Welcome to Pre-trained NNE#
(Note: This website is being updated over time. Last update on May 3, 2025.)
This is the companion website for Wei and Jiang (2025). It provides a pretrained estimator for a consumer search model used in economics & marketing. The estimator is based on a neural net that recognizes search model parameters from data patterns. We call it pretrained neural net estimator (NNE). The approach extends Wei and Jiang (2024) and is generally applicable to structural models, though here we focus on a search model.
Below is a brief overview of how to apply pretrained NNE to your search data. For Matlab code and detailed documentation, see code page. For examples to try out, see data page.
Overview#
The main function to execute estimation is nne_estimate.m, as shown below.
result = nne_estimate(nne, Y, Xp, Xa, Xc, consumer_idx)
Explanation for inputs and output:
Input
nnestores the trained neural net and some pre-defined settings, available from the filetrained_nne.mat.Inputs
Xp,Xa,Xc,Y, andconsumer_indexstore your data (more on them below).Output
resultis a table storing the parameter estimate for the search model.
Below shows an example. The total execution time is 0.78 sec on a laptop. The time includes overheads such as some data sanity checks.
>> load('trained_nne.mat', 'nne')
>> tic
result = nne_estimate(nne, Y, Xp, Xa, Xc, consumer_idx);
toc
Elapsed time is 0.784314 seconds.
>> result
result = 8×2 table
name val
---------- -------
"\alpha_0" -6.4546
"\alpha_1" -0.11333
"\eta_0" 5.929
"\eta_1" -0.048687
"\eta_2" 0.22004
"\eta_3" 0.052894
"\beta_1" 0.25836
"\beta_2" -0.53811
The rest of this page gives more details on the search model, how to format your data, and how to get standard errors.
1) The search model#
Sequential search models have been commonly applied in economics & marketing. A consumer faces \(J\) products (or options). She decides which options to search and which option to buy. Searching an option incurs a search cost but also reveals some utility for that option. The search model estimated by the pretrained NNE here is a standard one. The exact specification of it is given in Wei and Jiang (2025). Here we give a high-level description:
A consumer searches and chooses among a list of products, plus an outside good. A free search is endowed (because in most data each consumer searches at least once).
The list shows some product attributes that affect consumer’s utility for products. The effects of these attributes are described by coefficients \(\beta\).
There may be some consumer attributes that affect consumer’s outside utility. The effects of these attributes are described by coefficients \(\eta\).
There may also be advertising attributes that affect search costs (but not utility). The effects of these attributes are described by coefficients \(\alpha\).
For a survey on empirical applications of search models, see Ursu, Seiler, & Honka (2025).
2) Data format#
To use the pretrained NNE, organize data into five arrays: Y, Xp, Xa, Xc, and consumer_index. Respectively, they store search & purchase outcomes, product attributes, advertising attributes, consumer attributes, and consumer identifiers.
Below, we illustrate with an example of shopping at an online retailer. There are \(n\) = 10,000 consumers and \(J\) = 15 options per consumer. Below shows a preview of the top rows of consumer_index, Y, Xp, and Xa. Note there are \(nJ\) rows in total. We see:
consumer_idxis a column vector. Each value indicates the consumer.Yhas two columns; the 1st column indicates search and 2nd column indicates purchase. In this example, we see the first consumer searched the 1st, 3rd, and 8th options. She bought the 3rd option.Xpstores product attributes. In this example, there are two product attributes: a 1-5 product rating and log price.Xastores advertising attributes. In this example, there is one advertising attribute: whether the product is highlighted on the retailer website.Xcstores consumer attributes. It is not previewed below. It has only \(n\) rows, one for each consumer.
>> table(consumer_idx, Y, Xp, Xa)
ans = 150000×4 table
consumer_idx Y Xp Xa
____________ ______ ______________ __
1 1 0 4 0.67743 1
1 0 0 5 1.1052 1
1 1 1 1 -0.24542 1
1 0 0 5 0.78452 0
1 0 0 4 0.10519 0
1 0 0 5 0.068463 0
1 0 0 4 0.35691 0
1 1 0 5 0.61307 0
1 0 0 3 1.1809 0
1 0 0 5 0.91391 0
1 0 0 5 0.054537 0
1 0 0 3 1.0015 0
1 0 0 5 0.73938 0
1 0 0 3 -0.020808 0
1 0 0 5 0.23587 0
2 0 0 3 0.72159 1
2 1 0 5 -0.39847 1
2 0 0 5 0.73669 1
: : : :
Below show the dimensions of each variable. Outside this example, if your data do not feature advertising or consumer attributes, you can let Xa or Xc be an empty matrix.
>> whos Xp Xa Xc Y consumer_idx
Name Size Bytes Class Attributes
Xa 150000x1 1200000 double
Xc 10000x3 240000 double
Xp 150000x2 2400000 double
consumer_idx 150000x1 1200000 double
Y 150000x2 2400000 double
3) Bootstrap standard errors#
The nne_estimate.m function has standard error calculation built in. Simply add se = true option as shown below. The output will include an additional column of standard errors. The calculation bootstraps 50 samples so execution time will be somewhat longer, but it can take advantage of parallel computing toolbox if installed.
We see \(\alpha_1\) is negative, indicating that the products highlighted by the retailer enjoy a lower search cost (so they are more likely to be searched). We see \(\beta_1\) is positive, indicating that consumer utility increases with product rating. We see \(\eta_1\) is negative, indicating that the outside utility decreases with the first consumer attribute.
>> result = nne_estimate(nne, Y, Xp, Xa, Xc, consumer_idx, se = true)
result = 8×3 table
name val se
__________ _________ ________
"\alpha_0" -6.4546 0.071848
"\alpha_1" -0.11333 0.044997
"\eta_0" 5.929 0.061318
"\eta_1" -0.048687 0.011513
"\eta_2" 0.22004 0.029282
"\eta_3" 0.052894 0.023437
"\beta_1" 0.25836 0.004951
"\beta_2" -0.53811 0.011032
Papers#
Wei, Yanhao ‘Max’ and Zhenling Jiang (2024), “Estimating Parameters of Structural Models with Neural Networks,” Accepted at Marketing Science.
Wei, Yanhao ‘Max’ and Zhenling Jiang (2025), “Pretraining Estimators for Structural Models: Application to Consumer Search.”
Ursu, Raluca, Stephan Seiler, and Elisabeth Honka (2025), “The Sequential Search Model: A Framework for Empirical Research.” QME, 23(1): 165-213.