├── .gitignore ├── GPLv3.txt ├── LICENSE ├── README.org ├── _BLP.cp35-win_amd64.pyd ├── _BLP.cp36-win_amd64.pyd ├── _BLP.pyx ├── examples ├── Nevo_2000b.py ├── iv.mat └── ps2.mat ├── paper ├── paper.bib └── paper.md ├── pyBLP.py ├── setup.py └── tests └── test_BLP.py /.gitignore: -------------------------------------------------------------------------------- 1 | auto 2 | build 3 | _BLP.c 4 | -------------------------------------------------------------------------------- /GPLv3.txt: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | BLP-Python provides an implementation of Random coefficient model of 2 | Berry, Levinsohn and Pakes (1995) 3 | Copyright (C) 2011, 2013, 2016 Joon H. Ro 4 | 5 | This file is part of BLP-Python. 6 | 7 | BLP-Python is free software: you can redistribute it and/or modify 8 | it under the terms of the GNU General Public License as published by 9 | the Free Software Foundation, either version 3 of the License, or 10 | (at your option) any later version. 11 | 12 | BLP-Python is distributed in the hope that it will be useful, 13 | but WITHOUT ANY WARRANTY; without even the implied warranty of 14 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 15 | GNU General Public License for more details. 16 | 17 | You should have received a copy of the GNU General Public License 18 | along with this program. If not, see . 19 | -------------------------------------------------------------------------------- /README.org: -------------------------------------------------------------------------------- 1 | # Created 2017-04-05 Wed 10:52 2 | #+TITLE: BLP-Python 3 | #+DATE: [2017-04-05 Wed] 4 | #+AUTHOR: Joon Ro 5 | #+EMAIL: joon.ro@outlook.com 6 | * Introduction 7 | =BLP-Python= provides a Python implementation of random coefficient logit 8 | model of Berry, Levinsohn and Pakes (1995). The specific implementation 9 | follows the model described in Nevo (2000b). 10 | 11 | This code uses tight tolerances for the contraction mapping (Dube et 12 | al. 2012). With BFGS method, it quickly converges to the optimum (See Nevo 13 | (2000b) Example below). 14 | 15 | I would like to thank Prof. Nevo and others for making their MATLAB available, 16 | which this package is originally based on. Also, I would like to thank [[http://wingware.com][Wingware]], 17 | who generously provided a free license of [[http://wingware.com][WingIDE]] for this non-commercial open 18 | source project. 19 | 20 | ** Notes on the code 21 | - Use global states only for read-only variables 22 | - Avoid inverting matrices whenever possible for numerical stability 23 | - Use a tight tolerance for the contraction mapping 24 | - Use greek unicode symbols whenever possible for readability 25 | - μ and individual choice probability calculations are implemented in Cython, 26 | and it is parallelized across the simulation draws via openMP 27 | - Use n-dimensional arrays (via [[http://xarray.pydata.org][xarray]]) to represent data more naturally 28 | * Installation 29 | ** Dependencies 30 | - Python 3.5 (for ~@~ operator and unicode variable names). I recommend 31 | [[https://www.continuum.io/downloads][Anaconda Python Distribution]], which comes with many of the scientific libraries, 32 | as well as =conda=, a convenient script to install many packages. 33 | - =numpy= and =scipy= for array operations and linear algebra 34 | - =cython= for parallelized market share integration 35 | - =xarray= for multidimensional labeled arrays (does not come with Anaconda, 36 | install with =conda install xarray=) 37 | - =pandas= for result printing 38 | ** Download 39 | - With git: 40 | 41 | #+BEGIN_SRC sh 42 | git clone https://github.com/joonro/BLP-Python.git 43 | #+END_SRC 44 | 45 | - Or you can download the [[https://github.com/joonro/BLP-Python/archive/master.zip][master branch]] as a zip archive 46 | ** Compiling the Cython Module 47 | - I include the compiled Cython module (=_BLP.cp3X-win_amd64.pyd=) for Python 48 | 3.5 and 3.6 64bit, so you should be able to run the code without compiling the 49 | module in Windows. You have to compile it if you want to change the Cython 50 | module (=_BLP.pyx=) or if you are on GNU/Linux or Mac OS. GNU/Linux 51 | distributions come with =gcc= so it should be straightforward to compile the 52 | module. 53 | - ~cd~ into the =BLP-Python= directory, and compile the cython module with 54 | the following command: 55 | 56 | #+BEGIN_SRC sh 57 | python setup.py build_ext --inplace 58 | #+END_SRC 59 | *** Windows 60 | - For Windows users, to compile the cython module with the openMP 61 | (parallelization) support with 64-bit Python, you have to install Microsoft 62 | Visual C++ compiler following instructions at 63 | https://wiki.python.org/moin/WindowsCompilers. For Python 3.5 and 3.6, you 64 | either install Microsoft Visual C++ 14.0 standalone, or you can install 65 | Visual Studio 2015 which contains Visual C++ 14.0 compiler. 66 | * Nevo (2000b) Example 67 | =examples/Nevo_2000b.py= replicates the results from Nevo 68 | (2000b). In the =examples= folder, you can run the script as: 69 | 70 | #+BEGIN_SRC sh 71 | python ./Nevo_2000b.py 72 | #+END_SRC 73 | 74 | It evaluates the objective function at the starting values and creates the 75 | following results table: 76 | 77 | #+BEGIN_SRC python 78 | Mean SD Income Income^2 Age Child 79 | Constant -1.833294 0.377200 3.088800 0.000000 1.185900 0.00000 80 | 0.257829 0.129433 1.212647 0.000000 1.012354 0.00000 81 | Price -32.446922 1.848000 16.598000 -0.659000 0.000000 11.62450 82 | 7.751913 1.078371 172.776110 8.979257 0.000000 5.20593 83 | Sugar 0.142915 -0.003500 -0.192500 0.000000 0.029600 0.00000 84 | 0.012877 0.012297 0.045528 0.000000 0.036563 0.00000 85 | Mushy 0.801608 0.081000 1.468400 0.000000 -1.514300 0.00000 86 | 0.203454 0.206025 0.697863 0.000000 1.098321 0.00000 87 | GMM objective: 14.900789417017275 88 | Min-Dist R-squared: 0.2718388379589566 89 | Min-Dist weighted R-squared: 0.0946528053333926 90 | #+END_SRC 91 | 92 | This code uses a tight tolerance for the contraction mapping, and it 93 | minimizes the GMM objective function to the correct minimum of 94 | =4.56=. (With BFGS, it only needs 45 iterations). 95 | 96 | After running the code, you can try the full estimation with: 97 | 98 | #+BEGIN_SRC python 99 | BLP.estimate(θ20=θ20) 100 | #+END_SRC 101 | 102 | For example, in an IPython console: 103 | 104 | #+BEGIN_SRC python 105 | %run Nevo_2000b.py 106 | BLP.estimate(θ20=θ20) 107 | #+END_SRC 108 | 109 | You should get the following results: 110 | 111 | #+BEGIN_SRC python 112 | Optimization terminated successfully. 