A simple estimator for the distribution of random coefficients

Abstract

We propose a simple mixtures estimator for recovering the joint distribution of parameter heterogeneity in economic models, such as the random coefficients logit. The estimator is based on linear regression subject to linear inequality constraints, and is robust, easy to program, and computationally attractive compared to alternative estimators for random coefficient models. For complex structural models, one does not need to nest a solution to the economic model during optimization. We present a Monte Carlo study and an empirical application to dynamic programming discrete choice with a serially correlated unobserved state variable.

Usage-Based Pricing and Demand for Residential Broadband

“…We recover the joint distribution of the parameters using a method of moments approach similar to the two-step algorithms proposed by Ackerberg (2009), Bajari et al (2007), and Fox et al (2011). First, we solve the dynamic program for a wide variety of subscriber types, h. Second,…”

“…As pointed out by Bajari et al (2007) and Fox et al (2011), least squares minimization subject to linear constraints, and over a bounded support, is a well-defined convex optimization problem. Even though the optimization is over a potentially large number of weights, it is quick and easy to program in standard software as long as the moments are linear in the weights.…”

“…To estimate the model, we adapt the techniques of Ackerberg (2009), Bajari et al (2007) and Fox et al (2011). The basic idea is intuitive.…”

Usage-Based Pricing and Demand for Residential Broadband

“…We estimate the parameters of the model using a method-of-moments approach similar to the two-step algorithms proposed by Ackerberg (2009), Bajari, Fox, and Ryan (2007), and Fox et al (2011). First, we solve the dynamic program for a wide variety of subscriber types.…”

“…Using these data, we provide descriptive evidence that consumers respond to variation in the shadow price of usage. We then estimate a (finite horizon) dynamic choice model, by adapting the techniques of Ackerberg (2009), Bajari, Fox, and Ryan (2007), and Fox, Kim, Ryan, and Bajari (2011). Specifically, we solve the dynamic problem for a large number of subscriber types, once for each type.…”