GPT-4 Explains Econometrics (a new series): Estimating Demand with BLP

by Cunningham (r) and GPT-4 (r), prompted by Cunningham

This is a new series I decided to start called “GPT-4 Explains Econometrics”. The idea is simple: I am going to try and prompt GPT-4 to explain econometric methods that are outside my wheelhouse. The main substack will continue to be my own writings, unassisted by artificial intelligence, as that’s my passion. Which means the main substack will really just be more of the Rubin causal model treatment effects work and its adjacent material. The stuff here — that’ll just be me digging deep into the underbelly of things I have always wanted to learn but just don’t have the time. Like structural material in empirical IO. So, each week, probably Fridays, I’ll post in a new section called “GPT-4 Explains econometrics”.

You should be cautious about taking any of it seriously because I can’t confirm its accuracy. Rather, I am just like you — I’m listening to GPT-4 tell me stories about econometrics. But hey — nothing wrong with listening to a teacher who maybe isn’t always hitting the nail on its head right? So long as you’re aware that your beliefs are your responsibility, not mine, we’re all good! Also, this series will be for paying customers. And if you don’t want to receive it, you just need to unsubscribe from this newsletter, and that’s explained here. But this initial entry will give you a taste of what’s to come. So buckle up friend! We are going on the magical mystery tour in to GPT-4 Explains Econometrics! All of this was produced using prompts. I’ll always post the title first as the title is something that GPT-4 creates when I start out, and that’ll give you an idea of what I’m interested in. And the prompts will be listed at the bottom.

“Economic Parameter Estimation Limitations: A BLP Explainer”, co-produced by Cunningham (r) and GPT-4 (r), prompted by Cunningham

The BLP method of structural demand estimation is a widely used approach in empirical industrial organization and economics, which was introduced by Steven Berry, James Levinsohn, and Ariel Pakes in their 1995 paper. The method is based on a random-coefficients logit model and is commonly referred to as the Berry-Levinsohn-Pakes (BLP) model. The primary objective of the BLP model is to estimate consumer preferences and substitution patterns for differentiated products, such as automobiles, breakfast cereals, and consumer electronics.

The BLP model builds on the simple multinomial logit model by allowing for more flexible substitution patterns among products and incorporating consumer heterogeneity. The main components of the BLP model are as follows:

1. Utility function: Consumers derive utility from the products they choose, which depends on product characteristics, such as price and observable features (e.g., size, brand, power, etc.), as well as unobservable product characteristics (e.g., brand reputation, design, etc.). In the BLP model, consumer utility is given by:

\(U_{ij} = δ_j + μ_{ij}\)

where U_ij is the utility of consumer i from product j, δ_j is the mean utility of product j (which is common across all consumers), and μ_ij is a consumer-specific deviation from the mean utility.

2. Random coefficients: The BLP model allows for consumer heterogeneity by introducing random coefficients on product characteristics. These random coefficients capture the variation in preferences across consumers. The consumer-specific deviation in utility, μ_ij, is given by:

\(μ_{ij} = Σ_k β_{ik} * x_{jk} + α_i * p_j\)

where β_ik is the random coefficient for consumer i on the k-th product characteristic, x_jk is the value of the k-th characteristic for product j, α_i is the price sensitivity of consumer i, and p_j is the price of product j.

3. Market shares: The BLP model derives market shares for each product by integrating over the distribution of consumer preferences. This is typically done using numerical integration techniques, such as Monte Carlo or Gaussian quadrature.

4. Estimation: The model parameters are estimated by matching the predicted market shares from the model to the observed market shares in the data. This is typically done using a two-step estimation procedure, known as the Nested Fixed Point algorithm. In the first step, a candidate set of parameters is used to compute the mean utility, δ_j, for each product by inverting the market share equation. In the second step, the candidate parameters are updated using a GMM (Generalized Method of Moments) procedure that minimizes the distance between the predicted and observed market shares.

The BLP model has been widely applied in various industries and has become a standard tool for demand estimation in empirical industrial organization. It allows researchers to analyze the effects of various factors, such as changes in prices, product characteristics, and market structure, on consumer demand and substitution patterns.

