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Estimation of the two-tiered stochastic frontier model with the scaling property

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Abstract

The two-tiered stochastic frontier model has enjoyed success across a range of application domains where it is believed that incomplete information on both sides of the market leads to surplus which buyers and sellers can extract. Currently, this model is hindered by the fact that estimation relies on very restrictive distributional assumptions on the behavior of incomplete information on both sides of the market. However, this reliance on specific parametric distributional assumptions can be eschewed if the scaling property is invoked. The scaling property has been well studied in the stochastic frontier literature, but as of yet, has not been used in the two-tier frontier setting.

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Notes

  1. Other papers formalizing the two-tier stochastic frontier have used v and w to encapsulate incomplete information on each side of the market while letting u capture two sided noise. Given that v is almost universally used in textbook econometrics as random noise, and that the stochastic frontier literature has commonly used u to capture inefficiency, we have decided to use u and w to capture incomplete information. Moreover, in alphabetical order, you have that u is under v (hence −) and w is over v (hence +).

  2. Here Exp(σ z ) denotes a random variable z that is exponentially distributed with mean σ z and variance \(\sigma _z^2\).

  3. See Kumbhakar and Parmeter (2009) for the full derivation.

  4. Other examples include the Gamma or Weibull distributions with fixed shape parameters. In this case the shape parameter does not need to be known, but it has to be a constant w.r.t. (x, z).

  5. Note that δ may not be difficult to estimate if the information that δ u  = δ w  = δ is accounted for prior to estimation.

  6. See the supplemental appendix for additional simulations that assess the robustness of the findings to various degrees of correlation across the covariates.

  7. The R code used for to conduct these simulations is available upon request.

  8. I thank an anonymous referee for drawing my attention to this.

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  1. University of Miami, Miami, FL, USA

    Christopher F. Parmeter

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  1. Christopher F. Parmeter
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Correspondence to Christopher F. Parmeter.

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Parmeter, C.F. Estimation of the two-tiered stochastic frontier model with the scaling property. J Prod Anal 49, 37–47 (2018). https://doi.org/10.1007/s11123-017-0520-8

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