Calibrated Projection in MATLAB: User's Manual and Package

We present the calibrated-projection MATLAB package implementing the method to construct confidence intervals proposed by Kaido, Molinari, and Stoye in "Confidence Intervals for Projections of Partially Identified Parameters", forthcoming at Econometrica. This version of the code is what was used to carry out the empirical application in Section 4 of Kaido, Molinari, and Stoye (2019) and the Monte Carlo simulations in Appendix C. Please visit https://molinari.economics.cornell.edu/programs.html for the most up-to-date version of the code.

Getting Started

The file calibrated-projection-MATLAB/Manual/KMST_Manual.pdf provides details on how to use the package for inference on projections of partially identified parameters and instructions on how to replicate the empirical application and simulation results in the paper. The package is written in MATLAB, but calls MEX files that execute the CVXGEN linear prorgram, which is written in C. The key steps to run the package are to:

1. Specify the moment (in)equality constraints, the corresponding gradients, and standard deviation estimator.
2. Set up either CVXGEN or CVX
3. Specify the set of additional options in KMSoptions.m.
4. Call the file KMS_0_Main.m.

Working Examples

We have included a set of examples in the package that are discusssed in detail in the manual and in Kaido, Molinari, and Stoye (2019).

1. KT Application: The file KMS_Application.m runs the airline application of Kline and Tamer (2016, Quantitative Economics). This file specifies the additional options and calls KMS_0_Main.m. The moments, gradients, and standard deviation estimator are included in the files moments_w.m, moments_theta.m, moments_gradient.m, and moments_stdev.m under the DGP=9 if condition.
2. BCS Simulation: The file BCS_Simulation.m replicates the simulations for the game proposed in Bugni, Canay, and Shi (2017, Quantitative Economics). This example corresponds to DGP=8.
3. Monte Carlo Simulations: The file KMS_Simulation.m replicates the simulations, and there are 7 data-generating processes to choose from by setting DGP equal to either 1,2,..., or 7.

References

1. Bugni, F., I. Canay, and X. Shi (2017) "Inference for subvectors and other functions of partially identified parameters in moment inequality models," Quantitative Economics, 8(1), 1–38..

2. Kaido, H., F. Molinari, and J. Stoye (2019) "Confidence Intervals for Projections of Partially Identified Parameters," Forthcoming Econometrica.

3. Kline, B., and E. Tamer (2016): "Bayesian inference in a class of partially identified models," Quantitative Economics, 7(2), 329–366.