Nonparametric instrumental variables estimation for efficiency frontier

Abstract

leopold.simar@uclouvain.be. October 17, 2014Abstract The paper investigates endogeneity issues in nonparametric frontier models. It considers a non separable model for a cost function C = ϕ(Y, U ) where C and Y are the cost and the output, U is uniform in [0, 1] and ϕ is increasing with respect to U . The cost frontier corresponds to U = 0 and U can be interpreted as a normalized level of inefficiency. The endogeneity issue arises when Y is dependent of U . For identification and estimation, we use a nonparametric instrumental variables estimator of the model for fixed value U = α, and obtain an estimate of the α-quantile cost frontier ϕ(Y, α). This involves the solution of a non linear integral equation. If the true frontier ϕ(Y, 0) is wanted, it is then estimated by estimating the bias correction ϕ(Y, 0) − ϕ(Y, α) under additional regularity conditions. The procedure is illustrated through a simulated sample and with an empirical application to the efficiency of post offices.

Impact evaluation in a multi-input multi-output setting: Evidence on the effect of additional resources for schools

“…This paper contributes to four main strands of literature. First, it contributes to the emerging operational research literature dealing with endogeneity issues in non-parametric frontier estimation (Cazals et al, 2016;Cordero et al, 2015;Simar et al, 2016). Second, it adds to the literature pertaining to the impact evaluation in efficiency by providing a causal interpretation of the findings.…”

“…Using a conditional efficiency framework, the efficiency estimates are not only determined by the inputs (x ), the outputs (y) and the assignment variable (c), but also by the other environmental variables (z ) under a non-separable production context (Cazals et al, 2016). Adapting the notation, the input-oriented conditional order-m efficiency estimator ( θ s m,n ) is defined as follows:…”

“…With reference to the debate about the efficiency and effectiveness of school resources on educational outcomes, unsolved endogeneity problems might lead to biased results and explain the ambiguous findings of the literature (Jackson et al, 2016). First, endogeneity might arise from the various sources mentioned above while estimating the educational production function (Cazals et al, 2016;Cordero et al, 2015;Mayston, 2003;Sicilia, 2017a, 2018;Simar et al, 2016). Second, this might also occur when extending the focus of the efficiency in education studies from the overall production frontier estimation to the program efficiency evaluation.…”

A conditional directional distance function approach for measuring tax collection efficiency: evidence from Spanish regional offices

“…This possibility would imply the existence of endogeneity in data, that is, there is a certain level of correlation between the level of inputs or outputs and the efficiency term, which might lead to misleading efficiency estimates . Recently, some authors have developed different approaches to address the issue of unobserved heterogeneity and endogeneity in frontier estimations (Cazals et al., ; Simar et al., ), thus a potential area for further research could be applying these methods to derive more accurate estimates of performance that take those latent factors into account.…”

Unobserved heterogeneity and endogeneity in nonparametric frontier estimation

“…the case of Olley and Pakes (1996) where the endogeneity is obtained when the unobserved inefficiency is linked to the inputs (in an output orientation model). In nonparametric deterministic frontier models the same idea is developed in Cazals et al (2015), where they introduce links between X and the inefficiency through a treatment model. We explain now that in our model we create endogeneity in another way, by neglecting heterogeneity.…”