Random Coefficients Logit Model (BLP Model)


What we want to do?

Berry, Levinsohn, and Pakes (1995)—known as BLP—use instruments to isolate exogenous variation in price (a two-step procedure)

Previous Models for Differentiated Products Before BLP Model

Neoclassical Demand Models


Ways to simplify traditional neoclassical demand models

The Set-Up

The model set-up and the following replication code are mainly based on Nevo (2000)

Identification and Estimation

Instrumenting for Price

How do we estimate δjt\delta_{jt}?


Two steps

  1. Outer loop: search over (θ1,θ2)(\theta_1, \theta_2) to optimize the estimation objective function
    1. Inner loop: use the contraction mapping to find δ(θ1)\bm{\delta}(\theta_1)
    2. Use (θ1,θ2)(\theta_1, \theta_2) and δ(θ1)\bm{\delta}(\theta_1) to simulate choice probabilities
    3. Use choice probabilities to calculate the estimation objective function
  2. Estimate βˉ\bar{\bm{\beta}} by regressing δjt\delta_{jt} on (pjt,xjt)(p_{jt}, \bm{x}_{jt}) with price instruments, zjt\bm{z}_{jt}

Replication of BLP (1995) Using Python