Explain to me like I’m 5

The Berry-Levinsohn-Pakes (BLP) method is an approach used in economics to understand consumer preferences and choices for different products when there are many similar options available. This method is especially useful when you want to understand how consumers may substitute one product for another based on factors like price, features, and unobservable characteristics like brand reputation.

Here's a simplified explanation of the BLP model:

1. Utility function: The BLP model assumes that consumers get a certain level of satisfaction or utility from buying a product. This utility depends on the product's observable features (like price and size), and unobservable features (like design or brand reputation). The utility is split into two parts: a common part shared by all consumers and a part that varies across consumers to account for their different tastes and preferences.

2. Random coefficients: To capture the differences in consumer preferences, the BLP model introduces random coefficients. These coefficients show how much each consumer values a specific product characteristic, like size or brand. For example, some consumers may prefer larger cars while others prefer smaller ones. The random coefficients help us model these individual differences.

3. Market shares: Based on the utility that consumers get from each product and their individual preferences, the BLP model predicts the market share of each product (how many consumers choose to buy that product). This is done by taking into account the entire distribution of consumer preferences in the market.

4. Estimation: To estimate the parameters of the BLP model, we use a two-step process. First, we guess the parameters and calculate the average utility for each product. Then, we compare the market shares predicted by the model with the actual market shares observed in the data. We keep adjusting our guess of the parameters until the difference between the predicted and actual market shares is minimized.

In summary, the BLP model is a popular method used in economics to understand consumer choices and preferences for different products, especially when there are many options available. It helps us analyze the effects of factors like price and product features on consumer demand and understand how consumers may substitute one product for another.

Random coefficients and alternative methods to estimation

Random coefficients in the context of the BLP model represent the individual differences in consumer preferences for product characteristics. By introducing random coefficients, we can account for the fact that different consumers might have different tastes and valuation for the same product characteristics, such as color, brand, size, or price. In other words, random coefficients help capture the variation in how much consumers care about different features of a product.

Randomness, in this case, means that these preferences are drawn from a certain distribution (like a normal distribution) that represents the overall preference distribution of the consumer population. It doesn't mean that preferences are completely arbitrary or unpredictable; rather, it indicates that preferences follow a specific pattern but can vary across individuals.

Alternative modeling approaches that do not rely on random coefficients include:

1. Linear regression models: Linear regression is a simple statistical method used to understand the relationship between a dependent variable (like product demand) and one or more independent variables (like price, product features, or marketing expenditures). While linear regression can provide insights into general trends, it doesn't account for individual consumer heterogeneity or preferences as effectively as random coefficient models.

2. Multinomial logit models: These models are based on the logit function and can be used to estimate the probability of a consumer choosing a particular product among multiple alternatives. The basic multinomial logit model assumes that consumer preferences are homogeneous (i.e., consumers share the same preferences). This is a significant limitation, as it doesn't capture the individual differences in preferences. Random coefficients logit models, like the BLP model, were developed to address this limitation.

3. Nested logit models: Nested logit models are another way to relax the assumption of homogeneity in consumer preferences. In these models, products are grouped into "nests" based on shared characteristics. Consumers first choose a nest and then choose a product within that nest. This allows for more flexible substitution patterns between products, but it still does not account for individual preferences as directly as random coefficient models.

In conclusion, introducing random coefficients in the BLP model helps capture individual differences in consumer preferences, leading to a more accurate representation of consumer choice behavior. While there are alternative approaches to demand estimation, they often do not account for consumer heterogeneity as effectively as random coefficient models.

Connection to Daniel McFadden

The BLP model is considered a major breakthrough in econometrics and empirical industrial organization (IO). The model addressed several limitations of earlier demand estimation models, such as the basic multinomial logit model, by introducing random coefficients to capture consumer heterogeneity and allowing for more flexible substitution patterns among products. The BLP model has become a standard tool for demand estimation in empirical IO and has been applied to various industries to analyze the effects of factors like price, product characteristics, and market structure on consumer demand and substitution patterns.

