KamilMakiela
commented
6 years ago Hi Xiao,
First of all, thank you for the interest. Now lets get down to your question. The papers you cite employ two concepts: 1) a distance function oriented on inputs (i.e., the input distance function) and 2) endogeneity, which is inherent to distance functions and a system of equation to overcome this problem. Endogeneity in distance functions is due to the fact that some variables which are explanatory variables in the equation of interest (i.e., are on the right hand side of the equation) are regarded as endogeneous variables (e.g., in the papers you cite all inputs except x_1 are regarded endogeneous, which is reasonable in the case of airline industry, I am not so sure about banking). The reason why these papers use "input" distance functions is that they treat outputs exogenously rather then inputs (so inputs are the variables that can be in some way optimized by airlines/banks). Although they provide some compelling justification for this (especially the airlines article, electricity distribution would be another case) it is also for practical reasons. Things get much more complicated if you let outputs to be endogenous. Ad. 1. You can relatively easily include bad outputs as treated in these papers using the software. It is mostly a matter of rearranging it and then imposing restrictions on parameters (which the program can do). Note Eq. 7 in Assaf et al. (2014) as well as Assaf et al. (2014) were they write "we treat bad outputs as an exogenous technology shifter". This means that introducing bad outputs in their models boils down to restrictions similar to those on "other inputs", so if, e.g., you transform the remaining (good) output variables (e.g., ln(good_out)* = -ln(good_out)) in your translog (or Cobb-Douglas) you arrive at a simple non-decreasing restriction for the distance funcition (in respect to all explanatory variables). This can be done using the restrictions section of the programs interface. Afterwards you just have to remember to put a minus sign to all parameters of the "good" outputs when interpreting the results. Ad. 2. Endogeneity is a problem. Accounting for endogeneity (generally) requires us to build a system of equations. So apart from the one equation that you are interested in exploring you need to specify equations for all other endogenous variables (inputs other than x_1 in the case of these papers if I am correct) and estimate them jointly. I assume the papers rely on Atkinson and Dorfman (2005) to do so, which I am not familiar with. Since these "other" equations are often built very subjectively I don't really see how this could be included in a general purpose program like this one. So in this regard I suggest doing either of the following:
- Read the paper by Kumbhakar (2014) about maximizing return to the outlay. If your model can be framed in this context then a relatively simple procedure described there should mitigate the endogeneity problem. I think the trick had to do with inputs normalization, which Assaf (2013, 2014) also perform but I am not sure about how the two connect.
- Try to determine if your endogenous variables are in fact (or can be treated as) weakly exogenous. If the weak exogeneity assumption holds, you don't need information from "other" equations to estimate the one you are interested in (e.g., your distance function).
- Though Atkinson et al. (2013) say that they estimate a system of equations they end up using (pure) Gibbs sampler, which is implemented in the program. Normally the system estimation would require a much more complex procedure (Fernandez et al. 2000, 2002) so there must be some major simplification somewhere in the procedure they use, which is not made explicite in the two papers. This could mean that once the model is appropriately rewritten the program can still be used in the spirit of Atkinson and Dorfman (2005) estimation. Hope this helps, Kamil
Papers: Fernández, C., Koop, G., M.F.J. Steel. (2000). A Bayesian analysis of multiple-output production frontiers, Journal of Econometrics, 98(1), 47-79 Fernández, C., Koop, G., & M.F. J. Steel. (2002). Multiple-Output Production with Undesirable Outputs: An Application to Nitrogen Surplus in Agriculture. Journal of the American Statistical Association, 97(458), 432-442. Kumbhakar, S (2011). https://doi.org/10.1016/j.ejor.2010.09.015
Bayesian estimation with undesirable outputs in SFA is a new trend in recent years. Does "BSFAmk1" support this method? Here are some references:
Assaf, A. G., Matousek, R., & Tsionas, E. G. (2013). Turkish bank efficiency: Bayesian estimation with undesirable outputs. Journal of Banking & Finance, 37(2), 506-517.
Assaf, A. G., Josiassen, A., & Gillen, D. (2014). Measuring firm performance: Bayesian estimates with good and bad outputs. Journal of Business research, 67(6), 1249-1256.