Log with zero output - But in Stochastic Frontier Analysis

[Armando Martins]

Hi everyone,

I’m here because i'm trying to estimate a stochastic frontier model (in STATA 14), but I’ve run into an issue: some units in my sample produce zero output.

Since the most usual SFA specifications rely on log-linearized production functions (eg. cobb douglas, translog), I’m not sure how to properly handle these zero-output observations.

I've read Chen and Roth (2024) review, but it was not clear to me if their solutions apply for SFA models.

- Is there a recommended way to incorporate zero-output units in SFA?

- Would a two-stage approach make sense here? There is, first modeling the probability of positive output, and then estimating the stochastic frontier conditional on positive output?

- If so, are there references or best practices on implementing this in an SFA framework?

Thanks!

[Armando Martins]

(PS: I’ve tried to transform the output (at first continous) to discrete and use sfcount - using the denominator as a input - but convergence was never achieved)

[Jeff Wooldridge]

The Chen and Roth warning applies to any case where y = 0 is possible. You are better off using an exponential model. That should be possible with SFA, but I don't know that it's been done explicitly. Is there something special about it that precludes using Poisson regression and including logs of the inputs, including dummy variables for zero inputs?

[Armando Martins]

I'm sorry for the late reply, I'm glad to receive your feedback, Jeffrey! I forgot to mention, but the sfcount I used is STATA package for poisson/half-normal SFA (Fé and Hoefler, 2020), and the problem is on convergence not achieved. Your exponential model idea looks good, I'll try to code such a solution.

I came up with another solution, similar to Chen and Roth' mention of lee bounds estimates: Kumbhakar, Tsionas and Sipilainen (2009) propose to estimate a binary choice and SFA jointly with maximum likelihood. I'm still thinking if the binary choice needs to be over-identified, or other details to make it viable. Do you have any insights on this?