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Modeling dependence in two-tier stochastic frontier models

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Abstract

The two-tier stochastic frontier model has seen widespread application across a range of social science domains. It is particularly useful in examining bilateral exchanges where unobserved side-specific information exists on both sides of the transaction. These buyer and seller specific informational aspects offer opportunities to extract surplus from the other side of the market, in combination also with uneven relative bargaining power. Currently, this model is hindered by the fact that identification and estimation relies on the potentially restrictive assumption that these factors are statistically independent. We present three different models for empirical application that allow for varying degrees of dependence across these latent informational/bargaining factors.

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Notes

  1. See Papadopoulos (2021a), for a detailed literature review.

  2. As one variable goes to ∞, the other cannot, by definition, go below 0.

  3. The long mathematical derivations of this Section are collected in a Technical Appendix that is available from the authors upon request.

  4. A closely related result, for a different truncation schema, was obtained by Arnold et al. (1993).

  5. The HN density for the zero-correlation case was also mentioned in Horrace (2005).

  6. The distribution is known as "Freund’s Bivariate (Mixture) Exponential extension," see Kotz et al. (2000) pp. 355-362 and Balakrishnan and Lai (2009) ch.10.3, for a survey of the literature, properties and applications of the distribution. This section is based on Chapter 4 of the PhD thesis of Papadopoulos (2018), where one can find also the related mathematical derivations.

  7. This is an inconsequential assumption because while if it does not hold it will change the expressions for the marginal densities to avoid division by zero, it will not affect the marginal moments, or any other derived expression in the model.

  8. Note that for the Clayton Copula we have Kendall’s τ = θ/(2 + θ).

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Authors and Affiliations

  1. Athens University of Economics and Business, Athens, Greece

    Alecos Papadopoulos

  2. University of Miami, Miami, FL, USA

    Christopher F. Parmeter

  3. State University, Binghamton, NY, USA

    Subal C. Kumbhakar

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  1. Alecos Papadopoulos
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  2. Christopher F. Parmeter
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  3. Subal C. Kumbhakar
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Correspondence to Alecos Papadopoulos, Christopher F. Parmeter or Subal C. Kumbhakar.

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Papadopoulos, A., Parmeter, C.F. & Kumbhakar, S.C. Modeling dependence in two-tier stochastic frontier models. J Prod Anal 56, 85–101 (2021). https://doi.org/10.1007/s11123-021-00611-2

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