113 | Current function value: 4.561515 114 | Iterations: 45 115 | Function evaluations: 50 116 | Gradient evaluations: 50 117 | 118 | Mean SD Income Income^2 Age Child 119 | Constant -2.009919 0.558094 2.291972 0.000000 1.284432 0.000000 120 | 0.326997 0.162533 1.208569 0.000000 0.631215 0.000000 121 | Price -62.729902 3.312489 588.325237 -30.192021 0.000000 11.054627 122 | 14.803215 1.340183 270.441021 14.101230 0.000000 4.122563 123 | Sugar 0.116257 -0.005784 -0.384954 0.000000 0.052234 0.000000 124 | 0.016036 0.013505 0.121458 0.000000 0.025985 0.000000 125 | Mushy 0.499373 0.093414 0.748372 0.000000 -1.353393 0.000000 126 | 0.198582 0.185433 0.802108 0.000000 0.667108 0.000000 127 | GMM objective: 4.5615146550344186 128 | Min-Dist R-squared: 0.4591043336106454 129 | Min-Dist weighted R-squared: 0.10116438381046189 130 | #+END_SRC 131 | 132 | You can check the gradient at the optimum: 133 | 134 | #+BEGIN_SRC python 135 | >>> BLP._gradient_GMM(BLP.results['θ2']['x']) 136 | contraction mapping finished in 0 iterations 137 | 138 | array([ 1.23888940e-07, 1.15056001e-08, 1.58824491e-08, 139 | -4.45649242e-08, -9.61452074e-08, -1.75233503e-08, 140 | -9.94539619e-07, 9.60900497e-08, -3.30553299e-07, 141 | 1.24174991e-07, 4.17569410e-07, 1.33642515e-07, 142 | 1.94273594e-09]) 143 | #+END_SRC 144 | 145 | I verified that the optimum is achieved with =Nelder-Mead= (simplex), 146 | =BFGS=, =TNC=, and =SLSQP= [[https://www.docs.scipy.org/doc/scipy/reference/optimize.html][=scipy.optimize=]] methods. =BFGS= and 147 | =SLSQP= were the fastest, and =BFGS= is the default. 148 | 149 | * Unit Testing 150 | I use =pytest= for unit testing. You can run them with: 151 | 152 | #+BEGIN_SRC python 153 | python -m pytest 154 | #+END_SRC 155 | 156 | * References 157 | Berry, S., Levinsohn, J., & Pakes, A. (1995). /Automobile Prices In Market 158 | Equilibrium/. Econometrica, 63(4), 841. 159 | 160 | Dubé, J., Fox, J. T., & Su, C. (2012). Improving the Numerical Performance of 161 | BLP Static and Dynamic Discrete Choice Random Coefficients Demand 162 | Estimation. Econometrica, 1–34. 163 | 164 | Nevo, A. (2000). /A Practitioner’s Guide to Estimation of Random-Coefficients 165 | Logit Models of Demand/. Journal of Economics & Management Strategy, 9(4), 166 | 513–548. 167 | * License 168 | BLP-Python is released under the GPLv3. 169 | * Changelog 170 | ** 0.5.0 ([2017-09-23 Sat]) 171 | - Change data structure to =xarray=. 172 | - Major improvements on various aspects of the code. 173 | ** 0.4.2 ([2017-06-30 Fri]) 174 | - Fix =setup.py= for the Cython module for non-windows operating systems (thanks to [[https://github.com/cniedotus][Cheng Nie]]) 175 | ** 0.4.0 ([2016-12-18 Sun]) 176 | - Use global state only for read-only variables; now gradient-based 177 | optimization (such as BFGS) works and it converges quickly 178 | - Use pandas.DataFrame to show results cleanly 179 | - Implement estimation of parameter means 180 | - Implement standard error calculation 181 | - Use greek letters whenever possible 182 | - Add Nevo (2000b) example 183 | - Add a unit test 184 | - Improve README 185 | ** 0.3.0 ([2014-11-28 Fri]) 186 | - Implement GMM objective function and estimation of \( \theta_{2} \) 187 | ** 0.1.0 ([2013-03-28 Thu]) 188 | - Initial release 189 | -------------------------------------------------------------------------------- /_BLP.cp35-win_amd64.pyd: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/joonro/BLP-Python/9e341656fb5adae51cceacd1926ae36999290657/_BLP.cp35-win_amd64.pyd -------------------------------------------------------------------------------- /_BLP.cp36-win_amd64.pyd: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/joonro/BLP-Python/9e341656fb5adae51cceacd1926ae36999290657/_BLP.cp36-win_amd64.pyd -------------------------------------------------------------------------------- /_BLP.pyx: -------------------------------------------------------------------------------- 1 | # BLP-Python provides an implementation of random coefficient logit model of 2 | # Berry, Levinsohn and Pakes (1995) 3 | # Copyright (C) 2011, 2013, 2016 Joon H. Ro 4 | # 5 | # This file is part of BLP-Python. 6 | # 7 | # BLP-Python is free software: you can redistribute it and/or modify 8 | # it under the terms of the GNU General Public License as published by 9 | # the Free Software Foundation, either version 3 of the License, or 10 | # (at your option) any later version. 11 | # 12 | # BLP-Python is distributed in the hope that it will be useful, 13 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 14 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 15 | # GNU General Public License for more details. 16 | # 17 | # You should have received a copy of the GNU General Public License 18 | # along with this program. If not, see . 19 | 20 | #cython: boundscheck=False 21 | #cython: wraparound=False 22 | #cython: cdivision=True 23 | 24 | import numpy as np 25 | 26 | # "cimport" is used to import special compile-time information 27 | # about the numpy module (this is stored in a file numpy.pxd which is 28 | # currently part of the Cython distribution). 29 | cimport numpy as np 30 | 31 | from cython.parallel import prange 32 | from libc.math cimport abs, exp, fabs, log 33 | 34 | cimport cython 35 | 36 | def cal_delta(double[:] delta, 37 | double[:, :] theta2, 38 | double[:] ln_s_jt, 39 | double[:, :, :] v, 40 | double[:, :, :] D, 41 | double[:, :, :] X2, 42 | double etol, int iter_limit): 43 | """ 44 | calculate delta (mean utility) through contraction mapping 45 | """ 46 | cdef: 47 | int nmkts = v.shape[0] 48 | int nsiminds = v.shape[1] 49 | int nbrands = X2.shape[1] 50 | 51 | cdef: 52 | np.ndarray[np.float64_t, ndim=1] diff = np.empty(delta.shape[0]) 53 | np.ndarray[np.float64_t, ndim=1] mktshr = np.empty(delta.shape[0]) 54 | np.ndarray[np.float64_t, ndim=3] mu = np.zeros((nmkts, nsiminds, nbrands)) 55 | 56 | _cal_mu(theta2, v, D, X2, mu) 57 | 58 | cdef: 59 | np.ndarray[np.float64_t, ndim=3] exp_mu = np.exp(mu) 60 | np.ndarray[np.float64_t, ndim=3] exp_xb = np.empty_like(exp_mu) 61 | 62 | int i, j, ix, mkt, ind, brand 63 | int niter = 0 64 | 65 | double denom 66 | double diff_max, diff_mean 67 | 68 | # contraction mapping 69 | while True: 70 | diff_mean = 0 71 | diff_max = 0 72 | 73 | # calculate market share 74 | for mkt in range(nmkts): # each market 75 | for ind in range(nsiminds): # each simulated individual 76 | denom = 1 77 | 78 | # calculate denominator 79 | for brand in range(nbrands): 80 | exp_xb[mkt, brand, ind] = exp(delta[ix]) * exp_mu[mkt, brand, ind] 81 | denom += exp_xb[mkt, brand, ind] 82 | 83 | ix = nbrands * mkt 84 | for brand in range(nbrands): 85 | if ind == 0: # initialize mktshr 86 | mktshr[ix] = 0 87 | 88 | mktshr[ix] += exp_xb[mkt, brand, ind] / (denom * nsiminds) 89 | 90 | if ind + 1 == nsiminds: 91 | # the last individual - mktshr calculation is done 92 | # calculate the difference here to save some loop 93 | diff[ix] = ln_s_jt[ix] - log(mktshr[ix]) 94 | 95 | delta[ix] += diff[ix] 96 | 97 | if abs(diff[ix]) > diff_max: 98 | diff_max = abs(diff[ix]) 99 | 100 | diff_mean += diff[ix] 101 | 102 | ix += 1 103 | 104 | diff_mean /= delta.shape[0] 