Plan for Lecture 13

Su and Judd (2012) advocated for an alternative approach to solve and estimate dynamic structural models. The method is called Mathematical Programming with Equilibrium Constraints (MPEC) and is based on the idea that we maximize the likelihood function subject to the constraint that the Bellman equation (or other equilibrium constraints) need to hold. During the lecture I discuss in detail the implementation details, pros and cons of these two approaches to estimation. Finally, we will make a horse-race between NFXP and MPEC and do a code demonstration of implementations of both methods.

The lectures closely follow many of the same points raised in the computational exercises. Malene has distributed python code for NFXP,. that will be sued for the first few exercises on discrete choice problems. Later she will add MPEC, CCP and NPL ect.

In my derivations I put some emphasis on the matrix representation of the porblmem. Since MATLAB is arguably more well suited for Linear Algebra than Python, it may be simpler for you to implement in MATLAB. I Have therefore uploaded Matlab code for you to look at too.

run_busdata.m estimate the engine replacement problem using NFXP

run_nfxp_vs_mpec.m does a (very simplified) version of MPEC/MATLAB and compares to NFXP.

All this is translated to Python too, but some people just like the simplicity of the linear algebra syntax that MATLAB provide. Also, my MATLAB implementation is much faster; mot likely due to faster linear algebra operations compared to what Nubpy provides.... and because of more efficient use if sparse matrices.

The MATLAB code also implements a bunch of other methods that I have not covered so fa :BBL, NPL, CCP. The CCP is NPL estimators are covered later in the course. BBL is a two step simulation based approach that we do not cover in the lectures (see paper by P. BAJARI, C. L. BENKARD, AND J. LEVIN, Econometrica 2007), This approach is meant for games with both continuous and discrete choices.

Preparation:

Su and Judd (ECTA, 2012)
Iskhakov et. al (ECTA, 2016)
Take a look at the NFXP and MPEC code

Material:

Slides
MATLAB code for Rust model (Various methods NFXP, MPEC, NPL and BBL)

Online lectures

Lecture 13: Constrained and Unconstrained Optimization Approaches to Structural Estimation