blp nevo

Random coefficients logit model of demand proposed by Berry, Levinsohn and Pakes (1995) (thus, BLP) [1].

This is Wolfram Mathematica [5] version of famous Nevo's Matlab code [4] with toy BLP example.

Mathematica version has several advantages for educational purposes.

1. code is shorter and contains in one file;
2. code is immutable, so each step of the algorithm is easear to study separately;
3. optimization needs no jacobian (aka gradient);
4. contraction mapping is a one-liner here (FixedPoint function).

We keep naming of variables and functions after Nevo's code where appropriate. Detailed explanations of how the BLP model works can be found in [2] and [3].

use

1 way

Unpack BLP_main.nb from BLP_main.zip in the same folder where blp_import resides. blp_import folder has five .xlsx files with input data derived from Nevo's code [4]. Select all cells in the notebook and run Shift + Enter.

2 way

Put nevo_kernel_script.wl in the same folder where nevo_csv resides. Run wolframscript from location where it is visible:

$ wolframscript -file "..your/path/to/nevo_kernel_script.wl" -print

Usually optimization takes about 90 sec.

study

nevo_kernel_script.wl is a text file with comments. It has 'data', 'model' and 'run' parts that describe the whole logic of model building. The code can be copied into ordinary notebook to get intermediate results.

This is the shortest code with open internal logic of the BLP model we know about. Without auxiliary culculations it can be express in a less than 30 lines.

references

[1] Berry, Steven, James Levinsohn & Ariel Pakes (1995) “Automobile Prices in Market Equilibrium,” Econometrica, 63(4): 841-890.

[2] Nevo, Aviv (2000) "A Practitioner's Guide to Estimation of Random Coefficients Logit Models of Demand," Journal of Economics & Management Strategy 9(4): 513-548.

[3] Rasmusen, Eric. "The BLP Method of Demand Curve Estimation in Industrial Organization", mimeo (2007, 2011, 2016).

[4] Matlab code: https://eml.berkeley.edu/~bhhall/e220c/rc_dc_code.htm

[5] Wolfram Mathematica (v.10+) is required to run BLP_main.nb (notebook): https://www.wolfram.com/mathematica/