105 | 106 | if (diff_max < etol) and (diff_mean < 1e-3) or niter > iter_limit: 107 | break 108 | 109 | niter += 1 110 | 111 | print('contraction mapping finished in {} iterations'.format(niter)) 112 | 113 | def cal_mu(double[:, :] theta2, 114 | double[:, :, :] v, 115 | double[:, :, :] D, 116 | double[:, :, :] X2, 117 | ): 118 | ''' 119 | calculate mu: the individual specific utility 120 | 121 | Delta is the effect of demographics on the preference parameter 122 | D is the demographics 123 | 124 | v is the vector of draws from the \( N(0, I_{k+1}) \) 125 | Simga is the scaling parameter 126 | 127 | mu = Delta @ D + Sigma @ v 128 | 129 | here v is nmkts-by-nsiminds-by-nvars 130 | ''' 131 | cdef: 132 | int nmkts = v.shape[0] 133 | int nsiminds = v.shape[1] 134 | int nbrands = X2.shape[1] 135 | 136 | np.ndarray[np.float64_t, ndim=3] mu = np.zeros((nmkts, nsiminds, nbrands)) 137 | 138 | _cal_mu(theta2, v, D, X2, mu) 139 | 140 | return mu 141 | 142 | cdef double _cal_mu(double[:, :] theta2, 143 | double[:, :, :] v, 144 | double[:, :, :] D, 145 | double[:, :, :] X2, 146 | double[:, :, :] mu, 147 | ) nogil except -1: 148 | 149 | cdef: 150 | int mkt, ind, k, d, j # indices 151 | double beta_i # individual params 152 | 153 | int nmkts = v.shape[0] 154 | int nsiminds = v.shape[1] 155 | int nbrands = X2.shape[1] 156 | int nvars = X2.shape[2] 157 | 158 | for mkt in prange(nmkts, nogil=True, schedule='guided'): # each market 159 | for ind in range(nsiminds): # each simulated individual 160 | for k in range(nvars): # each betas 161 | beta_i = theta2[k, 0] * v[mkt, ind, k] 162 | 163 | for d in range(theta2.shape[1] - 1): 164 | beta_i += theta2[k, d + 1] * D[mkt, ind, d] 165 | 166 | for j in range(nbrands): 167 | mu[mkt, ind, j] += X2[mkt, j, k] * beta_i 168 | 169 | def cal_s(double[:, :] delta, double[:, :, :] mu, double[:, :] s): 170 | ''' Calculate market share by numerical integration 171 | 172 | Parameters 173 | ---------- 174 | delta : ndarray 175 | δ, mean utility (nmkts by nbrands) 176 | 177 | mu : ndarray 178 | μ, individual utility (nmkts by nsiminds by nbrands) 179 | 180 | s : ndarray 181 | market share (nmkts by nbrands) 182 | 183 | ''' 184 | cdef: 185 | int nmkts = mu.shape[0] 186 | int nsiminds = mu.shape[1] 187 | int nbrands = mu.shape[2] 188 | 189 | int mkt, ind, brand 190 | double denom, exp_Xb 191 | 192 | for mkt in prange(nmkts, nogil=True, schedule='guided'): # each market 193 | for brand in prange(nbrands): 194 | s[mkt, brand] = 0 195 | 196 | for ind in range(nsiminds): # each simulated individual 197 | denom = 1 # outside good 198 | 199 | for brand in range(nbrands): 200 | exp_Xb = exp(delta[mkt, brand] + mu[mkt, ind, brand]) 201 | denom += exp_Xb 202 | 203 | for brand in range(nbrands): 204 | s[mkt, brand] += exp(delta[mkt, brand] + mu[mkt, ind, brand]) / (denom * nsiminds) 205 | 206 | def cal_ind_choice_prob( 207 | double[:, :] delta, 208 | double[:, :, :] mu, 209 | double[:, :, :] ind_choice_prob, 210 | ): 211 | ''' 212 | calculate individual choice probability 213 | 214 | Parameters 215 | ---------- 216 | delta : ndarray 217 | δ, mean utility (nmkts by nbrands) 218 | 219 | mu : ndarray 220 | μ, individual utility (nmkts by nsiminds by nbrands) 221 | 222 | ind_choice_prob : ndarray 223 | Output array of market share (nmkts by nsiminds by nbrands) 224 | ''' 225 | _cal_ind_choice_prob(delta, mu, ind_choice_prob) 226 | 227 | cdef double _cal_ind_choice_prob( 228 | double[:, :] delta, # mean utility (nmkts by nbrands) 229 | double[:, :, :] mu, # individual utility (nmkts by nsiminds by nbrands) 230 | double[:, :, :] ind_choice_prob, 231 | ) nogil except -1: 232 | 233 | cdef: 234 | int nmkts = mu.shape[0] 235 | int nsiminds = mu.shape[1] 236 | int nbrands = mu.shape[2] 237 | 238 | int mkt, ind, brand 239 | 240 | double denom, exp_Xb 241 | 242 | for mkt in prange(nmkts, nogil=True, schedule='guided'): # each market 243 | for ind in range(nsiminds): # each simulated individual 244 | denom = 1 245 | 246 | for brand in range(nbrands): 247 | exp_Xb = exp(delta[mkt, brand] + mu[mkt, ind, brand]) 248 | ind_choice_prob[mkt, ind, brand] = exp_Xb 249 | denom += exp_Xb 250 | 251 | for brand in range(nbrands): 252 | ind_choice_prob[mkt, ind, brand] /= denom 253 | -------------------------------------------------------------------------------- /examples/Nevo_2000b.py: -------------------------------------------------------------------------------- 1 | # BLP-Python provides an implementation of random coefficient logit model of 2 | # Berry, Levinsohn and Pakes (1995) 3 | # Copyright (C) 2011, 2013, 2016 Joon H. Ro 4 | # 5 | # This file is part of BLP-Python. 6 | # 7 | # BLP-Python is free software: you can redistribute it and/or modify 8 | # it under the terms of the GNU General Public License as published by 9 | # the Free Software Foundation, either version 3 of the License, or 10 | # (at your option) any later version. 11 | # 12 | # BLP-Python is distributed in the hope that it will be useful, 13 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 14 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 15 | # GNU General Public License for more details. 16 | # 17 | # You should have received a copy of the GNU General Public License 18 | # along with this program. If not, see . 19 | 20 | import os 21 | import sys 22 | 23 | import pytest 24 | 25 | import numpy as np 26 | import scipy.io 27 | import xarray as xr 28 | 29 | sys.path.append('../') 30 | import pyBLP 31 | 32 | 33 | class Data(object): 34 | ''' Synthetic data for Nevo (2000b) 35 | 36 | The file iv.mat contains the variable iv which consists of an id column 37 | (see the id variable above) and 20 columns of IV's for the price 38 | variable. The variable is sorted in the same order as the variables in 39 | ps2.mat. 40 | 41 | ''' 42 | def __init__(self): 43 | try: 44 | ps2 = scipy.io.loadmat('examples/ps2.mat') 45 | Z_org = scipy.io.loadmat('examples/iv.mat')['iv'] 46 | except: 47 | ps2 = scipy.io.loadmat('ps2.mat') 48 | Z_org = scipy.io.loadmat('iv.mat')['iv'] 49 | 50 | nsiminds = self.nsiminds = 20 # number of simulated "indviduals" per market 51 | nmkts = self.nmkts = 94 # number of markets = (# of cities) * (# of quarters) 52 | nbrands = self.nbrands = 24 # number of brands per market 53 | 54 | ids = ps2['id'].reshape(-1, ) 55 | self.ids = xr.DataArray( 56 | ids.reshape((nmkts, nbrands), order='F'), 57 | coords=[range(nmkts), range(nbrands)], 58 | dims=['markets', 'brands'], 59 | attrs={'Desc': 'an id variable in the format bbbbccyyq, where bbbb ' 60 | 'is a unique 4 digit identifier for each brand (the ' 61 | 'first digit is company and last 3 are brand, i.e., ' 62 | '1006 is K Raisin Bran and 3006 is Post Raisin Bran), ' 63 | 'cc is a city code, yy is year (=88 for all observations ' 64 | 'in this data set) and q is quarter.'