Demand Estimation with Text and Image Data

Imagine you are trying to figure out why people buy the things they do. In the world of economics, this is called demand estimation. Traditionally, economists have tried to solve this puzzle by looking at a product's "ID card"—its specific, measurable features like price, weight, color, or screen size. They assume that if two products have similar ID cards, people will swap them easily if one goes out of stock.

But here's the problem: Products are more than just their ID cards.

Think about buying a book. You might choose a thriller not just because it's 300 pages long (a measurable fact), but because the cover art looks mysterious, or because the reviews say the plot twists are "mind-blowing." These are unstructured data—things like images, text descriptions, and customer reviews. They are messy, hard to count, and usually ignored by standard economic models because they are too difficult to quantify.

This paper introduces a new tool called DeepLogit that acts like a "super-spy" for economists. It uses Artificial Intelligence (AI) to read the messy stuff and turn it into a clear map of what people actually want.

Here is how it works, broken down into simple steps:

1. The "Magic Translator" (Embeddings)

Imagine you have a giant library of books, but you don't know what any of them are about. You can't read them all.

The Old Way: You ask a librarian to write down a few facts for each book (e.g., "Genre: Mystery," "Pages: 300").
The New Way (This Paper): You use a super-smart AI robot (a pre-trained deep learning model). You show the robot the book cover and the back-cover blurb. The robot doesn't just read the words; it "feels" the vibe. It turns the image and text into a secret code (called an embedding) that captures the essence of the book.
- Analogy: It's like the robot gives every book a unique "scent profile." Even if two books have different titles, if they smell like "spooky forest," the robot knows they are similar.

2. The "Compressor" (PCA)

The robot's secret code is huge and complicated (thousands of numbers). You can't put all that into a simple math equation.

The Solution: The authors use a technique called Principal Component Analysis (PCA). Think of this as a high-tech vacuum cleaner that sucks out all the noise and leaves only the most important "flavors."
It condenses the thousands of numbers into just a few key dimensions (like "Scary vs. Funny" or "Action vs. Romance") that actually matter to buyers.

3. The "Crystal Ball" (Prediction)

Now, the economists plug these "flavors" into a standard math model. They test it with a clever experiment:

They ask people to pick their favorite book from a list.
Then, they pretend that favorite book is sold out and ask, "What would you buy instead?"
The Result: The AI-powered model predicted the "second choice" much better than the old models that only looked at facts like page count. It knew that if you loved a specific fantasy book, you'd likely switch to another fantasy book with a similar "vibe," even if the page counts were different.

Why Does This Matter?

This isn't just about books. The authors tested this on 40 different categories on Amazon, from pet food to video games to clothing.

The Surprise: Sometimes, text is more important than pictures. For example, when buying clothes, you might think the photo is everything. But the authors found that for some items, the reviews and descriptions told them more about what people substitute than the photos did.
The Benefit: Before this, if a company wanted to know how a price hike on one cereal would affect sales of another, they had to guess the "substitution" based on limited data. Now, they can use the AI to read the product descriptions and reviews to see exactly how similar the products feel to consumers.

The Bottom Line

Think of this paper as giving economists a pair of X-ray glasses.

Old Glasses: You could only see the surface features (price, size, color).
New Glasses (DeepLogit): You can see the hidden "soul" of the product—the design, the story, and the feeling—that actually drives people to swap one item for another.

This allows businesses and policymakers to make better decisions about pricing, mergers, and new products because they finally understand the real reasons people choose what they choose.

1. Problem Statement

Traditional demand estimation for differentiated products (e.g., for merger analysis, pricing, or tariff evaluation) relies on observed product attributes (e.g., size, weight, brand) to model substitution patterns. This approach faces two critical limitations:

Data Scarcity and Subjectivity: Researchers rarely observe all choice-relevant attributes. They often rely on third-party data with unknown selection criteria or subjectively choose which attributes to collect, potentially missing key drivers of consumer preference.
Unquantifiable Attributes: Consumers value "hard-to-quantify" dimensions such as visual design, aesthetic appeal, and nuanced functional benefits described in text. Standard attribute-based models fail to capture these dimensions, leading to inaccurate substitution patterns and poor counterfactual predictions.

The authors propose a method to leverage unstructured data (product images, titles, descriptions, and reviews) to infer substitution patterns without requiring manual attribute collection.

2. Methodology

The proposed approach, implemented in the DeepLogit Python package, integrates unstructured data into a standard Mixed Logit demand model through a three-step pipeline:

Step 1: Embedding Extraction

The authors use pre-trained deep learning models to convert unstructured data into low-dimensional vector representations (embeddings):

Images: Four Convolutional Neural Networks (CNNs) are used: VGG19, ResNet50, InceptionV3, and Xception. The classification layers are removed to retain feature embeddings.
Text: Both simple models (Bag-of-Words, TF-IDF) and advanced pre-trained transformers are used: Universal Sentence Encoder (USE) and BERT Sentence Transformer (ST). These capture semantic similarity rather than just keyword matching.

