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Implementing Convex Optimization in R: Two Econometric Examples

Abstract

Economists specify high-dimensional models to address heterogeneity in empirical studies with complex big data. Estimation of these models calls for optimization techniques to handle a large number of parameters. Convex problems can be effectively executed in modern programming languages. We complement Koenker and Mizera (J Stat Softw 60(5):1–23, 2014)’s work on numerical implementation of convex optimization, with focus on high-dimensional econometric estimators. Combining R and the convex solver MOSEK achieves speed gain and accuracy, demonstrated by examples from Su et al. (Econometrica 84(6):2215–2264, 2016) and Shi (J Econom 195(1):104–119, 2016). Robust performance of convex optimization is witnessed across platforms. The convenience and reliability of convex optimization in R make it easy to turn new ideas into executable estimators.

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Notes

  1. 1.

    At the writing of this note, CVXR + MOSEK takes from minutes to hours to compute one estimation depending on sample sizes, which makes the full-scale simulation exercise computational infeasible.

  2. 2.

    CVXR + MOSEK does not support exponential/logarithm objective functions and hence is infeasible for REL.

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Acknowledgements

Shi thanks Roger Koenker for inspiration and hospitality during his visit to University of Illinois.

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Correspondence to Zhentao Shi.

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Gao, Z., Shi, Z. Implementing Convex Optimization in R: Two Econometric Examples. Comput Econ (2020). https://doi.org/10.1007/s10614-020-09995-z

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Keywords

  • Big data
  • Convex optimization
  • High-dimensional model
  • Numerical solver

JEL Classification

  • C13
  • C55
  • C61
  • C87