} 65 | ) 66 | 67 | X1 = np.array(ps2['x1'].todense()) 68 | 69 | self.X1 = xr.DataArray( 70 | X1.reshape(nmkts, nbrands, -1), 71 | coords=[range(nmkts), range(nbrands), 72 | ['Price'] + ['Brand_{}'.format(brand) 73 | for brand in range(nbrands)]], 74 | dims=['markets', 'brands', 'vars'], 75 | attrs={'Desc': 'the variables that enter the linear part of the ' 76 | 'estimation. Here this consists of a price variable ' 77 | '(first column) and 24 brand dummy variables.'} 78 | ) 79 | 80 | X2 = np.array(ps2['x2'].copy()) 81 | self.X2 = xr.DataArray( 82 | X2.reshape(nmkts, nbrands, -1), 83 | coords=[range(nmkts), range(nbrands), 84 | ['Constant', 'Price', 'Sugar', 'Mushy']], 85 | dims=['markets', 'brands', 'vars'], 86 | attrs={'Desc': 'the variables that enter the non-linear part of the ' 87 | 'estimation.'} 88 | ) 89 | 90 | self.id_demo = ps2['id_demo'].reshape(-1, ) 91 | 92 | D = np.array(ps2['demogr']) 93 | self.D = xr.DataArray( 94 | D.reshape((nmkts, nsiminds, -1), order='F'), 95 | coords=[range(nmkts), range(nsiminds), 96 | ['Income', 'Income^2', 'Age', 'Child']], 97 | dims=['markets', 'nsiminds', 'vars'], 98 | attrs={'Desc': 'Demeaned draws of demographic variables from the CPS for 20 ' 99 | 'individuals in each market.', 100 | 'Child': 'Child dummy variable (=1 if age <= 16)'} 101 | ) 102 | 103 | v = np.array(ps2['v']) 104 | self.v = xr.DataArray( 105 | v.reshape((nmkts, nsiminds, -1), order='F'), 106 | coords=[range(nmkts), range(nsiminds), 107 | ['Constant', 'Price', 'Sugar', 'Mushy']], 108 | dims=['markets', 'nsiminds', 'vars'], 109 | attrs={'Desc': 'random draws given for the estimation.'} 110 | ) 111 | 112 | s_jt = ps2['s_jt'].reshape(-1, ) # s_jt for nmkts * nbransd 113 | self.s_jt = xr.DataArray( 114 | s_jt.reshape((nmkts, nbrands)), 115 | coords=[range(nmkts), range(nbrands),], 116 | dims=['markets', 'brands'], 117 | attrs={'Desc': 'Market share of each brand.'} 118 | ) 119 | 120 | self.ans = ps2['ans'].reshape(-1, ) 121 | 122 | Z = np.c_[Z_org[:, 1:], X1[:, 1:]] 123 | self.Z = xr.DataArray( 124 | Z.reshape((self.nmkts, self.nbrands, -1)), 125 | coords=[range(nmkts), range(nbrands), range(Z.shape[-1])], 126 | dims=['markets', 'brands', 'vars'], 127 | attrs={'Desc': 'Instruments'} 128 | ) 129 | 130 | 131 | if __name__ == '__main__': 132 | """ Load data and evaluate the 133 | """ 134 | data = Data() 135 | 136 | BLP = pyBLP.BLP(data) 137 | 138 | θ20 = np.array([[ 0.3772, 3.0888, 0, 1.1859, 0], 139 | [ 1.8480, 16.5980, -.6590, 0, 11.6245], 140 | [-0.0035, -0.1925, 0, 0.0296, 0], 141 | [ 0.0810, 1.4684, 0, -1.5143, 0]]) 142 | 143 | BLP.estimate(θ20=θ20, method='Nelder-Mead', maxiter=1) 144 | 145 | results = BLP.results 146 | 147 | # Run the line below to get true estimation results 148 | # BLP.estimate(θ20=θ20) 149 | -------------------------------------------------------------------------------- /examples/iv.mat: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/joonro/BLP-Python/9e341656fb5adae51cceacd1926ae36999290657/examples/iv.mat -------------------------------------------------------------------------------- /examples/ps2.mat: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/joonro/BLP-Python/9e341656fb5adae51cceacd1926ae36999290657/examples/ps2.mat -------------------------------------------------------------------------------- /paper/paper.bib: -------------------------------------------------------------------------------- 1 | Automatically generated by Mendeley Desktop 1.17.11 2 | Any changes to this file will be lost if it is regenerated by Mendeley. 3 | 4 | BibTeX export options can be customized via Options -> BibTeX in Mendeley Desktop 5 | 6 | @online{BLP_Python_GitHub, 7 | author = {Joon H. Ro}, 8 | title = {BLP-Python: Random Coefficient Logit Model in Python}, 9 | year = {2017}, 10 | url = {https://github.com/joonro/BLP-Python}, 11 | urldate = {2017-09-22} 12 | } 13 | 14 | @article{Petrin_2002_J_Polit_Economy, 15 | author = {Petrin, Amil}, 16 | doi = {10.1086/340779}, 17 | file = {:home/joon/Documents/Mendeley Library/Journal of Political Economy/2002/Petrin - 2002 - Journal of Political Economy.pdf:pdf}, 18 | issn = {00223808}, 19 | journal = {Journal of Political Economy}, 20 | month = {aug}, 21 | number = {4}, 22 | pages = {705--729}, 23 | title = {{Quantifying The Benefits Of New Products: The Case Of The Minivan}}, 24 | url = {http://www.journals.uchicago.edu/cgi-bin/resolve?id=doi:10.1086/340779}, 25 | volume = {110}, 26 | year = {2002} 27 | } 28 | @article{Nevo_2000_J_Econ_Manage_Strategy, 29 | author = {Nevo, Aviv}, 30 | doi = {10.1162/105864000567954}, 31 | file = {:home/joon/Documents/Mendeley Library/Journal of Economics {\&} Management Strategy/2000/Nevo - 2000 - Journal of Economics {\&} Management Strategy.pdf:pdf;:C$\backslash$:/home/joon/Documents/Mendeley Library/Journal of Economics {\&} Management Strategy/2000/Nevo - 2000 - Journal of Economics {\&} Management Strategy.pdf:pdf}, 32 | issn = {15309134}, 33 | journal = {Journal of Economics {\&} Management Strategy}, 34 | month = {dec}, 35 | number = {4}, 36 | pages = {513--548}, 37 | title = {{A Practitioner'S Guide To Estimation Of Random-Coefficients Logit Models Of Demand}}, 38 | url = {http://www.catchword.com/cgi-bin/cgi?body=linker{\&}ini=xref{\&}reqdoi=10.1162/105864000567954}, 39 | volume = {9}, 40 | year = {2000} 41 | } 42 | @article{Sudhir_2001_Market_Sci, 43 | annote = {The reason why the cost side error, w is orthogonal with Z is in BLP was that in the cost equation the error is conditional on own model characteristics. ($\backslash$gamma W) 44 | 45 | But in this paper, the supply side errors have the price elasticity of competitor and also market share in it. And the supply side error is not conditioned with competitor characteristics. Then how can the error not correlated to competitor characteristics?}, 46 | author = {Sudhir, K.}, 47 | file = {:home/joon/Documents/Mendeley Library/Marketing Science/2001/Sudhir - 2001 - Marketing Science.pdf:pdf}, 48 | issn = {0732-2399}, 49 | journal = {Marketing Science}, 50 | keywords = {industrial-organization}, 51 | mendeley-tags = {industrial-organization}, 52 | number = {1}, 53 | pages = {42--60}, 54 | publisher = {JSTOR}, 55 | title = {{Competitive Pricing Behavior In The Auto Market: A Structural Analysis}}, 56 | url = {http://www.jstor.org/stable/193221}, 57 | volume = {20}, 58 | year = {2001} 59 | } 60 | @article{Nevo_2001_Econometrica, 61 | annote = {So basically this paper estimated the demand with BLP and Hausman type instruments, and then assuming different competition structure, estimated PCM (Price-Cost margin). 62 | 63 | Then compared the estimated PCM to the (crude) marginal cost information that he has gotten from somewhere else. 64 | 65 | This paper is somewhat similar to what I was thinking about, but it is also different. For the merger analysis, the important thing is the estimate for cost. 66 | 67 | One thing is that is it okay to assume that the retail margin as an additional cost to producers.