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Spatial stochastic frontier model with endogenous weighting matrix

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A Correction to this article was published on 03 February 2022

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Abstract

We propose a spatial autoregressive stochastic frontier model, which allows for endogenous weighting matrix (i.e., the spatial weighting matrix is not independent of the two-sided error term). The parameters of the model are estimated via the maximum likelihood estimation method. Monte Carlo simulations illustrate that our model performs well in finite samples. As an example, we employed our methodology to the US banks and found evidence for endogenous spillovers. The empirical example suggested potential biases in the parameter estimates when endogeneity of spillovers is ignored.

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Notes

  1. In the banking context, Mester (1997), Bos et al. (2009), Brissimis et al. (2010), Tecles and Tabak (2010, and Galán et al. (2015) exemplify studies that followed this distribution-based approach using non-spatial SFA models.

  2. Kutlu and Wang (2021) apply the method of Glass et al. (2016a, b) to estimate greenhouse gas emission inefficiency spillover effects. Hence, their method can be applied frameworks other than estimation of technical or cost efficiencies.

  3. Kutlu and Tran (2019) provide a literature review on endogeneity and heterogeneity in stochastic frontier models. Kutlu and Sickles (2012) use a similar approach to estimate market power of airlines in the Kalman filter setting.

  4. Glass et al. (2016a, b) present their model in the panel data context. Our model can easily be extended to panel data.

  5. \(N_{K} (.,.)\) is the K-variate normal distribution.

  6. See Almanidis et al. (2019), Berger and Mester (2003), and Kutlu et al. (2019).

  7. The dataset of Koetter et al. (2012) is hosted in https://dataverse.harvard.edu/dataverse/restat.

  8. The log-likelihood values are not directly comparable due to the additional term included in the log-likelihood function of endogenous version.

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Funding

The author received financial support from University of Texas Rio Grande Valley.

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  1. Department of Economics, University of Texas Rio Grande Valley, Edinburg, TX, USA

    Levent Kutlu

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  1. Levent Kutlu
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In the original online version of this article was revised: In the tables 1–3, the font sizes are incorrect. The expressions in the tables 6–7 were incorrectly provided in two lines which should be in single line. The signs of few parameter estimates are incorrectly given in table 7. Thus, the tables 1–3, 6–7 were corrected. The issue information were missing in the reference “Kutlu L, Tran KC, Tsionas MG (2020)” which has been updated.

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Kutlu, L. Spatial stochastic frontier model with endogenous weighting matrix. Empir Econ 63, 1947–1968 (2022). https://doi.org/10.1007/s00181-021-02189-y

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