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The traditional predictor of technical inefficiency proposed by Jondrow, Lovell, Materov, and Schmidt (1982) is a conditional expectation. This chapter explores whether, and by how much, the predictor can be improved by using auxiliary information in the conditioning set. It considers two types of stochastic frontier models. The first type is a panel data model where composed errors from past and future time periods contain information about contemporaneous technical inefficiency. The second type is when the stochastic frontier model is augmented by input ratio equations in which allocative inefficiency is correlated with technical inefficiency. Compared to the standard kernel-smoothing estimator, a newer estimator based on a local linear random forest helps mitigate the curse of dimensionality when the conditioning set is large. Besides numerous simulations, there is an illustrative empirical example.

This study focuses on the banking systems evaluation in Portugal, Italy, Ireland, Greece and Spain (known as the PIIGS) during the financial and post-financial crisis period from 2009 to 2018.

A conditional robust nonparametric frontier analysis (order-m estimators) is used to measure banking efficiency combined with variables highlighting the effects of Non-Performing Loans. Next, a truncated regression is used to examine if institutional, macroeconomic, and financial variables affect bank performance differently. Unlike earlier studies, we use the Corruption Perception Index (CPI) as an institutional variable that affects banking sector efficiency.

This research shows that the PIIGS crisis affects each bank/country differently due to their various efficiency levels. Most of the study variables — CPI, government debt to GDP ratio, inflation, bank size — significantly affect banking efficiency measures.

The contribution of this article to the relevant banking literature is two-fold. First, it analyses the efficiency of the PIIGS banking system from 2009 to 2018, focusing on NPLs. Second, this is the first empirical study to use probabilistic frontier analysis (order-m estimators) to evaluate PIIGS banking systems.

The objective of the study is to explore explanations for the capital structure compositions of farmer cooperatives, which have a unique equity structure with allocated equity as well as unallocated equity.

Data came from a panel of US grain marketing and input supply cooperatives for the 2010–2020 period. The study is concerned with the proportions of debt, allocated equity and unallocated equity, which requires the application of a fractional multinomial panel model to ensure predictions fall within the observed data range (i.e. 0–1).

Larger cooperatives have relatively high debt proportions. Diversification of the product portfolio has a positive effect on the debt proportion. Profitability is associated with higher debt proportions in input supply cooperatives and higher allocated equity proportions in grain marketing cooperatives. Over time, the proportion of unallocated equity increased. Overall, some results differ across grain marketing and input supply cooperatives.

Increasing proportions of unallocated equity warrant a debate about the future value of ownership and governance by members of farmer cooperatives.

Previous empirical investigations of the capital structure compositions of cooperatives lacked a distinction between allocated and unallocated equity. Our results show that the proportions of the two equity accounts respond differently to given predictors. Furthermore, much of the prior empirical literature fails to separate cooperatives on the basis of economic activities (i.e. marketing, supply and mixed).