Lecture 17: Nested Pseudo Likelihood (NPL) and CCP estimators.

Plan for lecture 17

In this lecture we cover the paper "Swapping the Nested Fixed Point Algorithm: A Class of Estimators for Discrete Markov Decision Models". It covers a class of estimators that that is based on the so-called Hotz-Miller inversion  where we express the Bellman Equation in probability space, rather than in value function space.   These are methods that does not require to (fully) solve the decision problem for each evaluation of like likelihood function. It has the Estimator by Hotz and Miller (ReStud 1993) Download Hotz and Miller (ReStud 1993)

as a special case. The CCP estimators and Aguirregabiria and Mira's NPL estimator  have had a major impact on empirical IO, due to their argued applicability of estimation of dynamic games and due to their simplicity. Essentially we just go out and estimate the CCP's: P(d|x) using data on x and d, invert the Bellman Equation so it can be expressed in probabilities rather than value functions, and the put the estimated CCPs into that equation to express the likelihood that has a form similar to that of  a static logit model.  So no DP. Just non-parametric estimation of CCPs, and then a static Logit. Can be done in a few lines of code in STATA.  

We cover Aguirregabiria and Mira, because their notation is more simple and elegant that the original contribution by Hotz-Miller and thus is more well suited for teaching purposes. Beyond that, then the show that by iteration on the CCP Hotz-Miller estimator, they can obtain the MLE that you would otherwise need NFXP to implement. What they essentially do is that they "Swap the nesting of the Nested Fix Point Algorithm."

What we cover in this lecture builds a natural bridge to the next topic on dynamic games. In this area, CCP type of estimators have been extremely popular due to the huge difficulty of dealing with multiplicity of equilibria.  

Will be updated...

Preparation (in order of priority): 

• Aguirregabiria & Mira (ECTA, 2002) Download Aguirregabiria & Mira (ECTA, 2002)
   (video follow this paper closely)
• Hotz and Miller (ReStud 1993) Download Hotz and Miller (ReStud 1993)
  . (Like Rust 1987, this is another path breaking paper ) 

Material: 

• Slides Download Slides
• MATLAB code Download MATLAB code (Will be available in Python for exercises)

Online lectures:

Lecture 17 on Nested Pseudo Likelihood (NPL) and CCP estimators Links to an external site.