Distribution-Free Estimation of Heteroskedastic Binary Response Models in Stata

Jason R. Blevins and Shakeeb Khan
Stata Journal 13 (2013), 588–602.

• Published version
• Preprint version
• 2015 Stata Conference slides

Abstract. In this article, we consider two recently proposed semiparametric estimators for distribution-free binary response models under a conditional median restriction. We show that these estimators can be implemented in Stata by using the nl command through simple modifications to the nonlinear least-squares probit criterion function. We then introduce dfbr, a new Stata command that implements these estimators, and provide several examples of its usage. Although it is straightforward to carry out the estimation with nl, the dfbr implementation uses Mata for improved performance and robustness.

Keywords: dfbr, binary response, heteroskedasticity, nonlinear least squares, semiparametric estimation, sieve estimation.

JEL Classification: C13, C14, C25, C87.

Stata Package Installation

To install the dfbr Stata package you first need to install a prerequisite package called moremata:

ssc install moremata

Next, install dfbr as follows:

net install dfbr, from(https://jblevins.org/)

Suggested Citation

When using dfbr in published work, please cite either the Stata Journal paper or the relevant paper for the specific estimator used (or both):

Citation for the Stata program:

• Blevins, J. R. and S. Khan (2013). Distribution-Free Estimation of Heteroskedastic Binary Response Models in Stata. Stata Journal 13, 588–602.

Citations for the sieve and local nonlinear least squares estimators, respectively:

• Khan, S. (2013). Distribution Free Estimation of Heteroskedastic Binary Response Models Using Probit Criterion Functions. Journal of Econometrics 172, 168–182.
• Blevins, J. R. and S. Khan (2013). Local NLLS Estimation of Semiparametric Binary Choice Models. Econometrics Journal 16, 135–160.

BibTeX Record

@Article{blevins-khan-2013-dfbr,
  author       = {Jason R. Blevins and Shakeeb Khan},
  title        = {Distribution-Free Estimation of Heteroskedastic Binary
                  Response Models in {Stata}},
  journal      = {Stata Journal},
  volume       = {13},
  year         = {2013},
  pages        = {588--602}
}

History

• June 22, 2015: Updated installation instructions to highlight moremata dependency.
• April 9, 2014: Updated help file to finalize citations.
• September 17, 2013: Published version available.
• March 18, 2013: Updated working paper.
• November 30, 2012: Updated working paper; dfbr version 1.1.0. Changes include:
  • Use multiple starting values including probit, logit, OLS, and LAD estimates.
  • Normalize covariates for optimization.
  • Store bootstrap replicates in e(BS).
  • Store estimated sieve parameters in e(alpha).
  • Allow custom jackknife constants in k1 and k2.
  • Perform $10k$ initial Nelder Mead iterations.
  • Add nmdelta and nmiter options for initial Nelder Mead run.
• June 20, 2012: Updated working paper.
• June 10, 2012: dfbr version 1.0.0. Changes include:
  • Full rewrite in Mata using optimize() with analytical derivatives.
  • Add alternative regression function with feasible optimal bandwidth.
  • Use jackknife local nonlinear least squares for normal CDF option.
  • Drop collinear independent variables.
  • Support factor variables in varlist and basis_vars.
  • Support in range qualifier.
  • Allow brep(0) to skip bootstrapping.
• July 22, 2011: Updated working paper and Stata help file.
• July 15, 2011: dfbr version 0.9.0. Changes include:
  • Automatic boostrap with bsrep and seed options.
  • Include constant term by default with noconstant option.
  • Implement level option in line with usual Stata practice.
  • Improved output and return values.
• January 9, 2009: Second revision of working paper; dfbr version 0.8.1.
• September 6, 2008: First revision of working paper; dfbr version 0.8.0.