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rblp

BLP Demand Estimation for Differentiated Products in R

An R implementation of the BLP (Berry, Levinsohn, Pakes 1995) framework for estimating demand models for differentiated products, translated from the pyblp Python package by Conlon and Gortmaker (2020).

Features

  • Plain logit and nested logit demand estimation
  • Random coefficients logit (mixed logit) with consumer heterogeneity
  • Demographics via Pi matrix interactions
  • Product fixed effects via the absorb parameter (Frisch-Waugh-Lovell)
  • GMM estimation (1-step and 2-step)
  • Integration: Gauss-Hermite product rule, Monte Carlo, Halton sequences
  • Post-estimation: elasticities, consumer surplus, HHI, diversion ratios
  • Simulation: generate equilibrium data with known parameters
  • Merger simulation: compute post-merger prices and welfare effects
  • BLP and differentiation instruments: build_blp_instruments(), build_differentiation_instruments()

Installation 

# Install from GitHub
# install.packages("devtools")
devtools::install_github("hchulkim/rblp")

Quick Start 

library(rblp)

# Load Nevo (2000) cereal data
products <- load_nevo_products()

# Plain logit: delta_jt = beta0 + alpha*p_jt + beta*X_j + xi_jt
f1 <- blp_formulation(~ prices + sugar + mushy)
problem <- blp_problem(list(f1), products)
results <- problem$solve(method = "1s")
print(results)

Logit with Product Fixed Effects 

# Absorb product-level FE (matches pyblp Nevo tutorial, alpha ~ -30)
f1_fe <- blp_formulation(~ prices, absorb = ~ product_ids)
fe_problem <- blp_problem(list(f1_fe), products)
fe_results <- fe_problem$solve(method = "1s")
print(fe_results)

Random Coefficients Logit 

f1_rc <- blp_formulation(~ prices + sugar + mushy)
f2_rc <- blp_formulation(~ prices + sugar + mushy)

rc_problem <- blp_problem(
  product_formulations = list(f1_rc, f2_rc),
  product_data = products,
  integration = blp_integration("product", size = 3)
)

rc_results <- rc_problem$solve(
  sigma = diag(c(0.5, 0.5, 0.5, 0.5)),
  method = "1s",
  optimization = blp_optimization("l-bfgs-b")
)
print(rc_results)

RC Logit with Demographics 

agents <- load_nevo_agents()
demo_form <- blp_formulation(~ 0 + income + income_squared + age + child)

# pyblp specification: prices with product FE in X1, full X2
demo_problem <- blp_problem(
  product_formulations = list(
    blp_formulation(~ 0 + prices, absorb = ~ product_ids),
    blp_formulation(~ prices + sugar + mushy)
  ),
  product_data = products,
  agent_formulation = demo_form,
  agent_data = agents
)

# Starting values near pyblp's converged estimates
sigma0 <- diag(c(0.558, 3.312, -0.006, 0.093))
pi0 <- matrix(c(
  2.292, 0, 1.284, 0,
  588.3, -30.19, 0, 11.05,
  -0.384, 0, 0.0524, 0,
  0.748, 0, -1.354, 0
), nrow = 4, ncol = 4, byrow = TRUE)

demo_results <- demo_problem$solve(
  sigma = sigma0, pi = pi0,
  method = "1s",
  optimization = blp_optimization("l-bfgs-b",
    method_options = list(maxit = 1000, factr = 1e7))
)
print(demo_results)
# Price coefficient ~ -63, matching pyblp

Post-Estimation 

# Own-price elasticities
E <- results$compute_elasticities(market_id = "C01Q1")
diag(E)

# Consumer surplus
cs <- results$compute_consumer_surplus()

# HHI
hhi <- results$compute_hhi()

# Merger simulation
new_firm_ids <- products$firm_ids
new_firm_ids[new_firm_ids == 3] <- 2
merger <- results$compute_merger(new_firm_ids = new_firm_ids)

Simulation 

# Create synthetic data with known parameters
id_data <- build_id_data(T = 50, J = 20, F = 4)
id_data$x <- runif(nrow(id_data))

sim <- blp_simulation(
  product_formulations = list(blp_formulation(~ prices + x)),
  product_data = id_data,
  beta = c(0.5, -2, 0.8),
  xi_variance = 0.3,
  seed = 42
)

# Solve for equilibrium
sim_data <- sim$replace_endogenous()

# Estimate back
sim_problem <- sim_data$to_problem()
est <- sim_problem$solve(method = "1s")

Comparison with pyblp

pyblp rblp
Formulation('prices', absorb='C(product_ids)') blp_formulation(~ prices, absorb = ~ product_ids)
Problem(formulation, product_data) blp_problem(list(f1), product_data)
problem.solve() problem$solve()
results.compute_elasticities() results$compute_elasticities()
Integration('product', size=5) blp_integration("product", size = 5)
Simulation(...) blp_simulation(...)

References

  • Berry, S., Levinsohn, J., & Pakes, A. (1995). Automobile Prices in Market Equilibrium. Econometrica, 63(4), 841-890.
  • Nevo, A. (2000). A Practitioner’s Guide to Estimation of Random-Coefficients Logit Models of Demand. Journal of Economics & Management Strategy, 9(4), 513-548.
  • Conlon, C. & Gortmaker, J. (2020). Best Practices for Differentiated Products Demand Estimation with pyblp. RAND Journal of Economics, 51(4), 1108-1161. doi:10.1287/mksc.2023.1440

License

GPL (>= 2)