The Stochastic Approach to International Price Comparisons

A flexible stochastic production frontier model with panel data

“…it 𝛾 0 (Li, 2000;Baltagi & Li, 2002); partially nonlinear models if (Huet et al, 2004;Xiao et al, 2014); additive model with interactions if 𝜇(•) = 𝜇 > 0 (Hajargasht, 2005) or 𝜇 = 0 (Sperlich et al, 2002). Our model (3) also generalizes the aforementioned models by adopting panel data structure to control for fixed effects 𝛼 i ≠ 0.…”

“…The regression form of our SF panel model in () nests many existing semiparametric SF or regression models without fixed effects (i.e., $$$ {\alpha}_i=0 $$$). Examples include, but not limited to, partially linear additive model if $$$ {H}_{jl}\left(\cdotp, \cdotp \right)=0 $$$ and $$$ \mu \left({Z}_{it};{\gamma}_0\right)={Z}_{it}^{\prime }{\gamma}_0 $$$ (Li, 2000; Baltagi & Li, 2002); partially nonlinear models if $$$ {H}_{jl}\left(\cdotp, \cdotp \right)=0,d=1 $$$, and $$$ \mu \left({Z}_{it};{\gamma}_0\right)\ne {Z}_{it}^{\prime }{\gamma}_0 $$$ (Huet et al, 2004; Xiao et al, 2014); additive model with interactions if $$$ \mu \left(\cdotp \right)=\mu >0 $$$ (Hajargasht, 2005) or $$$ \mu =0 $$$ (Sperlich et al, 2002). Our model () also generalizes the aforementioned models by adopting panel data structure to control for fixed effects $$$ {\alpha}_i\ne 0 $$$.…”

“…Remark Our two‐step estimation on the frontier combines advantages of both series and kernel estimators. Different from pure series estimator (Baltagi & Li, 2002; Hajargasht, 2005), our kernel backfitting estimator in the second step offers convenient asymptotic characterization (Horowitz & Mammen, 2004; Ozabaci et al, 2014). Using series as a pilot estimation, the kernel estimator for each additive function is oracle efficient.…”

“…For example, the extended translog production function, popular in empirical modeling, is generally not a special case of the smooth coefficient frontier model. Hajargasht (2005) proposes an additive frontier model with interactions for $$$ I $$$ and $$$ E $$$ but assumes no determinants in inefficiency. In our proposed frontier model, $$$ I $$$ and $$$ E $$$ do not need to be pre‐assigned, $$$ I $$$'s effect does not have to be linear, and the determinants of the inefficiency term can include any of $$$ I $$$ and $$$ E $$$, or even other exogenous environmental variables not appearing in the frontier.…”

“…Compared to existing partially nonlinear models, our model incorporates additive and interactive effects through unknown functions. Compared to conventional additive model with interactions (Hajargasht, 2005; Sperlich et al, 2002), our model specifies an additional nonlinear parametric function and alleviates the curse of dimensionality when estimating additive functions. Compared to both existing partially nonlinear and additive models, our model controls for unobserved individual heterogeneity freely correlated with all regressors.…”