The BLP model connects to Daniel McFadden's early work, as McFadden was instrumental in developing the multinomial logit model, which is the foundation for the BLP model. McFadden's work on the multinomial logit model won him the Nobel Prize in Economics in 2000. The multinomial logit model estimates the probability of consumers choosing among multiple alternatives based on product characteristics and consumer preferences. However, this basic model assumes homogeneous preferences among consumers, which means it does not account for individual differences in preferences.

The BLP model builds upon McFadden's multinomial logit model by incorporating random coefficients, which allows for consumer heterogeneity and more flexible substitution patterns. This innovation made the BLP model more suitable for analyzing differentiated product markets and consumer choice behavior, which are key concerns in empirical IO.

In summary, the BLP model is indeed considered a major breakthrough in econometrics and empirical IO. It builds upon Daniel McFadden's early work on the multinomial logit model by introducing random coefficients to account for consumer heterogeneity, leading to a more accurate representation of consumer choices and substitution patterns in differentiated product markets.

Prior Awareness of Limitations Created by Assuming Homogenous Preferences

The issue of assuming homogeneous consumer preferences was a widely recognized limitation in the field of econometrics and empirical industrial organization before the development of the BLP model. Researchers were aware that assuming homogeneous preferences could lead to biased estimates of demand elasticities and misrepresent the true nature of consumer choices and substitution patterns.

The problem couldn't be solved sooner for a few reasons:

1. Computational limitations: Early models like the basic multinomial logit model were simpler and required less computational power. The introduction of random coefficients and the need to integrate over the distribution of consumer preferences in the BLP model made it computationally intensive. Advances in computational capabilities, including faster processors and better numerical integration techniques, eventually made it feasible to estimate models with random coefficients, such as the BLP model.

2. Methodological developments: Before the BLP model, researchers had made some progress in developing models that relaxed the assumption of homogeneity in consumer preferences, such as nested logit models. However, these models were still limited in their ability to fully capture consumer heterogeneity. The BLP model was a significant step forward in this regard, as it provided a more flexible and general framework for estimating demand in differentiated product markets.

3. Data availability: The availability of detailed product-level data and consumer-level data has increased significantly over the years. This has allowed researchers to estimate more sophisticated models, like the BLP model, that rely on rich data sources to capture consumer heterogeneity and preferences.

The BLP model was indeed a breakthrough, building upon earlier contributions in econometrics and benefiting from advances in computational power, methodological developments, and data availability. The model's success in addressing the limitations of earlier demand estimation models and its ability to better represent consumer preferences and substitution patterns has made it a standard tool in empirical industrial organization and econometrics.

Daniel McFadden’s Opinions of BLP

There is no direct record of Daniel McFadden's specific response to the BLP model. However, it is important to note that McFadden's work on the multinomial logit model laid the groundwork for the BLP model, as well as other models that sought to relax the assumption of homogeneous consumer preferences. The BLP model is an extension and improvement of McFadden's multinomial logit model by incorporating random coefficients to account for consumer heterogeneity.

Given McFadden's pioneering work in the field of econometrics and his contributions to the development of choice models, it is likely that he would have recognized the value of the BLP model in addressing the limitations of earlier demand estimation models, including his own work.

In general, the BLP model has been well received by the economics and econometrics communities, as it has provided a more flexible and accurate representation of consumer choices and substitution patterns in differentiated product markets. This reception is a testament to the importance of McFadden's early work and the ongoing advancements in the field.

Criticisms of BLP

While the BLP model has been widely adopted and praised for its ability to estimate consumer preferences and substitution patterns for differentiated products, it is not without its limitations and criticisms. Some of the more common criticisms include:

1. Computational complexity: The BLP model can be computationally intensive due to the need to integrate over the distribution of consumer preferences. This can make the estimation process slow, particularly when dealing with large datasets or a high number of product characteristics. However, advances in computational methods and hardware have somewhat mitigated this issue over time.

2. Functional form assumptions: The BLP model makes specific assumptions about the functional form of consumer preferences and the distribution of random coefficients. While these assumptions simplify the estimation process, they may not always accurately represent the true underlying consumer preferences. Researchers have developed alternative models and extensions to the BLP model to address some of these concerns, such as the mixed logit model and the random coefficients probit model.

