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Lecture 14:  Zurcher on Steroids: Residential and Work Location Choice

An equilibrium life-cycle model of commuting, residential and work location choice and house prices

Plan for Lecture 14

For lecture 14, I  we cover an example of some recent applied work using dynamic discrete choice models similar the framework outlined in Rust (1987) covered in lecture 12.  The covered  in the video taped lecture is based on a recent working paper with Christian Carstensen, Maria Juul Hansen, Fedor Iskhakov andf John Rust: "An equilibrium life-cycle model of commuting, residential and work location choice and house prices",  where we develop and estimate a dynamic equilibrium life cycle model of residential and work location choices . 

I present this under the heading "Zurcher on Steroids", since the main component of the model is really just an application of the behavioral framework for Dynamic Discrete Choice outlined in Rust's paper.

Choices are no binary as in Zurchers paper but disctete choices of residential regions and discrete choices of regions where to search for a job. So there is more than one choice variable and several discrete states. Time time horizon is finite, so no fixed points. Just simple backward induction in the inner loop of NFXP.  Unobserved states are additive in the utility function and conditional independent, although the epsilons are not iid extreme value but generalized extreme valued. So the choice probabilities are not on the pure logit form as in Zurcher, but on Nested logit form where choice probabilities and integrated values  can be computed recursively using a sequence of the usual closed form logit formulas and log-sums.  

For structural estimation, we ned to take account the one of the modeled discrete decision is only partly observed. Agents choose where to search for job, but the econometrician only observes the realized outcome of the job search process. So this needs to be integrated out of the likelihood, so we can express it in terms of observables.  

Finally, we consider an equilibrium calculation in the counterfactual simulation, akin to what Rust suggested in the Bottom-Up approach with with micro aggregated demand.  Here we have more than one price, the vector of regional specific house prices than can be found by equating supply and model predicted demands for housing in all regions.  So therefore the title:  Zurcher on Steroids. 

In our model, commuting is endogenously determined by the distance between work and residence, and house prices are determined in equilibrium. We estimate the model using Danish register data for the entire population of households in the Greater Copenhagen area (GCA). Assuming a fixed supply of housing in the short run, we consider the effects on house prices, job mobility, residential sorting and commuting in two counterfactual equilibria with i) increased supply of housing in the center of the GCA and ii) increased cost of commuting between all residential and work location regions. We find that i) results in lower prices in equilibrium for all regions and a higher degree of urbanization. ii) implies lower average commute times, but also a higher share of people in non-employment, in particular for residents outside of the GCA. The equilibrium prices drop in peripheral regions with low job density.

The paper is preliminary work, but I think it has most of the bells and whistles you will meet in applied work based on dynamic disctete choice models.  

I have not posted any code. It is quite involved and written in MATLAB and C. However, if anyone is interesting pushing a project inspired by this model (perhaps a simplified version and with your own twist), I'm happy to share the code.. as long as it stays between us. 

 

Preparation: 

Material: 

Video lecture: 

Lecture 14: A dynamic equilibrium model of commuting, residential and work location choices Links to an external site.

This video is quite long. Perhaps also too long. Sorry about that. If you want to be selective, the skip the first part and fast forward to the summary of empirical facts and the introduction of the choice model. This happens after 40 mins 48 seconds. The the first part is by no means irrelevant, but if you find that the video is impossible to penetrate because it's length, its better to miss the first part than the last part. The first part conatins mostly motivation,  references to key papers in the literature, data description (some of it very known to you if you have worked with register data) and the some descriptive statistics to describe some of the key features of the data. It should be able to follow what is going on from the point where I go though the choice model. So the second part outlines the mode, the strategy for structural estimation,  the functional forms and parameter estimates, model fit, equilibrium calculation and counter factual simulations. I conclude the directions for future research and potential extension of the model. It may be that you find some ideas for term papers in that part.