}, 68 | author = {Nevo, Aviv}, 69 | file = {:home/joon/Documents/Mendeley Library/Econometrica/2001/Nevo - 2001 - Econometrica.pdf:pdf}, 70 | journal = {Econometrica}, 71 | keywords = {Reference,industrial-organization}, 72 | mendeley-tags = {Reference,industrial-organization}, 73 | number = {2}, 74 | pages = {307--342}, 75 | publisher = {Econometric Society}, 76 | title = {{Measuring Market Power In The Ready-To-Eat Cereal Industry}}, 77 | url = {http://www.jstor.org/stable/2692234}, 78 | volume = {69}, 79 | year = {2001} 80 | } 81 | @article{Dube_Fox_Su_2012_Econometrica, 82 | author = {Dub{\'{e}}, Jean-pierre and Fox, Jeremy T and Su, Che-lin}, 83 | file = {:home/joon/Documents/Mendeley Library/Econometrica/2012/Dub{\'{e}}, Fox, Su - 2012 - Econometrica.pdf:pdf}, 84 | journal = {Econometrica}, 85 | keywords = {MPEC,constrained optimization,dynamics,numerical methods,random coefficients logit demand}, 86 | mendeley-tags = {MPEC}, 87 | pages = {1--34}, 88 | title = {{Improving The Numerical Performance Of Blp Static And Dynamic Discrete Choice Random Coefficients Demand Estimation}}, 89 | year = {2012} 90 | } 91 | @article{Berry_Levinsohn_Pakes_1995_Econometrica, 92 | author = {Berry, Steven and Levinsohn, James and Pakes, Ariel}, 93 | doi = {10.2307/2171802}, 94 | file = {:home/joon/Documents/Mendeley Library/Econometrica/1995/Berry, Levinsohn, Pakes - 1995 - Econometrica.pdf:pdf}, 95 | issn = {00129682}, 96 | journal = {Econometrica}, 97 | keywords = {Automotive Industry,BLP,Discrete Choice,EMA,Econometrica,aggregation,automobile,demand and supply,differentiated,differentiated products,discrete choice,simultaneity}, 98 | mendeley-tags = {Automotive Industry,BLP,Discrete Choice}, 99 | number = {4}, 100 | pages = {841}, 101 | publisher = {Econometric Society}, 102 | title = {{Automobile Prices In Market Equilibrium}}, 103 | url = {http://www.jstor.org/stable/2171802?origin=crossref}, 104 | volume = {63}, 105 | year = {1995} 106 | } 107 | -------------------------------------------------------------------------------- /paper/paper.md: -------------------------------------------------------------------------------- 1 | --- 2 | title: 'BLP-Python: Random Coefficient Logit Model in Python' 3 | tags: 4 | - blp 5 | - python 6 | - economics 7 | - marketing 8 | - industrial organization 9 | - econometrics 10 | - structural model 11 | authors: 12 | - name: Joon H. Ro 13 | orcid: 0000-0002-5895-163X 14 | affiliation: 1 15 | affiliations: 16 | - name: Tulane University 17 | index: 1 18 | date: 22 September 2017 19 | bibliography: paper.bib 20 | nocite: | 21 | @BLP_Python_GitHub 22 | --- 23 | 24 | # Summary 25 | 26 | BLP-Python provides a Python implementation of random coefficient logit model 27 | of [@Berry_Levinsohn_Pakes_1995_Econometrica] (henceforth BLP), which is 28 | widely used in Economics (e.g., [@Nevo_2001_Econometrica]; 29 | [@Petrin_2002_J_Polit_Economy]) and Marketing (e.g., 30 | [@Sudhir_2001_Market_Sci]) for demand estimation from aggregate data. The 31 | specific implementation follows the model described in 32 | [@Nevo_2000_J_Econ_Manage_Strategy]. 33 | 34 | A user should provide data for estimation and random draws for simulating 35 | integrals as multidimensional `xarray.DataArray` objects. For better 36 | performance, calculations of mean utilities and individual choice 37 | probabilities are implemented with Cython with parallel loop via openMP. 38 | 39 | This package should be useful for researchers who want to estimate BLP-related 40 | model. Depending on the user's model specification (such as different utility 41 | specification, adding the supply side, and/or using micro-moments), 42 | modification of the code will be required. Hence, the code is written with 43 | readability in mind. For example, greek letters are used for variable names 44 | whenever possible to help understand the code. 45 | 46 | # References 47 | 48 | -------------------------------------------------------------------------------- /pyBLP.py: -------------------------------------------------------------------------------- 1 | # BLP-Python provides an implementation of random coefficient logit model of 2 | # Berry, Levinsohn and Pakes (1995) 3 | # Copyright (C) 2011, 2013, 2016 Joon H. Ro 4 | # 5 | # This file is part of BLP-Python. 6 | # 7 | # BLP-Python is free software: you can redistribute it and/or modify 8 | # it under the terms of the GNU General Public License as published by 9 | # the Free Software Foundation, either version 3 of the License, or 10 | # (at your option) any later version. 11 | # 12 | # BLP-Python is distributed in the hope that it will be useful, 13 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 14 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 15 | # GNU General Public License for more details. 16 | # 17 | # You should have received a copy of the GNU General Public License 18 | # along with this program. If not, see . 19 | 20 | import time 21 | 22 | import numpy as np 23 | from numpy.linalg import cholesky, inv, solve 24 | from scipy.linalg import cho_solve 25 | 26 | import scipy.optimize as optimize 27 | 28 | import pandas as pd 29 | 30 | import _BLP 31 | 32 | 33 | class BLP: 34 | """BLP Class 35 | 36 | Random coefficient logit model 37 | 38 | Parameters 39 | ---------- 40 | data : object 41 | Object containing data for estimation. It should contain: 42 | 43 | v : xarray.DataArray 44 | Random draws given for the estimation with (nmkts by nsiminds by nvars) dimension 45 | 46 | D : xarray.DataArray 47 | Demeaned draws of demographic variables with (nmkts by nsiminds by nvars) dimension 48 | 49 | X1 : xarray.DataArray 50 | The variables that enter the linear part of the estimation with 51 | (nmkts by nbrands by nvars) dimension 52 | 53 | X2 : xarray.DataArray 54 | The variables that enter the nonlinear part of the estimation with 55 | (nmkts by nbrands by nvars) dimension 56 | 57 | Z : xarray.DataArray 58 | Instruments with (nmkts by nbrands by nvars) dimension 59 | 60 | Attributes 61 | ---------- 62 | results : dictionary 63 | Results of GMM estimation 64 | 65 | Methods 66 | ------- 67 | GMM(θ2_cand) 68 | GMM objective function. 69 | 70 | minimize_GMM(results, θ20, method='BFGS', maxiter=2000000, disp=True) 71 | Minimize GMM objective function. 72 | 73 | estimate(θ20, method='BFGS', maxiter=2000000, disp=True) 74 | Run full estimation. 75 | """ 76 | 77 | def __init__(self, data): 78 | self.ids = data.ids 79 | self.s_jt = s_jt = data.s_jt 80 | self.ln_s_jt = np.log(self.s_jt.values) 81 | v = self.v = data.v 82 | self.D = data.D 83 | 84 | X1_nd = self.X1_nd = data.X1 85 | # vectorized version 86 | self.X1 = X1 = X1_nd.values.reshape(-1, X1_nd.shape[-1]) 87 | 88 | self.X2 = data.X2 89 | 90 | Z_nd = self.Z_nd = data.Z 91 | # vectorized version 92 | self.Z = Z = Z_nd.values.reshape(-1, Z_nd.shape[-1]) 93 | 94 | nmkts = self.nmkts = len(X1_nd.coords['markets']) 95 | nbrands = self.nbrands = len(X1_nd.coords['brands']) 96 | nsiminds = self.nsiminds = len(v.coords['nsiminds']) 97 | 98 | self.nX2 = len(self.X2.coords['vars']) 99 | self.nD = len(self.D.coords['vars']) 100 | 101 | # LinvW: choleskey root (lower triangular) of the inverse of the 102 | # weighting matrix, W. (W = (Z'Z)^{-1}). 