3. Endogeneity: The BLP model assumes that product characteristics, such as price, are exogenous. In reality, prices and other product characteristics may be endogenous, which means they are determined by factors within the model, such as demand and supply interactions. Endogeneity can lead to biased estimates if not addressed properly. Researchers have developed various methods to correct for endogeneity in the BLP model, such as using instrumental variables or control function approaches.

4. Identification: Properly identifying the model parameters, particularly the distribution of random coefficients, can be challenging in the BLP model. The identification of these parameters relies on sufficient variation in product characteristics and market shares across markets. If the data does not have enough variation, it can be difficult to separate consumer preferences from other factors influencing demand.

Despite these criticisms, the BLP model remains a popular and widely used tool in empirical industrial organization for estimating consumer preferences and demand in differentiated product markets. Researchers have developed various extensions and modifications to address some of these concerns and improve the performance of the model.

Usefulness of BLP within Private Industry

The BLP model can be useful for both private companies, like Pizza Hut, and for national policy analysis in the context of regulation. While the BLP model has been widely applied in empirical industrial organization to study market competition, market structure, and the effects of regulation, it can also be helpful for firms trying to understand consumer preferences and make strategic decisions.

For a large national restaurant like Pizza Hut, the BLP model can provide valuable insights into consumer preferences for various menu items, pricing strategies, and promotional efforts. By estimating demand elasticities and substitution patterns, the BLP model can help Pizza Hut better understand how consumers respond to changes in product characteristics, such as price, ingredients, or portion sizes. This information can be used to guide decisions on menu design, pricing, marketing, and expansion strategies.

In addition to helping firms like Pizza Hut make better strategic decisions, the BLP model can be used to analyze the effects of regulation on consumer demand and market competition. This can be particularly relevant for policymakers who are considering regulatory changes that might affect the restaurant industry or the broader economy.

In summary, the BLP model can be a valuable tool for both private companies and policymakers, as it provides a flexible framework for estimating consumer preferences, demand elasticities, and substitution patterns in differentiated product markets.

Two major publications that used BLP

It is difficult to determine the top two most cited papers using the BLP model specifically, as the model has been widely used and cited in numerous studies across different industries. However, I can provide information on two highly influential papers that employ the BLP framework to estimate demand:

1. "Automobile Prices in Market Equilibrium" by Steven Berry, James Levinsohn, and Ariel Pakes Citation: Berry, S., Levinsohn, J., & Pakes, A. (1995). Automobile Prices in Market Equilibrium. Econometrica, 63(4), 841-890.

This paper is a seminal work in empirical industrial organization and the first application of the BLP model. The authors use the BLP framework to estimate demand for automobiles in the United States, accounting for consumer heterogeneity and endogeneity of product characteristics such as price. The study provides insights into the relationship between automobile characteristics, market shares, and consumer preferences. The authors find that unobserved product characteristics are important determinants of demand and that accounting for consumer heterogeneity significantly affects the estimated elasticities of substitution.

1. Paper: "Estimating the Effects of Global Patent Protection in Pharmaceuticals: A Case Study of Quinolones in India" by Iain M. Cockburn, Jean O. Lanjouw, and Mark Schankerman Citation: Cockburn, I. M., Lanjouw, J. O., & Schankerman, M. (2016). Patents and the Global Diffusion of New Drugs. American Economic Review, 106(1), 136-64.

This paper uses the BLP framework to estimate the demand for pharmaceutical products, specifically quinolones, in India. The authors investigate the effects of global patent protection on the diffusion of new drugs, focusing on the Indian pharmaceutical market before and after the introduction of product patents. By using the BLP model, they are able to account for consumer heterogeneity and estimate the demand for different drugs in the quinolone class.

The authors find that stronger patent protection leads to faster diffusion of new drugs, particularly those that are more innovative, while having a modest impact on prices. They also find that the welfare impact of stronger patent protection varies across different consumer groups, with some groups benefiting more from faster access to new drugs while others face higher prices. This study highlights the importance of considering consumer heterogeneity and demand-side factors when analyzing the effects of policy changes in the pharmaceutical industry.