Step 2: Dimensionality Reduction (PCA)

Embeddings are high-dimensional (e.g., 512 dimensions), making direct inclusion in a Mixed Logit model computationally prohibitive due to the need for numerical integration.

Principal Component Analysis (PCA) is applied to the embeddings within each product category.
This reduces dimensionality while focusing on variation within the category (downweighting broad category differences) and ensures orthogonality to avoid multicollinearity.

Step 3: Demand Model Integration & Selection

The resulting Principal Components (PCs) are incorporated into a Mixed Logit model with random coefficients.

Utility Function: $u_{ij} = \delta_j + \alpha_i p_{ij} + \theta_i' PC_j + \epsilon_{ij}$ , where $\theta_i$ represents random coefficients on the PCs.
Model Selection Algorithm: Since researchers typically lack ground-truth substitution data, the authors propose an algorithm to select the best specification using in-sample Akaike Information Criterion (AIC).
- The algorithm iteratively adds random coefficients to subsets of candidate variables (Price + PCs) and selects the model with the lowest AIC.
- This process is repeated across all combinations of data types (text vs. image) and embedding models to find the global optimum.

3. Key Contributions

Methodological Innovation: A scalable framework to integrate unstructured data into standard econometric demand models, bypassing the need for manual attribute coding.
Novel Validation Strategy: The authors design a unique choice experiment to validate the model. Participants choose a "first choice" and a "second choice" from a list of books.
- Innovation: The model is estimated only on first-choice data. The second-choice data serves as a "ground truth" for substitution patterns (diversion ratios) to validate counterfactual predictions. This is the first known use of such an experiment to validate demand models.
Practical Tool: Release of the DeepLogit Python package to facilitate adoption by empirical researchers.
Empirical Breadth: Validation across a controlled experiment (books) and 40 diverse product categories on Amazon (electronics, groceries, clothing, etc.).

4. Key Results

Experimental Validation (Books)

Superior Performance: The best-performing model (Mixed Logit with random coefficients on PCs derived from Review text using the USE model) reduced the Root Mean Squared Error (RMSE) of counterfactual second-choice predictions by 23% compared to a plain Logit model.
Comparison to Benchmarks: The unstructured data model outperformed the standard Mixed Logit with observed attributes (genre, pages, year) by 14% in RMSE.
Insight: Text embeddings captured subtle substitution patterns (e.g., specific plot details, pacing, author style) that standard attributes missed. For instance, the model correctly identified that two books by the same author were close substitutes, whereas attribute-based models failed.
Model Selection: In-sample AIC was highly correlated (0.78) with out-of-sample counterfactual performance, validating the use of AIC for model selection when ground truth is unavailable.

Observational Application (Amazon Data)

Broad Applicability: Applied to 40 categories (e.g., tablets, monitors, clothing, pet food). Unstructured data consistently improved model fit (AIC reduction) over both Plain Logit and Attribute-based Mixed Logit models in every category.
Data Type Variability: There is no "one-size-fits-all" data type.
- In Electronics, text descriptions often outperformed images.
- In Clothing, results were mixed; titles were sometimes more predictive than images, contrary to intuition.
- Conclusion: Researchers should collect multiple data types and use model selection to determine the best signal for a specific category.
Diversion Ratios: The proposed approach generated significantly more variable and realistic diversion ratios (average 47% to closest substitute) compared to the flat diversion ratios of the Plain Logit (average 22%), indicating better identification of close substitutes.

5. Significance and Implications

Counterfactual Analysis: The approach is highly effective for applications where product design remains fixed, such as optimal pricing, merger simulations, and tax analysis. It allows researchers to simulate how consumers substitute between products based on visual and textual similarity.
Limitations: The method assumes embeddings are fixed. It is less suitable for counterfactuals where product design changes (altering the image/text) or where price changes directly alter the sentiment in reviews (e.g., "good value for the price").
Scalability: By automating the extraction of substitution signals, this method enables demand estimation across hundreds of categories without the prohibitive cost of manual attribute collection.
Future Directions: The paper suggests that fine-tuning embedding models specifically for demand prediction and combining unstructured data with more flexible demand functional forms are promising avenues for future research.

In summary, Compiani et al. demonstrate that unstructured data, when processed through deep learning and integrated into Mixed Logit models, provides a robust, scalable, and empirically superior method for estimating product substitution patterns compared to traditional attribute-based approaches.