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RE: efficiencies () [ Reply ] By: Arne Henningsen on 2014-12-13 06:44	[forum:41739]
Dear Laura I do not know whether you can estimate a linear output distance function, I just wrote that I have some doubt about your specification. I know that one can estimate a linear or quadratic *directional* distance function, but these functions usually have large problems with heteroskedasticity. Best regards, Arne

RE: efficiencies () [ Reply ] By: laura di giorgio on 2014-12-12 23:51	[forum:41738]
Dear Arne, thank you very much for your help. Do you know where could I find a confirmation (textbook or other source) that the distance function cannot be estimated for linear functions? The Cobb-Douglas function works fine. Best laura

RE: efficiencies () [ Reply ] By: Arne Henningsen on 2014-12-12 22:57

[forum:41737]

The Cobb-Douglas output distance function can be estimated by ODF_CD <- sfa( -log(outc) ~ log(outa/outc) +log(outb(outc) + log(ina) + log(inb) + log(inc), data = myData, ineffDecrease = FALSE ) myEff <- efficiencies( ODF_CD ) The efficiencies() method for "frontier" objects returns efficiency estimates of the individual observations/firms. The documentation of argument "minusU" of efficiencies.frontier() says: minusU: logical. If ‘TRUE’ (the default), the efficiencies are calculated by E[exp(-u)], i.e. Farrel-type efficiencies are returned for input-oriented models, Shepard-type efficiencies are returned for output-oriented models, and the returned efficiency estimates have values between zero and one, where a one indicates a fully efficient firm and a zero indicates a fully inefficient firm. If ‘FALSE’, the efficiencies are calculated by E[exp(u)], i.e. Shepard-type efficiencies are returned for input-oriented models, Farrell-type efficiencies are returned for output-oriented models, and the returned efficiency estimates have values larger than or equal to one, where a one indicates a fully efficient firm and plus infinity indicates a fully inefficient firm. The difference between Shepard-type efficiencies and Farrell-type efficiencies is briefly explained in sections 5.1.1.1 to 5.1.1.4 of my lecture notes: https://files.itslearning.com/data/ku/103018/teaching/lecturenotes.pdf Best regards, Arne

RE: efficiencies () [ Reply ] By: Arne Henningsen on 2014-12-12 22:42	[forum:41736]
Dear Laura I have some doubt that your linear specification is suitable, because it seems to me that it does not fulfil the properties that output distance functions must have. Best regards, Arne

RE: efficiencies () [ Reply ] By: laura di giorgio on 2014-12-10 21:55

[forum:41733]

Dear Arne, we also consider the traditional log-linear Cobb-Douglas distance function. So it might be easier to stick to this scenario to address my questions. So summarizing: - log-linear Cobb-Douglas distance function with multiple outputs (3) and inputs (3) - linear homogeneity imposed It would be very helpful if you could address my questions having this model in mind. thank you very much laura

RE: efficiencies () [ Reply ] By: laura di giorgio on 2014-12-10 19:53

[forum:41732]

Hi Arne, sorry about this. 1) Yes it is an output distance function, in which there are 3 outputs: outa, outb, outc. To estimate the distance function we transform the variables as follows: outa_lh = outb/outc outb_lh = outb/outc outcNEG = - outc 2) we are actually assuming that the underlying production form is in the linear form. I know this is not the typical scenario for this type of models as usually researchers assume Cobb-Douglas or Translog, but we are using simulated data and thinking of a production process that looks like this. The data generation process is more complex, but the final dataset follows this specification: y1a1 + y2a2 + y3a3 = x1b1 + x2b2 + x3b3 where ai and bi are the outputs- and inputs coefficients. is it possible to estimate a distance function of this form? If this scenario is too abstract to understand, Thanks, laura

RE: efficiencies () [ Reply ] By: Arne Henningsen on 2014-12-10 19:35

[forum:41731]

Dear Laura I find it difficult to answer your questions, because you provide insufficient and partly contradicting information: (a) First, you write that you estimate an output *distance* function and then you write that you estimate a (linear) *production* function. What kind of function do you want to estimate? (b) As you have multiple outputs and multiple inputs, I assume that you want to estimate an output distance function rather than a production function. You indicate that you want to estimate a linear functional form. However, I do not know any linear specification of an output distance function. Do you mean a log-linear (Cobb-Douglas) functional form? (c) Please define your variables "outcNEG", "outa_lh", and "outb_lh". Best regards, Arne

RE: efficiencies () [ Reply ] By: laura di giorgio on 2014-12-09 21:18	[forum:41730]
Sorry, this may be confusing. I mistakenly copied some text that did not need to be there. Please do not consider what is coming after my name. Thanks, laura > > > I have a second question: when I look at the results of the stochastic > frontier model, I get the following message. > > > > The dependent variable is logged

efficiencies () [ Reply ] By: laura di giorgio on 2014-12-09 21:14

[forum:41729]

Hi frontier group, I am trying to estimate an ouptut-oriented 3 inputs (ina, inb, inc), 3 outputs (outa, outb, outc) distance function for our model called DFO. The dataset is called dataDFO. We are using a linear production function, therefore the variables are not logged. This is the model we estimate: DFO <- sfa(outcNEG ~ outa_lh +outb_lh + ina + inb + inc, data=dataDFO, ineffDecrease=TRUE) DFOeff <- efficiencies(DFO, logDepVar=FALSE) My issue is that I am not sure how to get DMU-specific efficiency estimates after running this model for my particular case. And this question is related to the following specification of the command: 1) minusU: what is the difference between Farrell type and Shepard type and what would apply for this model? Is here TRUE or FALSE? 2) does the command "efficiencies" provide efficiency estimates directly or is any other step is needed to get the DMU-specific efficiency score ranging from 0 to 1? (e.g. 1-DFOeff) I read that "currently, the efficiency estimates based on models with non-logged dependent variable can be calculated only if 'ineffDecrease' is equal to 'minusU'". Is this my case? And if yes, is there any other way to estimate this model in R? Thanks a lot! laura > > > I have a second question: when I look at the results of the stochastic > frontier model, I get the following message. > > > > The dependent variable is logged