103 | LinvW = self.LinvW = (cholesky(Z.T @ Z), True) 104 | 105 | # Z'X1 106 | Z_X1 = self.Z_X1 = Z.T @ X1 107 | 108 | # calculate market share 109 | # outside good 110 | s_0t = self.s_0t = (1 - self.s_jt.sum(dim='brands')) 111 | 112 | y = self.y = np.log(s_jt) 113 | y -= np.log(s_0t) 114 | y = y.values.reshape(-1, ) 115 | 116 | # initialize δ 117 | self.δ = X1 @ (solve(Z_X1.T @ cho_solve(LinvW, Z_X1), 118 | Z_X1.T @ cho_solve(LinvW, Z.T @ y))) 119 | 120 | self.δ.shape = (nmkts, nbrands) 121 | 122 | # initialize s 123 | self.s = np.zeros_like(self.δ) 124 | self.ind_choice_prob = np.zeros((nmkts, nsiminds, nbrands)) 125 | 126 | self.θ2 = None 127 | self.ix_θ2_T = None # Transposed to be consistent with MATLAB 128 | 129 | def _cal_mu(self, θ2): 130 | """Calculate individual-specific utility 131 | 132 | Same speed as the single-thread Cython function (_BLP.cal_mu()), 133 | but slower than parallelized Cython module 134 | 135 | Mainly used for unit testing 136 | """ 137 | v, D, X2 = self.v, self.D, self.X2 138 | 139 | Π = θ2[:, 1:] 140 | Σ = np.diag(θ2[:, 0]) # off-diagonals of Σ are zero 141 | 142 | # these are nmkts by nsiminds by nvars arrays 143 | ΠD = (Π @ D.values.transpose([0, 2, 1])).transpose([0, 2, 1]) 144 | Σv = (Σ @ v.values.transpose([0, 2, 1])).transpose([0, 2, 1]) 145 | 146 | # nmkts by nsiminds by nbrands 147 | μ = (X2.values @ (ΠD + Σv).transpose(0, 2, 1)).transpose([0, 2, 1]) 148 | 149 | return μ 150 | 151 | def _cal_δ(self, θ2): 152 | """Calculate δ (mean utility) via contraction mapping""" 153 | v, D, X2 = self.v, self.D, self.X2 154 | nmkts, nsiminds, nbrands = self.nmkts, self.nsiminds, self.nbrands 155 | 156 | δ, ln_s_jt = self.δ, self.ln_s_jt # initial values 157 | 158 | niter = 0 159 | 160 | ε = 1e-13 # tight tolerance 161 | 162 | μ = self.μ = _BLP.cal_mu(θ2, v.values, D.values, X2.values) 163 | 164 | while True: 165 | s = self._cal_s(δ, μ) 166 | #_BLP.cal_s(δ, μ, s) # s gets updated 167 | 168 | diff = ln_s_jt - np.log(s) 169 | 170 | if np.isnan(diff).sum(): 171 | raise Exception('nan in diffs') 172 | 173 | δ += diff 174 | 175 | if (abs(diff).max() < ε) and (abs(diff).mean() < 1e-3): 176 | break 177 | 178 | niter += 1 179 | 180 | print('contraction mapping finished in {} iterations'.format(niter)) 181 | 182 | return δ 183 | 184 | def _cal_s(self, δ, μ): 185 | """Calculate market share 186 | 187 | Calculates individual choice probability first, then take the weighted 188 | sum 189 | 190 | """ 191 | nsiminds = self.nsiminds 192 | ind_choice_prob = self.ind_choice_prob 193 | 194 | _BLP.cal_ind_choice_prob(δ, μ, ind_choice_prob) 195 | s = ind_choice_prob.sum(axis=1) / nsiminds 196 | 197 | return s 198 | 199 | def _cal_θ1_and_ξ(self, δ): 200 | """Calculate θ1 and ξ with F.O.C""" 201 | X1, Z, Z_X1, LinvW = self.X1, self.Z, self.Z_X1, self.LinvW 202 | 203 | # Z'δ 204 | Z_δ = Z.T @ δ.flatten() 205 | 206 | #\[ \theta_1 = (\tilde{X}'ZW^{-1}Z'\tilde{X})^{-1}\tilde{X}'ZW^{-1}Z'\delta \] 207 | # θ1 from FOC 208 | θ1 = self.θ1 = solve(Z_X1.T @ cho_solve(LinvW, Z_X1), 209 | Z_X1.T @ cho_solve(LinvW, Z_δ)) 210 | 211 | ξ = self.ξ = δ.flatten() - X1 @ θ1 212 | 213 | return θ1, ξ 214 | 215 | def GMM(self, θ2_cand): 216 | """GMM objective function""" 217 | if self.θ2 is None: 218 | if θ2_cand.ndim == 1: # vectorized version 219 | raise Exception( 220 | "Cannot pass θ2_vec before θ2 is initialized!") 221 | else: 222 | self.θ2 = θ2_cand.copy() 223 | 224 | if self.ix_θ2_T is None: 225 | self.ix_θ2_T = np.nonzero(self.θ2.T) 226 | 227 | if θ2_cand.ndim == 1: # vectorized version 228 | self.θ2.T[self.ix_θ2_T] = θ2_cand 229 | else: 230 | self.θ2[:] = θ2_cand 231 | 232 | θ2, Z, X1, Z_X1, LinvW = self.θ2, self.Z, self.X1, self.Z_X1, self.LinvW 233 | 234 | # update δ 235 | δ = self._cal_δ(θ2) 236 | 237 | if np.isnan(δ).sum(): 238 | return 1e+10 239 | 240 | θ1, ξ = self._cal_θ1_and_ξ(δ) 241 | 242 | # Z'ξ = (\delta - \tilde{X}\theta_1) 243 | Z_ξ = Z.T @ ξ 244 | 245 | # \[ (\delta - \tilde{X}\theta_1)'ZW^{-1}Z'(\delta-\tilde{X}\theta_1) \] 246 | GMM = Z_ξ.T @ cho_solve(LinvW, Z_ξ) 247 | 248 | print('GMM value: {}'.format(GMM)) 249 | return GMM 250 | 251 | def _gradient_GMM(self, θ2_cand): 252 | """Return gradient of GMM objective function 253 | 254 | Parameters 255 | ---------- 256 | θ2_cand : array 257 | Description of parameter `θ2`. 258 | 259 | Returns 260 | ------- 261 | gradient : array 262 | String representation of the array. 263 | 264 | """ 265 | θ2, ix_θ2_T, Z, LinvW = self.θ2, self.ix_θ2_T, self.Z, self.LinvW 266 | 267 | if θ2_cand.ndim == 1: # vectorized version 268 | θ2.T[ix_θ2_T] = θ2_cand 269 | else: 270 | θ2[:] = θ2_cand 271 | 272 | # update δ 273 | δ = self._cal_δ(θ2) 274 | 275 | θ1, ξ = self._cal_θ1_and_ξ(δ) 276 | 277 | jacob = self._cal_jacobian(θ2, δ) 278 | 279 | return 2 * jacob.T @ Z @ cho_solve(LinvW, Z.T) @ ξ 280 | 281 | def _cal_varcov(self, θ2_vec): 282 | """calculate variance covariance matrix""" 283 | θ2, ix_θ2_T, Z, LinvW, X1 = self.θ2, self.ix_θ2_T, self.Z, self.LinvW, self.X1 284 | 285 | θ2.T[ix_θ2_T] = θ2_vec 286 | 287 | # update δ 288 | δ = self._cal_δ(θ2) 289 | 290 | jacob = self._cal_jacobian(θ2, δ) 291 | 292 | θ1, ξ = self._cal_θ1_and_ξ(δ) 293 | 294 | Zres = Z * ξ.reshape(-1, 1) 295 | Ω = Zres.T @ Zres # covariance of the momconds 296 | 297 | G = (np.c_[X1, jacob].T @ Z).T # gradient of the momconds 298 | 299 | WG = cho_solve(LinvW, G) 300 | WΩ = cho_solve(LinvW, Ω) 301 | 302 | tmp = solve(G.T @ WG, G.T @ WΩ @ WG).T # G'WΩWG(G'WG)^(-1) part 303 | 304 | varcov = solve((G.T @ WG), tmp) 305 | 306 | return varcov 307 | 308 | def _cal_se(self, varcov): 309 | se_all = np.sqrt(varcov.diagonal()) 310 | 311 | se = np.zeros_like(self.