These two papers showcase the versatility and usefulness of the BLP model in estimating demand across different industries and for various research questions. Both studies demonstrate the ability of the BLP framework to account for consumer heterogeneity, endogeneity of product characteristics, and substitution patterns, providing valuable insights into consumer preferences and the effects of market and policy changes on demand.

Known Use Cases in Industry

It is difficult to provide a specific list of firms that use the BLP model to estimate demand for their own products, as this information is often proprietary and not disclosed publicly. Companies typically rely on in-house teams or hire external consulting firms to conduct demand analysis, and they may use various demand estimation techniques, including the BLP model, depending on the nature of their products and markets.

However, it is likely that firms operating in industries with differentiated products, such as automobiles, consumer electronics, pharmaceuticals, and retail goods, could benefit from using the BLP model to estimate demand. The model's ability to account for consumer heterogeneity and estimate substitution patterns can provide valuable insights into consumer preferences and guide firms' strategic decisions related to pricing, product design, and marketing.

In addition to in-house teams, many consulting firms and market research agencies that specialize in industrial organization and econometrics offer services related to demand estimation, and they may employ the BLP model or similar techniques for their clients. These firms provide demand analysis and strategic advice to help businesses optimize their product offerings, pricing strategies, and market positioning.

In summary, while it is difficult to pinpoint specific firms that use the BLP model to estimate demand for their products, it is reasonable to assume that companies in industries with differentiated products could benefit from this approach, either through their internal teams or by hiring external consultants.

Python Code

The most common programming languages used for estimating demand with the BLP model are typically R and Python, as both languages offer extensive libraries and tools for econometric analysis. However, some researchers and practitioners may also use MATLAB or Stata for this purpose. Among these, Python and R have become increasingly popular in recent years due to their open-source nature and the availability of numerous packages for econometrics and optimization.

Here's an example of how to estimate a simple BLP model using Python with the pyblp library. The pyblp library, developed by Jeff Gortmaker, is specifically designed for estimating BLP demand models and has extensive documentation to help users get started.

First, you'll need to install the pyblp package, which can be done using pip:

pip install pyblp

Then, you can use the following example code to estimate a BLP demand model:

import pyblp
import pandas as pd

# Load data
product_data = pd.read_csv('path/to/your/product_data.csv')
agent_data = pd.read_csv('path/to/your/agent_data.csv')

# Define the product and agent formulas
product_formulation = pyblp.Formulation('1 + price + product_characteristic')
agent_formulation = pyblp.Formulation('1 + income')

# Set up the problem
problem = pyblp.Problem(
    product_formulation,
    agent_formulation,
    product_data,
    agent_data,
)

# Estimate the parameters using the NFP algorithm
results = problem.solve()

# Print the results
print(results)

In this example, replace 'path/to/your/product_data.csv' and 'path/to/your/agent_data.csv' with the paths to your own product and agent data files. The product and agent formulas should be defined based on the variables in your dataset.

The pyblp library offers many more features and options for estimating more complex BLP models, including endogeneity correction and flexible distributions for random coefficients. For more information and examples, refer to the pyblp documentation.

R Code

In R, you can use the gmm package to estimate the BLP demand model. Here's an example of how to set up and estimate a simple BLP model using R:

First, install the required packages:

install.packages("gmm")

Then, use the following example code:

library(gmm)

# Load data
product_data <- read.csv("path/to/your/product_data.csv")
agent_data <- read.csv("path/to/your/agent_data.csv")

# Define the objective function for GMM estimation
blp_obj_fun <- function(theta, data) {
  # Extract the parameters
  alpha <- theta[1]
  beta <- theta[2]
  
  # Compute the mean utilities
  data$mean_utility <- alpha * data$price + beta * data$product_characteristic
  
  # Compute the residuals
  data$residual <- data$market_share - exp(data$mean_utility)
  
  # Return the residuals
  return(data$residual)
}

# Set up the initial values for the parameters
theta_init <- c(1, 1)

# Estimate the parameters using GMM
gmm_result <- gmm(blp_obj_fun, x = product_data, t0 = theta_init)

# Print the results
summary(gmm_result)

In this example, replace "path/to/your/product_data.csv" and "path/to/your/agent_data.csv" with the paths to your own product and agent data files. Update the objective function to include the variables in your dataset.

