Stochastic Frontier Analysis in STATA with a conditional inefficiency term

[Harald Leber]

I try to estimate a stochastic frontier model with a cost to sales ratio (variable RATIO) as dependent variable using the following model:

ln(RATIO)i,t = b1*ln(VAR1)i,t + b2*ln(VAR2)i,t +  b3*(VAR3)i,t + vi,t + ui,t where v~N[0,sv²] and u~TN+[b'Fi,t, su2]

The last term means that the inefficiency term u_i,t is again conditional on further explanatory variables (here ln(VAR4) and VAR5).

Given the above model, the correct command using the STATA build-in frontier would be I guess (I was not able to implement a conditional inefficiency term using xtfrontier):

frontier lnRATIO lnVAR1 lnVAR2 VAR3, cost distribution(tnormal) cm(lnVAR4, VAR5)

However, the estimation iteration-process always produces log-likelihood values with the additional comment "(backed up)" and then runs forever...

Alternatively, if I use the user-written command sfpanel (ssc install sfpanel) as follows

sfpanel lnRATIO lnVAR1 lnVAR2 VAR3, cost model(bc95) emean(lnVAR4, VAR5)

STATA always returns the following error: "could not calculate numerical derivatives -- flat or discontinuous region encountered"..

What am I doing wrong here? Am I using the wrong STATA commands for the model described above?

[Harald Leber]

I found out that in order to get "good" starting values, I should pre-define them using the option ufrom() of STATA's frontier command.

So I run a simple OLS regression

 reg lnRATIO lnVAR1 lnVAR2 VAR3

and save the coefficients, the natural log of the square of the root mean square error and the value .1 in a matrix called b0 (taken from an old posting here http://www.stata.com/statalist/archi.../msg00519.html

matrix b0 = e(b), ln(e(rmse)^2) , .1

and run frontier again:

frontier lnRATIO lnVAR1 lnVAR2 VAR3, cost distribution(tnormal) cm(lnVAR4, VAR5) ufrom(b0)

However, STATA tells me that "ufrom() must specify a 1 x 6 matrix" - what am I missing?

[Scott Merryman]

I am not sure your code statement is what was actually typed - the comma in the conditional mean statement would generate an error. I would expected you need a 1x9 matrix : 4 in the lnRATIO equation (3 variables plus the constant), 3 in the Mu equation (2 variables plus the constant), ilgtgamma, and lnsigma2

[Richard Hofler]

Hello Harald,

Two observations:
1. You describe a panel data model in your original post. So, you should be using -xtfrontier-, not -frontier-.
2. -sfpanel- gives you many good choices for your panel data frontier model: 7 time-varying efficiency models and 4 time-invariant efficiency models. As a lot of folks have written on this forum many times, good advice is to think hard about which model makes the most sense for your particular problem. Most likely, -sfpanel- will allow you to estimate it.

I hope this helps,
Richard