Is Quantile Regression useful in Stochastic Frontier Analysis?

Posted: June 21, 2021 in Research
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Here is a presentation I recently made in the (virtual) North American Productivity Workshop XII (vNAPW-XII). Quantile regression has seen a large number of applications in econometrics, especially in Treatment Effects models, because it can capture also the “indirect” effects of the regressors on the dependent variable, along the quantiles of the latter.

But does the trick work in Stochastic Frontier Analysis (SFA)? My conclusion is that it doesn’t. Fundamentally, this is because in Treatment Effects models we consider equilibrium relations and we care about the total effect of the regressors on the dependent variable. But in SFA, we consider frontier relations, and we want to keep clearly separate the effects of the regressors on the “deterministic frontier”, from any other indirect effect they may have.

Moreover, the defining property of the estimator used in Quantile Regression (the Q-estimator), is not harmless in SFA models – in fact, it is devastating and we need distributional assumptions to mend the damage. This does not mean that we cannot use the “quantile approach” in SFA at all, it only means that we should expect different benefits, and perhaps, after all said and done, fewer: currently it appears that the value-added in using Quantile Regression in SFA is smaller than when using it in Treatment Effects models.

Download the presentation and think for your self. Hopefully, it will appear eventually as a paper somewhere. The paper will contain some more material than the presentation, and its current abstract goes like this:

We review fundamental properties of quantile regression and we examine the degree to which they are compatible with the special statistical and economic characteristics of stochastic frontier models, and with the goals of stochastic frontier analysis. We find that the scope and focus of quantile regression changes when applied to stochastic frontier models, compared to the conventional regression setup. We show that a “corrected” quantile estimator can be used to estimate the quantile probability of the deterministic frontier, given a distributional assumption. We examine the quantile estimator in the benchmark case of independence between the regressors and the error term, but also when “predictors of inefficiency” enter the model, in which case we obtain a non-linear median stochastic frontier regression model, where the deterministic frontier can be estimated without distributional assumptions. We show how quantiles can be used to obtain information on individual levels of inefficiency, and also as a basis for specification tests for the distributional assumptions.

  1. Shirong Zhao says:

    Hi, Alecos,

    I am very interested in this paper. I am wondering whether you have a working paper that can be shared. Thanks

    • Hello. Thank you for the interest in my work. This work is now being merged with a review Quantile SF paper that Chris Parmeter had written, and they will be published as a joint work in the Foundations and Trends series. So currently there is no sharable working paper version, it’s all fluid. I expect in approximately two months the joint work will have been complete.

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