Biases in the Maximum Simulated Likelihood Estimation of the Mixed Logit Model

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Here are the comments on the paper, Biases in the Maximum Simulated Likelihood Estimation of the Mixed Logit Model to Econometrics. 

1. The literature should be written in past tense as the work has already been completed, similar to the methods and the empirical results of this paper.

2, The abstract seems short.  The authors should add a few more sentences in the abstract.  Perhaps some on the empirical results found in this good paper. 

3. The authors stated in the introduction of the paper "Since the model does not have a closed-form, its estimation relies on simulation-based  methods, specifically the MSL estimator, which has been the dominant estimation strategy.."  That seems to be a general issue of MSL in the application of discrete choice models. 

4. What about the following reference: Bastin, F., & Cirillo, C. (2010). Reducing simulation bias in mixed logit model estimation. Journal of Choice Modelling, 3(2), 71-88.

5. What about the paper by Train (2003)?  The paper by Train (2003) seems like an important paper on MXL. 

6. Line 87 simulations is fixed (see Gourieroux and Monfort, 1996; Lee, 1995; and Hajivassiliou et al.,  would the simulations be Monte Carlo?

7. Under the section 2, Maximum Simulated Likelihood Estimator, MSL uses simulated probabilities than inserts these probabilities into the log-likelihood function, not the standard maximum likelihood.  Could the authors clearly state that this is the case? 

8. Lines 224-225, a bias is introduced?  Perhaps the bias is reduced? 

9. Lines 249-250, this seems far fetched but most likely something to consider. Is is possible to compare the estimates prior to EC1 and EC2 to prior specifications?  Perhaps I may be thinking out loud here. 

10.   What software was used to prepare these estimates in this paper? Perhaps I think maybe that new code was written for these models.  Is this code available somewhere?  Perhaps in the future? 

11. Is it possible for the use of bootstrapping rather than the use of Monte Carlo simulations?  How would the results in this paper differ from the bootstrapping results? I understand that Halton sequences are sequences used to generate points in space for numerical methods such as Monte Carlo simulations.  Perhaps the bootstrapping would not be appropriate via Halton sequences.  

Comments on the Quality of English Language

Just another read by the authors or a colleague to ensure that the English in this good paper is suitable for publication. 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Comments on “Biases in the Maximum Simulated Likelihood Estimation of the Mixed Logit Model" (2891332)

 

 

The study empirically illustrates biases from the MSL estimation of the error component mixed logit model (EC-MIXL). The paper is well written, straightforward, and easy to follow as authors estimate potential biasness of the MSL estimator for the EC-MIXL model by comparing the logit parameter estimates to true values used for the Monte Carlo simulated data.

 

I have a few minor comments.

 

1.     When authors discuss biases in tables 1 and 2, I feel that hypothesis test results are reported casually, mostly citing x standard error differences (which I believe can be considered t-statistic), and in some cases, their discussions are not correct or at least not clear. For example, on page 8, when σ₂ =0.569 (0.023) is tested against the true value 0.5, the authors state that the null is not rejected, even though the difference is 3 standard error. I am not sure what distribution and significance level are applied for this test. It could be Wald/t distribution or something that could be done nonparametrically.  I suggest readers be more specific about the test method throughout the manuscript.

 

2.     In Section 4.3 on page 13, authors report that choice probabilities are close, while marginal effects are considerably different, although parameter estimates are significantly biased. Authors also report that the bias becomes worse when the true variance parameter is small and the correlation parameter is large. What causes this outcome and why?  Are your findings consistent with earlier studies both theoretically and empirically?  Can any of your findings be applied to the random coefficient model?

 

3.     Your results on biasness are overall invariant with the number of Halton draws, which is not consistent with findings from earlier studies, for example Palma et al. (2020). What are the factors that might affect this result?

 

4.     On page 5, there is a typo on line182, the second error term should be ε_i2.

 

5.     On page 6, equation (8) needs to be (9).  Also, I suggest that authors change “L” used in equations (8) and (9) to something else to avoid confusion with “LL” in (13).

 

6.     On page 9, “withing” on line 304 needs to be “within.”     

Comments for author File: Comments.docx

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Here are the comments on the paper for the second review, Biases in the Maximum Simulated Likelihood Estimation of the Mixed Logit Model to Econometrics. 

1. No new comments.  This paper is great.