PIES

This repository contains code for the simulations in Torgovitsky, A. (2019), "Partial Identification by Extending Subdistributions." Quantitative Economics, 10 (1), pp. 105–144, doi:10.3982/QE634

Important

The code included in the supplemental material for Quantitative Economics is from April 9, 2018. Please download the most recent version of the code from the GitHub repository.

Software Requirements

• MATLAB. No special toolboxes are required.

• A Mathematical Programming Language (AMPL). The student version of AMPL is size restricted. Some simulations will probably run with the student version, but most will require a full license.

• A linear programming solver for AMPL. The default is Gurobi. It can easily be changed by passing e.g. Settings.LPSolver = 'cplex' when calling ./src/IdentifiedSet.m. See the discussion on usage below.

• The AMPL-MATLAB API.

• Linux (or perhaps OSX). I coded these simulations in Linux and made no attempt to be platform-independent. However, the code is primarily in MATLAB, so should be mostly platform-independent. Some file operations are used for recording the results of simulations. These would be likely sources of issues for other operating systems, but should be easy enough to fix.

Setup and Usage

• Important first step

  • Open ./cfg/Config.m.
  • Change SAVEDIRECTORY to a directory where you want simulations to be saved.
  • Change AMPLAPISETUPPATH to the correct location for your installation of the AMPL-MATLAB API.

• The primary code is contained is ./src/IdentifiedSet.m and the routines called from within. It contains many options that can be set, which are given default values in the structure called Settings that is defined at the top of that file. Another structure called Assumptions serves a similar purpose but only contains options that pertain to what assumptions are imposed when constructing the identified set.

• The directory ./run/ contains a file called ./Run.m that can be used to run IdentifiedSet.m under limited pre-set options. For example, the command Run(2,3,5) would run specification number 2 from the paper with (d_{1}, d_{2}) = (3,5) in the notation there.

• Sequentially running all of the simulations in the paper will take a long time. The process can be sped up by using the file ./run/MultiBatchRun.m, which opens multiple MATLAB threads. (Unfortunately, the AMPL-MATLAB API is not easy to parallelize.) The command to reproduce the results in the paper is

  MultiBatchRun(1:1:14, 'your-save-dir')`

  Note that this will open 14 MATLAB and AMPL instances at one time, which will strain a typical system. To open fewer threads, pass a smaller array of numbers in the first argument, wait a while, then pass the remaining ones, using the same directory name.

My Software Versions

The numerical results in the published paper were run with

• MATLAB version 8.6.0.267246 (R2015b)
• AMPL version 20170711
• Gurobi version 7.5.0
• AMPL-MATLAB API version 1.2.2.

Software Acknowledgment

The code uses the MATLAB function MergeBrackets.m written by Bruno Luong. A copy of this code is included in ./src/MergeBrackets.m.

Problems or Bugs?

Please use GitHub to open an issue and I will be happy to look into it.