θ2) 312 | se.T[self.ix_θ2_T] = se_all[-self.ix_θ2_T[0].shape[0]:] # to be consistent with MATLAB 313 | 314 | return se 315 | 316 | def _cal_jacobian(self, θ2, δ): 317 | """calculate the Jacobian with the current value of δ""" 318 | v, D, X2 = self.v, self.D, self.X2 319 | nmkts, nsiminds, nbrands = self.nmkts, self.nsiminds, self.nbrands 320 | 321 | ind_choice_prob = self.ind_choice_prob 322 | 323 | μ = _BLP.cal_mu(θ2, v.values, D.values, X2.values) 324 | 325 | _BLP.cal_ind_choice_prob(δ, μ, ind_choice_prob) 326 | ind_choice_prob_vec = ind_choice_prob.transpose(0, 2, 1).reshape(-1, nsiminds) 327 | 328 | nk = len(X2.coords['vars']) 329 | nD = len(D.coords['vars']) 330 | f1 = np.zeros((δ.flatten().shape[0], nk * (nD + 1))) 331 | 332 | # cdid relates each observation to the market it is in 333 | cdid = np.arange(nmkts).repeat(nbrands) 334 | 335 | cdindex = np.arange(nbrands, nbrands * (nmkts + 1), nbrands) - 1 336 | 337 | # compute ∂share/∂σ 338 | for k in range(nk): 339 | X2v = X2[..., k].values.reshape(-1, 1) @ np.ones((1, nsiminds)) 340 | X2v *= v[cdid, :, k].values 341 | 342 | temp = (X2v * ind_choice_prob_vec).cumsum(axis=0) 343 | sum1 = temp[cdindex, :] 344 | 345 | sum1[1:, :] = sum1[1:, :] - sum1[:-1, :] 346 | 347 | f1[:, k] = (ind_choice_prob_vec * (X2v - sum1[cdid, :])).mean(axis=1) 348 | 349 | # compute ∂share/∂pi 350 | for d in range(nD): 351 | tmpD = D[cdid, :, d].values 352 | 353 | temp1 = np.zeros((cdid.shape[0], nk)) 354 | 355 | for k in range(nk): 356 | X2d = X2[..., k].values.reshape(-1, 1) @ np.ones((1, nsiminds)) * tmpD 357 | 358 | temp = (X2d * ind_choice_prob_vec).cumsum(axis=0) 359 | sum1 = temp[cdindex, :] 360 | 361 | sum1[1:, :] = sum1[1:, :] - sum1[:-1, :] 362 | 363 | temp1[:, k] = (ind_choice_prob_vec * (X2d - sum1[cdid, :])).mean(axis=1) 364 | 365 | f1[:, nk * (d + 1):nk * (d + 2)] = temp1 366 | 367 | # compute ∂δ/∂θ2 368 | rel = np.nonzero(θ2.T.ravel())[0] 369 | jacob = np.zeros((cdid.shape[0], rel.shape[0])) 370 | n = 0 371 | 372 | for i in range(cdindex.shape[0]): 373 | temp = ind_choice_prob_vec[n:cdindex[i] + 1, :] 374 | H1 = temp @ temp.T 375 | H = (np.diag(temp.sum(axis=1)) - H1) / nsiminds 376 | 377 | jacob[n:cdindex[i] + 1, :] = - solve(H, f1[n:cdindex[i] + 1, rel]) 378 | 379 | n = cdindex[i] + 1 380 | 381 | return jacob 382 | 383 | def minimize_GMM( 384 | self, results, θ20, method='BFGS', maxiter=2000000, disp=True): 385 | """minimize GMM objective function""" 386 | 387 | self.θ2 = θ20.copy() 388 | θ20_vec = θ20.T[np.nonzero(θ20.T)] 389 | 390 | options = {'maxiter': maxiter, 391 | 'disp': disp, 392 | } 393 | 394 | results['θ2'] = optimize.minimize( 395 | fun=self.GMM, x0=θ20_vec, jac=self._gradient_GMM, 396 | method=method, options=options) 397 | 398 | varcov = self._cal_varcov(results['θ2']['x']) 399 | results['varcov'] = varcov 400 | results['θ2']['se'] = self._cal_se(varcov) 401 | 402 | def _estimate_param_means(self, results): 403 | """Estimate mean of the parameters with minimum-distance procedure 404 | 405 | In the current example (Nevo 2000), skip the first variable (price) 406 | which is included in the both X1 and X2 407 | """ 408 | X1_nd, X2 = self.X1_nd, self.X2 409 | nbrands = self.nbrands 410 | 411 | kX1 = len(X1_nd.coords['vars']) 412 | 413 | self.θ2.T[self.ix_θ2_T] = results['θ2']['x'] 414 | θ2 = self.θ2 415 | varcov = results['varcov'] 416 | 417 | δ = self._cal_δ(θ2) 418 | θ1, ξ = self._cal_θ1_and_ξ(δ) 419 | 420 | """Exclude variables present in both X1 and X2""" 421 | bool_ix_varcov = np.ones_like(varcov, dtype=bool) 422 | 423 | bool_ix_varcov[kX1:, :] = False 424 | bool_ix_varcov[:, kX1:] = False 425 | 426 | count = 0 427 | iix_include = [] 428 | for iix, var in enumerate(X1_nd.coords['vars'].values): 429 | if var in X2.coords['vars'].values: 430 | bool_ix_varcov[iix, :] = False 431 | bool_ix_varcov[:, iix] = False 432 | else: 433 | iix_include.append(iix) 434 | count += 1 435 | 436 | V = varcov[bool_ix_varcov].reshape(count, count) 437 | y = θ1[iix_include] # estimated brand (product) dummies 438 | 439 | iix_exclude_X2 = [] 440 | iix_include_X2 = [] 441 | for iix, var in enumerate(X2.coords['vars'].values): 442 | if var in X1_nd.coords['vars'].values: 443 | iix_exclude_X2.append(iix) 444 | else: 445 | iix_include_X2.append(iix) 446 | 447 | # these are the same across markets 448 | X = X2[0, :, iix_include_X2].values 449 | 450 | L = X.T @ solve(V, X) # X'V^{-1}X 451 | R = X.T @ solve(V, y) # X'V^{-1}y 452 | 453 | β = solve(L, R) # (X'V^{-1}X)^{-1} X'V^{-1}y 454 | β_se = np.sqrt(inv(L).diagonal()) 455 | 456 | results['β'] = {} 457 | results['β']['β'] = np.zeros((len(X2.coords['vars']), )) 458 | results['β']['se'] = np.zeros((len(X2.coords['vars']), )) 459 | 460 | kX2 = len(X2.coords['vars']) 461 | 462 | iix_θ1 = 0 463 | for iix in range(kX2): 464 | if iix in iix_include_X2: 465 | results['β']['β'][iix] = β[iix - iix_θ1] 466 | results['β']['se'][iix] = β_se[iix - iix_θ1] 467 | else: 468 | results['β']['β'][iix] = θ1[iix_θ1] 469 | results['β']['se'][iix] = np.sqrt(varcov[iix_θ1, iix_θ1]) 470 | iix_θ1 += 1 471 | 472 | r = y - X @ β 473 | y_demeaned = y - y.mean() 474 | r_demeaned = r - r.mean() 475 | 476 | Rsq = 1 - (r_demeaned @ r_demeaned) / (y_demeaned @ y_demeaned) 477 | results['β']['Rsq'] = Rsq 478 | 479 | Rsq_G = 1 - (r @ solve(V, r)) / (y_demeaned @ solve(V, y_demeaned)) 480 | results['β']['Rsq_G'] = Rsq_G 481 | 482 | Chisq = results['β']['Chisq'] = len(self.ids) * r @ solve(V, r) 483 | 484 | def estimate( 485 | self, θ20, method='BFGS', maxiter=2000000, disp=True): 486 | """ Run the full estimation 487 | """ 488 | 489 | self.GMM(θ20) 490 | 491 | results = self.results = {} 492 | 493 | starttime = time.time() 494 | 495 | self.minimize_GMM( 496 | results, θ20=θ20, method=method, maxiter=maxiter, disp=disp) 497 | 498 | results['GMM'] = results['θ2']['fun'] 499 | 500 | self._estimate_param_means(results) 501 | 502 | X2, D = self.X2, self.D 503 | 504 | index = [] 505 | for var in X2.coords['vars'].values: 506 | index.append(var) 507 | index.append('') 508 | 509 | table_results = pd.DataFrame( 510 | data=np.zeros((len(X2.coords['vars']) * 2, 2 + self.nD)), 511 | index=index, 512 | columns=['Mean', 'SD'] + list(D.coords['vars'].values), 513 | ) 514 | 515 | self.table_results = table_results 516 | 517 | θ2 = np.zeros_like(self.θ2) 518 | θ2.T[self.ix_θ2_T] = results['θ2']['x'] 519 | δ = self._cal_δ(θ2) 520 | θ1, ξ = self._cal_θ1_and_ξ(δ) 521 | 522 | table_results.values[::2, 1:] = θ2 523 | table_results.values[1::2, 1:] = results['θ2']['se'] 524 | 525 | β = results['β']['β'] 526 | se_β = results['β']['se'] 527 | 528 | table_results.values[::2, 0] = β 529 | table_results.values[1::2, 0] = se_β 530 | 531 | print(table_results) 532 | 533 | print('GMM objective: {}'.format(results['GMM'])) 534 | print('Min-Dist R-squared: {}'.format(results['β']['Rsq'])) 535 | print('Min-Dist weighted R-squared: {}'.format(results['β']['Rsq_G'])) 536 | print('run time: {} (minutes)'.format((time.time() - starttime) / 60)) 537 | -------------------------------------------------------------------------------- /setup.py: -------------------------------------------------------------------------------- 1 | import os 2 | from distutils.core import setup 3 | from distutils.extension import Extension 4 | from Cython.Build import cythonize 5 | 6 | import numpy 7 | 8 | if os.name == 'nt': 9 | ext_modules = [ 10 | Extension( 11 | "_BLP", 12 | ["_BLP.pyx"], 13 | include_dirs=[numpy.get_include()], 14 | extra_compile_args=['/openmp'], 15 | ) 16 | ] 17 | else: 18 | ext_modules = [ 19 | Extension( 20 | "_BLP", 21 | ["_BLP.pyx"], 22 | libraries=["m"], 23 | include_dirs=[numpy.get_include()], 24 | extra_compile_args=['-fopenmp'], 25 | extra_link_args=['-fopenmp'], 26 | ) 27 | ] 28 | 29 | setup( 30 | name='pyBLP', 31 | ext_modules=cythonize(ext_modules), 32 | ) 33 | -------------------------------------------------------------------------------- /tests/test_BLP.py: -------------------------------------------------------------------------------- 1 | # BLP-Python provides an implementation of random coefficient logit model of 2 | # Berry, Levinsohn and Pakes (1995) 3 | # Copyright (C) 2011, 2013, 2016 Joon H. Ro 4 | # 5 | # This file is part of BLP-Python. 