. To account for such interplay, we develop an epidemiological model that embeds an algorithm mimicking the self-adaptive policy mechanism effective in Italy between November 2020 and March 2022. This extension is key to tracking the historical evolution of health outcomes and restrictions in Italy. Focusing on the epidemic wave that started in mid-2021 after the diffusion of Delta, we compare the functioning of alternative mechanisms to show how the policy framework may affect the trade-off between health outcomes and the restrictiveness of mitigation measures. Mechanisms based on the reproduction number are generally highly responsive to early signs of a surging wave but entail severe restrictions. The emerging trade-off varies considerably depending on specific conditions (e.g., vaccination coverage), with less-reactive mechanisms (e.g., those based on occupancy rates) becoming more appealing in favorable contexts.

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