Note that this example is a simplified version of a BLP estimation in R, and it does not account for consumer heterogeneity, endogeneity of product characteristics, or the distribution of random coefficients. To implement a more complete BLP model in R, you would need to extend this code to incorporate these features, which may involve more advanced programming and optimization techniques. The example serves as a starting point for researchers interested in implementing BLP in R.

Big Picture Advice and Concluding Remarks

For researchers interested in exploring the BLP model after this discussion, here are some big-picture suggestions and advice:

1. Understand the fundamentals: Before diving into the BLP model, ensure you have a solid understanding of its theoretical underpinnings, the assumptions it makes, and its relationship to earlier demand estimation models like the multinomial logit. This will help you better appreciate its strengths and limitations.

2. Get hands-on experience: Try implementing the BLP model using real or simulated data in programming languages like Python or R. Familiarize yourself with the relevant libraries and packages (e.g., pyblp in Python) and experiment with different specifications and scenarios to develop a deeper understanding of the model and its nuances.

3. Explore applications: BLP can be particularly useful in industries with differentiated products. Consider applying the model to study consumer preferences, demand elasticities, and substitution patterns in sectors such as automobiles, consumer electronics, pharmaceuticals, and retail goods. This can help uncover new insights and inform policy decisions or business strategies.

4. Consider model extensions and alternatives: BLP is not the only demand estimation model available. Explore other models that address some of the BLP model's limitations, such as the mixed logit or random coefficients probit models. Investigate how these models may better capture consumer heterogeneity and preferences in specific contexts.

5. Questions to work on: Some potential research questions where BLP might be useful include:

   • How do consumers respond to changes in product characteristics, such as price, quality, or environmental impact?

   • How does market structure and competition affect consumer preferences and demand in differentiated product markets?

   • What is the impact of policy changes, such as regulation or taxation, on consumer demand and welfare in specific industries?

6. Questions to avoid: Be cautious when applying BLP to contexts where its assumptions may not hold or its limitations are particularly problematic. For example, avoid using BLP in markets with limited product differentiation, or where endogeneity and identification issues are difficult to address.

In summary, the BLP model is a powerful tool for estimating consumer preferences and demand in differentiated product markets. Researchers should invest time in understanding its fundamentals, gaining hands-on experience, and exploring its applications and extensions. By carefully considering the model's strengths and limitations, researchers can leverage the BLP framework to generate valuable insights into consumer behavior, market dynamics, and policy impacts.

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Cunningham Prompts

• Can you explain to me the BLP method of structural demand estimation using the random-coefficients logit model by Berry, Levinson and Pahke

• Can you explain this to me at an easier level so that it’s easier for an undergraduate to understand

• What is the purpose of introducing random coefficients? Is there an alternative modeling approach people have used to estimate demand that wasn’t based on random coefficients? Start by first explaining what randomness means and doesn’t mean and communicate it at a basic level

• Is BLP considered a major breakthrough in econometrics and empirical IO? How does it connect to Dan McFadden’s early work?

• Was this problem about assuming consumer preferences are homogenous across the population a widely recognized problem before BLP? If so, why couldn’t it be solved sooner? Was BLP a breakthrough because other contributions in econometrics already occurred without which BLP isn’t possible?

• What was Dan McFadden’s response to BLP?

• What are some of the more common criticisms of BLP?

• If I was an economist for a large National restaurant like Pizza Hut, would BLP help my company? Or is BLP mainly used for National policy like regulation?

• What is the top two most cited papers that use BLP to estimate demand? What are these papers about (briefly), who are the authors, what are the publication citations and what do the authors find?

• Who are some known firms that use BLP to estimate demand for their own products?

• What is the most common programming language used to estimate demand with BLP? Please provide an example of the code in that language.

• Can you now provide code implementing BLP in R?

• Conclude this discussion with some big picture suggestions to researchers out there wondering about BLP after having read this discussion. What advice can you give them? What sorts of questions could you suggest for them to work on where BLP might be useful? And are there any you think maybe they should avoid?