6 | # 7 | # BLP-Python is free software: you can redistribute it and/or modify 8 | # it under the terms of the GNU General Public License as published by 9 | # the Free Software Foundation, either version 3 of the License, or 10 | # (at your option) any later version. 11 | # 12 | # BLP-Python is distributed in the hope that it will be useful, 13 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 14 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 15 | # GNU General Public License for more details. 16 | # 17 | # You should have received a copy of the GNU General Public License 18 | # along with this program. If not, see . 19 | 20 | import os 21 | import sys 22 | 23 | import pytest 24 | 25 | import numpy as np 26 | import scipy.io 27 | import xarray as xr 28 | 29 | sys.path.append('../') 30 | import pyBLP 31 | import _BLP 32 | 33 | 34 | class Data(object): 35 | ''' Synthetic data for Nevo (2000b) 36 | 37 | The file iv.mat contains the variable iv which consists of an id column 38 | (see the id variable above) and 20 columns of IV's for the price 39 | variable. The variable is sorted in the same order as the variables in 40 | ps2.mat. 41 | 42 | ''' 43 | def __init__(self): 44 | try: 45 | ps2 = scipy.io.loadmat('examples/ps2.mat') 46 | Z_org = scipy.io.loadmat('examples/iv.mat')['iv'] 47 | except: 48 | ps2 = scipy.io.loadmat('../examples/ps2.mat') 49 | Z_org = scipy.io.loadmat('../examples/iv.mat')['iv'] 50 | 51 | nsiminds = self.nsiminds = 20 # number of simulated "indviduals" per market 52 | nmkts = self.nmkts = 94 # number of markets = (# of cities) * (# of quarters) 53 | nbrands = self.nbrands = 24 # number of brands per market 54 | 55 | ids = ps2['id'].reshape(-1, ) 56 | self.ids = xr.DataArray( 57 | ids.reshape((nmkts, nbrands), order='F'), 58 | coords=[range(nmkts), range(nbrands)], 59 | dims=['markets', 'brands'], 60 | attrs={'Desc': 'an id variable in the format bbbbccyyq, where bbbb ' 61 | 'is a unique 4 digit identifier for each brand (the ' 62 | 'first digit is company and last 3 are brand, i.e., ' 63 | '1006 is K Raisin Bran and 3006 is Post Raisin Bran), ' 64 | 'cc is a city code, yy is year (=88 for all observations ' 65 | 'in this data set) and q is quarter.'} 66 | ) 67 | 68 | X1 = np.array(ps2['x1'].todense()) 69 | 70 | self.X1 = xr.DataArray( 71 | X1.reshape(nmkts, nbrands, -1), 72 | coords=[range(nmkts), range(nbrands), 73 | ['Price'] + ['Brand_{}'.format(brand) 74 | for brand in range(nbrands)]], 75 | dims=['markets', 'brands', 'vars'], 76 | attrs={'Desc': 'the variables that enter the linear part of the ' 77 | 'estimation. Here this consists of a price variable ' 78 | '(first column) and 24 brand dummy variables.'} 79 | ) 80 | 81 | X2 = np.array(ps2['x2'].copy()) 82 | self.X2 = xr.DataArray( 83 | X2.reshape(nmkts, nbrands, -1), 84 | coords=[range(nmkts), range(nbrands), 85 | ['Constant', 'Price', 'Sugar', 'Mushy']], 86 | dims=['markets', 'brands', 'vars'], 87 | attrs={'Desc': 'the variables that enter the non-linear part of the ' 88 | 'estimation.'} 89 | ) 90 | 91 | self.id_demo = ps2['id_demo'].reshape(-1, ) 92 | 93 | D = np.array(ps2['demogr']) 94 | self.D = xr.DataArray( 95 | D.reshape((nmkts, nsiminds, -1), order='F'), 96 | coords=[range(nmkts), range(nsiminds), 97 | ['Income', 'Income^2', 'Age', 'Child']], 98 | dims=['markets', 'nsiminds', 'vars'], 99 | attrs={'Desc': 'Demeaned draws of demographic variables from the CPS for 20 ' 100 | 'individuals in each market.', 101 | 'Child': 'Child dummy variable (=1 if age <= 16)'} 102 | ) 103 | 104 | v = np.array(ps2['v']) 105 | self.v = xr.DataArray( 106 | v.reshape((nmkts, nsiminds, -1), order='F'), 107 | coords=[range(nmkts), range(nsiminds), 108 | ['Constant', 'Price', 'Sugar', 'Mushy']], 109 | dims=['markets', 'nsiminds', 'vars'], 110 | attrs={'Desc': 'random draws given for the estimation.'} 111 | ) 112 | 113 | s_jt = ps2['s_jt'].reshape(-1, ) # s_jt for nmkts * nbransd 114 | self.s_jt = xr.DataArray( 115 | s_jt.reshape((nmkts, nbrands)), 116 | coords=[range(nmkts), range(nbrands),], 117 | dims=['markets', 'brands'], 118 | attrs={'Desc': 'Market share of each brand.'} 119 | ) 120 | 121 | self.ans = ps2['ans'].reshape(-1, ) 122 | 123 | Z = np.c_[Z_org[:, 1:], X1[:, 1:]] 124 | self.Z = xr.DataArray( 125 | Z.reshape((self.nmkts, self.nbrands, -1)), 126 | coords=[range(nmkts), range(nbrands), range(Z.shape[-1])], 127 | dims=['markets', 'brands', 'vars'], 128 | attrs={'Desc': 'Instruments'} 129 | ) 130 | 131 | 132 | @pytest.fixture(scope="module") 133 | def data(): 134 | return(Data()) 135 | 136 | 137 | def test_cal_mu(data): 138 | BLP = pyBLP.BLP(data) 139 | 140 | v, D, X2 = BLP.v, BLP.D, BLP.X2 141 | 142 | θ20 = np.array([[ 0.3772, 3.0888, 0, 1.1859, 0], 143 | [ 1.8480, 16.5980, -.6590, 0, 11.6245], 144 | [-0.0035, -0.1925, 0, 0.0296, 0], 145 | [ 0.0810, 1.4684, 0, -1.5143, 0]]) 146 | 147 | mu_python = BLP._cal_mu(θ20) 148 | mu_cython = _BLP.cal_mu(θ20, v.values, D.values, X2.values) 149 | 150 | assert np.allclose(mu_python, mu_cython) 151 | 152 | def test_cal_s(data): 153 | BLP = pyBLP.BLP(data) 154 | 155 | v, D, X2 = BLP.v, BLP.D, BLP.X2 156 | 157 | θ20 = np.array([[ 0.3772, 3.0888, 0, 1.1859, 0], 158 | [ 1.8480, 16.5980, -.6590, 0, 11.6245], 159 | [-0.0035, -0.1925, 0, 0.0296, 0], 160 | [ 0.0810, 1.4684, 0, -1.5143, 0]]) 161 | 162 | BLP.GMM(θ20) 163 | 164 | δ, μ = BLP.δ, BLP.μ 165 | 166 | s_python = BLP._cal_s(δ, μ) 167 | s_cython = BLP.s 168 | _BLP.cal_s(δ, μ, s_cython) 169 | 170 | assert np.allclose(s_python, s_cython) 171 | 172 | def test_GMM(data): 173 | """ Replicate Nevo (2000b) results 174 | """ 175 | BLP = pyBLP.BLP(data) 176 | 177 | θ20 = np.array([[ 0.3772, 3.0888, 0, 1.1859, 0], 178 | [ 1.8480, 16.5980, -.6590, 0, 11.6245], 179 | [-0.0035, -0.1925, 0, 0.0296, 0], 180 | [ 0.0810, 1.4684, 0, -1.5143, 0]]) 181 | 182 | assert np.allclose(BLP.GMM(θ20), 14.900789417012428) 183 | 184 | def test_full_estimation(data): 185 | BLP = pyBLP.BLP(data) 186 | 187 | θ20 = np.array([[ 0.5580, 3.0888, 0, 1.2844, 0], 188 | [ 3.3124, 588.3252, -30.1920, 0, 11.0546], 189 | [-0.0057, -0.3849, 0, 0.0522, 0], 190 | [ 0.0934, 0.7483, 0, -1.3533, 0]]) 191 | 192 | BLP.estimate(θ20=θ20) 193 | 194 | assert np.allclose(BLP.results['GMM'], 4.561514655033999) 195 | 196 | 197 | if __name__ == '__main__': 198 | pass 199 | --------------------------------------------------------------------------------